Fundamentals of Soil Behavior Third Edition
James K. Mitchell Kenichi Soga
JOHN WILEY & SONS, INC.
This book is printed on acid-free paper. ⬁ Copyright 2005 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, e-mail:
[email protected]. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Mitchell, James Kenneth, 1930– Fundamentals of soil behavior / James K. Mitchell, Kenichi Soga.—3rd ed. p. cm. ISBN-13: 978-0-471-46302-7 (cloth : alk. paper) ISBN-10: 0-471-46302-7 (cloth : alk. paper) 1. Soil mechanics. I. Soga, Kenichi. II. Title. TA710.M577 2005 624.15136—dc22 2004025690 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1
CONTENTS
CHAPTER
1
Preface
xi
INTRODUCTION
1
1.1 1.2 1.3
CHAPTER
2
SOIL FORMATION 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10
CHAPTER
3
Soil Behavior in Civil and Environmental Engineering Scope and Organization Getting Started
Introduction The Earth’s Crust Geologic Cycle and Geological Time Rock and Mineral Stability Weathering Origin of Clay Minerals and Clay Genesis Soil Profiles and Their Development Sediment Erosion, Transport, and Deposition Postdepositional Changes in Sediments Concluding Comments Questions and Problems
SOIL MINERALOGY 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19
Importance of Soil Mineralogy in Geotechnical Engineering Atomic Structure Interatomic Bonding Secondary Bonds Crystals and Their Properties Crystal Notation Factors Controlling Crystal Structures Silicate Crystals Surfaces Gravel, Sand, and Silt Particles Soil Minerals and Materials Formed by Biogenic and Geochemical Processes Summary of Nonclay Mineral Characteristics Structural Units of the Layer Silicates Synthesis Pattern and Classification of the Clay Minerals Intersheet and Interlayer Bonding in the Clay Minerals The 1⬊1 Minerals Smectite Minerals Micalike Clay Minerals Other Clay Minerals
1 3 3
5 5 5 6 7 8 15 16 18 25 32 33
35 35 38 38 39 40 42 44 45 45 48 49 49 49 52 55 56 59 62 64 v
vi
CONTENTS
3.20 3.21 3.22 3.23 3.24 3.25
CHAPTER
4
Summary of Clay Mineral Characteristics Determination of Soil Composition X-ray Diffraction Analysis Other Methods for Compositional Analysis Quantitative Estimation of Soil Components Concluding Comments Questions and Problems
SOIL COMPOSITION AND ENGINEERING PROPERTIES 83 4.1 4.2
Introduction Approaches to the Study of Composition and Property Interrelationships 4.3 Engineering Properties of Granular Soils 4.4 Dominating Influence of the Clay Phase 4.5 Atterberg Limits 4.6 Activity 4.7 Influences of Exchangeable Cations and pH 4.8 Engineering Properties of Clay Minerals 4.9 Effects of Organic Matter 4.10 Concluding Comments Questions and Problems
CHAPTER
5
SOIL FABRIC AND ITS MEASUREMENT 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11
CHAPTER
6
65 65 70 74 79 80 81
Introduction Definitions of Fabrics and Fabric Elements Single-Grain Fabrics Contact Force Characterization Using Photoelasticity Multigrain Fabrics Voids and Their Distribution Sample Acquisition and Preparation for Fabric Analysis Methods for Fabric Study Pore Size Distribution Analysis Indirect Methods for Fabric Characterization Concluding Comments Questions and Problems
SOIL–WATER–CHEMICAL INTERACTIONS 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14 6.15 6.16 6.17
Introduction Nature of Ice and Water Influence of Dissolved Ions on Water Mechanisms of Soil–Water Interaction Structure and Properties of Adsorbed Water Clay–Water–Electrolyte System Ion Distributions in Clay–Water Systems Elements of Double-Layer Theory Influences of System Variables on the Double Layer Limitations of the Gouy–Chapman Diffuse Double Layer Model Energy and Force of Repulsion Long-Range Attraction Net Energy of Interaction Cation Exchange—General Considerations Theories for Ion Exchange Soil–Inorganic Chemical Interactions Clay–Organic Chemical Interactions
83 85 85 94 95 97 97 98 104 105 106
109 109 110 112 119 121 122 123 127 135 137 140 140
143 143 144 145 146 146 153 153 154 157 159 163 164 164 165 167 167 168
CONTENTS
6.18
CHAPTER
7
8
8.10 8.11 8.12 8.13 8.14 8.15 8.16 8.17 8.18
9
Introduction Principle of Effective Stress Force Distributions in a Particulate System Interparticle Forces Intergranular Pressure Water Pressures and Potentials Water Pressure Equilibrium in Soil Measurement of Pore Pressures in Soils Effective and Intergranular Pressure Assessment of Terzaghi’s Equation Water–Air Interactions in Soils Effective Stress in Unsaturated Soils Concluding Comments Questions and Problems
173 173 174 174 178 180 181 183 184 185 188 190 193 193
SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY 195 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9
CHAPTER
169 169
EFFECTIVE, INTERGRANULAR, AND TOTAL STRESS 173 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13
CHAPTER
Concluding Comments Questions and Problems
vii
Introduction Structure Development Residual Soils Surficial Residual Soils and Taxonomy Terrestrial Deposits Mixed Continental and Marine Deposits Marine Deposits Chemical and Biological Deposits Fabric, Structure, and Property Relationships: General Considerations Soil Fabric and Property Anisotropy Sand Fabric and Liquefaction Sensitivity and Its Causes Property Interrelationships in Sensitive Clays Dispersive Clays Slaking Collapsing Soils and Swelling Soils Hard Soils and Soft Rocks Concluding Comments Questions and Problems
CONDUCTION PHENOMENA 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9
Introduction Flow Laws and Interrelationships Hydraulic Conductivity Flows Through Unsaturated Soils Thermal Conductivity Electrical Conductivity Diffusion Typical Ranges of Flow Parameters Simultaneous Flows of Water, Current, and Salts Through Soil-Coupled Flows 9.10 Quantification of Coupled Flows
195 195 200 205 206 209 209 212 213 217 223 226 235 239 243 243 245 245 247
251 251 251 252 262 265 267 272 274 274 277
viii
CONTENTS
9.11 9.12 9.13 9.14 9.15 9.16 9.17 9.18 9.19 9.20 9.21 9.22 9.23
CHAPTER
10
11
279 282 284 288 291 294 298 303 305 305 307 310 319 320
VOLUME CHANGE BEHAVIOR
325
10.1 10.2 10.3 10.4 10.5 10.6 10.7
325 325 327 330 331 335
10.8 10.9 10.10 10.11 10.12 10.13
CHAPTER
Simultaneous Flows of Water, Current, and Chemicals Electrokinetic Phenomena Transport Coefficients and the Importance of Coupled Flows Compatibility—Effects of Chemical Flows on Properties Electroosmosis Electroosmosis Efficiency Consolidation by Electroosmosis Electrochemical Effects Electrokinetic Remediation Self-Potentials Thermally Driven Moisture Flows Ground Freezing Concluding Comments Questions and Problems
Introduction General Volume Change Behavior of Soils Preconsolidation Pressure Factors Controlling Resistance to Volume Change Physical Interactions in Volume Change Fabric, Structure, and Volume Change Osmotic Pressure and Water Adsorption Influences on Compression and Swelling Influences of Mineralogical Detail in Soil Expansion Consolidation Secondary Compression In Situ Horizontal Stress (K0) Temperature–Volume Relationships Concluding Comments Questions and Problems
339 345 348 353 355 359 365 366
STRENGTH AND DEFORMATION BEHAVIOR
369
11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10 11.11 11.12 11.13 11.14 11.15 11.16 11.17 11.18 11.19 11.20 11.21
369 370 379 383 389 393 400 404 411 415 417 422 425 432 436 438 444 447 452 456 460
Introduction General Characteristics of Strength and Deformation Fabric, Structure, and Strength Friction Between Solid Surfaces Frictional Behavior of Minerals Physical Interactions Among Particles Critical State: A Useful Reference Condition Strength Parameters for Sands Strength Parameters for Clays Behavior After Peak and Strain Localization Residual State and Residual Strength Intermediate Stress Effects and Anisotropy Resistance to Cyclic Loading and Liquefaction Strength of Mixed Soils Cohesion Fracturing of Soils Deformation Characteristics Linear Elastic Stiffness Transition from Elastic to Plastic States Plastic Deformation Temperature Effects
CONTENTS
11.22
CHAPTER
12
Concluding Comments Questions and Problems
ix 462 462
TIME EFFECTS ON STRENGTH AND DEFORMATION 465 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 12.11 12.12 12.13 12.14
Introduction General Characteristics Time-Dependent Deformation–Structure Interaction Soil Deformation as a Rate Process Bonding, Effective Stresses, and Strength Shearing Resistance as a Rate Process Creep and Stress Relaxation Rate Effects on Stress–Strain Relationships Modeling of Stress–Strain–Time Behavior Creep Rupture Sand Aging Effects and Their Significance Mechanical Processes of Aging Chemical Processes of Aging Concluding Comments Questions and Problems
465 466 470 478 481 488 489 497 503 508 511 516 517 520 520
List of Symbols
523
References
531
Index
559
PREFACE According to the National Research Council (1989, 2005), sound geoengineering is key in meeting seven critical societal needs. They are waste management and environmental protection, infrastructure development and rehabilitation, construction efficiency and innovation, security, resource discovery and recovery, mitigation of natural hazards, and the exploration and development of new frontiers. Solution of problems and satisfactory completion of projects in each of these areas cannot be accomplished without a solid understanding of the composition, structure, and behavior of soils because virtually all of humankind’s structures and facilities are built on, in, or with the Earth. Thus, the purpose of this book remains the same as for the prior two editions; namely, the development of an understanding of the factors determining and controlling the engineering properties and behavior of soils under different conditions, with an emphasis on why they are what they are. We believe that this understanding and its prudent application can be a valuable asset in meeting these societal needs. In the 12 years since publication of the second edition, environmental problems requiring geotechnical inputs have remained very important; dealing with natural hazards and disasters such as earthquakes, floods, and landslides has demanded increased attention; risk assessment and mitigation applied to existing structures and earthworks has become a major challenge; and the roles of soil stabilization, ground improvement, and soil as a construction material have expanded enormously. These developments, as well as the introduction of new computational, geophysical, and sensing methods, new emphasis on micromechanical analysis and behavior, and, perhaps regrettably, the reduced emphasis on laboratory measurement of soil properties have required looking at soil behavior in new ways. More and more it is becoming appreciated that geochemical and microbiological phenomena and processes play an essential role in many types of geotechnical problems. Some of these considerations have been incorporated into this new edition. Although the format of the book has remained much the same as in the first two editions, the contents have been reviewed and revised in detail, with deletion of some material no longer considered to be essential and introduction of substantial new material to incorporate important recent developments. We have reorganized the material among chapters to improve the flow of topics and logic of presentation. Time effects on soil strength and deformation behavior have been separated into a new Chapter 12. Additional soil property correlations have been incorporated. The addition of sets of questions and problems at the end of each chapter provide a feature not present in the first two editions. Many of these questions and problems are open ended and without single, clearly defined answers, but they are designed to stimulate broad thinking and the realization that judgment and incorporation of concepts and methods from a range of disciplines is often needed to provide satisfactory solutions to many geoengineering problems. We are indebted to innumerable students and professional colleagues whose inquiring minds and perceptive insights have helped us clarify issues and find new and better explanations for observed processes and behavior. J. Carlos Santamarina and David Smith provided helpful suggestions on the overall content and organization. Charles J. Shackelford reviewed and provided valuable suggestions for the sections of Chapter 9 on chemical osmosis and advective and diffusive chemical flows. Other important contributions to this third edition in the form xi
xii
PREFACE
of valuable comments, photos, resources, and proof checking were made by Hendrikus Allersma, Khalid Alshibli, John Atkinson, Bob Behringer, Malcolm Bolton, Lis Bowman, Jim Buckman, Pierre Delage, Antonio Gens, Henry Ji, Assaf Klar, Hideo Komine, Jean-Marie Konrad, Ning Liu, Yukio Nakata, Albert Ng, Masanobu Oda, Kenneth Sutherland, Colin Thornton, Yoichi Watabe, Siam Yimsiri, and Guoping Zhang. KS thanks his wife, Mikiko, for her encouragement and special support. We dedicate this book to the memory of Virginia (‘‘Bunny’’) Mitchell, whose continuing love, support, encouragement, and patience over more than 50 years, made this and the prior two editions possible. JAMES K. MITCHELL University Distinguished Professor, Emeritus Virginia Tech, Blacksburg, Virginia KENICHI SOGA Reader in Geomechanics University of Cambridge, Cambridge, England March 2005
References National Research Council. 1989. Geotechnology—Its Impact on Economic Growth, the Environment, and National Security. National Academy Press, Washington, DC. National Research Council. 2005. Geological and Geotechnical Engineering in the New Millennium, National Academy Press, Washington, DC.
CHAPTER 1
Introduction
1.1 SOIL BEHAVIOR IN CIVIL AND ENVIRONMENTAL ENGINEERING
Civil and environmental engineering includes the conception, analysis, design, construction, operation, and maintenance of a diversity of structures, facilities, and systems. All are built on, in, or with soil or rock. The properties and behavior of these materials have major influences on the success, economy, and safety of the work. Geoengineers play a vital role in these projects and are also concerned with virtually all aspects of environmental control, including water resources, water pollution control, waste disposal and containment, and the mitigation of such natural disasters as floods, earthquakes, landslides, and volcanoes. Soils and their interactions with the environment are major considerations. Furthermore, detailed understanding of the behavior of earth materials is essential for mining, for energy resources development and recovery, and for scientific studies in virtually all the geosciences. To deal properly with the earth materials associated with any problem and project requires knowledge, understanding, and appreciation of the importance of geology, materials science, materials testing, and mechanics. Geotechnical engineering is concerned with all of these. Environmental concerns—especially those related to groundwater, the safe disposal and containment of wastes, and the cleanup of contaminated sites—has spawned yet another area of specialization; namely, environmental geotechnics, wherein chemistry and biological science are important. Geochemical and microbiological phenomena impact the composition, properties, and stability of soils and rocks to degrees only recently beginning to be appreciated. Students in civil engineering are often quite surprised, and sometimes quite confused, by their first course in engineering with soils. After studying statics,
mechanics, and structural analysis and design, wherein problems are usually quite clear-cut and well defined, they are suddenly confronted with situations where this is no longer the case. A first course in soil mechanics may not, at least for the first half to two-thirds of the course, be mechanics at all. The reason for this is simple: Analyses and designs are useless if the boundary conditions and material properties are improperly defined. Acquisition of the data needed for analysis and design on, in, and with soils and rocks can be far more difficult and uncertain than when dealing with other engineering materials and aboveground construction. There are at least three important reasons for this. 1. No Clearly Defined Boundaries. An embankment resting on a soil foundation is shown in Fig. 1.1a, and a cantilever beam fixed at one end is shown in Fig. 1.1b. The free body of the cantilever beam, Fig. 1.1c, is readily analyzed for reactions, shears, moments, and deflections using standard methods of structural analysis. However, what are the boundary conditions, and what is the free body for the embankment foundation? 2. Variable and Unknown Material Properties. The properties of most construction materials (e.g., steel, plastics, concrete, aluminum, and wood) are ordinarily known within rather narrow limits and usually can be specified to meet certain needs. Although this may be the case in construction using earth and rock fills, at least part of every geotechnical problem involves interactions with in situ soil and rock. No matter how extensive (and expensive) any boring and sampling program, only a very small percentage of the subsurface material is available for observation and testing. In most cases, more than one stratum is 1
2
1
INTRODUCTION
Figure 1.1 The problem of boundary conditions in geo-
technical problems: (a) embankment on soil foundation, (b) cantilever beam, and (c) free body diagram for analysis of propped cantilever beam.
present, and conditions are nonhomogeneous and anisotropic. 3. Stress and Time-Dependent Material Properties. Soils, and also some rocks, have mechanical properties that depend on both the stress history and the present stress state. This is because the volume change, stress–strain, and strength properties depend on stress transmission between particles and particle groups. These stresses are, for the most part, generated by body forces and boundary stresses and not by internal forces of cohesion, as is the case for many other materials. In addition, the properties of most soils change with time after placement, exposure, and loading. Because of these stress and time dependencies, any given geotechnical problem may involve not just one or two but an almost infinite number of different materials. Add to the above three factors the facts that soil and rock properties may be susceptible to influences from changes in temperature, pressure, water availability, and chemical and biological environment, and one might conclude that successful application of mechanics to earth materials is an almost hopeless proposition. It has been amply demonstrated, of course, that such
is not the case; in fact, it is for these very reasons that geotechnical engineering offers such a great challenge for imaginative and creative work. Modern theories of soil mechanics, the capabilities of modern computers and numerical analysis methods, and our improved knowledge of soil physics and chemistry make possible the solution of a great diversity of static and dynamic problems of stress deformation and stability, the transient and steady-state flow of fluids through the ground, and the long-term performance of earth systems. Nonetheless, our ability to analyze and compute often exceeds considerably our ability to understand, measure, and characterize a problem or process. Thus, understanding and the ability to conceptualize soil and rock behavior become all the more important. The objectives of this book are to provide a basis for the understanding of the engineering properties and behavior of soils and the factors controlling changes with time and to indicate why this knowledge is important and how it is used in the solution of geotechnical and geoenvironmental problems. It is easier to state what this book is not, rather than what it is. It is not a book on soil or rock mechanics; it is not a book on soil exploration or testing; it is not a book that teaches analysis or design; and it is not a book on geotechnical engineering practice. Excellent books and references dealing with each of these important areas are available. It is a book on the composition, structure, and behavior of soils as engineering materials. It is intended for students, researchers, and practicing engineers who seek a more in-depth knowledge of the nature and behavior of soils than is provided by classical and conventional treatments of soil mechanics and geotechnical engineering. Here are some examples of the types of questions that are addressed in this book:
• What are soils composed of? Why? • How does geological history influence soil properties?
• How are engineering properties and behavior re• • • • • • • •
lated to composition? What is clay? Why are clays plastic? What are friction and cohesion? What is effective stress? Why is it important? Why do soils creep and exhibit stress relaxation? Why do some soils swell while others do not? Why does stability failure sometimes occur at stresses less than the measured strength? Why and how are soil properties changed by disturbance?
GETTING STARTED
• How do changes in environmental conditions • • • • • • • • • •
change properties? What are some practical consequences of the prolonged exposure of clay containment barriers to waste chemicals? What controls the rate of flow of water, heat, chemicals, and electricity through soils? How are the different types of flows through soil interrelated? Why is the residual strength of a soil often much less than its peak strength? How do soil properties change with time after deposition or densification and why? How do temperature changes influence the mechanical properties of soils? What is soil liquefaction, and why is it important? What causes frost heave, and how can it be prevented? What clay types are best suited for sealing waste repositories? What biological processes can occur in soils and why are they important in engineering problems?
Developing answers to questions such as these requires application of concepts from chemistry, geology, biology, materials science, and physics. Principles from these disciplines are introduced as necessary to develop background for the phenomena under study. It is assumed that the reader has a basic knowledge of applied mechanics and soil mechanics, as well as a general familiarity with the commonly used engineering properties of soils and their determination.
1.2
SCOPE AND ORGANIZATION
The topics covered in this book begin with consideration of soil formation in Chapter 2 and soil mineralogy and compositional analysis of soil in Chapter 3. Relationships between soil composition and engineering properties are developed in Chapter 4. Soil composition by itself is insufficient for quantification of soil properties for specific situations, because the soil fabric, that is, the arrangements of particles, particle groups, and pores, may play an equally important role. This topic is covered in Chapter 5. Water may make up more than half the volume of a soil mass, it is attracted to soil particles, and the interactions between water and the soil surfaces influence the behavior. In addition, owing to the colloidal
3
nature of clay particles, the types and concentrations of chemicals in a soil can influence significantly its behavior in a variety of ways. Soil water and the clay– water–electrolyte system are then analyzed in Chapter 6. An analysis of interparticle forces and total and effective stresses, with a discussion of why they are important, is given in Chapter 7. The remaining chapters draw on the preceding developments for explanations of phenomena and soil properties of interest in geotechnical and geoenvironmental engineering. The formation of soil deposits, their resulting structures and relationships to geotechnical properties and stability are covered in Chapter 8. The next three chapters deal with those soil properties that are of primary importance to the solution of most geoengineering problems: the flows of fluids, chemicals, electricity, and heat and their consequences in Chapter 9; volume change behavior in Chapter 10; and deformation and strength and deformation behavior in Chapter 11. Finally, Chapter 12 on time effects on strength and deformation recognizes that soils are not inert, static materials, but rather how a given soil responds under different rates of loading or at some time in the future may be quite different than how it responds today. 1.3
GETTING STARTED
Find an article about a problem, a project, or issue that involves some aspect of geotechnical soil behavior as an important component. The article can be from the popular press, from a technical journal or magazine, such as the Journal of Geotechnical and Geoenvironmental Engineering of the American Society of Civil Engineers, Ge´otechnique, The Canadian Geotechnical Journal, Soils and Foundations, ENR, or elsewhere. 1. Read the article and prepare a one-page informative abstract. (An informative abstract summarizes the important ideas and conclusions. A descriptive abstract, on the other hand, simply states the article contents.) 2. Summarize the important geotechnical issues that are found in the article and write down what you believe you should know about to understand them well enough to solve the problem, resolve the issue, advise a client, and the like. In other words, what is in the article that you believe the subject matter in this book should prepare you to deal with? Do not exceed two pages.
CHAPTER 2
Soil Formation
2.1
INTRODUCTION
The variety of geomaterials encountered in engineering problems is almost limitless, ranging from hard, dense, large pieces of rock, through gravel, sand, silt, and clay to organic deposits of soft, compressible peat. All these materials may exist over a wide range of densities and water contents. A number of different soil types may be present at any site, and the composition may vary over intervals as small as a few millimeters. It is not surprising, therefore, that much of the geoengineer’s effort is directed at the identification of soils and the evaluation of the appropriate properties for use in a particular analysis or design. Perhaps what is surprising is that the application of the principles of mechanics to a material as diverse as soil meets with as much success as it does. To understand and appreciate the characteristics of any soil deposit require an understanding of what the material is and how it reached its present state. This requires consideration of rock and soil weathering, the erosion and transportation of soil materials, depositional processes, and postdepositional changes in sediments. Some important aspects of these processes and their effects are presented in this chapter and in Chapter 8. Each has been the subject of numerous books and articles, and the amount of available information is enormous. Thus, it is possible only to summarize the subject and to encourage consultation of the references for more detail.
2.2
(acid) rocks predominate beneath the continents, and basaltic (basic) rocks predominate beneath the oceans. Because of these lithologic differences, the continental crust average density of 2.7 is slightly less than the oceanic crust average density of 2.8. The elemental compositions of the whole Earth and the crust are indicated in Fig. 2.1. There are more than 100 elements, but 90 percent of Earth consists of iron, oxygen, silicon, and magnesium. Less iron is found in the crust than in the core because its higher density causes it to sink. Silicon, aluminum, calcium, potassium, and sodium are more abundant in the crust than in the core because they are lighter elements. Oxygen is the only anion that has an abundance of more than 1 percent by weight; however, it is very abundant by volume. Silicon, aluminum, magnesium, and oxygen are the most commonly observed elements in soils. Within depths up to 2 km, the rocks are 75 percent secondary (sedimentary and metamorphic) and 25 percent igneous. From depths of 2 to 15 km, the rocks are about 95 percent igneous and 5 percent secondary. Soils may extend from the ground surface to depths of several hundred meters. In many cases the distinction between soil and rock is difficult, as the boundary between soft rock and hard soil is not precisely defined. Earth materials that fall in this range are sometimes difficult to deal with in engineering and construction, as it is not always clear whether they should be treated as soils or rocks. A temperature gradient of about 1C per 30 m exists between the bottom of Earth’s crust at 1200C and the surface.1 The rate of cooling as molten rock magma
THE EARTH’S CRUST
The continental crust covers 29 percent of Earth’s surface. Seismic measurements indicate that the continental crust is about 30 to 40 km thick, which is 6 to 8 times thicker than the crust beneath the ocean. Granitic
1 In some localized areas, usually within regions of recent crustal movement (e.g., fault lines, volcanic zones) the gradient may exceed 20C per 100 m. Such regions are of interest both because of their potential as geologic hazards and because of their possible value as sources of geothermal energy.
5
6
2
100% 90% 80%
SOIL FORMATION Other <1% Sodium 2.1% Potassium 2.3% Calcium 2.4% Magnesium 4% Iron 6%
Other <1% Sulfur 1.9% Nickel 2.4% Calcium 1.1% Magnesium 13%
Aluminum 8%
70% Iron 35%
60%
Silicon 28%
50%
Aluminum 1.1%
40%
Silicon 15%
30% 20%
Oxygen 46% Oxygen 30%
10%
Figure 2.2 Geologic cycle.
0%
Earth's Crust
Whole Earth
Figure 2.1 Elemental composition of the whole Earth and
the crust (percent by weight) (data from Press and Siever, 1994).
moves from the interior of Earth toward the surface has a significant influence on the characteristics of the resulting rock. The more rapid the cooling, the smaller are the crystals that form because of the reduced time for atoms to attain minimum energy configurations. Cooling may be so rapid in a volcanic eruption that no crystalline structure develops before solidification, and an amorphous material such as obsidian (volcanic glass) is formed.
2.3 GEOLOGIC CYCLE AND GEOLOGICAL TIME
The surface of Earth is acted on by four basic processes that proceed in a never-ending cycle, as indicated in Fig. 2.2. Denudation includes all of those processes that act to wear down land masses. These include landslides, debris flows, avalanche transport, wind abrasion, and overland flows such as rivers and streams. Weathering includes all of the destructive mechanical and chemical processes that break down existing rock masses in situ. Erosion initiates the transportation of weathering products by various agents from one region to another—generally from high areas to low. Weathering and erosion convert rocks into sediment and form soil. Deposition involves the accumulation of sediments transported previously
from some other area. Sediment formation pertains to processes by which accumulated sediments are densified, altered in composition, and converted into rock. Crustal movement involves both gradual rising of unloaded areas and slow subsidence of depositional basins (epirogenic movements) and abrupt movements (tectonic movements) such as those associated with faulting and earthquakes. Crustal movements may also result in the formation of new rock masses through igneous or plutonic activity. The interrelationships of these processes are shown in Fig. 2.3. More than one process acts simultaneously in nature. For example, both weathering and erosion take place at the surface during periods of uplift, or orogenic activity (mountain building), and deposition, sediment formation, and regional subsidence are generally contemporaneous. This accounts in part for the wide variety of topographic and soil conditions in any area.
Figure 2.3 Simplified version of the rock cycle.
ROCK AND MINERAL STABILITY
The stratigraphic timescale column shown in Fig. 2.4 gives the sequence of rocks formed during geological time. Rocks are grouped by age into eons, eras, periods, and epochs. Each time period of the column is represented by its appropriate system of rocks observed on Earth’s surface along with radioactive age dating. Among various periods, the Quaternary period (from 1.6 million years ago to the present) deserves special attention since the top few tens of meters of Earth’s surface, which geotechnical engineers often work in, were developed during this period. The Quaternary period is subdivided into the Holocene (the 10,000 years after the last glacial period) and the Pleistocene. The deposits during this period are controlled mainly by the change in climate, as it was too short a time for any major tectonic changes to occur in the positions of land masses and seas. There were as many as 20 glacial and interglacial periods during the Quaternary. At one time, ice sheets covered more than three times their present extent. Worldwide sea level oscillations due to glacial and interglacial cycles affect soil formation (weathering, erosion, and sedimentation) as well as postdepositional changes such as consolidation and leaching.
Eon
Era
Period
Epoch Holocene Pleistocene Pliocene
Quaternary Neogene Tertiary
Cenozoic
Paleogene
Cretaceous Phanerozoic Mesozoic
Jurassic Triassic Permian Pennsylvanian Mississippian
Paleozoic
Miocene Oligocene Eocene Paleocene
Devonian Silurian Ordovician Cambrian
0.01 1.6 5 23 35 57 65
146 208 245 290 323 363 409 439 510 570
Proterozoic 2500 Precambrian Archean
Figure 2.4 Stratigraphic timescale column. Numbers repre-
sent millions of years before the present.
2.4
7
ROCK AND MINERAL STABILITY
Rocks are heterogeneous assemblages of smaller components. The smallest and chemically purest of these components are elements, which combine to form inorganic compounds of fixed composition known as minerals. Hence, rocks are composed of minerals or aggregates of minerals. Rocks are sometimes glassy (volcanic glass, obsidian, e.g.), but usually consist of minerals that crystallized together or in sequence (metamorphic and igneous rocks), or of aggregates of detrital components (most sedimentary rocks). Sometimes, rocks are composed entirely of one type of mineral (say flint or rock salt), but generally they contain many different minerals, and often the rock is a collection or aggregation of small particles that are themselves pieces of rocks. Books on petrography may list more than 1000 species of rock types. Fortunately, however, many of them fall into groups with similar engineering attributes, so that only about 40 rock names will suffice for most geotechnical engineering purposes. Minerals have a definite chemical composition and an ordered arrangement of components (a crystal lattice); a few minerals are disordered and without definable crystal structure (amorphous). Crystal size and structure have an important influence on the resistance of different rocks to weathering. Factors controlling the stability of different crystal structures are considered in Chapter 3. The greatest electrochemical stability of a crystal is reached at its crystallization temperature. As temperature falls below the crystallization temperature, the structural stability decreases. For example, olivine crystallizes from igneous rock magma at high temperature, and it is one of the most unstable igneousrock-forming minerals. On the other hand, quartz does not assume its final crystal structure until the temperature drops below 573C. Because of its high stability, quartz is the most abundant nonclay mineral in soils, although it comprises only about 12 percent of igneous rocks. As magma cools, minerals may form and remain, or they may react progressively to form other minerals at lower temperatures. Bowen’s reaction series, shown in Fig. 2.5, indicates the crystallization sequence of the silicate minerals as temperature decreases from 1200C. This reaction series closely parallels various weathering stability series as shown later in Table 2.2. For example, in an intermediate granitic rock, hornblende and plagioclase feldspar would be expected to chemically weather before orthoclase feldspar, which would chemically weather before muscovite mica, and so on.
8
2
SOIL FORMATION
Physical Processes of Weathering
Physical weathering processes cause in situ breakdown without chemical change. Five processes are important:
Figure 2.5 Bowen’s reaction series of mineral stability. Each
mineral is more stable than the one above it on the list.
Mineralogy textbooks commonly list determinative properties for about 200 minerals. The list of the most common rock- or soil-forming minerals is rather short, however. Common minerals found in soils are listed in Table 2.1. The top six silicates originate from rocks by physical weathering processes, whereas the other minerals are formed by chemical weathering processes. Further description of important minerals found in soils is given in Chapter 3.
2.5
WEATHERING
Weathering of rocks and soils is a destructive process whereby debris of various sizes, compositions, and shapes is formed.2 The new compositions are usually more stable than the old and involve a decrease in the internal energy of the materials. As erosion moves the ground surface downward, pressures and temperatures in the rocks are decreased, so they then possess an internal energy above that for equilibrium in the new environment. This, in conjunction with exposure to the atmosphere, water, and various chemical and biological agents, results in processes of alteration. A variety of physical, chemical, and biological processes act to break down rock masses. Physical processes reduce particle size, increase surface area, and increase bulk volume. Chemical and biological processes can cause complete changes in both physical and chemical properties.
2
A general definition of weathering (Reiche, 1945; Keller, 1957) is: the response of materials within the lithosphere to conditions at or near its contact with the atmosphere, the hydrosphere, and perhaps more importantly, the biosphere. The biosphere is the entire space occupied by living organisms; the hydrosphere is the aqueous envelope of Earth; and the lithosphere is the solid part of Earth.
1. Unloading Cracks and joints may form to depths of hundreds of meters below the ground surface when the effective confining pressure is reduced. Reduction in confining pressure may result from uplift, erosion, or changes in fluid pressure. Exfoliation is the spalling or peeling off of surface layers of rocks. Exfoliation may occur during rock excavation and tunneling. The term popping rock is used to describe the sudden spalling of rock slabs as a result of stress release. 2. Thermal Expansion and Contraction The effects of thermal expansion and contraction range from creation of planes of weakness from strains already present in a rock to complete fracture. Repeated frost and insolation (daytime heating) may be important in some desert areas. Fires can cause very rapid temperature increase and rock weathering. 3. Crystal Growth, Including Frost Action The crystallization pressures of salts and the pressure associated with the freezing of water in saturated rocks may cause significant disintegration. Many talus deposits have been formed by frost action. However, the role of freeze–thaw in physical weathering has been debated (Birkeland, 1984). The rapid rates and high amplitude of temperature change required to produce necessary pressure have not been confirmed in the field. Instead, some researchers favor the process in which thin films of adsorbed water is the agent that promotes weathering. These films can be adsorbed so tightly that they cannot freeze. However, the water is attracted to a freezing front and pressures exerted during the migration of these films can break the rock apart. 4. Colloid Plucking The shrinkage of colloidal materials on drying can exert a tensile stress on surfaces with which they are in contact.3 5. Organic Activity The growth of plant roots in existing fractures in rocks is an important weathering process. In addition, the activities of worms, rodents, and humans may cause considerable mixing in the zone of weathering.
3 To appreciate this phenomenon, smear a film of highly plastic clay paste on the back of your hand and let it dry.
WEATHERING
Table 2.1
Common Soil Minerals
Name Quartz Feldspar Mica Amphibole Pyroxene Olivine Epidote Tourmaline Zircon Rutile Kaolinite Smectite, vermiculite, chlorite Allophane Imogolite Gibbsite Goethite Hematite Ferrihydrate Birnessite Calcite Gypsum
9
Chemical Formula
Characteristics
SiO2 (Na,K)AlO2[SiO2]3 CaAl2O4[SiO2]2 K2Al2O5[Si2O5]3Al4(OH)4 K2Al2O5[Si2O5]3(Mg,Fe)6(OH)4 (Ca,Na,K)2,3(Mg,Fe,Al)5(OH)2[(Si,Al)4O11]2 (Ca,Mg,Fe,Ti,Al)(Si.Al)O3 (Mg,Fe)2SiO4 Ca2(Al,Fe)3(OH)Si3O12 NaMg3Al6B3Si6O27(OH,F)4 ZrSiO4 TiO2 Si4Al4O10(OH)8 Mx(Si,Al)8(Al,Fe,Mg)4O20(OH)4, where M ⫽ interlayer cation
Abundant in sand and silt Abundant in soil that is not leached extensively
Si3Al4O12 nH2O Si2Al4O10 5H2O Al(OH)3 FeO(OH) Fe2O3 Fe10O15 9H2O (Na,Ca)Mn7O14 2.8H2O CaCO3 CaSO4 2H2O
Source of K in most temperate-zone soils Easily weathered to clay minerals and oxides Easily weathered Easily weathered Highly resistant to chemical weathering; used as ‘‘index mineral’’ in pedologic studies
Abundant in clays as products of weathering; source of exchangeable cations in soils Abundant in soils derived from volcanic ash deposits Abundant in leached soils Most abundant Fe oxide Abundant in warm region Abundant in organic horizons Most abundant Mn oxide Most abundant carbonate Abundant in arid regions
Adapted from Sposito (1989).
Physical weathering processes are generally the forerunners of chemical weathering. Their main contributions are to loosen rock masses, reduce particle sizes, and increase the available surface area for chemical attack. Chemical Processes of Weathering
Chemical weathering transforms one mineral to another or completely dissolves the mineral. Practically all chemical weathering processes depend on the presence of water. Hydration, that is, the surface adsorption of water, is the forerunner of all the more complex chemical reactions, many of which proceed simultaneously. Some important chemical processes are listed below. 1. Hydrolysis, probably the most important chemical process, is the reaction between the mineral and H⫹ and (OH)⫺ of water. The small size of
the ion enables it to enter the lattice of minerals and replace existing cations. For feldspar, Orthoclase feldspar: K silicate ⫹ H⫹OH⫺ → H silicate ⫹ K⫹OH⫺ (alkaline)
Anorthite: Ca silicate ⫹ 2H⫹OH⫺ → H silicate ⫹ Ca(OH)2 (basic)
As water is absorbed into feldspar, kaolinite is often produced. In a similar way, other clay minerals and zeolites (microporous aluminosilicates) may form by weathering of silicate minerals as the associated ions such as silica, sodium, potassium, calcium, and magnesium are lost into so-
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SOIL FORMATION
lution. Hydrolysis will not continue in the presence of static water. Continued driving of the reaction to the right requires removal of soluble materials by leaching, complexing, adsorption, and precipitation, as well as the continued introduction of H⫹ ions. Carbonic acid (H2CO3) speeds chemical weathering. This weak acid is formed by the solution in rainwater of a small amount of carbon dioxide gas from the atmosphere. Additional carbonic acid and other acids are produced by the roots of plants, by insects that live in the soil, and by the bacteria that degrade plant and animal remains. The pH of the system is important because it influences the amount of available H⫹, the solubility of SiO2 and Al2O3, and the type of clay mineral that may form. The solubility of silica and alumina as a function of pH is shown in Fig. 2.6. 2. Chelation involves the complexing and removal of metal ions. It helps to drive hydrolysis reactions. For example, Muscovite: K2[Si6Al2]Al4O20(OH)4 ⫹ 6C2O4H2 ⫹ 8H2O → 2K⫹ ⫹ 6C2O4Al⫹ ⫹ 6Si(OH)40 ⫹ 8OH⫺
Oxalic acid (C2O4H2), the chelating agent, releases C2O42⫺, which forms a soluble complex with Al3⫹ to enhance dissolution of muscovite. Ring-structured organic compounds derived from humus can act as chelating agents by holding metal ions within the rings by covalent bonding. 3. Cation exchange is important in chemical weathering in at least three ways: a. It may cause replacement of hydrogen on hydrogen bearing colloids. This reduces the ability of the colloids to bring H⫹ to unweathered surfaces. b. The ions held by Al2O3 and SiO2 colloids influence the types of clay minerals that form. c. Physical properties of the system such as the permeability may depend on the adsorbed ion concentrations and types. 4. Oxidation is the loss of electrons by cations, and reduction is the gain of electrons. Both are important in chemical weathering. Most important oxidation products depend on dissolved oxygen in the water. The oxidation of pyrite is typical of many oxidation reactions during weathering (Keller, 1957): 2FeS2 ⫹ 2H2O ⫹ 7O2 → 2FeSO4 ⫹ 2H2SO4 FeSO4 ⫹ 2H2O → Fe(OH)2 ⫹ H2SO4 (hydrolysis) Oxidation of Fe(OH)2 gives 4Fe(OH)2 ⫹ O2 ⫹ 2H2O → 4Fe(OH)3 2Fe(OH)3 → Fe2O3 nH2O (limonite)
Figure 2.6 Solubility of alumina and amorphous silica in
water (Keller, 1964b).
The H2SO4 formed in these reactions rejuvenates the process. It may also drive the hydrolysis of silicates and weather limestone to produce gypsum and carbonic acid. During the construction of the Carsington Dam in England in the early 1980s, soil in the reservoir area that contained pyrite was uncovered during construction following the excavation and exposure of air and water of the Namurian shale used in the embankment. The sulfuric acid that was released as a result of the pyrite oxidation reacted with limestone to form gypsum and CO2. Accumulation of CO2 in construction shafts led to the asphyxiation of workers who were unaware of its presence. It is believed that the oxidation process was mediated by bacteria (Cripps et al., 1993), as discussed fur-
WEATHERING
11
ther in the next section. Many iron minerals weather to iron oxide (Fe2O3, hematite). The red soils of warm, humid regions are colored by iron oxides. Oxides can act as cementing agents between soil particles. Reduction reactions, which are of importance relative to the influences of bacterial action and plants on weathering, store energy that may be used in later stages of weathering. 5. Carbonation is the combination of carbonate or bicarbonate ions with earth materials. Atmospheric CO2 is the source of the ions. Limestone made of calcite and dolomite is one of the rocks that weather most quickly especially in humid regions. The carbonation of dolomitic limestone proceeds as follows: CaMg(CO3)2 ⫹ 2CO2 ⫹ 2H2O → Ca(HCO3)2 ⫹ Mg(HCO3)2
The dissolved components can be carried off in water solution. They may also be precipitated at locations away from the original formation. Microbiological Effects
Several types of microorganisms are found in soils; there are cellular microorganisms (bacteria, archea, algae, fungi, protozoa, and slime molds) and noncellular microorganisms (viruses). They may be nearly round, rodlike, or spiral and range in size from less than 1 to 100 m, which is equivalent to coarse clay size to fine sand size. Figure 2.7a shows bacteria adhering to quartz sand grains, and Fig. 2.7b shows clay minerals coating around the cell envelope, forming what are called bacterial microaggregates.4 A few billion to 3 trillion microorganisms exist in a kilogram of soil near the ground surface and bacteria are dominant. Microorganisms can reproduce very rapidly. The replication rate is controlled by factors such as temperature, pH, ionic concentrations, nutrients, and water availability. Under ideal conditions, the ‘‘generation time’’ for bacterial fission can be as short as 10 min; however, an hour scale is typical. These high-speed generation rates, mutation, and natural selection lead to very fast adaptation and extraordinary biodiversity. Autotrophic photosynthetic bacteria, that is, photoautotrophs, played a crucial role in the geological de-
4
Further details of how microorganisms adhere to soil surfaces are given in Chenu and Stotzky (2002).
Figure 2.7 Microogranisms attached to soil particle sur-
faces: (a) bacteria attached to sand particle (from Robertson et al. 1993 in Chenu and Stotzky, 2002), (b) bacterial microaggregate [from Robert and Chenu (1992) in Chenu and Stotzky (2002)], and (c) biofilm on soil surface (from Chenu and Stotzky (2002).
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SOIL FORMATION
velopment of Earth (Hattori, 1973; McCarty, 2004). Photosynthetic bacteria, cyanobacteria, or ‘‘blue-green bacteria’’ evolved about 3.5 billion years ago (Proterozoic era—Precambrian), and they are the oldest known fossils. Cyanobacteria use energy from the sun to reduce the carbon in CO2 to cellular carbon and to obtain the needed electrons for oxidizing the oxygen in water to molecular oxygen. During the Archaean period (2.5 billion years ago), cyanobacteria converted the atmosphere from reducing to oxidizing and changed the mineral nature of Earth. Eukaryotic algae evolved later, followed by the multicellular eukaryotes including plants. Photosynthesis is the primary producer of the organic particulate matter in shale, sand, silt, and clay, as well as in coal, petroleum, and methane deposits. Furthermore, cyanobacteria and algae increase the water pH when they consume CO2 dissolved in water, resulting in carbonate formation and precipitation of magnesium and calcium carbonates, leading to Earth’s major carbonate formations. Aerobic bacteria live in the presence of dissolved oxygen. Anaerobic bacteria survive only in the absence of oxygen. Facultative bacteria can live with or without oxygen. Some bacteria may resort to fermentation to sustain their metabolism under anaerobic conditions (Purves et al., 1997). For example, in the case of anaerobic conditions, fermenting bacteria oxidize carbohydrates to produce simple organic acids and H2 that are used to reduction of ferric (Fe3⫹) iron, sulfate reduction, and the generation of methane (Chapelle, 2001). Microbial energy metabolism involves electron transfers, and the electron sources and acceptors can be both organic and inorganic compounds (Horn and Meike, 1995). Most soil bacteria derive their carbon and energy directly from organic matter and its oxidation. Some other bacteria derive their energy from oxidation of inorganic substances such as ammonium, sulfur, and iron and most of their carbon from carbon dioxide. Therefore, biological activity mediates geochemical reactions, causing them to proceed at rates that are sometimes orders of magnitude more rapid than would be predicted solely on the basis of the thermochemical reactions involved. Bacteria tend to adhere to mineral surfaces and form microcolonies known as biofilms as shown in Fig. 2.7c. Some biofilms are made of single-type bacteria, while others involve symbiotic communities where two or more bacteria types coexist and complement each other. For example, biofilms involved in rock weathering may involve an upper aerobic layer, followed by an intermediate facultative layer that rests on top of the aerobic layer that produces the weathering agents
(e.g., acids) directly on the rock surface (Ehrlich, 1998). Biofilms bind cations in the pore fluid and facilitate nucleation and crystal growth even at low ionic concentrations in the pore fluid (Konhauser and Urrutia, 1999). After nucleation is initiated, further mineral growth or precipitation can occur abiotically, including the precipitation of amorphous iron–aluminum silicates and poorly crystallized claylike minerals, such as allophone, imogolite, and smectite (Urrutia and Beveridge, 1995; Ehrlich, 1999; Barton et al., 2001). In the case of the Carsington Dam construction, Cripps et al. (1993) hypothesized that autotrophic bacteria greatly accelerated the oxidation rate of the pyrite, so that it occurred within months during construction. The resulting sulfuric acid reacted with the drainage blanket constructed of carboniferous limestone, which then resulted in precipitation of gypsum and iron hydroxide, clogging of drains and generation of carbon dioxide. Weathering Products
The products of weathering, several of which will generally coexist at one time, include: 1. Unaltered minerals that are either highly resistant or freshly exposed 2. Newly formed, more stable minerals having the same structure as the original mineral 3. Newly formed minerals having a form similar to the original, but a changed internal structure 4. Products of disrupted minerals, either at or transported from the site. Such minerals might include a. Colloidal gels of Al2O3 and SiO2 b. Clay minerals c. Zeolites d. Cations and anions in solution e. Mineral precipitates 5. Unused guest reactants The relationship between minerals and different weathering stages is given in Table 2.2. The similarity between the order of representative minerals for the different weathering stages and Bowen’s reaction series given earlier (Fig. 2.5) may be noted. Contrasts in compositions between terrestrial and lunar soils can be accounted for largely in terms of differences in chemical weathering. Soils on Earth are composed mainly of quartz and clay minerals because the minerals of lower stability, such as feldspar, olivine, hornblende, and glasses, are rapidly removed by chemical weathering. On the Moon, however, the absence of water and free oxygen prevent chemical weathering. Hence, lunar soils are made up mainly of fragmented parent rock and rapidly crystallized
WEATHERING
Table 2.2 Representative Minerals and Soils Associated with Weathering Stages Weathering Stage
Representative Minerals
Typical Soil Groups
Early Weathering Stages 1 2 3 4 5
Gypsum (also halite, sodium nitrate) Calcite (also dolomite apatite) Olivine-hornblende (also pyroxenes) Biotite (also glauconite, nontronite) Albite (also anorthite microcline, orthoclase)
Soils dominated by these minerals in the fine silt and clay fractions are the youthful soils all over the world, but mainly soils of the desert regions where limited water keeps chemical weathering to a minimum.
Intermediate Weathering Stages 6 7 8
Quartz Soils dominated by Muscovite (also illite) these minerals in the 2⬊1 layer silicates (infine silt and clay fractions are mainly those cluding vermiculite, of temperate regions expanded hydrous developed under grass mica) or trees. Includes the Montmorillonite major soils of the wheat and corn belts of the world. Advanced weathering stages
10 11 12 13
Many intensely weathKaolinite ered soils of the warm Gibbsite Hematite (also geothite, and humid equatorial regions have clay limonite) fractions dominated Anatase (also rutile, by these minerals. zircon) They are frequently characterized by their infertility.
From Jackson and Sherman (1953).
glasses. Mineral fragments in lunar soils include plagioclase feldspar, pyroxene, ilmenite, olivine, and potassium feldspar. Quartz is extremely rare because it is not abundant in the source rocks. Carrier et al. (1991) present an excellent compilation of information about the composition and properties of lunar soil.
13
Effects of Climate, Topography, Parent Material, Time, and Biotic Factors
The rate at which weathering can proceed is controlled by parent material and climate. Topography, apart from its influence on climate, determines primarily the rate of erosion, and this controls the depth of soil accumulation and the time available for weathering prior to removal of material from the site. In areas of steep topography, rapid mechanical weathering followed by rapid down-slope movement of the debris results in formation of talus slopes (piles of relatively unweathered coarse rock fragments). Climate determines the amount of water present, the temperature, and the character of the vegetative cover, and these, in turn, affect the biologic complex. Some general influences of climate are: 1. For a given amount of rainfall, chemical weathering proceeds more rapidly in warm than in cool climates. At normal temperatures, reaction rates approximately double for each 10C rise in temperature. 2. At a given temperature, weathering proceeds more rapidly in a wet climate than in a dry climate provided there is good drainage. 3. The depth to the water table influences weathering by determining the depth to which air is available as a gas or in solution and by its effect on the type of biotic activity. 4. Type of rainfall is important: short, intense rains erode and run off, whereas light-intensity, longduration rains soak in and aid in leaching. Table 2.3 summarizes geomorphologic processes in different morphoclimatic zones. The nature and rate of these geomorphologic processes control landform assemblages. During the early stages of weathering and soil formation, the parent material is much more important than it is after intense weathering for long periods of time. Climate ultimately becomes a more dominant factor in residual soil formation than parent material. Of the igneous rock-forming minerals, only quartz and, to a much lesser extent, feldspar, have sufficient chemical durability to persist over long periods of weathering. Quartz is most abundant in coarse-grained granular rocks such as granite, granodiorite, and gneiss, where it typically occurs in grains in the millimeter size range. Consequently, granitic rocks are the main source of sand. In addition to the microbiological activities discussed previously, biological factors of importance include the influences of vegetation on erosion rate and the cycling of elements between plants and soils. Mi-
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SOIL FORMATION
Table 2.3
Morphoclimatic Zones and the Associated Geomorphologic Processes
Morphoclimatic Zone Glacial
Mean Annual Temperature (C) ⬍0
Mean Annual Precipitation (mm) 0–1000
⫺1 to 2
100–1000
Wet midlatitude
0–20
400–1800
Dry continental
0–10
100–400
Hot dry (arid tropical)
10–30
0–300
Hot semidry (semiarid tropical)
10–30
300–600
Hot wet–dry (humid–arid tropical)
20–30
600–1500
Hot wet (humid tropical)
20–30
⬎1500
Azonal Mountain zone
Highly variable
Highly variable
Periglacial
From Fookes et al. (2000).
Relative Importance of Geomorphologic Processes Mechanical weathering rates (especially frost action) high; chemical weathering rates low, mass movement rates low except locally; fluvial action confined to seasonal melt; glacial action at a maximum; wind action significant Mechanical weathering very active with frost action at a maximum; chemical weathering rates low to moderate; mass movement very active; fluvial processes seasonally active; wind action rates locally high. Effects of the repeated formation and decay of permafrost. Chemical weathering rates moderate, increasing to high at lower latitudes; mechanical weathering activity moderate with frost action important at higher latitudes; mass movement activity moderate to high; moderate rates of fluvial processes; wind action confined to coasts. Chemical weathering rates low to moderate; mechanical weathering, especially frost action, seasonally active; mass movement moderate and episodic; fluvial processes active in wet season; wind action locally moderate. Mechanical weathering rates high (especially salt weathering), chemical weathering minimum, mass movement minimal; rates of fluvial activity generally very low but sporadically high; wind action at maximum. Chemical weathering rates moderate to low; mechanical weathering locally active especially on drier and cooler margins; mass movement locally active but sporadic; fluvial action rates high but episodic; wind action moderate to high. Chemical weathering active during wet season; rates of mechanical weathering low to moderate; mass movement fairly active; fluvial action high during wet season with overland and channel flow; wind action generally minimum but locally moderate in dry season. High potential rates of chemical weathering; mechanical weathering limited; active, highly episodic mass movement; moderate to low rates of stream corrosion but locally high rates of dissolved and suspended load transport. Rates of all processes vary significantly with altitude; mechanical and glacial action becomes significant at high elevations.
ORIGIN OF CLAY MINERALS AND CLAY GENESIS
crobial decomposition of the heavy layers of organic matter in top soils formed through photosynthesis results in oxygen depletion and carbon oxidation back to CO2, which is leached by rainwater that penetrates into the subsurface. The high CO2 concentration, lowered pH, and anaerobic nature of these penetrating waters cause reduction and solutioning of iron and manganese minerals, the reduction of sulfates, and dissolution of carbonate rocks. If the moving waters become comingled with oxygenated water in the ground, or as groundwater emerges into rivers and streams, iron, manganese, and sulfide oxidation results, and carbonate precipitation can occur (McCarty, 2004). The time needed to weather different materials varies greatly. The more unconsolidated and permeable the parent material, and the warmer and more humid the climate, the shorter the time needed to achieve some given amount of soil formation. The rates of weathering and soil development decrease with increasing time. The time for soil formation from hard rock parent materials may be very great; however, young soils can develop in less than 100 years from loessial, glacial, and volcanic parent material (Millar et al., 1965). Pyrite bearing rocks are known to break apart and undergo chemical and mineral transformations in only a few years. 2.6 ORIGIN OF CLAY MINERALS AND CLAY GENESIS
There are three general mechanisms of clay formation by weathering (Eberl, 1984): (1) inheritance, (2) neoformation, and (3) transformation. Inheritance means that a clay mineral originated from reactions that occurred in another area during a previous stage in the rock cycle and that the clay is stable enough to remain in its present environment. Origin by neoformation means that the clay has precipitated from solution or formed from reactions of amorphous materials. Transformation genesis requires that the clay has kept some of its inherited structure while undergoing chemical reactions. These reactions are typically characterized by ion exchange with the surrounding environment and/or layer transformation in which the structure of octahedral, tetrahedral, or fixed interlayer cations is modified. The behavior of nonclay colloids such as silica and alumina during crystallization is important in determining the specific clay minerals that form. Certain general principles apply.5
5
The considerations in Chapter 6 provide a basis for these statements.
15
Alkaline earths (Ca2⫹, Mg2⫹) flocculate silica. Alkalis (K⫹, Na⫹, Li⫹) disperse silica. Low pH flocculates colloids. High electrolyte content flocculates colloids. Aluminous suspensions are more easily flocculated than siliceous suspensions. 6. Dispersed phases are more easily removed by groundwater than flocculated phases.
1. 2. 3. 4. 5.
Factors important in determining the formation of specific clay minerals are discussed below. The structure and detailed characterization of these minerals are covered in Chapter 3. Kaolinite Minerals
Kaolinite formation is favored when alumina is abundant and silica is scarce because of the 1⬊1 silica⬊alumina structure, as opposed to the 2⬊1 silica to alumina structure of the three-layer minerals. Conditions leading to kaolinite formation usually include low electrolyte content, low pH, and the removal of ions that tend to flocculate silica (Mg, Ca, Fe) by leaching. Most kaolinite is formed from feldspars and micas by acid leaching of acidic (SiO2-rich) granitic rocks. Kaolinite forms in areas where precipitation is relatively high, and there is good drainage to ensure leaching of cations and iron. Halloysite forms as a result of the leaching of feldspar by H2SO4, which is often produced by the oxidation of pyrite, as shown earlier. The combination of conditions that results in halloysite formation is often found in high-rain volcanic areas such as Hawaii and the Cascade Mountains of the Pacific Northwest in the United States. Smectite Minerals
Smectites, because of their 2⬊1 silica⬊alumina structure, form where silica is abundant, as is the case where both silica and alumina are flocculated. Conditions favoring this are high pH, high electrolyte content, and the presence of more Mg2⫹ and Ca2⫹ than Na⫹ and K⫹. Rocks that are high in alkaline earths, such as the basic and intermediate igneous rocks, volcanic ash, and their derivatives containing ferromagnesian minerals and calcic plagioclase, are usual parent materials. Climatic conditions where evaporation exceeds precipitation and where there is poor leaching and drainage, such as in arid and semiarid areas, favor the formation of smectite. Illite (Hydrous Mica) and Vermiculite
Hydrous mica minerals form under conditions similar to those leading to the formation of smectites. In addition, the presence of potassium is essential; so ig-
16
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SOIL FORMATION
neous or metamorphic rocks and their derivatives are the usual parent rocks. Weathering of feldspar in cool climates often leads to the development of illite. Alteration of muscovite to illite and biotite to vermiculite during weathering is also a significant source of these minerals. Interstratifications of vermiculite with mica and chlorite are common. The high stability of illite is responsible for its abundance and persistence in soils and sediments. Chlorite Minerals
Chlorites can form by alteration of smectite through introduction of sufficient Mg2⫹ to cause formation of a brucitelike layer that replaces the interlayer water. Biotite from igneous and metamorphic rocks may alter to trioctahedral chlorites and mixed-layer chlorite– vermiculite. Chlorites also occur in low- to mediumgrade metamorphic rocks and in soils derived from such rocks. Discussion
The above considerations are greatly simplified, and there are numerous ramifications, alterations, and variations in the processes. One clay type may transform to another by cation exchange and weathering under new conditions. Entire structures may change, for example, from 2⬊1 to 1⬊1, so that montmorillonite forms when magnesium-rich rocks weather under humid, moderately drained conditions, but then alters to kaolinite as leaching continues. Kaolinite does not form in the presence of significant concentrations of calcium. The relative proportions of potassium and magnesium determine how much montmorillonite and illite form. Some montmorillonites alter to illite in a marine environment due to the high K⫹ concentration. Mixedlayer clays often form by partial leaching of K or Mg(OH)2 from between illite and chlorite layers and by incomplete adsorption of K or Mg(OH)2 in montmorillonite or vermiculite. Further details of the clay minerals are given in Chapter 3. More detailed discussions of clay mineral formation are given by Keller (1957, 1964a & b), Weaver and Pollard (1973), Eberl (1984), and Velde (1995), among others.
2.7 SOIL PROFILES AND THEIR DEVELOPMENT
In situ weathering processes lead to a sequence of horizons within a soil, provided erosion does not rapidly remove soil from the site. The horizons may grade abruptly from one to the next or be difficult to distin-
guish. Their thickness may range from a few millimeters to several meters. The horizons may differ in any or all of the following ways: 1. 2. 3. 4. 5.
Degree of breakdown of parent material Content and character of organic material Kind and amount of secondary minerals pH Particle size distribution
All the horizons considered together, including the underlying parent material, form the soil profile.6 The part of the profile above the parent material is termed the solum. Eluviation is the movement of soil material from one place to another within the soil, either in solution or in suspension as a result of excess precipitation over evaporation. Eluvial horizons have lost material; illuvial horizons have gained material. Master horizons are designated by the capital letters O, A, B, C, and R (Table 2.4). Subordinate symbols are used as suffixes after the master horizon designations to indicate dominant features of different kinds of horizons, as indicated in the table. The O horizons are generally present at the soil surface under native vegetation, but they may also be buried by sedimentation of alluvium, loess, or ash fall. The A horizon is the zone of eluviation where humified organic matter accumulates with the mineral fraction. The amount of organic matters (fibers to humic/fulvic acids) varies from 0.1 percent in desert soils to 5 percent or more in organic soils and affects many engineering properties including compressibility, shrinkage, strength and chemical sorption. The B horizon is the zone of illuviation where clay, iron compounds, some resistant minerals, cations, and humus accumulate. The R horizon is the consolidated rock, and the C horizon consists of the altered material from which A and B horizons are formed. Soil profiles developed by weathering can be categorized into three groups on the basis of their mineralogy and chemical composition as shown in Fig. 2.8 (Press and Siever, 1994). Pedalfers, which are formed in moist climate, are soils rich in aluminum and iron oxides and silicates such as quartz and clay minerals. All soluble minerals such as calcium carbonate is leached away. They have a thick A horizon and can be found in much of the areas of moderate to high rainfall in the eastern United States, Canada, and Europe. Pedocals, which are formed in dry climate, are soils rich
6 Residual soil profiles should not be confused with soil profiles resulting from successive deposition of strata of different soil types in alluvial, lake, or marine environments.
SOIL PROFILES AND THEIR DEVELOPMENT
17
Table 2.4 Designations of Master Horizons and Subordinate Symbols for Horizons of Soil Profiles Master Horizons O1 O2 A1 A2 A3 AB A and B AC B and A B
B1 B2 B3 C R
Organic undecomposed horizon Organic decomposed horizon Organic accumulation in mineral soil horizon Leached bleached horizon (eluviated) Transition horizon to B Transition horizon between A and B—more like A in upper part A2 with less than 50% of horizon occupied by spots of B Transition horizon, not dominated by either A or C B with less than 50% of horizon occupied by spots of A2 Horizon with accumulation of clay, iron, cations, humus; residual concentration of clay; coatings; or alterations of original material forming clay and structure Transition horizon more like B than A Maximum expression of B horizon Transitional horizon to C or R Altered material from which A and B horizons are presumed to be formed Consolidated bedrock Subordinate Symbols
b ca cs cn f g h ir m p sa si t x II, III, IV A2, B2
Buried horizon Calcium in horizon Gypsum in horizon Concretions in horizon Frozen horizon Gleyed horizon Humus in horizon Iron accumulation in horizon Cemented horizon Plowed horizon Salt accumulation in horizon Silica cemented horizon Clay accumulation in horizon Fragipan horizon Lithologic discontinuities Second sequence in bisequal soil
Adapted from Soil Survey Staff (1975).
in calcium from the calcium carbonates and other soluble minerals originated from sedimentary bedrock. Soil water is drawn up near the surface by evaporation, leaving calcium carbonate pellets and nodules. They can be found in the southwest United States. Laterite, which is formed in a wet, tropical climate, is rich in aluminum and iron oxides, iron-rich clays, and aluminum hydroxides. Silica and calcium carbonates are leached away from the soil. It has a very thin A ho-
rizon because most of the organic matter is recycled from the surface to the vegetation. Lithologic discontinuities may be common in landscapes where erosion is severe, and these discontinuities are often marked by stone layers from previous erosion cycles. In some places, soils have developed several sequences of A and B horizons, which are superimposed over each other. Superimposed soil sequences are likely the result of climate changes acting
18
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SOIL FORMATION
A
B
C
(a)
Humus and leached soil (quartz and clay minerals present)
A
Humus and leached soil
Some iron and aluminium oxides precipitated; all soluble materials, such as carbonates, leached away
B
Calcium carbonate pellets and nodules precipitated
Granite bedrock
C
(b)
Thin or absent humus Thick masses of insoluble iron and aluminum oxides; occasional quartz Iron-rich clays and aluminum hydroxides Thin leached zone
Sandstone, shale, and limestone bedrock
Mafic igneous bedrock
(c)
Figure 2.8 Major soil types: (a) Pedalfer soil profile developed on granite, (b) Pedocal soil profile developed on sedimentary bedrock, and (c) Laterite soil profile developed on mafic igneous rock (from Press and Siever, 1994).
on uniform geologic materials, or are the remnants of former soil profiles (paleosoils) that have been buried under younger soils (Olson, 1981).
2.8 SEDIMENT EROSION, TRANSPORT, AND DEPOSITION
Streams, ocean currents, waves, wind, groundwater, glaciers, and gravity continually erode and transport soils and rock debris away from the zone of weathering. Each of these transporting agents may cause marked physical changes in the sediment it carries. Although detailed treatment of erosion, transportation, and depositional processes is outside the scope of this book, a brief outline of their principles and their effects on the transported soil is helpful in understanding the properties of the transported material. Erosion
Erosion includes all processes of denudation that involve the wearing away of the land surface by me-
chanical action. The transporting agents, for example, water, wind, and ice, are by themselves capable only of limited wearing action on rocks, but the process is reinforced when these agents contain particles of the transported material. Transportation of sediment requires first that it be picked up by the eroding agent. Greater average flow velocities in the transporting medium may be required to erode than to transport particles. Particles are eroded when the drag and lift of the fluid exceed the gravitational, cohesive, and frictional forces acting to hold them in place. The stream velocity required to erode does not decrease indefinitely with decreasing particle size because small particles remain within the boundary layer adjacent to the stream bed where the actual stream velocity is much less than the average velocity. Relationships between particle size and average stream velocity required to erode and transport particles by wind and water are shown in Fig. 2.9. Ice has the greatest competency for sediment movement of all the transportation agents. There is no limit to the size of particles that may be carried. Ice pushes
SEDIMENT EROSION, TRANSPORT, AND DEPOSITION
19
Transportation
Figure 2.9 Comparison of erosion and transport curves for air and running water. The air is a slightly more effective erosional agent than streams for very small particles but is ineffective for those larger than sand (from Garrels, 1951).
material along in front and erodes the bottom and sides of the valleys through which it flows. In an active glacier (Fig. 2.10), there is continuous erosion and transport of material from the region of ice accumulation to the region of melting. A dead glacier has been cut off from a feeding ice field.
Figure 2.10 Characteristics of glaciers (from Selmer-Olsen,
1964).
The different agents of sediment transport are compared in Table 2.5. The relative effect listed in the last column of this table denotes the importance of the agent on a geological scale with respect to the overall amount of sediment moved, with one representing the greatest amount. Movement of sediment in suspension by wind and water depends on the settling velocity of the particles and the laws of fluid motion. Under laminar flow conditions, the settling velocity of small particles is proportional to the square of the particle diameter. For larger particles and turbulent fluid flow, the settling velocity is proportional to the square root of the particle diameter. Particles stay in suspension once they have been set in motion as long as the turbulence of the stream is greater than the settling velocity. The largest particles that can be transported by water are carried by traction, which consists of rolling and dragging along the boundary between the transporting agent and the ground surface. Particles intermediate in size between the suspended load and the traction load may be carried by saltation, in which they move by a series of leaps and bounds. Soluble materials are carried in solution and may precipitate as a result of changed conditions. The combined effects mean that the concentration of sediment is not constant through the depth of the transporting agent but is much greater near the stream bed than near the top. Fine particles may be fairly evenly distributed from top to bottom; however, coarser particles are distributed mainly within short distances from the bottom, as shown in Fig. 2.11, which applies to a river following a straight course. The major effects of transportation processes on the physical properties of sediments are sorting and abrasion. Sorting may be both longitudinal, which produces a progressive decrease in particle size with distance from the source as the slope flattens, and local, which produces layers or lenses with different grain size distributions. Reliable prediction of the sorting at any point along a sediment transport system is complicated by the fact that flow rates vary from point to point and usually with the seasons. Consequently, very complex sequences of materials may be found in and adjacent to stream beds. Particle size and shape may be mechanically modified by abrasive processes such as grinding, impact, and crushing during transportation. The abrading effects of wind are typically hundreds of times greater than those of water (Kuenen, 1959). In general, abrasion changes the shape and size of gravel size particles but only modifies the shapes of sand and smaller size particles. Water-working of sands causes rounding and
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Table 2.5
SOIL FORMATION
Comparison of Sediment Transport Agents
Type of Flow
Approximate Average Velocity
Maximum Size Eroded by Average Velocity
Streams
Turbulent
A few km/h
Sand
Waves
Turbulent
A few km/h
Wind
Turbulent
Glaciers
Groundwater
Agent
Gravity
Max Load per m3
Type of Transport
Relative Effect
All land
A few tens of kilograms
1
Sand
Coastlines
15 km/h
Sand
Laminar
A few m/yr
Large boulders
Arid, semiarid, beaches, plowed fields High latitudes and altitudes
A few tens of kilograms A kilogram
Laminar
A few m/yr
Colloids
A kilogram
Bed load, suspended load, solution Same as streams Bed load, suspended load Bed load, suspended load, surface load Solution
3
cm/yr to a few m/s
Boulders
2000 kg
Bed load
3
Areas Affected
Soluble material and colloids Steep slopes, sensitive clays, saturated cohesionless soils, unconsolidated rock
Hundreds of kilograms
2 3
2
Adapted from Garrels (1951).
polishing of grains, and wind-driven impact can cause frosting of grains. The shape and surface character of particles influences a soil’s stress–deformation and strength properties owing to their effects on packing, volume change during shear, and interparticle friction. Basic minerals, such as the pyroxenes, amphiboles, and some feldspars, are rapidly broken down chemically during transport. Quartz, which is quite stable because of its resistant internal structure, may be modified by mechanical action, but only at a slow rate. Quartz sand grains may survive a number of successive sedimentation cycles with no more than a percent or two of weight loss due to abrasion. The surface textures of quartz sand particles reflect their origin, as shown by the examples in Fig. 2.12 for different sands, each shown to three or four magnifications. The mechanical and chemical actions, associ-
ated with a beach environment, produce a relatively smooth, pitted surface texture. Aeolian sands exhibit a rougher surface texture, particularly over small distances. Some, but not all, river sands may have a very smooth particle surface that reflects the influence of chemical action. Sand that has undergone change after deposition and burial is termed diagenetic sand. Its surface texture may reflect a long and stable period of interaction with the groundwater. In some cases, very rough surface textures can develop. Ottawa sand, a material that has been used for numerous geotechnical research investigations, is such a material. Some effects of transportation on sediment properties are summarized in Table 2.6. The gradational characteristics of sedimentary materials reflect their transportation mode as indicated in Fig. 2.13. Sediments of different origins lie within specific zones of
SEDIMENT EROSION, TRANSPORT, AND DEPOSITION
21
Figure 2.11 Schematic diagram of sediment concentration with depth in a transporting
stream.
the figure, which are defined by the logarithm of the ratio of 75 percent particle size to 25 percent particle size and the median (50 percent) grain size. Deposition
Deposition of sediments from air and water is controlled by the same laws as their transportation. If the stream velocity and turbulence fall below the values needed to keep particles in suspension or moving with the bed load, then the particles will settle. When ice melts, the sediments may be deposited in place or carried away by meltwater. Materials in solution can precipitate when exposed to conditions of changed temperature or chemical composition, or as a result of evaporation of water. Sediments may be divided into those formed primarily by chemical and biological means and those composed primarily of mineral and rock fragments. The latter are sometimes referred to as detrital or clastic deposits. The deposition of sediments into most areas is cyclical. Some causes of cyclic deposition are: 1. Periodic earth movements 2. Climatic cycles of various lengths, most notably the annual rhythm 3. Cyclic shifting of tributaries on a delta 4. Periodic volcanism
The thickness of deposits formed during any one cycle may vary from less than a millimeter to hundreds of meters. The period may range from months to thousands of years, and only one or many types of sediments may be involved. One of the best known sediments formed by cyclical deposition is varved clay. Varved clays formed in glacial lakes during the ice retreat stage. Each layer consists of a lighter-colored, summer-deposited clayey silt grading into a darker winter-deposited silty clay. Spring and summer thaws contributed clay and siltladen meltwater to the lake. The coarsest particles settled first to form the summer layer. Because of the much slower settling velocity of the clay particles, most did not settle out until the quiet winter period. A photograph of a vertical section through a varved clay is shown in Fig. 2.14. The alternating coarser-grained, light-colored layers and finer-grained, darker layers are clearly visible. The shear resistance along horizontal varves is much less than that across the varves. Also, the hydraulic conductivity is much greater in the horizontal direction than in the vertical direction. Extensive deposits of varved clays are found in the northeast and north central United States and eastern Canada. Detailed description of the geology and engineering properties of Connecticut Valley varved clay is given by DeGroot and Lutenegger (2003). Complex soil deposition processes occur along coastlines, estuaries, and shallow shelves in relation to
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SOIL FORMATION
Figure 2.12 Surface textures of four sands of differing origins: (a) river sand, (b) beach
sand, (c) aeolian sand and (d) diagenetic sand (courtesy of Norris, 1975).
the location of the shoreline. Soil deposits include foreshore sand and gravels, which are sorted by wave actions, organic deposits, and clays preserved in lagoons, offshore fine sands, and muds. River channels may be overdeepened, and soft sediments then accumulate to form buried valleys. Most coastlines and estuaries of the world were subject to sea level changes in the Quaternary period. In particular, the post glacial rise of sea level, which ended about 6000 years ago, has had a worldwide influence on the present-day coastal forms. Figure 2.15 shows alternating layers of marine (Ma) and fluvial (Diluvial-D) sediments in the geotechnical profile down to 400 m depth below sea level at Osaka Bay, Japan (Tanaka and Locat, 1999). The observed variation corresponds well to the local relative sea level during its geological history up to 1 million years ago.
Chemical and biochemical sediments may consist of one or two kinds of materials. For example, calcium carbonate sediments are made of calcite, which originates from the shells of organisms in the deep sea (Fig. 2.16a). Some clays contain significant amounts of microfossils due to the depositional environment as shown in Fig. 2.16b; such clays include Mexico City clay (Diaz-Rodriguez et al., 1998), Ariake clay (Ohtsubo et al., 1995), and Osaka Bay clay (Tanaka and Locat, 1999). The microfossils include diatoms (siliceous skeleton of eukarya cells in either freshwater or marine environments), radiolaria (found in marine environments and consisting mostly of silica), and formanifera (calcium carbonate shell secreted by marine eukarya). The presence of microfossils can have a profound effect on the behavior of the soil mass, confer-
SEDIMENT EROSION, TRANSPORT, AND DEPOSITION
23
Figure 2.12 (Continued )
ring unusual geotechnical properties that deviate from general property expectations, including high porosity, high liquid limit, unusual compressibility, and uniquely high friction angle. For examples, see Tanaka and Locat (1999) and Locat and Tanaka (2001). While streams and rivers produce deposits according to grain size, a glacier transports the finest dust and large boulders side by side at the same rate of movement. If the material remains unsorted after deposition, it is called till. A mixture of all grain sizes from boulders to clays is known as boulder clay, which is a difficult material to work with because large boulders may damage excavation equipment. Loess, which is a nonstratified aeolian deposit, is probably the single most abundant Quaternary deposit on land. It consists of silt with some small fraction of clay, sand, and carbonate. It originated during the Qua-
ternary period from glacial out wash and deglaciated till areas. The deposits are spread widely and blanket preexisting landforms. The deposits are up to 30 m thick in the Missouri and Rhine River Valleys, more than 180 m thick in Tajikistan, and up to 330 m thick in northern China. Depositional Environment
The environment of deposition determines the complex of physical, chemical, and biological conditions under which sediments accumulate and consolidate. The three general geographical depositional environments are continental, mixed continental and marine, and marine. Continental deposits are located above the tidal reach and include terrestrial, paludal (swamp), and lacustrine (lake) sediments. Mixed continental and
24
2
Table 2.6
SOIL FORMATION
Effects of Transportation on Sediments Water
Size
Shape and roundness Surface texture
Sorting
Reduction through solution, little abrasion in suspended load, some abrasion and impact in traction load Rounding of sand and gravel Sand: smooth, polished, shiny Silt: little effect Considerable sorting
Air
Ice
Gravity
Considerable reduction
Considerable grinding and impact
Considerable impact
High degree of rounding Impact produces frosted surfaces Very considerable sorting (progressive)
Angular, soled particles Striated surfaces
Angular, nonspherical Striated surfaces
Very little sorting
No sorting
Adapted from Lambe and Whitman (1969).
Figure 2.13 Influence of geologic history on sorting of particle sizes (adapted from SelmerOlsen, 1964).
POSTDEPOSITIONAL CHANGES IN SEDIMENTS
25
Figure 2.14 Vertical section through varved clay from the New Jersey meadowlands (courtesy of S. Saxena).
Figure 2.16 Biochemical sediments: (a) Dogs Bay calcium carbonate sand (courtesy of E. T. Bowman) and (b) diatoms observed in Osaka Bay clay (courtesy of Y. Watabe).
environments (Locat et al., 2003). Characteristic soil types and properties associated with these depositional environments are described in Chapter 8. Figure 2.15 Soil profile of Osaka Bay showing alternating
marine (Ma) and fluvial (Diluvial-D) layers (modified from Tanaka and Locat, 1999).
marine deposits include littoral (between the tides), deltaic, and estuarine sediments. Marine deposits are located below the tidal reach and consist of continental shelf (neritic), continental slope and rise (bathyal), and deep ocean (abyssal) sediments. Table 2.7 summarizes main soil deposits that are formed in various types of
2.9 POSTDEPOSITIONAL CHANGES IN SEDIMENTS
Between the time a sediment is first laid down and the time it is encountered in connection with some human activity, it may have been altered as a result of the action of any one or more of several postdepositional processes. These processes can be physical, chemical, and/or biological. They occur because the young sediment is not necessarily stable in its new environment
26
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SOIL FORMATION
Table 2.7
Depositional Environment of Various Soil Deposits Deposits
Transported
Environment
Type
Air Water Shallow river
Aeolian sand
Sand
Fluvial (glacio-) Alluvial (glacio-) Littoral Muskeg Lacustrine (glacio-) Flow deposits Marls Estuarine Littoral Shelf Pelagic Oozes—calcareous Oozes—siliceous Flow Subglacial till Supraglacial till Tropical soils Saprolite Decomposed granite Colluvial soils Evaporites (sakkas) Evaporites Limestone Gas hydrates
Sand and gravel Silt and sand Sand and gravel Peat—organic Silt and clay Clay to gravel Silt (fossils) Silt and clay Silt and sand Silt and clay Silt and clay Silt and clay Silt and clay Clay to gravel Clay to boulders Sand to boulders Clay to sand Clay to boulders Clay to boulders Clay to boulders
Shallow lake Deep lake
Shallow ocean
Deep ocean
Glacier Residual
Land
Chemical and biochemical
Lake Sea
Texture
Adapted from Locat et al. (2003).
where the material is exposed to new conditions of temperature, pressure, and chemistry. An understanding of postdepositional changes is essential for understanding of properties, interpreting soil profile data, and in reconstructing geologic history. A brief outline of the processes is presented here; their effects on engineering properties are described in more detail in Chapter 8. Desiccation
The drying of fine-grained sediments is usually accompanied by shrinkage and cracking. Precompression of the upper portions of clay layers by drying is frequently observed. The effects of desiccation on the strength and water content variations with depth in London clay from the Thames estuary are shown in Fig. 2.17. Care must be exercised in interpreting profiles of this type because drying is only one of several possible causes of apparent overconsolidation (precon-
solidation pressure greater than present overburden effective pressure) at shallow depths. Other important mechanisms include partial consolidation under increased overburden and the effects of weathering. Weathering
Weathering and soil-forming processes are initiated in new sedimentary deposits after exposure to the atmosphere, just as they are on freshly exposed rock. In some instances, weathering can result in improvement in properties or protection of underlying material. For example, the weathering of uplifted marine clays can lead to the replacement of sodium by potassium as the dominant exchange cation (Moum and Rosenqvist, 1957). This increases both the undisturbed and remolded strength. Water content and strength data for a Norwegian marine clay profile are shown in Fig. 2.18. It may be seen that the upper 5 m of clay, which have been weathered, have water content and strength var-
Figure 2.17 Properties of Thames estuary clay. The overconsolidation in the upper 10 ft was caused by surface drying (Skempton and Henkel, 1953).
27
28
2
SOIL FORMATION
Figure 2.18 Clay characteristics at Manglerud in Oslo, Norway (Bjerrum, 1954).
iation characteristics similar to those of the Thames estuary clay (see Fig. 2.17). In the case of the Norwegian clay, however, the plasticity values have also changed in the upper 5 m, providing evidence of changed composition. Weathering of the surface of some loess deposits has resulted in the formation of a relatively impervious loam that protects the underlying metastable loess structure from the deleterious effects of water.
Consolidation and Densification
Consolidation (termed compaction in geology) of finegrained sediments occurs from increased overburden, drying, or changes in the groundwater level so that the effective stress on the material is increased. Deposits of granular material may be affected to some extent in the same way. More significant densification of cohesionless soil occurs, however, as a result of dynamic loading such as induced by earthquakes or the activi-
POSTDEPOSITIONAL CHANGES IN SEDIMENTS
ties of humans. The usual effects of consolidation are to increase strength, decrease compressibility, increase swell potential, and decrease permeability. Even under constant effective stress conditions, structural readjustments and small compressions may continue for long periods owing to the viscous nature of soil structures. This ‘‘secondary compression’’ provides an additional source of increased strength with time. Unloading
Erosion of overlying sediments due to glacial process leads to mechanical overconsolidation. A typical example of this is London clay, a marine clay deposited during the Eocene period. The erosion took place in late Tertiary and Pleistocene times and the amount of erosion is estimated to be about 150 m in Essex (Skempton, 1961) to 300 m in the Wraybury district (Bishop et al., 1965). After the unloading, small reloading occurred by new deposition of gravels in the late Quaternary period. Within the London clay, five major transgressive–regressive cycles are recognized during its deposition. The postdepositional processes are site specific; that is, the degree of weathering and desiccation and the amount of erosion vary depending on location. This variation in depositional and postdepositional processes results in complex mechanical behavior (Hight et al., 2003). Authigenesis, Diagenesis, Cementation, and Recrystallization
Authigenesis is the formation of new minerals in place after deposition. Authigenesis can make grains more angular, lower the void ratio, and decrease the permeability. Small crystals and rock fragments may grow into aggregates of coarser particles. Diagenesis refers to such phenomena as changes in particle surface texture, the conversion of minerals from one type to another, and the formation of interparticle bonds as a result of increased temperature, pressure, and time. Many diagenetic changes are controlled by the pH and redox potential of the depositional environment. With increasing depth of burial in a sedimentary basin, clayey sediments may undergo substantial transformation. Expansive clay minerals can transform to a nonexpansive form, for example, montmorillonite to mixed layer to illite, as a result of the progressive removal of water layers under pressure (Burst, 1969). Burial depths of 1000 to 5000 m may be required, and the transformation process appears thermally activated as a result of the increased temperature at these depths. Chlorite can form in mud and shale during deep burial (Weaver and Pollard, 1973).
29
The long-term stability of different clay minerals under conditions of elevated temperature and pressure and in different chemical environments is important relative to the use of clays as containment barriers for nuclear and toxic wastes. Diagenesis studies of locked sands show crystal overgrowths caused by pressure solution and compaction (Barton, 1993; Richards and Burton, 1999). Cementation has important effects on the properties and stability of many soil materials. Cementation is not always easily identified, nor are its effects always readily determined quantitatively. It is known to contribute to clay sensitivity, and it may be responsible for an apparent preconsolidation pressure. Removal of iron compounds from a very sensitive clay from Labrador, Canada, by leaching led to a 30-ton/m2 decrease in apparent preconsolidation pressure (Kenney et al., 1967). Coop and Airey (2003) show for carbonate soils that cementation develops soon after deposition and enables the soil to maintain a loose structure. Failure to recognize cementation has resulted in construction disputes. For example, a soil on a major project was marked on the contract drawings as glacial till. It proved to be so hard that it had to be blasted. The contractor claimed the soil was cemented because during digging failure took place through pebbles as well as the clay matrix. The owner concluded that this happened because the pebbles were weathered. Proper evaluation of the material before the award of the contract could have avoided the problem. Clay particles adhere to the surfaces of larger silt and sand particles, a process called clay bounding. Eventually the larger grains become embedded into a clay matrix and their influence on the geotechnical behavior becomes limited. The clay bounding provides arching of interparticle forces, maintaining a large void ratio even at high effective stresses. Time Effects
Even freshly deposited or densified sands can develop significant increases in strength and stiffness over relatively short time periods, that is, by a factor of 2 or more within a few months (Mitchell and Solymar, 1984). Time effects and the aging of both cohesive and cohesionless soils are analyzed and reviewed by Schmertmann (1991). Uncertainty remains as to whether the mechanisms for the observed increases in apparent preconsolidation pressure, strength, and stiffness are chemical, physical, or both. Research is continuing on this important aspect of soil behavior so that it will be possible to predict both the amount and the rate of property changes for use in the analysis of geotechnical problems. The aging process is of particular
30
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SOIL FORMATION
interest in connection with hydraulic fills and ground improvement projects, more details are given in Chapter 12.
shock. Cracks up to 2 ft wide, of unknown depth, and spaced several meters apart have caused damage to buildings and highways.
Leaching, Ion Exchange, and Differential Solution
Biological Effects
Postdepositional changes in pore fluid chemistry can result from the percolation of different fluids through a deposit. This may change the forces between colloidal particles. For example, the uplift of marine clay above sea level followed by freshwater leaching can lead to both ion exchange and the removal of dissolved salts. This process is important in the formation of highly sensitive, quick clays, as discussed in more detail in Chapter 8. Materials can be removed from sediments by differential solution and subsequent leaching. Calcareous and gypsiferous sediments are particularly susceptible to solution, resulting in the formation of channels, sink holes, and cavities.
Biological activity affects soil particles by modifying their arrangement, aggregating them, weathering mineral surfaces, mediating oxidation–reduction reactions, contributing to precipitation and dissolution of minerals, and degrading organic particles. The survival and activity of microorganisms are controlled partly by pore geometry and local physicochemical conditions. Therefore, apart from its impact on life itself, biological activity has influenced the evolution of the earth surface, impacted mineral, sediment, and rock formation, accelerated the rate of rock weathering and altered its products, influenced the composition of groundwater, and participated in the formation of gas and petroleum hydrocarbons. Bioturbance refers to the action of organisms living on or in sediments. By organic cementation, they modify grain size, density, or cohesion (Richardson et al., 1985; Locat et al., 2003). The aggregation activity of various worms densifies deposits by changing the grain size of the sediment. Tubes that form can provide local drainage and decrease the bulk density. The active zone of bioturbance is usually to depths less than 30 cm. Sticky organic mucus or polymer bridging binds together clay–silt particles, producing clusters. Chemical transformation processes are mediated by organisms. Some notable processes are summarized as follows (Mitchell and Santamarina, 2005):
Jointing and Fissuring of Clay Soils
Some normally consolidated clays, almost all floodplain clays, and many preconsolidated clays are weakened by joints and fissures. Joints in floodplain clays result from deposition followed by cyclic expansion and contraction from wetting and drying. Joints and fissures in preconsolidated clays result from unloading or from shrinkage cracks during drying. Closely spaced joints in these types of clays may contribute to slides some years after excavation of cuts. The unloading enables joints to open, water to enter, and the clay to soften. Fissures have been found in normally consolidated clays at high water contents that could not have been caused by drying or unloading (Skempton and Northey, 1952), and increased brittleness has been observed in soft clay chunks that have been stored for some time. These effects may be caused by syneresis, which is the mutual attraction of clay particles to form closely knit aggregates with fissures between them. Similar behavior is many times observed in gelatin after aging. Weathering and the release of potassium may also result in fissuring. Vegetation, especially large trees, can cause shrinkage and fissuring of clays (Barber, 1958; Holtz, 1983). The root systems suck up water, causing large capillary shrinkage pressures. When rain falls on crusted surface layers of dried-up saline lakes, it is rapidly absorbed by capillarity. The air may become so compressed that it causes tension cracking or blowouts in a form similar in appearance to root holes. These sediments may also undergo severe cracking, apparently as a result of
1. Sulfur Cycle Elemental sulfur (S0) and sulfides (S2⫺) are the stable forms of sulfur under anaerobic conditions, whereas sulfates (SO42⫺) are the stable forms of sulfur under aerobic conditions. Sulfides form under anaerobic conditions from sulfates already present in seawater and sediments or introduced by diffusion and groundwater flow. The sulfate ion is not reduced to sulfide at Earth surface temperature and pressure unless biologically mediated. Sulfate-reducing bacteria are anaerobic and grow best at neutral pH but are known to exist over a broad range of pH and salt content. When exposed to aerobic conditions, reduced sulfur compounds, hydrogen sulfides (H2S), and elemental sulfur are used as an energy source by sulfide-oxidizing bacteria and converted to sulfates. 2. Iron Cycle Iron in the subsurface exists predominantly in the reduced or ferrous (Fe2⫹) state
POSTDEPOSITIONAL CHANGES IN SEDIMENTS
or the oxidized ferric (Fe3⫹) state. Several microorganisms such as the genus Thiobacillus mediate the iron oxidation reaction. Chapelle (2001) notes that bacteria are able to derive only relative little energy from oxidizing Fe2⫹; therefore, they must process large amounts of Fe2⫹ and produce large amounts of Fe3⫹ to obtain sufficient energy to sustain their growth. One important consequence of the rapid oxidation of iron sulfide in the presence of oxygen is the formation of acid rock drainage. Although Fe(OH)3 has low solubility, the formation of H2SO4 provides a source of important reactions in the solid and pore water phases. The total dissolved solids increases owing to the dissolution of carbonates in the soil. Gypsum can form, with an associated volume increase, at the expense of carbonate minerals. The precipitated ferric hydroxide is thermodynamically unstable and rapidly transforms to yellow goethite, FeO–OH. Geothite, while stable under wet conditions, will slowly dehydrate to red hematite, Fe2O3, under dry conditions. Microorganisms have a limited effect on the formation of coarse grains. However, bioactivity can affect diagenetic evolution, promote the precipitation of cementing agents, cause internal weathering, and alter fines migration, filter performance, and drainage in silts and sands. Severely water-limited environments distress microorganisms and hinder biological activity. Nonetheless, there is great bacterial activity in the unsaturated organic surface layer of a soil where plant roots are found. Fierer et al. (2002) observed that bacterial activity decreases by 1 or 2 orders of magnitude by 2 m of depth. Horn and Meike (1995) conclude that microbial activity requires 60 to 80 percent saturation. Hence, there is less reduction in bacterial count with depth in saturated sediments. Hindered biological activities in unsaturated soils may reflect lack of nutrients in isolated water at menisci, slow nutrient flow in percolating water paths, and increased ionic concentration in the pore fluid as water evaporates and dissolved salts approach ion saturation conditions. The physical scales over which the physicochemical, bioorganic, and burial diagenetic processes act range from atomic dimensions to kilometers, and the timescales range from microseconds to years. Table 2.8 summarizes the processes, fabric characteristics, and scales associated with different mechanisms. Human Effects
The global human population has grown from approximately 600 million at the beginning of the eighteenth
31
century to close to 6 billion today. Human activities are now at such a scale as to rival forces of nature in their influence on soil changes. The activities include rapid changes in land use and the associated landforms, soil erosion related to forest removal, and soil contamination by urbanization, mining, and agricultural activities. Ten to 15 percent of Earth’s land surface is occupied by industrial areas and agriculture, and another 6 to 8 percent is pasture land (Vitousek et al., 1997). Mine wastes are the largest waste volumes produced by humankind. On October 21, 1966, 144 people, 116 of them children, were killed when a tip of coal waste slid onto the village of Aberfan in South Wales, United Kingdom. The collapse was caused by tipping of coal waste over a natural underground spring, and the coal slag slowly turned into a liquid slurry. The tragedy was caused by two days of continual heavy rain loosening the coal slag. As a result of the disaster at Aberfan, the Mines and Quarries Tips Act of 1969 was introduced. This act was passed in order to prevent disused tips from becoming a danger to members of the public. Over 8000 million tons of ore have been mined in the South African deep-level underground gold mining industry (Blight et al., 2000). Considerations for disposing these wastes into tailings ponds and dams include the physicochemical nature of the extracted minerals as well as the topography and climate of the disposal sites. Tailings dams have failed, resulting in destructive mudflows (Blight, 1997). One reported case was the failure of the Merriespruit ring-dyke gold tailings dam in South Africa in 1994, which killed 17 people in a village nearby. Overtopping of the tailings dyke occurred after a significant rainfall event, and approximately 500,000 m3 of tailings flowed through this breach. The liquefied tailings flowed for a distance of about 2 km. A large volume of tailings was in a metastable state in situ, and overtopping and erosion of the impoundment wall exposed this material, resulting in static liquefaction of the tailings and a consequent flow failure (Fourie et al., 2001). The urban underground in major cities is congested by utility lines, tunnels, and building foundations. Much may be more than 100 years old; for example, more than 50 percent of the water supply pipes in London were built using cast-iron during Victorian time. Aging infrastructure changes the in situ stress condition, as well as groundwater chemistry, and this can lead to changes in the stress–strain–time behavior of the subsoil. Underground openings are sources or sinks of different environments; tunnels can act as a groundwater drain as well as source for air into the ground.
32
2
SOIL FORMATION
Table 2.8 Summary of Processes and of the Fabric Signature and Temporal Scales Associated with Various Mechanisms Fabric Signaturesa (predominant)
Physical Time
Processes
Mechanisms
Physicochemical
Electromechanical
EF
Thermomechanical
FF (some EF)
Interface dynamics
FF and EF
m to ⬃ 0.5 mm
s
Biomechanical
EF
s to min
Biophysical
EE and FF
⬃ 0.5 mm to ⬎ 2.0 mm m to mm
s to min
Biochemical
Nonunique (unknown) FF localized swirl Nonunique (unknown)
m to mm
h to yr
cm to km
yr
Molecular
yr
Bioorganic
Burial diagenesis
Mass gravity Diagenesiscementation
Scales Atomic and molecular to ⬃ 4 m Molecular to 0.2 mm
Remarks
s to ms
Two particles may rotate FF
ms to min
Initial contacts EF then rotations to FF: common in selective environments Some large compound particles may be possible at high concentrations Some FF possible during bioturbation Some very large clay organic complexes possible New chemicals formed, some altered Can operate over large physical scales New minerals formed, some altered, changes in morphology
a
EF, edge-to-face; EE, edge-to-edge; FF, face-to-face. Adapted from Mitchell and Santamarina (2005) and Bennett et al. (1991).
Detailed studies of the geotechnical impacts of such problems have, so far, been limited (e.g., Gourvenec et al., 2005), and further studies of the impacts of aging on existing infrastructure are needed.
2.10
CONCLUDING COMMENTS
Knowledge of geologic and soil-forming processes aids in anticipating and understanding the probable composition, structure, properties, and behavior of a soil. Along with site investigation data, characterization of the landforms, that is, understanding of the former and current geomorphological processes associated with the past and present climatic conditions, often helps to define ground conditions for designing geotechnical structures and anticipating the long-term performance. For example, the knowledge can be used
to infer clay mineral types, to detect the presence of organic and high clay content layers, to locate borrow materials for construction, and to estimate the depth to unaltered parent material. Pedological data can be used to surmise compositions and soil physical properties. Transported soils are sorted, abraded, and have particle surface textures that reflect the transporting medium. Conditions of sedimentation and the depositional environment influence the grain size, size distribution, and grain arrangement. Thus, knowledge of the transportation and deposition history provides insight into geotechnical engineering properties. In short, the soil and its properties with which we deal today are a direct and predictable consequence of the parent material of many years ago and of all the things that have happened to it since. The better our knowledge of what that parent material was and what the intervening events have been, the better our ability
QUESTIONS AND PROBLEMS
to deal with the soil as an engineering material. Several examples are given in this chapter and more are given in Chapter 8.
QUESTIONS AND PROBLEMS
1. At what depth below the ground surface does quartz start to crystallize? 2. What are some likely consequences of the different physical and chemical weathering processes on the mechanical and flow properties of the rocks and soils on which they act? 3. Describe the chemical reactions of pyrite oxidation and explain how bacteria can mediate the chemical processes. 4. Discuss what types of clay minerals are likely to be produced under each morphoclimatic zone listed in Table 2.3. 5. Using Stokes’s law, derive the sedimentation speeds of spherical particles with different sizes in freshwater under hydrostatic condition. Would they change in saltwater? Compare the results to the data given in Fig. 2.9 and discuss the comparison. 6. List and discuss human activities that may potentially change the properties of soils.
33
7. Compare and contrast soil-forming processes on Earth and on the Moon in terms of the composition and engineering properties of the soils. Explain similarities and differences. What is the relative importance of physical, chemical, and biological soilforming processes on the Moon and on Earth? Why? 8. Considering rock and mineral stability, the types and characteristics of weathering processes, and the impacts of weathering on properties, what types of earth materials would you consider most suitable for use as chemical, radioactive, and mixed (chemical and radioactive) waste containment barriers? Why? 9. Prepare diagrams showing your estimates as a function of elevation of the following soil characteristics that you would expect to encounter between the bottom and the top of Mount Kilimanjaro in Tanzania. Give a brief explanation for each. a. Soil plasticity b. Soil gradation and mean particle size c. Angularity–roundness of sand and gravel particles d. Iron content e. Cementation between particles f. Organic matter content g. Water content
CHAPTER 3
Soil Mineralogy
3.1 IMPORTANCE OF SOIL MINERALOGY IN GEOTECHNICAL ENGINEERING
Soil is composed of solid particles, liquid, and gas and ranges from very soft, organic deposits through less compressible clays and sands to soft rock. The solid particles vary in size from large boulders to minute particles that are visible only with the aid of the electron microscope. Particle shapes range from nearly spherical, bulky grains to thin, flat plates and long, slender needles. Some organic material and noncrystalline inorganic components are found in most natural fine-grained soils. A soil may contain virtually any element contained in Earth’s crust; however, by far the most abundant are oxygen, silicon, hydrogen, and aluminum. These elements, along with calcium, sodium, potassium, magnesium, and carbon, comprise over 99 percent of the solid mass of soils worldwide. Atoms of these elements are organized into various crystalline forms to yield the common minerals found in soil. Crystalline minerals comprise the greatest proportion of most soils encountered in engineering practice, and the amount of nonclay material usually exceeds the amount of clay. Nonetheless, clay and organic matter in a soil usually influence properties in a manner far greater than their abundance. Mineralogy is the primary factor controlling the size, shape, and properties of soil particles. These same factors determine the possible ranges of physical and chemical properties of any given soil; therefore, a priori knowledge of what minerals are in a soil provides intuitive insight as to its behavior. Commonly defined particle size ranges are shown in Fig. 3.1. The divisions between gravel, sand, silt, and clay sizes are arbitrary but convenient. Particles smaller than about 200 mesh sieve size (0.074 mm), which is the boundary between sand and silt sizes, cannot be seen by the
naked eye. Clay can refer both to a size and to a class of minerals. As a size term, it refers to all constituents of a soil smaller than a particular size, usually 0.002 mm (2 m) in engineering classifications. As a mineral term, it refers to specific clay minerals that are distinguished by (1) small particle size, (2) a net negative electrical charge, (3) plasticity when mixed with water, and (4) high weathering resistance. Clay minerals are primarily hydrous aluminum silicates. Not all clay particles are smaller than 2 m, and not all nonclay particles are coarser than 2 m; however, the amount of clay mineral in a soil is often closely approximated by the amount of material finer than 2 m. Thus, it is useful to use the terms clay size and clay mineral content to avoid confusion. A further important difference between clay and nonclay minerals is that the nonclays are composed primarily of bulky particles; whereas, the particles of most of the clay minerals are platy, and in a few cases they are needle shaped or tubular. The great range in soil particle sizes in relation to other particulate materials, electromagnetic wave lengths, and other size-dependent factors can be seen in Fig. 3.2. The liquid phase of most soil systems is composed of water containing various types and amounts of dissolved electrolytes. Organic compounds, both soluble and immiscible, are found in soils at sites
Figure 3.1 Particle size ranges in soils.
35
36
Figure 3.2 Characteristics of particles and particle dispersoids (adapted from Stanford Re-
search Institute Journal, Third Quarter, 1961).
37
38
3
SOIL MINERALOGY
that have been affected by chemical spills, leaking wastes, and contaminated groundwater. The gas phase, in partially saturated soils, is usually air, although organic gases may be present in zones of high biological activity or in chemically contaminated soils. The mechanical properties of soils depend directly on interactions of these phases with each other and with applied potentials (e.g., stress, hydraulic head, electrical potential, and temperature). Because of these interactions, we cannot understand soil behavior in terms of the solid particles alone. Nonetheless, the structure of these particles tells us a great deal about their surface characteristics and their potential interactions with adjacent phases. Interatomic and intermolecular bonding forces hold matter together. Unbalanced forces exist at phase boundaries. The nature and magnitude of these forces influence the formation of soil minerals, the structure, size, and shape of soil particles, and the physicochemical phenomena that determine engineering properties and behavior. In this chapter some aspects of atomic and intermolecular forces, crystal structure, structure stability, and characteristics of surfaces that are pertinent to the understanding of soil behavior are summarized simply and briefly. This is followed by a somewhat more detailed treatment of soil minerals and their characteristics.
tronic energy can jump to a higher level by the absorption of radiant energy or drop to a lower level by the emission of radiant energy. No more than two electrons in an atom can have the same energy level, and the spins of these two electrons must be in opposite directions. Different bonding characteristics for different elements exist because of the combined effects of electronic energy quantization and the limitation on the number of electrons at each energy level. An atom may be represented in simplified form by a small nucleus surrounded by diffuse concentric ‘‘clouds’’ of electrons (Fig. 3.3). The maximum number of electrons that may be located in each diffuse shell is determined by quantum theory. The number and arrangement of electrons in the outermost shell are of prime importance for the development of different types of interatomic bonding and crystal structure. Interatomic bonds form when electrons in adjacent atoms interact in such a way that their energy levels are lowered. If the energy reduction is large, then a strong, primary bond develops. The way in which the bonding electrons are localized in space determines whether or not the bonds are directional. The strength and directionality of interatomic bonds, together with the relative sizes of the bonded atoms, determine the type of crystal structure assumed by a given composition.
3.2
3.3
ATOMIC STRUCTURE
Current concepts of atomic structure and interparticle bonding forces are based on quantum mechanics. An electron can have only certain values of energy. Elec-
INTERATOMIC BONDING
Primary Bonds
Only the outer shell or valence electrons participate in the formation of primary interatomic bonds. There are
Figure 3.3 Simplified representation of an atom.
SECONDARY BONDS
three limiting types: covalent, ionic, and metallic. They differ because of how the bonding electrons are localized in space. The energy of these bonds per mole of bonded atoms is from 60 ⫻ 103 to more than 400 ⫻ 103 joules (J; 15 to 100 kcal). As there are 6.023 ⫻ 1023 molecules per mole, it might be argued that such bonds are weak; however, relative to the weight of an atom they are very large. Covalent Bonds In the covalent bond, one or more bonding electrons are shared by two atomic nuclei to complete the outer shell for each atom. Covalent bonds are common in gases. If outer shell electrons are represented by dots, then examples for (1) hydrogen gas, (2) methane, and (3) chlorine gas are: 1. H ⫹ H ⫽ H:H H 2. C ⫹ 4H ⫽ H:C:H H 3. :Cl ⫹ Cl: ⫽ :Cl:Cl: In the solid state, covalent bonds form primarily between nonmetallic atoms such as oxygen, chlorine, nitrogen, and fluorine. Since only certain electrons participate in the bonding, covalent bonds are directional. As a result, atoms bonded covalently pack in such a way that there are fixed bond angles. Ionic Bonds Ionic bonds form between positively and negatively charged free ions that acquire their charge through gain or loss of electrons. Cations (positively charged atoms that are attracted by the cathode in an electric field) form by atoms giving up one or more loosely held electrons that lie outside a completed electron shell and have a high energy level. Metals, alkalies (e.g., sodium, potassium), and alkaline earths (e.g., calcium, magnesium) form cations. Anions (negatively charged atoms that are attracted to the anode) are those atoms requiring only a few electrons to complete their outer shell. Because the outer shells of ions are complete, structures cannot form by electron sharing as in the case of the covalent bond. Since ions are electrically charged, however, strong electrical attractions (and repulsions) can develop between them. The ionic bond is nondirectional. Each cation attracts all neighboring anions. In sodium chloride, which is one of the best examples of ionic bonding, a sodium cation attracts as many chlorine anions as will fit around it. Geometric considerations and electrical neutrality determine the actual arrangement of ionically bonded atoms. As ionic bonding causes a separation between the centers of positive and negative charge in a molecule, the molecule will orient in an electrical field forming a dipole. The strength of this dipole is expressed in
39
terms of the dipole moment . If two electrical charges of magnitude e, where e is the electronic charge, are separated by a distance d, then ⫽ d e
(3.1)
Covalently bonded atoms may also produce dipolar molecules. Metallic Bonds Metals contain loosely held valence electrons that hold the positive metal ions together but are free to travel through the solid material. Metallic bonds are nondirectional and can exist only among a large group of atoms. It is the large group of electrons and their freedom to move that make metals such good conductors of electricity and heat. The metallic bond is of little importance in most soils. Bonding in Soil Minerals
A combination of ionic and covalent bonding is typical in most nonmetallic solids. Purely ionic or covalent bonding is a limiting condition that is the exception rather than the rule in most cases. Silicate minerals are the most abundant constituents of most soils. The interatomic bond in silica (SiO2) is about half covalent and half ionic.
3.4
SECONDARY BONDS
Secondary bonds that are weak relative to ionic and covalent bonds also form between units of matter. They may be strong enough to determine the final arrangements of atoms in solids, and they may be sources of attraction between very small particles and between liquids and solid particles. The Hydrogen Bond
If a hydrogen ion forms the positive end of a dipole, then its attraction to the negative end of an adjacent molecule is termed a hydrogen bond. Hydrogen bonds form only between strongly electronegative atoms such as oxygen and fluorine because these atoms produce the strongest dipoles. When the electron is detached from a hydrogen atom, such as when it combines with oxygen to form water, only a proton remains. As the electrons shared between the oxygen and hydrogen atoms spend most of their time between the atoms, the oxygens act as the negative ends of dipoles, and the hydrogen protons act as the positive ends. The positive and negative ends of adjacent water molecules tie them together forming water and ice. The strength of the hydrogen bond is much greater than that of other secondary bonds because of the small size of the hydrogen ion. Hydrogen bonds are impor-
40
3
SOIL MINERALOGY
tant in determining some of the characteristics of the clay minerals and in the interaction between soil particle surfaces and water.
Examples of some common crystals are shown in Fig. 3.4. Characteristics of Crystals
van der Waals Bonds
Permanent dipole bonds such as the hydrogen bond are directional. Fluctuating dipole bonds, commonly termed van der Waals bonds, also exist because at any one time there may be more electrons on one side of the atomic nucleus than on the other. This creates weak instantaneous dipoles whose oppositely charged ends attract each other. Although individual van der Waals bonds are weak, typically an order of magnitude weaker than a hydrogen bond, they are nondirectional and additive between atoms. Consequently, they decrease less rapidly with distance than primary valence and hydrogen bonds when there are large groups of atoms. They are strong enough to determine the final arrangements of groups of atoms in some solids (e.g., many polymers), and they may be responsible for small cohesions in finegrained soils. Van der Waals forces are described further in Chapter 7.
3.5
Certain crystal characteristics are used to distinguish different classes or groups of minerals. Variations in these characteristics result in different properties. 1. Structure The atoms in a crystal are arranged in a definite orderly manner to form a threedimensional network termed a lattice. Positions within the lattice where atoms or atomic groups
CRYSTALS AND THEIR PROPERTIES
Particles composed of mineral crystals form the greatest proportion of the solid phase of a soil. A crystal is a homogeneous body bounded by smooth plane surfaces that are the external expression of an orderly internal atomic arrangement. A solid without internal atomic order is termed amorphous. Crystal Formation
Crystals may form in three ways: 1. From Solution Ions combine as they separate from solution and gradually build up a solid of definite structure and shape. Halite (sodium chloride) and other evaporites are examples. 2. By Fusion Crystals form directly from a liquid as a result of cooling. Examples are igneous rock minerals solidified from molten rock magma and ice from water. 3. From Vapor Although not of particular importance in the formation of soil minerals, crystals can form directly from cooling vapors. Examples include snowflakes and flowers of sulfur.
Figure 3.4 Examples of some common crystals. (hkl) are
cleavage plane indices. From Dana’s Manual of Mineralogy, by C. S. Hurlbut, 16th Edition. Copyright 1957 by John Wiley & Sons. Reprinted with permission from John Wiley & Sons.
CRYSTALS AND THEIR PROPERTIES
are located are termed lattice points. Only 14 different arrangements of lattice points in space are possible. These are the Bravais space lattices, and they are illustrated in Fig. 3.5. The smallest subdivision of a crystal that still possesses the characteristic composition and spatial arrangement of atoms in the crystal is the unit
41
cell. The unit cell is the basic repeating unit of the space lattice. 2. Cleavage and Outward Form The angles between corresponding faces on crystals of the same substance are constant. Crystals break along smooth cleavage planes. Cleavage planes lie between planes in which the atoms are most
Figure 3.5 Unit cells of the 14 Bravais space lattices. The capital letters refer to the type of cell: P, primitive cell; C, cell with a lattice point in the center of two parallel faces; F, cell with a lattice point in the center of each face; I, cell with a lattice point in the center of the interior; R, rhombohedral primitive cell. All points indicated are lattice points. There is no general agreement on the unit cell to use for the hexagonal Bravais lattice; some prefer the P cell shown with solid lines, and others prefer the C cell shown in dashed lines (modified from Moffatt et al., 1965).
42
3
SOIL MINERALOGY
densely packed. This is because the center-tocenter distance between atoms on opposite sides of the plane is greater than along other planes through the crystal. As a result, the strength along cleavage planes is less than in other directions. 3. Optical Properties The specific atomic arrangements within crystals allow light diffraction and polarization. These properties are useful for identification and classification. Identification of rock minerals by optical means is common. Optical studies in soil are less useful because of the small sizes of most soil particles. 4. X-ray and Electron Diffraction The orderly atomic arrangements in crystals cause them to behave with respect to X-ray and electron beams in much the same way as does a diffraction grating with respect to visible light. Different crystals yield different diffraction patterns. This makes Xray diffraction a powerful tool for the study and identification of very small particles, such as clay that cannot be seen using optical means. 5. Symmetry There are 32 distinct crystal classes based on symmetry considerations involving the arrangement and orientation of crystal faces. These 32 classes may be grouped into 6 crystal systems with the classes within each system bearing close relationships to each other. The six crystal systems are illustrated in Fig. 3.6. Crystallographic axes parallel to the intersection edges of prominent crystal faces are established for each of the six crystal systems. In most crystals, these axes will also be symmetry axes or axes normal to symmetry planes. In five of the six systems, the crystals are referred to three crystallographic axes. In the sixth (the hexagonal system), four axes are used. The axes are denoted by a, b, c (a1, a2, a3, and c in the hexagonal system) and the angles between the axes by , , and . Isometric or Cubic System There are three mutually perpendicular axes of equal length. Mineral examples are galena, halite, magnetite, and pyrite. Hexagonal System Three equal horizontal axes lying in the same plane intersect at 60 with a fourth axis perpendicular to the other three and of different length. Examples are quartz, brucite, calcite, and beryl. Tetragonal System There are three mutually perpendicular axes, with two horizontal of equal length, but different than that of the vertical axis. Zircon is an example. Orthorhombic System There are three mutually perpendicular axes, each of different length. Examples include sulfur, anhydrite, barite, diaspore, and topaz.
Figure 3.6 The six crystal systems.
Monoclinic System There are three unequal axes, two inclined to each other at an oblique angle, with the third perpendicular to the other two. Examples are orthoclase feldspar, gypsum, muscovite, biotite, gibbsite, and chlorite. Triclinic System Three unequal axes intersect at oblique angles. Examples are plagioclase feldspar, kaolinite, albite, microcline, and turquoise. 3.6
CRYSTAL NOTATION
Miller indices are used to describe plane orientations and directions in a crystal. This information, along with the distances that separate parallel planes is important for the identification and classification of different minerals. All lengths are expressed in terms of unit cell lengths. Any plane through a crystal may be described by intercepts, in terms of unit cell lengths, on the three or four crystallographic axes for the system in which the crystal falls. The reciprocals of these intercepts are used to index the plane. Reciprocals are used to avoid fractions and to account for planes parallel to an axis (an intercept of infinity equals an index value of 0).
CRYSTAL NOTATION
An example illustrates the determination and meaning of Miller indices. Consider the mineral muscovite, a member of the monoclinic system. It has unit cell dimensions of a ⫽ 0.52 nanometers (nm), b ⫽ 0.90 nm, c ⫽ 2.0 nm, and ⫽ 95 30. Both the composition and crystal structure of muscovite are similar to those of some of the important clay minerals. The muscovite unit cell dimensions and intercepts are shown in Fig. 3.7a. The intercepts for any plane of interest are first determined in terms of unit cell
43
lengths. Take plane mnp in Fig. 3.7a as an example. The intercepts of this plane are a ⫽ 1, b ⫽ 1, and c ⫽ 1. The Miller indices of this plane are found by taking the reciprocals of these intercepts and clearing of fractions. Thus, Reciprocals are 1/1, 1/1, 1/1 Miller indices are (111) The indices are always enclosed within parentheses and indicated in the order abc without commas. Paren-
Figure 3.7 Miller indices: (a) Unit cell of muscovite, (b) (002) plane for muscovite, (c)
(014) plane for muscovite, and (d) (623) plane for muscovite.
44
3
SOIL MINERALOGY
theses are always used to indicate crystallographic planes, whereas brackets are used to indicate directions. For example, [111] designates line oq in Fig. 3.7a. Additional examples of Miller indices for planes through the muscovite crystal are shown in Figs. 3.7b, 3.7c, and 3.7d. A plane that cuts a negative axis is designated by placing a bar over the index that pertains to the negative intercept (Fig. 3.7d). The general index (hkl) is used to refer to any plane that cuts all three axes. Similarly (h00) designates a plane cutting only the a axis, (h0l) designates a plane parallel to the b axis, and so on. For crystals in the hexagonal system, the Miller index contains four numbers. The (001) planes of soil minerals are of particular interest because they are indicative of specific clay mineral types.
3.7 FACTORS CONTROLLING CRYSTAL STRUCTURES
Organized crystal structures do not develop by chance. The most stable arrangement of atoms in a crystal is that which minimizes the energy per unit volume. This is achieved by preserving electrical neutrality, satisfying bond directionality, minimizing strong ion repulsions, and packing atoms closely together. If the interatomic bonding is nondirectional, then the relative atomic sizes have a controlling influence on packing. The closest possible packing will maximize the number of bonds per unit volume and minimize the bonding energy. If interatomic bonds are directional, as is the case for covalent bonds, then both bond angles and atomic size are important. Anions are usually larger than cations because of electron transfer from cations to anions. The number of nearest neighbor anions that a cation possesses in a structure is termed the coordination number (N) or ligancy. Possible values of coordination number in solid structures are 1 (trivial), 2, 3, 4, 6, 8, and 12. The relationships between atomic sizes, expressed as the ratio of cationic to anionic radii, coordination number, and the geometry formed by the anions are indicated in Table 3.1. Most solids do not have bonds that are completely nondirectional, and the second nearest neighbors may influence packing as well as the nearest neighbors. Even so, the predicted and observed coordination numbers are in quite good agreement for many materials. The valence of the cation divided by the number of coordinated anions is an approximate indication of the relative bond strength, which, in turn, is related to the structural stability of the unit. Some of the structural units common in soil minerals and their relative bond strengths are listed in Table 3.2.
Table 3.1 Stability Radius Ratioa 0–0.155 0.155– 0.225 0.225– 0.414 0.414– 0.732 0.732– 1.0 1.0
Atomic Packing, Structure, and Structural
Nb
Geometry
Example
Stability
2 3
Line Triangle
— (CO3)2⫺
— Very high
4
Tetrahedron
(SiO4)4⫺
6
Octahedron
[Al(OH)6]3⫺
Moderately high High
8
Body-centered cube Sheet
Iron
Low
K–O bond in mica
Very low
12
a
Range of cation to anion diameter ratios over which stable coordination is expected. b Coordination number.
Table 3.2 Relative Stabilities of Some Soil Mineral Structural Units
Structural Unit
Approximate Relative Bond Strength (Valence/N)
Silicon tetrahedron, (SiO4)4⫺ Aluminum tetrahedron, [Al(OH)4]1⫺ Aluminum octahedron, [Al(OH)6]3⫺ Magnesium octahedron, [Mg(OH)6]4⫺ K–O12⫺23
4/4 ⫽ 1 3/4 3/6 ⫽ 1/2 2/6 ⫽ 1/3 1/12
The basic coordination polyhedra are seldom electrically neutral. In crystals formed by ionic bonded polyhedra, the packing maintains electrical neutrality and minimizes strong repulsions between ions with like charge. In such cases, the valence of the central cation equals the total charge of the coordinated anions, and the unit is really a molecule. Units of this type are held together by weaker, secondary bonds. An example is brucite, a mineral that has the composition Mg(OH)2. The Mg2⫹ ions are in octahedral coordination with six (OH)⫺ ions forming a sheet structure in such a way that each (OH)⫺ is shared by 3Mg2⫹. In a sheet containing N Mg2⫹ ions, therefore, there must be 6N/3 ⫽ 2N (OH)⫺ ions. Thus, electrical neutrality results, and the sheet is in reality a large molecule. Successive oc-
SURFACES
tahedral sheets are loosely bonded by van der Waals forces. Because of this, brucite has perfect basal cleavage parallel to the sheets. Cations concentrate their charge in a smaller volume than do anions, so the repulsion between cations is greater than between anions. Cationic repulsions are minimized when the anions are located at the centers of coordination polyhedra. If the cations have a low valence, then the anion polyhedra pack as closely as possible to minimize energy per unit volume. If, on the other hand, the cations are small and highly charged, then the units arrange in a variety of ways in response to the repulsions. The silicon cation is in this category.
3.8
SILICATE CRYSTALS
Small cations form structures with coordination numbers of 3 and 4 (Table 3.1). These cations are often highly charged and generate strong repulsions between adjacent triangles or tetrahedra. As a result, such structures share only corners and possibly edges, but never faces, since to do so would bring the cations too close together. The radius of silicon is only 0.039 nm, whereas that of oxygen is 0.132 nm. Thus silicon and oxygen combine in tetrahedral coordination, with the silicon occupying the space at the center of the tetrahedron formed by the four oxygens. The tetrahedral arrangement satisfies both the directionality of the bonds (the Si–O bond is about half covalent and half ionic) and the geometry imposed by the radius ratio. Silicon is very abundant in Earth’s crust, amounting to about 25 percent by weight, but only 0.8 percent by volume. Almost half of igneous rock by weight and 91.8 percent by volume is oxygen. Silica tetrahedra join only at their corners, and sometimes not at all. Thus many crystal structures are possible, and there is a large number of silicate minerals. Silicate minerals are classified according to how the silica tetrahedra (SiO4)4⫺ associate with each other, as shown in Fig. 3.8. The tetrahedral combinations increase in complexity from the beginning to the end of the figure. The structural stability increases in the same direction. Island (independent) silicates are those in which the tetrahedra are not joined to each other. Instead, the four excess oxygen electrons are bonded to other positive ions in the crystal structure. In the olivine group, the minerals have the composition R22⫹ SiO44⫺. Garnets contain cations of different valences and coordination numbers R32⫹ R23⫹(SiO4)3. The negative charge of the SiO4 group in zircon is all balanced by the single Zr4⫹. Ring and chain silicates are formed when corners of tetrahedra are shared. The formulas for these structures
45
contain (SiO3)2⫺. The pyroxene minerals are in this class. Enstatite, MgSiO3, is a simple member of this group. Some of the positions normally occupied by Si4⫹ in single-chain structures may be filled by Al3⫹. Substitution of ions of one kind by ions of another type, having either the same or different valence, but the same crystal structure, is termed isomorphous substitution. The term substitution implies a replacement whereby a cation in the structure is replaced at some time by a cation of another type. In reality, however, the replaced cations were never there, and the mineral was formed with its present proportions of the different cations in the structure. Double chains of indefinite length may form with (Si4O11)6⫺ as part of the structure. The amphiboles fall into this group (Fig. 3.8). Hornblendes have the same basic structure, but some of the Si4⫹ positions are filled by Al3⫹. The cations Na⫹ and K⫹ can be incorporated into the structure to satisfy electrical neutrality; Al3⫹, Fe3⫹, Fe2⫹, and Mn2⫹ can replace part of the Mg2⫹ in sixfold coordination, and the (OH)⫺ group can be replaced by F⫺. In sheet silicates three of the four oxygens of each tetrahedron are shared to give structures containing (Si2O5)2⫺. The micas, chlorites, and many of the clay minerals contain silica in a sheet structure. Framework silicates result when all four of the oxygens are shared with other tetrahedra. The most common example is quartz. In quartz, the silica tetrahedra are grouped to form spirals. The feldspars also have three-dimensional framework structures. Some of the silicon positions are filled by aluminum, and the excess negative charge thus created is balanced by cations of high coordination such as potassium, calcium, sodium, and barium. Differences in the amounts of this isomorphous substitution are responsible for the different members of the feldspar family.
3.9
SURFACES
All liquids and solids terminate at a surface, or phase boundary, on the other side of which is matter of a different composition or state. In solids, atoms are bonded into a three-dimensional structure, and the termination of this structure at a surface, or phase boundary, produces unsatisfied force fields. In a fine-grained particulate material such as clay soil the surface area may be very large relative to the mass of the material, and, as is emphasized throughout this book, the influences of the surface forces on properties and behavior may be very large. Unsatisfied forces at solid surfaces may be balanced in any of the following ways:
46
3
SOIL MINERALOGY
Figure 3.8 Silica tetrahedral arrangements in different silicate mineral structures. Reprinted
Gillott (1968) with permission from Elsevier Science Publishers BV.
SURFACES
47
Figure 3.8 (Continued )
1. Attraction and adsorption of molecules from the adjacent phase 2. Cohesion with the surface of another mass of the same substance 3. Solid-state adjustments of the structure beneath the surface.
Each unsatisfied bond force is significant relative to the weight of atoms and molecules. The actual magnitude of 10⫺11 N or less, however, is infinitesimal compared to the weight of a piece of gravel or a grain of sand. On the other hand, consider the effect of reducing particle size. A cube 10 mm on an edge has a
48
3
SOIL MINERALOGY
surface area of 6.0 ⫻ 10⫺4 m2. If it is cut in half in the three directions, eight cubes result, each 5 mm on an edge. The surface area now is 12.0 ⫻ 10⫺4 m2. If the cubes are further divided to 1 m on an edge, the surface becomes 6.0 m2 for the same 1000 mm3 of material. Thus, as a solid is subdivided into smaller and smaller units, the proportion of surface area to weight becomes larger and larger. For a given particle shape, the ratio of surface area to volume is inversely proportional to some effective particle diameter. For many materials when particle size is reduced to 1 or 2 m or less the surface forces begin to exert a distinct influence on the behavior. Study of the behavior of particles of this size and less requires considerations of colloidal and surface chemistry. Most clay particles behave as colloids, both because of their small size and because they have unbalanced surface electrical forces as a result of isomorphous substitutions within their structure. Montmorillonite, which is one of the members of the smectite clay mineral group (see Section 3.17), may break down into particles that are only 1 unit cell thick (1.0 nm) when in a dispersed state and have a specific surface area of 800 m2 /g. If all particles contained in about 10 g of this clay could be spread out side by side, they would cover a football field.
3.10
GRAVEL, SAND, AND SILT PARTICLES
The physical characteristics of cohesionless soils, that is, gravel, sand, and nonplastic silts, are determined primarily by particle size, shape, surface texture, and size distribution. The mineral composition determines hardness, cleavage, and resistance to physical and chemical breakdown. Some carbonate and sulfate minerals, such as calcite and gypsum, are sufficiently soluble that their decomposition may be significant within the time frame of many projects. In many cases, however, the nonclay particles may be treated as relatively inert, with interactions that are predominantly physical in nature. Evidence of this is provided by the soils on the Moon. Lunar soils have a silty, fine sand gradation; however, their compositions are totally different than those of terrestrial soils of the same gradation. The engineering properties of the two materials are surprisingly similar, however. The gravel, sand, and most of the silt fraction in a soil are composed of bulky, nonclay particles. As most soils are the products of the breakdown of preexisting rocks and soils, they are weathering products. Thus, the predominant mineral constituents of any soil are those that are one or more of the following:
1. Very abundant in the source material 2. Highly resistant to weathering, abrasion, and impact 3. Weathering products The nonclays are predominantly rock fragments or mineral grains of the common rock-forming minerals. In igneous rocks, which are the original source material for many soils, the most prevalent minerals are the feldspars (about 60 percent) and the pyroxenes and amphiboles (about 17 percent). Quartz accounts for about 12 percent of these rocks, micas for 4 percent, and other minerals for about 8 percent. However, in most soils, quartz is by far the most abundant mineral, with small amounts of feldspar and mica also present. Pyroxenes and amphiboles are seldom found in significant amounts. Carbonate minerals, mainly calcite and dolomite, are also found in some soils and can occur as bulky particles, shells, precipitates, or in solution. Carbonates dominate the composition of some deep-sea sediments. Sulfates, in various forms, are found primarily in soils of semiarid and arid regions, with gypsum (CaSO4 2H2O) being the most common. Iron and aluminum oxides are abundant in residual soils of tropical regions. Quartz is composed of silica tetrahedra grouped to form spirals, with all tetrahedral oxygens bonded to silicon. The tetrahedral structure has a high stability. In addition, the spiral grouping of tetrahedra produces a structure without cleavage planes, quartz is already an oxide, there are no weakly bonded ions in the structure, and the mineral has high hardness. Collectively, these factors account for the high persistence of quartz in soils. Feldspars are silicate minerals with a threedimensional framework structure in which part of the silicon is replaced by aluminum. The excess negative charge resulting from this replacement is balanced by cations such as potassium, calcium, sodium, strontium, and barium. As these cations are relatively large, their coordination number is also large. This results in an open structure with low bond strengths between units. Consequently, there are cleavage planes, the hardness is only moderate, and feldspars are relatively easily broken down. This accounts for their lack of abundance in soils compared to their abundance in igneous rocks. Mica has a sheet structure composed of tetrahedral and octahedral units. Sheets are stacked one on the other and held together primarily by potassium ions in 12-fold coordination that provide an electrostatic bond of moderate strength. In comparison with the intralayer bonds, however, this bond is weak, which accounts for the perfect basal cleavage of mica. As a result of the
STRUCTURAL UNITS OF THE LAYER SILICATES
thin-plate morphology of mica flakes, sand and silts containing only a few percent mica may exhibit high compressibility when loaded and large swelling when unloaded, as may be seen in Fig. 3.9. The amphiboles, pyroxenes, and olivine have crystal structures that are rapidly broken down by weathering; hence they are absent from most soils. Some examples of silt and sand particles from different soils are shown in Fig. 3.10. Angularity and roundness can be used to describe particle shapes, as shown in Fig. 3.11. Elongated and platy particles can develop preferred orientations, which can be responsible for anisotropic properties within a soil mass. The surface texture of the grains influences the stress– deformation and strength properties.
3.11 SOIL MINERALS AND MATERIALS FORMED BY BIOGENIC AND GEOCHEMICAL PROCESSES
Evaporite deposits formed by precipitation of salts from salt lakes and seas as a result of the evaporation of water are sometimes found in layers that are several meters thick. The major constituents of seawater and their relative proportions are listed in Table 3.3. Also listed are some of the more important evaporite de-
49
posits. In some areas alternating layers of evaporite and clay or other fine-grained sediments are formed during cyclic wet and dry periods. Many limestones, as well as coral, have been formed by precipitation or from the remains of various organisms. Because of the much greater solubility of limestone than most other rock types, it may be the source of special problems caused by solution channels and cavities under foundations. Chemical sediments and rocks in freshwater lakes, ponds, swamps, and bays are occasionally encountered in civil engineering projects. Biochemical processes form marl, which ranges from relatively pure calcium carbonate to mixtures with mud and organic matter. Iron oxide is formed in some lakes. Diatomite or diatomaceous earth is essentially pure silica formed from the skeletal remains of small (up to a few tenths of a millimeter) freshwater and saltwater organisms. Owing to their solubility limestone, calcite, gypsum, and other salts may cause special geotechnical problems. Oxidation and reduction of pyrite-bearing earth materials, that is, soils and rocks containing FeS2, can be the source of many types of geotechnical problems, including ground heave, high swell pressures, formation of acid drainage, damage to concrete, and corrosion of steel (Bryant et al., 2003). The chemical and biological processes and consequences of pyritic reactions are covered in Sections 8.3, 8.11, and 8.16. More than 12 percent of Canada is covered by a peaty material, termed muskeg, composed almost entirely of decaying vegetation. Peat and muskeg may have water contents of 1000 percent or more; they are very compressible, and they have low strength. The special properties of these materials and methods for analysis of geotechnical problems associated with them are given by MacFarlane (1969), Dhowian and Edil (1980), and Edil and Mochtar (1984). 3.12 SUMMARY OF NONCLAY MINERAL CHARACTERISTICS
Important compositional, structural, and morphological characteristics of the important nonclay minerals found in soils are summarized in Table 3.4. Of these minerals, quartz is by far the most common, both in terms of the number of soils in which it is found and its abundance in a typical soil. Feldspar and mica are frequently present in small percentages. 3.13 STRUCTURAL UNITS OF THE LAYER SILICATES Figure 3.9 Swelling index as a function of mica content for
coarse-grained mixtures (data from Terzaghi, 1931).
Clay minerals in soils belong to the mineral family termed phyllosilicates, which also contains other layer
50
3
SOIL MINERALOGY
Figure 3.10 Photomicrographs of sand and silt particles from several soils: (a) Ottawa stan-
dard sand, (b) Monterey sand, (c) Sacramento River sand, (d) Eliot sand, and (e) lunar soil mineral grains (photo courtesy Johnson Space Center). Squares in background area are 1⫻1 mm. (ƒ) Recrystallized breccia particles from lunar soil (photo courtesy of NASA Johnson Space Center). Squares in background grid are 1⫻1 mm.
silicates such as serpentine, pyrophyllite, talc, mica, and chlorite. Clay minerals occur in small particle sizes, and their unit cells ordinarily have a residual negative charge that is balanced by the adsorption of cations from solution. The structures of the common layer silicates are made up of combinations of two simple structural units, the silicon tetrahedron (Fig. 3.12) and the aluminum or magnesium octahedron (Fig. 3.13). Different clay mineral groups are characterized by the stacking arrangements of sheets1 (sometimes chains) of these
units and the manner in which two successive two- or three-sheet layers are held together. Differences among minerals within clay mineral groups result primarily from differences in the type and amount of isomorphous substitution within the crystal structure. Possible substitutions are nearly endless in number, and the crystal structure arrangement may range from very poor to nearly perfect. Fortunately for engineering purposes, knowledge of the structural and compositional characteristics of each group, without detailed study of the subtleties of each specific mineral, is adequate.
1
Silica Sheet
In conformity with the nomenclature of the Clay Minerals Society (Bailey et al., 1971), the following terms are used: a plane of atoms, a sheet of basic structural units, and a layer of unit cells composed of two, three, or four sheets.
In most clay mineral structures, the silica tetrahedra are interconnected in a sheet structure. Three of the
STRUCTURAL UNITS OF THE LAYER SILICATES
51
Figure 3.11 Sand and silt size particle shapes as seen in
silhouette.
Silica Chains
Figure 3.10 (Continued )
four oxygens in each tetrahedron are shared to form a hexagonal net, as shown in Figs. 3.12b and 3.14. The bases of the tetrahedra are all in the same plane, and the tips all point in the same direction. The structure has the composition (Si4O10)4⫺ and can repeat indefinitely. Electrical neutrality can be obtained by replacement of four oxygens by hydroxyls or by union with a sheet of different composition that is positively charged. The oxygen-to-oxygen distance is 2.55 ang˚ ),2 the space available for the silicon ion is stroms (A ˚ 0.55 A, and the thickness of the sheet in clay mineral ˚ (Grim, 1968). structures is 4.63 A
2
In conformity with the SI system of units, lengths should be given in nanometers. For convenience, however, the angstrom unit is re˚ ⫽ 0.1 nm. tained for atomic dimensions, where 1 A
In some of the less common clay minerals, silica tetrahedra are arranged in bands made of double chains of composition (Si4O11)6⫺. Electrical neutrality is achieved and the bands are bound together by aluminum and/or magnesium ions. A diagrammatic sketch of this structure is shown in Fig. 3.8. Minerals in this group resemble the amphiboles in structure. Octahedral Sheet
This sheet structure is composed of magnesium or aluminum in octahedral coordination with oxygens or hydroxyls. In some cases, other cations are present in place of Al3⫹ and Mg2⫹, such as Fe2⫹, Fe3⫹, Mn2⫹, Ti4⫹, Ni2⫹, Cr3⫹, and Li⫹. Figure 3.13b is a schematic diagram of such a sheet structure. The oxygen-to˚ , and the space available for oxygen distance is 2.60 A ˚ . The the octahedrally coordinated cation is 0.61 A ˚ in clays (Grim, 1968). thickness of the sheet is 5.05 A If the cation is trivalent, then normally only twothirds of the possible cationic spaces are filled, and the structure is termed dioctahedral. In the case of aluminum, the composition is Al2(OH)6. This composition and structure form the mineral gibbsite. When combined with silica sheets, as is the case in clay mineral
52
3
SOIL MINERALOGY
Table 3.3
Major Constituents of Seawater and Evaporite Deposits
Ion
Grams per Liter
Percent by Weight of Total Solids
Sodium, Na⫹ Magnesium, Mg2⫹ Calcium, Ca2⫹ Potassium, K⫹ Strontium, Sr2⫹ Chloride, Cl⫺ Sulfate, SO42⫺ Bicarbonate, HCO3⫺ Bromide, Br⫺ Fluoride, F⫺ Boric Acid, H3BO3
10.56 1.27 0.40 0.38 0.013 18.98 2.65 0.14 0.065 0.001 0.026 34.485
30.61 3.69 1.16 1.10 0.04 55.04 7.68 0.41 0.19 — 0.08 100.00
Important Evaporite Deposits Anhydrite Barite Celesite Kieserite Gypsum Polyhalite Bloedite Hexahydrite Epsomite Kainite Halite Sylvite Flourite Bischofite Carnallite
CaSO4 BaSO4 SrSO4 MgSO4 H2O CaSO4 2H2O Ca2K2Mg(SO4) 2H2O Ma2Mg(SO4)2 4H2O MgSO4 6H2O MgSO4 7H2O K4Mg4(Cl/SO4) 1 1H2O NaCl KCl CaF2 MgCl2 6H2O KMgCl3 6H2O
Adapted from data by Degens (1965).
structures, an aluminum octahedral sheet is referred to as a gibbsite sheet. If the octahedrally coordinated cation is divalent, then normally all possible cation sites are occupied and the structure is trioctahedral. In the case of magnesium, the composition is Mg3(OH)6, giving the mineral brucite. In clay mineral structures, a sheet of magnesium octahedra is termed a brucite sheet. Schematic representations of the sheets are useful for simplified diagrams of the structures of the different clay minerals:
units does not necessarily form the naturally occurring minerals. The ‘‘building block’’ approach is useful, however, for the development of conceptual models. 3.14 SYNTHESIS PATTERN AND CLASSIFICATION OF THE CLAY MINERALS
The manner in which atoms are assembled into tetrahedral and octahedral units, followed by the formation
Silica sheet
or
Octahedral sheet
(Various cations in octahedral coordination)
Gibbsite sheet
(Octahedral sheet cations are mainly aluminum)
Brucite sheet
(Octahedral sheet cations are mainly magnesium)
Water layers are found in some structures and may be represented by for each molecular layer. Atoms of a specific type, for example, potassium, are represented thus: K. The diagrams are indicative of the clay mineral layer structure. They do not indicate the correct width-tolength ratios for the actual particles. The structures shown are idealized; in actual minerals, irregular substitutions and interlayering or mixed-layer structures are common. Furthermore, direct assembly of the basic
of sheets and their stacking to form layers that combine to produce the different clay mineral groups is illustrated in Fig. 3.15. The basic structures shown in the bottom row of Fig. 3.15 comprise the great preponderance of the clay mineral types that are found in soils. Grouping the clay minerals according to crystal structure and stacking sequence of the layers is convenient since members of the same group have gen-
SYNTHESIS PATTERN AND CLASSIFICATION OF THE CLAY MINERALS
Table 3.4
53
Properties and Characteristics of Nonclay Minerals in Soils
Mineral
Formula
Crystal System
Cleavage
Particle Shape
Specific Gravity
Occurrence in Soils of Engineering Hardness Interest
Quartz
SiO2
Hexagonal
None
Bulky
2.65
7
Orthoclase feldspar Plagioclase feldspar Muscovite mica Biotite mica Hornblende
KalSi3O8
Monoclinic
2 planes
Elongate
2.57
6
NaAlSi3O8 CaAl2Si3O8 (variable) Kal3Si3O10(OH)2
Triclinic
2 planes
2.62–2.76 6
Monoclinic
Perfect basal
Bulky— elongate Thin plates
2.76–3.1
2–21⁄2
Common
Thin plates Prismatic
2.8–3.2 3.2
21⁄2–3 5–6
Common Uncommon
Prismatic
3.2–3.4
5–6
Uncommon
Bulky
3.27–3.37 61⁄2–7
Uncommon
Bulky
2.72
21⁄2–3
May be abundant locally May be abundant locally May be abundant locally
K(Mg,FE)3AlSi3O10(OH)2 Monoclinic Na,Ca,Mg,Fe,Al silicate Monoclinic
Augite Ca(Mg,Fe,Al)(Al,Si)2O6 (pyroxene) Olivine (Mg,Fe)2SiO4
Monoclinic
Perfect basal Perfect prismatic Good prismatic
Calcite
CaCO3
Orthorhombic Conchoidal fracture Hexagonal Perfect
Dolomite
CaMg(CO3)2
Hexagonal
Perfect Bulky rhombohedral
2.85
31⁄2–4
Gypsum
CaSO4 2H2O
Monoclinic
4 planes
Elongate
2.32
2
Pyrite
FeS2
Isometric
Cubical
Bulky cubic 5.02
6–61⁄2
Data from Hurlbut (1957).
Figure 3.12 Silicon tetrahedron and silica tetrahedra arranged in a hexagonal network.
Very abundant Common Common
54
3
SOIL MINERALOGY
Figure 3.13 Octahedral unit and sheet structure of octahedral units.
Figure 3.14 Silica sheet in plan view.
erally similar engineering properties. The minerals have unit cells consisting of two, three, or four sheets. The two-sheet minerals are made up of a silica sheet and an octahedral sheet. The unit layer of the threesheet minerals is composed of either a dioctahedral or trioctahedral sheet sandwiched between two silica sheets. Unit layers may be stacked closely together or water layers may intervene. The four-sheet structure of chlorite is composed of a 2⬊1 layer plus an interlayer hydroxide sheet. In some soils, inorganic, claylike material is found that has no clearly identifiable crystal
structure. Such material is referred to as allophane or noncrystalline clay. The bottom row of Fig. 3.15 shows that the 2⬊1 minerals differ from each other mainly in the type and amount of ‘‘glue’’ that holds the successive layers together. For example, smectite has loosely held cations between the layers, illite contains firmly fixed potassium ions, and vermiculite has somewhat organized layers of water and cations. The chlorite group represents an end member that has 2⬊1 layers bonded by an organized hydroxide sheet. The charge per formula
INTERSHEET AND INTERLAYER BONDING IN THE CLAY MINERALS
55
Figure 3.15 Synthesis pattern for the clay minerals.
unit is variable both within and among groups, and reflects the fact that the range of compositions is great owing to varying amounts of isomorphous substitution. Accordingly, the boundaries between groups are somewhat arbitrary. Isomorphous Substitution
The concept of isomorphous substitution was introduced in Section 3.13 in connection with some of the silicate crystals. It is very important in the structure and properties of the clay minerals. In an ideal gibbsite sheet, only two-thirds of the octahedral positions are filled, and all of the cations are aluminum. In an ideal brucite sheet, all the octahedral spaces are filled by magnesium. In an ideal silica sheet, silicons occupy all tetrahedral spaces. In clay minerals, however, some of the tetrahedral and octahedral spaces are occupied by cations other than those in the ideal structure. Common examples are aluminum in place of silicon, magnesium instead of aluminum, and ferrous iron (Fe2⫹) for magnesium. This presence in an octahedral or tetrahedral position of a cation other than that normally found, without change in crystal structure, is isomorphous substitution. The actual tetrahedral and octahedral cation distributions may develop during initial formation or subsequent alteration of the mineral. 3.15 INTERSHEET AND INTERLAYER BONDING IN THE CLAY MINERALS
A single plane of atoms that are common to both the tetrahedral and octahedral sheets forms a part of the
clay mineral layers. Bonding between these sheets is of the primary valence type and is very strong. However, the bonds holding the unit layers together may be of several types, and they may be sufficiently weak that the physical and chemical behavior of the clay is influenced by the response of these bonds to changes in environmental conditions. Isomorphous substitution in all of the clay minerals, with the possible exception of those in the kaolinite group, gives clay particles a net negative charge. To preserve electrical neutrality, cations are attracted and held between the layers and on the surfaces and edges of the particles. Many of these cations are exchangeable cations because they may be replaced by cations of another type. The quantity of exchangeable cations is termed the cation exchange capacity (cec) and is usually expressed as milliequivalents (meq)3 per 100 g of dry clay. Five types of interlayer bonding are possible in the layer silicates (Marshall, 1964). 1. Neutral parallel layers are held by van der Waals forces. Bonding is weak; however, stable crystals of appreciable thickness such as the nonclay min-
Equivalent weight ⫽ combining weight of an element ⫽ (atomic weight / valence). Number of equivalents ⫽ (weight of element / atomic weight) ⫻ valence. The number of ions in an equivalent ⫽ Avogardro’s number / valence. Avogadro’s number ⫽ 6.02 ⫻ 1023. An equivalent contains 6.02 ⫻ 1023 electron charges or 96,500 coulombs, which is 1 faraday. 3
56
2.
3. 4.
5.
3
SOIL MINERALOGY
erals of pyrophyllite and talc may form. These minerals cleave parallel to the layers. In some minerals (e.g., kaolinite, brucite, gibbsite), there are opposing layers of oxygens and hydroxyls or hydroxyls and hydroxyls. Hydrogen bonding then develops between the layers as well as van der Waals bonding. Hydrogen bonds remain stable in the presence of water. Neutral silicate layers that are separated by highly polar water molecules may be held together by hydrogen bonds. Cations needed for electrical neutrality may be in positions that control interlayer bonding. In micas, some of the silicon is replaced by aluminum in the silica sheets. The resulting charge deficiency is partly balanced by potassium ions between the unit cell layers. The potassium ion just fits into the holes formed by the bases of the silica tetrahedra (Fig. 3.12). As a result, it generates a strong bond between the layers. In the chlorites, the charge deficiencies from substitutions in the octahedral sheet of the 2⬊1 sandwich are balanced by excess charge on the single-sheet layer interleaved between the three-sheet layers. This provides a strongly bonded structure that while exhibiting cleavage will not separate in the presence of water or other polar liquids. When the surface charge density is moderate, as in smectite and vermiculite, the silicate layers readily adsorb polar molecules, and also the adsorbed cations may hydrate, resulting in layer separation and expansion. The strength of the interlayer bond is low and is a strong function of charge distribution, ion hydration energy, surface ion configuration, and structure of the polar molecule.
Smectite and vermiculite particles adsorb water between the unit layers and swell, whereas particles of the nonclay minerals, pyrophyllite and talc, which have comparable structures, do not. There are two possible reasons (van Olphen, 1977): 1. The interlayer cations in smectite hydrate, and the hydration energy overcomes the attractive forces between the unit layers. There are no interlayer cations in pyrophyllite; hence, no swelling. 2. Water does not hydrate the cations but is adsorbed on oxygen surfaces by hydrogen bonds. There is no swelling in pyrophyllite and talc because the surface hydration energy is too small to overcome the van der Waals forces between
layers, which are greater in these minerals because of a smaller interlayer distance. Whatever the reason, the smectite minerals are the dominant source of swelling in the expansive soils that are so prevalent throughout the world.
3.16
THE 1⬊1 MINERALS
The kaolinite–serpentine minerals are composed of alternating silica and octahedral sheets as shown schematically in Fig. 3.16. The tips of the silica tetrahedra and one of the planes of atoms in the octahedral sheet are common. The tips of the tetrahedra all point in the same direction, toward the center of the unit layer. In the plane of atoms common to both sheets, two-thirds of the atoms are oxygens and are shared by both silicon and the octahedral cations. The remaining atoms in this plane are (OH) located so that each is directly below the hole in the hexagonal net formed by the bases of the silica tetrahedra. If the octahedral layer is brucite, then a mineral of the serpentine subgroup results, whereas dioctahedral gibbsite layers give clay minerals in the kaolinite subgroup. Trioctahedral 1⬊1 minerals are relatively rare, usually occur mixed with kaolinite or illite, and are hard to identify. A diagrammatic sketch of the kaolinite structure is shown in Fig. 3.17. The structural formula is (OH)8Si4Al4O10, and the charge distribution is indicated in Fig. 3.18. Mineral particles of the kaolinite subgroup consist of the basic units stacked in the c direction. The bonding between successive layers is by both van der Waals forces and hydrogen bonds. The bonding is sufficiently strong that there is no interlayer swelling in the presence of water. Because of slight differences in the oxygen-tooxygen distances in the tetrahedral and octahedral layers, there is some distortion of the ideal tetrahedral network. As a result, kaolinite, which is the most abundant member of the subgroup and a common soil mineral, is triclinic instead of monoclinic. The unit cell ˚ , b ⫽ 8.94 A ˚ , c ⫽ 7.37 A ˚, dimensions are a ⫽ 5.16 A ⫽ 91.8, ⫽ 104.5, and ⫽ 90. Variations in stacking of layers above each other, and possibly in the position of aluminum ions within the available sites in the octahedral sheet, produce different members of the kaolinite subgroup. The dickite unit cell is made up of two unit layers, and the nacrite unit cell contains six. Both appear to be formed by hydrothermal processes. Dickite is fairly common as secondary clay in the pores of sandstone and in coal beds. Neither dickite nor nacrite is common in soils.
THE 1⬊1 MINERALS
57
Figure 3.16 Schematic diagrams of the structures of kaolinite and serpentine: (a) kaolinite and (b) serpentine.
Halloysite
Figure 3.17 Diagrammatic sketch of the kaolinite structure.
Halloysite is a particularly interesting mineral of the kaolinite subgroup. Two distinct endpoint forms of this mineral exist, as shown in Fig. 3.19; one, a hydrated form consisting of unit kaolinite layers separated from each other by a single layer of water molecules and having the composition (OH)8Si4Al4O10 4H2O, and the other, a nonhydrated form having the same unit layer structure and chemical composition as kaolinite. The basal spacing in the c direction d(001) for the non˚ , as for kaolinite. Because hydrated form is about 7.2 A of the interleaved water layer, d(001) for hydrated hal˚ . The difference between these loysite is about 10.1 A
Figure 3.18 Charge distribution on kaolinite.
58
3
SOIL MINERALOGY
˚ ) and (b) Figure 3.19 Schematic diagrams of the structure of halloysite: (a) halloysite (10 A ˚ ). halloysite (7 A
˚ , is the approximate thickness of a single values, 2.9 A layer of water molecules. The recommended terms for the two forms of hal˚ ) and halloysite (10 A ˚ ). loysite are halloysite (7 A ˚ ) to halloysite (7 Transformation from halloysite (10 A ˚ ) by dehydration can occur at relatively low temperA atures and is irreversible. Halloysite is often found in soils formed from volcanic parent materials in wet environments. It can be responsible for special properties and problems in earthwork construction, as discussed later in this book.
determinations at high pH. This suggests that broken bonds are at least a partial source of exchange capacity. That a positive cation exchange capacity is measured under low pH conditions when edges are positively charged indicates that some isomorphous substitution must exist also. As interlayer separation does not occur in kaolinite, balancing cations must adsorb on the exterior surfaces and edges of the particles.
Isomorphous Substitution and Exchange Capacity
Well-crystallized particles of kaolinite (Fig. 3.20), nacrite, and dickite occur as well-formed six-sided plates. The lateral dimensions of these plates range from about 0.1 to 4 m, and their thicknesses are from about 0.05 to 2 m. Poorly crystallized kaolinite generally occurs as less distinct hexagonal plates, and the particle size is usually smaller than for the well-crystallized varieties.
Whether or not measurable isomorphous substitution exists within the structure of the kaolinite minerals is uncertain. Nevertheless, values of cation exchange capacity in the range of 3 to 15 meq/100 g for kaolinite and from 5 to 40 meq/100 g for halloysite have been measured. Thus, kaolinite particles possess a net negative charge. Possible sources are:
Morphology and Surface Area
1. Substitution of Al3⫹ for Si4⫹ in the silica sheet or a divalent ion for Al3⫹ in the octahedral sheet. Replacement of only 1 Si in every 400 would be adequate to account for the exchange capacity. 2. The hydrogen of exposed hydroxyls may be replaced by exchangeable cations. According to Grim (1968), however, this mechanism is not likely because the hydrogen would probably not be replaceable under the conditions of most exchange reactions. 3. Broken bonds around particle edges may give unsatisfied charges that are balanced by adsorbed cations. Kaolinite particles are charged positively on their edges when in a low pH (acid) environment, but negatively charged in a high pH (basic) environment. Low exchange capacities are measured under low pH conditions and high exchange capacities are obtained for
Figure 3.20 Electron photomicrograph of well-crystallized
kaolinite from St. Austell, Cornwall, England. Picture width is 17 m (Tovey, 1971).
SMECTITE MINERALS
˚ ) occurs as cylindrical tubes of Halloysite (10 A overlapping sheets of the kaolinite type (Fig. 3.21). The c axis at any point nearly coincides with the tube radius. The formation of tubes has been attributed to a misfit in the b direction of the silica and gibbsite sheets (Bates et al., 1950). The b dimension in kaolinite is ˚ ; in gibbsite it is only 8.62 A ˚ . This means that 8.93 A the (OH) spacing in gibbsite sheets is stretched in order to obtain a fit with the silica sheet. Evidently, in hal˚ ), the reduced interlayer bond, caused by loysite (10 A the intervening layer of water molecules, enables the ˚ , resulting in a curvature (OH) layer to revert to 8.62 A with the hydroxyls on the inside and the bases of the silica tetrahedra on the outside. The outside diameters of the tubular particles range from about 0.05 to 0.20 m, with a median value of 0.07 m. The wall thickness is about 0.02 m. The tubes range in length from a fraction of a micrometer to several micrometers. Dry˚ ) may result in splitting or uning of halloysite (10 A rolling of the tubes. The specific surface area of kaolinite is about 10 to 20 m2 /g of dry clay; that of ˚ ) is 35 to 70 m2 /g. halloysite (10 A
3.17
SMECTITE MINERALS
Structure
The minerals of the smectite group have a prototype structure similar to that of pyrophyllite, consisting of an octahedral sheet sandwiched between two silica sheets, as shown schematically in Fig. 3.22 and diagrammatically in three dimensions in Fig. 3.23. All the tips of the tetrahedra point toward the center of the unit cell. The oxygens forming the tips of the tetrahedra are common to the octahedral sheet as well. The anions in the octahedral sheet that fall directly above
Figure 3.21 Electron photomicrograph of halloysite from Bedford, Indiana. Picture width is 2 m (Tovey, 1971).
59
and below the hexagonal holes formed by the bases of the silica tetrahedra are hydroxyls. The layers formed in this way are continuous in the a and b directions and stacked one above the other in the c direction. Bonding between successive layers is by van der Waals forces and by cations that balance charge deficiencies in the structure. These bonds are weak and easily separated by cleavage or adsorption of water or other polar liquids. The basal spacing in the c direction, d(001), is variable, ranging from about ˚ to complete separation. 9.6 A The theoretical composition in the absence of isomorphous substitutions is (OH)4Si8Al4O20 n(interlayer)H2O. The structural configuration and corresponding charge distribution are shown in Fig. 3.24. The structure shown is electrically neutral, and the atomic configuration is essentially the same as that in the nonclay mineral pyrophyllite. Isomorphous Substitution in the Smectite Minerals
Smectite minerals differ from pyrophyllite in that there is extensive isomorphous substitution for silicon and aluminum by other cations. Aluminum in the octahedral sheet may be replaced by magnesium, iron, zinc, nickel, lithium, or other cations. Aluminum may replace up to 15 percent of the silicon ions in the tetrahedral sheet. Possibly some of the silicon positions can be occupied by phosphorous (Grim, 1968). Substitutions for aluminum in the octahedral sheet may be one-for-one or three-for-two (aluminum occupies only two-thirds of the available octahedral sites) in any combination from a few to complete replacement. The resulting structure, however, is either almost exactly dioctahedral (montmorillonite subgroup) or trioctahedral (saponite subgroup). The charge deficiency resulting from these substitutions ranges from 0.5 to 1.2 per unit cell. Usually, it is close to 0.66 per unit cell. A charge deficiency of this amount would result from replacement of every sixth aluminum by a magnesium ion. Montmorillonite, the most common mineral of the group, has this composition. Charge deficiencies that result from isomorphous substitution are balanced by exchangeable cations located between the unit cell layers and on the surfaces of particles. Some minerals of the smectite group and their compositions are listed in Table 3.5. An arrow indicates the source of the charge deficiency, which has been assumed to be 0.66 per unit cell in each case. Sodium is indicated as the balancing cation. The formulas should be considered indicative of the general character of the mineral, but not as absolute, because a variety of compositions can exist within the same basic crystal structure. Because of the large amount of unbalanced
60
3
SOIL MINERALOGY
Figure 3.22 Schematic diagrams of the structures of the smectite minerals: (a) montmoril-
lonite and (b) saponite.
Figure 3.24 Charge distribution in pyrophyllite (type structure for montmorillonite).
Figure 3.23 Diagrammatic sketch of the montmorillonite
structure.
substitution in the smectite minerals, they have high cation exchange capacities, generally in the range of 80 to 150 meq/100 g. Morphology and Surface Area
Montmorillonite may occur as equidimensional flakes that are so thin as to appear more like films, as shown
in Fig. 3.25. Particles range in thickness from 1-nm unit layers upward to about 1/100 of the width. The long axis of the particle is usually less than 1 or 2 m. When there is a large amount of substitution of iron and/or magnesium for aluminum, the particles may be lath or needle shaped because the larger Mg2⫹ and Fe3⫹ ions cause a directional strain in the structure. The specific surface area of smectite can be very large. The primary surface area, that is, the surface area exclusive of interlayer zones, ranges from 50 to 120 m2 /g. The secondary specific surface that is exposed
SMECTITE MINERALS
Table 3.5
61
Some Minerals of the Smectite Group
Mineral Dioctahedral, Smectites or Montmorillonites Montmorillonite
Tetrahedral Sheet Substitutions
None
Octahedral Sheet Substitutions
Formula/Unit Cella
1Mg2⫹ for every sixth Al3⫹
(OH)4Si8(Al3.34Mg0.66) O20
None
Na0.66 (OH)4(Si6.34Al1.66) Al4.34O20
Fe3⫹ for Al
Na0.66 (OH)4(Si7.34Al0.66) Fe43⫹O20
↓
Beidellite
Al for Si
↓
Nontronite
Al for Si
↓
Na0.66 Trioctahedral, Smectites, or Saponites Hectorite
None
Li for Mg
(OH)4Si8(Mg5.34Li0.66) O20
Fe3⫹ for Mg
Na0.66 (OH)4(Si7.34Al0.66) Mg6O20
Zn for Mg
Na0.66 (OH)4(Si8⫺yAly)(Zn6⫺xMgx) O20
↓
Saponite
Al for Si
↓
Sauconite
Al for Si
↓
Na0.66 a
Two formula units are needed to give one unit cell. After Ross and Hendricks (1945); Marshall (1964); and Warshaw and Roy (1961).
by expanding the lattice so that polar molecules can penetrate between layers can be up to 840 m2 /g. Bentonite
Figure 3.25 Electron photomicrograph of montmorillonite
(bentonite) from Clay Spur, Wyoming. Picture width is 7.5 m (Tovey, 1971).
A very highly plastic, swelling clay material known as bentonite is very widely used for a variety of purposes, ranging from drilling mud and slurry walls to clarification of beer and wine. The bentonite familiar to most geoengineers is a highly colloidal, expansive alteration product of volcanic ash. It has a liquid limit of 500 percent or more. It is widely used as a backfill during the construction of slurry trench walls, as a soil admixture for construction of seepage barriers, as a grout material, as a sealant for piezometer installations, and for other special applications. When present as a major constituent in soft shale or as a seam in rock formations, bentonite may be a cause of continuing slope stability problems. Slide problems at Portuguese Bend along the Pacific Ocean in southern California, in the Bearpaw shale in Saskatchewan, and in the Pierre shale in South Dakota are in large mea-
62
3
SOIL MINERALOGY
sure due to the high content of bentonite. Stability problems in underground construction may be caused by the presence of montmorillonite in joints and faults (Brekke and Selmer-Olsen, 1965).
3.18
MICALIKE CLAY MINERALS
Illite is the most commonly found clay mineral in soils encountered in engineering practice. Its structure is quite similar to that of muscovite mica, and it is sometimes referred to as hydrous mica. Vermiculite is also often found as a clay phase constituent of soils. Its structure is related to that of biotite mica. Structure
The basic structural unit for the muscovite (white mica) is shown schematically in Fig. 3.26a. It is the threelayer silica–gibbsite–silica sandwich that forms pyrophyllite, with the tips of all the tetrahedra pointing toward the center and common with octahedral sheet ions. Muscovite differs from pyrophyllite, however, in that about one-fourth of the silicon positions are filled by aluminum, and the resulting charge deficiency is balanced by potassium between the layers. The layers are continuous in the a and b directions and stacked in the c direction. The radius of the potassium ion, 1.33 ˚ , is such that it fits snugly in the 1.32 A ˚ radius hole A formed by the bases of the silica tetrahedra. It is in 12fold coordination with the 6 oxygens in each layer. A diagrammatic three-dimensional sketch of the muscovite structure is shown in Fig. 3.27. The structural configuration and charge distribution are shown
in Fig. 3.28. The unit cell is electrically neutral and has the formula (OH)4K2(Si6Al2)Al4O20. Muscovite is the dioctahedral end member of the micas and contains only Al3⫹ in the octahedral layer. Phlogopite (brown mica) is the trioctahedral end member, with the octahedral positions filled entirely by magnesium. It has the formula (OH)4K2(Si6Al2)Mg6O20. Biotite (black mica) is trioctahedral, with the octahedral positions filled mostly by magnesium and iron. It has the general formula (OH)4K2(Si6Al2)(MgFe)6O20. The relative proportions of magnesium and iron may vary widely. Illite differs from mica in the following ways (Grim, 1968): 1. Fewer of the Si4⫹ positions are filled by Al3⫹ in illite. 2. There is some randomness in the stacking of layers in illite. 3. There is less potassium in illite. Well-organized illite contains 9 to 10 percent K2O (Weaver and Pollard, 1973). 4. Illite particles are much smaller than mica particles. Some illite may contain magnesium and iron in the octahedral sheet as well as aluminum (Marshall, 1964). Iron-rich illite, usually occurring as earthy green pellets, is termed glauconite. The vermiculite structure consists of regular interstratification of biotite mica layers and double molecular layers of water, as shown schematically in Fig. 3.26b. The actual thickness of the water layer depends on the cations that balance the charge deficiencies in
Figure 3.26 Schematic diagram of the structures of muscovite, illite, and vermiculite: (a)
muscovite and illite and (b) vermiculite.
MICALIKE CLAY MINERALS
63
Figure 3.27 Diagrammatic sketch of the structure of muscovite.
the biotitelike layers. With magnesium or calcium present, which is the usual case in nature, there are ˚. A two water layers, giving a basal spacing of 14 A general formula for vermiculite is (OH)4(MgCa)x(Si8 xAlx)(MgFe)6O20 yH2O x ⬇ 1 to 1.4
y⬇8
Isomorphous Substitution and Exchange Capacity
Figure 3.28 Charge distribution in muscovite.
There is extensive isomorphous substitution in illite and vermiculite. The charge deficiency in illite is 1.3 to 1.5 per unit cell. It is located primarily in the silica sheets and is balanced partly by the nonexchangeable potassium between layers. Thus, the cation exchange capacity of illite is less than that of smectite, amounting to 10 to 40 meq/100 g. Values greater than 10 to 15 meq/100 g may be indicative of some expanding layers (Weaver and Pollard, 1973). In the absence of fixed potassium the exchange capacity would be about 150 meq/100 g. Interlayer bonding by potassium is so strong that the basal spacing of illite remains fixed at ˚ in the presence of polar liquids. 10 A The charge deficiency in vermiculite is 1 to 1.4 per unit cell. Since the interlayer cations are exchangeable, the exchange capacity of vermiculite is high, amount-
64
3
SOIL MINERALOGY
ing to 100 to 150 meq/100 g. The basal spacing, d(001), is influenced by both the type of cation and the hydration state. With potassium or ammonium in the exchange positions, the basal spacing is only 10.5 to ˚ . Lithium gives 12.2 A ˚ . Interlayer water can be 11 A driven off by heating to temperatures above 100C. This dehydration is accompanied by a reduction in ˚ . The mineral quickly rebasal spacing to about 10 A ˚ when exposed to hydrates and expands again to 14 A moist air at room temperature. Morphology and Surface Area
Illite usually occurs as very small, flaky particles mixed with other clay and nonclay materials. Highpurity deposits of illite are uncommon. The flaky particles may have a hexagonal outline if well crystallized. The long axis dimension ranges from 0.1 m or less to several micrometers, and the plate thickness may be as small as 3 nm. An electron photomicrograph of illite is shown in Fig. 3.29. Vermiculite may occur in nature as large crystalline masses having a sheet structure somewhat similar in appearance to mica. In soils, vermiculite occurs as small particles mixed with other clay minerals. The specific surface area of illite is about 65 to 100 m2 /g. The primary surface of vermiculites is 40 to 80 m2 /g, and the secondary (interlayer) surface may be as high as 870 m2 /g. 3.19
OTHER CLAY MINERALS
Chlorite Minerals Structure The chlorite structure consists of alternating micalike and brucitelike layers as shown schematically in Fig. 3.30. The structure is similar to that
Figure 3.30 Schematic diagram of the structure of chlorite.
of vermiculite, except that an organized octahedral sheet replaces the double water layer between mica layers. The layers are continuous in the a and b directions and stacked in the c direction. The basal spacing ˚. is fixed at 14 A Isomorphous Substitution The central sheet of the mica layer is trioctahedral, with magnesium as the predominant cation. There is often partial replacement of Mg2⫹ by Al3⫹, Fe2⫹ and Fe3⫹. There is substitution of Al3⫹ for Mg2⫹ in the brucitelike layer. The various members of the chlorite group differ in the kind and amounts of substitution and in the stacking of successive layers. The cation exchange capacity of chlorites is in the range of 10 to 40 meq/100 g. Morphology Chlorite minerals occur as microscopic grains of platy morphology and poorly defined crystal edges in altered igneous and metamorphic rocks and their derived soils. In soils, chlorites always appear to occur in mixtures with other clay minerals. Chain Structure Clay Minerals
Figure 3.29 Electron photomicrograph of illite from Morris, Illinois. Picture width is 7.5 m (Tovey, 1971).
A few clay minerals are formed from bands (double chains) of silica tetrahedra. These include attapulgite and imogolite. They have lathlike or fine threadlike morphologies, with particle diameters of 5 to 10 nm and lengths up to 4 to 5 m. An electron photomicrograph of bundles of attapulgite particles is shown in Fig. 3.31. Although these minerals are not frequently encountered, attapulgite is commercially mined and is used as a drilling mud in saline and other special environments because of its high stability in suspensions.
DETERMINATION OF SOIL COMPOSITION
Figure 3.31 Electron photomicrograph of attapulgite from Attapulgis, Georgia. Picture width is 4.7 m (Tovey, 1971).
65
Oxides All soils probably contain some amount of colloidal oxides and hydrous oxides (Marshall, 1964). The oxides and hydroxides of aluminum, silicon, and iron are most frequently found. These materials may occur as gels or precipitates and coat mineral particles, or they may cement particles together. They may also occur as distinct crystalline units; for example, gibbsite, boehmite, hematite, and magnetite. Limonite and bauxite, which are noncrystalline mixtures of iron and aluminum hydroxides, are also sometimes found. Oxides are particularly common in soils formed from volcanic ash and in tropical residual soils. Some soils rich in allophane and oxides may exhibit significant irreversible decreases in plasticity and increases in strength when dried. Many are susceptible to breakdown and strength loss when subjected to traffic or manipulation during earthwork construction (Mitchell and Sitar, 1982; Mitchell and Coutinho, 1991).
Mixed-Layer Clays
More than one type of clay mineral is usually found in most soils. Because of the great similarity in crystal structure among the different minerals, interstratification of two or more layer types often occurs within a single particle. Interstratification may be regular, with a definite repetition of the different layers in sequence, or it may be random. According to Weaver and Pollard (1973), randomly interstratified clay minerals are second only to illite in abundance. The most abundant mixed-layer material is composed of expanded water-bearing layers and contracted non-water-bearing layers. Montmorillonite–illite is most common, and chlorite–vermiculite and chlorite– montmorillonite are often found. Rectorite is an interstratified clay with high charge, micalike layers with fixed interlayer cations alternating in a regular manner with low-charge montmorillonite-like layers containing exchangeable cations capable of hydration. Noncrystalline Clay Materials Allophane Clay materials that are so poorly crystalline that a definite structure cannot be determined are termed allophane. Such material is amorphous to X-rays because there is insufficient long-range order of the octahedral and tetrahedral units to produce sharp diffraction effects, although in some cases there may be diffraction bands. Allophane has no definite composition or shape and may exhibit a wide range of physical properties. Some noncrystalline clay material is probably contained in all fine-grained soils. It is common in volcanic soils because of the abundance of glass particles.
3.20 SUMMARY OF CLAY MINERAL CHARACTERISTICS
The important structural, compositional, and morphological characteristics of the important clay minerals are summarized in Table 3.6. Data on the structural characteristics of the tetrahedral and octahedral sheet structures are included.
3.21 DETERMINATION OF SOIL COMPOSITION Introduction
Identification of the fine-grained minerals in a soil is usually done by X-ray diffraction. Simple chemical tests can be used to indicate the presence of organic matter and other constituents. The microscope may be used to identify the constituents of the nonclay fraction. Accurate determination of the proportions of different mineral, organic, and amorphous solid material in a soil, while probably possible with the expenditure of great time and at great cost, is unlikely to be worthwhile owing to our inability to make exact quantitative links from composition to properties. Accordingly, from knowledge of grain size distribution, the relative intensities of different X-ray diffraction peaks, and a few other simple tests a semiquantitative analysis may be made that is usually adequate for most purposes. A general approach is given in this section for the determination of soil composition, some of the techniques are described briefly, and criteria for identification of important soil constituents are stated.
66
3
Table 3.6
SOIL MINERALOGY
Summary of Clay Mineral Characteristics Structural 1. Silica Tetrahedron: Si atom at center. Tetrahedron units form hexagonal network ⫽ Si4O8(OH)4 ˚. 2. Gibbsite Sheet: Aluminum in octahedral coordination. Two-thirds of possible positions filled. Al2(OH)—O—O ⫽ 2.60 A ˚. 3. Brucite Sheet: Magnesium in octahedral coordination. All possible positions filled. Mg2(OH)—O—O ⫽ 2.60 A
Type
Subgroup and Schematic Structure
Mineral
a
Complete Formula / Unit Cell
Octahedral Layer Cations
Structure Tetrahedral Layer Isomorphous Substitution Interlayer Bond Cations
Allophane
Allophanes
Amorphous
—
—
Kaolinite
Kaolinite
(OH)8Si4Al4O11
Al4
Si4
Little
O—OH Hydrogen Strong
Dickite
(OH)8Si4Al4O10
Al4
Si4
Little
O—OH Hydrogen Strong
Nacrite
(OH)8Si4Al4O10
Al4
Si4
Little
Halloysite (dehydrated) Halloysite (hydrated)
(OH)8Si4Al4O10
Al4
Si4
Little
(OH)8Si4Al4O10 4H2O
Al4
Si4
Little
(OH)4Si8(Al3.34Mg.66O20nH2O ↓ * Na.66
Al3.34Mg.66
Si8
Mg for Al, Net charge always ⫽ 0.66- / unit cell
O—O Very weak expanding lattice
(OH)4(Si7.34Al66)(Al4)O20nH2O
Al4
Si7.34Al.66
Na.66 (OH)4(Si7.34Al.66)Fe43⫹O20nH2O
Fe4
Si7.34Al.66
Al for Si, Net charge always ⫽ 0.66- / for unit cell Fe for Al, Al for Si, Net charge always ⫽ 0.66/ for unit cell
O—O Very weak expanding lattice O—O Very weak expanding lattice
Mg, Li for Al, Net charge always ⫽ 0.66/ unit cell Mg for Al, Al for Si, Net charge always ⫽ 0.66- / for unit cell
O—O Very weak expanding lattice O—O Very weak expanding lattice O—O Very weak expanding lattice
1⬊1
Montmorillonite Montmorillonite (OH)4Si8Al4O20 NH2O (Theoretical Unsubsitituted) Beidellite Nontronite
↓ ↓
Na.66
2⬊1
Saponite
Hectorite
(OH)4Si8(Mg5.34Li.66)P20nH2O
Mg5.34Li.66
Si8
Saponite
Na.66 (OH)4(Si7.34Al.66)Mg6O20nH2O
Mg, Fe3⫹
Si7.34Al.66
Sauconite
2⬊1⬊1
Chain Structure
a b
↓
↓
Na.66 (Si6.94Al1.06)Al.66Fe.34Mg.36Zn4.80O20(OH)4 ↓ nH2O Na.66
Al.44Fe.34Mg.36Zn4.80 Si6.94Al1.06 Zn for Al
O—OH Hydrogen Strong O—OH Hydrogen Strong O—OH Hydrogen Strong
Hydrous Mica (Illite)
Illites
(K, H2O)2(Si)8(Al,Mg,Fe)4,6O20(OH)4
(Al,Mg,Fe)4-6
(Al,Si)8
Some Si always replaced K ions; strong by Al, Balanced by K between layers.
Vermiculite
Vermiculite
(OH)4(Mg,Ca)x(Si8⫺xAlx)(Mg.Fe)6O20.yH2O x ⫽ 1 to 1.4, y ⫽ 8
(Mg,Fe)6
(Si,Al)8
Al for Si not charge of 1 Weak to 1.4 / unit cell
Chlorite
Chlorite (OH)4(SiAl)8(Mg.Fe)6O20 (2⬊1 layer) (Several varieties (MgAl)6(OH)12 interlayer known)
(Mg,Fe)6(2⬊1 layer) (Si,Al)8 (Mg,Al)6 interlayer
Al for Si in 2⬊1 layer Al for Mg in interlayer
Sepiolite
Si4O11(Mg.H2)3H2O2(H2O)
Fe or Al for Mg
Attapulgite
(OH2)4 (OH)2Mg5Si8O20.4H2O
Some for Al for Si
Arrows indicate source of charge deficiency. Equivalent Na listed as balancing cation. Two formula units (Table 3.4) are required per unit cell. Electron microscope data.
Weak ⫽ chains linked by 0
DETERMINATION OF SOIL COMPOSITION
Table 3.6
67
(Continued )
Units ˚ —Space for Si ⫽ 0.55 A ˚ —Thickness8 4.93 A ˚ . C—C height ⫽ 2.1 A ˚. All bases in same plane. O—O ⫽ 2.55 A ˚ . Space for ion ⫽ 0.61 A ˚ . Thickness of unit ⫽ 5.05 A ˚ . Dioctahedral. OH—OH ⫽ 2.94 A ˚ . Space for ion ⫽ 0.61 A ˚ . Thickness of unit ⫽ 5.05 A ˚ . Trioctahedral. OH—OH ⫽ 2.94 A Structure Crystal Structure
Basal Spacing
b
Shape
Size
Cation Exchange Cap.(meq / 100 g)
Specific Gravity
Specific Surface m2 / g
Irregular, some- 0.05–1 what rounded Triclinic a ⫽ 5.14, b ⫽ 8.93, c ⫽ 7.37 ⫽ 91.6, ⫽ 104.8, ⫽ 89.9 Monoclinic a ⫽ 5.15, b ⫽ 8.95, c ⫽ 14.42 ⫽ 9648 Almost Orthorhombic a ⫽ 5.15, b ⫽ 8.96, c ⫽ 43 ⫽ 9020 a ⫽ 5.14 in O Plane a ⫽ 5.06 in OH Plane b ⫽ 8.93 in O Plane b ⫽ 8.62 in OH Plane ⬖ layers curve
˚ 7.2 A
˚ 14.4 A
6-sided flakes
Unit cell contains 2 unit layers Unit cell contains 6 unit layers Random stacking of unit cells Water layer between unit cells
6-sided flakes
˚ —Complete 9.6A separation
Dioctahedral
Flakes (equidimensional)
˚ —Complete 9.6A separation
Dioctahedral
˚ —Complete 9.6A separation
Dioctahedral
˚ —Complete 9.6A separation
Trioctahedral
˚ 43 A ˚ 7.2 A ˚ 10.1 A
Trioctahedral Trioctahedral
Common
冎
0.1–4 ⫻ 3–15 single 0.05–2 to 3000 ⫻ 4000 (stacks) 0.07–300 ⫻ 2.5– 1–30 1000
Rounded flakes
1 ⫻ 0.025– 0.15
Tubes
0.07 O.D. 0.04 I.D. 1 long.
Tubes
˚ ⫻ up to ⬎10 A 10
2.60–2.68 10–20
Very common
Rare Rare
5–10
2.55–2.56
Occasional
5–40
2.0–2.2
35–70
80–150
2.35–2.7
50–120 Primary Very common 700–840 Secondary
Occasional
Rare Laths
Similar to mont. Brand laths
˚ 10 A
Both Flakes dioctrahedral and trioctahedral
a ⫽ 5.34, b ⫽ 9.20 c ⫽ 28.91, ⫽ 9315
˚ 10.5–14 A
Alternating Mica and double H2O layers
Monoclinic (Mainly) a ⫽ 5.3, b ⫽ 9.3 c ⫽ 28.52, ⫽ 978
˚ 14 A
Monoclinic a ⫽ 2 ⫻ 11.6, b ⫽ 2 ⫻ 7.86 c ⫽ 5.33 a0 Sin ⫽ 12.9 b0 ⫽ 18 c0 ⫽ 5.2
Occurrence in Soils of Engineering Interest
Breadth ⫽ 1 / 5 length to several ⫻ unit cell
110–150
To 1 ⫻ unit cell breadth ⫽ 0.02 ⫺ 0.1 Similar to mont.
17.5
Chain
Flakes or fibers
Double silica chains
Laths
Rare
Rare 2.24–2.30
Rare
˚ Thick 50 A
0.003–0.1 ⫻ up to 10
Similar to illite
Similar to illite
70–90
2.2–2.7
Rare
10–40
2.6–3.0
100–150
1
Max, 4–5 ⫻ ˚ 50–100 A Width ⫽ 2t
65–100
Very common
40–80 Primary 870 Secondary
Fairly common
10–40
2.6–2.96
Common
20–30
2.08
Rare
20–30
Occasional
From Grim, R. E. (1968) Clay Mineralogy, 2d edition, McGraw-Hill, New York. Brown, G. (editor) (1961) The X-ray Identification and Crystal Structure of Clay Materials, Mineralogical Society (Clay Minerals Group), London.
68
3
SOIL MINERALOGY
Methods for Compositional Analysis
Methods and techniques that may be employed for determination of soil composition and study of soil grains include: 1. Particle size analysis and separation 2. Various pretreatments prior to mineralogical analysis 3. Chemical analyses for free oxides, hydroxides, amorphous constituents, and organic matter 4. Petrographic microscope study of silt and sand grains 5. Electron microscope study 6. X-ray diffraction for identification of crystalline minerals 7. Thermal analysis 8. Determination of specific surface area 9. Chemical analysis for layer charge, cation exchange capacity, exchangeable cations, pH, and soluble salts 10. Staining tests for identification of clays Procedures for determination of soil composition are described in detail in publications of the American Society of Agronomy. Part 1—Physical and Mineralogical Methods provides a set of procedures for mineralogical analyses for use by soil scientists and engineers. Part 2—Microbiological and Biochemical Properties, published in 1994, is useful for determinations needed for bioremediation and other geoenvironmental purposes. Part 3—Chemical Methods, published in 1996 contains methods for characterizing soil chemical properties as well as several methods for characterizing soil chemical processes. Part 4— Physical Methods, published in 2002, is an updated version of the physical methods covered in Part 1. For each method, principles are presented as well as the details of the method. In addition, the interpretation of results is discussed, and extensive bibliographies are given. Accuracy of Compositional Analysis
Techniques for chemical analysis are generally of a high order of accuracy. However, this accuracy does not extend to the overall compositional analysis of a soil in terms of components of interest in understanding and quantifying behavior. This is because knowledge of the chemical composition of a soil is of limited value by itself. Chemical analysis of the solid phase of a soil does not indicate the organization of the elements into crystalline and noncrystalline components. For quantitative mineralogical analysis of the clay fraction, it is usually necessary to assume that the
properties of the mineral in the soil are the same as those of a reference mineral. However, different samples of any given clay mineral may exhibit significant differences in composition, surface area, particle size and shape, and cation exchange capacity. Thus, selection of ‘‘standard’’ minerals for reference is arbitrary. Quantitative clay mineral determinations cannot be made to an accuracy of more than about plus or minus a few percent without exhaustive chemical and mineralogical tests. General Scheme for Compositional Analysis
A general scheme for determination of the components of a soil is given in Fig. 3.32. Techniques of the most value for qualitative and semiquantitative analysis are indicated by a double asterisk, and those of particular use for explaining unusual properties are indicated by a single asterisk. The scheme shown is by no means the only one that could be used; a feedback approach is desirable wherein the results of each test are used to plan subsequent tests. Brief discussions of the various techniques listed in Fig. 3.32 are given below. X-ray diffraction analysis is treated in more detail in the next section because of its particular usefulness for the identification of fine-grained soil minerals. Grain Size Analysis Determination of particle size and size distribution is usually done using sieve analysis for the coarse fraction [sizes greater than 74 m (i.e., 200 mesh sieve)] and by sedimentation methods for the fine fraction. Details of these methods are presented in standard soil mechanics texts and in the standards of the American Society for Testing and Materials (ASTM). Determination of sizes by sedimentation is based on the application of Stokes’s law for the settling velocity of spherical particles: v⫽
s ⫺ w 2 D 18
(3.2)
where s ⫽ unit weight of particle, w ⫽ unit weight of liquid, ⫽ viscosity of liquid, and D ⫽ diameter of sphere. Sizes determined by Stoke’s law are not actual particle diameters but, rather, equivalent spherical diameters. Gravity sedimentation is limited to particle sizes in the range of about 0.2 mm to 0.2 m, the upper bound reflecting the size limit where flow around the particles is no longer laminar, and the lower bound representing a size where Brownian motion keeps particles in suspension indefinitely. The times for particles of 2, 5, and 20 m equivalent spherical diameter to fall through water a distance of 10 cm are about 8 h, 1.25 h, and 5 min, respectively, at 20C. At 30C the required times are about 6.5 h, 1
DETERMINATION OF SOIL COMPOSITION
69
Figure 3.32 Flow sheet for compositional analysis of soils (adapted from Lambe and Martin,
1954).
h, and 4 min. A centrifuge can be used for accelerating the settlement of small particles and is the most practical means for extracting particles smaller than about a micrometer in size. Sedimentation methods call for treatment of a soil– water suspension with a dispersing agent and thorough mixing prior to the start of the test. This causes breakdown of aggregates of soil particles, and the degree of breakdown may vary greatly with the method of preparation. For example, the ASTM standard method of test permits the use of either an air dispersion cup or a blender-type mixer. The amount of material less than 2 m equivalent spherical diameter may vary by as much as a factor of 2 by the two techniques. The relationship between the size distribution that results
from laboratory preparation of the sample to that of the particles and aggregates in the natural soil is unknown. Optical and electron microscopes are sometimes used to study particle sizes and size distributions and to provide information on particle shape, aggregation, angularity, weathering, and surface texture. Pore Fluid Electrolyte The total concentration of soluble salts may be determined from the electrical conductivity of extracted pore fluid. Chemical or photometric techniques may be used to determine the elemental constituents of the extract (Rhoades, 1982). Removal of excess soluble salts by washing the sample with water or alcohol may be necessary before proceeding with subsequent analysis. If they are not re-
70
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SOIL MINERALOGY
moved, the soil may be difficult to disperse, it may be difficult to remove organic matter, reliable cation exchange capacity determinations will be impossible, and mineralogical analyses will be complicated (Kunze and Dixon, 1986). pH Determination of the acidity or alkalinity of a soil in terms of the pH is a relatively simple measurement that can be made using a pH meter or special indicators (American Society for Testing and Materials, 1970; McLean, 1982). The value obtained depends on the ratio of soil to water, so it is usual to standardize the measurement using a 1⬊1 ratio of soil to water by weight. For highly plastic soils a lower soil-to-water ratio may be required to produce a suspension suitable for pH measurement. The pH decreases with increasing concentration of neutral salts in solution and with increasing amounts of dissolved CO2. Carbonates Carbonates, in the form of calcite (CaCO3), dolomite [CaMg(CO3)2], marl, and shells are frequently found in soils, and they can be readily detected by effervescence when the soil is treated with dilute HCl. Many methods for determining inorganic carbonates, calcite, and dolomite in soils are available (Nelson, 1982). These include dissolution in acid, differential thermal analysis, X-ray diffraction, and chemical analyses. Gypsum Gypsum (CaSO4 2H2O) can be determined by a simple heating test. Visible grains will turn white when heated on a metal plate as a result of dehydration to form ‘‘dead-burnt gypsum’’ (Shearman, 1979). Quantitative determinations can be made using procedures described by Nelson (1982). Organic Matter Organic matter can be readily detected by treatment of the soil with a 15 percent hydrogen peroxide solution. H2O2 reacts with organic matter to give vigorous effervescence. As organic matter has an aggregating effect, and because its presence may interfere with other mineralogical analyses, it is desirable to remove most of it by digestion with H2O2 (Kunze and Dixon, 1986). Quantitative analysis methods for soil organic matter are given by the American Society for Testing and Materials (1970), Nelson and Sommers (1982), and Schnitzer (1982). Oxides and Hydroxides Free oxides and hydroxides that may be present in soils include crystalline and noncrystalline (amorphous) compounds of silicon, aluminum, and iron. These materials may occur as discrete particles, as coatings on particles, and as cementing agents between particles. They may make soil dispersion difficult, and they may interfere with other analysis procedures. Methods for oxide and hydroxide detection, quantitative analysis, and removal are given by Jackson et al. (1986).
Exchange Complex Determination of the cation exchange capacity (expressed in milliequivalents per hundred grams of dry soil) is made after first freeing the soil of excess soluble salts. The adsorbed cations are then replaced by a known cation species, and the amount of the known cation needed to saturate the exchange sites is determined analytically (Rhoades, 1982). The composition of the original cation complex can be determined by chemical analysis of the original extract (Thomas, 1982). Potash The hydrous mica minerals (illites) are the only minerals commonly found in the clay size fraction of soils that contain potassium in their crystal structure. Thus, knowledge of the K2O content is useful for quantitative determination of their abundance. A method for potassium determination is given by Knudsen et al. ˚ illite layers contain 9 to (1986). Well-organized 10-A 10 percent K2O (Weaver and Pollard, 1973). Specific Surface Area Ethylene glycol and glycerol adsorb on clay surfaces. As different clay minerals have different values of specific surface, the amount of glycol or glycerol retained under controlled conditions can be used to aid in the quantitative determinations of clay minerals and for estimation of specific surface area (Martin, 1955; Diamond and Kinter, 1956; and American Society for Testing and Materials, 1970). Use of ethylene glycol monoethyl ether (EGME) as the polar molecule for determining surface area offers the advantages of the attainment of adsorption equilibrium more rapidly and with greater precision (Carter et al., 1982). A monomolecular layer of EGME is assumed to form in vacuum on a predried clay sample. The weight of EGME adsorbed after equilibrium is reached is converted to specific surface using a factor of 0.000286 g EGME per square meter of surface.
3.22
X-RAY DIFFRACTION ANALYSIS
X-Rays and Their Generation
X-ray diffraction is the most widely used method for identification of fine-grained soil minerals and the study of their crystal structure. X-rays are one of several types of waves in the electromagnetic spectrum (Fig. 3.2). X-rays have wavelengths in the range of ˚ . When high-speed electrons impinge on 0.01 to 100 A a target material, one of two phenomena may occur: 1. The high-speed electron strikes and displaces an electron from an inner shell of one of the atoms of the target material. An electron from one of the outer shells then falls into the vacancy to lower the energy state of the atom. An X-ray photon of wavelength and intensity characteristic
X-RAY DIFFRACTION ANALYSIS
of the target atom and of the particular electronic positions is emitted. Because electronic transfers may take place in several shells and each has a characteristic frequency, the result is a relationship between radiation intensity and wavelength as shown in Fig. 3.33. 2. The high-speed electron does not strike an electron in the target material but slows down in the intense electric fields near atomic nuclei. The decrease in energy is converted to heat and to Xray photons. X-rays produced in this way are independent of the nature of the bombarded atoms and appear as a band of continuously varying wavelength as shown in Fig. 3.34. The resulting output of X-rays from these two effects acting together is shown in Fig. 3.35. X-rays are generated using a tube in which electrons stream from a filament to a target material across a voltage drop of 20 to 50 kV. Curved crystal monochrometers can be used to give X-rays of a single wavelength. Alternatively, certain materials are able to absorb X-rays of different wavelengths, so it is possible to filter the output of an X-ray tube to give rays of only one wave-
71
Figure 3.35 Composite relationship for X-ray intensity as a function of wavelength.
length. The wavelengths of monochromatic radiation (usually K, Fig. 3.33) produced from commonly used ˚ for molybdenum to target materials range from 0.71 A ˚ for chromium. Copper radiation, which is most 2.29 A frequently used for mineral identification, has a wave˚. length of 1.54 A Diffraction of X-rays
Figure 3.33 X-ray generation by electron displacement. Let-
ters designate shells in which electron transfer takes place.
Figure 3.34 X-ray generation by deceleration of electrons
in an electric field.
˚ are of the same Because wavelengths of about 1 A order as the spacing of atomic planes in crystalline materials, X-rays are useful for analysis of crystal structures. When X-rays strike a crystal, they penetrate to a depth of several million layers before being absorbed. At each atomic plane a minute portion of the beam is absorbed by individual atoms that then oscillate as dipoles and radiate waves in all directions. Radiated waves in certain directions will be in phase and can be interpreted in simplistic fashion as a wave resulting from a reflection of the incident beam. In-phase radiations emerge as a coherent beam that can be detected on film or by a radiation counting device. The orientation of parallel atomic planes, relative to the direction of the incident beam, at which radiations are in phase depends on the wave length of the X-rays and the spacing between atomic planes. Figure 3.36 shows a parallel beam of X-rays of wavelength striking a crystal at an angle to parallel atomic planes spaced at distance d. If the reflected wave from C is to reinforce the wave reflected from A, then the path length difference between the two waves must be an integral number of wave lengths n . From Fig. 3.36, this difference is distance BC ⫹ CD. Thus, BC ⫹ CD ⫽ n
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SOIL MINERALOGY
Figure 3.36 Geometrical conditions for X-ray diffraction according to Bragg’s law.
From symmetry, BC ⫽ CD, and by trigonometry, CD ⫽ d sin . Thus the necessary condition is given by n ⫽ 2d sin
(3.3)
This is Bragg’s law. It forms the basis for identification of crystals using X-ray diffraction. Since no two minerals have the same spacings of interatomic planes in three dimensions, the angles at which diffractions occur (and the atomic spacings calculated from them) can be used for identification. X-ray diffraction is particularly well suited for identification of clay minerals because the (001) spacing is characteristic for each clay mineral group. The basal planes generally give the most intense reflections of any planes in the crystals because of the close packing of atoms in these planes. The common nonclay minerals occurring in soils are also detectable by X-ray diffraction. Detection of Diffracted X-rays
Because the small size of most soil particles prevents the study of single crystals, use is made of the powder method and of oriented aggregates of particles. In the powder method, a small sample containing particles at all possible orientations is placed in a collimated beam of parallel X-rays, and diffracted beams of various intensities are scanned by a Geiger, proportional, or scintillation tube and recorded automatically to produce a chart showing the intensity of diffracted beam as a function of angle 2 . As an example, the diffraction pattern for quartz is shown in Fig. 3.37. The powder method works because the very large number of particles in a sample ensures that some will always be properly oriented to produce a reflection. All prominent atomic planes in a crystal will produce a reflection if properly positioned with respect to
the X-ray beam. Thus, each mineral will produce a characteristic set of reflections at values of corresponding to the interatomic spacings between the prominent planes. The intensities of the different reflections vary according to the density of atomic packing and other factors. When the oriented aggregate method is used, platy clay particles are precipitated onto a glass slide, usually by drying from a deflocculated suspension or separated from a suspension on a porous ceramic plate. With most particles oriented parallel to the slide, the (001) reflections are intensified, whereas reflections from (hk0) planes are minimized. In the Bragg equation, n may be any whole number. The reflection corresponding to n ⫽ 1 is termed the first-order reflection. If the first-order reflection for a ˚ , then for n ⫽ 2 there can mineral gives d(001) ⫽ 10 A ˚ , for n ⫽ 3 there can be a reflecbe a reflection at 5 A ˚ , and so on. It is common to refer to tion at 3.33 A these as higher-order reflections due to the (002) plane, the (003) plane, and so on, even though atomic planes do not exist at these spacings. They are, in reality, values of d/n ⫽ /(2 sin ) for integer values of n ⬎ 1. Analysis of X-ray Patterns
A complete X-ray diffraction pattern consists of a series of reflections of different intensities at different values of 2 . Each reflection must be assigned to some component of the sample. The first step in the analysis is to determine all values of d/n for the particular type of radiation (which determines ) using Eq. (3.3). The test pattern may be compared directly with patterns for known materials. The American Society for Testing and Materials maintains a file of patterns for many materials indexed on the basis of the strongest lines in the pattern. X-ray diffraction data for the clay minerals and other common soil minerals are given in Grim
X-RAY DIFFRACTION ANALYSIS
Figure 3.37 X-ray diffractometer chart for quartz. Peaks occur at specific 2 angles, which
can be converted to d spacings by Bragg’s law. Numbers in parentheses are the Miller indices for the crystal planes responsible for the indicated peak.
73
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3
SOIL MINERALOGY
(1968), Carroll (1970), Brindley and Brown (1980), Whittig and Allardice (1986), and Moore and Reynolds (1997). The most intense reflections for minerals commonly found in powder samples of soils are listed in Table 3.7. Basal spacings for different clay minerals associated with different pretreatments are listed in Table 3.8 and shown pictorially in Fig. 3.38. Criteria for Clay Minerals
The different clay minerals are characterized by first˚ . Positive idenorder basal reflections at 7, 10, or 14 A tification of specific mineral groups ordinarily requires specific pretreatments. Separation of size fractions requires thorough dispersion of the sample. As cementing compounds may both inhibit dispersion and adversely affect the quality of the diffraction patterns, their removal may be necessary. To ensure uniform expansion due to hydration for all crystals of a particular mineral, the clay should be made homoionic. Magnesium and potassium are most frequently used for saturation of the exchange sites. Detailed procedures for pretreatments useful in X-ray diffraction analysis of clay soils are given by Whittig and Allardice (1986) and Moore and Reynolds (1997). Kaolinite Minerals The kaolinite basal spacing of ˚ is insensitive to drying or moderate heatabout 7.2 A ing. Heating to 500C destroys kaolinite minerals, but not the other clay minerals. Hydrated halloysite has a ˚ , which collapses irreversibly to basal spacing of 10 A ˚ on drying at 110C. Organic chemical treatments 7A are sometimes used to distinguish dehydrated halloysite from kaolinite (MacEwan and Wilson, 1980). The electron microscope can also be used to distinguish dehydrated halloysite with its tubular morphology from kaolinite. Hydrous Mica (Illite) Minerals Illite is character˚ , which remains fixed both ized by d(001) of about 10 A in the presence of polar liquids and after drying. Smectite (Montmorillonite) Minerals The expansive character of this group of minerals provides the basis for their positive identification. When air dried, ˚. these minerals may have basal spacings of 12 to 15 A After treatment with ethylene glycol or glycerol, the ˚ . When smectites expand to a d(001) value of 17 to 18 A ˚ as a result of the oven dried, d(001) drops to about 10 A removal of interlayer water. Vermiculite Although an expansive mineral, the greater interlayer ordering in vermiculite results in less variability in basal spacing than occurs in the smectite minerals. When Mg saturated, the hydration states of vermiculite yield a discrete set of basal spacings, resulting from a changing but ordered arrangement of Mg cations and water in the interlayer complex. When ˚ , which reduces fully saturated, the d spacing is 14.8 A
˚ when heated at 70C. All interlayer water to 11.6 A can be expelled at 500C, but rehydration is rapid on cooling. Permanent dehydration and collapse to 9.02 ˚ can be achieved by heating to 700C. A Chlorite Minerals The basal spacing of chlorite ˚ because of the strong ordering minerals is fixed at 14 A of the interlayer complex. Chlorites often have a clear sequence of four or five basal reflections. The third˚ is often strong. Iron-rich chloorder reflection at 4.7 A rites have a weak first-order reflection but strong second-order reflections and, thus, may be confused with kaolinite. The facts that chlorite is destroyed when treated with 1 N HCl at 60C while kaolinite is unaffected, and that kaolinite is destroyed but chlorite may not be affected on heating to 600C, are useful for distinguishing the two clay mineral types. Criteria for Nonclay Minerals
Strong X-ray diffraction reflections for some of the nonclay minerals are listed in Table 3.7. These include feldspar, quartz, and carbonates. More detailed listings of X-ray powder data for specific iron oxide minerals, silica minerals, feldspars, carbonates, and calcium sulfate minerals are given in Brindley and Brown (1980) as well as in standard reference files. Quantitative Analysis by X-ray Diffraction
Quantitative determination of the amounts of different minerals in a soil on the basis of simple comparison of diffraction peak heights or areas are uncertain because of differences in mass absorption coefficients of different minerals, particle orientations, sample weights, surface texture of the sample, mineral crystallinity, hydration, and other factors. Estimates based on X-ray data alone are usually at best semiquantitative; however, in some cases techniques that account for differences in mass absorption characteristics and utilize comparisons with known mixtures or internal standards may give good results. Soils containing only two or three well-crystallized mineral components are more easily analyzed than those with multimineral compositions and mixed layering. For more detailed treatment of X-ray diffraction theory, identification criteria, and techniques, particularly as related to the study of clays, see Klug and Alexander (1974), Carroll (1970), Brindley and Brown (1980), Whittig and Allardice (1986), and especially Moore and Reynolds (1997). 3.23 OTHER METHODS FOR COMPOSITIONAL ANALYSIS Thermal Analysis Principle Differential thermal analysis (DTA) consists of simultaneously heating a test sample and a thermally inert substance at constant rate (usually
OTHER METHODS FOR COMPOSITIONAL ANALYSIS
Table 3.7
75
X-ray Diffraction Data for Clay Minerals and Common Nonclay Minerals
˚) d (A
Mineral a
˚) d (A
Mineral a
14 12 10 9.23 7 6.90 6.44 6.39 4.90–5.00 4.70–4.79 4.60 4.45–4.50 4.46 4.36 4.26 4.18 4.02–4.04 3.85–3.90 3.82 3.78 3.67 3.58 3.57 3.54–3.56 3.50 3.40 3.34 3.32–3.35 3.30 3.23 3.21 3.20 3.19 3.05 3.04 3.02 3.00 2.98
Mont. (VS) Chl. Verm. (VS)b Sepiolite, heated corrensite Illite, Mica (S), Halloysite Heated Verm. Kaol. (S). Chl. Chl. Attapulgite Felds. Illite, Mica, Halloysite Chlor. (S) Verm. (S) Illite (VS), Sepiolite Kaol. Kaol. Quartz (S) Kaol. Felds. (S) Felds. Sepiol. Felds. Felds. Carbonate, Chl. Kaol. (VS), Chl. Verm. Felds., Chlor. Carb. Quartz (VS) Illite (VS) Carb. Attapulgite Felds. Mica Felds. (VS) Mont. Carb. (VS) Felds. Heated Verm. Mica (S)
2.93–3.00 2.89–2.90 2.86 2.84 2.84–2.87 2.73 2.61 2.60 2.56 2.53–2.56 2.49 2.46 2.43–2.46 2.39 2.38 2.34 2.29 2.28 2.23 2.13 2.05–2.06 1.99–2.00 1.90 1.83 1.82 1.79 1.68 1.66 1.62 1.54B 1.55 1.58 1.53 1.50 1.48–1.50 1.45B 1.38 1.31, 1.34, 1.36
Felds. Carb. Felds. Carb. Chl. Chl. Carb. Attapulgite Verm., Sepiol. Illite (VS), Kaol. Chlor., Felds., Mont. Kaol. (VS) Quartz, heated Verm. Chlorite Verm., Illite Kaol. Kaol. (VS) Kaol. (VS) Quartz, Sepiol. Illite, Chl. Quartz, Mica Kaol. (WK) Mica, Illite (S), Kaol. Chl. Kaol. Carb. Quartz Kaol. Quartz Kaolin Kaolin Verm. (S), Quartz Quartz Chl. Verm., Illite Ill. (S), Kaol. Kaol. (VS), Mont. Kaol. Quartz, Chl. Kaol. (B)
(B) ⫽ broad; (S) ⫽ strong; (VS) ⫽ very strong; (WK) ⫽ weak; Mont. ⫽ montmorillonite; Ch1. ⫽ chlorite; Verm. ⫽ vermiculite; Kaol. ⫽ kaolinite; Carb. ⫽ carbonate; Felds. ⫽ feldspar; Sepiol. ⫽ sepiolite. b Italics indicates (001) spacing. a
about 10C/min) to over 1000C and continuously measuring differences in temperature between the sample and the inert material. Differences in temperature between the sample and the inert substance reflect reactions in the sample brought about by the heating. Thermogravimetric analyses, based on changes in weight caused by loss of water or CO2 or gain in ox-
ygen, are also used to some extent. Thermal analysis techniques are described in detail by Tan et al. (1986). The results of differential thermal analysis are presented as a plot of the difference in temperature between sample and inert material ( T) versus temperature (T) as indicated in Fig. 3.39. Endothermic reactions are those wherein the sample takes up heat,
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Table 3.8 X-ray Identification of the Principal Clay Minerals (⬍ 2 m) in an Oriented Mount of a Clay Fraction Separated from Sedimentary Material
Mineral
Basal d Spacings (001)
Glycolation Effect (1 h, 60C)
Kaolinite
˚ (001); 3.75 A ˚ (002) 7.15 A
No change
Kaolinite, disordered
˚ (001) broad; 3.75 A ˚ 7.15 A broad ˚ (001) broad 10 A
No change No change
˚ (001) broad 7.2 A
No change
˚ (002); 5 A ˚ (004) 10 A generally referred to as (001) and (002) ˚ (002), broad, other 10 A basal spacings present but small
No change
Montmorillonite group
˚ (001) and integral 15 A series of basal spacings
Vermiculite
˚ (001) and integral 14 A series of basal spacings ˚ (001) and integral 14 A series of basal spacings
(001) expands to 17 ˚ with rational A sequence of higher orders No change
Halloysite, 4H2O (hydrated) Halloysite, 2H2O (dehydrated) Mica
Illite
Chlorite, Mg-form
Chlorite, Fe-form
Mixed-layer minerals
Attapulgite (palygorskite) Sepiolite Amorphous clay, allophane
˚ (001) less intense 14 A than in Mg-form; integral series of basal spacings Regular, one (001) and integral series of basal spacings Random, (001) is addition of individual minerals and depends on amount of those present High intensity d reflections at 10.5, 4.5, 3.23, and ˚ 2.62 A High intensity reflections at ˚ 12.6, 4.31, and 2.61 A No d reflections
Compiled by Carroll (1970).
No change
No change
No change
Heating Effect (1 h) Becomes amorphous 550– 600C Becomes amorphous at lower temperatures than kaolinite Dehydrates to 2H2O at 110C Dehydrates at 125–150C; becomes amorphous 560– 590C (001) becomes more intense on heating but structure is maintained to 700C (001) noticeably more intense on heating as water layers are removed; at higher temperatures like mica ˚ At 300C (001) becomes 9 A
Dehydrates in steps (001) increases in intensity; ⬍800C shows weight loss but no structural change (001) scarcely increases; structure collapses below 800C
No change unless an expandable component is present Expands if montmorillonite is a constituent
Various, see descriptions of individual minerals
No change
Dehydrates stepwise (see description)
No change
Dehydrates stepwise (see description) Dehydrates and loses weight
No change
Depends on minerals present in interlayered mineral
OTHER METHODS FOR COMPOSITIONAL ANALYSIS
77
Figure 3.38 Pictorial representation of response of phyllosilicates to differentiating treat˚ ) (from Whittig and Allardice, 1986). ments. Approximate spacings in nm (1 nm ⫽ 10 A Reproduced with permission from The American Society of Agronomy, Inc., Madison, WI.
and in exothermic reactions, heat is liberated. Analysis of test results consists of comparing the sample curve with those for known materials so that each deflection can be accounted for. Apparatus Apparatus for DTA consists of a sample holder, usually ceramic, nickel, or platinum; a furnace; a temperature controller to provide a constant rate of heating; thermocouples for measurement of temperature and the difference in temperature between the sample and inert reference material; and a recorder for the thermocouple output. The amount of sample re-
quired is about 1 g. Although the temperatures at which thermal reactions take place are a function only of the sample, the size and shape of the reaction peaks depend also on the thermal characteristics of the apparatus and the heating rate. Reactions Producing Thermal Peaks The important thermal reactions that generate peaks on the thermogram are: 1. Dehydration Water in a soil may be present in three forms in addition to free pore water: (1)
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SOIL MINERALOGY
Figure 3.39 Thermogram of a sandy clay soil.
adsorbed water or water of hydration, which is driven off at 100 to 300C, (2) interlayer water such as in halloysite and expanded smectite, and (3) crystal lattice water in the form of (OH) ions, the removal of which is termed dehydroxylation. Dehydroxylation destroys mineral structures. The temperature at which the major amount of crystal lattice water is lost is the most indicative property for identification of minerals. Dehydration reactions are endothermic and occur in the range of 500 to 1000C. 2. Crystallization New crystals form from amorphous materials or from old crystals destroyed at a lower temperature. Crystallization reactions usually are accompanied by an energy loss and, thus, are exothermic, occurring between 800 and 1000C. 3. Phase Changes Some crystal structures change from one form to another at a specific temperature, and the energy of transformation shows up as a peak on the thermogram. For example, quartz changes from the to form reversibly at 573C. The peak for the quartz phase change is sharp, and its amplitude is nearly in direct proportion to the amount of quartz present. The quartz peak is frequently masked within the peak for some other reacting material, but may be readily identified by determining the thermogram during cooling of the sample or by letting it cool first and then rerunning it. The other minerals are destroyed during the initial run while the quartz reaction is reversible. 4. Oxidation Exothermic oxidation reactions include the combustion of organic matter and the oxidation of Fe2⫹ to Fe3⫹. Organic matter oxidizes in the 250 to 450C temperature range.
Beside quartz, the only common nonclay minerals in soils that give thermal reactions with large peaks are carbonates and free oxides such as gibbsite, brucite, and goethite. The carbonates give very large endothermic peaks between about 800 and 1000C, and the oxides have an endothermic peak between about 250 and 450C. Thermograms for many clay and nonclay minerals are presented by Lambe (1952). Quantitative Analysis Theoretically, the area of the reaction peak is a measure of the amount of mineral present in the sample. For sharp, large amplitude peaks such as the quartz inversion at 573C and the kaolinite endotherm at 650C, the amplitude can be used for quantitative analysis. In either case, calibration of the apparatus is necessary, and the overall accuracy is of the order of plus or minus 5 percent. Optical Microscope
Both binocular and petrographic microscopes can be used to study the identity, size, shape, texture, and condition of single grains and aggregates in the silt and sand size range; for study in the thin section of the fabric, that is, the spatial distribution and interrelationships of the constituents; and for study of the orientations of groups of clay particles. Because the in-focus depth of field decreases sharply as magnification increases, study of soil thin sections is impractical at magnifications greater than a few hundred. Thus, individual clay particles cannot usually be distinguished using an optical microscope. Useful information about the shape, texture, size, and size distribution of silt and sand grains may be obtained directly without formal previous training in petrographic techniques. Some background is needed to identify the various minerals; however, relatively simple diagnostic criteria that can be used for identification of over 80 percent of the coarse grains in most soils are given by Cady et al. (1986). These criteria are based on such factors as color, refractive index, birefringence, cleavage, and particle morphology. The nature of surface textures, the presence of coatings, layers of decomposition, and so on are useful both for interpretation of the history of a soil and as a guide to the soundness and durability of the particles. Electron Microscope
With modern electron microscopes it is possible to re˚ , thus making study solve distances to less than 100 A of small clay particles feasible. Electron diffraction study of single particles may also be useful. Electron diffraction is similar to X-ray diffraction except an electron beam instead of an X-ray beam is used.
QUANTITATIVE ESTIMATION OF SOIL COMPONENTS
Magnetic lenses that refract an electron beam form the basis of the transmission electron microscope (TEM) optical system. An electron beam is focused on the specimen, which is usually a replica of the surface structure of the material under study. Some of the electrons are scattered from the specimen, and different parts of the specimen appear light or dark in proportion to the amount of scattering. After passing through a series of lenses, the image is displayed on a fluorescent screen for viewing. Probably the most critical aspect of successful transmission electron microscopy is specimen preparation. In the scanning electron microscope (SEM), secondary electrons emitted from a sample surface form what appear to be three-dimensional images. The SEM has a ⫻20 to ⫻150,000 magnification range and a depth of field some 300 times greater than that of the light microscope. These characteristics, coupled with the fact that clay particles themselves and fracture surfaces through soil masses may be viewed directly, have led to extensive use of the SEM for study of clays. Examples of electron photomicrographs of clays and soils are given earlier in this chapter and in Chapter 5. Principles of electron microscopy techniques and additional examples are presented in McCrone and Delly (1973) and Sudo et al. (1981).
3.24 QUANTITATIVE ESTIMATION OF SOIL COMPONENTS
Qualitative X-ray diffraction and a few simple tests will generally indicate the minerals present in a soil. More data are needed, however, for more precise quantitative estimates. As a rule, the number of different analyses needed is equal to the number of mineral species present. The results of glycol adsorption, cation exchange capacity, X-ray diffraction, differential thermal analysis, and chemical tests all give data that may be used for quantitative estimations. Some pertinent identification criteria and reference values for the clay minerals are given in Table 3.9. After the quantities of organic matter, carbonates, free oxides, and nonclay minerals have been determined, the percentages of clay minerals are estimated using the appropriate glycol adsorption, cation exchange capacity, K2O, and DTA data. The nonclays can be identified, and their abundance determined, using the microscope, grain size distribution analysis, Xray diffraction, and DTA. The amount of illite is estimated from the K2O content since this is the only clay mineral containing potassium. The amount of kaolinite is most reliably determined from the 600C
79
DTA endotherm amplitude. If X-ray has indicated montmorillonite, chlorite, and/or vermiculite, then quantitative estimates are made based on the glycol adsorption and exchange capacity data. The total exchange capacity and glycol retention are ascribed to the clay minerals, and the measured values must be accounted for in terms of proportionate contributions by the different clay minerals present. As a simple example, assume that quartz, illite, and smectite are identified in the ⫺2 m fraction of a soil. Additional data indicate 4.0 percent K2O, ethylene glycol retention of 100 mg/g, and a cation exchange capacity of 35 meq/100 g. Then, assuming 9 percent as an average value of for pure illite (Table 3.9), the content of illite is estimated at 4.0/9.0, or 44 percent. Because only the illite and smectite will contribute to the glycol adsorption, the amount of smectite may be estimated: 0.44 ⫻ 60 ⫹ S ⫻ 300 ⫽ 100 ⬖S⫽
100 ⫺ 26.4 ⫽ 25% 300
The remaining 31 percent can be ascribed to quartz and other nonclay components. For this clay mineral composition, the theoretical cation exchange capacity should be, based on the reference values in Table 3.9: 0.44 ⫻ 25 ⫹ 0.25 ⫻ 85 ⫽ 11 ⫹ 21 ⫽ 33 meq/100 g This compares favorably with the measured quantity of 35 meq/100 g. Thus, the composition of the clay size fraction is Illite Smectite Quartz and other nonclays
44% 25% 31%
The main difficulty in this method for quantitative mineralogical analysis is the uncertainty in the reference values for the different clay minerals. A semiquantitative analysis is sufficient for most applications. This may be done as follows. The silt and sand fraction can be examined by microscope and the approximate proportion of nonclay minerals determined. The amount of clay size material ⫺2 m can be estimated by grain size distribution analysis. As a first approximation, it may be assumed that the amount of clay mineral equals at least the amount of clay size. This assumption is justified for the following reasons. Nonclay minerals, principally quartz, are found in the clay size fraction. On the other hand, for most soils,
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SOIL MINERALOGY
Table 3.9 Summary of Clay Mineral Identification Criteria—Reference Data for Clay Mineral Identification (⫺2-m fraction) CEC (meq/100 g)
K2O (%)
X-ray d(001)
Glycol (mg/g)
Kaolinite
7
16
3
0
Dehydrated halloysite
7
35
12
0
Hydrated halloysite
10
60
12
0
Illite
10
60
25
8–10
Clay
DTAa End. 500–660 ⫹ Sharpb Exo. 900–975 Sharp Same as kaolinite but 600 peak slope ratio ⬎ 2.5 Same as kaolinite but 600 peak slope ratio ⬎ 2.5 End. 500–650 Broad End. 800–900 Broad Exo. 950
Vermiculite Smectite
Chlorite
10–14 10–18
200 300
150 85
0
14c
30
40
0
End. End. Exo. End.
600–750 900 950 610 10 or 720 20
For clays prepared at same relative humidity the size of the 100–300C endotherm (adsorbed water removal) increases in the order kaolinite–illite–smectite. b For samples started at 50% RH the amplitude of 600 peak/amplitude of adsorbed water peak ⬎⬎⬎1. c ˚ line and weaken 7 A ˚ line. Heat treatment will accentuate 14 A a
the amount of clay mineral exceeds the amount of clay size. This most probably results from cementation of small clay particles into aggregates larger than 2 m in diameter. Approximate proportions of the different clay minerals in the clay fraction can be estimated from the relative intensities of the X-ray diffraction reflections for each mineral. The presence of organic matter and carbonates can be easily detected using the tests listed in Section 3.21.
3.25
CONCLUDING COMMENTS
The sizes, shapes, and surface characteristics of the particles in a soil are determined in large measure by their mineralogy. Mineralogy also determines interactions with fluid phases. Together, these factors determine plasticity, swelling, compression, strength, and fluid conductivity behavior. Thus, mineralogy is fundamental to the understanding of geotechnical properties, even though mineralogical determinations are not made for many geotechnical investigations. Instead, other characteristics that reflect both composition and engineering properties, such as Atterberg limits and grain size distribution, are determined.
Interatomic bonding, crystal structure, and surface characteristics determine the size, shape, and stability of soil particles and the interactions of soil particles with liquids and gases. The structural stability of the different minerals controls their resistance to weathering and hence accounts in part for the relative abundance of different minerals in different soils. Because interatomic bonds in soil particles are strong, primary valence bonds, whereas usual interparticle bonds are of the secondary valence or hydrogen bond type, individual particles are strong compared to groups of particles. Thus, most soil masses behave as assemblages of particles in which deformation processes are dominated by displacements between particles and not by deformations of particles themselves, although grain crushing becomes important in coarsegrained soils such as sands and gravels when they are under very high stresses. The type of bonding between the unit layers of the clay minerals, coupled with the adsorption properties of the particle surfaces, controls soil swelling. Adsorption and desorption processes are important in interactions between chemicals and soils. These interactions in turn determine the flow and attenuation of various substances through soil. Changes in surface
QUESTIONS AND PROBLEMS
forces owing to changes in chemical environment may alter the structural state of a soil. Mineralogy is related to soil properties in much the same way as the composition and structure of cement and aggregates are to concrete, or as the composition and crystal structure of steel relate to its strength and deformability. With these engineering materials—soil, concrete, and steel—mechanical properties can be measured directly; however, they cannot be explained without consideration of the composition and structure of their components. Since about 1980, environmental problems, especially those related to the safe disposal and containment of municipal, hazardous, and nuclear waste and to the clean up of contaminated sites and the protection of groundwater, have assumed a major role in geotechnical engineering practice. This has required a greatly increased focus on the compositional characteristics of soils and their relation to the long-term physical and chemical properties that control soil behavior under changed and extreme environmental conditions.
QUESTIONS AND PROBLEMS
1. A montmorillonite has a cation exchange capacity of 130 meq/100 g and a total external and internal surface area of 800 m2 /g. a. How many calcium ions will there be on a particle that is 0.4 m ⫻ 0.2 m ⫻ one unit cell in thickness? b. What percentage of the dry weight of the clay is composed of calcium? 2. An orthorhombic crystal has axial ratios of 0.6, ˚ horizontally 0.3, and 1.0. The (500) plane is 2.0 A from the origin. This crystal is irradiated with ˚ ). At what CuK X-rays (wave length of 1.54 A value of does the second-order (010) reflection occur?
81
d. (111) and (111) e. (112) and (001) 5. A clay has a surface density of charge of one ˚ 2. Its cation exchange capacity is charge per 150 A 10 meq/100 g. Determine the specific surface area. 6. Why are soils containing smectite often expansive, whereas soils containing illite and/or kaolinite are not? 7. As the geotechnical engineer on a project, you find an inorganic soil containing 15 percent by weight of particles finer than 100 m, as measured by hydrometer analysis. What soil components do you expect? Why? How could you confirm this expectation? Be specific in terms of tests and diagnostic criteria. 8. What is the smallest interplanar spacing that can be measured by X-ray diffraction using copper K radiation? 9. You suspect that a fine-grained soil sample contains kaolinite, illite, and smectite minerals. Describe in logical sequence the tests you would do to verify that these clay minerals are present. Indicate the reasons why you choose these tests and the criteria for distinguishing among the minerals. 10. An inorganic clay has a liquid limit of 350 percent. a. What is the most probable predominant clay mineral in this soil? b. Explain the high liquid limit in terms of the crystal structure of this mineral. c. Would you recommend founding light structures on shallow footings above this soil? Why?
3. Sketch the following planes relative to crystallographic axes: (001), (243), (hk0), (hkl), (111), (060), (010).
11. A soil sample has a cation exchange capacity of 30 meq/100 g and a specific surface area of 50 m2 /g. You wish to determine the type of clay mineral in this soil. Based on your general knowledge of the area from which it came, including the geology, you suspect the possibility of hydrated halloysite, illite, and smectite. State specifically how you would determine which mineral is present.
4. Consider an orthorhombic crystal of dimensions ˚ , b ⫽ 12 A ˚, c ⫽ 8 A ˚ . With the aid of a ⫽ 6A sketches determine the angle of intersection between the planes of each pair indicated below. If the planes do not intersect, then so indicate. a. (002) and (020) b. (001) and (002) c. (111) and (222)
12. An X-ray diffraction pattern for a soil sample from a site where light structures (houses, a shopping center) are to be located shows peaks at 2 ⫽ 5, 10, 12.2, 20.8, 24.7, and 26.7. Copper K radiation was used. a. What minerals are present in the sample? b. If the measure cation capacity is 40 meq/100 g, what is the approximate minimum amount of
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3
SOIL MINERALOGY
clay mineral in the sample by weight percentage? c. What concerns would you have about this soil as a foundation material? d. How could you minimize any problems identified in part (c)? 13. In general the average clay particle size as represented by some effective diameter D, for smectite particles (S) is less than that of hydrous mica (illite) (HM) particles, which, in turn, is less than that of kaolinite (K) particles. In addition, the average particle thicknesses are in the order tS ⬍ tHM ⬍ tK and values of the thickness-to-diameter ratio (t/D) are in the order (t/D)S ⬍ (t/D)HM ⬍ (t/D)K What are some implications of these relationships with respect to the relative values of plasticity, hydraulic conductivity, compression–swell behavior, and strength characteristics of three soils: one containing a large amount of smectite, one containing a large amount of hydrous mica (illite), and one containing a large amount of kaolinite?
14. The gradation curve for a sandy clay soil is shown in Fig. 3.40. a. What are the percentages by weight of sand, silt, and clay size material? b. Consider a 100-g sample of the soil and assume that all sand particles are of a size equal to the average particle size in the sand size range, the silt particles are of a size equal to the average particle size in the silt size range, and all clay particles are of a size equal to the average particle size in the clay size range. Base your determination of average particle size in each range on equal weights of particles coarser and finer than the average for each size range. Estimate the number of sand, silt, and clay particle in the sample. For purposes of this estimate, the sand and silt particles can be assumed to be spherical. Assume the clay particles to be flat disks having a diameter-tothickness ratio of 10. Assume the average size of clay particles on the gradation curve to represent the disk diameter. c. Estimate the specific surface area of this soil in square meters per gram. Determine the percentages of this total that are contributed by the sand, silt, and clay fractions. d. Are the estimates of the numbers of particles and specific surface area made in this way too high, too low, or correct? Why?
Figure 3.40 Gradation curve for a sandy clay soil.
CHAPTER 4
Soil Composition and Engineering Properties
4.1
INTRODUCTION
The engineering properties of a soil depend on the composite effects of several interacting factors. These factors may be divided into two groups: compositional factors and environmental factors. Compositional factors determine the potential range of values for any property. They include: 1. 2. 3. 4. 5. 6.
Types of minerals Amount of each mineral Types of adsorbed cations Shapes and size distribution of particles Pore water composition Type and amount of other constituents, such as organic matter, silica, alumina, and iron oxide
The influences of compositional factors on engineering properties can be studied using disturbed samples. Environmental factors determine the actual value of any property. They include: 1. 2. 3. 4. 5. 6.
ceeds 50 percent.1 The engineering properties of cohesionless soil are often determined by applied confining pressure and looseness or denseness as indicated by the relation of the current void ratio to the lowest and highest possible values of void ratio for the soil. The engineering properties of cohesive soil are often characterized by stiffness and strength and by relating the current water content and past consolidation history to the compositional characterization provided by the plasticity index. Some engineering characteristics of coarse-grained and fine-grained soils are listed and compared in Fig. 4.1. Detailed discussion of the combined effects of compositional and environmental factors on the three most important property classes for engineering problems, that is, conductivity, volume change, and deformation and strength, is given in Chapters 9, 10, and 11. Quantitative determination of soil behavior completely in terms of compositional and environmental factors is impractical for several reasons: 1. Most natural soil compositions are complex, and determination of soil composition is difficult. 2. Physical and chemical interactions occur between different phases and constituents. 3. The determination and expression of soil fabric in quantitatively useful ways is difficult. 4. Past geologic history and present in situ environment are difficult to simulate in the laboratory. 5. Physicochemical and mechanical theories for relating composition and environment to properties quantitatively are inadequate.
Water content Density Confining pressure Temperature Fabric Availability of water
Undisturbed samples, or in situ measurements, are required for the study of the effects of environmental factors on properties. Soils are classified as coarse grained, granular, and cohesionless if the amount of gravel and sand exceeds 50 percent by weight or fine grained and cohesive if the amount of fines (silt and clay-size material) ex-
1
The terms cohesionless and cohesive must be used with care, as even a few percent of clay mineral in a coarse-grained soil can impart plastic characteristics.
83
84
4
SOIL COMPOSITION AND ENGINEERING PROPERTIES
“Granular Soils” Silt
Sand
Gravel 75 mm 3 in.
“Fines”
5 mm 0.2 in.
Apples to English peas
0.07 mm 0.003 in. English peas to baking flour
Particles visible without magnification Grain size measurable with sieves Grains do not form a coherent mass even when wet – cohesionless
Nonplastic – there is no range of water content where the soil can be deformed without cracking or crumbling.
Clay 0.002 mm 0.00008 in.
Finer than baking flour
Much finer than baking flour
Particles not visible without magnification Grain size not measurable with sieves Grain size measured by sedimentation rate Grains stick together when mixed with water due to pore water suction and physicochemical pore fluid-mineral interaction – cohesive
Plastic – deforms without cracking over a range of water content between the liquid limit and the plastic limit Liquid (pancake batter)
Liquid Limit (LL)
Plastic (modeling clay) Semisolid (chocolate bar) Solid (chalk) Permeability is moderate to high (10 -6 to 10-1 m/s). Water flows easily through the voids. Drainage occurs rapidly except under dynamic loading; e.g., earthquakes. Only “drained” strength is important for conditions other than earthquake loading or rapid landslides. Most important indicators of mechanical behavior are relative density, Dr , and applied confining pressure
Dr = 0 to 20% Dr = 20 to 40% Dr = 40 to 60% Dr = 60 to 80% Dr = 80 to 100%
Very loose Loose Med. dense Dense Very dense
Shrinkage Limit
Permeability is low to very low (<10-7 m/s). Water flows slowly through the voids. Drainage takes weeks to tens of years. Both “drained” and “undrained” strengths are important. “Undrained” strength is low when preconsolidation pressure is low.
Behavior of silts varies from “sandlike” to “clay-like” as grain size decreases
Very loose _
Compressible Liquefiable during earthquakes φ ~30° Very dense _ Very low compressibility Stable during earthquakes φ ~45°
Plastic Limit (PL)
Very soft –
Most important mechanical behavior is “preconsolidation pressure pp” and applied confining pressure
pp = 0 to 50 kPa pp = 50 to 100 kPa pp = 100 to 200 kPa pp = 200 to 400 kPa pp = 400 to 800 kPa pp = 0.8 to 1.6 MPa
Very soft Soft Firm Stiff Very stiff Hard
Very highly compressible Undrained shear strength <12.5 kPa
Very dense _ Low compressibility Undrained shear strength >100 kPa
Figure 4.1 Compositional and environmental factors contributing to engineering properties (adapted from course notes by J. M. Duncan, 1994).
ENGINEERING PROPERTIES OF GRANULAR SOILS
Nonetheless, compositional data are valuable for development of an understanding of properties and for establishment of qualitative to semiquantitative guidelines for how real soils behave. Accordingly, some relationships between compositional factors and engineering properties are summarized in this chapter.
4.2 APPROACHES TO THE STUDY OF COMPOSITION AND PROPERTY INTERRELATIONSHIPS
Study of soil composition in relation to soil properties may be approached in two ways. In the first, natural soils are used, the composition and engineering properties are determined, and correlations are made. This method has the advantage that measured properties are those of naturally occurring soils. Disadvantages, however, are that compositional analyses are difficult and time consuming, and that in soils containing several minerals or other constituents such as organic matter, silica, alumina, and iron oxide the influence of any one constituent may be difficult to isolate. In the second approach, the engineering properties of synthetic soils are determined. Soils of known composition are prepared by blending different commercially available clay minerals of relatively high purity with each other and with silts and sands. Although this approach is much easier, it has the disadvantages that the properties of the pure minerals may not be the same as those of the minerals in the natural soil, and important interactions among constituents may be missed. Whether the influences of constituents such as organic matter, oxides and cementation, and other chemical effects can be studied successfully using this approach is uncertain. Regardless of the approach used, there are at least two difficulties. One is that often the variability in both composition and properties in any one soil deposit may be great, making the selection of representative samples difficult. Variations in composition and texture occur in sediments within distances as small as a few centimeters. Residual soils, in particular, are likely to be very nonhomogeneous. A second difficulty is that the different constituents of a soil may not influence properties in direct or even predictable proportion to the quantity present because of physical and physicochemical interactions. As an example of physical interactions, blending of equal proportions of uniform sand and clay, each having a compacted unit weight of 17 kN/m3, would not necessarily yield a mixture also having a unit weight of 17 kN/m3 after compaction. The resulting unit weight might be as high as 20 kN/m3 because the clay can fill void spaces between sand particles.
85
Physicochemical interaction between clay minerals is shown in Fig. 4.2. Mixtures of bentonite (sodium montmorillonite) and kaolinite and of bentonite and a commercial illite containing about 40 percent illite clay mineral, with the rest mostly silt-sized nonclay, were prepared, and the liquid limits were determined. The dashed line in Fig. 4.2 shows the liquid limit values to be expected if each mineral contributed in proportion to the amount present. The data points and solid lines show the actual measured values. Although the bentonite–kaolinite mixtures gave values close to theoretical, the liquid limit values for the bentonite–illite mixtures were much less than predicted. This resulted from excess salt in the illite that, when mixed with the bentonite, prevented full interlayer expansion of the montmorillonite particles in the presence of water.
4.3 ENGINEERING PROPERTIES OF GRANULAR SOILS
The mechanical behavior of granular materials is governed primarily by their structure and the applied effective stresses. Structure depends on the arrangement of particles, density, and anisotropy. Particle sizes, shapes, and distributions, along with the arrangement of grains and grain contacts comprise the soil fabric. The packing characteristics of granular materials are discussed further in Chapter 5. Particle Size and Distribution
Figure 4.3 illustrates the tremendous range in particle sizes that may be found in a soil, where different sizes are shown to the same scale. The largest size shown represents fine sand. It may be recalled that particles finer than about 0.06 mm cannot be seen by the naked eye. The orders of magnitude difference in particle sizes found in any one soil is often better appreciated from a representation such as that in Fig. 4.3 than by the usual size distribution (or grading) curve where particle diameters are shown to a logarithmic scale. The origin of a cohesionless soil can be reflected by its grading. Alluvial terrace deposits and aeolian deposits tend to be poorly graded or sorted. Glacial deposits such as Boulder clays and tills are often well graded, containing a wide variety of particle sizes. Small particles in a well-graded soil fit into the voids between larger particles. Well-graded cohesionless soils are relatively easy to compact to a high density by vibration. The loss of fine fraction by internal erosion can lead to large changes in engineering properties. Uniformly graded soils are usually used for controlled drainage applications because they are not susceptible to loss of fines by internal erosion and their
86
4
SOIL COMPOSITION AND ENGINEERING PROPERTIES
Figure 4.2 Interactions between clay minerals as indicated by liquid limit (data from Seed et al., 1964).
hydraulic conductivity can be maintained within definable and narrow limits. The slope of the grain size distribution curve is characterized by the coefficient of uniformity Cu: Cu ⫽
d60 d10
(4.1)
where d60 and d10 correspond to the sieve sizes that 60 and 10 percent of the particles by weight pass through. A soil with Cu ⬎ 5 to 10 is considered well-graded. The possible range of packing of soil particles is often related to the maximum and minimum void ratios (or minimum and maximum densities) reflecting the loosest and densest states, respectively. Uniformly graded soils tend to have a narrower range of possible densities compared to well-graded soils. Soils containing angular particles tend to be less dense than soils with rounded particles, as discussed later in this section. However, angular and weak materials may crush significantly more during compression, compaction, or deformation. Figure 4.4 shows how the maximum and
minimum void ratios change by mixing sand and silt in different proportions. At low silt contents, silt particles fit into the voids between larger sand particles, so the void ratio of sand–silt mixtures decreases with increase in silt content. However, at a certain silt content, the silt fully occupies the voids, and the increase in silt content results in sand particles floating inside the silt matrix. Then, the void ratios increase with further increase in silt content. The relative density, DR, a measure of the current void ratio in relation to the maximum and minimum void ratios, and applied effective stresses controls the mechanical behavior of cohesionless soils. Relative density is defined by DR ⫽
emax ⫺ e ⫻ 100% emax ⫺ emin
(4.2)
in which emax, emin, and e are the maximum, minimum, and actual void ratios. The relative density correlates well with other properties of granular soils. As different standard test meth-
ENGINEERING PROPERTIES OF GRANULAR SOILS
87
2.0 1.8
Maximum void ratio
1.6
Minimum void ratio
Void ratio
1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
0
10
20
30
40 50 60 70 Silt content (%)
80
90 100
Figure 4.4 Maximum and minimum void ratios of Monterey
sand–silt mixtures (from Polito and Martin, 2001).
Morphology (large scale)
Roundness Texture (intermediate scale) Figure 4.3 Different grain sizes in soil.
ods can give different limiting void ratios, the use of the relative density is sometimes criticized, especially when considered in relation to the random in situ variations of the density of most sand and gravel deposits. Nonetheless, if properly interpreted, relative density can provide a very useful measure of cohesionless soil properties. Particle Shape
Particle shape is an inherent soil characteristic that plays a major role in mechanical behavior of soils. Characterization of particle shape is scale dependent, as shown in Fig. 4.5. At larger scales, that is, that of the particle itself, the particle morphology might be described as spherical, rounded, blocky, bulky, platy,
Roundness Texture (intermediate scale)
Surface Texture (small scale)
Figure 4.5 Scale-dependent particle shape characterization. The solid line gives the particle outline. Morphology describes overall shape of the particle as given by the heavy dotted line. Texture reflects the smaller scale local features of the particles as identified by light dotted circles. The examples are surface smoothness, roundness of edges and corners, and asperities.
elliptical, elongated, and so forth. At smaller scales, the texture, which reflects the local roughness features such as surface smoothness, roundness of edges and corners, and asperities, is important. With the exception of mica, most nonclay minerals in soils occur as bulky particles.2 Most particles are
2 Quartz particles become flatter with decreasing size and may have a platy morphology when subdivided to a fineness approaching clay size (Krinsley and Smalley, 1973).
88
4
SOIL COMPOSITION AND ENGINEERING PROPERTIES
not equidimensional, however, and are at least slightly elongate or tabular. A frequency histogram of particle length-to-width ratio (L/W) for Monterey No. 0 sand is shown in Fig. 4.6. This well-sorted beach sand is composed mainly of quartz with some feldspar. The mean of all the particle measurements is an L/W ratio of 1.39. This distribution is typical of that for many sands and silty sands. Particle morphology in soil mechanics has historically been described using standard charts against which individual grains may be compared. A typical chart and some examples are shown in Fig. 4.7 (Krumbein, 1941; Krumbein and Sloss, 1963; Powers, 1953). Sphericity is defined as the ratio of the diameter of a sphere of equal volume to the particle to the diameter of the circumscribing sphere. Roundness is defined as the ratio of the average radius of curvature of the corners and edges of the particle to the radius of the maximum sphere that can be inscribed (Wadell, 1932). Sphericity and roundness are measures of two very different morphological properties. Sphericity is most dependent on elongation, whereas roundness is largely dependent on the sharpness of angular protrusions from the particle. Different definitions of sphericity and roundness are available, as shown in Table 4.1. Due to the variety of definitions available, the quantification of particle shape requires accurate specification of their definition. In recent years, techniques for computer analysis of shape data by digital imaging have improved greatly, and standard software applications include determina-
tion of aspect ratio and roundness. A convenient way to characterize particle shapes in more detail is by a Fourier mathematical technique. For instance, the (R, ) Fourier method is in the following form:
冘 (a cos n ⫹ b sin n ) N
R( ) ⫽ a0 ⫹
n
n
(4.3)
n⫽1
where R( ) is the radius at angle , N is the total number of harmonics, n is the harmonic number, and a and b are coefficients giving the magnitude and phase for each harmonic. The lower harmonic numbers give the overall shape; for instance, the sphericity is expressed by the first and second harmonics. The coefficient values for higher-order descriptors generally decay with increasing descriptor or harmonic number, which expresses smaller features (i.e., texture) (Meloy, 1977). Other mathematical methods to curve-fit particle shapes are listed in Table 4.1. Further discussion on particle shape characterization is given by Barrett (1980), Hawkins (1993), Santamarina et al. (2001), and Bowman et al. (2001). In an assembly of uniform size spherical particles, the loosest stable arrangement is the simple cubic packing giving a void ratio of 0.91. The densest packing is the tetrahedral arrangement giving a void ratio of 0.34. Particle shape affects minimum and maximum void ratios as shown in Fig. 4.8 (Youd, 1973). The values increase as particles become more angular or the roundness (defined as roundness 1 in Table 4.1)
Figure 4.6 Grain shape distribution of Monterey No. 0 sand. Results are based on study of 277 particles, d50 ⫽ 0.43 mm, Cu ⫽ 1.4 (Mahmood, 1973).
ENGINEERING PROPERTIES OF GRANULAR SOILS
89
0.9
Sphericity
0.7
0.5
0.3 0.1
0.3
0.5 Roundness (a)
0.7
0.9
High Sphericity
Low Sphericity
Very Angular
Angular
Subangular Subrounded Rounded
Well Rounded
(b) Figure 4.7 Particle shape characterization: (a) Chart for visual estimation of roundness and
sphericity (from Krumbein and Sloss, 1963). (b) Examples of particle shape characterization (from Powers, 1953).
decreases. When R ⫽ 1, the particle is a sphere. As particles become more angular, R decreases to zero. Void ratios are also a function of particle size distribution; the values decrease as the range of particle sizes increases (increase in the coefficient of uniformity Cu). The friction angle increases with increase in particle angularity, possibly as a result of an increase in coordination number. For example, values of the angle of repose3 are plotted against roundness in Fig. 4.9 and
the following linear fit to the relationship is proposed (Santamarina and Cho, 2004); repose ⫽ 42 ⫺ 17R
(4.4)
where R is the coefficient of roundness defined as roundness 1 in Table 4.1. Similar data relating friction angle from drained triaxial tests and particle shape is presented by Sukumaran and Ashmawy (2001). Particle Stiffness
3
Angle of repose can be determined by pouring soil in a graduated cylinder filled with water. Tilt the cylinder more than 60 and bring it back slowly to the vertical position. The angle of the residual sand slope is the angle of repose. Further details of the method can be found in Santamarina and Cho (2004).
Soil mass deformation at very small strains originates from the elastic deformations at points of contact between particles. Contact mechanics shows that the elastic properties of particles control the deformations at particle contacts (Johnson, 1985), and these deforma-
90
4
SOIL COMPOSITION AND ENGINEERING PROPERTIES
Table 4.1
Methods for Particle Shape Characterization
Method
Definition Morphology—Sphere
Sphericity 1
Diameter of a sphere of equal volume Diameter of circumscribing sphere
Sphericity 2
Particle volume Volume of circumscribing sphere
Sphericity 3 Projection sphericity
Area of particle outline Area of a circle with diameter equal to the longest length of outline
Inscribed circle sphericity
Diameter of the largest inscribed circle Diameter of the smallest inscribed circle Morphology—Ellipse
Eccentricity
p /Rap, where the ellipse is characterized by Rp ⫹ p cos 2 in polar coordinates
Elongation
Smallest diameter Diameter perpendicular to the smallest diameter
Slenderness
Maximum dimension Minimum dimension Texture—Roundness
Roundness 1
Average of radius of curvature of surface features, (兺ri)/N Radius of the maximum sphere that can be inscribed, rmax
Roundness 2
Radius of curvature of the most convex part 0.5 (longest diameter through the most convex part)
Roundness 3
Radius of curveture of the most convex part Mean radius Morphology—Texture
Fourier method
Fourier descriptor method Fractal analysis
Eq. (4.3), first and second harmonics, characterize sphericity, whereas higher harmonics (around 10th) characterizes roundness. Surface texture is characterized by much higher harmonics. More flexible than the Fourier method by using the complex plane (Bowman et al., 2001). Lower harmonics give shape characteristics such as elongation, triangularity, squareness, and asymmetry. Higher harmonics (larger than 8th) give textural features. Use as a measure of texture (Vallejo, 1995; Santamarina, et al. 2001).
From Hawkins (1993), Santamarina et al. (2001), and Bowman et al. (2001).
ENGINEERING PROPERTIES OF GRANULAR SOILS
tions in turn influence the stiffness of particle assemblages. Elastic properties of different minerals and rocks are listed in Table 4.2. The modulus of a single grain, which determines the particle contact stiffness, is at least an order of magnitude greater than that of the particle assembly. Further details on the relation between particle stiffness and particle assemblage stiffness are given in Chapter 11.
Maximum Void ratio, emax
1.4
1.2 An gu lar
1.0
R=
0.2 0
Particle Strength 0.8
0.20
Sub an Sub gular rou nde d Rou nde d
0.6 Minimum Void Ratio, emin
91
0.25 0.30 0.35
0.49 0.70
0.8 Ang ular
0.6
Ang ular Suba ngula r
0.4
0.2 1
Subrounded Rounded
R=0 .20 R=0 .17
0.20
0.25 0.30
0.35 0.49 0.70 15
2 3 4 6 10 Coefficient of Uniformity, Cu
Figure 4.8 Maximum and minimum void ratios of sands as
a function of roundness and the coefficient of uniformity (from Youd, 1973).
Angle of repose φrepose
50
The crushability of soil particles has large effects on the mechanical behavior of granular materials. At high stresses, the compressibility of sand becomes large as a result of particle crushing, and the shape of an e–log p compression curve becomes similar to that of normally consolidated clay (Miura et al., 1984; Coop, 1990; Yasufuku et al., 1991). Under constant states of stress, the amount of particle breakage increases with time, contributing to creep of the soil (Lade et al., 1996). The amount of crushing in a soil mass depends both on the stiffness and strength of the individual grains and how applied stresses are transmitted through the assemblage of soil particles. Particle strength or hardness is characterized by crushing at contacts or particle tensile splitting. There is a statistical variation in grain strength for particles of a specified material and of a given size (Moroto and Ishii, 1990; McDowell, 2001). Random variation in grain strengths leads to distributions of particle sizes when large stress is applied to a soil assembly. Table 4.3 lists the characteristic tensile strengths of some soil particles. The values are smaller than the yield strength of the material itself. The strength also depends on the particle shape. For example, Hagerty et al. (1993) show that angular glass beads were more susceptible to breakage than round glass beads.
Table 4.2 Elastic Properties of Geomaterials at Room Temperature
40
Material
30 20
φrepose = 42 – 17R
10 0.0
0.2
0.4 0.6 0.8 Roundness R
1.0
Figure 4.9 Angle of repose as a function of roundness (from Santamarina and Cho, 2004).
Quartz Limestone Basalt Granite Hematite Magnetite Shale
Young’s Shear Modulus Modulus (GPa) (GPa) 76 2–97 25–183 10–86 67–200 31 0.4–68
29 1.6–38 3–27 7–70 27–78 19 5–30
After Santamarina et al. (2001).
Poisson’s Ratio 0.31 0.01–0.32 0.09–0.35 0.00–0.30 — — 0.01–0.34
92
4
SOIL COMPOSITION AND ENGINEERING PROPERTIES
Table 4.3
Strength of Soil Particles
Sand Name
Size (mm)
Leighton Buzzard silica sand
1.18 2.0 3.36 0.2 0.85 1.0 1.18 1.4 1.7 0.5 1 2 0.28 0.66 1.55
Toyoura sand Aio quartz sand
Silica sand
Silica sand
Aio feldspar sand
0.85 1.0 1.18 1.4 1.7
Oolitic limestone particle
5 8 12 20 30 40 50 5 8 12 20 30 40 50 1 2 4 8 16
Carboniferous limestone particle
Quiou sand
37% Tensilea Strength (MPa) Quartz — — — 147.4 51.2 47.7 37.9 46.7 39.6 147.4 66.7 41.7 110.9 72.9 31.0
Mean Strengthb (MPa) 29.8 24.7 20.5 136.6 52.1 46.6 35.6 42.4 38.5 132.5 59.0 37.3 147.3 73.1 29.7
Reference Lee (1992)
Nakata et al. (2001) Nakata et al. (1999)
McDowell (2001)
Nakata et al. (2001)
Feldspar 20.9 24.3 18.1 23.1 18.9
24.6 22.8 18.2 21.4 18.3
Nakata et al. (1999)
Calcareous Sand — — — — — — — — — — — — — — 109.3 41.4 4.2 0.73 0.61
2.4 2.1 1.8 1.5 1.3 1.2 1.1 14.9 12.2 10.3 8.3 7.0 6.2 5.7 96.19 36.20 3.87 0.63 0.54
Lee (1992)
Lee (1992)
McDowell and Amon (2000)
Others Masado decomposed granite soil Glass beads Angular glass a b
1.55 0.93 0.93
24.2 365.8 62.1
Stress below which 37% of the particles do not fracture. Force/d 2 at which particle of size d is crushed.
22.1 339.6 60.0
Nakata et al. (2001) Nakata et al. (2001) Nakata et al. (2001)
ENGINEERING PROPERTIES OF GRANULAR SOILS
Leighton Buzzard Sand
50
100
Percent Finer by Weight
The breakage potential of a single soil particle increases with its size as illustrated in Table 4.3. This is because larger particles tend to contain more and larger internal flaws and hence have lower tensile strength. Fig. 4.10 shows that oolitic limestone, carboniferous limestone, and quartz sand exhibit near linear declines in strength with increasing particle size on a log–log plot (Lee, 1992). The amount of particle crushing in an assemblage of particles depends not only on particle strength, but also on the distribution of contact forces and arrangement of different size particles. It can be argued that larger size particles are more likely to break because the normal contact forces in a soil element increase with particle size and the probability of a defect in a given particle increases with its size as shown in Fig 4.10 (Hardin, 1985). However, if a larger particle has contacts with neighboring particles (i.e., larger coordination number), the load on it is distributed, and the probability of facture is less than for a condition with fewer contacts. Experimental evidences suggest that fines increase as particles break by increase in applied pressure. For example, the evolution of particle size distribution curves for Ottawa sand in one-dimensional compression is shown in Fig. 4.11 (Hagerty et al., 1993). Hence, the coordination number dominates over size-dependent particle strength. Larger particles have higher coordination numbers because they are in con-
Maximum stress 20.7 MPa 41.4 MPa 62.1 MPa 103 MPa 345 MPa 517 MPa 689 MPa
80
60
40
Uncrushed
20
0 0.01
0.1 Grain size (mm)
1.0
Figure 4.11 Evolution of particle size distribution curve
upon crushing (from Hagerty et al., 1993).
tact with many smaller particles. The very smallest particles have a lower coordination number because there are fewer smaller particles available for contact. Hence, the largest particles in the aggregate become protected by the surrounding newly formed smaller particles, and smaller particles are more likely to break
Rounded River Gravel Angular River Gravel Carboniferous Limestone
Particle Strength (MPa)
10 5.0
1.0
Oolitic Limestone
0.5
0.2 1
93
5 10 Average Particle Size (mm)
50
Figure 4.10 Relationship between tensile strength and particle size (from Lee, 1992).
100
94
4
SOIL COMPOSITION AND ENGINEERING PROPERTIES
or move. Further details on particle breakage effects on compression behavior of sands are given in Chapter 10.
冉
eG VGS ⫽ 1 ⫺
冊
C Ws e 100 GSG w G
(4.5)
The volume of water plus volume of clay is given by
4.4 DOMINATING INFLUENCE OF THE CLAY PHASE
In general, the more clay in a soil, the higher the plasticity, the greater the potential shrinkage and swell, the lower the hydraulic conductivity, the higher the compressibility, the higher the cohesion, and the lower the internal angle of friction. Whereas surface forces and their range of influence are small relative to the weight and size of silt sand particles, the behavior of small and flaky clay mineral particles is strongly influenced by surface forces, as discussed in Chapter 6. Water is strongly attracted to clay particle surfaces, also discussed in Chapter 6, and results in plasticity, whereas nonclay particles have much smaller specific surface and less affinity for water and do not develop significant plasticity, even when in finely ground form. If it is assumed as a first approximation that all of the water in a soil is associated with the clay phase, the amount of clay required to fill the voids of the granular phase and prevent direct contact between granular particles can be estimated for any water content. The weight and volume relationships for the different phases of a saturated soil are shown in Fig. 4.12. In this figure W represents weight, V is volume, C is the percent clay by weight, GSC is the specific gravity of clay particles, w is the water content in percent, w is the unit weight of water, and GSG is the specific gravity of the granular particles. The volume of voids in the granular phase is eG VGS, where eG is the void ratio of the granular phase and VGS is the volume of granular solids, given by
VW ⫹ VC ⫽
w WS C WS ⫹ 100 w 100 GSC w
(4.6)
If clay and water completely fill the voids in the granular phase, then
冉
冊
w Ws C W C Ws ⫹ ⫽ 1⫺ e 100 w 100 GSC w 100 GSG w G
(4.7)
which simplifies to
冉
冊
w C C eG ⫹ ⫽ 1⫺ 100 100GSC 100 GSG
(4.8)
The void ratio of a granular material composed of bulky particles is of the order of 0.9 in its loosest possible state. The specific gravity of the nonclay fraction in most soils is about 2.67, and that of the clay fraction is about 2.75. Inserting these values in Eq. (4.8) gives C ⫽ 48.4 ⫺ 1.42w
(4.9)
This relationship indicates that for water contents typically encountered in practice, say 15 to 40 percent, only a maximum of about one-third of the soil solids need be clay in order to dominate the behavior by preventing direct interparticle contact of the granular particles. In fact, since there is a tendency for clay particles to coat granular particles, the clay can significantly influence properties. For example, just 1 or 2 percent of highly plastic clay present in gravel used as a fill or aggregate may be sufficient to clog handling and batching equipment.
Figure 4.12 Weight–volume relationships for a saturated clay-granular soil mixture.
ATTERBERG LIMITS
4.5
ATTERBERG LIMITS
Atterberg limits are extensively used for identification, description, and classification of cohesive soils and as a basis for preliminary assessment of their mechanical properties. The potential usefulness of the Atterberg limits in soil mechanics was first indicated by Terzaghi (1925a) when he noted that ‘‘the results of the simplified soil tests (Atterberg limits) depend precisely on the same physical factors which determine the resistance and the permeability of soils (shape of particles, effective size, uniformity) only in a far more complex manner.’’ Casagrande (1932b) developed a standard device for determination of the liquid limit and noted that the nonclay minerals quartz and feldspar did not develop plastic mixtures with water, even when ground to sizes smaller than 2 m. Further studies led to the formation of a soil classification system based on the Atterberg limits for identification of cohesive soils (Casagrande, 1948). This system was adopted, with minor modifications, as a part of the Unified Classification System. A plot of plasticity index as a function of liquid limit that is divided into different zones, as shown in Fig. 4.13, is termed the plasticity chart. This chart forms an essential part of the Unified Soil Classification System.
95
Although both the liquid and plastic limits are easily determined, and their qualitative correlations with soil composition and physical properties are quite well established, fundamental interpretations of the limits and quantitative relationships between their values and compositional factors are more complex. Liquid Limit
The liquid limit test is a form of dynamic shear test. Casagrande (1932b) deduced that the liquid limit corresponds approximately to the water content at which a soil has an undrained shear strength of about 2.5 kPa. Subsequent studies have indicated that the liquid limit for all fine-grained soils corresponds to shearing resistance of about 1.7 to 2.0 kPa and a pore water suction of about 6 kPa (Russell and Mickle, 1970; Wroth and Wood, 1978; Whyte, 1982). Liquid limit values are determined using both the Casagrande liquid limit device and the fall cone device. Different standards adopt different devices and, therefore, correlations based on liquid limit should be used with some caution. The variation of undrained shear strength with water content can be obtained from a series of fall cone tests and solutions are available using the theory of plasticity for various geometries used in fall cones (Houlsby, 1982; Koumoto and Houlsby,
Figure 4.13 Plasticity chart.
96
4
SOIL COMPOSITION AND ENGINEERING PROPERTIES
2001). Furthermore, with the aid of critical state soil mechanics (see Chapter 11), some other engineering properties, such as compressibility, can be deduced (Wood, 1990). Values of hydraulic conductivity at the liquid limit for several clays are given in Table 4.4, from Nagaraj et al. (1991). The striking aspect of these data is that, although the water contents and void ratios at the liquid limit for the different clays vary over a very wide range, the hydraulic conductivity is very nearly the same for all of them. This means that the effective pore sizes controlling fluid flow must be about the same for all the clays at their liquid limit. Such a microfabric is consistent with the cluster model for hydraulic conductivity discussed in Chapter 9. In this model, the individual clay particles associate into aggregates or flocs, as shown schematically in Fig. 9.11. The size of voids between the clusters or aggregates controls the flow rate according to either model. The approximately equal strengths, pore water suctions, and hydraulic conductivities for all clays at their liquid limit can be explained by the concepts that (1) the aggregates or clusters are the basic units that interact to develop the strength, that is, the aggregates act somewhat like single particles, (2) the average adsorbed water layer thickness is about the same on all particle surfaces, and (3) the average size of intercluster pores is the same for all clays. Concept 2 provides the key to why different clays have different values of liquid limit. All clays have essentially the same surface structures, that is, a layer of oxygen atoms in tetrahedral coordination with silicon, or a layer of hydroxyls in octahedral coordination with aluminum or magnesium. The forces of interaction between these surfaces and adsorbed water should be about the same for the different clay minerals. Thus, the amount of water adsorbed per unit area of surface that corresponds to a pore water suction of 6 kPa should be about the same. This means that the greater the specific surface, the
Table 4.4
greater the total amount of water required to reduce the strength to that at the liquid limit. The specific surface areas of the different clay minerals (Table 3.6) are consistent with the liquid limit values of different clay minerals in Table 4.5. Additional support for this concept is given by the following relationship found for 19 British clays: LL ⫽ 19 ⫹ 0.56As
(20%)
where LL is the liquid limit and As is the specific surface in square meters per gram (Farrar and Coleman, 1967). The effects of electrolyte concentration, cation valence and size, and dielectric constant of the pore fluid on the liquid limit of kaolinite and montmorillonite are illustrated and discussed by Sridharan (2002). The effects are generally consistent with the above interpretation and can be explained also through double-layer (see Chapter 6) influences on swelling, flocculation and deflocculation of clay particles, and shear strength. Plastic Limit
The plastic limit has been interpreted as the water content below which the physical properties of the water no longer correspond to those of free water (Terzaghi, 1925a) and as the lowest water content at which the cohesion between particles or groups of particles is sufficiently low to allow movement, but sufficiently high to allow particles to maintain the molded positions (Yong and Warkentin, 1966). Whatever the structural status of the water and the nature of the interparticle forces, the plastic limit is the lower boundary of the range of water contents within which the soil exhibits plastic behavior; that is, above the plastic limit the soil can be deformed without volume change or cracking and will retain its deformed shape; below the plastic limit it cannot. Plastic limit values
Hydraulic Conductivity at Liquid Limit for Several Clays
Soil Type
Liquid Limit, wL (%)
Void Ratio at Liquid Limit, eL
Hydraulic Conductivity (10⫺7 cm/s)
Bentonite Bentonite ⫹ sand Natural marine soil Air-dried marine soil Oven-dried marine soil Brown soil
330 215 106 84 60 62
9.240 5.910 2.798 2.234 1.644 1.674
1.28 2.65 2.56 2.42 2.63 2.83
From Nagaraj et al. (1991).
(4.10)
INFLUENCES OF EXCHANGEABLE CATIONS AND pH
Table 4.5
97
Atterberg Limit Values for the Clay Minerals
Minerala
Liquid Limit (%)
Plastic Limit (%)
Shrinkage Limit (%)
Montmorillonite (1) Nontronite (1)(2) Illite (3) Kaolinite (3) Hydrated halloysite (1) Dehydrated halloysite (3) Attapulgite (4) Chlorite (5) Allophane (undried)
100–900 37–72 60–120 30–110 50–70 35–55 160–230 44–47 200–250
50–100 19–27 35–60 25–40 47–60 30–45 100–120 36–40 130–140
8.5–15 15–17 25–29
a
(1) Various ionic forms. Highest values are for monovalent; lowest are for di- and trivalent. (2) All samples 10% clay, 90% sand and silt. (3) Various ionic forms. Highest values are for di- and trivalent; lowest are for monovalent. (4) Various ionic forms. (5) Some chlorites are nonplastic. Data Sources: Cornell University (1950), Samuels (1950), Lambe and Martin (1955), Warkentin (1961), and Grim (1962).
for different clay minerals are listed in Table 4.5. The undrained shear strength at the plastic limit is reported to be in the ranges of 100 to 300 kPa with an average value of 170 kPa (Sharma and Bora, 2003). Liquidity Index
The liquidity index (LI) is defined by LI ⫽
water content ⫺ plastic limit plasticity index
(4.11)
wherein the plasticity index is given by PI ⫽ LL ⫺ PL. The liquidity index is useful for expressing and comparing the consistencies of different clays. It normalizes the water content relative to the range of water content over which a soil is plastic. It correlates well with compressibility, strength, and sensitivity properties of fine-grained soils as illustrated in later chapters of this book.
4.6
ACTIVITY
Both the type and amount of clay influence a soil’s properties, and the Atterberg limits reflect both of these factors. To separate them, the ratio of the plasticity index to the clay size fraction (percentage by weight of particles finer than 2 m), termed the activity, is very useful (Skempton, 1953):
Activity ⫽
plasticity index % ⬍ 2 m
(4.12)
For many clays, a plot of plasticity index versus clay content yields a straight line passing through the origin as shown for four clays in Fig. 4.14. The slope of the line for each clay gives the activity. Approximate values for the activities of different clay minerals are listed in Table 4.6. The greater the activity, the more important the influence of the clay fraction on properties and the more susceptible their values to changes in such factors as type of exchangeable cations and pore fluid composition. For example, the activity of Belle Fourche montmorillonite varies from 1.24 with magnesium as the exchangeable cation to 7.09 for sodium saturation of the exchange sites. On the other hand, the activity of Anna kaolinite only varies from 0.30 to 0.41 for six different cation forms (White, 1955). 4.7 INFLUENCES OF EXCHANGEABLE CATIONS AND pH
Cation type exerts a controlling influence on the amount of swelling of expansive clay minerals in the presence of water. For example, sodium and lithium montmorillonite may undergo almost unrestricted interlayer swelling provided water is available, the confining pressure is small, and the electrolyte
98
4
SOIL COMPOSITION AND ENGINEERING PROPERTIES
Figure 4.14 Relationship between plasticity index and clay fraction (from Skempton, 1953).
Table 4.6
Activities of Various Clay Minerals Mineral
Activity
Smectites Illite Kaolinite Halloysite (2H2O) Halloysite (4H2O) Attapulgite Allophane
1–7 0.5–1 0.5 0.5 0.5 0.5–1.2 0.5–1.2
concentration is low. On the other hand, divalent and trivalent forms of montmorillonite do not expand be˚ and form multiyond a basal spacing of about 17 A particle clusters or aggregates, regardless of other environmental factors. In soils composed mainly of nonexpansive clay minerals, adsorbed cation type is of the greatest importance in influencing the behavior of the material in suspension and the nature of the fabric in sediments that form. Monovalent cations, particularly sodium and lithium, promote deflocculation, whereas clay suspen-
sions ordinarily flocculate in the presence of divalent and trivalent cations. pH influences interparticle repulsions because of its effects on clay particle surface charge. Positive edge charges can exist in low pH environments. These effects are of greatest importance in kaolinite, lesser importance in illite, and relatively unimportant in smectite. In kaolinite, the pH may be the single most important factor controlling the fabric of sediments formed from suspension. The influences of cations and pH are examined further in Chapter 6.
4.8 ENGINEERING PROPERTIES OF CLAY MINERALS
Different groups of clay minerals exhibit a wide range of engineering properties. Within any one group, the range of property values may also be great. It is a function of particle size, degree of crystallinity, type of adsorbed cations, pH, the presence of organic matter, and the type and amount of free electrolyte in the pore water. In general, the importance of these factors increases in the order kaolin ⬍ hydrous mica (illite) ⬍
ENGINEERING PROPERTIES OF CLAY MINERALS
smectite. The chlorites exhibit characteristics in the kaolin–hydrous mica range. Vermiculites and attapulgite have properties that usually fall in the hydrous mica– smectite range. Because of the influences of the above compositional factors, only typical ranges of property values are given in this section. Factors that determine the actual values in any case are analyzed in more detail in subsequent chapters. Atterberg Limits
Plasticity values for different clay minerals are listed in Table 4.5 in terms of ranges in the liquid, plastic, and shrinkage limit values. Most of the values were determined using samples composed of particles finer than 2 m. Several general conclusions can be made concerning the Atterberg limits of the clay minerals. 1. The liquid and plastic limit values for any one clay mineral species may vary over a wide range. 2. For any clay mineral, the range in liquid limit values is greater than the range in plastic limit values. 3. The variation in values of liquid limit among different clay mineral groups is much greater than the variation in plastic limits.
4. The type of adsorbed cation has a much greater influence on the high plasticity minerals (e.g., montmorillonite) than on the low plasticity minerals (e.g., kaolinite). 5. Increasing cation valence decreases the liquid limit values of the expansive clays but tends to increase the liquid limit of the nonexpansive minerals. 6. Hydrated halloysite has an unusually high plastic limit and low plasticity index. 7. The greater the plasticity the greater is the shrinkage on drying (the lower the shrinkage limit). Particle Size and Shape
Different clay minerals occur in different size ranges (Table 3.6) because mineralogical composition is a major factor in determining particle size. There is some concentration of different clay minerals in different bands within the clay size range (less than 2 m), as indicated in Table 4.7. The shapes of the most common clay minerals are platy, except for halloysite, which occurs as tubes (Fig. 3.21). Particles of kaolinite are relatively large, thick, and stiff (Fig. 3.13). Smectites are composed of small, very thin, and filmy particles (Fig. 3.25). Illites are intermediate between kaolinite and smectite (Fig. 3.29) and are often terraced and thin
Table 4.7 Mineral Composition of Different Particle Size Ranges in Soils Particle Size (m) 0.1
0.1–0.2
Predominating Constituents
Common Constituents
Rare Constituents
Montmorillonite Beidellite Mica intermediates
Mica intermediates
Illite (traces)
Kaolinite Montmorillonite Illite Mica intermediates Micas Halloysite Quartz Kaolinite
Illite Quartz (traces) Quartz Montmorillonite Feldspar
0.2–2.0
Kaolinite
2.0–11.0
Micas Illites Feldspars
From Soveri (1950).
99
Halloysite (traces) Montmorillonite (traces)
100
4
SOIL COMPOSITION AND ENGINEERING PROPERTIES
at the edges. Attapulgite, owing to its double silica chain structure, occurs in lathlike particle shapes (Fig. 3.31). Hydraulic Conductivity (Permeability)
Mineralogical composition, particle size and size distribution, void ratio, fabric, and pore fluid characteristics all influence the hydraulic conductivity. This property is considered in detail in Chapter 9. Over the normal range of water contents (plastic limit to liquid limit), the hydraulic conductivity of all the clay minerals is less than about 1 ⫻ 10⫺7 m/s and may range to values less than 1 ⫻ 10⫺12 m/s for some of the monovalent ionic forms of smectite minerals at low porosity. The usual measured range for natural clay soils is about 1 ⫻ 10⫺8 to 1 ⫻ 10⫺10 m/s. For clay minerals compared at the same water content, the hydraulic conductivities are in the order smectite (montmorillonite) ⬍ attapulgite ⬍ illite ⬍ kaolinite.
Figure 4.15 Ranges in effective stress failure envelopes for pure clay minerals and quartz (from Olson, 1974). Reprinted with permission of ASCE.
Shear Strength
There are many ways to measure and express the shear strength of a soil, as described in most geotechnical engineering textbooks. In most cases, a Mohr failure envelope, where shear strength (usually peak, critical state, or residual) is plotted as a function of the direct effective stress on the failure plane, or a modified Mohr diagram, in which maximum shear stress is plotted versus the average of the major and minor principal effective stresses at failure, is used. A straight line is fit to the resulting curve over the normal stress range of interest and the shear strength is given by an equation of the form ⫽ c ⫹ n tan
(4.13)
where n is the effective normal stress on the shear plane, c is the intercept for n equals zero, often called the cohesion, and is the slope, usually called the friction angle. Effective stress strength envelopes are useful for relating strength to composition. Zones that encompass the effective stress failure envelopes, based on peak strength, for pure clay minerals and quartz are shown in Fig. 4.15. The increase in shear strength with increase in effective stress, that is, the friction angle, is greatest for the nonclay mineral quartz, followed in descending order by kaolinite, illite, and montmorillonite. The ranges in the position of a failure envelope for a given mineral result from differences in such factors as fabric, adsorbed cation, pH, and overconsolidation ratio. A similar pattern of failure envelopes for some natural soils is shown in Fig. 4.16. The finer
Figure 4.16 Strength envelopes for a range of soil types
(from Bishop, 1966).
grained the soil and the greater the amount of clay, the smaller the inclination of the failure envelope. From a number of studies [e.g., Hvorslev (1937, 1960), Gibson (1953), Trollope (1960), and Schmertmann and Osterberg (1960), and Schmertmann (1976)], it has been believed that the total strength of a clay is composed of two distinct parts: a cohesion that depends only on void ratio (water content), and a frictional contribution, dependent only on normal effective stress. Evaluation of these two parts was done by measurement of the strength of two samples both at the same void ratio or water content, but at different levels of effective stress. This condition is obtained by using one normally consolidated and one overconsolidated sample. The strength parameters determined in this way, often termed the Hvorslev parameters or true
ENGINEERING PROPERTIES OF CLAY MINERALS
cohesion and true friction, show increasing cohesion and decreasing friction with increasing plasticity and activity of the clay. However, two samples of the same clay at the same void ratio but different effective stresses are known to have different structures, as discussed in Chapter 8. Thus, they are not equivalent, and the strength tests measure the effects of both effective stress and structure differences. Furthermore, tests over large ranges of effective stress show that actual failure envelopes are curved in the manner of Fig. 4.16 and that the cohesion intercept is either zero or very small, except for cemented soils. Thus, a significant true cohesion, if defined as strength in the absence of normal stress on the failure plane, does not exist in the absence of chemical bonding. These considerations are discussed in more detail in Chapter 11.
Even the largest of the friction angle values for clay minerals is significantly less than the residual value for cohesionless soils, wherein values of drained friction angle are generally in the range of 30 to 50. The residual strengths of some quartz–clay mixtures are shown in Fig. 4.17. If each mineral were an equally important contributor to strength, then the curve for a given mixture should be symmetrical about the 50 percent point, as is the case for kaolinite and hydrous mica with no salt in the pore water. In the other mixtures, however, the clay phase begins to dominate at clay contents less than 50 percent. This is because with expansive clay minerals (montmorillonite) or flocculated fabrics (30 g salt/liter) the ratio of volume of wet clay to volume of quartz is greater than the ratio of dry volumes. It is further illustration of the dominating influence of the clay phase discussed earlier.
Figure 4.17 Residual friction angles for clay–quartz mixtures and natural soils (from Ken-
ney, 1967).
101
102
4
SOIL COMPOSITION AND ENGINEERING PROPERTIES
Compressibility
The compressibility of saturated specimens of clay minerals increases in the order kaolinite ⬍ illite ⬍ smectite. The compression index Cc, which is defined as the change in void ratio per 10-fold increase in consolidation pressure, is in the range of 0.19 to 0.28 for kaolinite, 0.50 to 1.10 for illite, and 1.0 to 2.6 for montmorillonite, for different ionic forms (Cornell University, 1950). The more compressible the clay, the more pronounced the influences of cation type and electrolyte concentration on compressibility. Compression index values for a number of different natural clays are shown in Fig. 4.18 as a function of plasticity index (Kulhawy and Mayne, 1990). The values for pure clays plot generally within the defined ranges in Fig. 4.18. The compression index for unloading and reloading is about 20 percent of the value for virgin compression. As both compressibility and hydraulic conductivity are strong functions of soil composition, the coefficient of consolidation cv is also related to composition because cv is directly proportional to hydraulic conductivity and inversely proportional to the coefficient of compressibility.4 Values of cv determined in one study 4
The coefficient of compressibility av is the negative of the rate of change of void ratio with effective stress.
(Cornell University, 1950) were in the ranges of 0.06 ⫻ 10⫺8 to 0.3 ⫻ 10⫺8 m2 /s for montmorillonite, 0.3 ⫻ 10⫺8 to 2.4 ⫻ 10⫺8 m2 /s for illite, and 12 ⫻ 10⫺8 to 90 ⫻ 10⫺8 m2 /s for kaolinite. Coefficients of consolidation for kaolinite, illite, montmorillonite, halloysite, and two-mineral mixtures of these clays ranged from 1 ⫻ 10⫺8 m2 /s for pure montmorillonite to 378 ⫻ 10⫺8 m2 /s for pure halloysite in another study (Kondner and Vendrell, 1964). Individual minerals did not influence the coefficient of consolidation in direct proportion to the amounts present. Approximate ranges of the coefficient of consolidation for natural clays are given in Fig. 4.19. The above values for pure clays and clay mineral mixtures are within the same general ranges. One conclusion that can be drawn from the comparability of compression index and coefficient of consolidation values for natural clays with those for pure clays is that the clay phase dominates the compression and consolidation behavior, with the nonclay material playing a passive role as relatively inert filler. Swelling and Shrinkage
The actual amount of volume change of a soil in response to a change in applied stress depends on the environmental factors listed in Section 4.1 as well as on the cation type, electrolyte type and concentration,
Figure 4.18 Compression and unload–reload indices as a function of plasticity index (from
Kulhawy and Mayne, 1990). Reprinted with permission from EPR1.
103
c ur (S
and pore fluid dielectric constant. However, the potential total amount of swell or shrinkage is determined by the type and amount of clay. From a consideration of the clay mineral structures and interlayer bonding (Chapter 3), it would be expected that smectite and vermiculite should undergo greater volume changes on wetting and drying than do kaolinite and hydrous mica. Experience indicates clearly that this is indeed the case. In general, the swelling and shrinking properties of the clay minerals follow the same pattern as their plasticity properties, that is, the more plastic the mineral, the more potential swell and shrinkage. Illustrations of the influences of adsorbed cation type and pore fluid composition are given in Chapter 10 and by Sridharan (2002). Because of the many problems encountered in the performance of structures founded on high volume change soils, numerous attempts have been made to develop reliable methods for their identification. The most successful of these are based on the determination of some factor that is related directly to the clay mineral composition, such as shrinkage limit, plasticity index, activity, and percentage finer than 1 m. Simple, unique correlations between swell or swell pressure and these parameters that reflect only the type and amount of clay are not possible because of the strong dependence of the behavior on initial state (moisture content, density, and structure) and the other environmental factors. This is illustrated by Fig. 4.20, which shows four different correlations between swelling potential and plasticity index (Chen, 1975). The two curves showing the Chen correlations were obtained for different natural soils compacted to dry unit weights between 100 and 110 pounds per cubic foot (15.7 and 17.3 kN/m3) at water contents between 15 and 20 percent. The large influence of surcharge pres-
esur res P e harg (Surc
1p .s.i .) . p.s 4 9 6.
i.)
liquid limit (from NAVFAC, 1982).
ha rg eP res sur e-
Figure 4.19 Coefficient of consolidation as a function of
(Sur char ge P ressu re - 1
(Sur char ge P ressu re - 1
p.s.i.)
p.s.i.)
ENGINEERING PROPERTIES OF CLAY MINERALS
Figure 4.20 Four correlations between swelling potential and plasticity index (from Chen, 1975).
sure during swelling is clearly shown. The tests by Seed et al. (1962b) were done using artificial mixtures of sand and clay minerals compacted at optimum water content using Standard AASHTO compactive effort allowed to swell under a surcharge pressure of 1 psi (7 kPa). The measurements by Holtz and Gibbs (1956) were made using both undisturbed and remolded samples allowed to swell from an air-dry state to saturation under a surcharge of 1 psi (7 kPa). The results of the tests on artificial sand–clay mineral mixtures obtained by Seed et al. (1962b) correlate well with compositional factors that reflect both the type and amount of clay, that is, the activity A, defined as PI/ C, and the percent clay size C (% ⬍ 2 m), according to S ⫽ 3.6 ⫻ 10⫺5 A2.44C 3.44
(4.14)
where S is the percent swell for samples compacted and tested as indicated above. A chart based on this relationship is shown in Fig. 4.21. For compacted natural soils the swelling potential could be related to the plasticity index with an accuracy of 35% according to
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In general, the greater the organic content and the wetter and more plastic the clay, the more pronounced is the time-dependent behavior. Both the type and amount of clay are important, as indicated, for example, by the variation of creep rate with clay content for three different clay mineral–sand mixtures, as shown in Fig. 4.22. In these tests, environmental factors were held constant by preparing all specimens to the same initial conditions (isotropic consolidation of saturated samples to 200 kPa) and application of a creep stress equal to 90 percent of the strength determined by a normal strength test. The variation in creep rate for these specimens as a function of plasticity index is shown in Fig. 4.23. The correlation is reasonably unique because the plasticity index reflects both the type and amount of clay. 4.9
Figure 4.21 Classification chart for swelling potential (modified from Seed et al., 1962b).
S ⫽ 2.16 ⫻ 10⫺3 (PI)2.44
EFFECTS OF ORGANIC MATTER
Organic matter in soil may be responsible for high plasticity, high shrinkage, high compressibility, low
(4.15)
Somewhat different relationships have been found to better classify the swell potential of some soils, and no single relationship is suitable for all conditions. Thus, while the above relationships and plots such as Figs. 4.20 and 4.21 illustrate the influences of compositional factors and provide preliminary guidance about the potential magnitude of swelling, reliable quantification of swell and swell pressure in any case should be based on the results of tests on representative undisturbed samples tested under appropriate conditions of confinement and water chemistry. Time-Dependent Behavior
Different soil types undergo varying amounts of timedependent deformations and stress variations with time, as exhibited by secondary compression, creep, and stress relaxation. The potential for these phenomena depends on compositional factors, whereas the actual amount in any case depends on environmental factors. For example, it is known that retaining walls with wet clay backfills must be designed for at-rest earth pressures because of stress relaxation along a potential failure plane that results in increased pressure on the wall. On the other hand, if dry clay is used, and if it is maintained dry, then designs based on active pressures are possible because time-dependent increases in pressure will be negligible.
Figure 4.22 Effect of amount and type of clay on ‘‘steadystate’’ creep rate (see Chapter 12).
CONCLUDING COMMENTS
Figure 4.23 Relationship between clay content, plasticity index, and creep rate.
hydraulic conductivity, and low strength. Soil organic matter is complex both chemically and physically, and many reactions and interactions between the soil and the organic matter are possible (Oades, 1989). It may occur in any of five groups: carbohydrates; proteins; fats, resins, and waxes; hydrocarbons; and carbon. Cellulose (C6H10O5) is the main organic constituent of soil. In residual soils organic matter is most abundant in the surface horizons. Organic particles may range down to 0.1 m in size. The specific properties of the colloidal particles vary greatly depending upon parent material, climate, and stage of decomposition. The humic fraction is gel-like in properties and negatively charged (Marshall, 1964). Organic particles can strongly adsorb on mineral surfaces, and this adsorption modifies both the properties of the minerals and the organic material itself. Soils containing significant amounts of decomposed organic matter are usually characterized by a dark gray to black color and an odor of decomposition. At high moisture contents, decom-
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posed organic matter may behave as a reversible swelling system. At some critical stage during drying, however, this reversibility ceases, and this is often manifested by a large decrease in the Atterberg limits. This is recognized by the Unified Soil Classification System, which defines an organic clay as a soil that would classify as a clay (the Atterberg limits plot above the A line shown in Fig. 4.13) except that the liquid limit value after oven drying is less than 75 percent of the liquid limit value before drying (ASTM, 1989). Increasing the organic carbon content by only 1 or 2 percent may increase the limits by as much as an increase of 10 to 20 percent in the amount of material finer than 2 m or in the amount of montmorillonite (Odell et al., 1960). The influences of organic matter content on the classification properties of a soft clay from Brazil are shown in Fig. 4.24. The maximum compacted densities and compressive strength as a function of organic content of both natural samples and mechanical mixtures of inorganic soils and peat are shown in Figs. 4.25 and 4.26, respectively. Both the compacted density and strength decrease significantly with increased organic content and the relationships for natural samples and the mixtures are about the same. Increased organic content also causes an increase in the optimum water content for compaction. The large increase in compressibility as a result of high organic content in clay is illustrated by the data in Fig. 4.27 for the clay whose classification properties are shown in Fig. 4.24. In Fig. 4.27 CR is the compression ratio, defined as CC /(1 ⫹ e0) expressed as a percentage, and C is the secondary compression ratio, defined as the change in void ratio per 10-fold increase in time after the end of primary consolidation. The effect of organic matter on the strength and stiffness of soils depends largely on whether the organic matter is decomposed or consists of fibers that can act as reinforcement. In the former case, both the undrained strength and the stiffness, or modulus, are usually reduced as a result of the higher water content and plasticity contributed by the organic matter. In the latter, the fibers can act as reinforcements, thereby increasing the strength.
4.10
CONCLUDING COMMENTS
Knowledge of soil composition is a useful indicator of the probable ranges of geotechnical properties and their variability and sensitivity to changes in environmental conditions. Although quantitative values of properties for analysis and design cannot be derived from compositional data alone, information on com-
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Figure 4.24 Influence of organic content on classification properties of Juturnaiba organic
clay, Brazil (from Coutinho and Lacerda, 1987).
position can be helpful for explaining unusual behavior, identification of expansive soils, selection of sampling and sample handling procedures, choice of soil stabilization methods, and prediction of probable future behavior. For example, if it is known that a soil to be used in earthwork construction contains either hydrated halloysite, organic matter, or expansive minerals, then airdrying laboratory samples prior to testing is likely to result in erroneous data on mechanical properties and must be avoided. If a soil contains a large amount of active clay minerals, then it can be anticipated that properties will be sensitive to changes in chemical environment. Compositional data on the soil and pore water are useful to estimate the dispersion and erosion potential of a soil (Chapter 8) and the risk of instability as a result of leaching and solutioning processes. In many cases, the effects of composition on behavior are reflected by information on particle size, shape, and size distribution of the coarse fraction, and the Atterberg limits of the fine fraction. On large projects and whenever unusual behavior is encountered, however, compositional data are valuable aids for interpretation of observations. Furthermore, the influences of compositional and structural factors are not always adequately reflected by the usual classification properties,
and more direct evaluation of their significance is needed. Examples of some soil types in which these factors may be especially important are decomposed granite, tropical residual soils, volcanic ash soils, collapsing soils, loess, and carbonate sand, as discussed in more detail by Mitchell and Coutinho (1991). QUESTIONS AND PROBLEMS
1. Show that the loosest and densest packings of uniform size particles give void ratios of 0.91 and 0.34, respectively. What is the coordination numbers (number of particle contacts for each particle) for each packing? 2. Explain why smaller particles are stronger than larger particles and why angular particles are more susceptible to breakage than round particles. 3. Using Figs. 4.8 and 4.11, show how the maximum and minimum void ratio changes with applied load as particles progressively break and the coefficient of uniformity Cu increases. Plot the data in e–log v space and discuss the result. 4. Using Eq. (4.8), derive a relationship between C (the percentage of clay) versus w (water content)
QUESTIONS AND PROBLEMS
107
Figure 4.27 Effect of organic content on the compressibility
properties of Juturnaiba organic clay, Brazil (from Coutinho and Lacerda, 1987). Figure 4.25 Maximum dry density as a function of organic
content for a natural soil and soil–peat mixtures (from Franklin et al., 1973). Reprinted with permission of ASCE.
for different values of eG (the void ratio of the granular phase). Discuss the sensitivity of eG on sand– clay mixture packing. What happens if silt is mixed instead of clay? 5. Using the reported undrained shear strengths at liquid limit and plastic limit, derive a relationship between the compression index Cc and plasticity index PI. Assume that the ratio of undrained shear strength to vertical effective stress, su / v, is 0.3. Compare the result with the data presented in Fig. 4.18.
Figure 4.26 Unconfined compressive strength as a function of organic content for a natural soil and soil–peat mixtures (from Franklin et al., 1973). Reprinted with permission of ASCE.
6. Assuming the thickness of adsorbed water layer is ˚ , estimate the amount of free water per gram 100 A of clay for the following conditions and discuss the results: a. Montmorillonite at its liquid limit with monovalent adsorbed cations (specific surface ⫽ 840 m2 /g of dry clay), liquid limit ⫽ 900 percent b. Montmorillonite at its plastic limit with monovalent adsorbed cations (specific surface ⫽ 840 m2 /g of dry clay), plastic limit ⫽ 100 percent c. Montmorillonite at its liquid limit with divalent adsorbed cations (specific surface ⫽ 50 m2 /g of dry clay), liquid limit ⫽ 100 percent d. Montmorillonite at its plastic limit with divalent adsorbed cations (specific surface ⫽ 50 m2 /g of dry clay), plastic limit ⫽ 50 percent
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e. Kaolinite at its liquid limit (specific surface ⫽ 15 m2 /g of dry clay), liquid limit ⫽ 70 percent f. Kaolinite at its plastic limit (specific surface ⫽ 15 m2 /g of dry clay), plastic limit ⫽ 30 percent 7. By examining the data presented in Figs. 4.24 and 4.29, discuss why organic clays exhibit larger compressibility compared to inorganic clays (see Fig. 4.18). 8. Assume that you are able to determine accurate, reliable quantitative values for all details of the mineralogical, chemical, and biological constituents of a given soil. All particle sizes, shapes, and distributions are also known. Speculate on your ability to predict the volume change, strength, and permeability properties of this soil over a range of water contents. Give reasons for why you would have low or high confidence in your predictions. 9. In light of what is known about the dependence of engineering properties on soil composition—both of the particles and of the other phases present in a
soil—discuss the strengths and weaknesses of the Unified Soil Classification System (USCS) in providing a clear and unambiguous picture of the probable behavior of the following soil types. In developing your answer, be specific concerning what is measured and the terms of reference used in the USCS and what is most important in determining any property being discussed. (Note: Some of the information in Chapter 8 may be useful in developing your answer to this question.) a. Clean sand b. Decomposed granite c. Calcareous sand d. Organic silt e. Expansive clay f. Glacial till g. Loess h. Dispersive clay i. Volcanic ash j. Estuarine mud
CHAPTER 5
Soil Fabric and Its Measurement
5.1
INTRODUCTION
Although soils are composed of discrete soil particles and particle groups, a soil mass is almost always treated as a continuum for engineering analysis and design. Nonetheless, the specific values of properties such as strength, permeability, and compressibility depend on the size and shape of the particles, their arrangements, and the forces between them. Thus, to understand a property requires knowledge of these factors. Furthermore, new theories of particulate mechanics and computational methods based on these theories are now becoming available. With these theories and methods it may ultimately be possible to predict the mechanical behavior of soil masses in terms of the characteristics of the particles themselves, although attaining this goal appears somewhat far off. Particle arrangements in soils remained largely unknown until suitable optical, X-ray diffraction, and electron microscope techniques made direct observations possible starting in the mid-1950s. Interest then centered mainly on clay particle arrangements and their relationships to mechanical properties. In the late 1960s, knowledge expanded rapidly, sparked by improved techniques of sample preparation and the development of the scanning electron microscope. In the early 1970s attention was directed also at particle arrangements in cohesionless soils. From this work came a realization that characterization of the properties of sands and gravels cannot be done in terms of density or relative density alone, as had previously been thought. Particle arrangements and stress history must be considered in these materials as well. In the 1970s and 1980s, micromechanics theories were developed that aimed to relate microstructure to macroscopic behavior. Various homogenization tech-
niques that incorporate small-scale features such as inhomogeneity and microfractures into continuum models became available (Mura, 1987; Nemat-Nasser and Hori, 1999). Increased computational speeds allowed simulation of an assembly of individual soil particles by modeling particle contact behavior, and this led to the development of numerical methods such as the discrete/distinct element method and contact dynamics (Cundall and Strack, 1979; Moreau, 1994; Cundall, 2001). In the early developments, simulations were limited to an assembly of two-dimensional circular disks. However, it is now possible to perform simulations with various three-dimensional particle shapes, complex contact models, and pore fluid interactions. These ‘‘digital’’-type studies offer possibilities for systematic investigation of soil fabric effects on mechanical properties in comparison to ‘‘laboratory’’type studies, which contain inherent errors associated with measuring soil fabrics of different specimens. Furthermore, mechanical responses under the stress paths that are difficult to apply in the laboratory can be investigated using distinct element methods. Other innovations in the past two decades have led to improved material measurement techniques and their interpretation using computers. These include the environmental scanning electron microscopy (ESEM), nanoindentation and probing, complex digital image analysis, magnetic resonance imaging (MRI), X-Ray tomography, and laser-aided tomography. Some of them have been used to characterize the microscopic properties of soils (Oda and Iwashita, 1999). The more established methods for studying and, where possible, quantifying the arrangements of particles, particle groups, and voids in different soils are described and illustrated in this chapter. Some ele109
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ments and applications of the newer methods are introduced in later chapters.
5.2 DEFINITIONS OF FABRICS AND FABRIC ELEMENTS
The term fabric refers to the arrangement of particles, particle groups, and pore spaces in a soil. The term structure is sometimes used interchangeably with fabric. It is preferable, however, to use structure to refer to the combined effects of fabric, composition, and interparticle forces. Methods for determination of soil fabric are described and examples of different fabric types are given in the following sections. The importance of soil fabric as a factor determining soil properties and behavior is discussed and illustrated in Chapter 8. In practice, special problems, unusual soils, and the need to ensure that measured properties properly reflect the in situ conditions may require application of these testing and interpretation methods. It is necessary to consider the size, the form, and the function of different fabric units and to keep in mind the scale at which the fabric is of interest. For example, a carefully compacted clay liner for an impoundment may have uniformly and closely packed particle groups within it, thus giving a material with very low hydraulic conductivity. If, however, the liner becomes broken into sections measuring a meter or so in each direction as a result of shrinkage cracking, then leakage through it will be dominated totally by flow through the cracks, and the small-scale fabric is unimportant. Similarly, the strength of intact, homogeneous soft clay will be influenced greatly by the particle arrangements on a microscale, whereas that of stiff fissured clay will be controlled by the properties along the fissures. Particle Associations in Clay Suspensions
Many soil deposits are formed by deposition from flowing or still water. Accordingly, knowledge of particle associations in suspensions is a good starting point for understanding how soil fabrics are formed and changed throughout the history of a soil. Clean sands and gravels are usually comprised of single grain arrangements, and these are discussed in Section 5.3. Particle associations in clay suspensions may be more complex. They can be described as follows and as illustrated in Fig. 5.1 (van Olphen, 1977): 1. Dispersed particles
No face-to-face association of clay
Figure 5.1 Modes of particle associations in clay suspensions and terminology. (a) Dispersed and deflocculated, (b) aggregated but deflocculated (face-to-face association, or parallel or oriented aggregation), (c) edge-to-face flocculated but dispersed, (d ) edge-to-edge flocculated but dispersed, (e) edge-to-face flocculated and aggregated, (ƒ ) edge-to-edge flocculated and aggregated, and (g) edge-to-face and edgeto-edge flocculated and aggregated. From An Introduction to Clay Colloid Chemistry, by H. van Olphen, 2nd ed., Copyright 1977 by John Wiley & Sons. Reprinted with permission from John Wiley & Sons.
2. Aggregated Face-to-face (FF) association of several clay particles 3. Flocculated Edge-to-edge (EE) or edge-to-face (EF) association of aggregates 4. Deflocculated No association between aggregates
DEFINITIONS OF FABRICS AND FABRIC ELEMENTS
111
Thicker and larger particles result from FF association. The EF and EE associations can produce cardhouse structures that are quite voluminous until compressed. The terms flocculated and aggregated are often used synonymously in a generic sense to refer to multiparticle assemblages, and the terms deflocculated and dispersed are used synonymously in a generic sense to refer to single particles or particle groups acting independently. Particle Associations in Soils
Particle associations in sediments, residual soils, and compacted clays assume a variety of forms; however, most of them are related to combinations of the configurations shown in Fig. 5.1 and reflect the difference in water content between a suspension and a denser soil mass. Fine-grained soils are almost always composed of multiparticle aggregates. Overall, three main groupings of fabric elements may be identified (Collins and McGown, 1974): 1. Elementary Particle Arrangements Single forms of particle interaction at the level of individual clay, silt, or sand particles 2. Particle Assemblages Units of particle organization having definable physical boundaries and a specific mechanical function, and which consist of one or more forms of the elementary particle arrangements 3. Pore Spaces Fluid and/or gas filled voids within the soil fabric Schematic illustrations of each of the fabric features in these three classes are shown in Figs. 5.2 through 5.4. Electron photomicrographs illustrating some of the features are shown in Fig. 5.5. Figure 5.6 shows the overall fabric of undisturbed Tucson silty clay, a freshwater alluvial deposit. The features shown in the figures are sufficient to describe most fabrics, although a number of additional terms have also been used to describe the same or similar features. Cardhouse is an edge-to-face arrangement forming an open fabric similar to the edge-to-face flocculated but dispersed arrangement of Fig. 5.1c (Goldschmidt, 1926). A domain (Aylmore and Quirk, 1960, 1962) or packet or book (Sloane and Kell, 1966) is an aggregate of parallel clay plates. An array of such fabrics is termed a turbostratic fabric and is similar to the interweaving bunches of Fig. 5.3h. An edge-to-face association of packets or books is termed a bookhouse and is similar to the arrangement of Fig. 5.1e. A cluster is a grouping of particles or aggregates into larger fabric
Figure 5.2 Schematic representation of elementary particle
arrangements (Collins and McGown, 1974). (a) Individual clay platelet interaction, (b) individual silt or sand particle interaction, (c) clay platelet group interaction, (d ) clothed silt or sand particle interaction, and (e) partly discernible particle interaction.
units (Olsen, 1962; Yong and Sheeran, 1973). In a fabric composed of groupings of clusters, it is useful to refer to intracluster and intercluster pore space and to cluster and total void ratios. The term ped (Brewer, 1964) has a similar meaning to cluster. Fabric Scale
The fabric of a soil may be viewed relative to three levels of scale. From smallest to largest they are: 1. Microfabric The microfabric consists of the regular aggregations of particles and the very small pores between them. Typical fabric units are up to a few tens of micrometers across. 2. Minifabric The minifabric contains the aggregations of the microfabric and the interassem-
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Figure 5.3 Schematic representations of particle assemblages (Collins and McGown, 1974).
(a) connectors, (b) connectors, (c) connectors, (d ) irregular aggregations by connector assemblages, (e) irregular aggregations in a honeycomb, (ƒ ) regular aggregation interacting with particle matrix, (g) interweaving bunches of clay, (h) interweaving bunches of clay with silt inclusions, (i) clay particle matrix, and ( j ) granular particle matrix.
blage pores between them. Minifabric units may be a few hundred micrometers in size. 3. Macrofabric The macrofabric may contain cracks, fissures, root holes, laminations, and the like that correspond to the transassemblage pores shown in Fig. 5.6.
and minifabrics. Time-dependent deformations such as creep and secondary compression are controlled most strongly by the mini- and microfabric.
Soil mechanical and flow properties depend on details of these three levels of fabric to varying degrees. For example, the hydraulic conductivity of a finegrained soil is almost totally dominated by the macro-
Sand and gravel particles are sufficiently large and bulky that they ordinarily behave as independent units. Attempts to describe the stress–deformation behavior of granular soils using particulate mechanics theories
5.3
SINGLE-GRAIN FABRICS
SINGLE-GRAIN FABRICS
113
Figure 5.4 Schematic representation of pore space types (Collins and McGown, 1974).
[e.g., Newland and Allely (1957), Rowe (1962, 1973), Horne (1965), Matsuoka (1974), Murayama (1983), Nemat-Nasser and Mehrabadi (1984), and Wan and Guo (2001)] have met with some success. The development of discrete element methods for numerical modeling of granular soils has greatly extended the potential for these methods as discussed in Section 5.1. These theories are based on elastic distortion of particles and the sliding and rolling of particles, usually assumed of spherical or disk shape. In real granular soils, the irregular particle shapes and distribution of sizes mean that packing is usually far from regular. Nonetheless, the theories and computations can provide valuable insights into behavior, and knowledge of the characteristics of ideal systems can be useful for interpreting data on real soils (see Chapter 11). Direct Observation of Cohesionless Soil Fabric
The study of the fabric of a cohesionless soil is usually done by optical means. The particles are large enough to be easily seen in the petrographic microscope. Thin sections can be made after impregnation of a sample by a suitable resin or plastic. Water-soluble materials are available for use in initially saturated sands. After the resin or plastic has hardened, thin sections can be prepared.
In some cases, sand samples can be dried prior to impregnation since sand fabrics are not generally affected by capillary stresses. A procedure for doing this to enable study of the fabrics produced in Monterey No. 0 sand by different methods of compaction is given by Mitchell et al. (1976). Packing of Equal-Sized Spheres
Regular packing of spheres of the same size provides insight into the maximum and minimum possible densities, porosities, and void ratios that are possible in single-grain fabrics. Five different possible packing arrangements are shown in Fig. 5.7, and properties of the arrangements shown are listed in Table 5.1. The range of possible porosities is from 25.95 to 47.64 percent, and the corresponding range of void ratios is from 0.35 to 0.91. Random packings of equal size spheres can be considered to be composed of clusters of simple packings, each present in an appropriate proportion to give the observed porosity. The relationship between coordination number N and porosity n in such systems is N ⫽ 26.486 ⫺ 10.726/n
(5.1)
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Figure 5.5 Scanning electron photomicrograph features of undisturbed soil fabrics (Collins
and McGown, 1974). (a) Partly discernible particle systems in Lydda silty clay, Israel (freshwater alluvial deposit); (b) grain–grain contacts in Ford silty loess, England (aeolian deposit); (c) connector assemblages in Breidmerkur silty till, Iceland (glacial ablation deposit); (d ) particle matrix assemblage in Immingham silty clay, England (estuarine deposit); (e) regular aggregation assemblage in Holon silty clay, Israel (consisting of elementary particle arrangements interacting with each other and silt) (freshwater alluvial deposit); ( ƒ ) interweaving bunch assemblage in Hurlford organic silty clay, Scotland (freshwater lacustrine deposit); and (g) irregular aggregation assemblage in Sundland silty clay, Norway (marine deposit).
Glass balls allowed to fall freely form an anisotropic assembly, with the balls tending to arrange themselves in chains (Kallstenius and Bergau, 1961). The number of balls per unit area in contact with a vertical plane can be different from the number in contact with a horizontal plane. The same behavior is observed for sand pluviated through air and water. Spontaneous segregation and stratification has been observed when granular mixtures of particles of two different predominant sizes are dumped into a pile (Makse et al., 1997; Fineberg, 1997). When a mixture of sizes is poured into a pile, the larger particles tend
to accumulate near the base. Makse and co-workers’ (1997) experiments produced the interesting additional result that if the large grains in a binary mixture have a greater angle of repose than the small grains, then the mixture stratifies into alternating layers of small and large grains. If the small grains have a larger angle of repose than the large grains, then segregation without stratification results. This type of behavior is relevant to such geoengineering problems as the stability of dumped mine waste piles, geological formations susceptible to static liquefaction, and the processing and transport of granular materials.
SINGLE-GRAIN FABRICS
115
Figure 5.5 (Continued )
Particle Packings in Granular Soils
Particle sizes in soil vary, and as a result, smaller particles can occupy pore spaces between larger particles. This results in a tendency toward higher densities and lower void ratios than for uniform spheres. On the other hand, irregular particle shapes produce a tendency toward lower densities and higher porosities and void ratios. The net result is that the range of porosities and void ratios in real soils with single-grain fabrics may not be much different from that for uniform
spheres shown by the values in Table 5.1, that is, porosity in the range of 26 to 48 percent and void ratio in the range of 0.35 to 0.91. This is illustrated by the data in Table 5.2. The lower values of porosity and density and higher unit weight for silty sand and gravel can be attributed to silt filling the large voids between the gravel particles. Many studies have shown that a given cohesionless soil can have different fabrics at the same void ratio or relative density. Characterization of this fabric can
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Figure 5.6 Overall microfabric in Tucson silty clay, United States (freshwater alluvial deposit) (Collins and McGown, 1974).
be done in terms of grain shape factors, grain orientations, and interparticle contact orientations (Lafeber, 1966; Oda, 1972a; Mahmood and Mitchell, 1974; Mitchell et al., 1976). More recently, application of image analysis techniques (Section 5.8) has led to better understanding and quantification of fabric features. The orientation of grains in a sand deposit can be described in terms of the inclination of the particle axes to a set of reference axes. For example, the orientation of the particle shown in Fig. 5.8 can be described by the angles and . In most studies, however, a thin section is studied to give the orientations of apparent long axes. The long axes of particles are referred to a single horizontal reference axis by an angle .1 The spatial orientation of the thin section it1
This method underestimates the value of L / W for elongate particles having their long axis out of the plane of the thin section.
self with respect to the sample and to the field deposit is also an essential part of the fabric description. Orientations of long axes for a large number of grains can be expressed by a histogram or rose diagram. A frequency histogram for a sand having a mean axial ratio equal to 1.65 and placed by tapping the side of a vertical, cylindrical mold is shown in Fig. 5.9. The orientation of each grain was assigned to one of the 15 intervals between 0 and 180. The V-section refers to a thin section from a vertical plane (oriented parallel to the cylinder axis). The H-section refers to orientations in the horizontal plane. Orientations of long axes in the vertical plane for two samples of well-graded crushed basalt [mean (length)/(width) ⫽ 1.64] are shown by the rose diagrams in Figs. 5.10 and 5.11. In this study, the orientations of at least 400 grains were measured for each sample, and the orientation of each was assigned to
SINGLE-GRAIN FABRICS
117
Figure 5.7 Ideal packings of uniform spheres: (a) simple cubic, (b) cubic tetrahedral, (c) tetragonal sphenoidal, (d ) pyramidal, and (e) tetrahedral.
Table 5.1
Properties of Ideal Packings of Uniformly Sized Spheres
Type of Packing
Coordination Number
Layer Spacing (R ⫽ radius)
Volume of Unit
Porosity (%)
Void Ratio
Simple cubic Cubical–tetrahedral Tetragonal–sphenoidal Pyramidal Tetrahedral
6 8 10 12 12
2R 2R 兹3R 兹2R 2兹2/3R
8R3 4兹3R3 6R3 4兹2R3 4兹2R3
47.64 39.54 30.19 25.95 25.95
0.91 0.65 0.43 0.35 0.35
one of the eighteen 10 intervals between 10 and 180. A completely random distribution would yield the dashed circles shown in the figures. There is a strong preferred orientation in the horizontal direction in the sample prepared by pouring (Fig. 5.10). Dynamic com-
paction, however, resulted in a more nearly random fabric (Fig. 5.11). Interparticle contact orientations and their distribution influence deformation and strength properties and anisotropy. These orientations can be described in
118
5
Table 5.2
SOIL FABRIC AND ITS MEASUREMENT
Maximum and Minimum Void Ratios, Porosities, and Unit Weights for Several Granular Soils
Void Ratio
Uniform spheres Standard Ottawa sand Clean uniform sand Uniform inorganic silt Silty sand Fine to coarse sand Micaceous sand Silty sand and gravel
Dry Unit Weight (kN m⫺3)
Porosity (%)
emax
emin
nmax
nmin
d min
d max
0.91 0.80 1.0 1.1 0.90 0.95 1.2 0.85
0.35 0.50 0.40 0.40 0.30 0.20 0.40 0.14
47.6 44 50 52 47 49 55 46
26 33 29 29 23 17 29 12
— 14.5 13.0 12.6 13.7 13.4 11.9 14.0
— 17.3 18.5 18.5 20.0 21.7 18.9 22.9
Modified from Lambe and Whitman (1969).
Figure 5.8 Three-dimensional orientation of a sand particle.
Figure 5.9 Frequency histograms of long particle axis orientations in two planes for a
uniform fine sand. Reprinted from Oda (1972a), with permission of The Japanese Society of SMFE.
CONTACT FORCE CHARACTERIZATION USING PHOTOELASTICITY
Figure 5.10 Particle orientation diagram for crushed basalt.
Vertical section through a sample prepared by pouring. Density is 1600 kg / m3 and the relative density is 62 percent.
Figure 5.11 Particle orientation diagram for crushed basalt.
Vertical section through a sample prepared by dynamic compaction. Density is 1840 kg / m3 and the relative density is 90 percent.
terms of a perpendicular Ni to the tangent plane at the point of contact. As most fabric characterization studies are done in a two-dimensional plane, and actual particle contact points rarely occur in the analyzed plane, measurement of contact normals can be prone to detection errors. The orientation of Ni is defined by angles and as shown in Fig. 5.12. A procedure for determination of the angular distributions of normals E(, ) is given by Oda (1972a). For a fabric with axial symmetry around the vertical axis, the function E(, ) is independent of , so the distribution of E() as a function of can be used to characterize the distribution of interparticle contact normals. Contact normal distributions for four sands deposited in water and compacted by tapping on the sides of their containers are shown in Fig. 5.13. The horizontal dashed lines represent the distributions for an isotropic fabric. In each case there is a greater proportion of contact plane normals in the near vertical direction; that is, there is a preferred orientation of contact planes near the horizontal.
119
Various methods to quantify long axis and contact distributions are available (Oda, 1972a; Fisher et al., 1987; Shih et al., 1998). The measured statistical distributions can be converted to a tensor that has the same dimensionality as stresses and strains (Satake, 1978; Kanatani, 1984; Oda et al., 1985; Kuo et al., 1998). One notable measure is the fabric tensor (Oda et al., 1982b) that characterizes the contact normal directions. This tensor and its evolution with plastic strains are used in development of micromechanics theories as well as continuum-based constitutive models (e.g., Tobita, 1989; Muhunthan et al., 1996; Yimsiri and Soga, 2000; Wan and Guo, 2001; Li and Dafalias, 2002). The mean value of the particle coordination number and its standard deviation are additional important fabric features in granular soils. The coordination number is the number of adjacent particles in contact with any given particle, and it is dependent on particle size, shape, size distribution, and void ratio. Relationships between the different orientation and packing parameters and mechanical properties of cohesionless soils are given in Chapter 8.
5.4 CONTACT FORCE CHARACTERIZATION USING PHOTOELASTICITY
Photoelasticity is a phenomenon in which light going through a photoelastic material (such as glass, rubber, and polymer) is polarized by the internal stresses of the material. The basic concept is that the speed of light depends on the direction of the plane of oscillation due to stress-induced optical anisotropy of the material. The planes of the limiting velocities coincide with the direction of the principal stresses. Utilizing this technique, the analysis of a photoelastically sensitive particle assembly under different boundary loading conditions gives information about the internal force structure through particle contacts. Averaging the contact forces over a number of particles in a region of interest gives the average effective stress. The downside of this technique is that actual soil particles cannot be used. However, the force information obtained from a transparent particulate assembly is useful for understanding how actual soil particle systems are likely to behave. Light propagates in a vacuum or in air at a speed C of 3 ⫻ 108 m/s. In other transparent materials, the speed V is lower and the ratio C/V is called the refractive index. In photoelastic materials, the change in refractive index in the i direction (ni) is proportional to the change in normal stress i in the same direction;
ni ⫽ Kso i, where Kso is the stress-optical material
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5
SOIL FABRIC AND ITS MEASUREMENT
Figure 5.12 Characterization of interparticle contact orientation.
constant. Hence, the velocity becomes direction dependent when the material is stressed in an anisotropic manner. Using a polarizer, the incoming light is polarized along a well-defined plane. If another polarizer is placed along the polarized light, complete extinction of the light can be achieved by making the filtering direction perpendicular to that of the first polarizer. When the polarized light goes through a stressed transparent material, two polarized lights are generated in the direction of principal strains (also the principal stress directions in an elastic material). The velocity of each component is inversely proportional to the different refractive indices of its particular plane, and there will be a relative retardation : ⫽ (nmax ⫺ nmin)l ⫽ Kso(max ⫺ min)l
Figure 5.13 Probability density functions of E() for (a) crushed chert, (b) Toyoura sand, (c) Soma sand, and (d ) Tochigi sand. The crushed chert and Toyoura sand are mainly rodlike or flat particles. Tochigi sand has spherical particles. Soma sand is intermediate in particle shape (from Oda, 1978). Reprinted by permission.
(5.2)
where l is the material thickness, nmax and nmin are the refractive indices of the two polarized lights, and max and min are the maximum and minimum principle stress, respectively. A polarizing analyzer can be placed along the polarized lights and it will transmit only one component of each of these waves. The polarized waves will interfere, and the light intensity of the polarized light coming out of the analyzer will be a function of and the angle between the analyzer and direction of prin-
MULTIGRAIN FABRICS
cipal strains. The light intensity becomes zero when the angle becomes zero and hence the principal strains directions can be determined. Optical filters known as quarter-wave plates can be added in the path of light propagation to produce circularly polarized light. By doing so, the image observed is not influenced by the direction of principal strains, but the intensity I viewed by a circular polariscope depends on by the following equation: I ⫽ I0 sin2( / )
(5.3)
where I0 is a constant and is the wavelength of the light. The light intensity becomes zero when ⫽ N (N ⫽ fringe order ⫽ 1, 2, ...), and hence the magnitude of principal stress difference at a given point can be evaluated from Eq. (5.3). Photoelastic images of a circular disk squeezed between two contacts are shown in Fig. 5.14 (Howell et al., 1999). The forces applied to particles are not equal. Instead, the spatial distribution of forces varies significantly due to random positions of the particles. Figure 5.15 shows images in an assemblage of pentagonal-shaped disks under (a) geostatic stresses by gravity and (b) both gravity loading and point loading at the center of the model (Geng et al., 2001). A chainlike force distribution, indicated by large light intensity paths, exists even under geostatic stress conditions. Strong force chains can develop in an assembly of pentagonalshaped polymer particles as shearing progresses (Geng
et al., 2003). A complicated network of force chains develops in the direction of the maximum principal stress. Microscopic investigations of the development of contact force distribution under different loading conditions provide physical insights to understand deformation behavior of granular materials. Further details are given in Chapter 11. Photoelasticity investigations can also be performed using three-dimensional particle assemblages. Although the actual material may be transparent, the particles become opaque due to refraction and reflection of light at the particle surfaces, which are often optically damaged. This adds difficulty in examining the contact force distributions. However, if the pores are filled with a fluid that has the same refractive index as the photoelastic material, the assembly becomes more transparent. Figure 5.16 shows the force distribution in crushed glass particles when a cone penetrometer is pushed into the material (Allersma, 1999). Again, development of a strong force network is evident.
5.5
MULTIGRAIN FABRICS
In Section 5.2, it was emphasized that single-grain fabrics are rare in soils containing clay-size particles. This is often true also for silts (particle sizes in the range of 2 to 74 m). For example, experiments have shown that silt-size quartz particles sedimented in water can
2
1.5
1
0.5
0 -1
-0.5
0 (a)
0.5
121
1 (b)
Figure 5.14 Photoelastic image of a circular disk squeezed between two contacts: (a) the-
oretically expected image and (b) actual image (from Howell et al., 1999).
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5
SOIL FABRIC AND ITS MEASUREMENT
Figure 5.16 Cone penetration test in photoelastic particles
(from Allersma, 1999).
Figure 5.15 Photoelastic images of pentagonal shape disk
assembly under (a) geostatic stresses by gravity and (b) both gravity loading and point loading at the center of the model (from Geng et al., 2001). Figure 5.17 Schematic diagram of a honeycomb fabric in
have a void ratio as large as 2.2. Quartz particles in this size range may be somewhat platy and can account for a part of this high void ratio as compared to an upper limit of about 1.0 for single-grain assemblages of bulky particles. However, silt-size particles form multigrain arrangements during slow sedimentation, because they are sufficiently small that their arrangements can be influenced by surface force interactions. An open honeycomb type of arrangement, as shown schematically in Fig. 5.17, is thought to exist in some silts (Terzaghi, 1925a). Loose fabrics such as this are metastable and subject to sudden collapse or liquefaction under the action of rapidly applied stresses. Multigrain fabrics of clays and clay–nonclay mixtures form because clay particle surface forces are significant relative to clay particle weight; clays can ad-
silt.
sorb on nonclay particle surfaces, and clay surfaces are often chemically reactive. In addition, clay particle groups in many soils may be remnants of a preexisting rock from which the soil was derived.
5.6
VOIDS AND THEIR DISTRIBUTION
Different types of pores are illustrated in Figs. 5.4 and 5.6. The pore sizes and their distribution complement the particle and particle group sizes and their distribution. Emphasis is usually placed on the solid phase rather than the liquid and gas phases when describing
SAMPLE ACQUISITION AND PREPARATION FOR FABRIC ANALYSIS
properties and behavior. However, the pores and voids determine the fluid and gas conductivity properties that, in turn, control such important processes as the rate of fluid and chemical transport, generation of excess pore pressures during deformation, consolidation rate, the ease and rate of drainage, capillary pressure development, and the potential for liquefaction under dynamic loading. Methods for determining and characterizing pore sizes and their distribution are described in Section 5.9.
5.7 SAMPLE ACQUISITION AND PREPARATION FOR FABRIC ANALYSIS
Obtaining representative soil samples with minimal disturbance is essential if reliable measurements of engineering properties are to be made. The same considerations apply in the selection and preparation of samples for the study of fabric. Accordingly, the sampling and preparation phases of fabric study are critical, and special methods are many times needed. Proven methods for reliable determination of fabric can also be used for evaluation of the effects of different sampling procedures used in engineering practice, although there does not appear to be much record of this having been done. Both direct and indirect methods are used to study the fabric and fabric features of soils, as listed in Table 5.3. An illustrative schematic diagram prepared by R. N. Yong that summarizes methods for analysis of soil composition and fabric using various parts of the electromagnetic spectrum is shown in Fig. 5.18. In interpreting the results from any of these methods, judgment is required to be sure that the conclusions pertain to properties and behavior of interest. For example, discontinuities, fractures, and anisotropy on a macroscale can override the influences of microfabric details. Of the methods listed in Table 5.3, optical and electron microscopy, X-ray diffraction, and pore size distribution offer the advantage of providing direct (usually) unambiguous information about specific fabric features, provided the samples are representative and the sample preparation procedures have not destroyed the original fabric. On the other hand, these techniques are limited to small samples, and they are destructive of the samples studied. The other techniques are nondestructive, at least in principle, and can be used for the study of soil fabric in situ and for the study of changes in fabric that accompany compression, shear, and fluid flow. However, with most of these methods interpretation is seldom straightforward or unambiguous. The use of several methods of fabric anal-
123
ysis may be appropriate in some cases in order to obtain information of more than one type or level of detail. Sample Preparation for Fabric Analysis
Acoustical, dielectric, thermal, and magnetic measurements can be made directly on samples in their undisturbed, wet state. Optical and electron microscopy, X-ray diffraction, and porosimetry require that the pore fluid be removed, replaced, or frozen. To do this without disturbance of the original fabric is difficult, and in most cases there is no way to determine how much disturbance there may have been. Pore Fluid Removal Air drying without significant disruption of the natural fabric may be possible for soils that do not undergo much shrinkage. For soft samples at high water content, oven drying may cause less fabric change than air drying, evidently because the longer time required for air drying allows for greater particle rearrangement (Tovey and Wong, 1973). On the other hand, the stresses induced during oven drying may result in some particle breakage. Water removal by drying at the critical point has also been used. If the temperature and pressure of the sample are raised above the critical values, which for water are 374C and 22.5 MPa, respectively, the liquid and vapor phases are indistinguishable. The pore water can then be distilled off without the presence of air–water interfaces that can lead to shrinkage. The high temperature and pressure may change the clay particles, however. To avoid this, replacement by carbon dioxide has been used. The critical temperature and pressure of carbon dioxide are 31.1C and 7.19 MPa, respectively. The procedure requires prior impregnation of the sample with acetone, which may cause swelling in partly saturated and expansive soils (Tovey and Wong, 1973). Both critical point and freeze-drying cause less sample disturbance and shrinkage than do air or oven drying, but they are more difficult and time consuming. Freeze-drying can be used for removal of water. Sublimation of the ice in a soil that has been rapidly frozen avoids the problem of air–water interfaces and shrinkage that accompany water removal by drying. Sample size must be small, usually thinner than about 3 mm, if disruption due to nonuniform freezing is to be avoided. Quick freezing is best done in a liquid that has been cooled to its melting point in liquid nitrogen, such as isopentane at ⫺160C or Freon 22 at ⫺145C. This avoids gaseous bubbling caused by direct immersion in liquid nitrogen at ⫺196C (Delage et al., 1982). The freezing temperature should be less than ⫺130C to avoid formation of crystalline ice. Sublimation of
124
Polarized Light Micrograph
Replica Transmission Electron Micrograph or Diffraction Pattern
Scanning Electron Micrograph
Figure 5.18 Methods for examining mineralogy, fabric, and structure of soils using parts of
the electromagnetic spectrum (prepared by R. N. Yong, McGill University Soil Mechanics Laboratory).
125
126
5
SOIL FABRIC AND ITS MEASUREMENT
Table 5.3
Techniques for Study of Soil Fabric
Method
Basis
Optical microscope (polarizing)
Direct observation of fracture surfaces of thin sections
Electron microscope
Direct observation of particles or fracture surfaces through soil sample (SEM) observation of surface replicas (TEM)
X-ray diffraction
Groups of parallel clay plates produce stronger diffraction than randomly oriented plates (1) Forced intrusion of a nonwetting fluid (usually mercury) (2) Capillary condensation Particle arrangement, density, and stress influences wave velocity Variation of dielectric constant and conductivity with frequency
Pore size distribution
Wave propagation
Dielectric dispersion and electrical conductivity Thermal conductivity
Magnetic susceptibility
Mechanical Properties strength modulus permeability compressibility shrinkage and swell
Particle orientations and density influence thermal conductivity Variation in magnetic susceptibility with change of sample orientation relative to magnetic field Properties reflect influences of fabric; see Chapter 11
Scale of Observations and Features Discernable Individual particles of silt size and larger, clay particle groups, preferred orientation of clay, homogeneity on a millimeter scale or larger, large pores, shear zones Useful upper limit of magnification about 300⫻ ˚ ; large Resolution to about 100 A depth of field with SEM; direct observation of particles; particle groups and pore space; details of microfabric; environmental SEM can be used to observe specimens containing water and gas Orientation in zones several square millimeters in area and several micrometers thick; best in single mineral clays (1) Pores in range from ⫺0.01 to ⬎10 m (2) 0.1 m maximum Anisotropy; measures fabric averaged over a volume equal to sample size Assessment of anisotropy, flocculation and deflocculation, and properties; measures fabric averaged over a volume equal to sample size Anisotropy; measures fabric averaged over a volume equal to sample size Anisotropy; measures fabric averaged over a volume equal to sample size Fabric averaged over a volume equal to sample size; anisotropy; macrofabric features in some cases
METHODS FOR FABRIC STUDY
the water is then done at temperatures between ⫺50 and ⫺100C rather than at the initial freezing temperature to increase the rate of water vapor removal. At temperatures less than ⫺100C the vapor pressure of the ice, about 10⫺5 torr, may be less than the capability of the vacuum system. The freezing process may produce fabric changes in very high water content systems such as a 10 percent by weight slurry of bentonite in water (Kumai, 1979). However, with more typical saturated clays at consistencies likely to be encountered in geotechnical investigations, the effects of freeze-drying on the fabric are small. Additional considerations in sample preparation by freeze-drying are given by Tovey and Wong (1973) and Gillott (1976). Pore Fluid Replacement If thin sections are required, as for optical microscopy or when drying shrinkage must be minimized, but the presence of a material in pore spaces is not objectionable, replacement of the pore water may be necessary. Various resins and plastics have been used for this purpose. High-molecular-weight ethylene glycol such as Carbowax 6000 is miscible with water in all proportions and has been used for many studies. Carbowax 6000 melts at 55C but is solid at lower temperatures. Impregnated samples are prepared by immersing an undisturbed cube sample, 10 to 20 mm on a side, in melted Carbowax at 60 to 65C. The top surface of the specimen should be left exposed to vapor for the first day of immersion to allow escape of trapped gases and prevent specimen rupture. The wax should be changed after 2 or 3 days to ensure water-free wax in the sample pores. Replacement of all water by the Carbowax is usually complete in a few days. After removal from the liquid wax and cooling, the sample is ready for sectioning. Thin sections are prepared by grinding using emery cloth or abrasive powders and standard thin-section techniques. However, heat, water, or other watersoluble liquids cannot be used at any stage of the grinding or section mounting process. Measurements by X-ray diffraction have shown that Carbowax replacement of water has essentially no effect on the fabric of wet kaolinite (Martin, 1966). Gelatins or water-soluble resins may be used in lieu of Carbowax, or the sample may be impregnated with methanol or acetone before replacement with resins or plastics. Further details on resin impregnation are given by Smart and Tovey (1982) and Jang et al. (1999). Preparation of Surfaces for Study
Surfaces chosen for study should reflect the original fabric of the soil and not the preparation method.
127
Grinding or cutting air-dried and Carbowax-treated samples may result in substantial particle rearrangement at the surface, thus making them of little value for study by the electron microscope. To overcome this problem, successive peels from the surface of a dried specimen using adhesive tape can be used to expose the original fabric. Alternatively, the surface may be coated with a resin solution that partly penetrates the sample. After hardening, the resin is peeled away revealing an undisturbed fabric. A comparison of surfaces before and after this procedure is shown in Fig. 5.19. The disturbed zone at the surface of Carbowaxtreated samples extends to a maximum depth of about 1 m in kaolinite (Barden and Sides, 1971). As thin sections used for polarizing microscope study are of the order of 30 m thick, this disturbed zone is of little consequence. It is also insignificant for X-ray diffraction studies. Fracture surfaces in dried specimens are sometimes taken as representative of the undisturbed fabric. Additional preparation, such as gentle blowing of the surface or peeling is needed following fracture because (1) there may be loose particles on the surface, and (2) a fracture surface may be more representative of a plane of weakness than of the material as a whole. An alternative approach to avoid these problems is to fracture a frozen wet specimen as described by Delage et al. (1982). The method of sample preparation should be selected after consideration of scale of fabric features of interest, method of observation to be used, and the soil type and state as regards water content, strength, disturbance, and so forth. With these factors in mind, the probable effects of the preparation methods on the fabric can be assessed.
5.8
METHODS FOR FABRIC STUDY
Once suitable samples and surfaces have been prepared, direct study of different fabric features is possible using one or more of several methods, as indicated in Fig. 5.18. Details of these methods are discussed in this section as well as the advantages and limitations of each. Polarizing Microscope
Individual particles of silt and sand can be seen using petrographic and binocular microscopes, and the sizes, orientations, and distributions of particles and pore spaces can be described systematically. Thin sections or polished surfaces can be used for two-dimensional
128
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SOIL FABRIC AND ITS MEASUREMENT
Figure 5.19 Effect of surface preparation on fabric seen by the scanning electron microscope (a) before peeling and (b) after one peeling, ⫻5000 (from Tovey and Wong, 1973).
analyses. Three-dimensional analyses require a series of parallel cross sections. Many petrographic techniques and special treatments are available to aid in identification of features of interest (e.g., Stoopes, 2003). Rose diagrams can be used to represent two-dimensional planar patterns. Three-dimensional patterns can be represented using stereo net projections. As an illustration of twodimensional representation, Fig. 5.20 shows the pore pattern in a section of a stony desert tableland soil from near Woomera, Australia, which suggests some degree
of preferred orientation. Rose diagrams are shown in Fig. 5.21 of both pore orientation (white figure) and silt and sand grain orientation (black figure). Considerable preferred orientation of both pores and particles is evident. It is not usually possible to see individual clay particles with the polarizing microscope because of limitations in resolving power and depth of field. Practical resolution is to a few micrometers using magnifications up to about 300 times. If, however, clay plates are aligned parallel to each other in a group, then they
Figure 5.20 Pore pattern of a section from a stony tableland soil from Woomera, Australia.
Pores in white, clay matrix in gray, and silt sand grains in black (from Lafeber, 1965). Reprinted with permission of AJSR.
METHODS FOR FABRIC STUDY
129
s2 L1
s1 R
R
s1
L1
s2 Figure 5.21 Distribution of elongated pores (white figure) and of elongated skeleton grains (black figure) in different directions for the pattern in Fig. 5.20. The broken circle represents an even distribution of lengths over all directions. s1 and s2 are the major maxima of the elongated pores, L1 is the major maximum of elongated grains, and R is the reference direction (from Lafeber, 1965). Reprinted with permission of AJSR.
behave optically as one large particle with definite optical properties. The optical axes and the crystallographic axes of the clay minerals are almost coincident. For plate-shaped particles, the refractive indices in the a and b directions are approximately equal, but different from that in the c-axis direction. The difference in refractive indices along different optical axes of a crystal determines the optical property termed the birefringence. If a group of parallel particles is viewed in plane polarized light looking down the c axis, a uniform field is seen as the group is rotated around the c axis. If the same particle group is viewed with the c axis normal to the direction of the light, no light is transmitted when the basal planes are parallel to the direction of polarization, and a maximum is transmitted when they are at 45 to it. Thus there are four positions of extinction and illumination when the sample is viewed using light passed through crossed nicols and the microscope stage is rotated through 360. For rod-shaped particles in parallel orientation, a uniform field is observed looking down the long axis, whereas illumination and extinction are seen when looking normal to this axis. Use of a tint plate in the microscope is often helpful because the resulting retardation of light waves results in distinct different colors for extinction and illumination. If particle orientation is less than perfect or if the caxis direction of a group of parallel plates is other than normal to the direction of light, then the minimum intensity is finite and the maximum intensity is less than for perfect orientation. The ratio of minimum intensity Imin to maximum intensity Imax is called the birefringence ratio . Photometric measurements of the birefringence ratio can be used to quantify clay particle orientation (Wu, 1960; Morgenstern and Tchalenko, 1967a). Although there may be difficulties in photometric methods when dealing with other than monomineral materials with
singular orientations of particles (Lafeber, 1968), the semiquantitative scale proposed by Morgenstern and Tchalenko (1967c) given in Table 5.4 is useful. A vertical section taken through varved clay is shown in Fig. 5.22. The upper half shows the winterdeposited clay varve and the lower half the summerdeposited silt varve. Strong preferred orientation of the
Table 5.4 Orientation Scale for Clay Aggregates Viewed in Plane Polarized Light Birefringence Ratio
Particle Parallelism
1.0 1.0–0.9 0.9–0.5 0.5–0.1 0
Random Slight Medium Strong Perfect
From Morgenstern and Tchalenko (1967c).
Figure 5.22 Thin section of varved clay under polarized
light (courtesy of Division of Building Research, National Research Council, Canada).
130
5
SOIL FABRIC AND ITS MEASUREMENT
clay is evident by comparison of illumination on the left and extinction on the right. Were the clay plates oriented randomly throughout, the thin section would have had the same appearance at both orientations. The upper portion of the silt varve is also seen to contain some zones of well-oriented clay. A series of planar pores is also visible. These pores probably were developed during impregnation of the sample or preparation of the thin section. Optical microscope study of fabric provides a view of some features that are too small to be seen by eye, too large to be appreciated using an electron microscope, but important to understanding soil behavior. Some of these features include distributions of silt and sand grains, silt and sand particle coatings, homogeneity of fabric and texture, discontinuities of various types, and shear planes (e.g., Mitchell, 1956; Morgenstern and Tchalenko, 1967b, 1967c; McKyes and Yong, 1971; Oda and Kazama, 1998). A thin section from a shear zone through a soft silty clay at the site of a foundation failure under an embankment at Fiddler’s Ferry on the floodplain of the Mersey River, England, is shown in Fig. 5.23a. Details of the shear zone deduced from the photomicrograph are shown in Fig. 5.23b. Electron Microscope
The electron microscope can reveal clay particles and their arrangements directly. The practical limit of res-
Photograph of Fiddler’s Ferry shear zone (from Morgenstern and Tchalenko, 1967c).
Figure 5.23a
Figure 5.23b Details of Fiddler’s Ferry shear zone (Morgenstern and Tchalenko, 1967c). F is a fragment of ambient material; the hatched areas indicate the shear matrix where the birefringence ratio ⫽ 0.45; and the direction of hatching is the average particle orientation over the stippled areas where ⫽ 1.00.
olution of the transmission electron microscope (TEM) ˚ , and atomic planes can be seen. The is less than 10 A practical limit of the scanning electron microscope ˚ ; however, lesser magnification (SEM) is about 100 A is sufficient to resolve details of clay particles and other very small soil constituents. The major advantages of the SEM relative to the TEM are the much greater depth of field, the wide, continuous range of possible magnifications (about 20⫻ to 20,000⫻), and the ability to study surfaces directly. Either surface replicas or ultra-thin sections are needed for the TEM. The main advantage of the TEM relative to the SEM is its higher limit of resolution. Historical developments along with its application to clay minerals and aggregates examination are given by McHardy and Birnie (1987) for SEM and Nadeau and Tait (1987) for TEM. Both types of electron microscopy require an evacuated sample chamber (1 ⫻ 10⫺5 torr), so wet soils cannot be studied directly unless they are housed in a special chamber. Cold stages are available, so frozen materials may be studied. It is usually necessary to coat SEM sample surfaces with a conducting film to prevent surface charging and loss of resolution. Gold
METHODS FOR FABRIC STUDY
placed in a very thin layer (20 to 30 nm) in a vacuum evaporator is often used. The main difficulty in the electron microscope study of fabric is the preparation of sample surfaces, surface replicas, or ultra-thin sections that retain the undisturbed fabric of the original soil. In general, the higher the water content and void ratio of the original sample, the greater the likelihood of disturbance. Soils containing expansive clay minerals may undergo changes in microfabric as a result of removal of interlayer water, or there may be shrinkage. The dry–fracture–peel technique and the freeze–fracture technique appear the best of the available methods for obtaining representative sample surfaces. That careful techniques are successful in preserving delicate fabrics is evidenced by Fig. 5.24, which shows the microstructures of six artificial clay sediments (Osipov and Sokolov, 1978). These samples were obtained by gradual sedimentation of clay particles ⬍1 m in
131
size from a 1 percent suspension followed by freezedrying. When sedimented in distilled water, the sediment porosities were kaolinite 96 percent, illite 90 percent, and montmorillonite 83 percent. When sedimented in electrolyte solution, the porosities were 97, 98 and 99 percent, respectively. The photomicrographs reflect the very high porosities of all samples and that the flocculating effect of the salt solution had a significant effect on the initial microfabric. Undisturbed silt microfabrics are shown in Fig. 5.25. These silty clay microfabrics are formed under conditions of uninterrupted sediment accumulation and have quite high porosities (60 to 90 percent). Sediments of this type are very compressible and weak. Progressive collapse of microfabric of a sensitive Champlain clay with increasing vertical loading is shown in Fig. 5.26 (Delage and Lefebvre, 1984). The preconsolidation pressure of the clay was 54 kPa. The SEM photos were taken along the vertical plane and the distribution of macropores at each loading stage was derived from the photos as shown in the figure. Aggregate structure is apparent at the intact stage below the preconsolidation pressure. At a loading of 124
Figure 5.24 Microfabrics of artificial clay sediments. Scale bar ⫽ 2 m for all micrographs: (a) kaolinite in distilled
water, (b) kaolinite in 0.5 N NaCl, (c) illite in distilled water, (d ) illite in 0.5 M NaCl, (e) montmorillonite in distilled water, and ( ƒ) montmorillonite in 0.5 NaCl (from Osipov and Sokolov, 1978).
Figure 5.25 Honeycomb microfabrics: (a) recent lacustrine
silt from Lake Vozhe and (b) recent marine silt from the Black Sea (from Sergeyev et al., 1980). Reprinted with permission from Blackwell Scientific Publications, Ltd.
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SOIL FABRIC AND ITS MEASUREMENT
(a)
10 μm intact
(b)
(c)
10 μm 124 kPa Pores
10 μm 421kPa Solid particles
(d)
10 μm 1452 kPa Voids due to pulling out of particles
Figure 5.26 SEM photographs of a sensitive Champlain clay under consolidation at (a) intact state, (b) 124 kPa, (c) 421 kPa, and (d ) 1452 kPa. The preconsolidation pressure of the clay is 54 kPa (from Delage and Lefebvre, 1984).
kPa, the collapse of macropores in the horizontal direction is observed. Aggregates are also aligning in the horizontal direction. As the loading increases (421 and 1452 kPa), aggregates become less apparent by the complete collapse of macropores and the particles are aligning in the horizontal direction. Although the field of view at high magnification is limited, mosaics of photomicrographs may be prepared to show larger fabric features. Such a composite is shown in Fig. 5.6. Accessories are available for the SEM to enable determination of the elemental composition of specific materials under observation (McHardy and Birnie, 1987; Bain et al., 1994). Further details on the techniques of electron microscopy used to examine the structures of soils can be found in Smart and Tovey (1981, 1982). Environmental SEM
Conventional SEM samples have to be dry, vacuum compatible, and electrically conductive. To examine liquid and hydrated samples, the pressure has to be at least 612 Pa, the minimum vapor pressure required to maintain liquid water at 0C. An environmental scanning electron microscope (ESEM) allows wet, natural, and nonconductive samples to be examined by having the specimen chamber at higher pressure separated from the high-vacuum electron optical regions in
which the SEM electromagnetic lens must exist. This pressure differentiation is achieved by a special device called a pressure-limiting aperture. Examination of samples can be done under a range of gaseous environments (H2O, CO2, N2, etc.), relative humidities (0 to 100 percent), pressures (up to 6.7 kPa), and temperatures (⫺180 to 1500C). ESEM images are taken using an electrical current detector that collects and processes signals generated by ionized gas molecules (usually water vapour) in the specimen chamber. Secondary electrons emitted by the sample collide with gas molecules, which then cause ionization of the gas, creating positive ions and additional secondary electrons. The cascading amplification of the signal from the original secondary electrons enables the secondary electron detector to create an image. The positive ions are attracted to the negatively charged sample surface and suppress the charging artefacts. This charge suppression allows imaging of nonconductive samples. A significant feature of ESEM is its ability to observe liquids inside the samples. The rate of sublimation and condensation of water can be controlled by manipulating the pressure and temperature. Figure 5.27 is an ESEM image of a sample containing illite clays (left side) and quartz grains (right side). Water droplets were placed on the sample by condensation of distilled water present as a gaseous phase in the testing cham-
METHODS FOR FABRIC STUDY
133
water is added to the specimen, the bentonite swells to completely fill the macropores. Image Analysis
Figure 5.27 ESEM image of illite clay (left side) and quartz
grains (right side). Water droplets placed on the samples show that the quartz surface is hydrophilic and the illite surface is hydrophobic (from Buckman et al., 2000).
ber. The photo shows the wettability of fluids on soil minerals. Spherical water droplets are observed on the clay surface, indicating that this illite is hydrophobic. Quartz sand, on the other hand, is hydrophilic as low domed droplets of water are formed on the surface. As pressure and temperature can be varied in the specimen chamber, the ESEM allows studies of dynamic changes in samples such as wetting, drying, absorption, melting, corrosion, and crystallization. Figure 5.28 shows ESEM images of the swelling of bentonite in a sand–bentonite mixture (Komine and Ogata, 2004). Initially, the bentonite particles are attached to the sand grains and macropores can be observed. As
Image analyzers can be used with both optical and electron microscopes for quantification of fabric features. Digital imaging cameras can resolve reflected or transmitted light from the sample into pixels. The amount of light per pixel is then converted into an analog signal. After the entire image is acquired, the analog signal for each pixel is converted to digital form for analysis, manipulation, and storage. Image analysis offers greatly increased potential for quantitative description of different fabric elements. Details of the method are beyond the scope of this book. Examples of image analysis of soil specimens are given by Frost and Wright (1993), Tovey and Hounslow (1995), and Frost and McNeil (1998). X-ray Diffraction
As discussed in Section 3.22, crystallographic planes in minerals refract X-rays at an intensity that depends on (1) the amount of mineral in the volume of soil irradiated and (2) the proportion of the mineral grains that are properly oriented. For clay minerals, parallel orientation of plates enhances the basal reflections but decreases the intensity of reflection from lattice planes oriented in other directions. The intensity of (001) reflections provides a measure of clay particle orientation. The relative heights of basal peaks for different samples of the same material give a measure of particle
Figure 5.28 ESEM images showing swelling process of bentonite clay in a sand–bentonite mixture (from Komine and Ogata, 2004).
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5
SOIL FABRIC AND ITS MEASUREMENT
orientation differences. A fabric Index (FI) based on areas of diffraction peaks is defined as (Gillott, 1970): FI ⫽ V/(P ⫹ V)
(5.4)
where V is the area of the basal peak in a section cut perpendicular to the orientation plane, and P is the area of the same peak from a section cut parallel to the plane of parallel orientation of particles. The value of FI ranges from zero for perfect preferred orientation to 0.5 for perfectly random orientation. A similar procedure that retains the concept of peak areas, but does not require their exact measurement, is given by Yoshinaka and Kazama (1973). The peak ratio (PR), defined as the ratio of the (002) reflection to that of the (020) reflection, can also be used as a measure of orientation. The PR has the advantages of being independent of the particle concentration within the total soil and of minimizing the effects of mechanical and instrumentation variables (Martin, 1966). The PR of kaolinite with completely random particle orientations is about 2.0. For maximum parallel orientation the PR is about 200. The reasons for choosing the (002) and (020) reflections are that (1) they are strong and (2) the corresponding 2 values are not too far apart, thus ensuring that about the same sample volume will be irradiated for determination of both peaks. X-ray diffraction methods had the advantage of quantification of data in a way that was not possible with optical and electron microscope methods. However, the development of image analysis techniques for use with the latter has largely overcome this problem. X-ray methods have some disadvantages, including (1) difficult interpretation in multimineral soils, (2) the data are weighted in favor of the fabric nearest the sample surface, and (3) the soil volume irradiated will usually include both microfabrics and minifabrics, and the results will average rather than distinguish them. Thus, X-ray diffraction is best suited for fabric analysis of single mineral clays in which particle orientations over regions the size of the X-ray beam (a few millimeters) are of interest or in conjunction with other methods that can provide detail on the character of the microfabric. Transmission X-Ray and Computed Tomography Scan
By detecting differences in electron density in materials, transmission X-ray is a useful and nondestructive method for the study of soil stratigraphy, homogeneity, and macrofabric. X-radiographs of samples while still in sample tubes provide information about the above
features as well as on texture and disturbance (Kenney and Chan, 1972). A number of laboratories routinely X-ray sample tubes prior to selection of samples for removal and testing for determination of deformation and strength properties. The procedure is simple, rapid, and inexpensive (apart from the initial cost of the equipment). X-radiography is also useful for the study of deformation patterns in soils. Lead shot is placed in regular patterns in samples or in blocks of soil used for model tests. The positions of the shot are determined at various stages throughout a test by comparison of successive radiographs. The results can be used to locate shear zones and compute strains and their variation throughout the material. X-ray computed tomography (CT) allows construction of a three-dimensional density profile inside a material by assembling X-ray radiographic twodimensional images taken at different angles. The resolution of a CT scanner is determined by the dimensions of a source and a detector as well as their positions in relation to the test specimen. The technique has been used to examine the locations of shear zones within a specimen as local dilation inside the shear band gives low electron density (Desrues et al., 1996; Otani et al., 2000; Alshibi et al., 2003; Otani and Obara, 2004). Figure 5.29 shows the locations of shear zones in cylindrical sand specimens that were sheared to different axial strains in triaxial compression. The specimens showed strain-softening behavior and exhibited uniform bulging with no apparent single or multiple shear bands. The CT images were taken at strains greater than the peak axial strain of approximately 2 percent. No apparent shear zones are observed at an axial strain of 4.6 percent, indicating that the strain softening was due to dilation throughout the specimens. As the axial strain increased, however, shear zones with large local void ratio appeared inside the specimens. The following two shear zone structures are apparent (Desrues et al., 1996; Alshibi et al., 2003): 1. Cone-Shaped Shear Zone The images of the horizontal plane show black circles appearing at the center, and they become smaller in diameter from the boundary toward the middle height of the specimen (Fig. 5.29a). This suggests a coneshaped shear zone from the midheight to the boundary. The tip of the cone is at the midheight and the symmetry exists at the central axis of the specimen. 2. Conjugate-Inclined Shear Zones The horizontally sliced images show radially oriented lines generating outward from the circle (Fig. 5.29a). These are the inclined lines in the vertically
PORE SIZE DISTRIBUTION ANALYSIS
135
Figure 5.29 CT scans of a dense sand specimen under triaxial compression: (a) Horizontal slice at the midheight, (b) vertical slice, and (c) 3D image (from Alshibi et al., 2003).
sliced images (Fig. 5.29b). Close examination of these lines reveal that there are several pairs of conjugate shear bands at two different inclined angles as shown in Fig. 5.29c.
determinations and from image analysis of thin sections and SEM pictures.
Further details of shear bands are given in Chapter 11. Other noninvasive techniques reported to observe particle packing arrangements include nuclear magnetic resonance imaging (Ehrichs et al., 1995; Ng and Wang, 2001) and laser-aided tomography (Matsushima et al., 2002).
Volumetric pore size distributions can be determined using forced intrusion of a nonwetting fluid, a capillary condensation method based on interpretation of adsorption and desorption isotherms, and by removal of water by suction or air pressure. The maximum pore size that can be measured using the capillary condensation method is about 0.1 m. With the possible exception of intraaggregate pores most soil pores are larger, so this method is of limited usefulness. The mercury intrusion method, however, is useful for measurement of pore sizes from about 0.01 m to several tens of micrometers. The basis of the method is that a nonwetting fluid (fluid-to-solid contact angle ⬎90) will not enter pores without application of
5.9
PORE SIZE DISTRIBUTION ANALYSIS
The shape and distribution of voids are one of the three most important measures of fabric, along with contact distributions and particle orientations. Pore information can be obtained by volumetric pore size distribution
Volumetric Pore Size Distribution Determinations
136
5
SOIL FABRIC AND ITS MEASUREMENT
pressure. For pores of cylindrical shape, the capillary pressure equation applies, and 4 cos d⫽⫺ p
(5.5)
where d is the diameter of pore intruded, is the surface tension of the intruding fluid, is the contact angle, and p is the applied pressure. The volume of mercury intruded into an evacuated dry sample that is about 1 g in weight is measured using successively higher pressures. The total volume of mercury intruded at any pressure gives the total volume of pores with an equivalent diameter larger than that corresponding to that pressure. The surface tension of mercury is 4.84 ⫻ 10⫺4 N/mm at 25C. The contact angle is about 140; measurements by Diamond (1970) gave 139 for montmorillonite and 147 for other clay mineral types. Limitations of the mercury intrusion method are: 1. Pores must be dry initially. Freeze-dried samples are often used to minimize the effect of volume change upon drying. 2. Isolated pores are not measured. 3. Pores accessible only through smaller pores will not be measured until the smaller pores are penetrated.
4. The apparatus may not have the capacity to penetrate the smallest pores in a sample. In spite of these limitations, pore size distributions determined by the mercury intrusion method can provide useful information about factors influencing fabric and fabric–property interrelationships. An example is shown in Fig. 5.30. The data are in the form of cumulative volumes of pore space intruded for a pore of the indicated size and larger. It may be seen that the pores cover a range of sizes and that changes in density and sample preparation method result in changes in pore size distributions. Pore size distributions may be estimated for sands, which are too coarse for mercury intrusion, by determination of the pore water volume that is drained either by application of suction to the sample or by application of air pressure to the pore water. Equation (5.5) applies. The surface tension of water, 7.5 ⫻ 10⫺5 N/mm at ordinary temperature, and a contact angle of 0 should be used. Image Analysis
The spatial distribution of local voids inside a soil specimen can be obtained by analyzing the images obtained from thin sections. Generally, two image analysis methods are available: (1) method of polygons and (2) mean free path. In the first method the centroids of
Figure 5.30 Pore size distributions in crushed basalt as affected by compaction method.
INDIRECT METHODS FOR FABRIC CHARACTERIZATION
particles are located and linked to produce polygons, representing individual void elements as shown in Fig. 5.31a. Using this method, Bhatia and Soliman (1990) found that looser specimens of sand exhibited a greater variability in local void ratio than denser specimens. Frost and Jang (2000) used this method to quantify the variation of local void distribution produced by different preparation methods. Moist tamped specimens had a higher standard deviation of local void ratio for the same mean void ratio than air-pluviated specimens. The mean free path method measures the mean free path between particles by use of a scanning line that passes through both particles and voids as shown in Fig. 5.31b. The spacing and orientation of the line are varied, and a representative void is then produced by summing over the void lines found on a number of scanned lines in each direction (Kuo et al., 1998). Using this method, Masad and Muhunthan (2000) found that larger local voids exist in the horizontal direction than the vertical for a pluviated specimen.
137
stress, and fabric of the soil. According to elastic theory, which is applicable to soils for the small deformations associated with wave propagation, the shear wave (S-wave) velocity Vs and the compression wave (P-wave) velocity Vp are related to the shear modulus G and the constrained modulus M by Vs ⫽ 兹G/
(5.6)
Vp ⫽ 兹M/
(5.7)
and
where is the mass density. The constrained modulus M is related to the more familiar Young’s modulus according to M⫽
1⫺ E (1 ⫹ )(1 ⫺ 2)
(5.8)
in which is Poisson’s ratio. Young’s modulus and the shear modulus are related to each other by 5.10 INDIRECT METHODS FOR FABRIC CHARACTERIZATION
All physical properties of a soil depend in part on the fabric; therefore, the measurement of a property provides indirect measure of the fabric. Some of the measurements that are particularly useful are listed in Table 5.3 and are discussed briefly in this section. Elastic Wave Propagation
The propagation velocities of compression and shear waves through a soil depend on the density, confining
E ⫽ 2(1 ⫹ )G
(5.9)
The moduli depend on the applied effective stresses, stress history, void ratio, and plasticity index. For cohesionless soils the modulus varies approximately as the square root of the effective confining pressure. For cohesive soils the modulus varies as the effective confining pressure to a power between 0.5 and 1.0. The small strain shear modulus of soil depends on contact stiffness and fabric state. Therefore, the change in shear wave velocity with confining pressure provides
Figure 5.31 Image analysis methods to determine void fabric: (a) polygon method (after
Bhatia and Soliman, 1990) and (b) mean free path method (Kuo et al., 1998).
5
SOIL FABRIC AND ITS MEASUREMENT
insight on the pressure dependency of contact stiffness. Equations (5.6) and (5.7) assume isotropic elasticity. If the material is viscoelastic, the wave velocities become frequency dependent. Solutions for various viscoelastic models are given by Santamarina et al. (2001). If two samples of the same soil have the same mass density and are under the same effective confining pressure but have different fabrics, they will have different modulus values. This difference will be reflected by differences in shear and compression wave velocities. These velocities can be measured, and this provides a means for assessing fabric. The shear wave velocity is the more useful of the two because shear waves are only transmitted through the solid grain structure of the soil mass, that is shear waves cannot be transmitted through water. Anisotropic soil structure and stress states can be detected on the basis of different shear wave velocities in different directions. Further details of the relationships between small strain moduli and compositional and environmental factors are given in Chapter 11. If the material is dry, the bulk modulus of the skeleton can be derived using both shear wave and compression wave velocity measurements. If the material includes water, the P-wave velocity depends on the elastic properties of soil solids and water, saturation, and porosity. For fully saturated conditions, solutions are available for two-phase media (Biot, 1956a, 1956b; Stoll, 1989; Mavko et al., 1998; Santamarina et al., 2001). The solutions show that there are two P-waves and one S-wave. The fast P-wave and S-wave are the standard waves and the velocities have weak dependency on frequency. The slow P-wave (or Biot wave), which is associated with the diffusional process of water flow in deforming porous media, especially at low frequency, and is very difficult to detect (Plona, 1980; Nakagawa et al., 1997). Hence, the fast P-wave and Swave are commonly used to characterize the soil. In fully saturated condition, the fast P-wave propagates with a velocity that is 10 to 15 percent faster than the velocity through water. This is because the stiffness of the soil skeleton contributes to increasing P-wave velocity. In very loose saturated soil, the Pwave velocity is essentially controlled by the bulk modulus of water and has a value of about 1500 m/s. When air is introduced, P-wave velocity decreases. Even with a small amount of air, the reduction is dramatic due to a large decrease in bulk modulus of the fluid–air mixture. The effect of B-value (or water saturation ratio Sw) on P- and S-wave velocities of Toyoura sand specimen (Dr ⫽ 30 percent) is shown in Fig. 5.32 (Tsukamoto et al., 2002). The fast P-wave velocity at B ⫽ 0.95 (Sw ⫽ 100 percent) is 1700 m/s,
2000 Toyoura sand Air pluviation
Vp Vs
Dr = 30% σo' = 98 kPa
1500
Vp & Vs (m/s)
138
Vw = 1492 (m/s)
[
4 + Vp2 = Vs2 – 3
2(1 + v )
b ––––––––– 3(1 – 2ν ) (1 – B) ] b
1000 vb = 0.4
vb = 0.35
500
vb = 0.25
vb = 0.5 Vs = 212 (ms) 0 0
0.2
0.4
0.6
0.8
1
B-value
Figure 5.32 Variation in P- and S-wave velocities with B
value in loose Toyoura sand under an isotropic compression stress of 98 kPa (after Tsukamoto et al., 2002).
whereas that at B ⫽ 0.05 (Sw ⫽ 90 percent) is only 500 m/s. The S-wave velocity, on the other hand, is independent of the water saturation. Kokusho (2000) derives the following relationship that relates the fast P-wave velocity to B value: Vp ⫽ Vs
⫺) 冪43 ⫹ 3(1 2(1 ⫺ )(1 ⫺ B) b
(5.10)
b
where b is Poisson’s ratio of soil skeleton. Equation (5.10) is plotted in Fig. 5.32 for different b values. There is a dramatic decrease in P-wave velocity with even a very small decrease in B value from fully saturated conditions. Dielectric Dispersion and Electrical Conductivity
The flow of electricity through a soil is a composite of (1) flow through the soil particles alone, which is small, because the solid phase is a poor conductor, (2) flow through the pore fluid alone, and (3) flow through both solid and pore fluid. The total electrical flow also depends on the porosity, tortuosity of flow paths, and conditions at the interfaces between the solid and liquid phases. These factors are, in turn, dependent on the particle arrangements and the density. Thus, a simple
INDIRECT METHODS FOR FABRIC CHARACTERIZATION
measurement of electrical conductivity would seem a rapid and reliable means for evaluation of soil fabric. However, electrical measurements in soils are complicated by the fact that if direct current is used, then there will be electrokinetic coupling phenomena, such as electroosmosis, and electrochemical effects that can cause irreversible changes in the system, as discussed in Chapter 9. On the other hand, if alternating current (AC) is used, then the measured responses depend on frequency. Thus the application of electrical methods and interpretation of the data require careful consideration of how the measurement method may influence what is being measured. At the same time, however, measurement of the frequency dependence of electrical properties can be useful for evaluation of fabric and as an index for engineering properties. The capacitance C and the resistance R can be measured relatively easily. If electrical flow is in one dimension only, then the electrical conductivity is given by ⫽ L/(RA)
(5.11)
where L is the sample length and A is the crosssectional area. The capacitance can be converted to the relative dielectric constant D (see Chapter 6) using D ⫽ CL/(A0)
(5.12)
where 0 is the permittivity of vacuum (8.8542 ⫻ 10⫺12 C2 J⫺1 m⫺1). In fine-grained materials such as clays, the application of an AC field causes the electrical charges that are concentrated adjacent to particle surfaces to move back and forth with amplitude dependent on such factors as type of charge, association of charge with surfaces, particle arrangement, and strength and frequency of the field. These oscillating charges contribute to a polarization current that can be measured. The number of charges per unit volume times the average displacement is the polarizability. The magnitude of the polarizability is determined by the composition and structure of the material and is reflected by the dielectric constant. Phenomena contributing to polarization include dipole rotation, accumulation of charges at interfaces between particles and their suspending medium, ion atmosphere distortion, coupling of flows, and distortion of a molecular system. The extent to which polarization can develop depends on ease of charge movement and time available for displacement. With increase in frequency the dielectric constant may decrease and the
139
conductivity may increase. These changes are termed anomalous dispersion. Several regions of anomalous dispersion may develop over the frequency range from zero to microwave (⬎1011 Hz). Different polarization mechanisms cease to be effective above different frequency values, thus accounting for the successive regions of anomalous dispersion. Electrolyte solutions alone do not exhibit dispersion effects at frequencies less than 108 Hz, but clays do in the radio frequency range. For example, the conductivity and dielectric dispersion behavior of saturated illite are shown in Fig. 5.33. The electrical response characteristics in the lowfrequency range depend on particle size and size distribution, water content, direction of current flow relative to the direction of preferred particle orientation, type and concentration of electrolyte in the pore water, particle surface characteristics, and sample disturbance. Relationships between dielectric properties and compositional and state parameters such as porosity, particle shape, fabric anisotropy, and specific surface area are given by Arulanandan (1991). The theory is based on Maxwell’s (1881) relationship between porosity and the dielectric properties of a mixture of solution and spherical particles, and its extension to ellipsoidal particles that are all oriented in one direction by Fricke (1953). Extensive discussion of electromagnetic properties of soils is given in Santamarina et al. (2001). The formation factor appears in the relationships used to describe soil properties and state in terms of electrical properties. The formation factor is the ratio of the electrical conductivity of the pore water to the electrical conductivity of the wet soil. It is a nondimensional parameter that depends on particle shape,
Figure 5.33 Dielectric and conductivity dispersion characteristics of saturated illite (Grundite) (from Arulanandan et al., 1973).
140
5
SOIL FABRIC AND ITS MEASUREMENT
long axis orientation, porosity, and degree of saturation. If a soil has an anisotropic fabric, then the formation factor is different in different directions.
Mechanical Properties
Thermal Conductivity
Heat transfer through soils is through soil grains, water, and pore air. As the thermal conductivity of soil minerals is about 2.9 W/(m C), and the values for water and air are 0.6 and 0.026 W/(m C), respectively, heat transfer is mainly through the soil particles. Accordingly, the lower the void ratio, the greater the number and area of interparticle contacts and the higher the degree of saturation, the higher is the thermal conductivity. The thermal conductivity of a typical soil is likely to be in the range of 0.5 to 3.0 W/(m C). This property is considered in more detail in Section 9.6. Thermal conductivity can be determined using a relatively simple transient heat flow method in which a line heat source, called a thermal needle, is inserted into the soil. The needle contains both a heating wire and a temperature sensor. When heat is introduced into the needle at a constant rate, the temperatures T2 and T1 at times t2 and t1 are related to the thermal conductivity k according to k⫽
ture caused by mechanically and environmentally induced changes in state of the soil.
4 ln(t2) ⫺ ln(t1) Q T2 ⫺ T1
(5.13)
where Q is the heat input between t1 and t2. This method and factors influencing the results are described by Mitchell and Kao (1978). Differences in thermal conductivity in different directions provide a measure of soil anisotropy. For example, the ratios of thermal conductivity in the horizontal direction kh to that in the vertical direction kv for three clays with preferred particle orientations in the horizontal direction were in the range of 1.05 to 1.70, depending on the clay type, consolidation pressure, and sample disturbance (Penner, 1963b). For the probe in the vertical position in a cross anisotropic fabric, the value of k determined from Eq. (5.13) is kh. For the probe in the horizontal direction, a value of ki is measured that is related to kv and kh according to (Carlslaw and Jaeger, 1957) kv ⫽
k2i kh
(5.14)
Thermal probe measurements can also be used to detect differences in density at different locations in the same material (Bellotti et al., 1991) and for evaluation of changes in density, water content, and struc-
The mechanical properties of soil, including stress– deformation behavior, strength, compressibility, and permeability, depend on fabric in ways that are reasonably well understood, as considered in Chapter 8. Therefore, information about fabric can be deduced from measurements of these properties and known interrelationships between properties and fabric.
5.11
CONCLUDING COMMENT
Fabric analyses are useful in research to show how mechanical properties are dependent on particle associations and arrangements. Fabric information can be used to deduce details of the depositional and postdepositional history of a deposit. The effects of different sampling methods can be assessed through the study of fabric changes. Insights can be gained into the mechanics of strength mobilization, the nature of peak and residual strengths, and the stress–strain behavior of soils from fabric studies. The indirect methods for fabric study are often useful for determination of properties, homogeneity, and anisotropy in situ. They may be of value also for assessing whether reconstituted samples used for laboratory testing correctly duplicate the field conditions. The particulate nature of soil and the many possible associations of discrete particles and particle groups mean that a soil of given composition can have many different fabrics and exist over a very wide range of states, each having its own unique set of geotechnical properties.
QUESTIONS AND PROBLEMS
1. Two samples of the same remolded clay have been consolidated from the liquid limit to the same water content. One was consolidated under an isotropic set of stresses and the other under anisotropic stresses. What differences in fabric would you anticipate? Why? 2. Two slurries of the same clay, one with flocculated clay particles and the other with deflocculated particles, have been consolidated under an effective stress of 100 kPa. Which will have the higher (a) void ratio, (b) sensitivity, (c) strength? Explain your answer.
QUESTIONS AND PROBLEMS
141
Exhibit 5.1 Soil fabrics.
3. A series of shrinkage tests was done on a finegrained soil mass, and it was found that the shrinkage was a maximum in the Z direction and was a minimum in all directions lying in a plane perpendicular to the Z direction. a. Was the soil mass likely to have been isotropically consolidated or anisotropically consolidated? b. If anisotropically consolidated, what was the major principal stress direction? c. Would you expect the soil to be isotropic with respect to hydraulic conductivity? Why? If anisotropic, in which direction would the hydraulic conductivity be greatest? Why? 4. Could X-ray diffraction alone be used to distinguish among the fabrics shown in Exhibit 5.1? Explain your answer. Pertinent geometrical parameters of typical X-ray diffractometers are: distance from Xray source to sample ⫽ 17 cm, divergence of X-ray beam ⫽ 1, angle of incidence of X-ray beam to the sample surface in the range of 10 to 35. 5. You are analyzing a new type of laboratory strength test that imposes unusual boundary conditions on the sample being tested. What methods of fabric study would you use to examine the location, direction, thickness, and fabric of shear zones within specimens? What would these methods tell you? 6. Several methods for study and characterization of soil fabric are listed in Table 5.3. Indicate some
specific soil types and states for which each of these methods might be useful for gaining insights and understanding of the macro- and microfabrics and their influences on volume change, strength, and permeability properties. 7. To obtain an essentially undisturbed sample of cohesionless soil from the field that preserves the in situ fabric is usually impossible without resorting to expensive and time-consuming procedures such as ground freezing or injection followed by setting of a grout or resin. Suppose that you do not have the time or budget that will allow this, but wish to reconstitute disturbed specimens of the soil in the laboratory by forming them in such a way that they will have fabrics that reasonably duplicate the undisturbed condition in the field. Suggest practical laboratory procedures that might be used, starting with dry and disturbed soil of the type indicated, to reproduce specimens that could then be used for fabric studies and measurements of mechanical properties: a. Beach sand b. Alluvial deposit c. Wind-blown dune sand d. Uniform sand placed as a hydraulic fill e. Uniform sand placed as a hydraulic fill and then densified using vibratory probes f. Sand fill placed as a pavement base and densified by a vibratory roller
CHAPTER 6
Soil–Water–Chemical Interactions
6.1
INTRODUCTION
Saturated soils at void ratios greater than 1.0 contain more water volume than solid volume, and void ratios greater than 1.0 are more the rule than the exception in fine-grained soils. Yet, the emphasis in the study of soil composition and properties has traditionally been almost entirely on the mineralogy and structure of the solid phase, with very little regard for the properties of the liquid phase. Perhaps this is because: 1. Classical soil mechanics is founded on the concept of effective stress, which postulates that volume change and strength behavior depend on the stresses carried by the solid grain structure and the water phase is neutral. 2. We all know that water is a clear, colorless, odorless, tasteless liquid that has a density very nearly equal to unity. It freezes at a temperature of 0C, boils at a temperature of 100C, and it has quite well-defined viscosity and thermal properties. We view it as such a familiar liquid that it is scarcely given a second thought. In reality, however, the situation is not so simple because neither water nor soil surfaces are inert chemically or biologically. Water and soil particles interact with each other because, under ordinary circumstances, water molecules are strongly attracted to and adsorbed on soil particle surfaces. The nature and consequences of these interactions are described in the first part of this chapter.
Unbalanced force fields at the interfaces between soil and water cause interactions between small soil particles, dissolved ions, and water. If two particles are in close proximity, their respective force fields overlap and influence the behavior of the system, especially when the magnitudes of these forces are large relative to the weights of the particles themselves. Clay particles, because of their very small size, unique crystal structure, and platy shapes, have very large specific surface areas and are especially influenced by these forces. Several types of interparticle attractive and repulsive forces determine the flocculation–deflocculation behavior of clays in suspension and the volume change and strength properties of soils at void ratios common in natural deposits. The fabric at the time of formation may have a profound influence on the engineering properties of a soil deposit, so an understanding of factors influencing flocculation–deflocculation behavior is of considerable value. Furthermore, postdepositional or postconstruction changes in soil structure and engineering properties may result from changes in physicochemical forces of interaction. Principles of surface, colloidal, and soil chemistry provide understanding of many of the interactions and their consequences in a clay–water–electrolyte system. The focus in the second part of this chapter is on development of an understanding and appreciation of these interactions in soils of interest in geotechnical engineering. Much of what is covered in this chapter is directly relevant to chemomechanical coupling processes in soils, wherein internal phenomena at the mi143
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croscale influence mechanical properties and responses at the macroscale. 6.2
NATURE OF ICE AND WATER
The water molecule (H2O) is composed of a V-shaped arrangement of H and O atomic nuclei. The outer shell electronic charges, six from the oxygen and one from each hydrogen, are distributed in the form of four electron pairs per molecule. The resulting configuration is tetrahedral, with two positive corners that are the sites of the hydrogen protons and two negative corners that are located above and below the plane of the atomic nuclei, as shown schematically in Fig. 6.1. Bond energy considerations (Pauling, 1960) indicate that the H–O bond is about 40 percent ionic and 60 percent covalent. As a result there is directional bonding, and the water molecule is a strong permanent dipole. Water can exist in many different crystalline forms. At least 13 have been identified, and, of these, 9 are stable over some range of temperature and pressure. For example, at atmospheric pressure, ordinary ice and liquid water are stable between 72 and 273 K and between 273 and 373 K, respectively. In water and ice, the positive corner of one molecule attracts the negative corner of another. Two oxygens share a proton, which results in hydrogen bonding and a tendency for each molecule to bond to 4 neighboring molecules in a tetrahedral arrangement. In ice-I, the stable crystalline state of water at temperatures less than 0C and atmospheric pressure, a hexagonal network structure is formed, as shown schematically in Fig. 6.2. Three molecules of the hexagon are in one plane, and 3 are in another. The oxygen-to-oxygen distance between hydrogen-bonded molecules is 0.276 nm, with the hydrogen located (statistically) 0.10 nm from one oxygen and 0.176 nm from the other. The distance between molecules in a given plane is 0.45 nm. The average
Figure 6.1 Schematic diagram of the structure of the water
molecule.
Figure 6.2 Arrangement of water molecules in ice-I.
H–O–H angle is 102.5 (Gu¨ven, 1992), which is close to the tetrahedral angle of 109.5. The bond energy in ice is about 19 kilojoules/mole (kJ/mol). As the melting point is approached, the number of broken or distorted hydrogen bonds increases. This explains the lower strength and higher creep rates in ice and frozen soil as the temperature increases. At temperatures above 0C (under atmospheric pressure), enough hydrogen bonds are ruptured or bent that ice loses its rigidity, and water exists in the liquid state. Rupture of 16 percent of the possible hydrogen bonds accounts for the heat of fusion of ice. The tetrahedral nature of water structure becomes local and transient in the liquid state; however, some hydrogen bonding and structure remain. Otherwise each water molecule would have 12 nearest neighbors, and water density would be 1.84. The energy needed to break hydrogen bonds accounts for the high melting point, boiling point, heat of fusion, heat of vaporization, specific heat, dielectric constant, and viscosity of water. The 9 percent volume decrease when ice melts is because each molecule acquires somewhat more than 4 nearest neighbors, even though the average intermolecular distance increases to about 0.29 nm as a result of increased thermal agitation. Bond rupture and distortion predominate at temperatures below 4C, whereas increased intermolecular distances prevail above, thus giving maximum water density at 4C. Several models have been proposed for the structure of water based on available physical and chemical evidence (Eisenberg and Kauzman, 1969): 1. Mixture models assume a mixture (at any instant) of a small number of distinguishable species of water molecules. There are clusters of hydrogenbonded molecules and non-H-bonded molecules. Increased temperature increases the concentration of non-H-bonded molecules. 2. Interstitial models are a special class of mixture models, wherein one species of molecule forms an H-bonded framework containing cavities in which non-H-bonded molecules reside.
INFLUENCE OF DISSOLVED IONS ON WATER
3. The distorted hydrogen bond model (Pople, 1951) assumes the majority of hydrogen bonds to be distorted rather than broken. Bending of hydrogen bonds permits some of the second and third neighbors to penetrate into regions near the central molecule, resulting in an apparent number of nearest neighbors greater than four. 4. The random network model (Bernal, 1960, 1964) is an extension of the distorted H-bond model. Distortion of H bonds produces an irregular network of rings rather than an ordered lattice as in ice. It is postulated that many rings contain five molecules because the H–O–H angle is close to the 108 angle of a five-membered ring, but others may contain four, six, seven, or more molecules. According to Bernal, in a noncrystalline, irregular structure, a fivefold arrangement is, for geometrical reasons, likely to be the rule. Fivecoordinated structures cannot exist in crystalline solids because regular, repeating patterns with this coordination cannot be formed. The liquid state could be explained precisely because of this, and solids and liquids can be distinguished as coherent materials with and without regular structure, respectively. Eisenberg and Kauzman (1969) concluded that mixture models are not supported by the data, but the distorted H-bond models (including random networks) seem to accord with most of what is known about water from experiments. Irrespective of the model details, the molecular structure of water is dynamic and depends on the timescale used to observe it (Sposito, 1984). Various molecular level models for water have been proposed to examine the interaction between two water molecules, and some of them are summarized by Gu¨ven (1992). A water molecule can be modeled as a unit comprised of four interaction sites (one oxygen, two hydrogen, and one negatively charged position). Evaluation of the interaction between the modeled molecules gives the energetics, hydrogen-bonded structure, and dynamics of bulk water reasonably well. These models are useful to calculate the equilibrium thermodynamic properties of clay–fluid systems using molecular simulations, in which molecular particles of water, counterions, and clay interact through a set of potential energy functions. Stillinger (1980, p. 451) describes liquid water structure as follows: Liquid water consists of a macroscopically connected, random network of hydrogen bonds, with frequent strained and broken bonds, that is continually undergoing topological reformation. The properties of water arise from the competition between relatively bulky ways of connecting
145
molecules into local patterns characterized by strong bonds and nearly tetrahedral angles and more compact arrangements characterized by more strain and bond breakage.
6.3 INFLUENCE OF DISSOLVED IONS ON WATER
Because of the uneven charge distribution and dipolar character of water molecules, they are attracted to ions in solution, leading to ion hydration. Positive ions attract the negative corners of water molecules, and vice versa. Water molecules move from their normal structure into positions in the hydration shell of an ion provided the energy is less as water of hydration than as normal water. Not all ions hydrate, although the common cations in soils do. Ions disrupt normal water structure, whether they hydrate or not. Those dissolved ions that do not hydrate still occupy space; those that do hydrate attract only those corners of water molecules of opposite electrical charge, whereas in normal water there is an alternating character to the directions of positive and negative corners. A schematic model for ion–water interaction is shown in Fig. 6.3 (Frank and Wen, 1957). Region A is a zone of immobilization. Water molecules are strongly oriented in the field of the ion and have little kinetic energy. In region B, the water structure is broken down and more random than in normal water. Region C contains water with normal structure that is polarized by the ionic field. More specific details about the number and characteristics of the water molecules in zone A surrounding monovalent and divalent cations are given by Sposito (1984). As ion hydration in water
Figure 6.3 Ion–water interaction as postulated by Frank and
Wen (1957).
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involves interactions between ions and clusters of water molecules, the actual state is more complicated than the above model. Various potential functions are available to describe the interactions between ions and water molecules, and more detailed and quantitative reviews of the structure and energetics of ion hydration are given by Gu¨ven (1992) and Ohtaki and Radnai (1993).
6.4 MECHANISMS FOR SOIL–WATER INTERACTION
Water is strongly attracted to soil mineral surfaces, particularly to clays. Dried clays adsorb water from the atmosphere even at low relative humidity, many soils swell when given access to water, and temperatures above 100C are needed to remove all the water from a soil. In fact, it is not always evident just what is meant by a dry soil (Lambe, 1949). Several possible mechanisms for water adsorption have been proposed (Low, 1961). They are shown schematically in Fig. 6.4. Hydrogen Bonding
Surfaces of soil minerals are composed of a layer of either oxygens or hydroxyls, so hydrogen bonds can form easily, with oxygens attracting the positive corners and hydroxyls attracting the negative corners of water molecules (Fig. 6.4a). Early concepts of the structure of adsorbed water suggested an icelike character because of the similarity between the hexagonal symmetry of the oxygens and hydroxyls in clay surfaces and the structure of ice; however, subsequent studies have shown that the structure cannot be that of ice. The formation of hydrogen bonds with particle surfaces would alter the electron distribution from that in normal water, thus making it easier for bonded molecules to form additional bonds with molecules in the same and next layer. The directional properties of the bonds would induce a tetrahedral arrangement of water molecules, which would become less rigid with distance from the surface due to a decrease in the surface force fields and an increase in the force fields of normal water structure. Hydration of Exchangeable Cations
Because cations are attracted to negatively charged clay surfaces, so is their water of hydration (Fig. 6.4b). Further details of hydrated ion water attraction to clay surfaces are discussed later.
Attraction by Osmosis
Cation concentration increases as negatively charged clay surfaces are approached (Fig. 6.4c). This increased concentration means that water molecules tend to diffuse toward the surface in an attempt to equalize concentrations. Charged Surface–Dipole Attraction
Clay particles can be viewed as negative condenser plates. Water dipoles then orient with their positive poles directed toward the negative surfaces, with the degree of orientation decreasing with increasing distance from the surface. However, at the midplane between parallel plates there would be structural disorder because like poles would be adjacent to each other. Ingles (1968) suggested that because of the high hydration number and energy of aluminum in the clay structure, water is so strongly attracted to the surfaces that it interposes itself between the surfaces and the counterions, with the counterions removed as far as possible from the surface, that is, to the midplane between opposing parallel sheets. With this model the structure shown in Fig. 6.4d can be conceived. The same type of arrangement could result simply from ion hydration. In dry clay, adsorbed cations occupy positions in holes on the clay surfaces. On hydration they surround themselves with water and move to the central region between clay layers. Attraction by London Dispersion Forces
Van der Waals attractive forces could bond water molecules to clay surfaces. In-phase fluctuations of electron clouds form temporary dipoles and induce displacements in neighboring molecules so that dipole–dipole attraction occurs. Because such bonds would be nondirectional, the water structure would be closely packed and more fluid than the H-bonded structure. Capillary Condensation
A range of pore sizes and distributions usually exists in a soil. The pores may fill with liquid water and water vapor. At saturation less than 100 percent, the water is retained in micro- and minipores through the combined effects of surface tension and attraction to particle surfaces. 6.5 STRUCTURE AND PROPERTIES OF ADSORBED WATER
Different arrangements of water molecules are associated with each of the postulated mechanisms for
STRUCTURE AND PROPERTIES OF ADSORBED WATER
147
Figure 6.4 Some possible mechanisms of water adsorption by clay surfaces: (a) hydrogen bonding, (b) ion hydration, (c) attraction by osmosis, and (d ) dipole attraction.
soil–water interaction. It would be anticipated that different water structures would give different properties, and many studies have been made to better define the specific structural, chemical, thermodynamic, and mechanical properties of soil water. Evidence concerning the validity of different models has come from a variety of sources, including X-ray and electron diffraction data, density measurements, dielectric and fluid flow measurements, swell and swell pressure studies, nuclear magnetic resonance and infrared spectra, and
behavior on freezing. Knowledge of soil water properties is important for better understanding and quantifying such geotechnical phenomena as fluid flow through soil, diffusion, freezing and thawing, creep and stress relaxation, strength, swelling, and consolidation. Density of Adsorbed Water
Data on the density of water adsorbed on sodium montmorillonite as a function of water content were
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summarized by Martin (1960). Determinations were made using pycnometer and X-ray diffraction techniques. For water contents less than needed to give about three molecular layers on the clay surfaces (a 1.0-nm-thick layer), the density is greater than for normal water, whereas at greater water contents it may be slightly less. Thus, the water structure and density within the first few molecular layers at very low water contents may differ from that in the same region when the clay is nearly saturated. X-ray Evidence of Adsorbed Water Structure
X-ray analyses of frozen clay pastes of montmorillonite, halloysite, and kaolinite at low water contents by Anderson and Hoekstra (1965) indicated water films 0.5 to 1.0 nm in thickness. In samples containing some unfrozen water, the ice was separated from the clay surfaces by liquid water, where the adsorbed cations were also located. Normal ice structure was observed. The c axes of the ice crystals were at right angles to the c axes of the clay plates. This is strong evidence against a rigid, icelike structure for adsorbed water fitted directly to the particle surfaces. Ravina and Low (1972) found that as the water content of several montmorillonites increased, so also did the b dimension of their crystal lattices, as shown in Fig. 6.5. Differences in the b dimensions of different
montmorillonites in the dry state are caused by differences in isomorphous substitution, which results in small rotations of the silica tetrahedra in alternating clockwise and counterclockwise directions. When swelling was complete, the b dimension was 0.9 nm. Whatever the water structure at the end of swelling, it is in energy equilibrium with normal water. At smaller values of the b dimension, the water structure must be such as to give an energy level lower than that of free water or swelling would not be spontaneous. A change in b dimension accompanies a change in water content because both clay and water have preferred internal structures. Each exerts an influence on the other as long as there is attraction between the water and the clay. Theoretical analyses (Lahay and Bresler, 1973) suggest that change in the b dimension with change in the water content may also be caused by variation in the penetration of cations into the hexagonal holes on the silica surfaces of the montmorillonite structure. Diffusion, Viscosity, and Fluid Flow Properties
The results of measurements of hydraulic flow rates, diffusion coefficients, and activation energy for flow and diffusion have been used to infer details of water structure in clays. Data interpretation usually requires assumptions concerning tortuosity of flow path. Changes in fabric and/or chemical environment during measurements, bacterial growth, and electrokinetic and chemical coupling effects (see Chapter 9) also may affect the results, sometimes making them difficult to interpret. Darcy’s law is the commonly used relationship between flow rate q and hydraulic gradient i in analyses of groundwater flow, seepage, and soil consolidation, that is, q ⫽ kia
Figure 6.5 Relation between b dimension and water content
for six Na-saturated dioctahedral montmorillonites (from Ravina and Low, 1972).
(6.1)
where k is hydraulic conductivity (permeability) and a is cross-sectional area. According to Darcy’s law, hydraulic flow rate should be directly proportional to hydraulic gradient. However, if the water in a soil has a special structure so that it possesses non-Newtonian flow properties, or if it has abnormally high viscosity, or is crystalline adjacent to particle surfaces, then deviations from this proportionality could exist. Evidence (Olsen, 1965, 1969; Gray and Mitchell, 1967; Miller et al., 1969) suggests, however, that Darcy’s law is obeyed exactly in saturated clays, although apparent deviations may result from particle migrations, electrokinetic effects, and chemical concentration gradients.
STRUCTURE AND PROPERTIES OF ADSORBED WATER
Measurements on thin water films between mica surfaces have indicated that water retains its bulk viscosity down to the last molecular layer (Christenson et al., 1987). Diffusion, heat of immersion, and nuclear magnetic resonance measurements led Fripiat et al. (1984) to conclude that the water in clay gels and suspensions is in two phases. Phase a is free water in the pores. Phase b is a layer about three molecules thick adjacent to particle surfaces that is directly affected by surface force fields. The diffusion coefficient of the water in phase a is the same as that in pure water, that is, 2.2 ⫻ 10⫺5 cm2 /s at a temperature of 20C. Thus, for practical purposes, the water in clays, whatever its structure, behaves essentially the same as pure water in terms of its viscosity and diffusion characteristics. This is an important conclusion relative to the analysis of seepage, consolidation, and chemical transport processes through soils. Dielectric and Magnetic Properties
The dielectric properties of a material depend on the ease with which its constituent molecules can be polarized. There are two contributions to polarization in an electrical field: distortion polarization, which is instantaneous, and orientation polarization, which is time dependent. In a low-frequency AC field, dipoles can rotate with changes in current direction. As the frequency increases, however, less time is available for dipole rotation. Above some frequency the molecules are no longer able to follow the field, and the dielectric constant drops. The relationship between dielectric constant and frequency for a material might appear as in Fig. 6.6. The dielectric losses and the frequencies at which they occur are dependent on the intermolecular bond types and strengths. Measured values of dielectric constant for clay– water systems are less than those for normal water [between 2 and 50 in adsorbed water versus 80 in bulk water (Sposito, 1989)], but they are consistent with
Figure 6.6 Variation of dielectric constant with frequency.
149
both an ordered water structure or a ‘‘two-dimensional liquid’’ model (Martin, 1960). A two-dimensional fluid would consist of water molecules that are bonded strongly to the surfaces of clay particles, but that can slide along the surface with relative ease. A twodimensional fluid would resist significant normal stress but would shear easily along planes parallel to the surface. Such a structure is consistent with the conclusion by Christenson et al. (1987) from viscosity measurements that alignment of fluid molecules in layers parallel to surfaces or pore walls does not significantly affect flow along the walls. Nuclear magnetic resonance (NMR) measurements (Pickett and Lemcoe, 1959; Graham et al., 1964; Wu, 1964) provide information on the time required for a molecule to move through a distance comparable with its dimensions (about 2 ⫻ 10⫺12 s for normal water at a temperature of 20C), magnetic field nonhomogeneity over the sample, proton mobility, and the number of resonating nuclei. Nuclear magnetic resonance data confirm that water is tightly held by clay, the structure is not that of ice, and that the mechanism of attraction is not simple dipole adsorption. Supercooling and Freezing of Adsorbed Water
Water in clay can both supercool and exhibit freezing point depression. Supercooling is a reduction of temperature below the normal freezing point without the initiation of freezing. Freezing point depression is a reduction in the usual freezing temperature of a liquid, such as caused by dissolving salt in water. Adsorbed water cannot have the structure of ice because, if it did, it would act as a crystallization nucleus, and there could be neither effect. Both supercooling and freezing point depression could result from more or less molecular order in the water relative to normal water. If there were more order, then it would be more difficult to rearrange the water molecule into the ice structure. With a less ordered water structure, more energy would need to be removed to initiate freezing. An interesting practical problem relating to freezing point depression and supercooling arose during the design and construction of the Trans-Alaska Oil Pipeline. Pilelike vertical support members (VSM) are used to elevate the pipeline above the ground surface, as shown in Fig. 6.7. The VSM and the pipeline are supported by permafrost that exists beneath an active layer that freezes and thaws annually. It was necessary to know and to control the depth of the active layer to ensure sufficient VSM penetration into the permafrost to provide the necessary support. During the winter, heat pipes within the VSM circulate a refrigerant that vaporizes while removing heat from the permafrost
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SOIL–WATER–CHEMICAL INTERACTIONS
in which S is the change in partial molar entropy. As
F ⫽ 0,
S ⫽
H
T
(6.4)
Entropy is a measure of molecular randomness, so
S reflects the change in disorder of water molecules in going from the vapor to the adsorbed state. H is
Figure 6.7 Schematic diagram of the vertical support member (VSM) system for the aboveground portions of the TransAlaska Pipeline.
and then condenses as the heat is radiated into colder air above ground. In this way it is possible to prevent the thickness of the active zone from increasing beyond a specified amount during the summer. Analysis of the heat exchange requirements required knowledge of the soil water freezing point and supercooling properties. Thermodynamics of Soil Water
Moisture adsorption from the vapor phase, calorimetric measurements of heat of wetting, and measurements of free energy changes have been used to evaluate the thermodynamic properties of soil water. Thermodynamic measurements provide information on differences in properties between one state and another; however, they do not provide specific information on the mechanisms responsible for the changes. The heat of adsorption can be determined using the Clausius–Clapeyron equation:
冉冊
ln
p2
H T2 ⫺ T1 ⫽ p1 R T1T2
(6.2)
in which p1 and p2 are equilibrium vapor pressures above the clay at temperature T1 and T2 and constant soil water content, R is the gas constant, and H is the change in partial molar heat content of the water on adsorption from the vapor state. At equilibrium, the partial molar free energy of the water in the clay is the same as that in the vapor. The change in partial molar free energy on adsorption,
F, is defined by
F ⫽ H ⫺ T S
(6.3)
greater for water vapor adsorption onto clays than for condensation of pure water. Thus, by Eq. (6.4), if the decrease in partial molar entropy is greater for adsorption on the clay than for condensation to the liquid state, then it is concluded that adsorbed water should be more ordered than free water. This interpretation has been challenged (e.g., Martin, 1960; Cary, et al., 1964) on the basis that integral thermodynamic functions should be used for analysis of the systems studied (Hill, 1950) rather than differential thermodynamic functions. Figure 6.8 illustrates the difference between differential and integral entropy. It may be seen that the integral entropy of adsorbed water at any water content could be greater than that of free water even if the differential entropy is less. Thus, we are left with a rather confused picture of adsorbed water based on entropy data. Less order than normal water would certainly not be inconsistent with the density data and the unfrozen zones observed by Anderson and Hoekstra (1965). All these observations pertain to the first few molecular layers adsorbed onto dry clay surfaces. Heat of wetting (heat liberated as a result of wetting a clay with liquid water) measurements have shown that a large amount of energy is released on adsorption of the first one or two molecular layers, but it becomes almost zero after formation of the first few water layers. Exchangeable cations influence the amount of heat released. Specific heat values for soil water as great as 4.6 J/g have been measured (Oster and Low, 1964) at very low clay water content, decreasing to values close to 4.2 J/g at higher water content. Evidence referred to by Oster and Low (1964) indicates that the heat capacity of the water in clay increases with time of rest after remolding. This is consistent with the finding that moisture tension increases (pore pressure decreases) with time after disturbance of a thixotropic clay–water mixture (Kolaian and Low, 1960; Mitchell, 1960; Ripple and Day, 1966). This reflects a time-dependent change in the free energy and structure of the water as a new at-rest equilibrium condition develops. Because the moisture tension depends on the free energy of the whole clay–water system, however, and time-
STRUCTURE AND PROPERTIES OF ADSORBED WATER
151
Figure 6.8 Differential and integral entropy. Differential entropy is the slope at any point.
If it is less than slope of, then the conclusion is that there is more order in adsorbed water. Integral entropy of soil–water ⫽ gh / og or gh / og. The integral entropy of system (1) is greater than for free water; therefore, there is less order in the adsorbed water.
dependent changes in fabric have been observed to accompany thixotropic hardening, the data cannot be accepted as proof of a change in water structure. Nonetheless, it does not seem unreasonable to expect that mechanical disturbance can change the structural state of water in a clay–water system.
It has also been shown (Mulla and Low, 1983; Sun et al., 1986) that
Infrared and Neutron Diffraction Data
Infrared spectroscopy measurements (Low and White, 1970) showed that hydrogen bonds in clay adsorbed water are weaker than those in bulk water. Weak hydrogen bonds do not necessarily imply disorder in the water, nor do the data mean that there cannot be as many or more H bonds developed than in normal water. Neutron diffraction measurements give information about the spatial distribution of atoms in the system. Powell et al. (1997) conducted studies of interlayer water in Na-Wyoming montmorillonite, and the data were compared to the data for bulk liquid water. The comparison indicated that water molecules in the clay have nearest-neighbor configurations that differ from the tetrahedral ordering of nearest neighbors of bulk liquid water as described in Section 6.2. Quantification of Property Variations
From the results of several studies, primarily with smectite clays, Low (1979, 1994) and Sun et al. (1986) showed that the following general empirical equation describes the variation of thermodynamic, hydrodynamic, and spectroscopic properties with water layer thickness: Ji /J 0i ⫽ exp(i /w)
where Ji ⫽ value of property I in clay–water system J 0i ⫽ value of property I in pure water i ⫽ constant characteristic of the property and the clay w ⫽ water content of the clay (as a decimal)
(6.5)
i ⫽ ki As
(6.6)
where ki is a constant characteristic of the property and As is the specific surface of the clay (area/mass). If all the water in clay is assumed to be spread uniformly over the available surface area, then the average thickness, t, of the water films on the particle surfaces is t ⫽ w/( w As)
(6.7)
in which w is the density of the water. Combining Eqs. (6.5), (6.6), and (6.7) gives Ji /J 0i ⫽ exp[ki /( wt)]
(6.8)
The values of three properties—(1) apparent specific thermal expansibility,1 J1 / J01 ⫽ (v / T)P /(v / T)P0 , (2) apparent specific compressibility, J2 / J02 ⫽ (v / P)T /(v / P)0T , and (3) molar absorptivity, J3 / J30 ⫽
The term v is the apparent specific volume of the water in a clay– water system of volume V. The volume V is the sum of two components; unperturbed clay and water that is perturbed by the surfaces of the clay particles (Low, 1994). V ⫽ mcv0c ⫹ mwv, where v0c is the specific volume of the pure clay and mc and mw are the respective masses of clay and water (i.e., water content w ⫽ mw / mc). 1
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SOIL–WATER–CHEMICAL INTERACTIONS
/ 0, a spectroscopic property,2 as a function of water
layer thickness in sodium smectites—are shown in Fig. 6.9, from Low (1987). Equation (6.8), computed for ki ⫽ 7.22 ⫻ 10⫺8, ⫺0.807 ⫻ 10⫺8 and ⫺13.68 ⫻ 10⫺8 g/cm2 and w ⫽ 1.0 g/cm3 for curves 1, 2, and 3, respectively, and t in centimeters, fits the data well. In the figure, the different symbols represent smectites with different values of the surface charge. As a common curve can be fitted to the data, this implies that the interaction between clay and water does not depend on clay surface characteristics (Low, 1994). Figure 6.9 shows that the properties are altered rel˚ (10 nm). ative to normal water out to about 100 A Extending the above data interpretation, Low (1994) further investigated the thickness of the films of perturbed water next to the particle surfaces and con-
cluded that this thickness is at least 3.5 nm. For highly plastic clays, that is, clays with a large specific surface area, a significant proportion of the water is influenced by the particle surfaces. For example, for clay having a specific surface area of 100 m2 /g, the average thick˚ (10 nm) at ness of water layer, t, will be about 100 A a water content of 100 percent. On the other hand, for coarser-grained and less plastic soils, the proportion of water in the clay that is influenced by surface interactions is much less. For example, a soil with a specific surface area of 20 m2 /g at a water content of 40 percent would have an average water layer thickness of ˚ (20 nm), so much of the water would be at a 200 A distance beyond the influence of particle surface forces. Clay swelling, high swelling pressures, and heave of expansive soils can be explained, at least in part, in terms of the structural changes of water caused by interactions with clay surfaces (Low, 1987). Expansive soils are characterized by smectite clay minerals of high specific surface area and relatively low water content, so the average water layer thicknesses are well within the range of influence of surface forces. Concluding Comments
From this rather cursory review of the nature of water and of water in soils, there are several implications relative to the understanding of soil behavior in geotechnical engineering. They include:
Figure 6.9 Relation between Ji / J 0i and t for three different
properties of the water in Na–smectites: namely, the apparent specific thermal expansibility (n / T )p, the apparent specific compressibility (v / P )T, and the molar absorptivity at the frequency of O-D stretching . (Note: each symbol represents a different smectite having its own surface characteristics.) Reprinted with permission from Low (1987).
2
The term depends on the strength of the hydrogen bonds.
1. The volume of water in a soil is often equal to or greater than the volume of solid material. 2. The distribution of electrons in a water molecule gives a tetrahedral geometry, with the hydrogen protons at two of the corners. Thus, a variety of molecular configurations held together by hydrogen bonds is possible. 3. The structure of ice is known. Various electrostatic models are available to represent the energetics, hydrogen-bonded structure, and dynamics of bulk water. 4. Dissolved ions disrupt water structure. Various potential functions are available to describe the interactions between ions and water molecules. 5. Water is strongly attracted to soil particle surfaces, and the resulting interactions may influence the water properties to distances of several nanometers from the surface. The water to a distance of about 1.0 nm, that is, three molecular layers, from a silicate layer surface is strongly adsorbed (Sposito, 1984, 1989) and has a structure different from that of normal water.
ION DISTRIBUTIONS IN CLAY–WATER SYSTEMS
6. Adsorbed water structure differs from that of ice and normal water. 7. Adsorbed water exhibits both supercooling and freezing point depression. 8. Energy is released by the adsorption of water by clays. 9. Time-dependent increases in the moisture tension of water are evident after mechanical disturbance of the at-rest structure of a clay–water system. 10. The interaction of water with clay surfaces causes a change in the b dimension of the clay particle lattice. A mutual adjustment of both the clay and water structures develops during adsorption. 11. The thermodynamic, hydrodynamic, and spectroscopic properties of adsorbed water vary exponentially with distance from particle surfaces, and surface interaction effects may be evident to distances of up to 10 nm from the surface. This corresponds to water contents of about 800 percent in a fully expanded pure smectite and 15 percent in a pure kaolinite. 12. There is no evidence for abnormal water viscosity or failure of Darcy’s law in clays of the type usually encountered in geotechnical practice. The viscosity and diffusion properties are, for practical purposes, the same as for pure water. At low water contents, characteristic of low saturation, the water structure can be quite different than that in wet or saturated clays. At very low water contents, competition for water molecules between the adsorbed cations and the surfaces is keen. A strong attraction to the surface with disorder in the arrangement of water molecules and high lateral mobility are reasonable consequences. At higher water contents, cations, at least of some types, are diffused from the surface. If a random network water structure exists, then it seems reasonable that the development of networks that could both adapt to the clay surfaces and incorporate adsorbed cations should be possible. Because both the surfaces and cations influence the nature of the networks developed, it would be expected that the bond strengths and thermodynamic properties would differ from those in normal water. A gradual transition from one structure at the surface to another in the bulk water seems reasonable. Sposito (1989) and Gu¨ven (1992) provide more specific details about the structure and physical characteristics of soil water on an atomic and molecular scale.
6.6
153
CLAY–WATER–ELECTROLYTE SYSTEM
Clays are lyophobic (liquid hating) or hydrophobic (water hating) colloids rather than lyophilic or hydrophilic colloids, even though water wets clays and is adsorbed on particle surfaces. This designation resulted from the need, historically, to distinguish colloids such as clay from colloids already termed hydrophilic, such as gums, which exhibit such an affinity for water that they spontaneously form a colloidal solution (van Olphen, 1977). Hydrophobic colloids are liquid dispersions of small, solid particles that are (1) two-phase systems with a large interfacial surface area, (2) have a behavior dominated by surface forces, and (3) can flocculate in the presence of small amounts of salt. Clay–water–electrolyte systems satisfy all of these criteria. 6.7 ION DISTRIBUTIONS IN CLAY–WATER SYSTEMS
Adsorbed cations are tightly held on surfaces of negatively charged dry clay particles. Cations in excess of those needed to neutralize the electronegativity of the clay particles and associated anions are present as salt precipitates. When water is present, the precipitates can go into solution. The adsorbed cations, because of their high concentration near the surfaces of particles, try to diffuse away in order to equalize concentrations throughout the pore fluid. Their freedom to do so, however, is restricted by both the negative electrical field originating in the particle surfaces and ion–surface interactions that are unique to specific cations. The escaping tendency due to diffusion and the opposing electrostatic attraction lead to ion distributions adjacent to a single clay particle in suspension that are often idealized as shown in Fig. 6.10. This distribution of cations is analogous to that of air molecules in the atmosphere, where the escaping tendency of the gas is countered by the gravitational attraction of Earth. Anions are excluded from the negative force fields of the particles, with the distribution shown in Fig. 6.10. The charged surface and the distributed charge in the adjacent phase are together termed the diffuse double layer.3 Several theories have been proposed for the quantitative description of ion distributions adjacent to charged surfaces. The most frequently cited theory for ionic distribution was developed by Gouy (1910) and
3 In some clay minerals and under some conditions, broken bonds at particle edges create a positive edge charge. This charge is balanced by a negative diffuse layer. The practical consequences of positive particle edges and negative surfaces are considered later.
154
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SOIL–WATER–CHEMICAL INTERACTIONS
Figure 6.10 Distributions of ions adjacent to a clay surface according to the concept of the diffuse double layer.
Chapman (1913). Subsequently, Derjaguin and Landau (1941) and Verwey and Overbeek (1948) extended the Gouy–Chapman theory to description of the repulsive energies and forces of interaction between colloidal particles and prediction of the stability of colloidal suspensions. Their theory is now often referred to as the DLVO theory. The results have been applied to clay particles and clusters of clay particles that might be representative of actual soils. It reasonably describes the actual distribution of ions only for smectite particles suspended in monovalent electrolyte solutions at very low (less than 100 mol/m3, or 0.001 molar) concentration (Sposito, 1989). Nonetheless, it can be useful for understanding several aspects of physicochemical forces of interaction, aggregation, flocculation, dispersion, and deflocculation and the relationships of these processes to formation of soil structure and of clay compression and swelling. However, discrepancies between predictions of this theory and the behavior of most other types of clay, both in suspension and in more condensed forms, has focused attention on other theories. In particular, an alternative description of the interparticle forces proposed by Langmuir (1938) and extended by Sogami and Ise (1984), discussed in more detail in Section 6.10 postulates that long-range Coulombic attractions, as well as London–van der Waals forces, counter double-
layer repulsions. Thus, given the present controversial status of DLVO theory and considerable uncertainty about its quantitative applicability to most soil systems, it is described but not developed in detail in the following sections. Those results that are applicable to aspects of soil behavior of interest in geoengineering are noted. Readers interested in further details of the DLVO theory will find them in Mitchell (1993) and the references cited therein.
6.8
ELEMENTS OF DOUBLE-LAYER THEORY
Mathematical description of the diffuse double layer has been developed for the assumptions of both planar and spherical surfaces. The planar (one-dimensional) case is a reasonable assumption for platy clay particles. The following idealizing assumptions are made: 1. Ions in the double layer are point charges, and there are no interactions between them. 2. Charge on the particle surface is uniformly distributed. 3. The particle surface is a plate that is large relative to the thickness of the double layer (onedimensional condition).
155
ELEMENTS OF DOUBLE-LAYER THEORY
4. The permittivity4 of the medium adjacent to the particle surface is independent of position. The concentration of ions (ions/m3) of type i, ni , in a force field at equilibrium is given by the Boltzmann equation: ni ⫽ ni0 exp
冉
冊
Ei0 ⫺ Ei kT
(6.9)
The subscript 0 represents the reference state, taken to be at a large distance from the surface, E is the potential energy, T is temperature (K), and k is the Boltzmann constant (the gas constant per molecule) (1.38 ⫻ 10⫺23 J K⫺1). The potential energy of an ion in an electric field is Ei ⫽ vi e
(6.10)
where vi is the ionic valence, e is the electronic charge (1.602 ⫻ 10⫺19 C), and is the electrical potential at the point.5 Potential varies with distance from a charged surface in the manner shown by Fig. 6.11. In clays, is negative because of the negative surface charge. The potential at the surface is designated as 0. As Ei0 ⫽ 0, because ⫽ 0 at a large distance from the surface,
Figure 6.11 Variation of electrical potential with distance from a charged surface according to the idealized Gouy– Chapman theory. Except in very unusual cases, in soils is negative.
Ei0 ⫺ Ei ⫽ ⫺vi e so the Boltzmann equation [Eq. (6.7)] becomes ni ⫽ ni0 exp
冉 冊 ⫺vie
kT
(6.11)
Equation (6.11) relates concentration to potential, as illustrated by Fig. 6.12. For negatively charged clay
4
The permittivity is a measure of the ease with which molecules can be polarized and oriented in an electric field. Quantitatively, the permittivity is defined by in Coulomb’s equation for the force of electrostatic attraction F between two charges Q and Q separated by a distance d; that is, F⫽
QQ d 2
The relative permittivity or dielectric constant D is given by ⫽ 0D in which 0 is the permittivity of vacuum. D is the ratio of the electrostatic capacity of condenser plates separated by the given material to that of the same condenser with vacuum between the plates. The dielectric constant of free water at 20C is about 80. The permittivity of vacuum 0 is 8.8542 ⫻ 10⫺12 C2 J⫺1 m⫺1. 5 The electrical potential is defined as the work to bring a positive unit charge from a reference state to the specified point in the electric field.
Figure 6.12 Ion concentrations in a potential field.
⫺ particles, n⫹ i ⬎ ni0 and ni ⬍ ni0,, where ⫹ and ⫺ are for cations and anions, respectively. The Poisson equation relates potential, charge, and distance. In one-dimension:
d 2 ⫽⫺ dx 2
(6.12)
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6
SOIL–WATER–CHEMICAL INTERACTIONS
in which x is distance from the surface (m), is charge density (C/m3), and is the static permittivity of the medium (C2 J⫺1 m⫺1 or F m⫺1). The charge density in the diffuse layer is contributed by the ions so that
冘 vn
⫽e
(6.13)
i i
y⫽ z⫽
冘 vn
i i0
冉 冊
exp
⫺vie
kT
冧
kT
Potential functions
ve0
kT
⫽ Kx
Distance function
冘 vn
i i0
冉 冊
exp
⫺vie
kT
where K2 ⫽
(6.15)
Equation (6.15) is the differential equation for the electric double layer adjacent to a planar surface. Solutions of this equation provide a basis for computation of electrical potential and ion concentrations as a function of distance from the surface. For the case of a single cation and anion species of ⫺ equal valence, that is, i ⫽ 2 and n⫹ 0 ⫽ n0 ⫽ n0 and ⫹ ⫺ v ⫽ ⫺v ⫽ v, Eq. (6.15) simplifies to the Poisson– Boltzmann equation: d 2 2n0ve ve ⫽ sinh 2 dx kT
(6.18)
(6.14)
which, when substituted into Eq. (6.12), yields d 2 e ⫽⫺ 2 dx
(6.17)
and
with ni expressed as ions per unit volume. Substitution for ni from Eq. (6.11) gives ⫽e
ve
(6.16)
Some explicit solutions of Eq. (6.16) are available (Verwey and Overbeek, 1948; Bolt, 1955, 1956; Babcock, 1963; van Olphen, 1977; Mitchell, 1993). Clay particles are characterized by a constant surface charge density determined by the amount of unbalanced isomorphous substitution in the clay structure. The surface charge density is proportional to the cation exchange capacity divided by the specific surface. Double layers in many colloidal systems are controlled by a constant surface potential, determined by the concentration of ‘‘potential-determining ions’’ in solution. Diffuse layers that form at the edges of clay particles are of this type because the ions in solution control the amount of dissociation of alumina in the octahedral sheets of clay minerals. The equations given here are for constant surface charge. Single Diffuse Double Layer
Solutions of the differential equation of the double layer are usually given in terms of the dimensionless quantities
2n0e2v2 kT
(6.19)
The solution to Eq. (6.16) describes a roughly exponential decay of potential with distance from the surface. For surface potentials less than about 25 mV, the potential decreases purely exponentially with distance, and the center of gravity of the diffuse charge is at a distance x ⫽ 1/K from the surface. This distance is a measure of the ‘‘thickness’’ of the double layer. According to Eq. (6.19) the value of 1/K depends only on the characteristics of the dissolved salts and the fluid phase. However, the actual values of concentration and potential at any distance from the surface also depend on the particle surface charge, surface potential, and specific surface and dissolved ion interactions, and these depend on the type of clay and conditions in the pore solution. The double-layer charge is given by
冕
⫽⫺
⬁
0
dx
(6.20)
the solution of which is ⫽ (8n0kT)1 / 2 sinh
z 2
(6.21)
which for small values of 0 reduces to ⫽ k0
(6.22)
A single diffuse double layer is not representative of the actual conditions in most clay systems because double layers of adjacent particles will overlap. Nonetheless, the above equations are useful for understanding some effects of changes in solution composition and concentration on diffuse layer thickness, which can then be related to the behavior of clay suspensions, as discussed later.
INFLUENCES OF SYSTEM VARIABLES ON THE DOUBLE LAYER
Interacting Double Layers
The electrical potential and charge distributions for the case of interacting double layers from parallel flat plates, separated at distance 2d are shown in Fig. 6.13. The potential function at the midplane y ⫽ vec /kT is denoted by u, and the integration boundary conditions for Eq. (6.20) are that for ⫽ Kd, y ⫽ u, and dy/d ⫽ 0. Values of u for conditions of constant surface charge are tabulated by van Olphen (1977) for given values of surface potential, 2d, and K. For small interactions, that is, for large values of Kd, as would be the case for large plate separation, high n, high v, or small 0, the midplane potential is close to the sum of the double-layer potentials at distance d based on the so-
157
lutions for a single plate.6 Concentrations at the midplane can be obtained from Boltzmann’s equation: n⫺ ⫽ n0 exp(u)
n⫹ ⫽ n0 exp(⫺u)
(6.23)
As the overlap of double layers of the same sign generates an interparticle repulsion, it is important to investigate whether double layers in typical finegrained soils are sufficiently thick that interactions between adjacent particles will actually occur. Using 1/K, the distance from the surface to the center of gravity of the diffuse layer, as the thickness of double layer, values of 1 nm in a 0.1 M solution of cation, increasing to 10 nm in a 0.001 M solution are obtained. For water distributed uniformly on surfaces of clay particles, the water layer thickness is equal to half the particle spacing, or d in Fig. 6.13. This thickness is given by the volumetric water content (cm3 /g) divided by the specific surface area (m2 /g). On this basis, for a water content of 50 percent (water weight/dry solid weight) and a specific surface in the range of 50 to 300 m2 /g, values of d from 1.7 to 10.0 nm are obtained. These spacings are well within the range where interactions can be important. There is much higher concentration of divalent cations than monovalent cations near the particle surface in a system that contains both monovalent and divalent cations, even if the concentration of monovalent cations is much greater in the bulk solution. According to the DLVO theory, the ratio of concentrations of divalent cations to monovalent cations required to coagulate colloidal suspensions of clay minerals is only 0.0156 (Sposito, 1989). This value is consistent with experimental observations of the concentrations required to cause coagulation according to the Shultze– Hardy rule, developed over 100 years ago. This rule states that the critical coagulation concentration of ions in suspension of opposite sign to the charge on the colloid is proportional to an inverse power of the valence of the ion, and the power according to DLVO is 6 (Sposito, 1989). 6.9 INFLUENCES OF SYSTEM VARIABLES ON THE DOUBLE LAYER
Some significant deficiencies in the theory presented in the previous section are discussed further later. Nonetheless, it is still useful in developing an understanding of several aspects of fine-grained soil beFigure 6.13 Potential and charge distributions for interacting double layers from parallel flat plates: (a) potential and (b) charge.
6 A more rigorous solution for this problem is given by Ohshima (1995).
158
6
SOIL–WATER–CHEMICAL INTERACTIONS
havior. Ion concentration and potential distributions adjacent to charged surfaces are sensitive to variations in surface charge density or surface potential 0, electrolyte concentration n0, cation valence v, dielectric constant of the medium D, and temperature T. Approximate measures of the influences of n0, v, D, and T are given by the previously defined ‘‘thickness’’ of the double layer, 1/K.7 From Eq. (6.19)
冉
冊
1 0DkT ⫽ K 2n0e2v2
1/2
(6.24)
This relationship shows that the thickness varies inversely with the valence and the square root of the concentration and directly with the square root of the dielectric constant and temperature, other factors remaining constant. Since the long-range repulsive force between particles depends on the amount of overlap or interaction between opposing double layers, the probable influences on behavior that result from changes in system composition can be estimated. In general, the thicker the diffuse layer the less the tendency for particles in suspension to flocculate and the higher the swelling pressure in expansive soils. Effects of Electrolyte Concentration
The effective thickness of the diffuse layer, 1/K, varies inversely with the square root of pore solution concentration [Eq. (6.24)]. In addition, an increase in electrolyte concentration reduces the surface potential for the condition of constant surface charge, and the decay of potential with distance is much more rapid. The diffuse layer becomes thinner. The midplane concentration and electrical potential for interacting parallel plates (clay particles) at a given spacing decrease as concentration increases. Thus, the interparticle repulsive forces decrease. One practical consequence of this is that particle flocculation in suspension is facilitated by an increase in electrolyte concentration. Another is that one explanation for clay swelling is based on diffuse layer interactions (Chapter 10), with higher magnitudes of swell and swell pressure associated with greater interactions. Thus, swelling behavior should and does depend, at least in part, on the electrolyte concentration in the pore water.
7
Numerical examples and illustrations using the complete equations are given in Chapter 7 of Mitchell (1993).
Effects of Cation Valence
For solutions of the same concentration and constant surface charge, a change in cation valence decreases both surface potential and thickness of the double layer. The effect of valence on diffuse layer thickness is large, as can be seen from 1/K 1/ v. An increase in valence suppresses the midplane concentration and potential between interacting plates, thus leading to a decrease in interplate repulsion. Preferential adsorption of multivalent cations, which is a well-established experimental fact, means that even relatively small amounts of di- or trivalent cations added to clay–water–monovalent electrolyte systems has a significant influence on diffuse layer interactions and physical properties. In fact, multivalent cations usually limit the separation distances between clay platelets, thus imposing severe restrictions on the quantitative applicability of the Gouy–Chapman equations for the double-layer and applicability of DLVO theory. Effects of Dielectric Constant
The permittivity of the pore fluid, ⫽ 0D, can be considered in terms of the relative permittivity D, referred to as the dielectric constant. The dielectric constant influences both the surface potential and the diffuse layer thickness. For constant surface charge, the surface potential function increases as D decreases, according to
冉冊
sinh
z ⫽ (8n00DkT)⫺1/2 2
(6.25)
from Eq. (6.21). For example, for a 0.83 ⫻ 10⫺4 M solution of NaCl in ethyl alcohol (D ⫽ 24.3) compared to water (D ⫽ 80),
冉冊 冉 冊
sinh
z 80 ⫽ 94 2 24.3
1/2
⫽ 170
z ve0 ⫽ ⫽ 5.83 2 kT z ⫽ 11.66 and 0 ⫽ 292 mV
is obtained compared to 261 mV for water. The effect of dielectric constant on thickness of the double layer is given by
LIMITATIONS OF THE GOUY–CHAPMAN DIFFUSE DOUBLE LAYER MODEL
1/K D 1 / 2
6.10 LIMITATIONS OF THE GOUY–CHAPMAN DIFFUSE DOUBLE LAYER MODEL
so that with alcohol, the diffuse layer thickness is reduced by a factor of (24.3/80)0.5 or 0.55 compared to that in water. Detailed consideration of the influences of dielectric constant may, at first, seem academic because the pore fluid in soils usually is water.8 However, clay soils may be in contact with chemicals of various types, either deliberately, as when clay liners are used for impoundments and waste storage landfills, or accidentally in the case of spills and leaks. Oils, solvents, or other organic chemicals may replace the pore water in such cases. The dielectric constants of these materials, especially non-aqueous-phase liquids (NAPL), are usually much lower than that of water. Effect of Temperature
According to Eqs. (6.24) and (6.25), an increase in temperature should cause an increase in diffuse layer thickness and a decrease in surface potential for a constant surface charge, all other factors constant. However, an increase in temperature results also in a decrease in dielectric constant owing to the increased energy needed to polarize fluid molecules as the temperature increases. The variation for water is as follows:
T (C) 0 20 25 60
Effect of Temperature on the Dielectric Constant of Water T (K) D DT 273 293 298 333
88 80 78.5 66
159
2.40 2.34 2.34 2.20
⫻ ⫻ ⫻ ⫻
104 104 104 104
The small variation of the product DT with change in temperature means that the net effect on the diffuse layer is small. This accounts, in part, for apparent contradictory findings that have been reported on the effects of temperature change on such soil properties as strength, compressibility, and swelling.
The theory of the diffuse double layer provides useful insights into ionic distributions adjacent to clay particles, which, in turn, allow for reasonable predictions of some things, such as flocculation–deflocculation, swelling, and the effects of pore fluid compositional changes under idealized conditions. However, there are serious discrepancies in many cases, owing both to factors that are not accounted for by the theory, for example, pH, ion size, particle interference, and forces that are neglected, and to deviations from the idealizing assumptions. The DLVO theory, based on the Gouy–Chapman model, gives reasonable prediction for freely swelling clay systems of very fine clay particles with monovalent ions, such as Na and Li montmorillonite. The DLVO models have had limited quantitative success for other clays. Gu¨ven (1992) lists the following assumptions as unrealistic: 1. Ions are assumed to be point charges, and their sizes are ignored. 2. Water structure and the electrical properties of water molecules are not taken into account. The dielectric constant of the water is assumed the same as that of free water. 3. The clay particle charge is assumed distributed uniformly on the surface. In reality, there is charge localization, and whether the charge results from isomorphic substitution in the octahedral or tetrahedral layer influences the potential fields differently. 4. Both the ions and clay surfaces are hydrated, and this is neglected. 5. The ionic distributions based on the Boltzmann equation lead to unrealistically high concentrations at the particle surface. For example, Gu¨ven (1992) shows that for a moderate surface potential of ⫺103 mV, the concentration of sodium at the particle surface would be 0.6 M, whereas that of calcium would have to be 20.8 M for a bulk solution concentration of 0.01 M. The theory also assumes that the counterion distributions remain the same, even when two clay particles come together. In addition, there may be Coulombic attractive forces, as proposed by Sogami and Ise (1984), which are not accounted for, as noted in Section 6.7 and discussed further below. Ion Size and Type
8
Although a value of 80 is usually assumed for the dielectric constant of water in soil, experiments have indicated that adsorbed water has a much lower dielectric constant (between 2 and 50) than free water (Sposito, 1989).
The hydrated radii of cations determine their maximum possible concentrations. Values of hydrated radius for some cations are as follows:
160
6
SOIL–WATER–CHEMICAL INTERACTIONS
Ion
Hydrated Radius (nm)
Li⫹ Na⫹ K⫹ NH⫹ Rb⫹ Cs⫹ Mg2⫹ Ca2⫹ Sr2⫹ Ba2⫹
0.73–1.00 0.56–0.79 0.38–0.53 0.54 0.36–0.51 0.36–0.50 1.08 0.96 0.96 0.88
Finite ion size was taken into account by Stern (1924) and Carnie and Torrie (1984), among others. The Stern layer consists of counterions in a closely packed layer close to the surface, with an adjacent diffuse layer extending outward into the solution. Equations based on Stern’s theory are given by van Olphen (1977) for both single and interacting flat double layers. These equations can be used to compute the charge in each layer and the potential at their interface. Stern layer potentials were deduced from the results of coagulation rate measurements on four clays having about 0.5 m mean particle size, at pH 10 (Novich and Ring, 1984). The values obtained were ⫺42.7 mV for kaolinite, ⫺40.7 mV for illite, ⫺21.2 mV for montmorillonite, and ⫺66.9 mV for palygorskite. These values are significantly less than the surface potentials calculated when the computations are made without consideration of a Stern layer. However, these results are consistent with those from other studies that indicate that about 75 percent of the diffuse layer ions reside within about 1.0 nm of the particle surface (Sposito, 1989). In another series of experiments using four techniques and three smectites, Low (1987) found that almost all the counterions are in the Stern layer. This, and data and analyses reviewed in Low (1992), lead to conclusions that there is little dissociation of exchangeable cations from the particle surface, the diffuse layer is small and poorly developed, and the swelling of clay is due primarily to water hydration of particle surfaces. This explanation for swelling is discussed further in Chapter 10. The diffuse double-layer model does not account for adsorption selectivity differences among cations of the same valence. Sposito (1989) identified three mechanisms of cation adsorption on a silicate surface, as shown in Fig. 6.14. Inner-sphere cations are ions that are held within the hexagonal ‘‘hole’’ in the silicate surface, with no water molecule between the surface and the cation. Inner-sphere cations involve ionic and/or covalent bonding and are tightly held (ion fix-
Figure 6.14 Three mechanisms of cation adsorption on a silicate surface, for example, montmorillonite (from Sposito, 1989).
ation). The outer-sphere cations are solvated and adsorbed on the surface electrostatically. The readily exchangeable ions are those in the diffuse ion swarm and the outer-sphere complex. Based on considerations such as these, Gu¨ven (1992) proposed the hypothetical model shown in Fig. 6.15 for the distribution of water and ions adjacent to a clay surface. In this figure the plane is water molecule dipoles on the clay surface. Inner-sphere cations may be in this region as well. The plane is the closest plane of hydrated counterions to the surface. The D plane is the beginning of the diffuse layer. The 1/ plane is in the diffuse region where the potential has decreased to 0 /e (center of gravity of the diffuse layer charge). The plane is the shear plane that separates the portion of the bound water and cations that move with the particle from the remainder of the pore water in electrokinetic flow (see Chapter 9). Reformulations and modifications of the simple Gouy–Chapman theory have been made and evaluated (Carnie and Torrie, 1984). Modified Gouy–Chapman (MGC) theory, in which ion size is taken into account, is summarized by Sposito (1992). He concluded that the MGC provided a reasonable model for the diffuse ion swarm adjacent to basal planes of Namontmorillonite particles in low concentration (⬍100 moles/m3) solutions of 1⬊1 electrolytes. On the other hand MGC was inaccurate for electrolyte solutions containing bivalent ions, even at concentrations as low as 5 mol/m3. Computer simulations offer possibilities for better definition of the actual conditions. The consequences of the following 10 interactions must be considered (Gu¨ven, 1992): (1) water molecule–water molecule, (2) counterion–counterion, (3) coion–coion, (4) clay particle–clay particle, (5) water molecule–counterion,
LIMITATIONS OF THE GOUY–CHAPMAN DIFFUSE DOUBLE LAYER MODEL
Figure 6.15 (a) Multilayer configuration of water and ions adjacent to a clay particle surface as proposed by Gu¨ven (1992). (b) Decay of surface potential 0 with distance from the
surface.
161
162
6
SOIL–WATER–CHEMICAL INTERACTIONS
(6) water molecule–coion, (7) water molecule–clay particle, (8) counterion–coion, (9) counterion–clay, and (10) coion–clay. The net interaction potential of the system is the sum of the interaction energies of the components. Gu¨ven (1992) outlines both Monte Carlo (MC) and molecular dynamics (MD) computer simulation procedures for finding this sum as follows. First, several hundred particles are put in a box with finite dimensions. The coordinates of the particles are defined, and interactions between them are defined in terms of potentials. MC simulations involve sampling all particle configurations in the box and finding changes in potential energy caused by particle movements. The most stable configuration is that where the energy is least. In MD simulations, the equations of motion are solved numerically for the particle in the box. Both the configuration and the dynamics of particle in a liquid are determined. According to Gu¨ven (1992), both MC and MD methods can be used to better describe clay–water interface details and help in the understanding of clay particle interactions with each other. Recent applications of Monte Carlo simulations for study of net interaction forces between clay particles are described by Delville (2002). Skipper (2002) describes the application of both MC and MD computer simulations for modeling of clay–fluid interactions in Wyoming bentonite. Ion Redistributions
As noted earlier, the capabilities of diffuse doublelayer models, in which the electrical force is assumed to be repulsive at all interparticle separations, have been challenged by McBride (1997), McBride and Baveye (2002a, 2002b), and others. An alternative description of the fundamental forces is proposed based on the work by Langmuir (1938) and backed up by the electrostatic attraction theory (Sogami and Ise, 1984, Smalley, 1990) and simulation studies using the Monte Carlo technique. When two clay particles merge, an attractive electrostatic force results due to redistribution of counterions (Fig. 6.16b), which is not considered in the DLVO theory (Fig. 6.16a). The attractive force model is supported by the observation that particles in stable dispersions do not necessarily occupy all the volume of the solution as would be expected from the long-range repulsive forces of the DLVO model. Rather they tend to cluster at separations that are not space filling (McBride, 1997). In such a system, the long-range Coulombic attractive force is resisted by hydration and osmotic forces, and the overall force changes from attractive to repulsive due to osmotic forces once the clay plates separate by more than ˚ ) based on the work by some distance (10 to 30 A
Figure 6.16 Ion distributions according to DLVO and alter-
native (electrostatic attraction) theories: (a) DLVO repulsive and (b) alternative attractive.
MacEwan (1948) and Norrish (1954). McBride (1997) and McBride and Baveye (2002a) review numerous experimental observations, including dispersion, osmotic swelling, and transitions among ordered and disordered phases of colloidal particles in dilute salt solutions, to support the existence of an electrostatic attractive term. Clay Platelet Associations and Particle Interference
Diffuse double-layer theory assumes individual and independent colloidal particles. When applied to smectite clay particles, it is usually assumed that the total specific surface, about 800 m2 /g, is covered with a uniformly thick layer of water and adsorbed cations. In reality, however, this is usually not the case, and the platelets stack into tactoids or quasi-crystals (Quirk and Aylmore, 1971). When calcium is the adsorbed cation, a typical quasi-crystal consists of four to seven montmorillonite platelets interspersed by two or three molecular layers of water. Each calcium ion is solvated by six water molecules and acts as a cross-link holding the platelets together. This type of cross-linking is probable with any divalent cation and smectite type (Sposito, 1989). There is clear evidence from light-scattering, neutron-scattering, and other experiments that quasicrystals also form in the presence of monovalent cations (Sposito, 1989, 1992). The number of platelets per quasi-crystal in monovalent cation systems ranges from 1 to 2 and increases on the order Li ⬍ Na ⬍ K. For nonexpansive clay minerals such as kaolinite and illite, the situation is somewhat different. Individual particles of these minerals are much thicker than smectite unit layer platelets and may consist of up to several hundred unit cell layers. The particle thickness
163
ENERGY AND FORCE OF REPULSION
is large relative to the diffuse layer thickness. As a result, gravity forces are important in suspensions of these minerals, and physical interferences between particles are important in sediments in addition to the influences of double-layer interaction effects. Effect of pH
Hydroxyls (OH)⫺ are exposed on the surfaces and edges of clay particles. The tendency for hydroxyls to dissociate in water, SiOH → SiO⫺ ⫹ H⫹ is influenced strongly by the pH. By definition, pH ⫽ ⫺log10 H⫹ concentration: pH ⬍ 7 is acid (high H⫹ concentration), and pH ⬎ 7 is basic (low H⫹ concentration). The higher the pH, the greater is the tendency for H⫹ from the hydroxyls to go into solution, and the greater the effective negative charge of the particle. Hence, the octahedral face of 1⬊1 minerals such as kaolinite and the OH termination sites on the edges of both 1⬊1 and 2⬊1 clay minerals are affected by the pH. In addition, alumina, which is exposed at the edges of clay particles, is amphoteric, and it ionizes positively at low pH and negatively at high pH. As a result, positive diffuse layers can develop at the edges of some clay particles in an acid environment. Such layers are of the constant surface potential type, as opposed to the constant surface charge type, with H⫹ serving as the potential determining ion. The surface potential is related to the pH of the solution, and therefore pH plays a very important role in the behavior of clay suspensions, especially kaolinite. A low pH promotes positive edge to negative surface interaction, often leading to flocculation from suspension. Stable suspensions or dispersions of clay particles often require high pH conditions. For clay minerals with a small thickness-to-length ratio such as smectite, the contribution of OH termination sites at the edges is small relative to the total charge of the particles. Anion Adsorption
Some anion types may be attracted to, and become essentially a part of, particle surfaces or edges, thereby increasing the particle’s electronegativity. Some negatively charged radicals, for example, phosphate, arsenate, and borate, have about the same size and geometry as the silica tetrahedron and are in this category. Phosphates, in particular, are strongly attracted, and certain of the phosphate compounds are among the most effective deflocculating agents for soil suspensions. Tannates can improve the stability of drilling muds (van Olphen, 1977). The tannate ions are ad-
sorbed at particle edges by complexing with the exposed octahedral aluminum ions. This produces a negative edge charge that prevents edge-to-face flocculation. The surface chemistry of anion adsorption is discussed in some detail by Sposito (1989). Little is known about whether clays have anion exchange spots on basal surfaces, although replacement of (OH)⫺ is a possible mechanism for their existence. Anions, particularly bicarbonate, appear to be important in spontaneous dispersion followed by erosion of some low-to-medium sodium content Australian soils (Ingles, 1972).
6.11
ENERGY AND FORCE OF REPULSION
The DLVO theory is used to compute the potential and charge distribution between interacting diffuse double layers and the force of electrostatic repulsion per unit area of parallel plates. The repulsive energy VR is given by VR ⫽ 2(Fd ⫺ F⬁)
(6.26)
where Fd is the free energy of the double layer per unit area at a plate spacing of 2d, and F⬁ is the free energy of a single noninteracting double layer. Although cations are free to redistribute around the negatively charged clay particles, they are unlikely to leave the space between the particles because of the need to preserve an electrically neutral condition. An osmotic pressure develops as free water molecules in the bulk fluid try to move into the interparticle space to reduce the concentration. The repulsive force per unit area (repulsive pressure) that is generated equals the difference in osmotic pressure (see Chapter 10) midway between plates relative to that in the equilibrium solution. The osmotic pressure difference depends directly on the difference in numbers of ions in the two regions, that is, ⫺ ⫹ ⫺ p n⫹ c ⫹ nc ⫺ (n0 ⫹ n0 )
Therefore, using Eq. (6.23), p n0eu ⫺ n0 ⫹ n0e⫺u ⫺ n0 ⫽ 2n0 (cosh u ⫺ 1) The resulting equation p ⫽ 2n0kT (cosh u ⫺ 1)
(6.27)
is valid for both constant charge and constant potential surfaces, with u computed for the appropriate condition. This relationship has been used, with limited suc-
164
6
SOIL–WATER–CHEMICAL INTERACTIONS
cess, for physicochemical description of clay swelling and swelling pressure, as considered further in Chapter 10.
F2 ⫽
C dyn/cm2 d 4
(6.29)
where d is separation distance in micrometers and 6.12
C ⫽ 1.0 ⫻ 10⫺3 to 2.0 ⫻ 10⫺3
LONG-RANGE ATTRACTION
Fluctuating dipole bonds, or van der Waals forces (Section 3.4), act between all units of matter and cause attraction between colloidal particles. The theory for attractive energy between pairs of molecules VA (London, 1937) was extended to obtain the attraction energy between parallel plates by assuming interactions to be additive (Casimir and Polder, 1948). The following equation was obtained:
冋
A 1 1 2 VA ⫽ ⫺ ⫹ ⫺ 2 2 48 d (d ⫹ ) (d ⫹ /2)2
册
(6.28)
where d is the half distance between plates measured from the plane of surface layer atoms, is the thickness of the plate measured between the same planes, and A is the Hamaker constant, which is on the order of 2 ⫻ 10⫺20 J for soil colloids, although there is considerable uncertainty about its value in silicate–water systems (Sridharan, 2002). Values of A calculated from theoretical analysis of coagulation measurements are 3.1 ⫻ 10⫺20 J for kaolinite, 2.5 ⫻ 10⫺20 J for illite, 2.2 ⫻ 10⫺20 J for montmorillonite, and 1.63 ⫻ 10⫺19 J for palygorskite (Novich and Ring, 1984). The van der Waals forces are electromagnetic, and the instantaneous electric moment is frequency dependent. As a result, the Casimir–Polder theory is not exact, but it is a good approximation for particle ˚ ), which separations less than about 100 nm (1000 A would seem to cover the practical range of interest for geotechnical problems. The attractive forces are dependent on distance according to
F1
Ak d3
Casimir–Polder theory
F2
Bk d4
Lifshitz theory
where A, B, k and k are constants (Ingles, 1962); B, an analytically deducible constant (Lifshitz, 1955), is on the order of 10⫺28 J-m. Black et al. (1960) determined a force per square centimeter between parallel quartz plates given by
⫺3
C ⫽ 0.6 ⫻ 10
⫺3
to 1.6 ⫻ 10
(experimental) (Lifshitz theory)
According to the general theory, there is a dependence of the attractive forces on the dielectric constant of the fluid medium. As the strength of a soil depends in part on interparticle attractions, it would be expected that the strength would also be influenced by dielectric constant. The variation of the undrained strength of kaolinite (normalized to that with water as the pore fluid) with dielectric constant is shown in Fig. 6.17. In each case samples were consolidated initially in water, followed by leaching with water-miscible pore fluids. This procedure was used to produce samples of essentially the same fabric (particle arrangements) for each test. The form of the relationship defined by the data agrees well with predictions of the Lifshitz theory (Moore and Mitchell, 1974). With the introduction of the electrostatic attraction theory, discussed earlier, as an alternative to the DLVO theory, there appears to be increased uncertainty about the actual magnitude and importance of van der Waals attractive forces in soil–water systems.
6.13
NET ENERGY OF INTERACTION
By combining relationships for diffuse layer energies of repulsion with those for van der Waals attraction, curves of net energy of interaction as a function of
Figure 6.17 Dependence of the strength of Peerless #2 ka-
olinite on dielectric constant of the pore fluid.
CATION EXCHANGE—GENERAL CONSIDERATIONS
distance of the type shown in Fig. 6.18 are obtained.9 The energy of repulsion is sensitive to changes in electrolyte concentration, cation valence, dielectric constant, and pH, whereas, in theory, the attractive energy is sensitive only to changes in the dielectric constant and temperature. If the net curve of interaction exhibits a high repulsive energy barrier, particles in suspension are prevented from close approach, and the suspension is stable. If the repulsive energy barrier does not exist, particles can easily come into close proximity, and flocculation results, represented by the minima in the energy curves. In these systems, flocs or aggregates of several particles settle together from suspension. The character of the net curve of interaction has a major influence on particle arrangement and stability in sedimented, consolidated, or compacted deposits of fine-grained soils. Changes in system chemistry, which in turn cause changes in the net curve of interaction,
9
In reality there are important interparticle forces additional to double-layer repulsions and van der Waals attractions, as defined and discussed in Chapter 7 of Mitchell (1993) and by Gu¨ven (1992), as well as the electrostatic attraction hypothesized by Sogami and Ise (1984), that should be accounted for in a comprehensive treatment. However, the basic DLVO model given here is suitable for developing basic concepts of interparticle interactions and the stability of clay suspensions.
can have important consequences in terms of the subsequent behavior of the soil if it is disturbed or subjected to the action of flowing water, as discussed in later chapters.
6.14 CATION EXCHANGE—GENERAL CONSIDERATIONS
Under a given set of environmental conditions (temperature, pressure, pH, chemical and biological composition of the water), clay adsorbs cations of specific types and amounts. The total amount adsorbed balances the charge deficiency of the solid particles. Exchange reactions can occur in response to changes in the environmental conditions. These reactions involve replacement of a part or all of the adsorbed ions of one type by ions of another type. Although the exchange reactions do not ordinarily affect the structure of the clay particles themselves, important changes in the physical and physicochemical properties of the soil may result. Common Ions in Soils
The most common adsorbed cations in residual and nonmarine sedimentary soils are calcium, magnesium, sodium, and potassium, usually in that decreasing or-
Figure 6.18 Energies of repulsion, attraction, and net curves of interaction for parallel flat
plates.
165
166
6
SOIL–WATER–CHEMICAL INTERACTIONS
der of abundance. Marine clays and most saline soils contain sodium as the dominant adsorbed cation. The most common anions are sulfate, chloride, phosphate, and nitrate.
Na⫹ ⬍ Li⫹ ⬍ K⫹ ⬍ Rb⫹ ⬍ Cs⫹ ⬍ Mg2⫹ ⬍ Ca2⫹ ⬍ Ba2⫹ ⬍ Cu2⫹ ⬍ Al3⫹ ⬍ Fe3⫹ ⬍ Th4⫹
Sources of Exchange Capacity
There are three sources of clay exchange capacity: 10
3⫹
4⫹
1. Isomorphous Substitution Al for Si in the silica sheet and Mg2⫹ for Al3⫹ in the octahedral sheet are the most common. Balancing cations are attracted to cleavage surfaces. This is the major source of clay exchange capacity, except for the kaolin minerals. 2. Broken Bonds Exchange sites along particle edges and on noncleavage surfaces may be the major source of the exchange capacity of kaolinite and contribute up to 20 percent of the total in smectite. The importance of broken bond sites increases with decreasing particle size. 3. Replacement The hydrogen of an exposed hydroxyl is replaced by another type of cation. The contributions of each of these sources depends on various environmental and compositional factors, so a given clay mineral does not have a fixed, single value of exchange capacity. The capacity is directly related to the specific surface and surface charge density. Exchange Capacities of the Clay Minerals
The cation exchange capacity, that is, the number of exchangeable charges, is usually between 1 and 150 meq/100 g. Ranges of cation exchange capacity for different clay types are given in Table 3.6. These values represent the amount of exchangeable cations that can be replaced easily by leaching with a solution containing other dissolved cations of higher replacing power than the adsorbed cation. The manner in which cations are held by clay particles was illustrated in Fig. 6.14. Cation Replaceability
Cations of one type can replace cations of another type. For example, Ca2⫹ may replace Na⫹, Na⫹ can replace Ca2⫹, Fe3⫹ can replace Mg2⫹, and so forth, depending on the conditions. The ease of replacement depends mainly on the valence, relative abundance of the different ion types, and ion size. Other things equal, trivalent cations are held more tightly than divalent cations, and divalent cations are held more tightly than
10
monovalent cations. Ordinarily, small cations tend to displace large cations. A typical replaceability series is
See Chapter 3 for definition and discussion of isomorphous substitution.
However, it is possible to displace a cation of high replacing power, such as Al3⫹, by one of low replacing power, such as Na⫹, by mass action, if the concentration in solution of the ion of low replacing power is high relative to that of the ion of high replacing power. Rate of Exchange
The rate of exchange depends on clay type, solution concentrations, temperature, and the like. In general, exchange reactions in the kaolin minerals are almost instantaneous. In illite, a few hours may be needed for completion because a small part of the exchange sites may be between unit layers. A longer time is required in smectite because the major part of the exchange capacity is located in the interlayer regions. Stability of Adsorbed Ion Complexes
Ion exchange reactions usually occur in an aqueous environment; however, clays can also adsorb ions from trace concentrations in solution of rather insoluble substances, even when little water is present. The deterioration of clay samples after prolonged storage in steel Shelby tubes is a good example. The process involves adsorption by the clay minerals of iron ions as soon as they pass into solution from the tube wall. Because the clay immobilizes the iron ions quickly, there is further solution from the metal tube, and the process continues. The result is that after some weeks or months, the clay in contact with the sample tube is altered and no longer representative of the in situ material from which it was taken. Stainless steel, brass, or plastic tube liners are often used to minimize the corrosive process; however, they are usually not effective over long time periods. Attempts to prepare hydrogen clay in which the exchange sites are filled with hydrogen ions have been unsuccessful. The resulting material is more similar to clay containing di- or trivalent cations than monovalent cations. The reason is that after preparation of the hydrogen clay, aluminum ions move from octahedral lattice positions and displace the hydrogen ions from the exchange sites, thus producing aluminum clay. The selectivity of clay surfaces for different ions in mixed-ion systems is temperature dependent. For example, the composition of the interstitial waters of a clayey marine sediment was altered as a result of a change in temperature from 5C at the ocean bottom
167
SOIL–INORGANIC CHEMICAL INTERACTIONS
to 22.5C in the laboratory (Bischoff et al., 1970). The free pore water concentrations of potassium and chlorine were increased by 13 and 1.4 percent, respectively, whereas magnesium and calcium concentrations were depleted by 2.4 and 4.9 percent. The proportions of these constituents in the exchange complex must have changed in the opposite direction. In another case, the interstitial silica concentration in water squeezed from a marine sediment was 51 percent higher after warming to a temperature 20C above the in situ value, and the pH was slightly increased (Fanning and Pilson, 1971). Testing should be done at in situ temperatures if in situ conditions are to be maintained and representative property values are to be measured. 6.15
THEORIES FOR ION EXCHANGE
Development of generally applicable quantitative theories for equilibrium concentrations and the rate of ion exchange is difficult because of the great complexity of the system and the large number of variables involved. Theoretical approaches have included application of the mass law, kinetic theory, double-layer theory, and molecular dynamics. Some publications in soil and clay chemistry that present detailed thermodynamic and physicochemical treatment of the subject include Townsend (1984), Laudelout (1987), McBride (1989), and Sposito (1989). For mixed cations of the same valence, the ratio of counterion concentrations in the double layer is not the same as in the equilibrium solution because of differences in ion size and specific interaction energies. These differences are responsible for different positions of the monovalent cations in the replaceability series given earlier. In systems containing both monovalent and divalent cations, the ratio of divalent to monovalent cations is much higher in the adsorbed layer than in the equilibrium solution. The Gapon equation is useful for estimating the proportions of monovalent and divalent ions, except in highly acid soils. If subscript s refers to the exchange complex of the soil, subscript e refers to the equilibrium solution, M and N are monovalent cation concentrations, and P refers to the concentration of divalent ions, then
冉 冊 冉 冊 M⫹ N⫹
M⫹ P2⫹
⫽ k1
S
S
⫽ k2
冉 冊 冋 册 M⫹ N⫹
(6.30)
e
M⫹ (P2⫹)1/2
(6.31)
e
where k1 and k2 are selectivity constants, which must be determined experimentally.
A useful practical form of the Gapon equation is
冉
冊 冋
Na⫹ Ca2⫹ ⫹ Mg2⫹
⫽k
S
[(Ca2⫹
册
Na⫹ ⫹ Mg2⫹)/2]1/2
e
(6.32) in which concentrations are in milliequivalents per liter. The quantity
冋
2⫹
[(Ca
Na⫹ ⫹ Mg2⫹)/2]1/2
册
⫽ SAR (meq/liter)1/2
e
(6.33) is termed the sodium adsorption ratio (SAR). The SAR can be determined by chemical analysis of the pore water. The selectivity constant k is about 0.017 for a range of arid zone soils. Thus, if the composition of the pore fluid is known, the relative amounts of monovalent and divalent ions in the adsorbed cation complex can be estimated. Bruggenwert and Kamphorst (1979) provide data on the exchange properties and selectivity coefficients for a large number of clays. The proportion of sodium in the adsorbed layer has an important influence on the structural status of a soil and can be described in terms of the exchangeable sodium percentage (ESP), defined by ESP ⫽
(Na⫹)S ⫻ 100 total exchange capacity
(6.34)
The ESP and the SAR are good indicators of the stability of clay soil structure to breakdown and particle dispersion, at least for nonmarine clays. Soils with ESP greater than about 2 percent may be susceptible to spontaneous dispersion in water and behave as dispersive clays, as discussed in Section 8.14. The ESP and the SAR are uniquely related for most soils, as can be seen from manipulation of Eqs. (6.33) and (6.34) and from the test data shown in Fig. 6.19. Since the SAR is more easily determined than the ESP, it is more widely used in practice.
6.16 SOIL–INORGANIC CHEMICAL INTERACTIONS
The preceding sections of this chapter focus on the interactions of water with soil particle surfaces and on the forces between small soil particles in the presence of water and electrolytes. The phenomena described have little or no effect on the soil particles themselves. Nonetheless, the consequences of these interactions, for example, flocculation, dispersion, swelling, shrink-
168
6
SOIL–WATER–CHEMICAL INTERACTIONS
• Organic matter is reactive in high and low pH environments.
The magnitudes and rates of these reactions are often central to the evaluation of their geotechnical importance; however, our knowledge and ability to predict them well are limited. More details about some of them and their geotechnical consequences are given throughout this book.
6.17 CLAY–ORGANIC CHEMICAL INTERACTIONS
Figure 6.19 Correlation between exchangeable sodium per-
centage and sodium adsorption ratio. Reprinted from Sherard et al. (1972) with permission of ASCE.
age, and plasticity, are fundamental to virtually all aspects of soil behavior, as illustrated by the discussions and illustrations throughout this book. In addition, exposure of soil materials to some inorganic chemicals can initiate a variety of processes that cause reactions and alterations of the particles and other constituents of the soil mass. Among these reactions are:
• Acids dissolve carbonates, iron oxides, and the
•
• • •
alumina octahedral layers of clay mineral. The use of hydrochloric acid for identification of carbonate minerals by observation of a rapid effervescence reaction is standard practice. Bases can break down silicate minerals. The creation of a high pH environment (pH of 12.4 or greater) is essential to the effectiveness of lime [CaO or Ca(OH)2] stabilization of clays by means of pozzolanic reactions wherein calcium–silicate– hydrate cementing materials are formed using silicate from the broken down clay minerals. If sulfates are present, highly expansive minerals may form, as well. Oxidation of sulfides, especially pyrite, leads to formation of sulfuric acid that, in turn, can break down some rock minerals and generate gas. Reduction of sulfates creates an alkaline environment and, among other things, this is important in the formation of quick clay (see Section 8.11). Iron oxidation and reduction reactions are important in the formation and dissolution of iron particle coatings and iron oxide precipitates.
Clay–organic chemical reactions occur in many forms and are important in agriculture, petroleum engineering, the technology of drilling fluids, the stability control of clay suspensions, the manufacture of lubricants, and even the origins and development of life itself. Clay–organic chemical interactions are important in geotechnical and geoenvironmental engineering in such problems as the migration, containment, and cleanup of toxic wastes; the influences of organics of various types on physical properties; geomicrobiological phenomena; and soil grouting and soil stabilization using organic compounds and polymers. Organic materials interact with clays by (1) adsorption on particle surfaces, for example, by hydrogen bonds, (2) ion exchange, (3) attraction of large organic molecules to clay surfaces by van der Waals forces, and (4) intercalation (Lagaly, 1984). Intercalation is the entry of organic molecules between silicate layers. Adsorption of organic compounds on clay surfaces in aqueous systems depends on the available surface and the ability of the organic molecules to displace water molecules that would otherwise be adsorbed. Cationic organics can exchange for inorganic adsorbed cations; however, if the organic cation is larger than the cation site, then all exchangeable cations cannot be displaced. Attraction of large organic molecules to clay surfaces by van der Waals forces may contribute to the total amount of organics held (Raussell-Colom and Serratosa, 1987). The most important properties of organic molecules relative to their interactions with clays are their polarity, polarizability, solubility, size, and shape. Because of the many types of clays and the range of physical and chemical environments in which they are found and the almost limitless number of different organic compounds, clay–organic chemical interactions are both numerous and complex. Many of these interactions are described by Lagaly (1984), Raussell-Colom and Serratosa (1987), Oades (1989), and Sposito (1989). Yariv (2002) provides a comprehensive and detailed overview of organoclay interactions. House
QUESTIONS AND PROBLEMS
(1998) discusses interactions of nonvolatile microorganic pollutants with clays in the near-surface environment. Jackson (1998) describes interactions between heavy metals, colloids, complexing agents, and organisms. Organically modified clays are available that can be used for a variety of applications, including waste stabilization, water purification, oil and hydrocarbon spill control, and landfill liners. Organophilic clays, most commonly composed of bentonite, are manufactured by attaching an organic compound to the clay by an ion exchange reaction. The modified clay can act as an adsorbent for other organic compounds with which it comes into contact. The science and technology of these materials are described by Alther et al. (1988) and Stockmeyer (1990).
6.18
CONCLUDING COMMENTS
Water is strongly adsorbed by clay minerals, and this has important consequences as regards almost all aspects of soil behavior. The energy status of adsorbed water is different than that of normal water, and this can influence measured pore pressures, be responsible for time-dependent changes in water structure, and influence physical properties. These effects are considered further in subsequent chapters. The viscosity and diffusion properties of adsorbed water in clays are essentially the same as those for bulk water. This means that linear flux–force relationships for analysis of flow problems, such as Darcy’s law for hydraulic flow and Fick’s law for chemical diffusion, should be applicable even in high plasticity clays. Understanding the colloidal behavior of clays gives insight into flocculation–deflocculation phenomena in suspensions, swelling behavior, and the structure and structural stability of fine-grained soils. It provides a basis for predicting the effects of changes in pore solution chemistry on engineering properties. These applications are developed more fully in later chapters of this book. Some methods of soil stabilization using admixtures depend, at least in part, on ion exchange and changes in diffuse layer interactions to alter interparticle forces and particle arrangements. One example is the use of dispersing chemicals to produce deflocculated, dispersed particle arrangements and a high density to ensure a low hydraulic conductivity. Another is the use of a flocculating chemical to give a higher strength or a more open particle arrangement to facilitate drainage. Ion exchange reactions are important in determining properties and stability control of clays used in slurry walls. As the composition of the exchange complex relative to that of the free pore water is influenced by
169
both temperature and composition of the free water, and as mechanical properties are influenced by the adsorbed ion types, controls on laboratory testing conditions are needed if properties that properly mirror those in situ are to be obtained. Understanding the colloidal and ion exchange properties of clays is crucial for the appropriate usage of clays in waste containment barrier systems. Both the ion exchange and structural stability properties are important, as ion exchange determines the adsorption and desorption of different chemicals and the structural status controls the hydraulic conductivity and strength. Potential changes over times of several tens of years are important in safe storage of hazardous waste; times of several tens of thousands of years are of concern in safe storage of nuclear waste. Reliable assessment of the long-term stability of clay–water–electrolyte systems when used in these applications is one of the most challenging current geotechnical problems.
QUESTIONS AND PROBLEMS
1. What is likely to happen in response to the following actions? Why? a. Sodium hydroxide is added to a suspension of flocculated kaolinite particles. b. Hydrochloric acid is added to a suspension of dispersed kaolinite particles. c. A dispersed suspension of kaolinite in water is dumped into seawater. d. Water is mixed with dry bentonite. e. Kerosene is mixed with dry bentonite. f. Water is added and mixed with a previously mixed bentonite–kerosene mixture. g. Kerosene is added and mixed with a bentonite– water paste. h. Stiff clay consisting primarily of smectite is exposed by excavation and given access to rainwater. i. The same stiff clay as in part (h) is exposed by excavation and given access to saltwater. j. A dispersant chemical, for example, a sodium polyphosphate, is mixed with a sandy clay prior to compaction for use in the core of an earth dam. k. If the dam core in part (j) is well compacted, what are the likely consequences if the dispersing chemical is subsequently leached out by reservoir seepage through the core? 2. Are changes in pH likely to have a greater effect on a suspension of smectite or kaolinite? Why?
170
6
SOIL–WATER–CHEMICAL INTERACTIONS
3. Assume that a clay–water–electrolyte system behaves in accordance with the assumptions of the Gouy–Chapman theory. Show the effects of changes in the following on diagrams of (1) cation and anion concentration as a function of distance from a negatively charged particle surface and (2) electrical potential as a function of distance from surface: a. Ionic concentration in the pore solution b. Valence of adsorbed cation c. Dielectric constant of the pore fluid d. pH e. Temperature f. Anion adsorption 4. Indicate whether increases in each of the following characteristics of the pore water of a fine-grained soil will promote flocculation or deflocculation of a clay suspension. Justify each answer either analytically or by a clear statement of cause and effect. a. Electrolyte concentration b. Cation valence c. pH of the pore water d. Dielectric constant 5. Should changes in pore water chemistry have greater influence on the properties of clay at water content near the liquid limit or the plastic limit? Why? 6. Estimate the electrical potential at the surface of an illite clay particle suspended in (1) freshwater and (2) seawater assuming that the assumptions of the Gouy–Chapman theory of the double layer apply. The cation exchange capacity of the clay is 25 meq/100 g. There are 500 ppm of salt dissolved in the freshwater, which may all be assumed to be NaCl for this analysis. The specific surface area of the clay is 80 m2 /g. The exchangeable cation on the clay is sodium. Assume that the dielectric constant of the solution is 80 and that T ⫽ 15C. 7. Do the following: a. Estimate the water content of sodium montmorillonite when it contains 0.01 M NaCl solution, and the amount of solution present is sufficient to provide a water layer thickness on particle surfaces equal to the double-layer ‘‘thickness’’ of 1/K. Assume the dielectric constant of solution is 80 and the temperature is 20C.
b. Estimate the water content of sodium kaolinite in the same solution. c. On the basis of the values obtained in parts (a) and (b) draw a conclusion about the probable importance of double-layer interactions in the compression and swelling of kaolinite and montmorillonite. What mechanisms other than double-layer interactions can resist compression under applied stress? 8. If a direct current electric field is placed across saturated soft clay, what might happen? 9. If a direct current electric field is placed across a dispersion of clay particles in water, what might happen? 10. Which, if either, should be most affected by exposure to chemicals when used as a waste containment barrier: (1) a bentonite slurry wall or (2) a compacted clay liner? Why? 11. Are marine clays likely to behave as dispersive clays? Why? 12. Tests on a clay indicate the following properties: Cation exchange capacity ⫽ 50 meq/100 g Specific gravity of solids ⫽ 2.70 Specific surface ⫽ 250 m2 /g Water content ⫽ 50 percent Degree of saturation ⫽ 100 percent a. What is the average interparticle spacing? b. If ferrous iron is the exchangeable cation, what percentage of the dry soil weight is attributable to exchangeable iron? Atomic weight of iron ⫽ 56 Valence of ferrous iron ⫽ 2 Atomic number of iron ⫽ 26 c. Would you expect this clay to be dispersive? If not, what transformations might make it become dispersive? 13. Consider undisturbed normally consolidated, saturated, soft, illitic marine clay. Indicate the probable effects of each of the following changes: (1) decrease pore water salt content, (2) disturbance and remolding, and (3) ion exchange to Ca2⫹ on the following: a. Strength b. Liquid limit
QUESTIONS AND PROBLEMS
c. Permeability d. Sensitivity e. Void ratio under constant effective stress The probable effects should be indicated as I for increase, D for decrease, or N for negligible. Give reasons for your choices. 14. Compounds such as sodium hydroxide and sodium polyphosphates are frequently used as dispersing agents in soil testing laboratories. Compounds such as calcium chloride and hydrochloric acid are normally used as flocculating agents to accelerate sedimentation of clay suspensions. Indicate the mechanisms responsible for the effectiveness of each of these chemicals.
171
15. Present evidence indicates that the viscosity of water in clays is not influenced by the attraction of the water molecules to the clay surface, that is, the viscosity of free water and adsorbed water should be about the same. If this is true, then the flow of water through a clay pore should be Newtonian, that is, the velocity of flow will be directly proportional to the driving force. Given that the hydraulic gradient is a direct measure of the driving force, it would seem to follow that Darcy’s law should always be obeyed. There are situations, however, where measurements have indicated that this is not true, and the flow rate has been found to vary with gradient and/or time. What are some possible causes of this behavior?
CHAPTER 7
Effective, Intergranular, and Total Stress
7.1
INTRODUCTION
The compressibility, deformation, and strength properties of a soil mass depend on the effort required to distort or displace particles or groups of particles relative to each other. In most engineering materials, resistance to deformation is provided by internal chemical and physicochemical forces of interaction that bond the atoms, molecules, and particles together. Although such forces also play a role in the behavior of soils, the compression and strength properties depend primarily on the effects of gravity through self weight and on the stresses applied to the soil mass. The state of a given soil mass, as indicated, for example, by its water content, structure, density, or void ratio, reflects the influences of stresses applied in the past, and this further distinguishes soils from most other engineering materials, which, for practical purposes, do not change density when loaded or unloaded. Because of the stress dependencies of the state, a given soil can exhibit a wide range of properties. Fortunately, however, the stresses, the state, and the properties are not independent, and the relationships between stress and volume change, stress and stiffness, and stress and strength can be expressed in terms of definable soil parameters such as compressibility and friction angle. In soils with properties that are influenced significantly by chemical and physicochemical forces of interaction, other parameters such as cohesion may be needed. Most problems involving volume change, deformation, and strength require separate consideration of the stress that is carried by the grain assemblage and that carried by the fluid phases. This distinction is essential because an assemblage of grains in contact can resist both normal and shear stress, but the fluid and gas
phases (usually water and air) can carry normal stress but not shear stress. Furthermore, whenever the total head in the fluid phases within the soil mass differs from that outside the soil mass, there will be fluid flow into or out of the soil mass until total head equality is reached. In this chapter, the relationships between stresses in a soil mass are examined with particular reference to stress carried by the assemblage of soil particles and stress carried by the pore fluid. Interparticle forces of various types are examined, the nature of effective stress is considered, and physicochemical effects on pore pressure are analyzed.
7.2
PRINCIPLE OF EFFECTIVE STRESS
The principle of effective stress is the keystone of modern soil mechanics. Development of this principle was begun by Terzaghi about 1920 and extended for several years (Skempton, 1960a). Historical accounts of the development are described in Goodman (1999) and de Boer (2000). A lucid statement of the principle was given by Terzaghi (1936) at the First International Conference on Soil Mechanics and Foundation Engineering. He wrote: The stresses in any point of a section through a mass of soil can be computed from the total principal stresses, 1, 2, 3, which act in this point. If the voids of the soil are filled with water under a stress u, the total principal stresses consist of two parts. One part, u, acts in the water and in the solid in every direction with equal intensity. It is called the neutral stress (or the pore water pressure). The balance 1 ⫽ 1 ⫺ u, 2 ⫽ 2 ⫺ u, and 3 ⫽ 3 ⫺ u represents an excess over the neutral stress u, and it has its seat exclusively in the solid phase of the soil.
173
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EFFECTIVE, INTERGRANULAR, AND TOTAL STRESS
This fraction of the total principal stresses will be called the effective principal stresses . . . . A change in the neutral stress u produces practically no volume change and has practically no influence on the stress conditions for failure . . . . Porous materials (such as sand, clay, and concrete) react to a change of u as if they were incompressible and as if their internal friction were equal to zero. All the measurable effects of a change of stress, such as compression, distortion and a change of shearing resistance are exclusively due to changes in the effective stresses 1, 2 and 3. Hence every investigation of the stability of a saturated body of soil requires the knowledge of both the total and the neutral stresses.
In simplest terms, the principle of effective stress asserts that (1) the effective stress controls stress– strain, volume change, and strength, independent of the magnitude of the pore pressure, and (2) the effective stress is given by ⫽ ⫺ u for a saturated soil.1 There is ample experimental evidence to show that these statements are essentially correct for soils. The principle is essential to describe the consolidation of a liquid-saturated deformable porous solid, as was done for the one-dimensional case by Terzaghi and further developed for the three-dimensional case by others such as Biot (1941). It is also an essential concept for the understanding of soil liquefaction behavior during earthquakes. The total stress can be directly measured or computed using the external forces and the body force due to weight of the soil–water mixture. A pore water pressure, denoted herein by u0, can be measured at a point remote from the interparticle zone. The actual pore water pressure in the interparticle zone is u. We know that at equilibrium the total potential or head of the water at the two points must be equal, but this does not mean that u ⫽ u0, as discussed in Section 7.7. The effective stress is a deduced quantity, which in practice is taken as ⫽ ⫺ u0.
7.3 FORCE DISTRIBUTIONS IN A PARTICULATE SYSTEM
The term intergranular stress has become synonymous with effective stress. Whether or not the intergranular stress i is indeed equal to ⫺ u cannot be ascertained without more detailed examination of all the interpar-
1 The terms and are the principal total and effective stresses. For general stress conditions, there are six stress components (11, 22, 33, 12, 23, and 31), where the first three are the normal stresses and the latter three are the shear stresses. In this case, the effective ⫽ 11 ⫺ u, 22 ⫽ 22 ⫺ u, 33 ⫽ 33 ⫺ stresses are defined as 11 u, 12 ⫽ 12, 23 ⫽ 23, and 31 ⫽ 31.
ticle forces in a soil mass. Interparticle forces at the microscale can be separated into the following three categories (Santamarina, 2003): 1. Skeletal Forces Due to External Loading These forces are transmitted through particles from the forces applied externally [e.g., foundation loading) (Fig. 7.1a)]. 2. Particle Level Forces These include particle weight force, buoyancy force when a particle is submerged under fluid, and hydrodynamic forces or seepage forces due to pore fluid moving through the interconnected pore network (Fig. 7.1b). 3. Contact Level Forces These include electrical forces, capillary forces when the soil becomes unsaturated, and cementation-reactive forces (Fig. 7.1c). When external forces are applied, both normal and tangential forces develop at particle contacts. All particles do not share the forces or stresses applied at the boundaries in equal manner. Each particle has different skeletal forces depending on the position relative to the neighboring particles in contact. The transfer of forces through particle contacts from external stresses was shown in Fig. 5.15 using a photoelastic model. Strong particle force chains form in the direction of major principal stress. The evolution and distribution of interparticle skeletal forces in soils govern the macroscopic stress–strain behavior, volume change, and strength. As the soil approaches failure, buckling of particle force chains occurs and shear bands develop due to localization of deformation. Further discussion of microbehavior in relation to deformation and strength is given in Chapter 11. Particle weights act as body forces in dry soil and contribute to skeletal forces, observed in the photoelastic model shown in Fig. 5.15. When the pores are filled with fluids, the weight of the fluids adds to the body force of the soil–fluids mixture. However, hydrostatic pressure results from the fluid weight, and the uplift force due to buoyancy reduces the effective weight of a fluid-filled soil. This leads to smaller skeletal forces for submerged soil compared to dry soil. Seepage forces that result from additional fluid pressures applied externally produce hydrodynamic forces on particles and alter the skeletal forces.
7.4
INTERPARTICLE FORCES
Long-range particle interactions associated with electrical double layers and van der Waals forces are dis-
INTERPARTICLE FORCES
175
Body Force
External Load
Buoyancy Force if Saturated Viscous Drag by Seepage Flow Interparticle Forces
Capillary Force or Cementation-reactive Force Interparticle Forces
Seepage
(a)
Electrical Forces
(b)
(c)
Figure 7.1 Interparticle forces at the particle level: (a) skeletal forces by external loading,
(b) particle level forces, and (c) contact level forces (after Santamarina, 2003).
cussed in Chapter 6. These interactions control the flocculation–deflocculation behavior of clay particles in suspension, and they are important in swelling soils that contain expanding lattice clay minerals. In denser soil masses, other forces of interaction become important as well since they may influence the intergranular stresses and control the strength at interparticle contacts, which in turn controls resistance to compression and strength. In a soil mass at equilibrium, there must be a balance among all interparticle forces, the pressure in the water, and the applied boundary stresses. Interparticle Repulsive Forces Electrostatic Forces Very high repulsion, the Born repulsion, develops at contact points between particles. It results from the overlap between electron clouds, and it is sufficiently great to prevent the interpenetration of matter. At separation distances beyond the region of direct physical interference between adsorbed ions and hydration water molecules, double-layer interactions provide the major source of interparticle repulsion. The theory of these forces is given in Chapter 6. As noted there, this repulsion is very sensitive to cation valence, electrolyte concentration, and the dielectric properties of the pore fluid. Surface and Ion Hydration The hydration energy of particle surfaces and interlayer cations causes large repulsive forces at small separation distances between unit layers (clear distance between surfaces up to about 2 nm). The net energy required to remove the last few
layers of water when clay plates are pressed together may be 0.05 to 0.1 J/m2. The corresponding pressure required to squeeze out one molecular layer of water may be as much as 400 MPa (4000 atm) (van Olphen, 1977). Thus, pressure alone is not likely to be sufficient to squeeze out all the water between parallel particle surfaces in naturally occurring clays. Heat and/or high vacuum are needed to remove all the water from a finegrained soil. This does not mean, however, that all the water may not be squeezed from between interparticle contacts. In the case of interacting particle corners, edges, and faces of interacting asperities, the contact stress may be several thousand atmospheres because the interparticle contact area is only a very small proportion (⬍⬍ 1%) of the total soil cross-sectional area in most cases. The exact nature of an interparticle contact remains largely a matter for speculation; however, there is evidence (Chapter 12) that it is effectively solid to solid. Hydration repulsions decay rapidly with separation distance, varying inversely as the square of the distance. Interparticle Attractive Forces Electrostatic Attractions When particle edges and surfaces are oppositely charged, there is attraction due to interactions between double layers of opposite sign. Fine soil particles are often observed to adhere when dry. Electrostatic attraction between surfaces at different potentials has been suggested as a cause. When the
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EFFECTIVE, INTERGRANULAR, AND TOTAL STRESS
gap between parallel particle surfaces separated by distance d at potentials V1 and V2 is conductive, there is an attractive force per unit area, or tensile strength, given by (Ingles, 1962) F⫽
4.4 ⫻ 10⫺6 (V1 ⫺ V2)2 N/m2 d2
(7.1)
where F is the tensile strength, d is in micrometers, and V1 and V2 are in millivolts. This force is independent of particle size and becomes significant (greater than 7 kN/m2 or 1 psi) for separation distances less than 2.5 nm. Electromagnetic Attractions Electromagnetic attractions caused by frequency-dependent dipole interactions (van der Waals forces) are described in Section 6.12. Anandarajah and Chen (1997) proposed a method to quantify the van der Waals force between particles specifically for fine-grained soils with various geometric parameters such as particle length, thickness, orientation, and spacing. Primary Valence Bonding Chemical interactions between particles and between the particles and adjacent liquid phase can only develop at short range. Covalent and ionic bonds occur at spacings less than 0.3 nm. Cementation involves chemical bonding and can be considered as a short-range attraction. Whether primary valence bonds, or possibly hydrogen bonds, can develop at interparticle contacts without the presence of cementing agents is largely a matter of speculation. Very high contact stresses between particles could squeeze out adsorbed water and cations and cause mineral surfaces to come close together, perhaps providing opportunity for cold welding. The activation energy for soil deformation is high, in the range characteristic for rupture of chemical bonds, and strength behavior appears in reasonable conformity with the adhesion theory of friction (Chapter 11). Thus, interatomic bonding between particles seems possible. On the other hand, the absence of cohesion in overconsolidated silts and sands argues against such pressure-induced bonding. Cementation Cementation may develop naturally from precipitation of calcite, silica, alumina, iron oxides, and possibly other inorganic or organic compounds. The addition of stabilizers such as cement and lime to a soil also leads to interparticle cementation. If two particles are not cemented, the interparticle force cannot become tensile; they loose contact. However, if a particle contact is cemented, it is possible for some interparticle forces to become negative due to the tensile resistance (or strength) of the cemented bonds.
There is also an increase in resistance to tangential force at particle contacts. However, when the bond breaks, the shear capacity at a contact reduces to that of the uncemented contacts. An analysis of the strength of cemented bonds should consider three cases: (i) failure in the cement, (ii) failure in the particle and (iii) failure at the cement–particle interface. The following equation can be derived (Ingles, 1962) for the tensile strength T per unit area of soil cross section:
冉 冊冘
T ⫽ Pk
1
1⫹e
n
(7.2)
n
Ai
1
where P is the bond strength per contact zone, k is the mean coordination number of a grain, e is the void ratio, n is the number of grains in an ideal breakage plane at right angles to the direction of T, and Ai is the total surface area of the ith grain. For a random and isotropic assembly of spheres of diameter d, Eq. (7.2) becomes T ⫽
Pk d (1 ⫹ e) 2
(7.3)
For a random and isotropic assembly of rods of length l and diameter d T ⫽
Pk d(l ⫹ d/2)(1 ⫹ e)
(7.4)
Bond strength P is evaluated in the following way (Fig. 7.2) for two cemented spheres of radius R. It may be shown that cosh
(R ⫺ cos ) ⫽ R sin
(7.5)
so for known , can be computed. Then, for cement failure, P ⫽ c ⫻ 2
(7.6)
where c is the tensile strength of the cement; for sphere failure, P ⫽ s ⫻ ()2
(7.7)
where ⫽ R sin , and s is the tensile strength of the sphere, and for failure at the interface
INTERPARTICLE FORCES
177
mented natural materials, if the soil is unloaded from high overburden stress, elastic rebound may disrupt cemented bonds. Cementation allows interparticle normal forces to become negative, and, therefore, the distribution and evolution of skeletal forces may be different than in uncemented soils, even though the applied external stresses are the same. Thus, the stiffness and strength properties of a soil are likely to differ according to when and how cementation was developed. How to account for this in terms of effective stress is not yet clear. Capillary Stresses Because water is attracted to soil particles and because water can develop surface tension, suction develops inside the pore fluid when a saturated soil mass begins to dry. This suction acts like a vacuum and will directly contribute to the effective stress or skeletal forces. The negative pore pressure is usually considered responsible for apparent and temporary cohesion in soils, whereas the other attractive forces produce true cohesion. When the soil continues to dry, air starts to invade into the pores. The air entry pressure is related to the pore size and can be estimate using the following equation, assuming a capillary tube as shown in Fig. 7.3a: Figure 7.2 Contact zone failures for cemented spheres.
P ⴖ ⫽ 1 ⫻
sin
⫻ 2R2(1 ⫺ cos )
(7.8)
where 1 is the tensile strength of the interface bond. In principle, Eq. (7.6), (7.7), or (7.8) can be used to obtain a value for P in Eq. (7.2) enabling computation of the tensile strength T of a cemented soil. The behavior of cemented soils can depend on the timing of cementation development. Artificially cemented soils are often loaded after cementation has developed, whereas cementation develops during or after overburden loading in natural soils. In the former case, the particles and cementation bonding are loaded together and contact forces can become negative depending on the tensile resistance of cementation bonding. The distribution and magnitude of skeletal forces are therefore influenced by both geometric arrangement of particles and the cementation bonding at the particle contacts. In the latter case, on the other hand, the contact forces induced by external loading are developed before cementation coats the already loaded particles. In this case, it is possible that cementation creates extra forces at particle contacts. In some ce-
Pˆ c ⫽
2aw cos rp
(7.9)
where Pˆ c is the capillary pressure at air entry, aw is the air–water interfacial tension, is contact angle defined in Fig. 7.3, and rp is the tube radius. For pure water and air, aw depends on temperature, for example, it is 0.0756 N/m at 0C, 0.0728 N/m at 20C, and 0.0589 N/m at 100C. If the capillary pressure Pc (⫽ ua ⫺ uw, where ua and uw are the air and water pressures, respectively) is larger than Pˆ c, then air invades the pore.2 Since soil has pores with various sizes, the water in the largest pores is displaced first followed by smaller pores. This leads to a macroscopic model of the soil–water characteristic curve (or the capillary pressure–saturation relationship), as discussed in Section 7.11. If the water surrounding the soil particles remains continuous [termed the ‘‘funicular’’ regime by Bear (1972)], the interparticle force acting on a particle with radius r can be estimated from
2 It is often assumed that ua ⫽ 0 (for gauge pressure) or 1 atm (for absolute pressure). However, this may not be true in cases such as rapid water infiltration when air in the pores cannot escape or the air boundary is completely blocked.
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EFFECTIVE, INTERGRANULAR, AND TOTAL STRESS
Capillary Tube Representing a Pore 2 rp
ua
θ ^
uw Pc = ρw gdc = dc
2σaw cosθ rp
(a)
(b)
Figure 7.3 Capillary tube concept for air entry estimation: (a) capillary tube and (b) bundle
of capillary tubes to represent soil pores with different sizes.
2 r 2 aw cos Fc ⫽ r 2 Pˆ c ⫽ rp
(7.10)
where rp is the size of the pore into which the air has entered. Since the fluid acts like a membrane with negative pressure, this force contributes directly to the skeletal forces like the water pressure as shown in Fig. 7.4a. As the soil continues to dry, the water phase becomes disconnected and remains in the form of menisci or liquid bridges at the interparticle contacts [termed the ‘‘pendular’’ regime by Bear (1972)]. The curved air–water interface produces a pore water tension, which, in turn, generates interparticle compressive forces. The force only acts at particle contacts in contrast to the funicular regime, as shown in Fig. 7.4b. The interparticle force generally depends on the separation between the two particles, the radius of the liquid bridge, interfacial tension, and contact angle (Lian et al., 1993). Once the water phase becomes discontinuous, evaporation and condensation are the primary mechanisms of water transfer. Hence, the humidity of the gas phase and the temperature affect the water vapor pressure at the surface of water menisci, which in turn influences the air pressure ua.
7.5
INTERGRANULAR PRESSURE
Several different interparticle forces were described in the previous section. Quantitative expression of the in-
teractions of all these forces in a soil is beyond the present state of knowledge. Nonetheless, their existence bears directly on the magnitude of intergranular pressure and the relationship between intergranular pressure and effective stress as defined by ⫽ ⫺ u. A simplified equation for the intergranular stress in a soil may be developed in the following way. Figure 7.5 shows a horizontal surface through a soil at some depth. Since the stress conditions at contact points, rather than within particles, are of primary concern, a wavy surface that passes through contact points (Fig. 7.5a) is of interest. The proportion of the total wavy surface area that is comprised of intergrain contact area is very small (Fig. 7.5c). The two particles in Fig. 7.5 that contact at point A are shown in Fig. 7.6, along with the forces that act in a vertical direction. Complete saturation is assumed. Vertical equilibrium across wavy surface x–x is considered.3 The effective area of interparticle contact is ac; its average value along the wavy surface equals the total mineral contact area along the surface divided by the number of interparticle contacts. Define area a as
3 Note that only vertical forces at the contact are considered in this simplified analysis. It is evident, however, that applied boundary normal and shear stresses each induce both normal and shear forces at interparticle contacts. These forces contribute both to the development of soil strength and resistance to compression and to the slipping and sliding of particles relative to each other. These interparticle movements are central to compression, shear deformations, and creep as discussed in Chapters 10, 11, and 12.
INTERGRANULAR PRESSURE
179
Continuous Water Film
Interparticle Forces Soil Particles Soil Particles
Air Liquid Bridges Pores of Radius rp Filled with Air Negative pore pressure acts all around the particles (a)
Suction forces act only at particle contacts and the magnitude of the forces depends on the size of liquid bridges. (b)
Figure 7.4 Microscopic water–soil interaction in unsaturated soils: (a) funicular regime and (b) pendular regime.
Figure 7.6 Forces acting on interparticle contact A.
the average total cross-sectional area along a horizontal plane served by the contact. It equals the total horizontal area divided by the number of interparticle contacts along the wavy surface. The forces acting on area a in Fig. 7.6 are:
Figure 7.5 Surfaces through a soil mass.
1. a, the force transmitted by the applied stress , which includes externally applied forces and body weight from the soil above.
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EFFECTIVE, INTERGRANULAR, AND TOTAL STRESS
2. u(a ⫺ ac), the force carried by the hydrostatic pressure u. Because a ⬎⬎ ac and ac is very small, the force may be taken as ua. Long-range, double-layer repulsions are included in ua. 3. A(a ⫺ ac) ⬇ Aa, the force caused by the longrange attractive stress A, that is, van der Waals and electrostatic attractions. 4. Aac, the force developed by the short-range attractive stress A, resulting from primary valence (chemical) bonding and cementation. 5. Cac, the intergranular contact reaction that is generated by hydration and Born repulsion. Vertical equilibrium of forces requires that a ⫹ Aa ⫹ Aac ⫽ ua ⫹ Cac
(7.11)
Division of all terms by a converts the forces to stresses per unit area of cross section, ⫽ (C ⫺ A)
ac ⫹u⫺A a
where ⫽ aw /a. Although it is clear that for a dry soil ⫽ 0, and for a saturated soil ⫽ 1.0, the usefulness of Eq. (7.15) has been limited in practice because of uncertainties about for intermediate degrees of saturation. Further discussion of the effective stress concept for unsaturated soils is given in Section 7.12. Limiting the discussion to saturated soils, two questions arise: 1. How does the intergranular pressure i relate to the effective stress as defined for most analyses, that is, ⫽ ⫺ u? 2. How does the intergranular pressure i relate to the measured quantity, m ⫽ ⫺ u0, that is taken as the effective stress, recalling (Section 7.2) that pore pressure can only be measured at points outside the true interparticle zone? Answers to these questions require a more detailed consideration of the meaning of fluid pressures in soils.
(7.12) 7.6
The term (C ⫺ A)ac /a represents the net force across the contact divided by the total cross-sectional area (soil plus water) that is served by the contact. In other words, it is the intergrain force divided by the gross area or the intergranular pressure in common soil mechanics usage. Designation of this term by i gives i ⫽ ⫹ A ⫺ u
(7.13)
Equations analogous to Eqs. (7.11), (7.12), and (7.13) can be developed for the case of a partly saturated soil. To do so requires consideration of the pressures in the water uw and in the air ua and the proportions of area a contributed by water aw and by air aa with the condition that a w ⫹ aa ⫽ a
i.e., ac → 0
Pressures in the pore fluid of a soil can be expressed in several ways, and the total pressure may involve several contributions. In hydraulic engineering, problems are analyzed using Bernoulli’s equation for the total heads and head losses associated with flow between two points, that is, Z1 ⫹
p1 v2 p v2 ⫹ 1 ⫽ Z2 ⫹ 2 ⫹ 2 ⫹ h1–2 w 2g w 2g
aw (u ⫺ ua) a w
(7.14)
In the absence of significant long-range attractions, this equation is similar to that proposed by Bishop (1960) for partially saturated soils i ⫽ ⫺ ua ⫹ (ua ⫺ uw)
(7.15)
(7.16)
where Z1 and Z2 are the elevations of points 1 and 2, p1 and p2 are the hydrostatic pressures at points 1 and 2, v1 and v2 are the flow velocities at points 1 and 2, w is the unit weight of water, g is the acceleration due to gravity, and h1–2 is the loss in head between points 1 and 2. The total head H (dimension L) is H⫽Z⫹
The resulting equation is i ⫽ ⫹ A ⫺ ua ⫺
WATER PRESSURES AND POTENTIALS
p v2 ⫹ w 2g
(7.17)
Flow results only from differences in total head; conversely, if the total heads at two points are the same, there can be no flow, even if Z1 ⫽ Z2 and p1 ⫽ p2. If there is no flow, there is no head loss and h1–2 ⫽ 0. The flow velocity through soils is low, and as a result v 2 /2g → 0, and in most cases it may be neglected. Therefore, the relationship
WATER PRESSURE EQUILIBRIUM IN SOIL
Z1 ⫹
p1 p ⫽ Z2 ⫹ 2 ⫹ h1–2 w w
(7.18)
is the basis for evaluation of pore pressures and analysis of seepage through soils and other porous media. Although the absence of velocity terms is a factor that seems to simplify the analysis of flows and pressures in soils, there are other considerations that tend to complicate the problem. These include: 1. The use of several terms to describe the status of water in soils, for example, potential, pressure, and head. 2. The possible existence of tensions in the pore water. 3. Compositional differences in the water from point-to-point and adsorptive force fields from particle surfaces. 4. Differences in interparticle forces and the energy state of the pore fluid from point to point owing to thermal, electrical, and chemical gradients. Such gradients can cause fluid flows, deformations, and volume changes, as considered in more detail in Chapter 9. Some formalism in definition and terminology is necessary to avoid confusion. The status of water in a soil can be expressed in terms of the free energy relative to free, pure water (Aitchison, et al., 1965). The free energy can be (and is) expressed in different ways, including 1. Potential (dimensions—L2T⫺2: J/kg) 2. Head (dimensions—L: m, cm, ft) 3. Pressure (dimensions—ML⫺1 T⫺2: kN/m2, dyn/ cm2, tons/m2, atm, bar, psi, psf) If the free energy is less than that of pure water under the ambient air pressure, the terms suction and negative pore water pressure are used. The total potential (head, pressure) of soil water is the potential (head, pressure) in pure water that will cause the same free energy at the same temperature as in the soil water. An alternative definition of total potential is the work per unit quantity to transport reversibly and isothermally an infinitesimal amount of pure water from a pool at a specified elevation at atmospheric pressure to the point in soil water under consideration. The selection of the components of the total potential (total head H, total pressure P) is somewhat arbitrary (Bolt and Miller, 1958); however, the following have gained acceptance for geotechnical work (Aitchison, et al., 1965):
181
1. Gravitational potential g (head Z, pressure pz) corresponds to elevation head in normal hydraulic usage. 2. Matrix or capillary potential m (head hm, pressure p) is the work per unit quantity of water to transport reversibly and isothermally an infinitesimal quantity of water to the soil from a pool containing a solution identical in composition to the soil water at the same elevation and external gas pressure as that of the point under consideration in the soil. This component corresponds to the pressure head in normal hydraulic usage. It results from that part of the boundary stresses that is transmitted to the water phase, from pressures generated by capillarity menisci, and from water adsorption forces exerted by particle surfaces. A piezometer measures the matrix potential if it contains fluid of the same composition as the soil water. 3. Osmotic (or solute) potential s (head hs, pressure ps) is the work per unit quantity of water to transport reversibly and isothermally an infinitesimal quantity of water from a pool of pure water at a specified elevation and atmospheric pressure to a pool containing a solution identical in composition to the soil water, but in all other respects identical to the reference pool. This component is, in effect, the osmotic pressure of the soil water, and it depends on the composition and ability of the soil particles to restrain the movement of adsorbed cations. The osmotic potential is negative, that is, water tends to flow in the direction of increasing concentration. The total potential, head, and pressure then become ⫽ g ⫹ m ⫹ s
(7.19)
H ⫽ Z ⫹ hm ⫹ hs
(7.20)
P ⫽ pz ⫹ p ⫹ ps
(7.21)
At equilibrium and no flow there can be no variations in , H, or P within the soil. 7.7
WATER PRESSURE EQUILIBRIUM IN SOIL
Consider a saturated soil mass as shown in Fig. 7.7. Conditions at several points will be analyzed in terms of heads for simplicity, although potential or pressure could also be used with the same result. The system is assumed at constant temperature throughout. At point 0, a point inside a piezometer introduced to measure
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7
EFFECTIVE, INTERGRANULAR, AND TOTAL STRESS
Figure 7.7 Schematic representation of a saturated soil for analysis of pressure conditions.
pore pressure, Z ⫽ 0, hm ⫽ hm0, and hs0 ⫽ 0 if pure water is used in the piezometer. Thus, H0 ⫽ 0 ⫹ hm0 ⫹ 0 ⫽ hm0 It follows that
At point 2, which is between the same two clay particles as point 1 but closer to a particle surface, there will be a different ion concentration than at 1. Thus, at equilibrium, and assuming Z2 ⬇ 0, hm2 ⫹ hs2 ⫽ hm1 ⫹ hs1 ⫽ hm0 ⫽
P0 ⫽ hm0 w ⫽ u0
(7.22)
the measured pore pressure. Point 1 is at the same elevation as point 0, except it is inside the soil mass and midway between two clay particles. At this point, Z1 ⫽ 0, but hs ⫽ 0 because the electrolyte concentration is not zero. Thus, H1 ⫽ 0 ⫹ hm1 ⫹ hs1
A similar analysis could be applied to any point in the system. If point 3 were midway between two clay particles spaced the same distance apart as the particles on either side of point 1, then hs3 ⫽ hs1, but Z3 ⫽ 0. Thus, u0 ⫽ Z3 ⫹ hm3 ⫹ hs3 ⫽ Z3 ⫹ hm3 ⫹ hs1 w
(7.24)
A partially saturated system can also be analyzed, but the influences of curved air–water interfaces must be taken into account in the development of the hm terms. The conclusions that result from the above analysis of component potentials are:
If no water is flowing, H1 ⫽ H0, and hm1 ⫹ hs1 ⫽ hm0 Also, because p1 ⫽ p0 ⫽ u0 u0 ⫽ hm1 w ⫹ hs1 w
u0 w
(7.23)
1. As the osmotic and gravitational components vary from point to point in a soil at equilibrium,
MEASUREMENT OF PORE PRESSURES IN SOILS
the matrix or capillary component must also vary to maintain equal total potential. The concept that hydrostatic pressure must vary with elevation to maintain equilibrium is intuitive; however, the idea that this pressure must vary also in response to compositional differences is less easy to visualize. Nonetheless, this underlies the whole concept of water flow by chemical osmosis. 2. The total potential, head, and pressure are measurable, and separation into components is possible experimentally, although it is difficult. 3. A pore pressure measurement using a piezometer containing pure water gives a pressure u0 ⫽ wh, where h is the pressure head at the piezometer. When referred back to points between soil particles, u0 is seen to include contributions from osmotic pressures as well as matrix pressures. Since osmotic pressures are the cause of longrange repulsions due to double-layer interactions, measured pore water pressures may include contributions from long-range interparticle repulsive forces.
7.8 MEASUREMENT OF PORE PRESSURES IN SOILS
Several techniques for the measurement of pore water pressures are available. Some are best suited for laboratory use, whereas others are intended for use in the field. Some yield the pore pressure or suction by direct measurement, while others require deduction of the value using thermodynamic relationships. 1. Piezometers of Various Types Water in the piezometer communicates with the soil through a porous stone or filter. Pressures are determined from the water level in a standpipe, by a manometer, by a pressure gauge, or by an electronic pressure transducer. A piezometer used to measure pressures less than atmospheric is usually termed a tensiometer. 2. Gypsum Block, Porous Ceramic, and Filter Paper The electrical properties across a specially prepared gypsum block or porous ceramic block are measured. The water held by the block determines the resistance or permittivity, and the moisture tension in the surrounding soil determines the amount of moisture in the block (Whalley et al., 2001). The same principle can be applied by placing a dry filter paper on a soil specimen and allowing the soil moisture to absorb into the paper. When the suction in the filter paper is equal to the suction in the soil, the two
3.
4.
5.
6.
7.
183
reach equilibrium, and the suction can be determined by the water content of the filter paper. These techniques are used for measurement of pore pressures less than atmospheric. Pressure-Membrane Devices An exposed soil sample is placed on a membrane in a sealed chamber. Air pressure in the chamber is used to push water from the pores of the soil through the membrane. The relationship between water content and pressure is used to establish the relationship between soil suction and water content. Consolidation Tests The consolidation pressure on a sample at equilibrium is the soil water suction. If the consolidation pressure were instantaneously removed, then a negative water pressure or suction of the same magnitude would be needed to prevent water movement into the soil. Vapor Pressure Methods The relationship between relative humidity and water content is used to establish the relationship between suction and water content. Osmotic Pressure Methods Soil samples are equilibrated with solutions of known osmotic pressure to give a relationship between water content and water suction. Dielectric Sensors Such as Capacitance Probes and Time Domain Reflectometry Soil moisture can be indirectly determined by measuring the dielectric properties of unsaturated soil samples. With the knowledge of soil water characteristics relationship (Section 7.11), the negative pore pressure corresponding to the measured soil moisture can be determined. The capacitance probe measures change in frequency response of the soil’s capacitance, which is related to dielectric constants of soil particle, water, and air. The capacitance is largely influenced by water content, as the dielectric constant of water is large compared to the dielectric constants of soil particle and air. Time domain reflectrometry measures the travel time of a high-frequency, electromagnetic pulse. The presence of water in the soil slows down the speed of the electromagnetic wave by the change in the dielectric properties. Volumetric water content can therefore be indirectly measured from the travel time measurement.
Piezometer methods are used when positive pore pressures are to be measured, as is usually the case in dams, slopes, and foundations on soft clays. The other methods are suitable for measurement of negative pore pressures or suction. Pore pressures are often negative in expansive and partly saturated soils. More detailed
184
7
EFFECTIVE, INTERGRANULAR, AND TOTAL STRESS
descriptions and comparisons of these and other methods are given by Croney et al. (1952), Aitchison et al. (1965), Richards and Peter (1987), and Ridley et al. (2003).
defined effective stress ⫽ ⫺ u0 differ by the net interparticle stress due to physicochemical contributions, i ⫺ ⫽ A ⫺ R
7.9 EFFECTIVE AND INTERGRANULAR PRESSURE
In Section 7.5, it was shown that the intergranular pressure is given by i ⫽ ⫹ A ⫺ u
(7.25)
where u is the hydrostatic pressure between particles (or hm w in the terminology of Section 7.7). Generalized forms of Eq. (7.24) are u0 ⫽ Z w ⫹ hm w ⫹ hs w
(7.26)
u ⫽ hm w ⫽ u0 ⫺ Z w ⫺ hs w
(7.27)
and
Thus, Eq. (7.25) becomes, for the case of no elevation difference between a piezometer and the point in question (i.e., Z ⫽ 0), i ⫽ ⫹ A ⫺ u0 ⫹ hs w
(7.28)
Because the quantity hs w is an osmotic pressure and the salt concentration between particles will invariably be greater than at points away from the soil (such as in a piezometer), hs w will be negative. This pressure reflects double-layer repulsions. It has been termed R in some previous studies (Lambe, 1960; Mitchell, 1962). If hs w in Eq. (7.28) is replaced by the absolute value of R, we obtain i ⫽ ⫹ A ⫺ u0 ⫺ R
(7.30)
When A and R are both small, as would be true in granular soils, silts, and clays of low plasticity, or in cases where A ⬇ R, the intergranular and effective stress are approximately equal. Only in cases where either A or R is large, or both are large but of significantly different magnitude, would the intergranular and effective stress be significantly different. Such a condition appears not to be common, although it might be of importance in a well-dispersed sodium montmorillonite, where compression behavior can be accounted for reasonably well in terms of double-layer repulsions (Chapter 10).4 The derivation of Eq. (7.30) assumed vertical equilibrium, with contributing forces parallel to each other, that is, the intergranular stress i is the sum of the skeletal forces (defined as ⫽ ⫺ u0) and the electrochemical stress (A ⫺ R), as illustrated in Fig. 7.8a. This implies that the deformation induced by the electrochemical stress (A ⫺ R) is equal to the deformation induced by the skeletal forces at contacts [i.e., a ‘‘parallel’’ model as described by Hueckel (1992)]. The change in pore fluid chemistry at constant confinement () leads to changes in intergranular stresses (i), resulting in changes in shear strength, for example. An alternative assumption can be made; the total deformation of soil is the sum of the deformations of the particles and in the double layers as illustrated in Fig. 7.8b. The effective stress is then equal to the electrochemical stress (R ⫺ A): i ⫽ R ⫺ A ⫽ ⫽ ⫺ u0
(7.31)
(7.29)
From Eq. (7.25), it was seen that the intergranular pressure was dependent on long-range interparticle attractions A as well as on the applied stress and the pore water pressure between particles u. Equation (7.29) indicates that if intergranular pressure i is to be expressed in terms of a measured pore pressure u0, then the long-range repulsion R must also be taken into account. The actual hydrostatic pressure between particles u ⫽ u0 ⫹ R includes the effects of long-range repulsions as required by the condition of constant total potential for equilibrium. In the general case, therefore, the true intergranular pressure i ⫽ ⫹ A ⫺ u0 ⫺ R and the conventionally
This is called the ‘‘series’’ model (Hueckel, 1992), and the model can be applicable for very fine soils at high water content, in which particles are not actually in contact with each other but are aligned in a parallel arrangement. Increase in intergranular stress i or effective stress changes the interparticle spacing, which may contribute to changes in strength properties upon shearing.
4 A detailed analysis of effective stress in clays is presented by Chattopadhyay (1972), which leads to similar conclusions, including Eq. (7.29). i was termed the true effective stress and it governed the volume change behavior of Na–montmorillonite.
ASSESSMENT OF TERZAGHI’S EQUATION
Skeletal Force
Skeletal Force Electrochemical Force
185
Electrochemical Force Skeletal Force
Skeletal Force
Electrochemical Force Electrochemical Force
σi
σi Skeletal Force
Skeletal Force
Electrochemical Force A _ R
σ = σ _ u0
σ = σ _ u0 Particle Deformation by Skeletal Force
Electrochemical Force A _ R Deformation at the Contact
σi σi = σ _ u0 + A _ R (a)
Total Deformation at the Contact
σi
σi = σ _ u0 = A _ R (b)
Figure 7.8 Contribution of skeletal force ( ⫺ u0) and electrochemical force (A ⫺ R) to intergranular force i: (a) parallel model and (b) series model.
Since the particles are arranged in parallel as well as nonparallel manner, the chemomechanical coupling behavior of actual soils can be far from the predictions made by the above two models. In fact, Santamarina (2003) argues that the impact of skeletal forces by external forces, particle-level forces, and contact-level forces on soil behavior is different, and mixing both types of forces in a single algebraic expression in terms of effective stress can lead to incorrect prediction [e.g., Eq. (7.15) for unsaturated soils and Eq. (7.30) for soils with measurable interparticle repulsive and attractive forces].
of saturated soils. Skempton proposed three possible relationships for effective stress in saturated soils: 1. The true intergranular pressure for the case when A⫺R⫽0 ⫽ ⫺ (1 ⫺ ac)u
(7.32)
in which ac is the ratio of contact area to total cross-sectional area. 2. The solid phase is treated as a real solid that has compressibility Cs and shear strength given by i ⫽ k ⫹ tan
7.10
ASSESSMENT OF TERZAGHI’S EQUATION
The preceding equations and discussion do not confirm that Terzaghi’s simple equation is indeed the effective stress that governs consolidation and strength behavior of soils. However, its usefulness has been established from the experience of many years of successful application in practice. Skempton (1960b) showed that the Terzaghi equation does not give the true effective stress but gives an excellent approximation for the case
(7.33)
where is an intrinsic friction angle and k is a true cohesion. The following relationships were derived: For shear strength,
冉
⫽ ⫺ 1 ⫺
冊
ac tan u tan
(7.34)
where is the effective stress angle of shearing resistance. For volume change,
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EFFECTIVE, INTERGRANULAR, AND TOTAL STRESS
冉
⫽ ⫺ 1 ⫺
冊
Cs u C
(7.35)
where C is the soil compressibility. 3. The solid phase is a perfect solid, so that ⫽ 0 and Cs ⫽ 0. This gives ⫽ ⫺ u
(7.36)
To test the three theories, available data were studied to see which related to the volume change of a system acted upon by both a total stress and a pore water pressure according to
V
V
⫽ ⫺C
(7.37)
and also satisfied the Coulomb equation for drained shear strength d : d ⫽ c ⫹ tan
(7.39)
where is the fraction of the pore pressure that gives the effective stress.5 Different expressions for proposed by several researchers are listed in Table 7.2. A more general expression has been proposed as ij ⫽ ij ⫹ iju, where ij is the tensor that accounts for the constitutive characteristics of the solid such as complex kinematics associated with anisotropic elastic materials (Carroll and Katsube, 1983; Coussy, 1995; Didwania, 2002). 5
Compressibility a per kN/m2 ⫻ 10⫺6 Material
C
Quartzitic sandstone 0.059 Quincy granite (30 m deep) 0.076 Vermont marble 0.18 Concrete (approx.) 0.20 Dense sand 18 Loose sand 92 London clay (over cons.) 75 Gosport clay (normally cons.) 600
Cs
Cs /C
0.027 0.019 0.014 0.025 0.028 0.028 0.020 0.020
0.46 0.25 0.08 0.12 0.0015 0.0003 0.00025 0.00003
After Skempton (1960b). a Compressibilities at p ⫽ 98 kN/m2; water Cw ⫽ 0.49 ⫻ 10⫺6 per kN/m2.
(7.38)
when both a total stress and a pore pressure are acting. It may be noted that this approach assumes that the Coulomb strength equation is valid a priori. The results of Skempton’s analysis showed that Eq. (7.32) was not a valid representation of effective stress. Equations (7.34) and (7.35) give the correct results for soils, concrete, and rocks. Equation (7.36) accounts well for the behavior of soils but not for concrete and rock. The reason for this latter observation is that in soils Cs /C and ac tan /tan approach zero, and, thus, Eqs. (7.34) and (7.35) reduce to Eq. (7.36). In rock and concrete, however, Cs /C and ac tan /tan are too large to be neglected. The value of tan /tan may range from 0.1 to 0.3, ac clearly is not negligible, and Cs /C may range from 0.1 to 0.5 as indicated in Table 7.1. Effective stress equations of the form of Eqs. (7.32), (7.34), (7.35), and (7.36) can be generalized to the general form (Lade and de Boer, 1997): ⫽ ⫺ u
Table 7.1 Compressibility Values for Soil, Rock, and Concrete
A more rigorous evaluation of the contribution of soil particle compressibility to effective stress was made by Lade and de Boer (1997) using a two-phase mixture theory. The volume change of the soil skeleton can be separated into that due to pore pressure increment u and that due to the change in confining pressure ( ⫺ u) (or ⫺ u). The effective stress increment is defined as the stress that produces the same volume change, CV0 ⬅ Vsks ⫹ Vsku ⫽ CV0( ⫺ u) ⫹ CuV0 u
(7.40)
where Vsks is the volume change of soil skeleton due to change in confining pressure, Vsku is the volume change of soil skeleton due to pore pressure change, V0 is the initial volume, C is the compressibility of the soil skeleton by confining pressure change, and Cu is the compressibility of the soil skeleton by pore pressure change. Rearranging Eq. (7.40) leads to
⫽ ⫺
冉
1⫺
冊
Cu
u C
(7.41)
Lade and de Boer (1997) used this equation to derive an effective stress equation for granular materials under drained conditions. Consider a condition in which the total confining pressure is constant [ ( ⫺
ASSESSMENT OF TERZAGHI’S EQUATION
Table 7.2
187
Expressions for to Define Effective Stress
Pore Pressure Fraction 1 n
Reference
n ⫽ porosity ac ⫽ grain contact area per unit area of plane Equation (7.34)
1 ⫺ ac tan 1 ⫺ ac tan C 1⫺ s C
1 ⫺ (1 ⫺ n)
Note
Equation (7.35); for isotropic elastic deformation of a porous material; for solid rock with small interconnected pores and low porosity (Lade and de Boer, 1997) Equation (7.43)
Cs C
Terzaghi (1925b) Biot (1955) Skempton and Bishop (1954) Skempton (1960b) Biot and Willis (1957), Skempton (1960b), Nur and Byerlee (1971), Lade and de Boer (1997) Suklje (1969); Lade and de Boer (1997)
After Lade and de Boer (1997).
u) ⫽ 0], but the pore pressure changes by u.6 The volume change of soil skeleton caused by change in pore pressure ( Vsku) is attributed solely from the volumetric compression of the solid grains ( Vgu). Hence,
Vsku ⬅ CuV0 u ⫽ Cs(1 ⫺ n)V0 u ⬅ Vgu
Cu ⫽ Cs(1 ⫺ n)
or (7.42)
where Cs is the compressibility of soil grains due to pore pressure change and n is the porosity. Substituting Eq. (7.42) into (7.41) gives
⫽ ⫺
冋
冋
1 ⫺ (1 ⫺ n)
⫽ 1 ⫺ (1 ⫺ n)
册
Cs C
册
Cs
u C
or (7.43)
Figure 7.9 shows the variations of with stress for quartz sand and gypsum sand (Lade and de Boer, 1997). For a stress level less than 20 MPa, is essentially one. Thus, Terzaghi’s effective stress equation, while not rigorously correct, is again shown to be an excellent approximation in almost all cases for saturated soils (i.e., solid grains and pore fluid are considered to be incompressible compared to soil skeleton compressibility).
6
An example of this condition is a soil under a seabed, in which the sea depth varies. This condition is often called the ‘‘unjacked condition.’’
Figure 7.9 Variation of with stress for quartz sand and
gypsum sand (Lade and de Boer, 1997).
Can the effective stress concept also be applied for undrained conditions where drainage is prevented? That is, when an isotropic total stress load of iso is applied, is u equal to iso? Using a two-phase mixture theory, the total stress increment ( iso) is separated into partial stress increments for the solid phase ( s) and the fluid phase ( ƒ) (Oka, 1996). Considering that the macroscopic volumetric strains by two phases are equal but of opposite sign for undrained
188
7
EFFECTIVE, INTERGRANULAR, AND TOTAL STRESS
conditions, Oka (1996) showed that the partial stresses are related to the total stress as follows:
ƒ ⫽
C ⫺ Cs
iso (C/n) ⫺ (1 ⫹ 1/n)Cs ⫹ Cl
θ Solid Surface
(7.44)
(a)
[(1/n) ⫺ 1]C ⫺ (Cs /n) ⫹ Cl
s ⫽
iso (C/n) ⫺ (1 ⫹ 1/n)Cs ⫹ Cl
Water (reference fluid)
where n is the porosity, C is the compressibility of soil skeleton, Cs is the compressibility of soil particles, and Cl is the compressibility of pore fluid. If the excess pore pressure generated by undrained isotropic loading is u, the partial stress increment for the fluid phase becomes (Oka, 1996)
ƒ ⫽ n u
(7.45)
C ⫺ Cs
iso C ⫺ Cs ⫹ n(Cl ⫺ Cs)
Solid surface (b)
Water
(7.46)
WATER–AIR INTERACTIONS IN SOILS
Wettability refers to the affinity of one fluid for a solid surface in the presence of a second or third fluid or gas. A measure of wettability is the contact angle, which was introduced in Eq. (7.9). Figure 7.10 illustrates a drop of the reference liquid (water for Fig. 7.10a and air for Fig. 7.10b) resting on a solid surface in the presence of another fluid (air for Fig. 7.10a and water for 7.10b). The interface between the two fluids meets the solid surface at a contact angle . If the angle is less than 90, the reference fluid is referred to as the wetting fluid for a given solid surface. If the angle is greater than 90, the reference liquid is referred to as the nonwetting phase. The figure shows that water and
7
θ
Solid
The multiplier in the right-hand side of the above equation is in fact Bishop’s pore water pressure coefficient B (Bishop and Eldin, 1950).7 For typical soils (Cs ⬇ 1.9 ⫺ 2.7 ⫻ 10⫺8 m2 / kN, Cl ⬇ 4.9 ⫻ 10⫺9 m2 /kN, C ⬇ 10⫺5 ⫺ 10⫺4 m2 /kN), so the values of B are roughly equal to 1. Hence, it can be concluded that Terzaghi’s effective stress equation is also applicable for undrained conditions for most soils.
7.11
Air
Air
Combining Eqs. (7.45) and (7.46),
u ⫽
Air
Water (reference fluid)
A similar equation for B value has been proposed by Lade and de Boer (1997).
(c) Figure 7.10 Wettability of two fluids (water and air) on a solid surface: (a) contact angle less than 90, (b) contact angle more than 90, and (c) unsaturated sand with water as the
wetting fluid and air as the nonwetting fluid.
air are the wetting and nonwetting fluid, respectively.8 The environmental SEM photos in Fig. 5.27 showed that water can be either wetting or nonwetting fluid depending soil mineralogy. The contact angle is a property related to interactions of solid and two fluids (water and air, in this case). cos ⫽
as ⫺ ws aw
(7.47)
where as is the interfacial tension between air and solid, ws is the interfacial tension between water and solid, and aw is the interfacial tension between
8 Some contaminated sites contain non-aqueous-phase liquids (NAPLs). In general, NAPLS can be assumed to be nonwetting with respect to water since the soil particles are in general primarily strongly water-wet. Above the water table, it is usually appropriate to assume that the water is the wetting fluid with respect to NAPL and that NAPL is a wetting fluid with respect to air, implying that the wettability order is water ⬎ NAPL ⬎ air. Below the water table, water is the wetting fluid and NAPL is the nonwetting fluid.
WATER–AIR INTERACTIONS IN SOILS
air and water. The microscopic scale distribution of water and air is illustrated in Fig. 7.10c, whereby it is assumed that water is wetting the grain surfaces. The aforementioned discussion on wettability and contact angle assumes static water drops on solid surfaces. It has been observed for movement of water relative to soil that the ‘‘dynamic’’ contact angle formed by the receding edge of a water droplet is generally less than the angle formed by its advancing edge. Matric suction (or capillary pressure) refers to the pressure discontinuity across a curved interface separating two fluids. This pressure difference exists because of the interfacial tension present in the fluid– fluid interface. Matric suction is a property that causes porous media to draw in the wetting fluid and repel the nonwetting fluid and is defined as the difference between the nonwetting fluid pressure and the wetting fluid pressure. For a two-phase system consisting of water and air, the matric suction is ⫽ un ⫺ uw
1 Dune Sand 2 Loamy Sand 3 Calcareous Fine Sandy Loam 4 Calcareous Loam 5 Silt Loam Derived from Loess 6 Young Oligotrophous Peat Soil 7 Marine Clay
Matric suction ua – uw (kPa)
106 105 7 104
6
103
5
102
3
101
2
189
4
1 100 10-1 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Volumetric Water Content θ w
(7.48)
Figure 7.11 Soil–water characteristic curves for some Dutch
soils (from Koorevaar et al., 1983; copied from Fredlund and Rahardjo, 1993).
where un is the pressure of the nonwetting fluid (air) and uw is the pressure of the wetting fluid (water). Assuming that the soil pores have a cylindrical shape, like a bundle of capillary tubes as illustrated in Fig 7.3b, the interface between two liquids in each tube forms a subsection of a sphere. The capillary pressure is then related to the tube radius, contact angle, and the interfacial tension between the two liquids. The pressure drop across the interface is directly proportional to the interfacial tension and inversely proportional to the radius of curvature. It follows that higher air pressure is required for air to enter water-saturated fine-grained than coarse-grained materials. Soil contains a range of different pore sizes, which will drain at different capillary pressure values. This leads to a soil–water characteristic relationship in which the matric suction is plotted against the volumetric water content (or sometimes water saturation ratio) such as shown in Fig. 7.11.9 The curves are often determined during air invasion into a previously watersaturated soil. As the volumetric water content decreases, as a result of drainage or evaporation, the matric suction increases. When water infiltrates into the soil (wetting or imbibition), the conditions reverse, with the volumetric water content increasing and matric suction decreasing. Usually drainage and wetting
processes do not follow the same curve and the volumetric water content versus matric suction curves exhibit hysteresis during cycles of drainage and wetting as shown in Fig. 7.12a. One cause of hysteresis is the existence of ‘‘ink bottle neck’’ pores at the microscopic scale as shown in Fig. 7.12b. Larger water-filled pores can remain owing to the inability of water to escape through smaller openings below in the case of drainage or above in the case of evaporation. Another cause is irreversible change in soil fabric and shrinkage during drying. The curves in Fig. 7.11 have two characteristic points—the air entry pressure a and residual volumetric water content r as defined in Fig. 7.12a. The entry pressure is the matric suction at which the air begins to enter the pores and the pores become interconnected (Corey, 1994). At this point, the air permeability becomes greater than zero. Corey (1994) also introduced the term ‘‘displacement pressure’’ ( d in Fig. 7.12b) and defined it as the matric suction at which the first water desaturation occurs during a drainage cycle.10 The entry pressure is always slightly
9
10
The soil–water characteristic curve is referred to by a variety of names depending on different disciplines. They include moisture retention, soil–water retention, specific retention, and moisture characteristic.
For the Dense NAPL–water two-phase system (often Dense NAPL is the nonwetting fluid and water is the wetting fluid), the displacement pressure may be important to examine the potential of DNAPL invading into a noncontaminated water-filled porous media.
7
EFFECTIVE, INTERGRANULAR, AND TOTAL STRESS
Scanning Curve
Suction
190
Hysteresis
Scanning Curve Initial drainage Curve
ψa ψd
Main Drying Curve
Main Wetting Curve θr
Draining
Water Content Wetting
θ r Residual Water Content ψ a Air Entry Value ψ d Displacement pressure
(b)
(a)
Figure 7.12 Hysteresis of a soil–water characteristic curve: (a) effect of hysteresis and (b) ink bottle effect: a possible physical explanation for the hysteresis.
greater than the displacement pressure because pore throats smaller than the maximum must be penetrated to establish air connectivity. The air entry pressure is much greater for fine-grained than for coarse-grained soils because of their smaller pore sizes. Residual water content r is defined as the water content that cannot be further reduced by the increase in matric suction. At this stage, the water phase becomes essentially discontinuous and the regime changes from the funicular to pendular state, as described in Section 7.4. However, this does not mean that the soil cannot have a degree of saturation less that the residual saturation because residual water can continue to evaporate. Hence, it is important to note that the residual saturation defined here is a mathematical fitting parameter without a specific quantitative value. The shape of the soil–water characteristic curve depends on many factors, including the grain size distribution, soil fabric, the contact angle, and the interfacial tension [see Eq. (7.11)]. If the material is uniform with a narrow range of pore sizes, the curve has three distinct parts: a straight part up to the air entry pressure, a relatively horizontal middle part, and an end part that is almost vertical (soil 1 in Fig. 7.11). On the other hand, if the material is well graded, the curve is smoother (soils 3, 4, and 5 in Fig. 7.11). The capillary pressure increases gradually as the water saturation decreases and the middle part is not horizontal. Many
algebraic formulas have been proposed to fit the measured soil-water characteristic relations. The most popular ones are (a) the Brooks–Corey (1966) equation: ⫽ m ⫽ d
when d
冉
冊
⫺ r m ⫺ r
(7.49)
⫺1/
when d
(7.50)
where m is the volumetric water content at full saturation and is the curve-fitting parameter called the pore size distribution index and (b) the van Genuchten equation (1980):
冋冉
⫽ 0
冊
⫺ r m ⫺ r
⫺1 / m
册
⫺1
1⫺m
(7.51)
where 0 and m are curve-fitting parameters. Various modifications have been proposed to these equations to include behaviors such as hysteresis, nonwetting fluid trapping, and three-phase conditions.
7.12 EFFECTIVE STRESS IN UNSATURATED SOILS
Although it seems clear that the volume change and strength behavior of partly saturated soils are con-
EFFECTIVE STRESS IN UNSATURATED SOILS
⫽ ⫺ ua ⫹ (ua ⫺ uw)
(7.52)
Limitations in Bishop’s equation were highlighted by Jennings and Burland (1962) in their experiments investigating the volume change characteristics of unsaturated soils. Figure 7.14 shows that the oedometer compression curve of air-dry silt falls above that of saturated silt. Also, as shown in the figure, some airdry samples were consolidated at four different pressures (200, 400, 800, and 1600 kPa) and then soaked.
The term ⫺ ua is the net total stress. The term ua ⫺ uw represents the soil water suction that adds to the effective stress since uw is negative. Thus, the Bishop equation is appealing intuitively because negative pore pressures are known to increase strength and decrease compressibility. Using Eq. (7.52), the shear strength of unsaturated soil can be expressed as (7.53)
where is the effective friction angle of the soil. However, difficulties in the evaluation of the parameter , its dependence on saturation ( ⫽ 1 for saturated soils and ⫽ 0 for dry soils), and that the relationship between and saturation is soil dependent, as shown in Fig. 7.13a, all introduce problems in the application of Eq. (7.53). Since water saturation is related to matric suction as described in Section 7.11, it is possible that depends on matric suction as shown in Fig. 7.13b. Nonetheless, because of the complexity in determining , the attempt to couple total stress and suction together into a single equivalent effective stress is uncertain (Toll, 1990).
0.80
0.76
Void Ratio e
⫽ {( ⫺ ua) ⫹ (ua ⫺ uw)}tan
0.84
Air Dry (8 specimens)
0.68
Soaked at Constant Void Ratio Soaked at Constant Applied Pressure
0.64 10
100
1000
Applied Pressure (kPa ) Figure 7.14 Oedometer compression curves of unsaturated silty soils (after Jennings and Burland, 1962 in Leroueil and Hight, 2002).
1. Compacted Boulder Clay 2. Compacted Shale 3. Breadhead silt 4. Silt 5. Silty clay 6. Sterrebeek silt 7. White clay
Coefficient χ
Initially Soaked Test
0.72
χ= Coefficient χ
trolled by an effective stress that is not the same as the total stress, the appropriate formulation for the effective stress is less certain than for a fully saturated soil. As noted earlier, Bishop (1960) proposed Eq. (7.15) (assuming ⫽ i ):
191
(ua – uw) (ua – uw)
– 0.55
(ua_uw)b = Air Entry Value
Degree of SaturationS(%)
(ua_uw)/(ua_uw)b
(a)
(b)
Figure 7.13 Variation of parameter with the degree of water saturation Sr for different soils: (a) versus water saturation (after Gens, 1996) and (b) versus suction (after Khalili and Khabbaz, 1998).
192
7
EFFECTIVE, INTERGRANULAR, AND TOTAL STRESS
The void ratio decreased upon soaking and the final state was very close to the compression curve of the saturated silt. Additional tests in which constant volume during soaking was maintained by adjusting the applied load were also done. Again, after equilibrium, the state of soaked samples was close to the compression curve of the saturated silt. Soaking reduces the suction and, hence, Bishop’s effective stress decreases. This decrease in effective stress should be associated with an increase in void ratio. However, the experimental observations gave the opposite trend (i.e., a decrease in void ratio is associated with irreversible compression). The presence of meniscus water lenses in the soil before wetting was stabilizing the soil structure, which is not taken into account in Bishop’s equation (7.52). An alternative approach is to describe the shear strength/deformation and volume change behavior of unsaturated soil in terms of the two independent stress variables ⫺ ua and ua ⫺ uw (Coleman, 1962; Bishop and Blight, 1963; Fredlund and Morgenstern, 1977; Fredlund, 1985; Toll, 1990, Fredlund and Rahardjo, 1993; Tarantino et al., 2000). Figure 7.15 shows the results of isotropic compression tests of compacted kaolin. Different compression curves are obtained for constant suction conditions, and relative effects of ⫺ ua and ua ⫺ uw on volume change behavior can be observed. Furthermore, the preconsolidation pressure (or yield stress) increases with suction. On this basis, the dependence of shear strength on stress is given by equations of the form ⫽ a( ⫺ ua) ⫹ b(ua ⫺ uw)
1.25
(7.54)
Preconsolidation pressure
Void Ratio e
1.20 1.15 1.10
ua _ uw (kPa)
1.05
300 kPa
1.00 0.95 25
Curves are Averages of Several Tests 50
100
200 kPa 100 kPa 0 kPa
200
in which a and b are material parameters that may also depend on degree of saturation and stress. For example, Fredlund et al. (1978) propose the following equation: ⫽ ( ⫺ ua)tan ⫹ (ua ⫺ uw)tan b
(7.55)
where b is the angle defining the rate of increase in shear strength with respect to soil suction. An example of this parameter as a function of water content, friction angle, and matric suction is given by Fredlund et al. (1995). Similarly, the change in void ratio e of an unsaturated soil can be given by (Fredlund, 1985)
⫽ at ( ⫺ ua) ⫹ am (ua ⫺ uw)
(7.56)
where at is the coefficient of compressibility with respect to changes in ⫺ ua and am is the coefficient of compressibility with respect to changes in capillary pressure. A similar equation, but with different coefficients, can be written for change in water content. For a partly saturated soil, change in water content and change in void ratio are not directly proportional. The two stress variables, or their modifications that include porosity and water saturation, have been used in the development of elasto-plastic-based constitutive models for unsaturated soils (e.g., Alonso et al., 1990; Wheeler and Sivakumar, 1995; Houlsby, 1997; Gallipoli et al., 2003). The choice of stress variables is still in debate; further details on this issue can be found in Gens (1996), Wheeler and Karube (1996), Wheeler et al. (2003), and Jardine et al. (2004). Bishop’s parameter in Eq. (7.52) is a scalar quantity, but microscopic interpretation of water distribution in pores can lead to an argument that is directional dependent (Li, 2003; Molenkamp and Nazemi, 2003).11 During the desaturation process, the number of soil particles under a funicular condition decreases, and they change to a pendular condition with further drying. For particles in the funicular region, the suction pressure acts all around the soil particles like the water pressure as illustrated in Fig. 7.4a. Hence, the effect is isotropic even at the microscopic level. However, once the microscopic water distribution of a particle changes to the pendular condition, the capillary forces only act on a particle at locations where water bridge forms and the contribution to the interparticle forces becomes
400
σ _ ua (kPa) 11
Figure 7.15 Isotropic compression tests of compacted kaolin
(after Wheeler and Sivakumar, 1995 in Leroueil and Hight, 2002).
A microstructural analysis by Li (2003) suggests the following effective stress expression: ij ⫽ ij ⫺ uaij ⫹ ij (ua ⫺ uw)
QUESTIONS AND PROBLEMS
more or less point wise, as shown in Fig. 7.4b. As described in Section 7.3, the magnitude of capillary force depends on the size of the water bridge and the separation of the two particles, and hence, the contact force distribution in the particle assembly becomes dependent not only on pore size location and distribution but also on the relative locations of particles to one another (or soil fabric). It is therefore possible that the distribution of the pendular-type capillary forces becomes directional dependent. In clayey soils, water is attracted to clay surface by electrochemical forces, creating large matric suction. Although uw ⫽ u0 is used in practice, the actual pore pressure u acting at interparticle contacts may be different from u0, as discussed in Section 7.9. The contribution of the long-range interparticle forces to mechanical behavior of unsaturated clayey soils remains to be fully evaluated.
7.13
CONCLUDING COMMENTS
The concepts in this chapter provide insight into the meanings of intergranular pressure, effective stress, and pore water pressure and the factors controlling their values. Because soils behave as particulate materials and not as continua, knowledge of these stresses and of the factors influencing them is a necessary prerequisite to the understanding and quantification of compressibility, deformation, and strength in constitutive relationships for behavior. Various interparticle forces have been identified and their possible effects on soil behavior are highlighted. The effective stress in a soil is a function of its state, which depends on the water content, density, and soil structure. These factors are, in turn, influenced by the composition and ambient conditions. The relationships between soil structure and effective stress are developed further in Chapter 8. Chemical, electrical, and thermal influences on effective pressures and fluid pressures in soils have not been considered in the developments in this chapter. They may be significant, however, as regards soil structure stability fluid flow, volume change, and strength properties. They are analyzed in more detail in subsequent chapters. An understanding of the components of pore water pressure is important to the proper measurement of pore pressure and interpretation of the results. Inclusion of the effect of pore water suction and air or gas pressure on the mechanical behavior of unsaturated soils requires modification of the effective stress equation used for saturated soils. Complications arise from the difficulty in the choice of stress variables and in treatment of contact-level forces (i.e., capillary forces
193
in the pendular regime) in the macroscopic effective stress equations.
QUESTIONS AND PROBLEMS
1. A sand in the ground has porosity n of 0.42 and specific gravity Gs of 2.6. It is assumed that these values remain constant throughout the depth. The water table is 4 m deep and the groundwater is under hydrostatic condition. The suction–volumetric water content relation of the sand is given by soil 1 in Fig. 7.11. a. Calculate the saturated unit weight and dry unit weight. b. Evaluate the unit weights at different saturation ratios Sw. c. Plot the hydrostatic pore pressures with depth down to a depth of 10 m and evaluate the saturation ratios above the water table. d. Along with the hydrostatic pore pressure plot, sketch the vertical total stress with depth using the unit weights calculated in parts (a) and (b). e. Estimate the vertical effective stress with depth. Use Bishop’s equation (7.52) with ⫽ Sw. Comment on the result. 2. Repeat the calculations done in Question 1 with soil 5 in Fig. 7.11. The specific gravity of the soil is 2.65. Comment on the results by comparing them to the results from Question 1. 3. Using Eq. (7.3), estimate the tensile strength of a soil with different values of tensile strengths of cement, sphere, and interface. The soil has a particle diameter of 0.2 mm and the void ratio is 0.7. Assume k/(1 ⫹ e) ⫽ 3.1. Consider the following two cases: (a) ⫽ 0.0075 mm and ⫽ 5 and (b) ⫽ 0.025 and ⫽ 30. Comment on the results. 4. Compute the following contact forces at different particle diameters d ranging from 0.1 to 10 mm. Comment on the results in relation to the effective and intergranular pressure described in Section 7.9. a. Weight of the sphere, W ⫽ –61 Gs wd 3, where Gs is the specific gravity (say 2.65) and w is the unit weight of water. b. Contact force by external load, N ⫽ d 2, where is the external confining pressures applied. The equation is approximate for a simple cubic packing of equal size spheres (Santamarina, 2003). Consider two cases, (i) ⫽ 1 kPa (⬇ depth of 0.1 m) and (ii) ⫽ 100 kPa (⬇ depth of 10 m).
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EFFECTIVE, INTERGRANULAR, AND TOTAL STRESS
c. Long-range van der Waals attraction force, A ⫽ Ahd/(24t 2), where Ah is the Hamaker constant (Section 6.12) and t is the separation between particles (Israelachvili, 1992, from Santamarina, ˚. 2003). Use Ah ⫽ 10⫺20 N-m and t ⫽ 30 A 5. Discuss why it is difficult to measure suction using a piezometer-type tensiometer for long-term monitoring of pore pressures. Describe the advantages of other indirect measurement techniques such as porous ceramic and dielectric sensors. 6. For the following cases, compare the effective stresses calculated by the conventional Terzaghi’s equation and by the modified equation (7.39) with values presented in Fig. 7.8. Discuss the possible errors associated with effective stress estimation by Terzaghi’s equation. a. Pile foundation at a depth of 20 m. b. A depth of 5 km from the sea level where the subsea soil surface is 1 km deep.
7. Give a microscopic interpretation for why an unsaturated soil can collapse and decrease its volume upon wetting as shown in Fig. 7.14 even though the Bishop’s effective stress decreases. 8. Clay particles in unsaturated soils often aggregate creating matrix pores and intraaggregate pores. Air exists in the matrix pores, but the intraaggregate pores are often saturated by strong water attraction to clay surfaces. The total potential of unsaturated soil can be extended from Eq. (7.19) to ⫽ g ⫹ m ⫹ s ⫹ p, where p is the gas pressure potential.12 Discuss the values of each component of the above equation in the matrix pores and the intraaggregate pores.
12
This was proposed by a Review Panel in the Symposium on Moisture Equilibrium and Moisture Changes in Soils Beneath Covered Areas in 1965.
CHAPTER 8
Soil Deposits—Their Formation, Structure, Geotechnical Properties, and Stability
8.1
INTRODUCTION
Long before methods were available to confirm specific soil fabrics and structures, hypotheses were advanced about them, their formation, and their stability in an attempt to account for such phenomena as strength loss of clays on remolding, differences in properties of soils deposited in different environments, collapsing soils and soil liquefaction, creep and secondary compression, pore pressure generation during deformation, anisotropy, thixotropic hardening, and the mobilization of friction and cohesion. Two soils can have the same fabrics but different properties if the forces between particles and particle groups are not the same. Fabric stability is sensitive to changes in stresses and chemical environment. To take both fabric and its stability into account, the term structure is used. Particles, particle groups, and their associations, together with interparticle forces and applied stresses, determine the overall soil structure. The term structure is also used to account for differences between the properties of a soil in its natural state and of the same soil at the same void ratio but thoroughly remolded, or between the soil in its natural state and after remolding and the reapplication of the original stress state. Thoroughly remolded and reworked soil is said to be destructured. Virtually every natural, undisturbed soil has structure. As emphasized by Leroueil and Vaughan (1990), the structure can be as significant in determining engineering behavior as can such important factors as porosity and stress history. How residual and transported soil deposits are formed, how the formative processes and subsequent changes over time act to produce unique types of soil
structures with characteristic properties, how these properties and the associated behavior are interelated, and why these processes and properties are relevant to geotechnical applications are the subjects of this chapter.
8.2
STRUCTURE DEVELOPMENT
Early Concepts
Early ideas about soil fabric and structure were largely speculative because techniques for direct observation of particles had not yet been developed. There was particular interest in the development of explanations for the loss of strength that accompanied the disturbance of many natural clays at constant water content. This sensitivity of the undisturbed structure, which is quantified as the ratio of the undisturbed to fully remolded strength at the same water content, can be great enough to give the strength loss due to remolding shown in Fig. 8.1. Terzaghi (1925a) theorized that adsorbed water layers had a high viscosity near particle surfaces and were responsible for strong adhesion between mineral grains at points of contact between particles. Disturbance of the clay caused contacts to rupture, more water to fill in around the old contact points, and the strength to drop. Different adsorbed ions were also recognized as possibly responsible for differences in strength and sensitivity (Terzaghi, 1941). Goldschmidt (1926) hypothesized that particles in sensitive clay are arranged in a ‘‘cardhouse’’ that collapses on remolding. A load-carrying skeleton consisting of highly compressed ‘‘bond clay’’ trapped between silt and fine sand 195
196
8
SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
properties of soil, to interrelate structure and properties. Modern concepts of soil structure and its importance in geotechnics began to be formulated in the early 1950s, for example, Lambe (1953) and in the comprehensive review of clay microstructure given by Bennett and Hurlbut (1986). General Considerations in Structure Development
Figure 8.1 Strength loss of a clay that is extremely sensitive
to remolding. Clay that becomes fluid on remolding is termed quick clay (photograph courtesy of Haley and Aldrich, Inc.).
particles was suggested by Casagrande (1932a) as responsible for marine clay sensitivity. Such a fabric is assumed to form by simultaneous deposition of flocculated clay particles and silt and sand grains in the saltwater environment. The clay deposited in the interstices between the elements of the skeleton, termed matrix clay, is assumed to be only partly consolidated and remain at high water content. Remolding mixes the matrix and bond clays, thereby destroying the primary load-carrying structure and causing a reduction in strength. Winterkorn and Tschebotarioff (1947) suggested that sensitivity resulted from a cementation similar to that in loess and sandstone. This cementation was attributed to slow recrystallization or formation of cementing materials from inorganic substances of low solubility. In the years since the formulation of these ideas of soil structure, it has been possible to determine fabrics and compositions in more detail and, along with a better understanding of the stress–deformation–strength
A soil’s structure is composed of a fabric and interparticle force system that reflect all facets of the soil composition, history, present state, and environment. Structure-determining factors and processes are summarized in Fig. 8.2. Initial conditions dominate the structure of young deposits at high porosity or freshly compacted soils, whereas older soils at lower porosity are likely to be influenced more by the postdepositional changes. Single-grain fabrics are uncommon in soils containing clay. Complex fabric units of micrometer-tomillimeter size or greater consisting of skeleton grains, clay aggregates, and pores are characteristic of most fine-grained soil structures. The principle of chemical irreversibility of clay fabric (Bennett and Hurlbut, 1986) applies generally to fine-grained soil deposits. This principle recognizes that the chemical environment is critical during the initial stages of sediment fabric formation in water. However, after the initial flocculation of particles and deposition, the chemistry is much less important in influencing fabric changes and subsequent states. Mechanical energy rather than chemical energy becomes the dominant factor influencing subsequent behavior. Residual Soils
The texture of residual soils formed by the in-place weathering of crystalline rocks may be quite similar to that of the parent rock. Clay particles may form coatings over silt and sand grains as a result of repeated wetting and drying. Open, porous fabrics form in some zones, while dense, low-porosity fabrics form in others, and heterogeneity is common. Intense weathering and leaching, coupled with an abundance of aluminum and iron oxides, produces fabrics and textures ranging from open granular to dense and clayey in tropical and subtropical soils. Concretions and nodules are common in some of these materials. For example, a red kaolinitic clay from Kenya is composed of ‘‘crumbs’’ made up of ‘‘subcrumbs’’ that can in turn break up into ‘‘sub-subcrumbs’’ that contain a random arrangement of individual particles (Barden, 1973). Pores are in two classes: irregular pores of about 1 m and very small pores of about 5 nm.
STRUCTURE DEVELOPMENT
197
Figure 8.2 Structure-determining factors and processes.
Alluvial Soils
Alluvial soils can be deposited in marine, brackish water, or freshwater basins. Single clay particles are rare, and flocculated fabrics of particle groups can form in water over the full range of salinities. Edge-to-face flocculated and aggregated arrangements, similar to Fig. 5.3e, are common in marine clays, with dispersed groups and turbostratic groups, similar to interweaving bunches (Fig. 5.3h) found mainly in brackish water clays (Collins and McGown, 1974). Silt and sand grains are reasonably evenly distributed, except in varved or stratified clays, and the larger grains are not usually in contact with each other. Open initial fabrics are characteristic of water-laid sediments, with the degree of openness dependent on clay mineralogy, particle size, and water chemistry, including both the total salt content and the monovalent/divalent cation ratio. The intensity of flocculation may be less in brackish and freshwater deposits, so subsequent consolidation can cause greater preferred orientation of platy particles and particle groups than in saltwater clays. Very slow accumulation rates allow for more stability in open fabrics than is possible when the sediment accumulates rapidly. Aggregates in illitic clay contain particle arrangements ranging from random to booklike. Booklike aggregates are most common in kaolinite. The concentration and type of adsorbed cations usually controls the basic fabric units in smectite. Na–montmorillonite can separate into unit layers, and an interwoven net-
work of filmy particles may form. Ca–montmorillonite particles are usually made up of several unit layers. Some heavily consolidated montmorillonites exhibit surprisingly little preferred orientation. There is little or no preferred particle orientation in soft marine and brackish water illitic clays, except within aggregates, whereas in soft freshwater clays, particles larger than 0.5 m align with their long axes normal to the direction of the consolidation pressure. In clay sediments derived from preexisting shale, the aggregates themselves may be small rock fragments within which the clay plates are intensely oriented. The open packing of sensitive postglacial clay may be due in part to the presence of very small quartz particles of platy morphology (Krinsley and Smalley, 1973; Smalley et al., 1973). Below a critical size of about a cleavage mechanism appears to exist, so platy particles of quartz and possibly other nonclay minerals form as a result of grinding. Organic matter in the form of microscopic animal and plant fragments, microorganisms, and organic compounds can have a profound effect on the structure and properties of postglacial clays (So¨derblom, 1966; Pusch, 1973a, 1973b). The number of bacteria in the oceans is from 1 ⫻ 109 to 3 ⫻ 1011 per m3 at depths of 10 to 50 m beneath the surface (Reinheimer, 1971). It is probable that microorganisms were prevalent in the ocean at the time postglacial clays were formed as well. As organic material and clay surfaces interacted, organic matter was attached to the sedimentary aggre-
198
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SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
gates. In the new environment most of the organisms died or became dormant because of the absence of nutrients, subsequently contributing humic acids, fulvic acids, and humus. Either aggregating or dispersing tendencies result, depending on the environment. Electron micrographs of ultrathin sections (Pusch, 1973a) show organic matter both as fluffy bodies and as distinct objects associated with aggregates. Fabric anisotropy as a result of one-dimensional compression after deposition will ordinarily result in some anisotropy of mechanical properties. Currents, waves, and slopes may also cause preferred orientations of particles. An example for Portsea Beach sand is shown in Fig. 8.3. The long axes of elongate particles show preferred orientations parallel to the coastline and dipping landward at an angle of about 10. Aeolian Soils
Wind-deposited soils such as loess are characterized by particles in the silt and fine sand ranges, although small amounts of clay are often present. These deposits, which are usually partly saturated, are often subject to collapse if saturated. The loose metastable fabric is maintained by clay and light carbonate cementation at grain contacts. The overall macrofabric can be described as bulky granular. Directional, preferred orientation in Vicksburg (Mississippi) loess was observed and described by Matalucci et al. (1969). The long axes of grains concentrated in an azimuth direction of 285 to 289, with an inclination of 3 to 8. A prevailing wind direction of 290 at the time of deposition was deduced from the thinning pattern of the loess in the area, thus accounting for the observed three-dimensional anisotropy. Glacial Deposits
The wide range of particle sizes within and among glacial soils, as well as their widely varying rates of deposition from meltwater, produces a range of fabric types. The presence of small, platy quartz particles derived by glacial grinding was noted earlier. Many silty and sandy ablation tills have a multimodal grain size distribution, with coarser particles distributed through a fine-particle matrix (McGown, 1973). The fabric of the matrix is variable. Many fabric forms are similar to those observed in collapsing soils (Barden et al., 1973). Boulder clays differ from soft, sedimentary clays in that they contain a wider range of grain sizes, with some particles extending into the gravel to boulder ranges, and they are much denser. Many boulder clays have been subjected to high vertical and tangential stresses as a result of readvancing ice sheets. Poor sorting and the presence of a large number of different
mineral types are characteristic of these materials. Well-developed domains of clay are common, and there may be soft clay zones that bridge over some pores caused by the arching action of the large particles. High past stresses on some boulder clays have developed macrofabric features that include shear zones and shear planes. Remolded and Compacted Soil Fabrics
The fabric immediately after remolding or compacting a soil depends on several factors, including strength of preexisting fabric units, compaction method, and compaction or remolding effort. The general effects of disturbance and remolding at constant water content are to break down flocculated aggregations, destroy shear planes, eliminate large pores, and produce a more homogeneous fabric (on a macroscopic scale). Whether or not there will be a preferred direction of particle orientation depends on the methods used. When welldefined shear planes are formed, there usually is an alignment of platy particles or particle groups along the shear plane. Under anisotropic consolidation conditions, plates align with their long axes in the plane acted on by the major principle stress. An isotropic (hydrostatic) consolidation stress produces an isotropic fabric, provided the fabric was isotropic at the start of consolidation. Soil compaction can be done using different methods, including impact, kneading, vibratory, and static. The method used and the initial state of the soil can have profound effects on the fabrics of both sands and clays and on the properties of the compacted soil. In clays, the water content is important; it controls the ease with which particles and particle groups can be rearranged under the compactive effort. A major factor in formation of fabric in a compacted fine-grained soil is whether or not the compaction rammer induces large shear strains. If the hammer (impact compaction), tamper (kneading compaction), or piston (static compaction) does not penetrate the soil, as is usual for compaction dry of optimum water content, then there may be a general alignment of particles or particle groups in horizontal planes. If the soil is sufficiently wet of optimum that the compaction rammer penetrates the soil surface as a result of a bearing capacity failure under the rammer face, there is an alignment of particles along the failure surfaces. A series of such zones is developed as a result of successive rammer blows, and a folded or convoluted fabric may result, as shown, for example, by Fig. 8.4. Effects of Postformational Changes
As listed in Fig. 8.2, a large number of postformational factors can modify the initial structure of a soil.
STRUCTURE DEVELOPMENT
Figure 8.3 Fabric and particle orientation in Portsea Beach sand (Lafeber and Willoughby,
1971). (a) Vertical cross section (perpendicular to the coastline) where B is the dip direction of bedding plane, H is the horizontal plane, and I is the imbrication plane. (b) Distribution of long axis orientations.
199
200
8
SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
Figure 8.4 Microfabric of Takahata kaolin compacted wet of optimum using impact compaction ⫻1000. Reprinted from Yoshinaka and Kazama (1973) with permission of The Japanese Society of SMFE.
Time Chemical diffusion and chemical reactions are time dependent. Following deposition, remolding, or compaction, the interparticle forces, and therefore the mechanical properties, can also change simply as a result of pore pressure redistribution in the new environment. Seepage and Leaching The flow of fluids through a soil can do at least four things:
1. Move particles. 2. Cause compression due to seepage forces. 3. Remove chemicals, colloids, and microorganisms by leaching. 4. Introduce chemicals, colloids, and microorganisms. Precipitation/Cementation Precipitation of materials onto particle surfaces, at interparticle contacts, and in pores can produce cementation. A fabric of partly discernable particle groups may form. Weathering In the zone of weathering, some materials are broken down and others are formed. Changes in pore water chemistry influence the interparticle forces and flocculation–deflocculation tendencies. Weathering can disrupt the initial soil fabric. Cyclical wetting and drying and freezing and thawing disrupt weak particle assemblages and intergroup associations. Wetting generally means weakening and may lead to collapse of some structures, particularly those with open fabrics where particles are only
weakly bonded, such as in loess. Shrinkage associated with drying collapses open particle arrangements and creates domain-type aggregates in some soils and tension cracking in others. Drying concentrates clay around sand and silt particles and between their contact points. Ice lens formation in frost-susceptible soils can open cracks and fissures, followed later by collapse on thawing. Pressure and Consolidation Consolidation under pressure usually strengthens the structure through decrease in porosity and the formation of stronger interparticle contacts. However, in some soils that possess bonding and cementation in their initial states, consolidation stresses greater than some critical value can break down the structure, thus causing weakening and collapse. Temperature Transformations of structure associated with leaching, precipitation, cementation, weathering, and pressure increase develop more rapidly at high temperatures than at low temperatures. Shearing Shearing collapses some structures, whereas in others, such as heavily overconsolidated clay, it may change the structure significantly only in the immediate vicinity (a few millimeters) of the shear plane. Unloading Stress relief as a result of unloading can allow elastic rebound of particles and particle groups and the onset of swelling. Some very stiff materials may split and/or spall after unloading. The following sections of this chapter describe and discuss the structures, properties, and stability of many of the soils identified above in more detail.
8.3
RESIDUAL SOILS
Our geotechnical understanding of residual and tropical soils is much less developed than it is for sedimentary sands, clays, silts, and tills. This is because by far the greatest amount of what might be termed ‘‘classical’’ geotechnical engineering has developed from research and projects involving sedimented soils, that is, materials that have been eroded, transported, and redeposited in a new environment. Much work with these materials has been in areas of temperate climate. However, the need for knowledge and understanding of the engineering behavior of tropical residual soils is great, owing to the extensive construction worldwide in areas covered by these soils. Residual soils differ from sedimentary soils in that they have formed in place in response to the local parent material, climate, topography, and drainage conditions. They may retain elements of the parent material structure; they are usually nonuniform and
RESIDUAL SOILS
201
characterized by highly variable thickness or depth to bedrock. Frequently encountered residual soils include tropical soils, saprolite, and decomposed granite. Various engineering classification systems are available, and they can be categorized into three types (Wesley, 1988): (a) methods based on weathering profile, (b) methods based on pedological classification (see Section 8.4), and (c) methods for specific local soils. Discussion of these systems is given by Wesley (1988) and Wesley and Irfan (1997). Due to the great diversity in residual soil types and properties, development of a single engineering classification system that has universal applicability is unlikely. Tropical Soils
In regions of high temperature and abundant rainfall, rock weathering is intensive and is characterized by the rapid breakdown of feldspars and ferromagnesian minerals, the removal of silica and bases (Na2O, K2O, MgO), and the concentration of iron and aluminum oxides. This process is termed laterization (Gidigasu, 1972; Grant, 1974; and others) and involves leaching of SiO2 and deposition of Fe2O3 and Al2O3. A laterite is a soil whose ratio of SiO2 to Al2O3 is less than 1.33, whereas a lateritic soil has a ratio between 1.33 and 2.00 (Bawa, 1957). With abundant rainfall, high temperature, good drainage, and crystalline parent materials, feldspars weather initially to kaolinite, hydrated iron and aluminum oxides (sesquioxides) are formed, and the more resistant quartz and mica particles may remain. As weathering proceeds, the content of kaolinite decreases, and the hydrated iron and aluminum oxides (goethite and gibbsite) progressively alter to hematite (Fe2O3). Because of the high iron concentration, the resulting soils, termed oxisols, are usually red. The tropical weathering of volcanic ash and rock leads to formation of allophane and halloysite, along with the sesquioxides of iron and aluminum. Smectites (montmorillonites) may also form in the early stages of weathering of volcanic materials. Ultimately, kaolinite and gibbsite may form. Soils formed from weathering of volcanic ash and rocks are termed andisols. Allophane as a clay mineral type is described in Chapter 3. The term allophane soil is also used to refer to andisols. They occur commonly in the Caribbean, the Andes, and the Pacific areas of the United States, Indonesia, Japan, and New Zealand. A comprehensive presentation of the structure and properties of allophane soils is given by Maeda et al. (1977) and Wesley (1977). A typical deep weathering profile in the tropics is shown schematically in Fig. 8.5. Boundaries between
Figure 8.5 Schematic diagram of a typical tropical residual
soil profile (from Little, 1969).
the layers are not always clearly defined, and there are several systems for classifying them based on the degree of weathering and engineering properties (Little, 1969; Deere and Patton, 1971; Tuncer and Lohnes, 1977). Owing to their compositions, structures, and formational histories, laterites and andisols have several unique properties relative to those of typical sand and clay deposits formed from transported sediments (Mitchell and Sitar, 1982). 1. Cemented particle aggregates and clusters susceptible to mechanical breakdown are common. Continued mechanical working or the removal of sesquioxides from such soils can result in significant changes in properties. The effects of remolding and sesquioxide removal on the classification properties of a lateritic soil are shown in Table 8.1. 2. Air drying may cause clay size particles to form aggregates of silt and sand size and a loss of plasticity, as shown by the data in Table 8.2. The significant decrease in plasticity that resulted
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SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
Table 8.1 Physical Properties of Unremolded, Remolded, and Sesquioxide-Free Lateritic Soil
Property
Unremolded
Remolded
Sesquioxide Free
Liquid limit (%) Plastic limit (%) Plasticity index (%) Specific gravity Proctor density (kN/m3) Optimum moisture content (%)
57.8 39.5 18.3 2.80 13.3
69.0 40.1 28.0 2.80 13.0
51.3 32.1 19.2 2.67 13.8
35.0
34.5
29.5
From Townsend et al. (1971).
Table 8.2
Effect of Air Drying on Index Properties of a Hydrated Laterite Clay from the Hawaiian Islands Wet (at Natural Moisture Content)
Moist (Partial Air Drying)
Dry (Complete Air Drying)
Sand content (%)
30
42
86
Silt content (%) (0.05–0.005 mm) Clay content (%) (⬍0.005 mm) Liquid limit (%) Plastic limit (%) Plasticity index (%)
34
17
11
36
41
3
245 135 110
217 146 71
NP NP NP
Index Properties
Remarks Dispersion prior to hydrometer test with sodium silicate
Soaking in water for 7 days did not cause regain of plasticity lost due to the air drying
After Willis (1946); in Gidigasu (1974). Reprinted with permission from Elsevier Science Publishers.
from drying a number of different tropical soils is shown in Fig. 8.6. 3. Drying may cause hardening, and this hardening may be irreversible in some cases. British Standard BS1377 (1990) recognizes the irreversible changes that occur during drying and recommends that tropical residual soils be tested in their natural state wherever possible. 4. The compacted dry density, plasticity index, and compressibility of tropical residual soils are likely to be less than the values for temperate soils of comparable liquid limit. On the other hand, the strength and permeability may be higher. 5. Tropical residual soils commonly are heterogeneous in structure and texture.
6. Soils in tropical areas exist at water contents higher than those that are desirable for most earthwork construction. As a result, difficulties in soil handling and compaction are common. The yielding and strength of residual soils reflect their bonded structure. The preconsolidation pressure may have no connection with the stress history or overburden pressure on the soil. Typical preconsolidation pressure values of residual soils are given in Table 8.3. After yielding, residual soils exhibit large compressibility as a result of structure degradation and particle breakage. A relationship between compression index and in situ void ratio for several soils is given in Fig. 8.7. Extensive discussion on the mechanical behavior of residual soils in relation to their bonded structure is given by Vaughan (1988).
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RESIDUAL SOILS
Figure 8.6 Effect of drying on the Atterberg limits of some tropical soils (from Morin and
Todor, 1975).
Ne w
Gu
ine
a)
Table 8.3 Yield Stresses of Various Residual Soils Obtained from Odometer or K0 Triaxial Tests
60–450 50–200 200–550 50–150 50–300
0.5
Saprolite
Saprolite is derived from the in situ decomposition of parent rock and typically contains soil-like components and partially weathered and/or fresh rock components. Saprolites usually retain some visible remnant rock structure, such as schistosity, relict joints, and parent rock fabric. Often the contact between saprolitic soil and the underlying parent rock is gradational and indistinct. Although saprolites may retain much of their rocklike appearance, they break down easily into a soil-like material. The cracks and joints in a saprolite are often filled with clay, and this can result in low resistance to sliding when wet.
(P ap
a Lateritic (Brazil) iss e Gn il) om az Fr (Br
ite d an ne
From Basalt (Brazil) From Volcanic Ash (Italy) Gurl. Venezuela (Field)
200–500
After Fookes (1997).
Ha
Seprolitic (Sea USA) Tuccarul, various (Brazil) From Basalt (Brazil)
ha
1.0
Sensitivity 8 Sensitivity 4
llo ys
Soft Clay (Canada)
lop
100–350 110–270
1.5
Al
Halloysite and allophone, Papua New Guinea Volcanic clay Gneiss, basalt, and sandstone, Brazil Granite, basalt, and sandstone, Brazil Halloysite and allophone, Japan Granite, gneiss, and schist, USA Gneiss, Venezuela Volcanic ash, Indonesia and New Zealand
Yield Stress (kPa)
Compression Index, Cc
Soil Type and Location
1.0
2.0
3.0
4.0
In Situ Void Ratio
Figure 8.7 Relationship between compression index, measured by odometer tests and initial void ratio (after Vaughan, 1988).
Decomposed Granite
Selective and progressive decomposition of unstable minerals in granitic bedrock breaks up the rock by spheroidal weathering, disintegration, and disaggregation. Granitic rock may weather to depths of 30 m or more and may contain mixtures of solid rock and residual debris throughout most of the profile. The proportion of solid rock usually decreases gradually from the base upward.
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SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
Granitic rock weathers in general accordance with Bowen’s reaction series. Biotite decomposes first, followed by plagioclase feldspar. When part of the plagioclase has decomposed and breakdown of the orthoclase begins, the rock breaks into fragments of decomposed granite called gruss. When most of the orthoclase has weathered to kaolinite, the gruss crumbles to silty sand, which typically contains mica flakes. Apart from some mechanical breakdown, the quartz fragments remain unchanged. Decomposed granite profiles generally contain four zones as shown in Fig. 8.8. The deepest zone consists of angular granitic blocks. The amount of residual debris is small, although the rock may be relatively highly altered. The next zone above contains abundant angular to subangular core stones in a matrix of gruss and residual debris. The upper middle zone is the most variable part of the weathering profile and typically contains about equal amounts of rounded core stones, gruss, and residual debris. The topmost zone usually consists of an unstructured mass of clayey sand with a highly variable grain size distribution. Construction can be difficult in areas underlain by decomposed granite. The bedrock profile is highly irregular, and competent bedrock may be located at variable depths below the ground surface. The core stones can present significant obstacles to excavation. Seemingly sound pieces of rock and gravel break down when excavated or used in earthwork construction. The presence of mica may cause cohesionless soils composed of decomposed granite to be highly compressible. Decomposed granite can be used successfully as an embankment fill material provided it is remembered that particles may undergo substantial breakage under relatively low stresses. Breakage is greatest in materi-
als that are coarse and uniformly graded, and for highly angular particles and particles with high intragranular void content. Consequences of this may include substantial reductions in the peak frictional strength with increasing confining pressure. For example, Yapa et al. (1995) found a reduction in friction angle of 25 percent in densely compacted specimens and about 15 percent in loose specimens over the confining pressure range from 100 to 1500 kPa. Friction angles assigned to decomposed granites used in 12 embankment dam fills constructed in California in the 1960s were conservatively selected and ranged from 29 to 38. Compaction to greater than 90 percent modified Proctor maximum relative compaction at optimum water content is recommended to minimize settlement due to postconstruction hydrocompression when the fill is wetted. During the 1995 Kobe, Japan, earthquake, many reclaimed land sites in Kobe liquefied extensively. The soil used for reclamation was decomposed granite called Masado, which is a well-graded material with particles ranging from gravels to fines. The liquefaction of this soil was surprising because of its higher uniformity coefficient and greater dry density than sandy soils. The weak and crushable character of Masado particles is considered to be one of the causes. The undrained cyclic shear strength of the decomposed granite was found to be much smaller than that of a gravelly soil that had a similar particle size distribution but with strong particles (Kokusho et al., 2004). Colluvial Soils
Colluvium is soil that has formed in place but subsequently has been transported down slope by gravity. Colluvial soils frequently consist of abundant parent rock fragments in a heterogeneous clayey to sandy matrix. They are often found on hillsides and may accumulate in topographic depressions or swales. Slope stability problems may be associated with thick accumulations of colluvium. For example, the colluviums in Hong Kong can be up to 30 m thick, often exist in a loose state on steep slopes, and have been responsible for catastrophic landslides leading to significant loss of life. (Philipson and Brand, 1985). Pyritic Soils
Figure 8.8 Zones of a mature profile of decomposed granite.
Pyrite (FeS2) bearing rocks and soils are responsible for foundation heave, concrete degradation, steel corrosion, environmental damage, acid drainage, accelerated weathering of rock, and loss of strength and stability of geomaterials. Sulfur occurs in rock and soil in the forms of sulfide (S⫺ or S2⫺), sulfate (SO42⫺), and organic sulfur. The amount of sulfide sulfur (also
SURFICIAL RESIDUAL SOILS AND TAXONOMY
known as pyritic sulfur) in a material is a good indicator of the potential for weathering. Sulfide-induced heave has occurred in materials containing as little as 0.1 percent sulfide sulfur (Belgeri and Siegel, 1998). Products of pyrite oxidation include sulfate minerals, insoluble iron oxides, such as goethite (FeOOH) and hematite (Fe2O3), and sulfuric acid (H2SO4). Sulfuric acid can dissolve other sulfides, heavy metals, and the like that are present in the oxidation zone, thus allowing the effects of oxidation to increase as the process builds upon itself. Sulfate crystals form in capillary zones and localize along discontinuities due to reduced confining stress in these regions. Volume increase from the growth of sulfate minerals along bedding planes is a dominant factor in the vertical heave that occurs in shale and other layered materials. The production of sulfates by pyrite oxidation also increases the potential for further deleterious reactions, such as the formation of gypsum (CaSO4 2H2O) and other expansive sulfate minerals (e.g., ettringite). Pyrite oxidation processes proceed in the following way: FeS2 ⫹ –72 O2 ⫹ H2O → Fe2⫹ ⫹ 2SO42⫺ ⫹ 2H⫹ Fe2⫹ ⫹ –14 O2 ⫹ H⫹ → Fe3⫹ ⫹ –21 H2O Fe3⫹ ⫹ 3H2O → Fe(OH)3 ⫹ 3H⫹ FeS2 ⫹ 14Fe3⫹ ⫹ 8H2O → 15Fe2⫹ ⫹ 2SO42⫺ ⫹ 16H⫹
These reactions are usually catalyzed by microbial activity. The sulfuric acid that is produced is often the source of acid rock drainage (ARD) and acid mine drainage (AMD). Gypsum forms when sulfate ions react with calcium in the presence of water, H2SO4 ⫹ CaCO3 ⫹ H2O → CaSO4 2H2O ⫹ CO2 and is accompanied by very large volume increases, as the products of pyrite oxidation reactions are significantly less dense than the initial sulfide (pyrite). Pyrite, of specific gravity (Gs ⫽ 4.8–5.1), reacts with calcite (Gs ⫽ 2.7) to create gypsum (Gs ⫽ 2.3) (Hawkins and Pinches, 1997). Mitigation options that are useful for preventing or reducing sulfide-induced problems include controlling the pyrite oxidation process, use of restraining forces to prevent ground movement, design measures that allow for movement, and removal or neutralization of acid. A recent review of geotechnical problems, heave
205
mechanisms, and mitigation strategies associated with pyrite-bearing soils and rocks is given by Bryant et al. (2003).
8.4 SURFICIAL RESIDUAL SOILS AND TAXONOMY
Agricultural soil maps are often available for areas where engineering data are lacking. They can be useful for preliminary assessments of surficial soils and their properties. These soils are of particular importance in highway, airfield, and land development projects. Surface soils are classified so that they can be aggregated into categories that are useful for understanding genesis, properties, and behavior, especially in relation to agriculture. All soils in the United States (more than 11,000 in 1980) and numerous soils in other countries have been classified according to soil taxonomy (Soil Survey Staff, 1975). Soil taxonomy is a multicategory system of soil classification that includes 10 orders, about 47 suborders, 200 great groups, 1000 subgroups, 2000 families, and 10,000 series. Unlike most classification systems, each category of soil taxonomy carries elements of the higher category so that when a soil is classified at the family level, the family name indicates the order, suborder, great group, and subgroup to which the soil belongs. The soil family name also may contain information on particle size, mineralogy, mean annual soil temperature, pH, soil slope, and soil depth. Soil orders and suborders of the world are related to climate. The orders and their characteristics are given below. The general characteristics of residual soil profiles and the definitions of specific horizons within profiles are given in Section 2.7 and Table 2.4. Entisols (recent soils) are generally without profile development and include alluvial deposits of clay to gravel, deep, soft mineral deposits such as sand dunes, loess, glacial drift, and masses of rock fragments from imperfectly weathered, consolidated rocks. Entisols include some recent, young soils formed in poorly drained areas. In general, geotechnical engineers encounter these soils more than any other because large construction activities tend to concentrate in areas where these soils accumulate, such as in river valleys and in areas bounded by water. The majority of large urban areas are located in such regions. To understand the characteristics of these soils requires consideration of transportation, deposition, and postdepositional sedimentary processes. These topics are considered in Section 2.8. Vertisols (inverted soils) are deep and clayey and are known also as black cotton, black earth, and blackland
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SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
soils. They are associated with a climate that has very dry and very wet seasons. The texture of all horizons is clayey, and the dominant clay mineral is smectite. The soils are expansive. Inceptisols, or new soils, include tundra and selected soils of marshes, swamps, and flat areas. Tundra is a dark gray, peaty accumulation over gray mottled mineral horizons. The soil is poorly drained and boggy. The clay mineral content is low. Permafrost (permanently frozen soil) is frequently present in the substratum. Humic-gley inceptisols are mineral soils formed in poorly drained areas that possess a sticky, compact, gray, or olive-gray B or C horizon. The A horizon may contain 5 to 10 percent organic matter. Aridisols (arid soils) are characterized by surface accumulations of salts from upward movement of water, and usually consist of several centimeters of soil over a calcareous parent material. The soils may be alkaline, with high concentrations of soluble salts of calcium, magnesium, and sodium near the surface. Illite and smectite are common in these soils. Mollisols generally form in cool areas having annual rainfall of 400 to 650 mm. They typically have a dark A1 horizon, and the horizon boundaries are indistinct. Smectites predominate in the clay fraction over illite. There may be local accumulations of sepiolite, palygorskite, and attapulgite, and calcium salts may be present. Spodosols are found south of the tundras in areas where rainfall exceeds 600 mm/yr, and summers are short and cool. Spodosols are characterized by moderate humus accumulation, a thin A1 horizon, and a strongly eluviated A2 horizon. The B horizon is dark brown to reddish brown and often cemented by organic compounds and iron oxides. The texture of all horizons except O is often sandy. The soils are acid, have a low cation exchange capacity, and illite dominates the clay fraction. Alfisols are found south of the spodosol region and east of the prairies in northeastern United States and southeastern Canada and in the humid, temperate areas of western Europe and eastern Asia, where rainfall averages 750 to 1300 mm annually. These soils are characterized by a thin A1 horizon (50 to 150 mm) and a well-developed gray to yellowish A2 horizon. The B horizon is gray to reddish brown, darker, and of finer texture than either the A or C horizons. They are acid soils, and kaolinite is the dominant clay mineral. Ultisols are found in areas of high temperature and high rain (1000 to 1500 mm/yr). Leaching is great, and mineral decay is rapid. Surface accumulation of organic matter is small, and the leached A horizon is
deep. A relatively thick B horizon may be brightly colored (red and yellow) as a result of oxidation and hydration of iron. The B horizon has more than twice the clay content of the A horizon. The cation exchange capacity is low in all horizons, and the clay fraction is composed mainly of kaolinite, illite, and quartz. Many lateritic soils of subtropical regions are ultisols. Oxisol is an iron oxide and aluminum oxide-rich, highly weathered clayey material that changes irreversibly to concretions, hardpans, or crusts when dehydrated. Clay minerals are rapidly broken down and removed. What little clay remains is usually kaolinitic. Deposits of these soils may be up to 30 m or more in depth and may range in texture from friable soils to hard rock. Some oxisols are strong and resistant to breakdown; however, others may lose their granular characteristics when worked, becoming soft, clayey, and impervious. Most laterites of the tropics are oxisols. Histosols, or organic soils, are bog soils whose characteristics depend largely on the nature of the vegetation from which they form. An 11th order, andisols was also proposed to accommodate the soil developed from volcanic ash.
8.5
TERRESTRIAL DEPOSITS
Aeolian Deposits
Of the various sediment transporting agents, wind is the only one that can move material uphill for any distance. Wind is most easily able to move sand. It is not a universal agent of erosion, as its effects are restricted to areas of a particular climate such as deserts or to specific places such as beaches and plowed fields. The load suspended by the wind, which is composed primarily of silt-size particles, is carried high above the ground and may be transported for great distances. The bed load, moved by saltation and traction, moves slowly and as a unit. Deposition from wind occurs with reduction in wind velocity. Consequently, accumulations are found in the lee of desert areas. Coarser particles of sand, carried by saltation and traction, pile in dunes with their long axis parallel to the wind. Loess deposits, composed of silt-size particles, are of particular interest because of their unique structure and properties and are described more fully in Section 8.16. Glacial Deposits
Several types of deposit form from glacial melting, as listed in Table 8.4. Moraines are dropped directly from
TERRESTRIAL DEPOSITS
Table 8.4
207
Deposits of the Glacial Environment
I. Ice Deposited Material A. Sediments 1. Boulder clay or till (drift includes glacial and glacio-fluvial sediments) 2. Erratics B. Structures 1. Moraines a. Lateral moraine—ribbon of debris on sides of glacier b. Medial moraine—merging of inner lateral moraines of two joining glaciers c. Englacial moraine—material within ice d. Subglacial moraine—material at sole of glacier e. Ground moraine—deposited subglacial moraine f. Terminal or end moraine—ridge of deposits built up at end of glacier g. Recessional moraine—terminal moraine of receding glacier 2. Drumlins Mounds of boulder clay formed under deep ice II. Glacio-Fluvial Deposited Material A. Sediments 1. Coarse gravel to clay, progressively sorted dams and deltas 2. Crudely bedded gravel and sand in kames and eskers B. Structures 1. Alluvial fans for glaciers terminating on land 2. Outwash plains merged with fans 3. Deltas for glaciers terminating in standing water 4. Kettle holes caused by melting of stranded ice blocks 5. Kames—mounds of crudely bedded sand and gravel caused by stream from melting ice 6. Esker—winding ridge of sand and gravel from meltwater stream in ice tunnel or from receding ice III. Glacial Lake Deposited Material A. Sediments 1. Sands to clay 2. Poor sorting and stratification of channel deposits 3. Excellent stratification of lake floor deposits B. Structures 1. Overflow channels where lake water escaped 2. Shore line deposits and terraces from waves and currents 3. Deltas 4. Lake floor sediments including varved clays
the melting ice. There are several types of moraine, depending on where the material is dumped relative to the ice mass, as indicated in the table. Moraines usually contain a wide range of unsorted particle sizes, and the material is known as till. When large amounts of boulders and clay are present, the deposit is referred to as boulder clay. Some glacial moraines are densely compacted owing to compression under advancing ice masses. Glacio-fluvial deposits are transported from the melting point by flowing meltwater; kames and eskers (Fig. 8.9) are examples. Kames and eskers are poorly
sorted gravel and sand deposits. Many lateral moraines and dead ice deposits are mixed glacial and glaciofluvial deposits. Glacial lake deposits are quiet water sediments that are usually composed of fine-grained materials. Varved clay is an example (see Fig. 2.13). The formation and characteristics of varved clay are discussed in Section 2.8. The characteristics of a specific glacial deposit depend on the type and erodability of the parent material, the type and distance of transportation, gradients, and pressures. For example, bottom moraines are usually
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SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
Figure 8.9 Glacio-fluvial sediments (Selmer-Olsen, 1964).
finer grained and more consolidated than lateral or end moraines. Finely ground (silt and clay size) rock flour is produced by the grinding action of the ice and may be a major constituent of postglacial marine and lake clays found in Canada and Scandinavia. More extensive and detailed information on glaciers and the characteristics of glacial deposits can be found in Leggett and Hatheway (1988) and West (1995), among many other texts and references. Alluvial Deposits
Alluvial deposits form from pluvial (high rain area) and fluvial (river) deposition and are generally characterized by laterally discontinuous, lenticular beds that are oriented downstream and have different particle size characteristics. Gravels are often in contact with sand and silt. Deposition from streams results from a decrease in slope, increased resistance to flow, a decrease in stream discharge, or a discharge into the more quiet waters of oceans and lakes. As the slope flattens, the stream loses energy, and all particles larger than a certain size are dumped in a jumble of large and small particles. The flow then slips to one side following the steepest slope. The channel may subsequently fill, and the flow shifts again. When this process occurs at the base of a slope, the result is an alluvial fan, a temporary feature that is a symmetrical pile of material spread out radially from the point of slope change. In advanced stages of stream development, the stream occupies only a small part of a broad, flat val-
ley. As the stream overflows its banks during flood stage, friction against the ground surface outside the channel decreases the energy of the water, and a layer consisting mainly of sands and gravels is dropped. This process leads to the formation of natural levees. The alluvial valley of the lower Mississippi River is illustrative of alluvial deposits and their complexity. The valley covers and extends from Cairo, Illinois, to the Gulf of Mexico. All types of deposits from sands to highly plastic clays may be found at some point within the valley. The fall of sea level during the last stages of glaciation led to scouring of a valley beneath the present floodplain surface. Rising sea at the end of the glacial period resulted in deposition of sands and gravels in the bottom of the valley followed by finer material above. In the 25,000 years since the last glaciation, the Mississippi River has changed from an overloaded, shallow, braided stream to a deep, singlechannel, and meandering river. The variety of deposits found within the Mississippi River Valley is great, and their interrelationships are complex; however, each can be accounted for in a logical way in terms of the factors governing its deposition and history, as described by Kolb and Shockley (1957). The coarser materials were laid down initially in the bottom of the valley. Occasional lenses of clay, sandy silt, and silty sand are found in these substratum deposits. The depths to these materials vary from about 3 m in the north to 30 m in the southern part of the river, and the thickness varies from 15 to 125 m in the same direction. Braided stream deposits are usually remote from present large streams. Most are relatively dense, sandy silts and clayey sands. Natural levees rise to 5 m or more above the floodplain and decrease in grain size away from the crest and in a downstream direction. Point bar deposits composed of silts and silty sands form on the inside of river bends during high-water periods. Clayey swales with high organic and water contents form between the bars and the original riverbank. The alternating pervious bars and impervious swales have been responsible for seepage problems in connection with artificial levees. Abandoned sections of the river, left behind as oxbow lakes, fill with weak and compressible clay and silty clay layers with thicknesses up to 30 m or more. Abandoned river courses many miles long fill with materials similar to those of the oxbow lakes. Medium- to high-plasticity clays, often organic, termed backswamp deposits, form in shallow areas during flood stage. Because of desiccation between periods of deposition, they have water contents lower than the abandoned channel deposits.
MARINE DEPOSITS
Lacustrine and Paludal Deposits
Lacustrine, or lake, deposition can occur under freshwater or saline conditions. Gravity settling of sediments discharged into saline lakes may be accelerated by flocculation of clay particles. Saline deposition can lead to precipitation of salt beds, or evaporite deposits. Freshwater lacustrine deposits are generally finegrained, quiet water deposits, except for narrow shore zones of sand. As an example, large shallow lakes, present in much of the western United States during Pleistocene time, have resulted in the formation of laterally continuous and thick clay beds. The Corcoran clay, which covers an area of about 15,000 km2 in California’s San Joaquin Valley, forms an extensive confining bed and aquiclude in the valley and is a significant feature influencing groundwater development. Paludal, or swamp, deposits usually consist of plastic silts, muds, and clays with high water content and organic matter. Difficult problems may be associated with these deposits because of their low strength and high compressibility and from the formation of marsh gas.
8.6 MIXED CONTINENTAL AND MARINE DEPOSITS Littoral Deposits
Littoral deposits form in the tidal zone and consist of tidal lagoon, tidal flat, and beach sediments. Lagoon sediments include fine-grained sands and silts in the channels and organic-rich silt and clay in the quiet areas. Organic matter and carbonates may be abundant. Tidal flat deposits consist of fine-grained dark muds, with lenses or stringers of sand and gravel, and are free of intermediate-size sediments. Beach deposits consist of clean fine- to coarse-grained sand with occasional stringers of gravel. Estuarine Deposits
Estuaries are semienclosed coastal bodies of water that have a free connection with the sea. The sediments consist of channel muds, silts, and sands deposited in response to seasonal river processes and tidal rhythms. Estuarine sediments typically grade seaward into finegrained tidal deposits and landward into coarsergrained river (alluvial) deposits. Fine-grained tidal flats with salt marshes often fringe estuaries. Deltaic Deposits
Deltas form at the mouth of rivers where they enter the sea. They build up where there is no tidal or current
209
action capable of removing the sediment as fast as it is deposited. Deltas build forward from the coastline in a complex process that leads to the formation of a number of separate channels, isolated lagoons, levees, marshy ground, and small streams. As a result, deltas may consist of coarse and fine material, organic matter, and marl (a loose or friable deposit of sand, silt, or clay containing calcium carbonate). Coarse and fine materials alternate owing to the continual shifting of the stream. Suspended silt and clay in the main stream is flocculated by salts in the seawater to form marine mud in the seaward delta face, which is later covered by alluvial, lacustrine, and beach deposits as the delta grows. The complex formations of the Mississippi River delta reflect the composite effects of the advancing delta and the encroaching sea. Pleistocene sediments consisting of dense clays, sands, and gravels underlie the delta. Sand and shell beaches, often 5 m high or more, are among the most suitable deltaic formations for foundation support. Conversely, difficult geotechnical problems are associated with fine-grained and organic delta sediments because of their low strength and high compressibility.
8.7
MARINE DEPOSITS
An averaged and idealized profile through the marine environment is shown in Fig. 8.10. The continental shelf extends from low tide to an average water depth of about 130 m (nearly 450 ft). The steeper continental slope (average of 4 leads down to the more gently sloping continental rise. The average water depth in the deep ocean is more than 3500 m (11,500 ft). There are three main types of marine sediments: lithogenous (derived from terrestrial, volcanic, or cosmic sources), biogenous (remains of marine organisms), and hydrogenous (precipitates from the seawater or interstitial water). An engineering classification system that incorporates compositional and depositional characteristics of these sediments was developed by Noorany (1989) as shown in Fig. 8.11. This system is patterned after the Unified Soil Classification System, the most widely used system for classification of terrestrial soils for engineering purposes. Biogenous sediments, formed from the remains of marine plants and animals, cover about half of the continental shelves, more than half of the deep-sea abyssal plains, and parts of the continental slopes and rises (Noorany, 1989). They are abundant as coarse-grained bioclastic sediments in shallow waters of the coastal zones in tropical regions (between 30N and 30S latitude).
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SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
Figure 8.10 Idealized profile of the continental margin, with vertical exaggeration (after
Heselton, 1969).
Neritic Deposits
The neritic, or continental shelf, environment extends to water depths of up to 200 m. In shallow water, deposition occurs when the intensity of wave-caused turbulence decreases. Generally there is a decrease in particle size and increased influences of biological and chemical factors in the seaward direction, although the sediment distributions may be irregular due to tidal currents and seasonal climatic variations. Neritic deposits reflect sediment source areas and climatic conditions, with sandstone, shale, and limestone typically present in shelf areas. With the exception of the biogenous sediments, the physical properties of continental shelf deposits are essentially the same as those of comparable terrestrial soils. Calcareous Sands Calcareous bioclastic sands are formed from the skeletal remains of corals, shells of mollusks, and algae. They are widely distributed in the
oceans in tropical and subtropical regions of the world. Most consist of porous or hollow particles. An electron photomicrograph of a calcareous sand is shown in Fig. 8.12. Special geotechnical features of the calcareous sediments are (Semple, 1988) that they are composed of weak, angular particles, particle sizes and size distributions are variable, there is uneven cementation over short distances, and they have high void ratio relative to silicate sediments. As a result, these materials may be the source of special geotechnical problems. For example, the side friction developed on driven piles in calcareous sands is often very much lower than anticipated based on the behavior of piles in quartz sand (Noorany, 1985; Murff, 1987; Jewell et al., 1988). Bathyal Deposits
The bathyal environment includes the continental slope and the continental rise. Bathyal sediments are typi-
Figure 8.11 Chart for classification of marine sediments (from Noorany, 1989). Reprinted
with permission of ASCE.
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SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
slide scar now exists. The exact triggering mechanisms for such events are unknown in most cases; however, earthquakes are believed to be the cause of some of them. Abyssal Deposits
Figure 8.12 Electron photomicrographs of calcareous sand from Guam. Magnification is 45⫻ (courtesy of I. Noorany).
cally fine sand, silt, and mud of high water content and low shear strength. The tectonic setting of the depositional area and the characteristics of the continental source materials largely control the distribution, geometry, and properties of these sediments. Erosion, transport, and deposition of these sediments may be caused by the frictional effects of contourfollowing undercurrents that result in thick sequences of sediment ‘‘drift’’ consisting of alternating thin layers of very fine sands, silts, and muds (Leeder, 1982). Appreciable quantities of sediments can be transported from the continental slope and rise to the deep-ocean abyssal plains by slumps, debris flows, and turbidity flows. Detailed exploration of the ocean margins indicates that debris flows are probably a much more important depositional process on the seafloor than has been previously suspected. For example, debris flow deposits of enormous extent have been identified that were generated by large sediment slides on the northwestern African continental margin. The flow traveled on a slope as flat as 0.1 for a distance of several hundred kilometers. The deposits cover an area of about 30,000 km2 and originated from a massive slump of about 600 km3 on the upper continental rise where a prominent
Deep-ocean (abyssal) deposits consist primarily of brown clays and calcareous and silicious oozes, with thicknesses of 300 to 600 m. Terrigenous deposits are derived from land, whereas pelagic sediments settle from the water alone and contain the shells and skeletal remains of tiny marine organisms and plants. Accumulation rates range from less than a millimeter per thousand years in the deep sea to a few tens of centimeters per year in near-shore areas close to the mouths of large rivers (Griffin et al., 1968). Oozes contain more than 50 percent biotic material. Calcareous ooze, composed of empty shells or tests, covers about 35 percent of the seafloor for water depths up to about 5 km. It is usually nonplastic, cream to white in color, and composed of easily crushed sand- to silt-size particles. Brown clay is found beneath most of the deeper ocean areas. Its origin is believed to be atmospheric dust and fine material circulated by ocean currents. About 60 percent of this material is finer than 60 m, and the clay fraction contains chlorite, smectite, illite, and kaolinite, with illite often the most abundant. Brown clays have high water contents, moderate-to-high plasticity, and low strength. Siliceous ooze, composed of plant remains, is found mainly in the Antarctic, northeast of Japan, and in some areas of the equatorial Pacific. Except near their surface, deep-sea deposits are normally consolidated and highly compressible. There is an apparent overconsolidation of the near-surface material at many locations. This evidently reflects bonding developed as a result of the extremely slow rate of deposition and physicochemical effects (Noorany and Gizienski, 1970). Much of the available data on the mechanical properties of deep-seafloor soils pertains to material from the upper 6 m.
8.8
CHEMICAL AND BIOLOGICAL DEPOSITS
Evaporite deposits formed by precipitation of salts from salt lakes and seas as a result of the evaporation of water are sometimes found in layers that are up to several meters thick. The major constituents of seawater, their relative proportions, and some of the more important evaporite deposits are listed in Table 8.5. In some areas alternating layers of evaporite and clay or
FABRIC, STRUCTURE, AND PROPERTY RELATIONSHIPS: GENERAL CONSIDERATIONS
Table 8.5
213
Major Constituents of Seawater and Evaporite Deposits
Ion
Grams per Liter
Percent by Weight of Total Solids
Sodium, Na⫹ Magnesium, Mg2⫹ Calcium, Ca2⫹ Potassium, K⫹ Strontium, Sr2⫹ Chloride, Cl⫺ Sulfate, So42⫺ Bicarbonate, HCO3⫺ Bromide, Br⫺ Fluoride, F⫺ Boric Acid, H3BO3
10.56 1.27 0.40 0.38 0.013 18.98 2.65 0.14 0.065 0.001 0.026 34.485
30.61 3.69 1.16 1.10 0.04 55.04 7.68 0.41 0.19 — 0.08 100.00
Important Evaporite Deposits Anhydrite Barite Celesite Kieserite Gypsum Polyhalite Bloedite Hexahydrite Epsomite Kainite Halite Sylvite Flourite Bischofite Carnallite
CaSO4 BaSO4 SrSO4 MgSO4 H2O CaSO4 2H2O Ca2K2Mg(SO4 ) 2H2O Ma2Mg(SO4)2 4H2O MgSO4 6H2O MgSO4 7H2O K4Mg4(Cl/SO4 ) 11H2O NaCl KCl CaF2 MgCl2 6H2O KMgCl3 6H2O
Adapted from data by Degens (1965).
other fine-grained clastic sediments are formed during cyclic wet and dry periods. Many limestones have been formed by precipitation or from the remains of various organisms. Because of the much greater solubility of limestones than of most other rock types, they may be the source of special problems caused by solution channels and cavities under foundations. More than 12 percent of Canada is covered by a peaty material, termed muskeg, composed almost entirely of decaying vegetation. Peat and muskeg may have water contents of 1000 percent or more, they are very compressible, and they have low strength. The special properties of these materials and methods for analysis of geotechnical problems associated with them are given by MacFarlane (1969), Dhowian and Edil (1980), and Edil and Mochtar (1984). Chemical sediments and rocks in freshwater lakes, ponds, swamps, and bays are occasionally encountered in civil engineering projects. Biochemical processes form marls ranging from relatively pure calcium carbonate to mixtures with mud and organic matter. Iron oxide is formed in some lakes. Diatomite or diatomaceous earth is essentially pure silica formed from the skeletal remains of small (up to a few tenths of a millimeter) freshwater and saltwater organisms. Compacted fills of diatomaceous earth can have very low dry unit weights (1.0 to 1.2 Mg/m3) and high moisture contents (40 percent or more). The material may behave as a dense granular material at stresses below
about 50 kPa, owing to the roughness and interlocking of the diatoms, but becomes more compressible under higher stresses owing to crushing of the diatoms (Day, 1995).
8.9 FABRIC, STRUCTURE, AND PROPERTY RELATIONSHIPS: GENERAL CONSIDERATIONS
The variety of possible soil fabrics and the many possible interparticle force systems associated with each mean that the potential number of soil structures is almost limitless. The mechanical properties of a soil reflect the influences of the structure to a degree that depends on the soil type, the structure type, and the particular property of interest. The effects of structure can be of equal importance to those of initial void ratio and stress. In this sense, structure refers to the differences between the actual void ratio and effective stress and the corresponding values for the same soil in the destructured state. The difference between void ratio under a given effective stress for a soil with some structure, which is the case for consolidation of virtually all sediments from a high void ratio, and the void ratio of a completely destructured soil is illustrated in Fig. 8.13. It is possible that a soil can be at state to the right of the virgin compression curve in Fig. 8.13 as a result of bonding by chemical cementation or aging effects. Thus the full range of possible states in void ratio–
214
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SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
Figure 8.13 The influence of metastable fabric on void ratio under and effective consoli-
dation pressure.
Figure 8.14 Possible states in void ratio–effective stress space.
FABRIC, STRUCTURE, AND PROPERTY RELATIONSHIPS: GENERAL CONSIDERATIONS
215
effective stress space is greater than shown in Fig. 8.13, as may be seen in Fig. 8.14. Virgin compression from an initial state at o to a is followed by the development of bonding, which enables the soil to resist additional compressive stress a–b. At point b the soil is under effective stress b. The completely destructured soil under the same stress would be at point d. The difference in void ratios between the structured soil at b and the destructured soil at d results from a bonding contribution b–c and a fabric contribution c–d. Figure 8.15a shows one-dimensional compression curves for various reconstituted clays with a wide range of plasticities. The void index, was proposed by Burland (1990) for correlating the compression behavior of different clays and for assessing the influence of structure on properties. The void index Iv is defined as Iv ⫽
e ⫺ e* 100 C*c
(8.1)
in which e is the void ratio, e* 100 is the ‘‘intrinsic’’ void ratio under an effective vertical stress of 100 kPa in the one-dimensional odometer test, and C* c is the intrinsic compression index. The intrinsic properties are determined for a reconstituted samples of clay that have been prepared at a water content of about 1.25 times the liquid limit. The intrinsic compression curves can be normalized as shown in Fig. 8.15b. Knowledge of the intrinsic compression curve is useful because the departure of a compression curve for the soil in its natural state from the intrinsic compression curve indicates the existence of soil structure resisting the applied load. Figure 8.16a shows the sedimentation compression curves of several marine deposits reported by Skempton (1970). The water contents (or void ratios) of naturally sedimented clays were plotted against the in situ vertical effective overburden stress. The normalized compression curves, termed the sedimentation compression line (SCL), are shown in Fig. 8.16b along with the intrinsic compression curve, termed the intrinsic compression line (ICL). At a given void ratio, the effective overburden pressure carried by a sedimented clay is approximately five times the pressure that can be resisted by the equivalent reconstituted clay owing to the fabric and soil structure developed during sedimentation and postdepositional processes. For instance, the compression curves of a freshwater glacial lake clay lie well above the sedimentation compression line and the intrinsic compression line before yielding as shown in Fig. 8.17. Once the loading exceeds the preconsolidation pressure, the
Figure 8.15 (a) One-dimensional compression curves for
several clays. (b) Normalized compression curves defining the intrinsic compression line (ICL) (from Burland, 1990).
soil structure degrades and the compression curves move toward the intrinsic compression curve. A generalized view of in situ states of natural soils in relation to the void index and vertical overburden pressure is given in Fig. 8.18 (Chandler et al., 2004). Several principles relate the fabric and structure of a soil to the mechanical properties of interest in engineering:
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SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
Figure 8.16 (a) Compression curves for several clays (from Skempton, 1970). (b) Normal-
ized compression curves for clays in (a) showing the intrinsic compression line (ICL) and sedimentation compression line (SCL).
1. Under a given effective consolidation pressure, a soil with a flocculated fabric is less dense than the same soil with a deflocculated structure. 2. At the same void ratio, a flocculated soil with randomly oriented particles and particle groups is more rigid than a deflocculated soil. 3. Once the maximum precompression stress has been reached, a further increment of pressure causes a greater change in fabric of a flocculated soil structure than in a deflocculated soil structure. 4. The average pore diameter and range of pore sizes is smaller in deflocculated and/or destructured soils than in flocculated and/or undisturbed soils. 5. Shear displacements usually orient platy particles and particle groups with their long axes parallel to the direction of shear. 6. Anisotropic consolidation stresses tend to align platy particles and particle groups with their long axes in the major principal plane. 7. Stresses are usually not distributed equally among all particles and particle groups. Some
particles and particle groups may be essentially stress free as a result of arching by surrounding fabric elements, as discussed further in Chapter 11. 8. Two samples of a soil without cementation can have a different structure at the same void ratioeffective stress coordinates if they have different stress histories. In Fig. 8.19, a sample initially at point a on the virgin compression curve can deform to point b as a result of disturbance and reconsolidation or by secondary compression under stress a stained for a long time. A sample initially at c can reach point b as a result of unloading from c. The stress–deformation properties of the two samples will differ. The overconsolidation ratio (OCR), defined as the ratio of the maximum past consolidation effective stress to the present overburden effective stress is a good measure of stress history. The OCR of sample 2 in Fig. 8.19 is c / a. 9. Volume change tendencies determine pore pressure development during undrained deformation.
SOIL FABRIC AND PROPERTY ANISOTROPY
217
Figure 8.16 (Continued )
10. Changes in structure of a saturated soil at constant volume are accompanied by changes in effective stress. These effective stress changes are immediate. 11. Changes in structure of a saturated soil at constant effective stress are accompanied by changes in void ratio. The change in void ratio is not immediate but depends on the time for water to drain from or enter the soil. Figure 8.20 illustrates points 9, 10, and 11. For any saturated, destructured soil there is a unique relationship between combinations of void ratio and effective consolidation pressure termed the critical state or steady state line, as discussed in more detail in Chapter 11. If the soil is on this line, there is no tendency for change in volume during shear deformation. However, if the state of the soil is in the region above and to the right of the critical state line it will either contract if
the rate of deformation is slow or positive pore pressures will be generated if deformation is rapid. On the other hand, if the soil is initially at a state in the dilative zone, slow deformation will be accompanied by swelling and rapid deformation will be accompanied by generation of negative pore pressures. In general, normally consolidated to slightly overconsolidated clays and saturated loose sands are contractive, whereas heavily overconsolidated clays and dense sands are dilative. 8.10 SOIL FABRIC AND PROPERTY ANISOTROPY
Anisotropic consolidation, shear, directional transportation components, method of remolded or compacted soil preparation, and compaction of soil in layers each may produce anisotropic fabrics. Fabric anisotropy on
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SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
Figure 8.17 Compression curves for freshwater glacial lake clay at pressures below and
above yield (from Burland, 1990).
Figure 8.18 Void index in relation to stress states for different clay types (from Chandler et al., 2004).
Figure 8.19 Illustration of different paths to reach the same present void ratio–effective stress state.
SOIL FABRIC AND PROPERTY ANISOTROPY
219
Figure 8.20 Initial state in relation to the critical-state or steady-state line and its influence
on pore pressure or volume changes during deformation.
a macroscale usually leads to mechanical property anisotropy, and the property differences in different directions may be significant. Examples of anisotropic fabrics in sands are given in Figs. 5.9 and 5.10. Some examples are presented in this section to illustrate the general nature and magnitudes of anisotropy in properties that may be associated with a homogeneous anisotropic fabric. These considerations are separate from property anisotropy caused by stratification of different soil layers, although the latter may be very important in the field, especially with respect to fluid flow. Additional analysis and discussion of the effects of fabric and stress anisotropy on soil stress– deformation and strength are given in Chapter 11. Sands and Silts
The strength of crushed basalt, both along and across the direction of preferred orientation of grains, is shown in Fig. 8.21. Preferred orientation of the somewhat elongated particles (mean particle length to width ratio ⫽ 1.64) was obtained by pouring the soil into a shear box. Intense preferred orientation was obtained at moderate relative densities, as shown by Fig. 5.11. At the lower relative densities the strength was about 40 percent greater across the plane of particle orientation than along it. As shown by Fig. 8.21, this difference decreased with increasing density, and for relative densities above 90 percent, the strengths in the two directions were the same. This is consistent with
the finding that as the density increased the intensity of preferred orientation decreased. The sample stiffness, as measured by the ratio of stress to shear displacement at 50 percent of peak strength, was about twice as high for shear across the direction of preferred orientation than parallel to it. Figure 8.22 shows the variation in friction angle as a function of the loading direction in plane strain and triaxial compression in relation to the initial bedding plane measured on dense Toyoura sand specimens (Park and Tatsuoka, 1994). The term is the angle of the bedding plane relative to the maximum principal stress direction, and the measured friction angles are normalized by the friction angle in plane strain compression with ⫽ 90. The friction angle is the lowest when the loading direction is approximately at ⫽ 30. This is partly because the failure shear plane coincides with the bedding plane. The friction angles in triaxial compression are generally less than those in plain strain compression due to the intermediate stress effect (see Chapter 11). Less bedding effect is also observed in triaxial compression because multiple shear planes at different directions are often produced in triaxial compression samples, whereas fewer, but more distinct, shear plane are observed in plane strain compression. The orientations of contact planes between particles have significant influence on the stress–strain and volume change behavior of granular soils when they are
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SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
sheared in different directions. The contact plane orientation can be represented by the normal to the plane , as shown in Fig. 5.12. Probability density functions E() of these normals for four sands are shown in Fig. 5.13. The fabric of each sand was formed by pouring the sand through water into a cylindrical mold followed by tapping to attain the desired density. From Fig. 5.13 it may be noted that there was considerable anisotropy in particle contact orientations for sands with rodlike or flat particles and for sands with nearly spherical particles. Triaxial compression tests were done on samples of these sands with different maximum principal stress directions relative to the original horizontal plane. The results of these tests for Toyoura sand (b in Fig. 5.13) are shown in Fig. 8.23. Toyoura sand is composed of elongated, flat particles having an axial ratio of 1.65, but similar results were obtained also for the Tochigi sand (Fig. 5.13d). The results of these and other tests reported by Oda (1972a) included tests at different relative densities. They illustrate important aspects of anisotropic granular soil fabric on mechanical properties, for example:
Figure 8.21 Effect of shear direction on strength of samples of crushed basalt prepared by pouring into a shear box (from Mahmood and Mitchell, 1974).
Figure 8.22 Variation of friction angles in plane strain and
triaxial compression as a function of principal stress direction relative to bedding plane orientation (from Park and Tatsuoka, 1994).
1. The stress–strain and volume change behavior are different for different principal stress directions. 2. The effects of fabric anisotropy are somewhat greater in sand with elongated grains than in sand with more spherical grains. 3. The deformation modulus and dilation decrease as the angle decreases from 90 to 0 for sand fabric formed by pluviation. 4. The stress–strain–volume change properties of dense sand tested at ⫽ 0 are comparable to those for loose samples tested at ⫽ 90. 5. The secant modulus at 50 percent of peak strength decreases with decreasing values of . The ratio of E50 for ⫽ 90 to that at ⫽ 0 is 2 to 3 for dense sand. Overall, the major influence of anisotropy of granular soil fabric, as measured by both particle long axis orientations and interparticle contact orientations, is to give different volume change (dilatancy) tendencies, which, in turn, give different stress–deformation and strength behavior for different directions of loading. Fabric and mechanical property anisotropy are also found in undisturbed sands and silts in the field. Undisturbed samples of Vicksburg loess exhibit up to 12 percent higher strength when sheared perpendicular to grain orientation than parallel to it (Matalucci et al., 1970). The friction angle measured in triaxial tests decreased from 34 to 31 for dry loess and from 24 to
SOIL FABRIC AND PROPERTY ANISOTROPY
221
Figure 8.23 Effect of initial fabric anisotropy on stress–strain and volume change behavior of Toyoura sand. Angle is between major principal stress direction and the original horizontal plane (from Oda, 1972a). Reprinted with permission of The Japanese Society of SMFE.
21 for moist samples as the direction of the major principal stress was changed from normal to the preferred orientation of particles to 45 to it. Anisotropic fabric in undisturbed Portsea Beach sand is shown in Fig. 8.3. The effect of this anisotropy on the behavior in triaxial compression was studied by
testing undisturbed samples1 cut as shown in Fig. 8.24. 1 To handle undisturbed sand samples, Lafeber and Willoughby (1971) used a two-stage replacement of the original seawater by polyethylene glycol (Carbowax 4000). Triaxial tests were done after first heating the samples to melt the Carbowax.
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SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
Figure 8.24 Orientations of triaxial cylinders of Portsea Beach sand in relation to in situ conditions (Lafeber and Willoughby, 1971).
Values of mean secant modulus for samples at different orientations are given in Table 8.6. There are significant differences among samples tested in different directions, and there is no horizontal plane of isotropy for deformation modulus. Collectively, the results of studies of the effects of fabric anisotropy on properties of granular soils show the following:
Table 8.6 Effect of Sample Orientation on Secant Modulus of Undisturbed Samples of Portsea Beach Sand Sample Axis Direction Vertical Horizontal Horizontal Horizontal Horizontal
Sample Axis Azimuth Parallel to coastline 30 with coastline 60 with coastline Perpendicular to coastline
1. Anisotropic fabric, as indicated by particle orientations and interparticle contact orientations, is likely in natural deposits, compacted fills, and laboratory samples. 2. Anisotropic fabrics produce anisotropic mechanical properties. 3. Strengths and deformation moduli are higher for shear directions across planes of preferred orientation than along them. 4. The magnitude of strength and modulus anisotropy depends on density and the extent to which particles are platy and elongated. Differences in peak strength of the order of 10 to 15 percent may exist when the axial ratios of particles are 1.6 or greater. 5. Differences in moduli in different directions are greater than differences in peak strength. Moduli in different directions may differ by a factor of 2 or 3. 6. The effect of fabric anisotropy on mechanical property anisotropy is primarily through differences in volume change tendencies for deformation in different directions.
Secant Modulus (kN/m2)
Standard Deviation (kN/m2)
5.41 ⫻ 104
0.27 ⫻ 104
4.01 ⫻ 104
0.24 ⫻ 104
3.85 ⫻ 104
0.18 ⫻ 104
3.76 ⫻ 104
0.23 ⫻ 104
Clays
0.53 ⫻ 104
Clay fabric anisotropy studies in clays have dealt mainly with effects on strength and hydraulic conductivity. Undrained strength anisotropy results from stress anisotropy during consolidation, apart from any pos-
3.55 ⫻ 104
Data from Lafeber and Willoughby (1971).
SAND FABRIC AND LIQUEFACTION
sible fabric anisotropy. In terms of the effective stress strength parameters c and , analysis of the effects of stress anisotropy by Brinch-Hansen and Gibson (1949) leads to cu c ⫽ cos ⫹ (1 ⫹ K0) sin (2Aƒ ⫺ 1) p p ⫻ ⫹
冋冉 冊 冉 冊册 cu p
2
⫺
1 ⫺ K0 2
冉
冊
cu (1 ⫺ K0) cos2 45 ⫹ ⫺ p 2
2
223
ume change tendencies. This, in turn, influences the dilatancy contribution to the strength of sands and the volume changes in drained deformation and the pore pressures in undrained shear of clays. Anisotropy of soil fabric and natural stratification are responsible for higher hydraulic conductivities in the horizontal direction than in the vertical direction for most soil deposits, and this topic is discussed in more detail in Section 9.3.
1/2
(8.2)
where cu is undrained shear strength, p is vertical consolidation pressure, K0 is the coefficient of lateral Earth pressure at rest, and is the inclination of the failure plane to the horizontal. The pore pressure parameter Aƒ is defined as Aƒ ⫽
uƒ ( 1 ⫺ 3)ƒ
(8.3)
where uƒ is the change in pore water pressure at failure, and ( 1 ⫺ 3)ƒ is the deviator stress at failure. The degree of mobilization of c and at peak stress difference and the strain at failure in an undrained test vary with orientation of principal stresses. Data on the variation of undrained compressive strength with orientation of the failure plane are summarized in Fig. 8.25. Strengths in the vertical and horizontal directions may differ by as much as 40 percent as a result of fabric anisotropy. The differences in undrained strength in the different directions result from differences in pore pressures developed during shear (Duncan and Seed, 1966; Bishop, 1966; Nakase and Kamei, 1983; Kurukulasuriya et al., 1999). The effective stress strength parameters are independent of sample orientation. The drained strength is independent of shear stress orientation relative to fabric orientation, as demonstrated by tests on kaolin (Duncan and Seed, 1966; Morgenstern and Tchalenko, 1967b). Stress paths for two samples from a clay with anisotropic fabric but isotropic initial stresses are shown schematically in Fig. 8.26. The facts that both the effective stress strength parameters and the drained strength are independent of fabric anisotropy, but that pore pressures developed in undrained shear are strongly influenced by anisotropy, suggest that the effect of fabric anisotropy on strength is the same for both sands and clays. Changes in stress orientation relative to fabric orientation influence vol-
8.11
SAND FABRIC AND LIQUEFACTION
If saturated sand is at a void ratio above the criticalstate or steady state line (Fig. 8.20) and sheared rapidly, it will try to densify. As water cannot escape from the pores instantaneously, the collapsing structure will transfer normal stress to the pore water. The accompanying decrease in effective stress reduces the shear strength to a low value, and the soil mass liquefies. Cyclic loading due to earthquakes is perhaps the most common cause of dynamic liquefaction. The resistance to liquefaction depends on characteristics of the sand, including gradation, particle size, and particle shape; relative density; confining pressure; and initial stress state. A comprehensive review of the state of knowledge of the causes and effects of soil liquefaction during earthquakes was published by the National Research Council (NRC, 1985) and by Kramer (1996). Liquefaction depends on a sand’s resistance to deformation and the degree to which rapidly applied shear stresses cause a tendency for the structure to reduce in volume or collapse. Since samples of the same sand at the same density but having different fabrics have different stress–strain and volume change properties, see Section 8.8, it follows that different fabrics should influence liquefaction resistance as well. Figure 8.27 shows for three sands that preparation of samples by two different methods produced distinctly different resistances to liquefaction, as measured by the number of load cycles to cause liquefaction at a particular value of cyclic stress ratio. The cyclic stress ratio for these tests was defined as the ratio of half the cyclic deviator stress to the initial effective confining pressure. The differences in liquefaction behavior result from differences in the sand fabric owing to different sample preparation methods (Mitchell et al., 1976). Results similar to those in Fig. 8.27 are shown in Fig. 8.28 for samples of Monterey No. 0 sand at a relative density of 50 percent prepared by three different methods. Similar behavior was measured for samples of the same sand at a relative density of 80 percent (Mulilus et al., 1977). Monterey No. 0 sand is a uniform me-
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SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
Figure 8.25 Variation of compressive strength with orientation of failure plane (from Dun-
can and Seed, 1966). Reprinted with permission of ASCE.
Figure 8.26 Stress paths in triaxial compression for differently oriented samples for clay
with anisotropic fabric.
SAND FABRIC AND LIQUEFACTION
Figure 8.27 Influence of sand sample preparation method on liquefaction resistance (from
Mulilis et al., 1977). Reprinted with permission of ASCE.
Figure 8.28 Liquefaction resistance of Monterey No. 0 sand prepared to a relative density of 50 percent by three methods (Mulilus et al., 1977).
225
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SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
dium sand with rounded to subrounded grains consisting predominantly of quartz with some feldspar and mica. That the fabrics were different for the different preparation methods was determined by analysis of particle long axis and interparticle contact on normal orientations measured on thin sections cut through the samples. Pluviation resulted in distinct preferred orientation of particle long axes in the horizontal direction. Moist vibration produced the most random orientation of particle long axes, with moist tamping giving intermediate values. The results of static triaxial compression tests (Fig. 8.29) showed stress–strain and volume change behavior consistent with the observed fabrics and liquefaction resistance. That is, the weakest and least dilative material was that prepared by dry pluviation, and the strongest and most dilative material was prepared by moist vibration. From results such as these, it is clear that relative density by itself is insufficient for characterization of the sand properties. This means that sand samples reconstituted in the laboratory ordinarily cannot be used for determination of properties that are representative
of undisturbed sand in the field since the field fabric is not usually known, and undisturbed samples are virtually impossible to obtain. It also explains partially why such heavy reliance is placed on the results of in situ tests such as the standard penetration test and the cone penetration test for assessment of the in situ liquefaction resistance of sand deposits. Of several laboratory methods that can be used to prepare sand samples, pluviation usually produces the most compressible and weakest fabrics at any relative density. Thus this method can be used to obtain a lower bound or most conservative estimate of the properties that the same sand at the same relative density can have in the undisturbed state in the field. Most sands in situ are stronger because of prestressing effects, aging, and cementation. The difference between the pluviated sample lower bound values and the actual in situ values can be large. A corollary of this is that undisturbed sand deposits can suffer a stress loss on disturbance; that is, they are sensitive in the same way as many clay deposits owing to loose metastable structures.
8.12
Figure 8.29 Influence of sample preparation method on drained triaxial compression behavior of Monterey No. 0 sand at 50 percent relative density.
SENSITIVITY AND ITS CAUSES
As noted at the beginning of this chapter, early concepts of fabric and structure in geotechnical engineering were developed, at least in part, to explain the loss of undrained strength when undisturbed clay is remolded. Although virtually all normally consolidated soils exhibit some amount of sensitivity, quick clay, as illustrated in Fig. 8.1, is the most sensitive. Large deposits of this material, which turns into a heavy viscous fluid on remolding, are found in previously glaciated areas of North America and Scandinavia. The ratio of peak undisturbed strength (Sup) to remolded strength (Sur), as determined by the unconfined compression test, was used initially as the quantitative measure of sensitivity St (⫽ Sup /Sur) (Terzaghi, 1944). The remolded strength of some clay is so low, however, that unconfined compression test specimens cannot be formed. Therefore, the vane shear test is often used to measure sensitivity, both in the field and in the laboratory, as is also the Swedish fall-cone test (Swedish State Railways, 1922; Karlsson, 1961). Several classifications of sensitivity have been proposed; one of them is given in Table 8.7. Marine clays with high salinity may exhibit considerable sensitivity up to 30 (Torrance, 1983). Clays become quick not because the undisturbed strength becomes very high but because the remolded strength becomes very low. Salt leaching is a requirement for the development of very high sensitivity of more than 100. Leaching de-
SENSITIVITY AND ITS CAUSES
Table 8.7
227
Classification of Clay Sensitivity Values St
Insensitive Slightly sensitive clays Medium sensitive clays Very sensitive clays Slightly quick clays Medium quick clays Very quick clays Extra quick clays
⬃1.0
1–2 2–4 4–8 8–16 16–32 32–64 ⬎64
From Rosenqvist (1953). Figure 8.30 Photomicrograph of undisturbed Leda clay, air dried. Picture width is 8 m (Tovey, 1971).
creases the liquid limit of low-activity clays and consequently the remolded strength, while the void ratio remains essentially constant or decreases only a small amount. Composition of Sensitive Clays
Quick clays may not differ from clays of low sensitivity in terms of mineral composition, grain size distribution, or fabric. Most quick clays are postglacial deposits, with the mineralogy of the clay fraction dominated by illite and chlorite and that of the nonclay fraction by quartz and feldspar. Amphibole and calcite are also common. The activity of quick clays is usually less than 0.5. The pore fluid composition and the changes in composition that have developed between the time of deposition and the present are of paramount importance. Changes in the type and amount of electrolyte, organic compounds, and small quantities of surface-active agents are controlling factors in the development of quick clay. Fabric of Sensitive Clays
With the possible exception of strongly cemented soils, the undisturbed fabric of sensitive clays is composed of flocculated assemblages of particles or aggregates. Electron photomicrographs show open and flocculated particle arrangements in medium sensitive to quick clays. The contribution of fabric to high sensitivity is through open networks of particles and aggregates that are linked by unstable connections. The fabric of undisturbed Leda clay is shown in Fig. 8.30. A very wide range of particle sizes may be seen. The microfabric of quick clay and that of adjacent zones of much less sensitive clay may be the same. Thus, while an open flocculated fabric is necessary, it is not a sufficient condition for quick clay development. Some preferred orientation might develop in
quick clays as a consequence of delayed or secondary compression. This compression can be accelerated as a result of leaching of salts during formation of the deposit (Torrance, 1974). Causes of Sensitivity
At least six different phenomena may contribute to the development of sensitivity: 1. 2. 3. 4. 5.
Metastable fabric Cementation Weathering Thixotropic hardening Leaching, ion exchange, and change in the monovalent/divalent cation ratio 6. Formation or addition of dispersing agents Metastable Fabric When particles and particle groups flocculate and/or pack inefficiently, the initial fabric after deposition is open and involves some amount of edge-to-edge and edge-to-face associations in a cardhouse arrangement of elongate and platy particles. A consequence of this is well illustrated by the sedimentation compression line relative to the intrinsic compression line in Fig. 8.16b. During consolidation this fabric can carry effective stress at a void ratio higher than would be possible if the particles and particle groups were arranged in an efficient, parallel array. When saturated soil is mechanically remolded from a state such as represented by point 1 in Fig. 8.13, the fabric is disrupted, effective stresses are reduced because of the tendency for the volume to decrease, and the strength is less. If the original consolidation stress is reapplied, then there will be additional consolidation, and the void ra-
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tio will decrease to a point as represented by 2 in Fig. 8.13. Mechanical remolding and reapplication of stresses will cause consolidation to point 3, and continued repetition of the process will lead ultimately to a minimum void ratio for the fully destructured soil at n. Thus, if the soil is at any state within the shaded zone of Fig. 8.13, it will have some degree of metastability of structure and could be further consolidated if disturbed and recompressed. Sensitivity values resulting from metastable particle arrangements were measured in undrained triaxial tests on saturated kaolinite samples consolidated from high initial water content (Houston, 1967). They decreased from 12 at high water content and low consolidation pressure to 2 at low water content and high consolidation pressure. Consolidated, undrained triaxial compression tests on saturated sand–kaolinite mixtures consolidated initially under an effective stress of 200 kPa gave the results shown in Fig. 8.31. The loss in strength due to disturbance was accompanied by a large increase in pore water pressure and decrease in
Figure 8.31 Stress–strain characteristics of kaolinite–sand mixtures illustrating the effects of disturbance.
effective stress to almost zero from the initial value of 200 kPa. This illustrates the interdependence of effective stress and structure, as well as the effects of structure metastability. A point of practical importance is that the continuing generation of metastable fabrics following disturbance explains why some sand deposits have been observed to reliquefy at the same locations in successive earthquakes. Cementation Many soils contain carbonates, iron oxide, alumina, and organic matter that may precipitate at interparticle contacts and act as cementing agents. On disturbance, the cemented bonds are destroyed leading to a loss of strength. Four naturally cemented Canadian clays tested by Sangrey (1970) had sensitivities of 45 to 780. Late glacial plastic clay from near Lilla Edit in the Gota Valley of Sweden has a sensitivity of 30 to 70. The apparent preconsolidation pressure as determined by odometer tests is much greater than the maximum past overburden pressure (Bjerrum and Wu, 1960). When consolidation pressure greater than this apparent maximum past pressure is applied, there is a marked reduction in cohesion. This was interpreted to result from a rupture of cemented interparticle bonds that were created by carbonation of microfossils and organic matter and precipitation of pore water salts at particle contacts. Removal of carbonates, gypsum, and iron oxide by leaching with EDTA (a disodium salt of ethylene-diaminetetraacetic acid) resulted in a marked reduction in the apparent preconsolidation pressure of quick clay from Labrador (Bjerrum, 1967). A quasi-preconsolidation effect (Leonards and Ramiah, 1960) results if clay remains under constant stress for a long period. Whether or not the additional resistance is due to a true chemical cementation is debatable; however, the effect is the same, and an increase in sensitivity results. Weathering Weathering processes change the types and relative proportions of ions in solution, which, in turn, can alter the flocculation–deflocculation tendencies of the soil after disturbance. Some change in the undisturbed strength is also probable; however, the major effect on sensitivity is usually through change in the remolded strength. Strengths and sensitivities may be increased or decreased, depending on the nature of the changes in ionic distributions (Moum et al., 1971). Thixotropic Hardening Thixotropy is an isothermal, reversible, time-dependent process occurring under conditions of constant composition and volume whereby a material stiffens while at rest and softens or liquefies upon remolding. The properties of a purely thixotropic material are shown in Fig. 8.32. Thixo-
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229
of the same clay that is allowed to rest at constant water content and pore fluid composition. However, the results of studies on samples allowed to harden starting from present composition suggest that sensitivities up to about 8 or so may be possible due to thixotropy (Skempton and Northey, 1952; Seed and Chan, 1957; Mitchell, 1960).2 Leaching and Changes in Monovalent/Divalent Cation Ratios Reduction in salinity of marine clay by
Figure 8.32 Properties of a purely thixotropic material.
tropic hardening may account for low to medium sensitivity and for a part of the sensitivity of quick clays (Skempton and Northey, 1952). The mechanism of thixotropic hardening is explained as follows (Mitchell, 1960). Sedimentation, remolding, and compaction produce soil structures compatible with these processes. Once the externally applied energy of remolding or compaction is removed, however, the structure is no longer in equilibrium with the surroundings. If the interparticle force balance is such that attraction is somewhat in excess of repulsion, there will be a tendency toward flocculation of particles and particle groups and for reorganization of the water–cation structure to a lower energy state. Both effects, which have been demonstrated experimentally, take time because of the viscous resistance to particle and ion movement. The effect of time after disturbance on the pressure in the pore water is particularly significant. Several studies show that there is a continual decrease in pore water pressure, or increase in pore water tension, with time after compaction or remolding. Figure 8.33 and Ripple and Day (1966) show that shear of thixotropic clay pastes causes an abrupt decrease in pore water tension (increase in pore water pressure) followed by slow regain during periods of rest. The concurrent time-dependent increase in effective stress accounts for the observed increase in undrained strength. The importance of thixotropic hardening in contributing to the sensitivity of clay in the field is impossible to determine. Laboratory studies start with a specific present composition and density. The initial state of a clay deposit in nature is usually far different than at the present time, and the history of an undisturbed clay bears little resemblance to that of a remolded sample
leaching is an essential first step in the development of quick clay, as first suggested by Rosenqvist (1946). Freshwater leaching following a drop in sea level or rise in land level results in removal of the seawater environment. Percolating freshwater in silt and sand lenses is sufficient to remove salt from the clay by diffusion without the requirement that the water flow through all the pores of intact clay (Torrance, 1974). Although leaching causes little change in fabric, the interparticle forces are changed, resulting in a decrease in undisturbed strength of up to 50 percent, and such a large reduction in remolded strength that quick clay forms. The large increase in interparticle repulsion is responsible for the deflocculation and dispersion of the clay on mechanical remolding. It results in part from the decrease in electrolyte concentration causing increase in double-layer thickness. Changes in strength and the increase in sensitivity accompanying the leaching of salt from a Norwegian marine clay are shown in Fig. 8.34. The relationship between sensitivity and salt content for several Norwegian marine clays is shown in Fig. 8.35. Confirmation of the leaching hypothesis was obtained by means of leaching tests on artificially sedimented clays (Bjerrum and Rosenqvist, ˚ srum clay sedimented in saltwater (35 g/liter) 1956). A and then leached of salt exhibited an increase in sensitivity from 5 to 110. A sample sedimented in freshwater had a sensitivity of 5 to 6. Although leaching of salt is necessary, it may not be sufficient for the development of quick clay. The salt content of Champlain clay in eastern Canada rarely exceeds 1 to 2 g/liter and is usually less than 1 g/liter, yet the sensitivities of different samples range from as low as 10 to over 1000 (Eden and Crawford, 1957; Penner, 1963c, 1964, 1965). The reason for this large range is that the essential condition for development of quick clay is an increase in interparticle repulsions. Considerations in Chapter 6 show that the type of cations and the relative amounts of monovalent and divalent cations have a controlling influence on equilibrium particle arrangements.
2 Sherard (1975, personal communication) indicated that thixotropic strength ratios of up to 100 have been measured in Champlain clay.
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Figure 8.33 Effect of shear on pore water tensions for various clays (after Day, 1955).
The electrokinetic or zeta potential in Champlain clay, as determined using electroosmosis (see Chapter 9), correlates well with sensitivity, as shown in Fig. 8.36 (Penner, 1965). The electrokinetic potential is a measure of the double-layer potential, with higher values associated with thicker double layers and higher sensitivity. For clays of low salinity (⬍1 or 2 g salt/ liter of pore water) the sensitivity correlates well with the percent of monovalent cations in the pore water,
also shown in Fig. 8.36. The percent monovalent cations in the pore water is given by Na⫹ ⫹ K⫹ ⫻ 100 Na ⫹ K⫹ ⫹ Ca2⫹ ⫹ Mg2⫹ ⫹
with all concentrations in milliequivalents per liter. The dependence of sensitivity on monovalent to total cation
SENSITIVITY AND ITS CAUSES
231
ratio was also shown by Moum et al. (1971). An analysis in terms of sodium adsorption ratio (Section 6.15) leads to a similar result (Balasubramonian and Morgenstern, 1972). The percent monovalent cation in seawater is only about 75 on a meq/liter basis. Thus, according to the relationship in Fig. 8.36, if seawater is leached without change in the relative concentrations of Na⫹, K⫹, Mg2⫹, and Ca2⫹, very high sensitivities cannot develop. Selective removal of divalent cations is necessary. In quick clay, Ca2⫹ and Mg2⫹ are removed from the system, possibly by organic matter (So¨derblom, 1969; Lessard and Mitchell, 1985). The mechanism by which these changes occur as deduced by Lessard (1981) is summarized as follows. Organic matter from marine organisms deposits simultaneously with the illite, feldspar, and quartz that constitute the bulk of a postglacial marine clay. Iron oxide minerals are also present in small quantities. As the depth of burial increases with continued deposition, so does the distance to oxygen supply from the seawater above. Bacterial oxidation of the organic matter depletes the oxygen content of the pore water, and an anaerobic environment develops that reduces ferric oxides to soluble ferrous iron. Simultaneously, sulfates in the pore water are reduced to hydrogen sulfide by the organic matter with the aid of sulfate-reducing bacteria. The formation of iron sulfide materials then follows: Fe2⫹ ⫹ H2S → black amorphous FeS → slowly crystallizes → FeS2 (pyrite)
Figure 8.34 Changes in properties of a normally consoli-
dated marine clay when subjected to leaching by freshwater (Bjerrum, 1954).
The amount of FeS and FeS2 produced is limited by the rate of diffusion of sulfate from the overlying seawater and/or by the amount and reactivity of detrital iron. Carbon dioxide generated by the bacterial oxidation of organic matter produces an increase in alkalinity (pH increase) and decrease in the amount of dissolved Ca2⫹ and Mg2⫹, as the latter precipitate as Mg–calcite. All of these transformations can occur in a period of only several years. If the deposit is uplifted above sea level, sulfate becomes scarce, oxidation of organic matter is slow because of the depleted O2 content, and sulfides remain stable. Freshwater leaching decreases the salt content, which in combination with the low Ca2⫹ and Mg2⫹ concentrations that result from the sulfate reduction processes, provides the necessary conditions for the existence of a quick clay, that is, low-salt content, high percentage of monovalent cations in the adsorbed layers on the clay particles, and high pH.
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Figure 8.35 Relationship between sensitivity and salt concentration for some Norwegian
clay deposits (Bjerrum, 1954).
Aging of Quick Clay Samples
Important changes in the properties of quick clays have been observed to develop with time after sampling, including increases in remolded strength and liquid limit and decrease in the liquidity index, all without change in water content. For example, the changes that occurred in remolded quick clay from Outardes-2 in Quebec over a 1-year period are shown in Fig. 8.37. Changes such as these mean that laboratory tests on aged samples can give results that are misleading relative to the clay properties in situ. The liquidity index, see Section 4.5, is useful for expressing and comparing the consistencies of different clays, as it normalizes the water content relative to the plasticity index.3 3
Similarly, the void index, Iv [Eq. (8.1)] is often used for correlating the compression behavior of different clays and for assessing the influence of structure on properties (Burland, 1990; Cotecchia and Chandler, 2000; Jardine et al., 2004). Iv ⫽
* e ⫺ e 100 C *c
From studies on the quick clay from LaBaie, Quebec, it was possible to explain the transformations that cause changes in properties after sampling, such as those shown in Fig. 8.37 (Lessard and Mitchell, 1985). Geotechnical properties of the LaBaie clay determined within one month after sampling are shown in Fig. 8.38. This clay is composed primarily of rock flour containing plagioclase, K-feldspar, quartz, amphibole, and calcite, with about 10 percent illite and trace amounts of kaolinite and chlorite. Samples of the LaBaie clay were stored under different conditions. The changes in remolded strength, liquidity index, pH, and concentrations of several ion types as a function of storage time are shown in Fig. 8.39. These results show that aging leads to increases in both pore water salinity and the concentrations of divalent cations in the pore water and decreases in pH. Collectively, the compositional changes are responsible for increase in remolded strength (Fig. 8.37) and decrease in liquidity index (Fig. 8.39) because each depresses the double layer, thereby decreasing the interparticle repulsive forces. The remolded strength
SENSITIVITY AND ITS CAUSES
233
forms sulfuric acid and ferric hydroxide. The reactions can be rapid at high pH. Slow transformation of Fe(OH)3 to yellow goethite (FeO–OH) may give a brownish color to the clay. The sulfuric acid reacts with the Mg–calcite to increase the concentrations of Ca2⫹ and Mg2⫹ in the pore water and in the adsorbed complex on the clay particles. Concurrently, sodium and potassium are displaced from the double layer to the pore water. The salinity increases, and the increase in concentrations of the divalent cations causes increases in the remolded strength and the liquid limit and decreases in the sensitivity and liquidity index. More complete descriptions of the reactions, including phase diagrams and reaction kinetics are given by Lessard (1981) and Lessard and Mitchell (1985). An important role of bacteria in mediating the oxidation and reduction reactions associated with quick clay formation and aging is suggested. The importance of geochemical and microbiological processes in geotechnical engineering has been given little attention in the past. Future studies of the phenomena and processes are likely to provide important new insights and understanding. Significance of Aging in Practice
Figure 8.36 Relationship between sensitivity and monova-
lent cations in low-salt-content clays and between sensitivity and electrokinetic potential (data from Penner, 1965).
correlates well with both the concentration of divalent cations and the total cation concentration, as shown in Fig. 8.40. The method of storage (see Fig. 8.39) does not affect the correlations shown in Fig. 8.40; rather, it influences the time required for the chemical concentration changes to occur. These changes in chemistry and properties are caused by the following sequence of events. When quick clay is sampled or exposed, some contact with the air and oxygen is inevitable. This air causes some of the remaining organic matter to oxidize and form carbonic acid, which, in turn, dissolves calcium carbonate, thus increasing the concentrations of calcium and bicarbonate in the pore water. Even extremely low partial pressures of O2 are sufficient to initiate oxidation phases of the sulfur cycle. The oxidation of pyrite
The aging of quick clays shows how even seemingly small changes in environmental conditions can result in significant changes in properties. These changes can occur over times typical of those associated with the field and laboratory phases of many projects, for example, from several weeks to a few months. If extreme care is not exercised during sample storage, laboratory tests may give misleading results. Simple pH measurements at the time of sampling and again at the time of testing can provide a rapid and easy means for assessing whether aging processes have occurred. To minimize the aging effects the exposure of samples to air should be minimized, thick wax caps should be used with rust-free sample tubes, and samples should be stored at low temperatures to slow down reaction rates. Summary of Sensitivity-Causing Mechanisms
The six causes for the development of sensitivity discussed above are summarized in Table 8.8. An estimate of the upper limit of sensitivity for each mechanism is also given. Virtually all natural soils, including many sands, are sensitive in that they lose some strength on disturbance and remolding. Exceptions are heavily overconsolidated stiff fissured clays that can gain strength because of the elimination of fissures and planes of weakness. Quick clays are formed from soft glacial marine clays only after removal of excess salt by leaching and further increase in double-layer repulsions as
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Figure 8.37 Changes in the remolded strength and consistency of a Canadian quick clay as
a function of time (Lessard, 1978).
Figure 8.38 Geotechnical characteristics of the quick clay from LaBaie as a function of
depth (after Lessard, 1981).
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235
a result of an increase in the relative proportion of monovalent cations (mainly sodium) in the pore water and increase in pH. More than one mechanism may contribute to the total sensitivity of any one soil.
8.13 PROPERTY INTERRELATIONSHIPS IN SENSITIVE CLAYS
The geotechnical properties of normally consolidated, noncemented sensitive clays fit a pattern that is predictable in terms of sensitivity, liquidity index, and effective stress using the concepts given in the preceding sections. General Characteristics of Sensitive Clays
Figure 8.39 Effect of time and storage conditions on the properties of LaBaie quick clay.
Glacial and postglacial clays of high and low sensitivity exhibit significant differences, as shown by the profiles in Fig. 8.41 for a normal clay from Drammen and a quick clay from Manglerud, both in Norway. One of the most important of these differences is that at Manglerud the water content is well above the liquid limit; that is, the liquidity index is greater than 1.0. This is characteristic of quick clays. Plasticity and Activity When normal clays are converted to highly sensitive or quick clays by the chemical changes described in Section 8.12, the liquid limit, plasticity index, and activity decrease. These changes are reflected by an increase in the liquidity index at constant effective stress. The liquid limit of highly sensitive clay is usually less than 40 percent and rarely greater than 50 percent. Plastic limit values are usually about 20 percent. The activity of most normal inorganic marine clays is of the order of 0.5 to 1.0, whereas the activity of quick clays can be as low as 0.15. The sensitivity of a given clay type usually correlates uniquely with liquidity index, as may be seen in Fig. 8.42 for Norwegian marine clays. Pore Pressure Parameter, Aƒ [Eq. (8.3)] High pore pressures are developed when sensitive soils are sheared. For some quick clay, pore pressures as high as two times the peak deviator stress have been measured. Loose sand may develop excess pore pressure equal to the initial confining effective stress when sheared rapidly without drainage, thereby losing its strength completely. Undrained Shear Strength to Consolidation Pressure Ratio, Su /p The Su /p ratio (often indicated as the c/
Figure 8.40 Dependence of remolded strength on cation concentration in LaBaie quick clay.
p ratio) decreases with increasing sensitivity, ranging from 0.3 or more for normally consolidated insensitive clays to less than 0.1 for quick clays. This is illustrated by Fig. 8.43 for normally consolidated clay. In this figure the consolidation pressure p is taken as the over-
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Table 8.8
SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
Summary of the Causes of Sensitivity in Soils
Mechanism
Approximate Upper Limit of Sensitivitya
Metastable fabric Cementation
Slightly quick (8–16) Extra quick (⬎64)
Weathering Thixotropic hardening Leaching, ion exchange, and change in monovalent/divalent cation ratio Formation or addition of dispersing agents
Medium sensitive (2–4) Very sensitiveb Extra quick (⬎64) Extra quick (⬎64)
Predominant Soil Types Affected All soils Soils containing Fe2O3, Al2O3, CaCO3, free SiO2 All soils Clays Glacial and postglacial marine clays Inorganic clays containing organic compounds in solution or on particle surfaces
a
Adjectival descriptions according to Rosenqvist (1953). Pertains to samples starting from present composition and water content. Role of thixotropy in causing sensitivity in situ is indeterminate. b
burden vertical effective stress, vo, and CIUC means isotropically consolidated undrained compression tests were used for determination of strength. Stress–Strain Relationships In general, strain at failure decreases with increasing sensitivity. Some quick clays are quite brittle during unconfined loading and fracture at very low strains, sometimes by axial splitting. Further working of the fractured specimen may cause it to turn into a fluid mass. Compressibility The compressibility of highly sensitive clays is relatively low until the consolidation stress exceeds the preconsolidation pressure. It then increases sharply as shown by Fig. 8.44 for Champlain clay. As the void ratio reduces under higher consolidation pressures, the compressibility eventually assumes a lower value. Property, Effective Stress, and Water Content Relationships Consolidation Because the initial structure depends on many factors and the volume changes under pressure are a function of structure, a soil does not have a unique consolidation curve. All states and compression curves must be above the curve for the fully destructured material. Strength of Normally Consolidated Soil The higher the effective stress at a given water content, the greater the undrained strength because of increased frictional resistance between particles. For constant effective stress, strength increases with decreasing water content because of increased dilatancy. Thus the general behavior shown in Fig. 8.45 is observed.
Sensitivity As each point on the curves for fully destructured soil in Figs. 8.13 and 8.14 represents completely remolded material, the sensitivity at any point on this curve must be unity. Thus this curve is a line of constant sensitivity or sensitivity contour. Saturated clay at a given water content and pore fluid composition cannot be made weaker than its thoroughly remolded strength. Therefore, a water content–effective stress relationship to the left of that for the fully destructured soil is not possible. The undisturbed strength increases with increasing effective stress at constant water content (Fig. 8.45), and the sensitivity at all points to the right of the fully destructured soil curve is greater than 1. Thus, the maximum gradient of sensitivity increase is generally normal to the contour for the fully destructured soil. Pore Pressure Parameter, Aƒ The pore pressure at failure is controlled by the tendency of the soil to dilate or contract. Thus Aƒ decreases with decreasing water content at constant initial effective stress. At constant water content, the lower the effective stress, the easier it is for the soil to dilate since less energy is required for expansion against low pressures than high. Therefore, the maximum gradient of Aƒ is as shown in Fig. 8.46. Strain at Failure Restrained dilation increases effective stress, thus increasing shearing resistance. Consequently, the deformation required to cause failure increases with increasing dilation. On the other hand, strain at failure should decrease with increase in Aƒ because Aƒ varies inversely with dilation tendencies. Consequently, the maximum positive gradient of strain
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237
Figure 8.41 Soil profiles for marine clays of low and high sensitivity (from Bjerrum, 1954).
at failure should be opposite to the maximum gradient for Aƒ . Example of Relationships The results of triaxial compression tests on kaolinite (Houston, 1967) illustrate the above relationships. By consolidating different samples from several different initial water contents and remolding and reconsolidating them in various ways, samples covering a range of initial effective stress and water content values, each reflecting a different structure, were obtained. The results of undrained triaxial tests yield values of strength,
sensitivity, Aƒ , and strain at failure. Contours based on these values are shown in Fig. 8.47. The variations in the measured values are in general accord with the predictions stated previously. Sensitivity–Effective Stress–Liquidity Index Relationship
General relationships between sensitivity, effective stress, and water content can be established based on normalization of the remolded strength versus water
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Figure 8.42 Sensitivity as a function of liquidity index for
Norwegian marine clays. Relationship was averaged from many more data points than those shown (data from Bjerrum, 1954).
Figure 8.44 Consolidation curves for Champlain (Leda)
clay. Reproduced with permission from the National Research Council of Canada, from the Canadian Geotechnical Journal, Vol. 3, pp. 61–73, 1966.
Figure 8.43 Normalized undrained shear strength of normally consolidated clay as a function of liquidity index (from Bjerrum and Simons, 1960). Reprinted with permission of ASCE.
content relationship. The liquidity index (LI) provides a basis for this normalization. A unique relationship between sensitivity, liquidity index, and effective stress exists if: 1. The LI–effective stress relationship is the same for thoroughly remolded specimens of all clays. This relationship is the contour for a sensitivity of 1.0. 2. The relationship between remolded strength and liquidity index is the same for all clays. 3. At any value of liquidity index, the variation of Su /p with effective consolidation pressure is the same for all clays. This fixes the undisturbed strength in terms of LI and effective stress. These conditions hold sufficiently well for most sensitive clays. Remolded shear strength as a function of
Figure 8.45 Gradient of strength increase with water content
and effective stress variation.
liquidity index for several clays is shown in Fig. 8.48. The data points in this figure were based on fall-cone tests for determination of the liquidity index. The wider band of values reported by Houston and Mitchell (1969) resulted, at least in part, from the use of different methods for determination of the strength and liquidity index values. A general relationship between the undrained shear strength of the remolded clay and the liquidity index for the heavy curve in Fig. 8.48 is
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239
available, to estimate changes in strength and sensitivity due to change in effective stress or liquidity index, and as a guide for extrapolating a small amount of data to a larger pattern. A very similar approach that relates sensitivity, stress state, and void index Iv is proposed by Cotecchia and Chandler (2000) and Chandler (2000).
8.14
Figure 8.46 Gradient of pore pressure parameter Aƒ with
water content and effective stress variations.
Su ⫽
1 (kPa) (LI ⫺ 0.21)2
(8.4)
The following equation that can be deduced from Sharma and Bora (2003) also fits the relationship defined by Eq. (8.4) well: log ⫽ log LL ⫹
2 w ⫻ log L log(wL /wp ) w
(8.5)
In Eq. (8.5) is the undrained strength and w, wL, and wp are the water content, liquid limit, and plastic limit values. By averaging data for several clays, the relationship between liquidity index, effective stress, and sensitivity shown in Fig. 8.49 is obtained. Figure 8.49 is also valid for moderately overconsolidated clays, provided the preconsolidation pressure is used instead of the present effective stress. This is because the water content and undrained strength depend more on the preconsolidation pressure than on the present effective stress. Some deviations from the values in Fig. 8.49 are to be expected because of the extensive averaging used in its preparation. These deviations may be greatest for extra quick clays because of the very low remolded strength, the difficulty in determining it accurately, and its controlling influence on the calculated value of sensitivity. Nonetheless, the relationships in Figs. 8.48 and 8.49 can be used to estimate sensitivity and strength when undisturbed samples or in situ strength data are not
DISPERSIVE CLAYS
Some fine-grained soils are structurally unstable, easily dispersed, and, therefore, easily eroded. Soils in which the clay particles will detach spontaneously from each other and from the soil structure and go into suspension in quiet water are termed dispersive clays. The consequences of the exposure of dispersive clays to water may be several, as shown by Figs. 8.50 and 8.51. The surface erosion pattern on an excavated slope, which is characteristic of ‘‘badlands’’ topography, is shown in Fig. 8.50. Erosion tunnels in a flood control dike are shown in Fig. 8.51. Failures of this type have occurred in well-constructed, low homogeneous dams. In each case shown, the soil contained readily dispersed clay particles that went easily into suspension in flowing water. Failures of this type have occurred in embankments, dams, and slopes composed of clays with low-to-medium plasticity (CL and CL–CH) that contain montmorillonite. Dispersive piping in dams has occurred either on the first reservoir filling or, less frequently, after raising the reservoir to a higher level. Dispersive clay failures are usually initiated when water flows into small cracks and fissures. When a reservoir is filled for the first time, settlement may accompany saturation of the soil, particularly if the soil was placed dry of optimum and not well compacted. Settlement below the phreatic surface and arching above it can result in crack formation. Water moving through the crack picks up dispersive clay particles, with the rate of removal increasing as the seepage velocity and size of opening increase. This is a fundamentally different mechanism than erosive piping, which develops and works backward from the discharge face. Tunneling has been initiated in soils with a hydraulic conductivity as low as 1 ⫻ 10⫺7 m/s. Visual classification, Atterberg limits, and particle size analyses do not provide a basis for differentiation between dispersive clays and ordinary erosion-resistant clays. However, relatively simple chemical tests, a dispersion test, a ‘‘crumb’’ test, and the pinhole test (Sherard et al., 1976) can be used for identification of dispersive clays. In the pinhole test, distilled water is allowed to flow through a 1.0-mm-diameter hole drilled through a compacted specimen. If the soil is dispersive, the water
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Figure 8.47 Strength properties of normally consolidated kaolinite as a function of effective
stress and water content: (a) shear strength, (b) strain at failure, (c) pore pressure parameter Aƒ , and (d ) sensitivity.
becomes muddy and the hole rapidly erodes. For nondispersive clays the water remains clear and there is no erosion. The pinhole test and test procedure are described in ASTM Standard D4647-93 (1998) (ASTM 2000). As noted in Section 6.15, the exchangeable sodium percentage (ESP) is a strong indicator of potential dispersive behavior, with an ESP greater than 2 indicating possible dispersion, and an ESP greater than 10 to 15
indicating probable dispersive clay behavior in soils of relatively low total salt concentration in the pore water. As determination of the ESP requires measurement of both the cation exchange capacity and the amount of sodium in the exchange complex, it is not a simple or rapid method for identification of dispersive clay. A simpler chemical measure of potential dispersivity, supported by the results of tests on many samples, was proposed by Sherard et al. (1972, 1976) that is based
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241
Figure 8.50 Erosion pattern in excavated slope of sensitive clay (courtesy of J. L. Sherard).
Figure 8.48 Relation between shear strength of remolded
clay and liquidity index (from Leroueil et al., 1983). Reproduced with permission from the National Research Council of Canada.
on the percent sodium in the saturation extract from a soil–water paste. This correlation is shown in Fig. 8.52. Many subsequent tests have shown, however, that the zones in Fig. 8.52 are not always reliable indicators of dispersibility. For example, Craft and Acciardi (1984) found that only 62.3 percent of 223 samples were classified correctly. This is not surprising because
Figure 8.49 General relationships between sensitivity, liquidity index, and effective stress.
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Figure 8.51 Erosion damage on the crest of 5-m-high flood control dike caused by rain runoff concentrating in drying cracks, Rio Zulia, Venezuela (courtesy of J. L. Sherard).
whether or not a soil will exhibit dispersive behavior depends not only on its chemical and mineralogical composition but also on its state, as reflected by water content, density, and structure, on the chemistry of the water to which it is exposed, and on the specific conditions of exposure, including temperature, confining
pressure, and velocity of flowing water. The influence of the chemistry of the water used for evaluation of dispersibility was illustrated by the results of pinhole tests on compacted samples of shale by Statton and Mitchell (1977). A decrease in pH of the eroding water to less than about 4, using hydrochloric acid, or an increase to greater than about 11, using calcium hydroxide or sodium hydroxide, caused a change from dispersive to nondispersive behavior. Similarly, increasing the salt concentration of the water at its natural pH of 6.3 to 0.1 N CaCl2 or 0.5 N NaCl caused erosion of the dispersive clay to stop. In the dispersion test the percentage of particles finer than 5 m is determined by hydrometer analyses of samples with and without dispersing agent in the suspension water (Sherard et al., 1972). The higher the ratio of percentage material finer than 5 m by weight measured in the test without dispersing agent to that measured in the test with a dispersing agent, the greater the probability of dispersion in the field. This ratio, when expressed as a percentage, is termed the percent dispersion. Values greater than 20 to 25 percent indicate that dispersion may be a problem. Values greater than 50 percent are nearly always indicative of soils susceptible to severe erosion damage initiated by clay dispersion. In the crumb test a small clod of the soil is placed in a beaker and submerged in water. If the soil clod is
Figure 8.52 Relationship between dispersibility (susceptibility to colloidal erosion) and dissolved pore water salts based on pinhole tests and field observations. SAR ⫽ sodium absorption ratio, Eq. (6.33). Concentrations in meq / liter (from Sherard et al., 1976). Reprinted with permission of ASCE.
COLLAPSING SOILS AND SWELLING SOILS
initially dry, it will often slake. If it is dispersive, clay particles will go into suspension in the quiet water, and the zone around the clod will become cloudy. Of the several tests developed for identification of dispersive clays, the pinhole test is considered the most reliable. But even with this test, it is important that the samples correctly simulate the soil state and the water composition to be expected in the field. Several methods can be used to mitigate the adverse effects of dispersive soils. The addition of 2 to 3 percent hydrated lime during construction will usually convert a soil to a nondispersive form. Filters that are designed to retain small particle sizes should be used on the discharge side of dams and dam cores. For an existing dam, in which tunneling erosion is expected to develop, lime can be added at the upstream face to be carried inward by the percolating water. Additional strategies were suggested and evaluated by Sherard and Decker (1977).
8.15
SLAKING
Most fine-grained soils slake after exposure to air and subsequent unconfined immersion in water; an initially intact piece of soil will disintegrate into a pile of pieces or sediment of small particles. This disintegration may begin immediately upon immersion or develop slowly with time. Slaking usually is more rapid and vigorous in materials that have been dried prior to immersion compared to the same material immersed at its initial water content. Whether a material slakes or not has been proposed as a basis for distinguishing between soil and rock (Morgenstern and Eigenbrod, 1974). The slaking of hard clays and clay shale is a concern in the stability of open excavations and the shale durability when it is used as an aggregate or rockfill for construction. From controlled tests on relatively pure samples of different clays (Moriwaki and Mitchell, 1977) and on clay shales (Seedsman, 1986), four modes of disintegration were identified. These are: 1. Dispersion Slaking Particles of clay detach from the surface of the intact clay by dispersion into the adjacent water. 2. Swelling Slaking Water is adsorbed by the clay and the material swells and softens. 3. Surface Slaking Aggregates of clay particles spall off the surface and accumulate as sediment in the adjacent water. 4. Body Slaking The material splits and disintegrates into pieces, and the failure appears to develop from the inside out.
243
Three mechanisms are responsible for these modes of failure. Dispersion, which is dependent on the clay and water chemistry, was described in the preceding section. Swelling slaking results from stress relief and water intake due to water adsorption and osmotic forces. Compression of entrapped air in partially saturated soils is responsible for body slaking and, to some extent, for surface slaking. Rapid water absorption into the material compresses the air, which, in turn, exerts tensile stresses on the soil structure. If the structural strength is insufficient to withstand these stresses, then the material splits apart. Seedsman (1986) found that the slaking mechanism was related to the bulk density, and the higher the density the more resistant the material to slaking by any mode.
8.16 COLLAPSING SOILS AND SWELLING SOILS
Large areas of Earth’s surface, particularly in the Midwest and Southwest United States, parts of Asia, South America, and southern Africa, are covered by soils that are susceptible to large decreases in bulk volume when they become saturated. Such materials are termed collapsing soils. Collapse may be triggered by water alone or by saturation and loading acting together. Soils with collapsible structures may be residual, water deposited, or aeolian. In most cases, the deposits have a loose structure of bulky shaped grains, often in the silt-tofine-sand range. Collapsible grain structures are left behind in residual soils as a result of leaching of soluble and colloidal material. Water- and wind-deposited collapsing soils are usually found in arid and semiarid regions and are a consequence of the loose fabrics and weak structures that form. Debris flows (mudflows and torrential stream deposits) are deposited suddenly and locally, and may form a loose, metastable structure. Torrential stream sediments, in particular, form a loose, poorly graded material. Some small amount of clay is present that serves as a binder for the deposit after it dries. Some cementation may also develop because in the arid climates where such deposits form, water moves upward to evaporate, leaving behind its content of dissolved salts. If subsequently wetted, the loose structure can collapse and cause large settlements. When a large canal was constructed through the San Joaquin Valley during the 1960s to carry water from northern California to southern California, it was necessary to cross many collapsible debris flow deposits. In order to minimize future settlements of the canal and appurtenant structures as a result of canal leakage,
244
8
SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
extensive preponding was carried out before construction of the canal. Soils susceptible to large collapse as a result of wetting can be identified using a density criterion. If the density is sufficiently low that the void space is larger than needed to hold the liquid limit water content, then collapse problems are likely (Gibbs and Bara, 1967). If the void space is less than that needed for the liquid limit water content, then collapse is not likely unless the soil is loaded. Loess deposits are widespread throughout the midwestern United States and parts of Asia. This material, which is wind-blown silt, is light brown in color, crumbly, and essentially devoid of stratification. The particles are predominantly silt size and composed of feldspar and quartz. A small amount of clay, usually less than 15 percent, may be present. Smectite is the usual clay mineral type. Calcite may be present in amounts up to 30 percent and can act as weak cement that precipitates along the sides of vertical root holes and at interparticle contacts. Densities of undisturbed loess may be as low as 1.2 g/cm3, and the natural water content of metastable deposits of loess is low, on the order of 10 percent. Most loesses plot near the A-line on the plasticity chart. Because of vertical root holes formed by gradual burial of grassy plains, the absence of stratification, and light cementation, loess cleaves on vertical planes, and vertical faces cut in loess are quite stable, as shown in Fig. 8.53. In fact, if inclined slopes are cut, they will gradually erode back to a series of steplike vertical faces.
The low density and light cementation of the loess structure make it susceptible to collapse. When maintained dry, it is reasonably strong and incompressible. The porous structure may persist even beneath 60 m of overburden. When saturated, however, loess deposits may lose their stability. Compression due to saturation alone may be small, but with a surcharge, it may be very large, as shown in Fig. 8.54. Watering lawns around new houses founded on loess has been known to cause large settlements. If saturated loess deposits
Figure 8.54 Compression properties of Missouri River basin
loess (from Clevenger, 1958). Reprinted with permission of ASCE.
Figure 8.53 Loess deposit. Note vertical slopes.
CONCLUDING COMMENTS
are subjected to dynamic loading, such as from an earthquake, there may be instantaneous liquefaction and large flow slides. The undisturbed density of a loess deposit may be a fair indicator of the potential settlement and loss of strength that may result from saturation. Detailed information about the nature and behavior of Mississippi loess, a widespread loess deposit, is given by Krinitzky and Turnbull (1967).
8.17
HARD SOILS AND SOFT ROCKS
Among the continuum of soils and rocks that are encountered in engineering and construction, very heavily overconsolidated fine-grained soils and mudstones, shales, and siltstones are sometimes among the most difficult to deal with. It is not always clear whether such materials should be treated as soil or rock. If behavior is rocklike, the material can be used in earthwork construction like a rock and placed in thick lifts without much compaction. If the shale is susceptible to break down, however, it must be treated as a soil and placed in thin, well-compacted lifts. If considered a rock and subsequent deterioration under the actions of stress, water, and chemical change causes breakdown, loss of strength and increase in compressibility, then there can be failures. Conversely, if the durability and mechanical properties are too conservatively assigned, then unnecessary overdesigns and excessive costs may result. Shale is a prime example of a material that illustrates the soft rock-hard soil problem. According to Terzaghi et al. (1996): Shale is a clastic sedimentary rock mainly composed of silt-size and clay-size particles. Most shales are laminated and display fissility; the rock has a tendency to split along relatively smooth and flat surfaces parallel to the bedding. When fissility is completely absent, the clastic sedimentary deposit is called mudstone, or clay rock.
Unweathered, intact shale, although considerably weaker and less durable than most igneous and metamorphic rocks, may still have adequate resistance and long-term stability to be stable on cut slopes or to be used as an embankment fill or stable pavement subgrade. On the other hand, many shales that appear intact and rocklike when exposed or excavated can have properties that deteriorate with time. The problems, then, are to determine whether degradation is likely, and if so, how much and how fast. Degradation, apart from that caused by mechanical processes such as unloading, compression, crushing, and shearing, is usually by slaking (see Section 8.15) initiated by exposure to air, moisture, and changed chemical environment. Cementation shales are likely
245
to be more durable over the long term than compaction shales, unless exposure to water and ions in solution leads to dissolution of the cementing material. Pyrite or sulfates in sedimentary rocks can be the cause of geochemical processes, often catalyzed by microbiological activity, that result in heave and loss of the intact rock strength. This deterioration can occur in time periods as short as a few months. Chemically nondurable shales are likely to be especially troublesome in environments with pH less than 6. Recommendations for identifying these materials are given by Noble (1977, 1983). Knowledge of the geologic history of a deposit, the mineralogical and chemical composition, and the new loading and exposure conditions provides initial insights about whether shales, siltstones, and sandstones can be expected to degrade. Accelerated weathering and durability tests are used to classify shale durability. Tests used for this purpose have been described and reviewed by Huber (1997). They include water adsorption, wet–dry, freeze–thaw, jar slaking, crushing, point load strength, ultrasonic disaggregation, and slake durability tests in which the breakdown of shale submerged in a rotating wire basket (Franklin and Chandra, 1972) is determined. The results of these tests form the basis of several shale durability classification systems that have as their goal to distinguish shales that cause problems from those that do not. One of the first such systems was developed by Underwood (1967) for engineering evaluations. Table 8.9, adapted from Underwood’s study, is a listing of physical and composition properties associated with the indicated types of unfavorable behavior. It may be seen that the range of most properties within which unfavorable behavior is likely to develop is rather broad, which means that any single test or observation by itself is unlikely to be sufficient for confirmation of favorable or unfavorable behavior.
8.18
CONCLUDING COMMENTS
This chapter is concerned with how residual and transported soil deposits are formed, how the formative processes and subsequent changes over time act to produce unique types of soil structures with characteristic properties, and how these properties and the associated behavior are interrelated. Several illustrations of the relevance of these processes and properties to geotechnical applications are among the subjects of this chapter. The structure of a soil depends on its fabric and interparticle force system. It reflects all facets of the soil’s composition, history, present state, and environmental influences. Soil particles come in a great variety
246 Table 8.9
Properties and Conditions Likely to Cause Problems with Shale
Physical and Compositional Properties Lab tests and in situ observations Compressive strength, kPa Modulus of elasticity, MPa Cohesive strength, kPa Angle of internal friction, deg. Dry unit weight, kN/m3 Potential swell, % Natural moisture content, % Hydraulic conductivity, m/s Predominant clay minerals Activity Wetting and drying cycles Spacing of rock defects Orientation of rock defects State of stress
Unfavorable behavior probable for values in indicated range ⬍300–1800
Probable in Situ Behavior High pore pressure
Low bearing capacity
⫻
⫻
⬍140–1400
Tendency to rebound
Slope stability problems
Rapid slaking
Rapid erosion
⫻
Tunnel support problems ⫻
⬍30–700
⫻
⫻
⫻
⬍10–20
⫻
⫻
⫻
⬍11.0–17.3
⫻
⫻(?)
⬎3–15 ⬎20–35
⫻
⬍10⫺5
⫻
⫻
Smectite or illite
⫻
⫻
⫻
⬎0.75–2.0
⫻ ⫻
⫻
⫻ ⫻
⫻
⫻
Reduces to grain sizes Closely spaced
⫻
⫻
⫻(?)
Adverse
⫻
⫻
⫻
⬎Existing
overburden Adapted from Underwood (1967).
⫻
⫻
⫻
⫻
⫻
QUESTIONS AND PROBLEMS
of sizes, shapes, and compositions. The possible particle arrangements (fabric) and stabilities of these arrangements (structure) are many; therefore, any single soil can exist in many different states, each of which can be viewed as a somewhat different material. Geochemical and microbiological influences on the geological processes and properties that are important in geoengineering are only now beginning to be studied and understood by geotechnical engineers. It is likely that knowledge drawn from these fields will be very useful in the future.
QUESTIONS AND PROBLEMS
1. Indicate whether each of the following statements is True or False. Justify your answer with a brief statement. a. Rearrangement of particles during shear provides an important contribution to the residual strength of a highly plastic clay. b. The relationship between critical void ratio and effective confining pressure is the same for undisturbed and reconstituted samples of the same sand. c. The sensitivity of a clay can be explained by the change in effective stress caused by remolding. d. Collapse of structure in a saturated soil is usually accompanied by an increase in effective stress. e. Relative density is a suitable single parameter for characterizing sand properties. f. Strength loss when a sensitive clay is disturbed is related to the liquidity index. g. Marine clays have very high values of sodium adsorption ratio and exchangeable sodium percentage, which means that they are dispersive clays. h. Two samples of the same sand have the same relative density and are confined under the same mean effective stress. Therefore, they have the same stress–deformation, volume change, and strength properties. i. A compacted clay liner is to be used for containment of nonpolar organic solvent wastes. Time can be saved in determining the hydraulic conductivity of this clay by mixing the soil with the solvent and then compacting samples for testing, rather than doing the compaction using water and then using the solvents as permeants. Each procedure will give the same result.
247
2. The results of unconfined compression tests on two samples of kaolinite compacted by two different methods are shown in Fig. 11.20. a. Why is the peak strength greater by static compaction than by kneading compaction? (Kneading compaction is the type produced by a sheepsfoot roller, and static compaction is produced by a smooth steel roller.) b. Why are the ultimate or residual strengths of the materials prepared by the two methods the same? c. If this kaolinite were to be used for a structural fill, which method of compaction would you specify? Why? d. If this kaolinite were to be used for the core of an earth dam, which method of compaction would you specify? Why? e. If each material was saturated without further change in dry unit weight and then sheared undrained, sketch the curves of pore water pressure versus strain that you would expect to obtain for each. 3. Given heavily overconsolidated clay under a present vertical effective overburden stress of 200 kPa, the maximum past effective stress on the horizontal plane was 600 kPa. Consider this to be state I. It has been determined that this clay has a peak friction angle of 30 and a residual friction angle r of 17. There is no cementation of the clay structure. Rapid shear is defined as deformation at a rate fast enough so there can be no change in pore pressure in the shear zone. Slow shear is deformation at a rate slow enough that there can be no change in pore pressure in the shear zone. a. What is the overconsolidation ratio? b. Show paths on a diagram of shear stress versus effective normal stress on the failure plane to represent the following, and state for each whether the accompanying changes in volume ( V) and pore pressure ( u) are positive, negative, or zero: i. Rapid shear from I to peak strength ii. Slow shear from I to peak strength iii. Rapid shear from peak strength to residual strength c. What changes in fabric would you anticipate in going from I to peak strength and from peak strength to residual strength? d. Deep cuts in heavily overconsolidated clay sometimes fail many years after they are made, and stability analyses have indicated that the av-
248
8
SOIL DEPOSITS—THEIR FORMATION, STRUCTURE, GEOTECHNICAL PROPERTIES, AND STABILITY
erage strength at the time of failure corresponds to that at residual state. i. Account for the time delay. ii. Is it reasonable to assume simultaneous development of residual strength at all points along the failure surface? If not, how can the behavior be explained? Take into account stress–strain properties and water content changes that may be involved. 4. Suggest ways by which a quick clay might be stabilized in situ, that is, made less susceptible to large strength loss.
Na⫹ ⫽ 1.0 meq/liter Ca2⫹ ⫽ 2.5 meq/liter Mg2⫹ ⫽ 1.0 meq/liter Comment on the probable structural state of the soil at the time of construction. d. The reservoir water to be stored behind this dam will contain the following cation concentrations:
Na⫹ ⫽ 4.0 meq/liter
5. It is shown in Fig. 8.48 that there is a unique relationship between remolded shear strength and liquidity index that seems to be independent of the particular clay. Explain why this should be so.
Mg2⫹ ⫽ 0.3 meq/liter
6. Which is easier to determine, the exchangeable sodium percentage or the sodium adsorption ratio? Why?
Comment on the possible consequences of prolonged percolation by this water. Justify your conclusions numerically.
7. Salt-affected soils are classified by agronomists as follows:
8. State special geotechnical characteristics of the following soil types and relate them to their (1) formational processes, (2) composition, (3) environmental setting, and (4) structure. By all means consult references in addition to the relevant sections in this book to enhance the quality of your answers. a. Loess b. Organic clay c. Decomposed granite d. Expansive soil e. Pyrite-rich soil f. Loose sand g. Carbonate sand h. Glacial moraine i. Saprolite j. Torrential stream deposits and mudflows
Soil Group
Exchangeable Sodium Percentage
Saline Saline-alkali Nonsaline alkali Nonsaline, nonalkali
⬍15 ⬎15 ⬎15 ⬍15
Usual pH
Usual Structural State
⬍8.5 8.5
8.5–10.0 ⬍8.5
a. Complete the above table by filling in the last column on the right. b. Which, if any, of these soil types may be a problem soil? Why? c. A practical form of the Gapon equation is Na* ⫽ 0.17 (SAR) Na* ⫹ Mg* where SAR is the sodium adsorption ratio and * refers to the cation concentrations adsorbed on the clay. At the time of construction of a small earth dam, the soil was compacted and the water in it contained the following cation concentrations:
Ca2⫹ ⫽ 0.5 meq/liter
9. Manned missions to the Moon are likely to resume within the next several years for several purposes, including scientific studies, astronomical observations, resource development, military advantage, and development of a launching platform for further space exploration. The lunar soil and its properties will have important impacts on many aspects of these activities, especially facilities construction, their operation, and maintenance. Consider the following aspects of the Moon and its surface environment: a. Lunar rocks are primarily basaltic. b. The gravitational field is one-sixth that of Earth.
QUESTIONS AND PROBLEMS
c. The lunar surface temperature ranges from ⫺150C at lunar midnight to ⫹120C at lunar noon. d. There is no free water. e. Atmospheric pressure is 10⫺13 Earth atmospheres. f. There is much higher cosmic and solar radiation on the Moon than on Earth. g. There is a high frequency of meteorite impact compared to Earth. Use principles relating to geologic and soil-forming processes, soil composition, surfaces, fabric, structure, and any other relevant concepts to make reasoned estimates of or comments on the following: a. Soil particle composition
249
b. Soil particle sizes and size distributions c. Whether or not lunar soils will be cohesive d. The nature and magnitude of lunar soil weathering e. Local and regional variability of lunar soil compositions and densities f. Coefficient of friction between soil particles (see Chapter 11) g. The ultimate bearing capacity of a cohesionless soil on the Moon compared to that of the same soil on Earth. h. The optimum size of particles that might form metastable honeycomb structures on the Moon as opposed to a finding by Terzaghi that silt-size particles in the range of 6- to 20-m diameter are most susceptible to this effect on Earth.
CHAPTER 9
Conduction Phenomena
9.1
INTRODUCTION
Virtually all geotechnical problems involve soil or rock deformations and stability and/or the flow through earth materials of fluids, chemicals, and energy in various forms. Flows play a vital role in the deformation, volume change, and stability behavior itself, and they may control the rates at which the processes occur. Descriptions of these flows, predictions of flow quantities, their rates and changes with time, and associated changes in the properties and composition of both the permeated soil and the flowing material are the subjects of this chapter. Water flow through soil and rock has been most extensively studied because of its essential role in problems of seepage, consolidation, and stability, which form a major part of engineering analysis and design. As a result, much is known about the hydraulic conductivity and permeability of earth materials. Chemical, thermal, and electrical flows in soils are also important. Chemical transport through the ground is a major concern in groundwater pollution, waste disposal and storage, remediation of contaminated sites, corrosion, leaching phenomena, osmotic effects in clay layers, and soil stabilization. Heat flows are important relative to frost action, construction in permafrost areas, insulation, underground storage, thermal pollution, temporary ground stabilization by freezing, permanent ground stabilization by heating, underground transmission of electricity, and other problems. Electrical flows are important to the transport of water and ground stabilization by electroosmosis, insulation, corrosion, and subsurface investigations. In addition to the above four flow types, each driven by its own potential gradient, several types of coupled
flow are important under a variety of circumstances. A coupled flow is a flow of one type, such as hydraulic, driven by a potential gradient of another type, such as electrical. This chapter includes a review of the physics of direct and coupled flow processes through soils and their quantification in practical form, an evaluation of relevant parameters, their magnitudes, and factors influencing them, and some examples of applications.
9.2
FLOW LAWS AND INTERRELATIONSHIPS
Fluids, electricity, chemicals, and heat flow through soils. Provided the flow process does not change the state of the soil, each flow rate or flux Ji (as shown in Fig. 9.1) relates linearly to its corresponding driving force Xi according to Ji ⫽ Lii Xi
(9.1)
in which Lii is the conductivity coefficient for flow. When written specifically for a particular flow type and using familiar phenomenological coefficients, Eq. (9.1) becomes, for cross section area A Water flow
qh ⫽ khih A
Darcy’s law
(9.2)
Heat flow
qt ⫽ ktit A
Fourier’s law
(9.3)
Electrical flow
I ⫽ eie A
Ohm’s law
(9.4)
Chemical flow
JD ⫽ Dic A
Fick’s law
(9.5)
In Eqs. (9.2) to (9.5) qh, qt, I, and JD are the water, heat, electrical, and chemical flow rates, respectively. 251
252
9
CONDUCTION PHENOMENA
9.3
HYDRAULIC CONDUCTIVITY
Darcy’s law1 states that there is a direct proportionality between apparent water flow velocity vh or flow rate qh and hydraulic gradient ih, that is,
Figure 9.1 Four types of direct flow through a soil porous
mass. A is the total cross-section area normal to flow; n is porosity.
Coefficients kh, kt, e, and D are the hydraulic, thermal, electrical conductivities, and the diffusion coefficient, respectively. Typical ranges of values for these properties are given later. The driving forces for flow are given by the respective hydraulic, thermal, electrical, and chemical gradients, ih, it, ie, and ic, respectively. The terms in Eqs. (9.2) through (9.5) are identified in Fig. 9.1 and in Table 9.1, which also shows analogs between the various flow types. As long as the flow rates and gradients are linearly related, the mathematical treatment of each flow type is the same, and the equations for flow of one type may be used to solve problems of another type provided the property values and boundary conditions are properly represented. Two well-known practical illustrations of this are the correspondence between the Terzaghi theory for clay consolidation and one-dimensional transient heat flow, and the use of electrical analogies for the study of seepage problems.
vh ⫽ kh ih
(9.6)
qh ⫽ kh ih A
(9.7)
where A is the cross-section area normal to the direction of flow. The constant kh is a property of the material. Steady-state and transient flow analyses in soils are based on Darcy’s law. In many instances, more attention is directed at the analysis than at the value of kh. This is unfortunate because no other property of importance in geotechnical problems is likely to exhibit such a great range of values, up to 10 orders of magnitude, from coarse to very fine grained soils, or show as much variability in a given deposit as does the hydraulic conductivity. Some soils exhibit 2 or 3 orders of magnitude variation in hydraulic conductivity as a result of changes in fabric, void ratio, and water content. These points are illustrated by Fig. 9.2 in which hydraulic conductivity values for a number of soils are shown. Different units for hydraulic conductivity are often used by different groups or agencies; for example, centimeters per second by geotechnical engineers, feet per year by groundwater hydrologists, and Darcys by petroleum technologists. Figure 9.3 can be used to convert from one system to another. The preferred unit in the SI system is meters/second. Theoretical Equations for Hydraulic Conductivity
Fluid flow through soils finer than coarse gravel is laminar. Equations have been derived that relate hydraulic conductivity to properties of the soil and permeating fluid. A usual starting point for derivation of such equations is Poiseuille’s law for flow through a round capillary, which gives the average flow velocity, vave, according to vave ⫽
p R2 i 8 h
(9.8)
where is viscosity, R is tube radius, and p is unit 1 This ‘‘law’’ was established empirically by Darcy based on the results of flow tests through sands. Its general validity for the description of hydraulic flow through most soil types has been verified by many subsequent studies. Historical accounts of the development of Darcy’s law are given by Brown et al. (2003).
HYDRAULIC CONDUCTIVITY
Table 9.1
253
Conduction Analogies in Porous Media Fluid
Heat
Electrical
Chemical
Electrical conductivity (siemens/m)
Chemical potential or concentration c (mol m⫺3) Total mass per unit total volume, m (mol/m3) Diffusion coeff. D (m2 /s)
Current I (amp) I/A (amp/m2) V ie ⫽ ⫺ (v/m) x Ohm’s law V V I ⫽ ⫺e A⫽ x R Capacitance C (farads ⫽ coul/volt)
jD (mol/s) JD ⫽ jD /A (mol s⫺1 m⫺2) c ic ⫽ ⫺ (mol m⫺4) x Fick’s law c JD ⫽ ⫺D A x Retardation factor, Rd (dimensionless)
Potential
Total head h (m)
Temperature T (C)
Voltage V (volts)
Storage
Fluid volume W (m3 /m3) Hydraulic conductivity kh (m/s) qh (m3 /s) qh /A (m3 /s/m2) h ih ⫽ ⫺ (m/m) x Darcy’s law h qh ⫽ ⫺kh A x Coefficient of volume change dW a M⫽ ⫽ w v ⫽ dh 1⫹e kh cv W q ⫹ h ⫽0 t A 2qh ⫽ 0 h k 2h ⫽ h 2 t M x
Thermal energy u (J/m3) Thermal conductivity kt (W/m/ C) qt (J/s) qt /A (J/s/m2) T it ⫽ ⫺ (C/m) x Fourier’s law T qt ⫽ ⫺kt A x Volumetric heat C(J/ C/m3) dQ C⫽ dT
Charge Q (Coulomb)
Conductivity
Flow Flux Gradient Conduction
Capacitance
Continuity Steady state Diffusion
冉冊
冉
冊
k ⫽ cv M
冉冊
u q ⫹ t ⫽0 t A 2qt ⫽ 0 T k 2T ⫽ t 2 t C x
冉 冊
flow channel cross-section area wetted perimeter
is useful. For a circular tube flowing full, RH ⫽
R2 R ⫽ 2R 2
so Poiseuille’s equation becomes
(m) ⫹ JD ⫽ 0 t 2JD ⫽ 0 c D* 2c ⫽ t RD x2
k ⫽a C
weight of the flowing fluid. Because the flow channels in a soil are of various sizes, a characteristic dimension is needed to describe average size. The hydraulic radius RH RH ⫽
冉冊
Q I ⫹ ⫽0 t A 2I ⫽ 0 V 2V ⫽ t C x2
qcir ⫽
1 p 2 R ia 2 Hh
where a is the cross-sectional area of the tube. For other shapes of cross section, an equation of the same form will apply, differing only in the value of a shape coefficient Cs, so q ⫽ Cs
(9.9)
(9.10)
p RH2 ia h
(9.11)
For a bundle of parallel tubes of constant but irregular cross section contributing to a total cross-sectional area A (solids plus voids), the area of flow passages Aƒ filled with water is
254
9
CONDUCTION PHENOMENA
Figure 9.2 Hydraulic conductivity values for several soils. Soil identification code: 1, compacted caliche; 2, compacted caliche; 3, silty sand; 4, sandy clay; 5, beach sand; 6, compacted Boston blue clay; 7, Vicksburg buckshot clay; 8, sandy clay; 9, silt—Boston; 10, Ottawa sand; 11, sand—Gaspee Point; 12, sand—Franklin Falls; 13, sand–Scituate; 14, sand–Plum Island; 15, sand–Fort Peck; 16, silt—Boston; 17, silt—Boston; 18, loess; 19, lean clay; 20, sand—Union Falls; 21, silt—North Carolina; 22, sand from dike; 23, sodium Boston blue clay; 24, calcium kaolinite; 25, sodium montmorillonite; 26–30, sand (dam filter) (From Lambe and Whitman (1969). Copyright 1969 by John Wiley & Sons. Reprinted with permission from John Wiley & Sons.
Figure 9.3 Hydraulic conductivity and permeability conversion chart.
HYDRAULIC CONDUCTIVITY
Aƒ ⫽ SnA
(9.12)
where S is the degree of saturation and n is the porosity. For this condition the hydraulic radius is given by RH ⫽ ⫽
Aƒ Aƒ L volume available for flow ⫽ ⫽ P PL wetted area Vw Vs S0
(9.13)
where P is the wetted perimeter, L is the length of flow channel in the direction of flow, Vs is the volume of solids and S0 is the wetted surface area per unit volume of particles. The wetted surface area depends on the particle sizes and the soil fabric and may be considered as an effective surface area per unit volume of solids. It is less than the total specific surface area of the soil since flow will not occur adjacent to all particle surfaces. For void ratio e and volume of solids Vs, the volume of water Vw is Vw ⫽ eVs S
(9.14)
Equation (9.11) becomes q ⫽ Cs
冉冊
冉冊 冉 冊
p e RH2 Snih A ⫽ Cs p RH2 S i A 1⫹e h
(9.15) and substitution for RH using Eqs. (9.13) and (9.14) gives
冉 冊冉 冊 冉 冊
q ⫽ Cs
p 3 e3 S i A 1⫹e h
1 S 02
(9.16)
By analogy with Darcy’s law,
冉冊 冉 冊
kh ⫽ Cs
p 1 e3 S3 2 S0 1 ⫹ e
(9.17)
For full saturation, S ⫽ 1, and denoting Cs by 1/ (k0T 2), where k0 is a pore shape factor and T is a tortuosity factor, Eq. (9.17) becomes K ⫽ kh
冉冊
冉 冊
1 e3 ⫽ 2 2 p k0 T S 0 1 ⫹ e
(9.18)
This is the Kozeny–Carman equation for the permeability of porous media (Kozeny, 1927; Carman, 1956). The hydraulic conductivity kh has units of velocity
255
(LT⫺1), and the absolute or intrinsic permeability K has units of area (L2). The effects of permeant properties are accounted for by the / p term, provided the fabric of the soil is the same in the presence of different fluids. The pore shape factor k0 has a value of about 2.5 and the tortuosity factor has a value of about 兹2 in porous media containing approximately uniform pore sizes. For equal size spheres, S0 becomes 6/D (⫽surface area/volume of a sphere), where D is the diameter. If a soil is considered to consist of spheres of different sizes, an effective diameter Deff can be computed from the particle size distribution (Carrier, 2003) according to Deff ⫽
100% 兺(ƒi /Dave,i)
(9.19)
where fi is the fraction of particles between two sizes (Dli and Dsi) and Dave,i is the average particle size be0.5 tween two sizes (⫽D0.5 li Dsi ); S0 can also be estimated from the specific surface area. Methods for nonplastic soils and clayey soils are given in Chapter 3 and also are summarized by Chapuis and Aubertin (2003). Various modifications for S0 are available to take irregular particle shapes (Loudon, 1952; Carrier, 2003) into account. The Kozeny–Carman equation accounts well for the dependency of permeability on void ratio in uniformly graded sands and some silts; however, serious discrepancies are often found when it is applied to clays. The main reasons for these discrepancies are that most clay soils do not contain uniform pore sizes and changes in pore fluid type are often accompanied by changes in the clay fabric. Particles in clays are grouped in clusters or aggregates that have large intercluster pores and small intracluster pores. The influences of fabric and nonuniform pore sizes on the hydraulic conductivity of fine-grained soils are discussed further later in this section. If comparisons are made using materials having the same fabric, the influence of permeant on hydraulic conductivity is quite well accounted for by the p / term. If, however, a fine-grained soil is molded or compacted in different permeants, then the fabrics may be quite different, and the hydraulic conductivities for samples at the same void ratio can differ greatly. If Cs in Eq. (9.17) is taken as a composite shape factor, and noting that total surface area per unit volume is inversely proportional to particle size, then kh ⫽ CD2s
冉冊
w e3 S3 1⫹e
where Ds is a characteristic grain size.
(9.20)
256
9
CONDUCTION PHENOMENA
Like the Kozeny–Carman equation, Eq. (9.20) describes the behavior of cohesionless soils reasonably well, but it is inadequate for clays. For a uniform sand with bulky particles and a given permeant, Eqs. (9.17) and (9.20) indicate that kh should vary directly with e3 /(1 ⫹ e) and D2s , and experimental observations support this. Despite the inability of the theoretical equations to predict the hydraulic conductivity accurately in many cases, they do reflect the overwhelming importance of pore size. Flow velocity depends on the square of pore radius, and hence the flow rate depends on radius to the fourth power. The specific surface in the Kozeny– Carman equation and the representative grain size term in Eq. (9.20) are both measures of pore size. All other factors equal, the hydraulic conductivity depends far more on the fine particles than on the large. A small percentage of fines can clog the pores of an otherwise coarse material and result in a manyfold lower hydraulic conductivity. On the other hand, the presence of fissures, cracks, root holes, and the like can result in enormous increases in the rate of water flow through an otherwise compact soil layer. Equation (9.20) predicts that the hydraulic conductivity should vary with the cube of the degree of saturation, and some, but not all, experimental data support this, even in the case of fine-grained soils. Consideration of flow through unsaturated soils is given in Section 9.4. Validity of Darcy’s Law
A basic premise of Darcy’s law is that flow is laminar and steady through saturated porous media. If particle and pore sizes and flow rates are sufficiently great, then flow is turbulent, and Darcy’s law no longer applies. Turbulent flow conditions are likely in flows through gravel and rockfill (Ahmed and Sunada, 1969; Arbhabhirama and Dinoy, 1973; George and Hansen, 1992; Hansen et al., 1995; Li et al., 1998).2 Some modification of Darcy’s law is needed also to account for nonsteady and wave-induced flows through sands, silts,
2
Flow transitions from laminar to turbulent flow when the Reynolds number Re, defined as the ratio of inertial to viscous forces, exceeds a critical value. For flow through soils the critical value of interstitial flow Re is in the range of 1 to 10, with Re defined as (Khalifa et al., 2002) Re ⫽
4 v (1 ⫺ n)Avd
in which is fluid density, is tortuosity (ratio of flow path mean length to thickness), v is flow velocity, n is porosity, and Avd is the ratio of pore surface area exposed to flow to the volume of solid.
and clays (Khalifa et al., 2002). These nonsteady and turbulent flow conditions are not treated herein. As early as 1898, instances were cited in which hydraulic flow velocity in fine-grained materials in which laminar flow can be expected increased more than proportionally with increases in gradient (King, 1898). The absence of water flow at finite hydraulic gradients in ceramic filters of 0.1-m average pore diameter was reported by Derjaguin and Krylov (1944). Oakes (1960) found no detectable flow through a 30-cm-long suspension of 6 percent Wyoming bentonite subjected to a 50-cm head of water. Experiments by Miller and Low (1963) led to the conclusion that there was a threshold gradient for flow through sodium montmorillonite. Flow rates through clay-bearing sandstones were found to increase more than directly with gradient up to gradients of 170 by von Englehardt and Tunn (1955). Deviations from Darcy’s law in pure and natural clays up to gradients of 900 were measured by Lutz and Kemper (1959). Apparent deviations from Darcy’s law for flow in undisturbed soft clay are shown in Fig. 9.4. The reported deviations from linearity between flow rate and hydraulic gradient are most significant in the lower range of gradients. Hydraulic gradients in the field are seldom much greater than one. Thus, deviations from Darcy’s law, if real, could have very important implications for the applicability of steady-state and transient flow analyses, including consolidation, that are based on it. Furthermore, gradients typically used in laboratory testing are high, commonly more than 10, and often up to several hundred. This brings the suitability of laboratory test results as indicators of field behavior into question. Three hypotheses have been proposed to account for nonlinearity between flow velocity and gradient: (1) non-Newtonian water flow properties, (2) particle migrations that cause blocking and unblocking of flow passages, and (3) local consolidation and swelling that is inevitable when hydraulic gradients are applied across a compressible soil. The apparent existence of a threshold gradient below which flow was not detected was attributed to a quasi-crystalline water structure. It is now known, however, that many of the effects interpreted as resulting from unusual water properties can be ascribed to undetected experimental errors arising from contamination of measuring systems (Olsen, 1965), local consolidation and swelling, and bacterial growth (Gupta and Swartzendruber, 1962). Additional careful measurements by a number of investigators (e.g., Olsen, 1969; Gray and Mitchell, 1967; Mitchell and Younger, 1967; Miller et al., 1969; Chan and Kenney, 1973) failed to confirm the existence of a threshold gradient in clays. Darcy’s law was
HYDRAULIC CONDUCTIVITY
257
Figure 9.4 Dependence of flow velocity on hydraulic gradient. Undisturbed soft clay from Ska˚ Edeby, Sweden (from Hansbo, 1973).
obeyed exactly in several of these studies. Thus it is unlikely that unusual water properties are responsible for non-Darcy flow behavior. On the other hand, particle migrations leading to void plugging and unplugging, electrokinetic effects, and chemical concentration gradients can cause apparent deviations from Darcy’s law. Analysis of interparticle bond strengths in relation to the magnitude of seepage forces shows that particles that are not participating in the load-carrying skeleton of a soil mass can be moved under moderate values of hydraulic gradient. Soils with open, flocculated fabrics and granular soils with a relatively low content of fines appear particularly susceptible to the movement of fine particles during permeation. Internal swelling and dispersion of clay particles during permeation can cause changes in flow rate and apparent non-Darcy behavior. Tests on illite–silt mixtures showed that the hydraulic conductivity depends on clay content, sedimentation procedure, compression rate, and electrolyte concentration. Subsequent behavior was quite sensitive to the type and concentration of electrolyte used for permeation and the total throughput volume of permeant. Changes in relative hydraulic conductivity that occurred while the
electrolyte concentration was changed from 0.6 to 0.1 N NaCl are shown in Fig. 9.5. The cumulative throughput is the ratio of the total flow volume at any time to the sample pore volume. The hydraulic conductivities for these materials ranged from more than 1 ⫻ 10⫺7 to less than 1 ⫻ 10⫺9 m/s. Practical Implications Evidence indicates that Darcy’s law is valid, provided that all system variables are held constant. However, unless fabric changes, particle migrations, and internal void ratio redistributions caused by effective stress and chemical changes can be shown to be negligible, hydraulic conductivity measurements in the laboratory should be made under conditions of temperature, pressure, hydraulic gradient, and pore fluid chemistry as closely approximating those in the field as possible. This is particularly important in connection with the testing of clays as potential waste containment barriers, such as slurry walls and liners for landfills and impoundments (Daniel, 1994). Microbial activities may be important as well, as they can lead to formation of biofilms, pore clogging, and large reductions in hydraulic conductivity as shown, for example, by Dennis and Turner (1998). Unfortunately, duplication of field conditions is not always possible, especially as regards the hydraulic
258
9
CONDUCTION PHENOMENA
Figure 9.5 Reduction in hydraulic conductivity as a result of internal swelling (from Hardcastle and Mitchell, 1974).
gradient. If hydraulic gradients are low enough to duplicate those in most field situations, then the laboratory testing time usually becomes unacceptably long. In such cases, tests over a range of gradients are desirable in order to assess the stability of the soil structure against changes due to seepage forces. Similarly, the gradients that are developed in laboratory consolidation tests on thin samples are many times greater than exist in thick layers of the same clay in the field. The variation of hydraulic gradient i with time factor T during one-dimensional consolidation according to the Terzaghi theory is shown in Fig. 9.6. The solution of the Terzaghi equation gives excess pore pressure u as a function of position (z/H) and time factor
冘 2uM 冉sin MzH 冊e ⬁
u⫽
⫺M2T
0
(9.21)
m⫽0
where M ⫽ (2m ⫹ 1)/2. Thus, the hydraulic gradient is i⫽ z
冉冊
u 2u0 ⫽ w wH
冘 ⬁
m⫽0
冉 冊
Mz ⫺M2T cos e H
冘 cos冉MzH 冊e ⬁
m⫽0
Eq. (9.22) becomes
⫺M2T
u0 p wH
(9.24)
The real gradient for any layer thickness or loading intensity can be obtained by using actual values of u0 and H and the appropriate value of p from Fig. 9.6. For small values of u0 / w H, as is the case in the field, for example, for u0 ⫽ 50 kPa, H ⫽ 5m, then u0 / w H ⫽ 1, and the field gradients are low throughout most of the layer thickness during the entire consolidation process. On the other hand, for a laboratory sample of 10 mm thickness and the same stress increase, u0 / w H is 500, and the hydraulic gradients are very large. In this case a gradient-dependent hydraulic conductivity could be the cause of significant differences between the laboratory-measured and field values of coefficient of consolidation. Constant rate of strain or constant gradient consolidation testing of such soils is preferable to the use of load increments because lower gradients minimize particle migration effects. Anisotropy
(9.22)
If a parameter p is defined by p⫽2
i⫽
(9.23)
Anisotropic hydraulic conductivity results from both preferred orientation of elongated or platy particles and stratification of soil deposits. Ratios of horizontal-tovertical hydraulic conductivity from less than 1 to more than 7 were measured for undisturbed samples of several different clays (Mitchell, 1956). These ratios correlated reasonably well with preferred orientation of the clay particles, as observed in thin section. Ratios of 1.3 to 1.7 were measured for kaolinite consolidated one dimensionally from 4 to 256 atm, and 0.9 to 4.0
HYDRAULIC CONDUCTIVITY
259
Figure 9.6 Hydraulic gradients during consolidation according to the Terzaghi theory.
were measured for illite and Boston blue clay consolidated over a pressure range up to more than 200 atm (Olsen, 1962). A ratio of approximately 2 was measured for kaolinite over a range of void ratios corresponding to consolidation pressures up to 4 atm (Morgenstern and Tchalenko, 1967b). Thus, an average hydraulic conductivity ratio of about 2 as a result of microfabric anisotropy may be typical for many clays. Large anisotropy in hydraulic conductivity as a result of stratification of natural soil deposits or in earthwork compacted in layers is common. Varved clays have substantially greater hydraulic conductivity in the horizontal direction than in the vertical direction owing to the presence of thin silt layers between the thin clay layers. The ratio of horizontal values to vertical values determined in the laboratory, rk, is 10 5 for Connecticut Valley varved clay (Ladd and Wissa, 1970). Similar values were measured for the varved clay in the New Jersey meadows. Values less than 5 were measured for New Liskeard, Ontario, varved clay (Chan and Kenney, 1973). The practical importance of a high hydraulic conductivity in the horizontal direction depends on the distance to a drainage boundary and the type of flow. For example, the rate of groundwater flow will clearly be affected, as will the rate of consolidation when vertical
drains are used. On the other hand, lateral drainage beneath a loaded area may not be greatly influenced by a high ratio of horizontal to vertical conductivity if the width of loaded area is large compared to the thickness of the drainage layer. Fabric and Hydraulic Conductivity
The theoretical relationships developed earlier in this section indicate that the flow velocity should depend on the square of the pore radius, and the flow rate is proportional to the fourth power of the radius. Thus, fabrics with a high proportion of large pores are much more pervious than those with small pores. For example, remolding several undisturbed soft clays reduced the hydraulic conductivity by as much as a factor of 4, with an average of about 2 (Mitchell, 1956). This reduction results from the breakdown of a flocculated open fabric and the destruction of large pores. An illustration of the profound influence of compaction water content on the hydraulic conductivity of fine-grained soil is shown in Fig. 9.7. All samples were compacted to the same density. For samples compacted using the same compactive effort, curves such as those in Fig. 9.8 are typical. For compaction dry of optimum,
260
9
CONDUCTION PHENOMENA
Figure 9.8 Influence of compaction method on the hydraulic
conductivity of silty clay. Constant compactive effort was used for all samples. Figure 9.7 Hydraulic conductivity as a function of compac-
tion water content for samples of silty clay prepared to constant density by kneading compaction.
clay particles and aggregates are flocculated, the resistance to rearrangement during compaction is high, and a fabric with comparatively large pores is formed. For higher water contents, the particle groups are weaker, and fabrics with smaller average pore sizes are formed. Considerably lower values of hydraulic conductivity are obtained wet of optimum in the case of kneading compaction than by static compaction (Fig. 9.8) because the high shear strains induced by the kneading compaction method break down flocculated fabric units.
Three levels of fabric are important when considering the hydraulic conductivity of finer-grained soils. The microfabric consists of the regular aggregations of particles and the very small pores, perhaps with sizes up to about 1 m, between them through which very little fluid will flow. The minifabric contains these aggregations and the interassemblage pores between them. The interassemblage pores may be up to several tens of micrometers in diameter. Flows through these pores will be much greater than through the intraaggregate pores. On a larger scale, there may be a macrofabric that contains cracks, fissures, laminations, or root holes through which the flow rate is so great as to totally obscure that through the other pore space types.
HYDRAULIC CONDUCTIVITY
261
These considerations are of particular importance in the hydraulic conductivity of compacted clays used as barriers for waste containment. The controlling units in these materials are the clods, which would correspond to minifabric units. Acceptably low hydraulic conductivity values are obtained only if clods and interclod pores are eliminated during compaction (Benson and Daniel, 1990). This requires that compaction be done wet of optimum using a high effort and a method that produces large shear strains, such as by sheepsfoot roller. The wide range of values of hydraulic conductivity of compacted fine-grained soils that results from the large differences in fabric associated with compaction to different water contents and densities is illustrated by Fig. 9.9. The grouping of contours means that selection of a representative value for use in a seepage analysis is difficult. In addition, if it is required that the hydraulic conductivity of earthwork not exceed a certain value, such as may be the case for a clay liner for a waste pond, then specifications must be carefully drawn. In so doing, it must be recognized also that other properties, such as strength, also vary with compaction water content and density and that the compaction conditions that are optimal for one property may not be suitable for the other. A procedure for the development of suitable specifications for compacted clay liners is given by Daniel and Benson (1990). The primary reason equations such as (9.18) and (9.20) fail to account quantitatively for the variation of the hydraulic conductivity of fine-grained soils with change in void ratio is unequal pore sizes (Olsen, 1962). A typical soil has a fabric composed of small
aggregates or clusters as shown schematically in Fig. 9.10. These aggregates of N particles each have an intracluster void ratio ec. The spaces between the aggregates comprise the intercluster voids and are responsible for the intercluster void ratio ep. The total void ratio eT is equal to the sum of ec and ep. The clusters and intracluster voids comprise the microfabric, whereas the assemblage of clusters comprises the minifabric. Fluid flow in such a system is dominated by flow through the intercluster pores because of their larger size. The sizes of clusters depend on the mineralogical and pore fluid compositions and the formational process. Conditions that favor aggregation of individual clay plates produce larger clusters than deflocculating, dispersing environments. There is general consistency with the interparticle double-layer interactions described in Chapter 6. When a fine-grained soil is sedimented in or mixed with waters of different electrolyte concentration or type or with fluids of different dielectric constants, quite different fabrics result. This explains why the / term in Eqs. (9.18) and (9.20) is inadequate to account for pore fluid differences, unless comparisons are made using samples having identical fabrics. This will only be the case when a pore fluid of one type replaces one of another type without disturbance to the soil. The cluster model developed by Olsen (1962) accounts for discrepancies between the predicted and measured variations in flow rates through different soils. The following equation can be derived for the ratio of estimated flow rate for a cluster model, qCM to the flow rate predicted by the Kozeny–Carman equation (9.18) qKC:
Figure 9.9 Contours of constant hydraulic conductivity for silty clay compacted using kneading compaction.
Figure 9.10 Cluster model for permeability prediction (after Olsen, 1962).
262
9
CONDUCTION PHENOMENA
qCM (1 ⫺ ec /eT)3 ⫽ N2/3 qKC (1 ⫹ ec)4 / 3
(9.25)
Application of Eq. (9.25) requires assumptions for the variations of ec with eT that accompany compression and rebound. Olsen (1962) considered the relative compressibility of individual clusters and cluster assemblages. The compressibility of individual clusters is small at high total void ratios, so compression is accompanied by reduction in the intercluster pore sizes, but with little change in intracluster void ratio. This assumption is supported by the microstructure studies of Champlain clay by Delage and Lefebvre (1984) Thus, the actual hydraulic conductivity decreases more rapidly with decreasing void ratio during compression than predicted by the Kozeny–Carman equation until the intercluster pore space is comparable to that in a system of closely packed spheres, when the clusters themselves begin to compress. Further decreases in porosity involve decreases in both ec and eT. As the intercluster void ratio now decreases less rapidly, the hydraulic conductivity decreases at a slower rate with decreasing porosity than predicted by the Kozeny–Carman equation. During rebound increase in porosity develops mainly by swelling of the clusters, whereas the flow rate continues to be controlled primarily by the intercluster voids. Recent attempts to quantify saturation and hydraulic conductivity of fine-grained soils containing a distribution of particle sizes and fabric elements in terms of pore-scale relationships have given promising results (Tuller and Or, 2003). Expressions for clay plate spacing in terms of surface properties and solution composition derived using DLVO theory (see Chapter 6), combined with assumed geometrical representations of clay aggregates and pore space in combination with silt and sand components, are used in the formulation. 9.4
FLOWS THROUGH UNSATURATED SOILS
Darcy’s law [Eq. (9.7)] also applies for flow through unsaturated soils such as those in the vadose zone above the water table where pore water pressures are negative. However, the hydraulic conductivity is not constant and depends on the amount and connectivity of water in the pores. For instance, Eq. (9.20) predicts that hydraulic conductivity should vary as the cube of the degree of saturation.3 This relationship has been 3
The hydraulic conductivity can also be a function of volumetric moisture content or matric suction . These variables are related to each other by the soil–water characteristic curve as described in Chapter 7.
found reasonable for compacted fine-grained soils and degrees of saturation greater than about 80 percent. Similarly to Eq. (9.7), the unsaturated flow equation in the direction i can be written as vi ⫽ ⫺k(S)
冉
冊
z ⫹ xi xi
(9.26)
where k(S) is saturation-dependent hydraulic conductivity, is the matric suction equivalent head (L), and z/ xi is the unit gravitational vector measured upward in direction z (1.0 if xi is the direction of gravity z). When percolating water infiltrates vertically into dry soil, the hydraulic gradient near the sharp wetting front can be very large because of a large value of the / x term. However, the wetting front becomes less sharp as the infiltration proceeds and the gravity term then dominates. The hydraulic gradient then is close to one and the magnitude of flux is equal to the hydraulic conductivity k(S). Using Eq. (9.26), the equation of mass conservation becomes (nS) ⫽ t xi
冋 冉 k(S)
冊册
z ⫹ xi xi
R w
⫹
(9.27)
where n is the porosity, w is the density of the water, and R is a source or sink mass transfer term such as water uptake by plant roots (ML⫺3). If the soil is assumed to be incompressible and there is no sink/sources (R ⫽ 0), Eq. (9.27) becomes n
S ⫽ t xi
or C( )
⫽ t xi
冋 冉 冋 冉
冊册 冊册
k( )
z ⫹ xi xi
k( )
z ⫹ xi xi
(9.28)
where C( ) ⫽ n(S/ ) and k(S) is converted to k( ) using the soil–water characteristic curve (S– relationships). Equation (9.28) is called the Richards equation (Richards, 1931). For given S– and k( ) relationships and initial/boundary conditions, the nonlinear governing equation can be solved for (often numerically by the finite difference or finite element method). The hydraulic conductivity of unsaturated soils can be a function of saturation, water content, matric suction, or others. Measured hydraulic conductivities of well-graded sand and clayey sand as a function of (a) matric suction and (b) saturation ratio are shown in Fig. 9.11. Both figures are related to each other, as the matric suction is a function of saturation ratio by the soil moisture characteristic curve as described in Sec-
FLOWS THROUGH UNSATURATED SOILS 1.E+01
1.E+01 Sand
Clayey Sand Clayey Sand > Sand
1.E-11 1.E-13 1.E-15 1.E-17
Sand Clayey Sand
1.E-01 1.E-03 1.E-05 1.E-07 1.E-09
Hydraulic Conductivity (m/s)
1.E-01 1.E-03 1.E-05 1.E-07 1.E-09
Hydraulic conductivity (m/s)
263
1.E-11 1.E-13 1.E-15 1.E-17
Sand > Clayey Sand 1.E-19 1.E-21 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 Matric Suction (kPa)
1.E-19 1.E-21 0
20
(a)
40 60 Saturation (%)
80
100
(b) 1.E+00 Sand
Relative Permeability kr
1.E-02
Clayey Sand
1.E-04 1.E-06 1.E-08 1.E-10 1.E-12
Relative Permeability kr
1.E+00
1.E-02 1.E-04 1.E-06 1.E-08 1.E-10 1.E-12
1.E-14
1.E-14
1.E-16 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 Matric Suction (kPa)
1.E-16
(c)
Sand Clayey Sand 0
20
40 60 Saturation (%)
80
100
(d)
Figure 9.11 Hydraulic conductivity of partially saturated sand and clayey sand as a function of matric suction and degree of saturation (from Stephens, 1996).
tion 7.12. Various methods to measure the hydraulic conductivity of unsaturated soils are available (Klute, 1986; Fredlund and Rahardjo, 1993). However, the measurement in unsaturated soils is more difficult to perform than in saturated soils because the hydraulic conductivity needs to be determined under controlled water saturation or matric suction conditions. A general expression for the hydraulic conductivity k of unsaturated soils can be written as k ⫽ krK
g ⫽ kr ks
(9.29)
where ks is the saturated conductivity, K is the intrinsic permeability of the medium (L2) such as given by Eq. (9.18), is the density of the permeating fluid (ML⫺3), g is the acceleration of gravity (LT⫺2), is the dynamic viscosity of the permeating fluid (MT⫺1L⫺1), and ks is the conductivity under the condition that the pores are fully filled by the permeating fluid (i.e., full saturation). The dimensionless parameter kr is called the relative permeability, and the values range from 0 (⫽ zero per-
meability, no interconnected path for the permeating fluid) to 1 (⫽ permeating fluid at full saturation). The equation can be used for a nonwetting fluid (e.g., air) by substituting the values of and of the nonwetting fluid. The data in Fig. 9.11a and 9.11b can be replotted as the relative permeability against matric suction in Fig. 9.11c and against saturation ratio in Fig. 9.11d. The two different curves in Fig. 9.11d clearly show that kr ⫽ S3 derived from Eq. (9.20) is not universally applicable. At very low water contents, the water in the pores becomes disconnected as described in Chapter 7. Careful experiments show that the movement of water exists even at moisture contents of a few percent, but vapor transport becomes more important at this dry state (Grismer et al., 1986). Therefore, Eq. (9.20) is not suitable for low saturations. One reason for this discrepancy is that soil contains pores of various sizes rather than the assumption of uniform pore sizes used to derive Eq. (9.20). Considering that the soil contains pores of random sizes, Marshall (1958) derived the following equation
264
9
CONDUCTION PHENOMENA
for hydraulic conductivity as a function of pore sizes for an isotropic material: K⫽
n2 r 21 ⫹ 3r 22 ⫹ 5r 23 ⫹ ⫹ (2m ⫺ 1)r 2m m2 8 (9.30)
in which K is the specific hydraulic conductivity (permeability) (L2), n is the porosity, m is the total number of pore classes, and ri is the mean radius of the pores in pore class i. Pore sizes can be measured from data on the amount of water withdrawn as the suction on the soil is progressively increased. Using the capillary equation, the radius of the largest water-filled pore under a suction of (L) is given by 2 r⫽ wg
(9.31)
in which is the surface tension of water, w is the density of water, and g is the acceleration of gravity. As it is usually more convenient to use moisture suction than pore radius, Eq. (9.29) can be rewritten as K⫽
2 n2 ⫺2 [ ⫹ 3 2⫺2 ⫹ 5 ⫺2 3 22wg2 m2 1
(9.32)
The permeability K can be converted to the hydraulic conductivity k by multiplying the unit weight (wg) divided by the dynamic viscosity of water . This gives 2 n2 ⫺2 ⫺2 [ ⫹ 3 ⫺2 2 ⫹ 5 3 2wg m2 1 ⫹ ⫹ (2m ⫺ 1) ⫺2 m ]
(9.33)
Following Green and Corey (1971), the porosity n equals the volumetric water content of the saturated condition S, and m is the total number of pore classes between S and zero water content ⫽ 0. A matching factor is usually used in Eq. (9.33) to equate the calculated and measured hydraulic conductivities. Matching at full saturation is preferable to matching at a partial saturation point because it is simpler and gives better results. Rewriting Eq. (9.33) and introducing a matching factor gives k( i) ⫽
ks 2 2S ksc 2wg m2
m S ⫽ l S ⫺ L
冘 [(2j ⫹ 1 ⫺ 2i) l
⫺2 j
]
j⫽1
(i ⫽ 1, 2, . . . , l)
(9.34)
(9.35)
A constant value of l is used at all water contents, and the value of l establishes the number of pore classes for which ⫺2 terms are included in the calculation at j saturation. Other pore size distribution models for unsaturated soils are available, and an excellent review of these models is given by Mualem (1986). Equation (9.34) can be written in an integration form as (after Fredlund et al., 1994)
冕
ks 2 Sp ksc 2wg
k( ) ⫽
⫹ ⫹ (2m ⫺ 1) ⫺2 m ]
k⫽
in which k( i) is the calculated hydraulic conductivity for a specified water content i; is i the last water content class on the wet end, for example, i ⫽ 1 denotes the pore class corresponding to the saturated water content S, and i ⫽ l denotes the pore class corresponding to the lowest water content L for which hydraulic conductivity is calculated; ks /ksc is the matching factor, defined as the measured saturated hydraulic conductivity divided by the calculated saturated hydraulic conductivity; and l is the total number of pore classes (a pore class is a pore size range corresponding to a water content increment) between ⫽ L and S. Thus
L
⫺x dx 2(x)
(9.36)
where suction is given as a function of volumetric water content , and x is a dummy variable. The hydraulic conductivity for fully saturated condition is calculated by assigning ⫽ S. For generality, the term 2S in Eq. (9.34) is replaced by ps , where p is a constant that accounts for the interaction of pores of various sizes (Fredlund et al., 1994). From Eq. (9.36), the relative permeability kr is a function of water content as follows: kr( ) ⫽
冕
r
冒冕
⫺x dx 2(x)
S
r
⫺x dx 2(x)
(9.37)
Herein, the lowest water content L is assumed to be the residual water content r. If the moisture content –suction relationship (or the soil–water characteristic curve) is known, the relative permeability kr can be computed from Eq. (9.37) by performing a numerical integration. The hydraulic conductivity k is then estimated from Eq. (9.29) with the knowledge of saturated hydraulic conductivity ks. The use of the soil–water characteristic curve to estimate the hydraulic conductivity of unsaturated soils is attractive because it is easier to determine this curve
THERMAL CONDUCTIVITY
in the laboratory than it is to measure the hydraulic conductivity directly. Apart from Eq. (9.37), the following relative permeability function proposed by Mualem (1976) is often used primarily because of its simplicity: kr( ) ⫽
冊 冉冕 d( )冒冕
冉
⫺ r s ⫺ r
q
r
s
r
d ( )
冊
2
(9.38)
where q describes the degree of connectivity between the water-conducting pores. Mualem (1976) states that q ⫽ 0.5 is appropriate based on permeability measurements on 45 soils. van Genuchten et al. (1991) substituted the soil–water characteristic equation (7.52) into Eq. (9.38) and obtained the following closed-form solution4: kr( ) ⫽
冉
冊再 冋 冉
⫺ r S ⫺ r
p
1⫺ 1⫺
冊 册冎
⫺ r S ⫺ r
1/m
m
2
(9.39) Both Eq. (9.39) as well as Eq. (9.37) using the soil– water characteristic curve by Fredlund and Xing (1994) give good predictions of measured data as shown in Fig. 9.12. The two hydraulic conductivity–matric suction curves shown in Fig. 9.11a cross each other at a matric suction value of approximately 50 kPa (or 5 m above the water table under hydrostatic condition). Below this value, the hydraulic conductivity of sand is larger than that of the clayey sand. However, as the matric suction increases, the water in the sand drains rapidly toward its residual value, giving a very low hydraulic conductivity. On the other hand, the clayey sand holds the pore water by the presence of fines and the hydraulic conductivity becomes larger than that of the sand at a given matric suction. If the sand is overlain by the clayey sand, then the matric suction at the interface is larger than 50 kPa, and the water infiltrating downward through the finer clayey sand cannot enter into the coarser sand layer because the underlying sand layer is less permeable than the overlying clayey sand. The water will instead move laterally along the bedding interface. This phenomenon is called a capillary barrier (e.g., Zaslavsky and Sinai, 1981; Yeh et al., 1985; Miyazaki, 1988). The barrier will be maintained as long as the lateral discharge along the interface (preferably inclined) is
4 m ⫽ 1 ⫺ 1 / n is assumed (van Genuchten et al., 1991). See Eq. (7.52).
265
larger than the vertically infiltrating water flow. However, if the matric suction is reduced by large infiltration, the barrier breaks and water enters into the initially dry coarse layer. Solutions are available to evaluate the amount of water flowing laterally across the capillary barrier interface at the point of breakthrough for a given set of fine and coarse soil hydraulic properties and interface inclination (Ross, 1990; Steenhuis et al., 1991; Selkar, 1997; Webb, 1997). Capillary barriers have received increased attention as a means for isolating buried waste from groundwater flow and as part of landfill cover systems in dry climates (Morris and Stormont, 1997; Selkar, 1997; Khire et al., 2000). The barrier can be used to divert the flow laterally along an interface and/or to store infiltrating water temporarily in the fine layer so that it can be removed ultimately by evaporation and transpiration. Capillary barriers are constructed as simple two-layer systems of contrasting particle size or multiple layers of fine- and coarse-grained soils. If the thickness of the overlying fine layer is too small, capillary diversion is reduced because of the confining flow path in the fine layer. The minimum effective thickness is several times the air-entry head of the fine soil (Warrick et al., 1997; Smersrud and Selker, 2001). Khire et al. (2000) stress the importance of site-specific metrological and hydrological conditions in determining the storage capacity of the fine layer. The soil for the underlying coarse layer should have a very large particle size contrast with the fine soil, but fines migrations into the coarse sand should be avoided. Smesrud and Sekler (2001) suggest the d50 particle size ratio of 5 to be ideal. The thickness of the coarse sand layer does not need to be great, as the purpose of the layer is simply to impede the downward water migration.
9.5
THERMAL CONDUCTIVITY
Heat flow through soil and rock is almost entirely by conduction, with radiation unimportant, except for surface soils, and convection important only if there is a high flow rate of water or air, as might possibly occur through a coarse sand or rockfill. The thermal conductivity controls heat flow rates. Conductive heat flow is primarily through the solid phase of a soil mass. Values of thermal conductivity for several materials are listed in Table 9.2. As the values for soil minerals are much higher than those for air and water, it is evident that the heat flow must be predominantly through the solids. Also included in Table 9.2 are values for the heat capacity, volumetric heat, heat of fusion, and heat of vaporization of water. The heat capacity can be used
266
9
CONDUCTION PHENOMENA
Hydraulic Conductivity, k (cm/day)
Hydraulic Conductivity, k × 10(m/s)
10
1
0.1
0.01
0.001
Predicted coefficient of permeability (drying) Predicted coefficient of permeability (wetting) Measured coefficient of permeability (drying) Measured coefficient of permeability (wetting)
0.0001 20
30 40 50 Volumetric Water Content (a)
60
Figure 9.12 Comparisons of predicted and measured relationships between hydraulic con-
ductivity and volumetric water content for two soils. (a) By Eq. (9.37) with the measured data for Guelph loam (from Fredlund et al., 1994) and (b) by Eq. (9.39) with the measured data for crushed Bandelier Tuff (van Genuchten et al., 1991).
to compute the volumetric heat using the simple relationships for frozen and unfrozen soil given in the table. Volumetric heat is needed for the analysis of many types of transient heat flow problems. The heat of fusion is used for analysis of ground freezing and thawing, and the heat of vaporization applies to situations where there are liquid to vapor phase transitions. The denser a soil, the higher is its composite thermal conductivity, owing to the much higher thermal conductivity of the solids relative to the water and air. Furthermore, since water has a higher thermal conductivity than air, a wet soil has a higher thermal conductivity than a dry soil. The combined influences of soil unit weight and water content are shown in Fig. 9.13, which may be used for estimates of the thermal conductivity for many cases. If a more soil-specific value is needed, they may be measured in the laboratory using the thermal needle method (ASTM, 2000). More detailed treatment of methods for the measurement of the thermal conductivity of soils are given by Mitchell and Kao (1978) and Farouki (1981, 1982). The relationship between thermal resistivity (inverse of conductivity) and water content for a partly saturated soil undergoing drying is shown in Fig. 9.14. If drying causes the water content to fall below a certain value, the thermal resistivity increases significantly. This may be important in situations where soil is used as either a thermally conductive material, for example,
to carry heat away from buried electrical transmission cables, or as an insulating material, for example, for underground storage of liquefied gases. The water content below which the thermal resistivity begins to rise with further drying is termed the critical water content, and below this point the system is said to have lost thermal stability (Brandon et al., 1989). The following factors influence the thermal resistivity of partly saturated soils (Brandon and Mitchell, 1989). Mineralogy All other things equal, quartz sands have higher thermal conductivity than sands containing a high percentage of mica. Dry Density The higher the dry density of a soil, the higher is the thermal conductivity. Gradation Well-graded soils conduct heat better than poorly graded soils because smaller grains can fit into the interstitial spaces between the larger grains, thus increasing the density and the mineral-to-mineral contact. Compaction Water Content Some sands that compacted wet and then dried to a lower water content have significantly higher thermal conductivity than when compacted initially at the lower water content. Time Sands containing high percentages of silica, carbonates, or other materials that can develop ce-
ELECTRICAL CONDUCTIVITY
Table 9.2
Thermal Properties of Materials a
Thermal Conductivity
Heat Capacity
Volumetric Heat
Heat of Fusion Heat of Vaporization a
267
Material
Btu/h/ft2 / F/ft
W/m/K
Air Water Ice Snow (100 kg m⫺3) (500 kg m⫺3) Shale Granite Concrete Copper Soil Polystyrene
0.014 0.30 1.30
0.024 0.60 2.25
0.03 0.34 0.90 1.60 1.0 225 0.15–1.5 (⬇1.0) 0.015–0.035
0.06 0.59 1.56 2.76 1.8 389 0.25–2.5 (⬇1.7) 0.03–0.06
Material
Btu/lb/ F
kJ/kg/K
Water Ice Snow (100 kg m⫺3) (500 kg m⫺3) Minerals Rocks
1.0 0.5
4.186 2.093
0.05 0.25 0.17 0.20–0.55
0.21 1.05 0.710 0.80–2.20
Material
Btu/ft3 / F
kJ/m3 /K
Unfrozen Soil Soil Frozen soil Snow (100 kg m⫺3) (500 kg m⫺3) Water Soil Water Soil
d (0.17 ⫹ w/100)
d (72.4 ⫹ 427w/100)
d (0.17 ⫹ 0.5w/100)
d (72.4 ⫹ 213w/100)
3.13 15.66 143.4 Btu/lb 143.4(w/100) d Btu/ft3 970 Btu/lb 970(w/100) d Btu/ft3
210 1050 333 kJ/kg 3.40 ⫻ 104(w/100) d kJ/m3 2.26 MJ/kg 230(w /100) d MJ/m3
d ⫽ dry unit weight, in lb/ft3 for U.S. units and in kN/m3 for SI units; w ⫽ water content in percent.
mentation may exhibit an increased thermal conductivity with time. Temperature All crystalline minerals in soils have decreasing thermal conductivity with increasing temperature; however, the thermal conductivity of water increases slightly with increasing temperature, and the thermal conductivity of saturated pore air increases markedly with increasing temperature. The net effect is that the thermal conductivity of moist sand increases somewhat with increasing temperature.
9.6
ELECTRICAL CONDUCTIVITY
Ohm’s law, Eq. (9.4), in which e is the electrical conductivity, applies to soil–water systems. The electrical conductivity equals the inverse of the electrical resistivity, or e ⫽
1 L (siemens/meter; S/m) RA
(9.40)
where R is the resistance ( ), L is length of sample
268
9
CONDUCTION PHENOMENA
fects particle size, shape, and surface conductance, soil structure, including fabric and cementation, and temperature. Electrical measurements found early applications in the fields of petroleum engineering, geophysical mapping and prospecting, and soil science, among others. The inherent complexity of soil–water systems and the difficulty in characterizing the wide ranges of particle size, shape, and composition have precluded development of generally applicable theoretical equations for electrical conductivity. However, a number of empirical equations and theoretical expressions based on simplified models may provide satisfactory results, depending on the particular soil and conditions. They differ in assumptions about the possible flow paths for electric current through a soil–water matrix, the path lengths and their relative importance, and whether charged particle surfaces contribute to the total current flow. Figure 9.13 Thermal conductivity of soil (after Kersten,
1949).
Nonconductive Particle Models Formation Factor The electrical conductivity of clean saturated sands and sandstones is directly proportional to the electrical conductivity of the pore water (Archie, 1942). The coefficient of proportionality depends on porosity and fabric. Archie (1942) defined the formation factor, F, as the resistivity of the saturated soil, T, divided by the resistivity of the saturating solution, W, that is, F⫽
T ⫽ W W T
(9.41)
where W and T are the electrical conductivities of the pore water and saturated soil, respectively. An empirical correlation between formation factor and porosity for clean sands and sandstones is given by F ⫽ n⫺m
Figure 9.14 Typical relationship between thermal resistivity
and water content for a compacted sand.
(m), and A is its cross-sectional area (m2). The value of electrical conductivity for a saturated soil is usually in the approximate range of 0.01 to 1.0 S/m. The specific value depends on several properties of the soil, including porosity, degree of saturation, composition (conductivity) of the pore water, mineralogy as it af-
(9.42)
where n is porosity, and m equals from 1.3 for loose sands to 2 for highly cemented sandstones. An empirical relation between formation factor at 100 percent water saturation and ‘‘apparent’’ formation factor at saturation less than 100 percent is FatSw⫽1 ⫽ (Sw)p
W T
(9.43)
where p is a constant determined experimentally. Archie suggested a value of p ⫽ 2; however, other published values of p range from 1.4 to 4.6, depending on the soil and
ELECTRICAL CONDUCTIVITY
269
whether a given saturation is reached by wetting or by drainage. Capillary Model In this and the theoretical models
tance of clayey particles to the total current flow would be small.
that follow, direct current (DC) conductivity is assumed, although they may apply to low-frequency alternating current (AC) models as well. Consider a saturated soil sample of length L and cross-sectional area A. If the pores are assumed to be connected and can be represented by a bundle of tubes of equal radius and length Le and total area Ae, where Ae ⫽ porosity ⫻ A, and Le is the actual length of the flow path, then an equation for the formation factor as a function of the porosity n and the tortuosity T ⫽ Le /L is
Conductive Particle Models
F⫽
T2 n
(9.44) T ⫽ X(W ⫹ s)
For S ⬍ 1, and assuming that the area available for electrical flow is nSA, then F ⫽ T 2 /nS. In principle, if F is measured for a given soil and n is known, a value of tortuosity can be calculated to use in the Kozeny– Carman equation for hydraulic conductivity. Cluster Model As discussed earlier in connection with hydraulic conductivity, the cluster model (Olsen, 1961, 1962) shown in Fig. 9.10 assumes unequal pore sizes. Three possible paths for electrical current flow can be considered: (1) through the intercluster pores, (2) through the intracluster pores, and (3) alternately through inter- and intracluster pores. On this basis the following equations for formation factor as a function of the cluster model parameters can be derived (Olsen, 1961): F ⫽ T2
冉
冊冉 冊
1 ⫹ eT eT ⫺ ec
1 1⫹X
X⫽Y⫹Z Y⫽
冉
ec
冊冉 冊
eT ⫺ ec
(9.45) (9.46)
[(1 ⫹ eT)/(eT ⫺ ec)]2 1 ⫹ (Tc /T)2 [(1 ⫹ ec)2 /ec(eT ⫺ ec)] Z⫽a
In conductive particle models the contribution of the ions concentrated at the surface of negatively charged particles is taken into account. Two simple mixture models are presented below; other models can be found in Santamarina et al. (2001). Two-Parallel-Resistor Model A contribution of surface conductance is included, and the soil–water system is equivalent to two electrical resistors in parallel (Waxman and Smits, 1968). The result is that the total electrical conductivity T is
T Tc
(9.47)
2
(9.48)
in which T is the intercluster tortuosity, Tc is the intracluster tortuosity, and a is the effective cluster ‘‘contact area.’’ The cluster contact area is very small except for heavily consolidated systems. This model successfully describes the flow of current in soils saturated with high conductivity water. In such systems, the contribution of the surface conduc-
(9.49)
in which s is a surface conductivity term, and X is a constant analogous to the reciprocal of the formation factor that represents the internal geometry. This approach yields better fits of T versus W data for clay-bearing soils. However, it assumes a constant value for the contribution of the surface ions that is independent of the electrolyte concentration in the pore water, and it fails to include a contribution for the surface conductance and pore water conductance in a series path. Three-Element Network Model A third path is included in this formulation that considers flow along particle surfaces and through pore water in series in addition to the paths included in the two-parallelresistor model. The flow paths and equivalent electrical circuit are shown in Fig. 9.15. Analysis of the electrical network for determination of T gives T ⫽
aWs ⫹ bs ⫹ cW (1 ⫺ e)W ⫹ es
(9.50)
If the surface conductivity s is negligible, the simple formulation proposed by Archie (1942) for sands is obtained; that is, T ⫽ constant ⫻ W. Some of the geometric parameters a, b, c, d, and e can be written as functions of porosity and degree of saturation; others are obtained through curve regression analysis of T versus W data. Soil conductivity as a function of pore fluid conductivity is shown in Fig. 9.16 for a silty clay. The three-element model fits the data well over the full range, the two-element model gives good predictions for the higher values of conductivity, and the simple formation factor relationship is a reasonable average
270
9
CONDUCTION PHENOMENA
Figure 9.15 Three-element network model for electrical conductivity: (a) current flow paths
and (b) equivalent electrical circuit.
for conductivity values in the range of about 0.3 to 0.6 S/m. Alternating Current Conductivity and Dielectric Constant
The electrical response of a soil in an AC field is frequency dependent owing to the polarizability properties of the system constituents. Several scale-dependent polarization mechanisms are possible in soils, as shown in Fig. 9.17. The smaller the element size the higher the polarization frequency. At the atomic and molecular scales, there are polarizations of electrons [electronic resonance at ultraviolet (UV) frequencies], ions [ionic resonance at infrared (IR) frequencies], and dipolar molecules (orientational relaxation at microwave frequencies). A mixture of components (like water and soil particles) having different polarizabilities and conductivities produces spatial polarization by charge accumulation at interfaces (called Maxwell– Wagner interfacial polarization). The ions in the Stern layer and double layer are restrained (Chapter 6), and hence they also exhibit polarization. This polarization results in relaxation responses at radio frequencies. Further details of the polarization mechanisms are given by Santamarina et al. (2001). The effective AC conductivity eff is expressed as eff ⫽ ⫹ !ⴖ"0
(9.51)
where is the conductivity, !ⴖ is the polarization loss (called the imaginary relative permittivity), " is the
frequency, and 0 is the permittivity of vacuum [8.85 ⫻ 10⫺12 C2 /(Nm2)]. The frequency-dependent effective conductivities of deionized water and kaolinite–water mixtures at two different water contents (0.2 and 33 percent) are shown in Fig. 9.18a. The complicated interactions of different polarization mechanisms are responsible for the variations shown. A material is dielectric if charges are not free to move due to their inertia. Higher frequencies are needed to stop polarization at smaller scales. The dielectric constant (or the real relative permittivity !5) decreases with increasing frequency; more polarization mechanisms occur at lower frequencies. The frequency-dependent dielectric constants of deionized water and kaolinite–water mixtures are shown in Fig. 9.18b. The value for deionized water is about 79 above 10 kHz. Below this frequency, the values increase with decrease in frequency. This is attributed to experimental error caused by an electrode effect in which charges
5 To describe the out-of-phase response under oscillating excitation, the electrical properties of a material are often defined in the complex plane:
⫽ ⫺ jⴖ
where is the complex permittivity, j is the imaginary number (兹⫺1), and and ⴖ are real and imaginary numbers describing the electrical properties. The permittivity is often normalized by the permittivity of vacuum 0 as !⫽
⫽ ! ⫺ j!ⴖ 0
where ! is called the relative permittivity.
ELECTRICAL CONDUCTIVITY
271
100
σeff (S/m)
Deionized Water 10–2 33%
0.2% 10–6 100
106 33%
Figure 9.16 Soil electrical conductivity as a function of pore
fluid conductivity and comparisons with three models.
κ
No Data Available
10–4
102
104 106 Frequency (Hz) (a)
108
1010
Electrode Effect Deionized Water
104 0.2%
No Data Available
102 100
accumulate at the electrode–specimen interface (Klein and Santamarina, 1997). Similarly to the observations made for the effective conductivities, the real permittivity values of the mixtures show complex trends of frequency dependency. For analysis of AC conductivity and dielectric constant as a function of frequency in an AC field, Smith and Arulanandan (1981) modified the three-element model shown in Fig. 9.15 by adding a capacitor in parallel with each resistor. The resulting equations can be fit to experimental frequency dispersions of the con-
100
102
104 106 Frequency (Hz) (b)
108
1010
Figure 9.18 (a) Conductivity and (b) relative permittivity as a function of frequency for deionized water and kaolinite at water contents of 0.2 and 33 percent (from Santamarina et al., 2001).
Figure 9.17 Frequency ranges associated with different polarization mechanisms (from Santamarina et al., 2001).
272
9
CONDUCTION PHENOMENA
ductivity and apparent dielectric constant by computer optimization of geometrical and compositional parameters. The resulting parameter values are useful for characterizing mineralogy, porosity, and fabric. More detailed discussions on electrical models, data interpretation, and correlations with soil properties are given by Santamarina et al. (2001).
9.7
DIFFUSION
Chemical transport through sands is dominated by advection, wherein dissolved and suspended species are carried with flowing water. However, in fine-grained soils, wherein the hydraulic flow rates are very small, for example, kh less than about 1 ⫻ 10⫺9 m/s, chemical diffusion plays a role and may become dominant when kh becomes less than about 1 ⫻ 10⫺10 m/s. Fick’s law, Eq. (9.5), is the controlling relationship, and D(L2T⫺1), the diffusion coefficient, is the controlling parameter. Diffusive chemical transport is important in clay barriers for waste containment, in some geologic processes, and in some forms of chemical soil stabilization. Comprehensive treatments of the diffusion process, values of diffusion coefficients and methods for their determination, and applications, especially in relation to chemical transport and waste containment barrier systems, are given by Quigley et al. (1987), Shackelford and Daniel (1991a, 1991b), Shincariol and Rowe (2001) and Rowe (2001). Diffusive flow is driven by chemical potential gradients, but for most applications chemical concentration gradients can be used for analysis. The diffusion coefficient is measured and expressed in terms of chemical gradients. Maximum values of the diffusion coefficient D0 are found in free aqueous solution at infinite dilution. Self-diffusion coefficients for a number of ion types in water are given in Table 9.3. Usually cation–anion pairs are diffusing together, thereby slowing down the faster and speeding up the slower. This may be seen in Table 9.4, which contains values of some limiting free solution diffusion coefficients for some simple electrolytes. Diffusion through soil is slower and more complex than diffusion through a free solution, especially when adsorptive clay particles are present. There are several reasons for this (Quigley, 1989): 1. Reduced cross-sectional area for flow because of the presence of solids 2. Tortuous flow paths around particles 3. The influences of electrical force fields caused by the double-layer distributions of charges
Table 9.3 Self-Diffusion Coefficients for Ions at Infinite Dilution in Water Anion (1)
D0 ⫻ 1010(m2 /s) (2)
Cation (3)
D0 ⫻ 1010(m2 /s) (4)
OH⫺ F⫺ Cl⫺ Br⫺ I⫺ HCO3⫺ NO3⫺ SO42⫺ CO32⫺ — — — — — — — — — — —
52.8 14.7 20.3 20.8 20.4 11.8 19.0 10.6 9.22 — — — — — — — — — — —
H⫹ Li⫹ Na⫹ K⫹ Rb⫹ Cs⫹ Be2⫹ Mg2⫹ Ca2⫹ Sr2⫹ Ba2⫹ Pb2⫹ Cu2⫹ Fe2⫹a Cd2⫹a Zn2⫹ Ni2⫹a Fe3⫹a Cr3⫹a Al3⫹a
93.1 10.3 13.3 19.6 20.7 20.5 5.98 7.05 7.92 7.90 8.46 9.25 7.13 7.19 7.17 7.02 6.79 6.07 5.94 5.95
a
Values from Li and Gregory (1974). Reprinted with permission from Geochimica et Cosmochimica Acta, Vol. 38, No. 5, pp. 703–714. Copyright 1974, Pergamon Press.
4. Retardation of some species as a result of ion exchange and adsorption by clay minerals and organics or precipitation 5. Biodegradation of diffusing organics 6. Osmotic counterflow 7. Electrical imbalance, possibly by anion exclusion The diffusion coefficient could increase with time of flow through a soil as a result of such processes as (Quigley, 1989): 1. K⫹ fixation by vermiculite, which would decrease the cation exchange capacity and increase the free water pore space 2. Electrical imbalances that act to pull cations or anions 3. The attainment of adsorption equilibrium, thus eliminating retardation of some species In an attempt to take some of these factors, especially geometric tortuosity of interconnected pores, into account, an effective diffusion coefficient D* is
DIFFUSION
transient diffusion, that is, the time rate of change of concentration with distance:
Table 9.4 Limiting Free Solution Diffusion Coefficients for Some Simple Electrolytes D0 ⫻ 1010(m2 /s) (2)
Electrolyte (1) HCl HBr LiCl LiBr NaCl NaBr NaI KCl KBr KI CsCl CaCl2 BaCl2
33.36 34.00 13.66 13.77 16.10 16.25 16.14 19.93 20.16 19.99 20.44 13.35 13.85
Reported by Shackelford and Daniel, 1991a after Robinson and Stokes, 1959. Reprinted from the Journal of Geotechnical Engineering, Vol. 117, No. 3, pp. 467–484. Copyright 1991. With permission of ASCE.
used. Several definitions have been proposed (Shackelford and Daniel, 1991a) in which the different factors are taken into account in different ways. Although these relationships may be useful for analysis of the importance of the factors themselves, it is sufficient for practical purposes to use D* ⫽ a D0
273
(9.52)
in which a is an ‘‘apparent tortuosity factor’’ that takes several of the other factors into account, and use values of D* measured under representative conditions. The effective coefficient for diffusion of different chemicals through saturated soil is usually in the range of about 2 ⫻ 10⫺10 to 2 ⫻ 10⫺9 m2 /s, although the values can be one or more orders of magnitude lower in highly compacted clays and clays, such as bentonite, that can behave as semipermeable membranes (Malusis and Shackelford, 2002b). Values for compacted clays are rather insensitive to molding water content or method of compaction (Shackelford and Daniel, 1991b), in stark contrast to the hydraulic conductivity, which may vary over a few orders of magnitude as a result of changes in these factors. This suggests that soil fabric differences have relatively minor influence on the effective diffusion coefficient. Whereas Fick’s first law, Eq. (9.5), applies for steady-state diffusion, Fick’s second law describes
c 2c ⫽ D* 2 t x
(9.53)
For transient diffusion with constant effective diffusion coefficient D*, the solution for this equation is of exactly the same form as that for the Terzaghi equation for clay consolidation and that for one-dimensional transient heat flow. An error function solution for Eq. (9.53) (Ogata, 1970; Freeze and Cherry, 1979), for the case of onedimensional diffusion from a layer at a constant source concentration C0 into a layer having a sufficiently low initial concentration that it can be taken as zero at t ⫽ 0, is C x x ⫽ erfc ⫽ 1 ⫺ erf C0 2兹D*t 2兹D*t
(9.54)
where C is the concentration at any time at distance ⫻ from the source. Curves of relative concentration as a function of depth for different times after the start of chloride diffusion are shown in Fig. 9.19a (Quigley, 1989). An effective diffusion coefficient for chloride of 6.47 ⫻ 10⫺10 m2 /s was assumed. Also shown (Fig. 9.19b) is the migration velocity of the C/C0 front within the soil as a function of time. As chloride is one of the more rapidly diffusing ionic species, Fig. 9.19 provides a basis for estimating maximum probable migration distances and concentrations as a function of time that result solely from diffusion. When there are adsorption–desorption reactions, chemical reactions such as precipitation–solution, radioactive decay, and/or biological processes occurring during diffusion, the analysis becomes more complex than given by the foregoing equations. For adsorption– desorption reactions and the assumption that there is linearity between the amount adsorbed and the equilibrium concentration, Eq. (9.53) is often written as c D* 2c ⫽ t Rd x2
(9.55)
where Rd is termed the retardation factor, and it is defined by Rd ⫽ 1 ⫹
d K d
(9.56)
in which d is the bulk dry density of the soil, is the
274
9
CONDUCTION PHENOMENA
tailed discussions of distribution coefficients and their determination are given by Freeze and Cherry (1979), Quigley et al., (1987), Quigley (1989), and Shackelford and Daniel (1991a, b).
9.8 TYPICAL RANGES OF FLOW PARAMETERS
Usual ranges for the values of the direct flow conductivities for hydraulic, thermal, electrical, and diffusive chemical flows are given in Table 9.5. These ranges are for fine-grained soils, that is, silts, silty clays, clayey silts, and clays. They are for full saturation; values for partly saturated soils can be much lower. Also listed in Table 9.5 are values for electroosmotic conductivity, osmotic efficiency, and ionic mobility. These properties are needed for analysis of coupling of hydraulic, electrical, and chemical flows, and they are discussed further later.
9.9 SIMULTANEOUS FLOWS OF WATER, CURRENT, AND SALTS THROUGH SOIL-COUPLED FLOWS
Figure 9.19 Time rate of chloride diffusion (from Quigley,
1989). (a) Relative concentration as a function of depth after different times and (b) velocity of migration of the front having a concentration C / C0 of 0.5.
volumetric water content, that is, the volume of water divided by the total volume (porosity in the case of a saturated soil), and Kd is the distribution coefficient. The distribution coefficient defines the amount of a given constituent that is adsorbed or desorbed by a soil for a unit increase or decrease in the equilibrium concentration in solution. Other reactions influencing the amount in free solution relative to that fixed in the soil (e.g., by precipitation) may be included in Kd, depending on the method for measurement and the conditions being modeled. Distribution coefficients are usually determined from adsorption isotherms, and they may be constants for a given soil–chemical system or vary with concentration, pH, and temperature. More de-
Usually there are simultaneous flows of different types through soils and rocks, even when only one type of driving force is acting. For example, when pore water containing chemicals flows under the action of a hydraulic gradient, there is a concurrent flow of chemical through the soil. This type of chemical transport is termed advection. In addition, owing to the existence of surface charges on soil particles, especially clays, there are nonuniform distributions of cations and anions within soil pores resulting from the attraction of cations to and repulsion of anions from the negatively charged particle surfaces. The net negativity of clay particles is caused primarily by isomorphous substitutions within the crystal structure, as discussed in Chapter 3, and the ionic distributions in the pore fluid are described in Chapter 6. Because of the small pore sizes in fine-grained soils and the strong local electrical fields, clay layers exhibit membrane properties. This means that the passage of certain ions and molecules through the clay may be restricted in part or in full at both microscopic and macroscopic levels. Owing to these internal nonhomogeneities in ion distributions, restrictions on ion movements caused by electrostatic attractions and repulsions, and the dependence of these interactions on temperature, a variety of microscopic and macroscopic effects may be observed when a wet soil mass is subjected to flow
SIMULTANEOUS FLOWS OF WATER, CURRENT, AND SALTS THROUGH SOIL-COUPLED FLOWS
Table 9.5
275
Typical Range of Flow Parameters for Fine-Grained Soilsa
Parameter
Symbol
Units
Minimum
Maximum
Porosity Hydraulic conductivity Thermal conductivity Electrical conductivity Electro osmotic conductivity Diffusion coefficient Osmotic efficiencyb Ionic mobility
n kh
— m s⫺1
0.1 1 ⫻ 10⫺11
0.7 1 ⫻ 10⫺6
kt
W m⫺1 K⫺1
0.25
2.5
e
siemens m⫺1
0.01
1.0
ke
m2 s⫺1 V⫺1
1 ⫻ 10⫺9
1 ⫻ 10⫺8
D
m2 s⫺1
2 ⫻ 10⫺10
2 ⫻ 10⫺9
—
0
1.0
m2 s⫺1 V⫺1
3 ⫻ 10⫺9
1 ⫻ 10⫺8
"
u
a
The above values of flow coefficients are for saturated soil. They may be much less in partly saturated soil. b 0 to 1.0 is the theoretical range for the osmotic efficiency coefficient. Values greater than about 0.7 are unlikely in most fine-grained materials of geotechnical interest.
gradients of different types. A gradient of one type Xj can cause a flow of another type Ji, according to Ji ⫽ Lij Xj
(9.57)
The Lij are termed coupling coefficients. They are properties that may or may not be of significant magnitude in any given soil, as discussed later. Types of coupled flow that can occur are listed in Table 9.6, along with terms commonly used to describe them.6 Of the 12 coupled flows shown in Table 9.6, several are known to be significant in soil–water systems, at least under some conditions. Thermoosmosis, which is water movement under a temperature gradient, is important in partly saturated soils, but of lesser importance in fully saturated soils. Significant effects from thermally driven moisture flow are found in semiarid and arid areas, in frost susceptible soils, and in expansive soils. An analysis of thermally driven moisture
6
Mechanical coupling also occurs in addition to the hydraulic, thermal, electrical, and chemical processes listed in Table 9.6. A common manifestation of this in geotechnical applications is the development of excess pore pressure and the accompanying fluid flow that result from a change in applied stress. This type of coupling is usually most easily handled by usual soil mechanics methods. A few other types of mechanical coupling may also exist in soils and rocks (U.S. National Committee for Rock Mechanics, 1987).
flow is developed later. Electroosmosis has been used for many years as a means for control of water flow and for consolidation of soils. Chemicalosmosis, the flow of water caused by a chemical gradient acting across a clay layer, has been studied in some detail recently, owing to its importance in waste containment systems. Isothermal heat transfer, caused by heat flow along with water flow, has caused great difficulties in the creation of frozen soil barriers in the presence of flowing groundwater. Electrically driven heat flow, the Peltier effect, and chemically driven heat flow, the Dufour effect, are not known to be of significance in soils; however, they appear not to have been studied in any detail in relation to geotechnical problems. Streaming current, the term applied to both hydraulically driven electrical current and ion flows, has importance to both chemical flow through the ground (advection) and the development of electrical potentials, which may, in turn, influence both fluid and ion flows as a result of additional coupling effects. The complete roles of thermoelectricity and diffusion and membrane potentials are not yet known; however, electrical potentials generated by temperature and chemical gradients are important in corrosion and in some groundwater flow and stability problems. Whether thermal diffusion of electrolytes, the Soret effect, is important in soils has not been evaluated;
276
9
Table 9.6
CONDUCTION PHENOMENA
Direct and Coupled Flow Phenomena Gradient X
Flow J
Hydraulic Head
Fluid
Heat
Current
Ion
Temperature
H
L
Chemical Concentration
Hydraulic conduction Darcy’s law Isothermal heat transfer or thermal filtration Streaming current
Thermoosmosis
Electroosmosis
Chemical osmosis
Thermal conduction Fourier’s law Thermoelectricity Seebeck or Thompson effect
Peltier effect
Dufour effect
Electric conduction Ohm’s law
Streaming current ultrafiltration (also known as hyperfiltration)
Thermal diffusion of electrolyte or Soret effect
Electrophoresis
Diffusion and membrane potentials or sedimentation current Diffusion Fick’s law
however, since chemical activity is highly temperature dependent, it may be a significant process in some systems. Finally, electrophoresis, the movement of charged particles in an electrical field, has been used for concentration of mine waste and high water content clays. The relative importance of chemically and electrically driven components of total hydraulic flow is illustrated in Fig. 9.20, based on data from tests on kaolinite given by Olsen (1969, 1972). The theory for description of coupled flows is given later. A practical form of Eq. (9.57) for fluid flow under combined hydraulic, chemical, and electrical gradients is qh ⫽ ⫺kh
Electrical
A ⫹ kc
log(CB /CA)
E A ⫺ ke A (9.58) L L
in which kh, kc, and ke are the hydraulic, osmotic, and electroosmotic conductivities, H is the hydraulic head difference, E is the voltage difference, and CA and CB are the salt concentrations on opposite sides of a clay layer of thickness L. In the absence of an electrical gradient, the ratio of osmotic to hydraulic flows is
冉冊
qhc k log(CB /CA) ⫽⫺ c qh kh
H
( E ⫽ 0)
(9.59)
and, in the absence of a chemical gradient, the ratio of electroosmotic flows to hydraulic flows is
冉冊
qhe ke E ⫽ qh kh H
( C ⫽ 0)
(9.59a)
The ratio (kc /kh) in Fig. 9.20 indicates the hydraulic head difference in centimeters of water required to give a flow rate equal to the osmotic flow caused by a 10fold difference in salt concentration on opposite sides of the layer. The ratio ke /kh gives the hydraulic head difference required to balance that caused by a 1 V difference in electrical potentials on opposite sides of the layer. During consolidation, the hydraulic conductivity decreases dramatically. However, the ratios kc /kh and ke /kh increase significantly, indicating that the relative importance of osmotic and electroosmotic flows to the total flow increases. Although the data shown in Fig. 9.20 are shown as a function of the consolidation pressure, the changes in the values of kc /kh and ke /kh are really a result of the decrease in void ratio that accompanies the increase in pressure, as may be seen in Fig. 9.20c. These results for kaolinite provide a conservative estimate of the importance of osmotic and electroosmotic flows because coupling effects in kaolinite are usually smaller than in more active clays, such as montmorillonite-based bentonites. In systems containing confined clay layers acted on by chemical and/or electrical gradients, Darcy’s law by itself may be an insufficient basis for prediction of hydraulic flow rates, particularly if the clay is highly plastic and at a very low void ratio. Such conditions can be found in deeply buried clay
QUANTIFICATION OF COUPLED FLOWS
277
Figure 9.20 Hydraulic, osmotic, and electroosmotic conductivities of kaolinite (data from
Olsen 1969, 1972): (a) consolidation curve, (b) conductivity values, and (c) conductivities as a function of void ratio.
and clay shale and in densely compacted clays. For more compressible clays, the ratios kc /kh and ke /kh may be sufficiently high to be useful for consolidation by electrical and chemical means, as discussed later in this chapter.
9.10
QUANTIFICATION OF COUPLED FLOWS
Quantification of coupled flow processes may be done by direct, empirical determination of the relevant parameters for a particular case or by relationships derived from a theoretical thermodynamic analysis of the complete set of direct and coupled flow equations.
Each approach has advantages and limitations. It is assumed in the following that the soil properties remain unchanged during the flow processes, an assumption that may not be justified in some cases. The effects of flows of different types on the state and properties of a soil are discussed later in this chapter. However, when properties are known to vary in a predictable manner, their variations may be taken into account in numerical analysis methods. Direct Observational Approach
In the general case, there may be fluid, chemical, electrical, and heat flows. The chemical flows can be sub-
278
9
CONDUCTION PHENOMENA
divided according to the particular chemical species present. Each flow type may have contributions caused by gradients of another type, and their importance depends on the values of Lij and Xj in Eq. (9.57). A complete and accurate description of all flows may be a formidable task. However, in many cases, flows of only one or two types may be of interest, some of the gradients may not exist, and/or some of the coupling coefficients may be either known or assumed to be unimportant. The matrix of flows and forces then reduces significantly, and the determination of coefficients is greatly simplified. For example, if simple electroosmosis under isothermal conditions is considered, then Eq. (9.57) yields qw ⫽ LHH (⫺H) ⫹ LHE (⫺E) ⫹ LHC (⫺C)
(9.60)
I ⫽ LEH (⫺H) ⫹ LEE (⫺E) ⫹ LEC (⫺C)
(9.61)
JC ⫽ LCH (⫺H) ⫹ LCE (⫺E) ⫹ LCC (⫺C)
(9.62)
where qw I Jc H E C Lij
⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽
water flow rate electrical current chemical flow rate hydraulic head electrical potential chemical concentration coupling coefficients; the first subscript indicates the flow type and the second denotes the type of driving force
If there are no chemical concentration differences across the system, then the last terms on the right-hand side of Eqs. (9.60), (9.61), and (9.62) do not exist. In this case, Eqs. (9.60) and (9.61) become, when written in more familiar terms, qw ⫽ khih ⫹ keie I ⫽ hih ⫹ eie
(9.63) (9.64)
where kh ⫽ hydraulic conductivity ke ⫽ electroosmotic hydraulic conductivity h ⫽ electrical conductivity due to hydraulic flow e ⫽ electrical conductivity ih ⫽ hydraulic gradient ie ⫽ electrical potential gradient If permeability tests are done in the absence of an electrical potential difference, then the hydraulic con-
ductivity coefficient kh is readily determined.7 The coefficient of electroosmotic hydraulic conductivity is usually determined by measuring the hydraulic flow rate developed in a known DC potential field under conditions of ih ⫽ 0. The electrical conductivity e is obtained from the same experiment through measurement of the electrical current. The main advantage of this empirical, but direct, approach is simplicity. It is particularly useful when only a few of the possible couplings are likely to be important and when some uncertainty in the measured coefficients is acceptable. General Theory for Coupled Flows
When several flows are of interest, each resulting from several gradients, a more formal methodology is necessary so that all relevant factors are accounted for properly. If there are n different driving forces, then there will be n direct flow coefficients Lii and n(n ⫺ 1) coupling coefficients Lij(i ⫽ j). The determination of these coefficients is best done within a framework that provides a consistent and correct description of each of the flows. Irreversible thermodynamics, also termed nonequilibrium thermodynamics, offers a basis for such a description. Furthermore, if the terms are properly formulated, then Onsager’s reciprocal relations apply, that is, Lij ⫽ Lji
(9.65)
and the number of coefficients to be determined is significantly reduced. In addition, the derived forms for the coupling coefficients, when cast in terms of measurable and understood properties, provide a basis for rapid assessment of their importance. The theory of irreversible thermodynamics as applied to transport processes in soils is only outlined here. More comprehensive treatments are given by DeGroot and Mazur (1962), Fitts (1962), Katchalsky and Curran (1967), Greenberg, et al. (1973), Yeung and Mitchell (1992), and Malusis and Shackelford (2002a). Irreversible thermodynamics is a phenomenological, macroscopic theory that provides a basis for descrip-
7 Note that unless the ends of the sample are short circuited to prevent the development of a streaming potential, there will be a small electroosmotic counterflow contributed by the keie term in Eq. (9.63). Streaming potentials may be up to a few tens of millivolts in soils. Streaming potential is one of four types of electrokinetic phenomena that may exist in soils, as discussed in more detail in Section 9.16.
SIMULTANEOUS FLOWS OF WATER, CURRENT, AND CHEMICALS
tion of systems that are out of equilibrium. It is based on three postulates, namely,
in the formulation of the flow equations. And # is also the sum of products of fluxes and driving forces:
1. Local equilibrium, a criterion that is satisfied if local perturbations are not large. 2. Linear phenomenological equations, that is,
冘L X n
Ji ⫽
ij
j
( j ⫽ 1,2, . . . , n)
(9.66)
j⫽1
3. Validity of the Onsager reciprocal relations, a condition that is satisfied if the Ji and Xj are formulated properly (Onsager, 1931a, 1931b). Experimental verification of the Onsager reciprocity for many systems and processes has been obtained and is summarized by Miller (1960). Both the driving forces and flows vanish in systems that are in equilibrium, so the deviations of thermodynamic variables from their equilibrium values provide a suitable basis for their formulation. The deviations of the state parameters Ai from equilibrium are given by i ⫽ Ai ⫺ A 0i
(9.67)
where A 0i is the value of the state parameter at equilibrium and Ai is its value in the disturbed state. Criteria for deriving the forces and flows are then developed on the basis of the second law of thermodynamics, which states that at equilibrium, the entropy S is a maximum, and i ⫽ 0. The change in entropy
S that results from a change in state parameter gives the tendency for a variable to change. Thus S/ i is a measure of the force causing i to change, and is called Xi. The flows Ji, termed fluxes in irreversible thermodynamics, are given by i / t, the time derivative of i. On this basis, the resulting entropy production per unit time becomes ⫽
dS ⫽ dt
冘JX
279
冘JX n
#⫽
i
i
(9.69)
i⫽1
The units of # are energy per unit time, and it is a measure of the rate of local free energy dissipation by irreversible processes. Application of the thermodynamic theory of irreversible processes requires the following steps: 1. Finding the dissipation function # for the flows 2. Defining the conjugated flows Ji and driving forces Xi from Eq. (9.69) 3. Formulating the phenomenological equations in the form of Eq. (9.66) 4. Applying the Onsager reciprocal relations 5. Relating the phenomenological coefficients to measurable quantities When the Onsager reciprocity is used, the number of independent coefficients Lij reduces from n2 to [(n ⫹ 1)n]/2. Application
The quantitative analysis and prediction of flows through soils, for a given set of boundary conditions, depends on the values of the various phenomenological coefficients in the above flow equations. Unfortunately, these are not always known with certainty, and they may vary over wide ranges, even within an apparently homogeneous soil mass. The direct flow coefficients, that is, the hydraulic, electrical, and thermal conductivities, and the diffusion coefficient, exhibit the greatest ranges of values. Thus, it is important to examine these properties first before detailed analysis of coupled flow contributions. For many problems, it may be sufficient to consider only the direct flows, provided the factors influencing their values are fully appreciated.
n
i
i
(9.68)
i⫽1
The entropy production can be related explicitly to various irreversible processes in terms of proper forces and fluxes (Gray, 1966; Yeung and Mitchell, 1992). If the choices satisfy Eq. (9.68), then the Onsager reciprocity relations apply. It has been found more useful to use # ⫽ T, the dissipation function, in which T is temperature, than
9.11 SIMULTANEOUS FLOWS OF WATER, CURRENT, AND CHEMICALS
Use of irreversible thermodynamics for the description of coupled flows as developed above is straightforward in principle; however, it becomes progressively more difficult in application as the numbers of driving forces and different flow types increase. This is because of (1) the need for proper specification of the different coupling coefficients and (2) the need for independent
280
9
CONDUCTION PHENOMENA
methods for their measurement. Thus, the analysis of coupled hydraulic and electrical flows or of coupled hydraulic and chemical flows is much simpler than the analysis of a system subjected to electrical, chemical, and hydraulic gradients simultaneously. Relationships for the volume flow rate of water for several cases and for thermoelectric and thermoosmotic coupling in saturated soils are given by Gray (1966, 1969). The simultaneous flows of liquid and charge in kaolinite and the fluid volume flow rates under hydraulic, electric, and chemical gradients were studied by Olsen (1969, 1972). The theory for coupled salt and water flows was developed by Greenberg (1971) and applied to flows in a groundwater basin (Greenberg et al., 1973) and to chemicoosmotic consolidation of clay (Mitchell et al., 1973). Equations for the simultaneous flows of water, electricity, cations, and anions under hydraulic, electrical, and chemical gradients were formulated by Yeung (1990) using the formalism of irreversible thermodynamics as outlined previously. The detailed development is given by Yeung and Mitchell (1993). The results are given here. The chemical flow is separated into its anionic and cationic components in order to permit determination of their separate movements as a function of time. This separation may be important in some problems, such as chemical transport through the ground, where the fate of a particular ionic species, a heavy metal, for example, is of interest. The analysis applies to an initially homogeneous soil mass that separates solutions of different concentrations of anions and cations, at different electrical potentials and under different hydraulic heads, as shown schematically in Fig. 9.21. Only one anion and one cation species are assumed to be present, and no adsorption or desorption reactions are occurring. The driving forces are the hydraulic gradient (⫺P), the electrical gradient (⫺E), and the concentrationdependent parts of the chemical potential gradients of the cation (cc) and of the anion (ca). The fluxes are the volume flow rate of the solution per unit area Jv, the electric current I, and the diffusion flow rates of the cation Jdc and the anion Jda per unit area relative to the flow of water. These diffusion flows are related to the absolute flows according to
Figure 9.21 Schematic diagram of system for analysis of
simultaneous flows of water, electricity, and ions through a soil.
Jv ⫽ L11 (⫺P) ⫹ L12 (⫺E) ⫹ L13 (⫺cc) ⫹ L14 (⫺ca)
(9.71)
I ⫽ L21 (⫺P) ⫹ L22 (⫺E) ⫹ L23 (⫺cc) ⫹ L24(⫺ca)
(9.72)
Jcd ⫽ L31 (⫺P) ⫹ L32 (⫺E) ⫹ L33 (⫺cc) ⫹ L34 (⫺ca)
(9.73)
Jad ⫽ L41 (⫺P) ⫹ L42 (⫺E) ⫹ L43 (⫺cc) ⫹ L44 (⫺ca)
(9.74)
These equations contain 4 conductivity coefficients Lii and 12 coupling coefficients Lij. As a result of Onsager reciprocity, however, the number of independent coupling coefficients reduces because L12 ⫽ L21 L13 ⫽ L31 L14 ⫽ L41 L23 ⫽ L32
Ji ⫽ Jid ⫹ ci Jv
(9.70)
L24 ⫽ L42 L34 ⫽ L43
in which ci is the concentration of ion i. The set of phenomenological equations that relates the four flows and driving forces is
Thus there are 10 independent coefficients needed for a full description of hydraulic, electrical, anionic,
281
SIMULTANEOUS FLOWS OF WATER, CURRENT, AND CHEMICALS
and cationic flows through a system subjected to hydraulic, electrical, and chemical gradients. If three of the four forces can be set equal to zero during a measurement of the flow under the fourth force, then the ratio of the flow rate to that force will give the value of its corresponding Lij. However, such measurements are not always possible or convenient. Accordingly, two forces and one flow are usually set to zero and the appropriate Lij are evaluated by solution of simultaneous equations. For measurements of hydraulic conductivity, electroosmotic hydraulic conductivity, electrical conductivity, osmotic efficiency, and effective diffusion coefficients done in the usual manner in geotechnical and chemical laboratories, the detailed application of irreversible thermodynamic theory led Yeung (1990) and Yeung and Mitchell (1993) to the following definitions for the Lij. It was assumed in the derivations that the solution is dilute and there are no interactions between cations and anions.8 k L L L11 ⫽ h ⫹ 12 21 wn L22
L13 ⫽ L31 ⫽
⫺"cckh L L ⫹ 12 23 wn L22
(9.77)
L14 ⫽ L41 ⫽
⫺"cakh L L ⫹ 12 24 wn L22
(9.78) (9.79)
L23 ⫽ L32 ⫽ ccu* c
(9.80)
L24 ⫽ L42 ⫽ ⫺cau*a
(9.81)
D* c cc RT
(9.82)
L34 ⫽ L43 ⫽ 0 L44 ⫽
D* a ca RT
冋 冋
(9.84)
The Lij coefficients in Eqs. (9.75) to (9.84) were derived in terms of the cross-sectional area of the soil voids. They may be redefined in terms of the total cross-sectional area by multiplying each term on the right-hand side by the porosity, n.
(1 ⫺ ")D* c k"2 c ⫹ c RT wn
册 册
(1 ⫺ ")D* c k"2 a ⫹ a RT wn
(9.85) (9.86)
This modification becomes important in clays wherein osmotic efficiency, that is, the ability of the clay to restrict the flow of ions, is high. As the flows of ions relative to the soil are of more interest than relative to the water, Eq. (9.70) and Eqs. (9.73) and (9.74) can be combined to give Jc ⫽ (L31 ⫹ ccL11) w (⫺h) ⫹ (L32 ⫹ ccL12) (⫺E) ⫹ (L33 ⫹ ccL13)
RT (⫺cc) cc
⫹ (L34 ⫹ ccL14)
RT (⫺ca) ca
(9.83)
where kh ⫽ hydraulic conductivity as usually measured (no electrical short circuiting) ke ⫽ coefficient of electroosmotic hydraulic conductivity 8
Subsequently, Manassero and Dominijanni (2003) pointed out that the practical equations for diffusion L33 and L44 do not take the osmotic efficiency " (Section 9.13) into account, so Eqs. (9.82) and (9.84) more properly should be
L44 ⫽ ca
(9.76)
L33 ⫽
bulk electrical conductivity of the soil coefficient of osmotic efficiency unit weight of water concentration of cation concentration of anion effective ionic mobility of the cation effective ionic mobility of the anion effective diffusion coefficient of the cation effective diffusion coefficient of the anion soil porosity universal gas constant (8.314 J K⫺1 mol⫺1) absolute temperature (K)
(9.75)
ke n
e n
⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽
L33 ⫽ cc
L12 ⫽ L21 ⫽
L22 ⫽
e " w cc ca u* c u* a D* c D* a n R T
(9.87)
Ja ⫽ (L41 ⫹ caL11) w (⫺h) ⫹ (L42 ⫹ caL12) (⫺E) ⫹ (L43 ⫹ caL13)
RT (⫺cc) cc
⫹ (L44 ⫹ caL14)
RT (⫺ca) ca
(9.88)
where (⫺h) is the hydraulic gradient. In Eqs. (9.87) and (9.88) the gradient of the chemical potential has been replaced by the gradient of the concentration according to
282
9
CONDUCTION PHENOMENA
(⫺ci ) ⫽
RT (⫺ci) ci
(9.89)
These equations reduce to the known solutions for special cases such as chemical diffusion, advection– dispersion, osmotic pressure according to the van’t Hoff equation [see Eq. (9.98)], osmosis, and ultrafiltration. They predict reasonably well the distribution of single cations and anions as a function of time and position in compacted clay during the simultaneous application of hydraulic, electrical, and chemical gradients (Mitchell and Yeung, 1990). The analysis of multicomponent systems is more complex. The use of averaged chemical properties and the assumption of composite single species of anions and cations may yield reasonable approximate solutions in some cases. Malusis and Shackelford (2002a) present a more general theory for coupled chemical and hydraulic flow, based on an extension of the Yeung and Mitchell (1993) formulation, which accounts for multicomponent pore fluids and ion exchange processes occurring during transport.9 The flow equations can be incorporated into numerical models for the solution of transient flow problems. Conservation of mass of species i requires that ci ⫽ ⫺ Ji ⫺ Gi t
(9.90)
in which Gi is a source–sink term describing the addition or removal rate of species i from the solution. As commonly used in groundwater flow analyses of contaminant transport, Gi is given by
冋
Gi ⫽ 1 ⫹
册
Kd Kd ci ici ⫹ n n t
(9.90a)
where i is the decay constant of species i, is the bulk dry density of the soil, Kd is the distribution coefficient, and n is the soil porosity. As defined previously, the distribution constant is the ratio of the amount of chemical adsorbed on the soil to that in solution. The quantity in the brackets on the right-hand side of Eq. (9.90) is the retardation factor Rd defined by Eq. (9.56). Advection rather than diffusion is the dominant chemical transport mechanism in coarse-grained soils.
At the pore scale level, the fluid particles carrying dissolved chemicals move at different speeds because of tortuous flow paths around the soil grains and variable velocity distribution in the pores, ranging from zero at the soil particle surfaces to a maximum along the centerline of the pore. This results in hydrodynamic dispersion and a zone of mixing rather than a sharp boundary between two flowing solutions of different concentrations. Mathematically, this is accounted for by adding a dispersion term to the diffusion coefficient in the L33 and L44 terms to account for the deviation of actual motion of fluid particles from the overall or average movement described by Darcy’s law. More details can be found in groundwater and contamination textbooks such as Freeze and Cherry (1979) and Dominico and Schwartz (1997). Numerical models are available for groundwater flow and contaminant transport into which the above flow equations can be introduced (e.g., Anderson and Woessner, 1992; Zheng and Bennett, 2002). The most widely used groundwater flow numerical code is MODFLOW developed by the United States Geological Survey (USGS); various updated versions are available (e.g., Harbaugh et al., 2000). To solve single-species contaminant transport problems in groundwater, MT3DMS (Zheng and Wang, 1999) can be used. The code utilizes the flow solutions from MODFLOW. More complex multispecies reactions can be simulated by RT3D (Clement, 1997). POLLUTE (Rowe and Booker, 1997) provides ‘‘one- and onehalf-dimensional’’ solution to the advection–dispersion equation and is widely used in landfill design. A variety of public domain groundwater flow and contaminant transport codes is available from the web sites of the USGS, the U.S. Environmental Protection Agency (U.S. EPA), and the U.S. Salinity Laboratory.
9.12
ELECTROKINETIC PHENOMENA
Coupling between electrical and hydraulic flows and gradients can generate four related electrokinetic phenomena in materials such as fine-grained soils, where there are charged particles balanced by mobile countercharges. Each involves relative movements of electricity, charged surfaces, and liquid phases, as shown schematically in Fig. 9.22. Electroosmosis
9
Malusis and Shackelford (2002a) defined parameters in terms of the total cross-sectional area for flow rather than the cross-sectional area of voids as used in the development of Eqs. (9.75) through (9.84).
When an electrical potential is applied across a wet soil mass, cations are attracted to the cathode and anions to the anode (Fig. 9.22a). As ions migrate, they
ELECTROKINETIC PHENOMENA
283
Figure 9.22 Electrokinetic phenomena: (a) electroosmosis, (b) streaming potential, (c) elec-
trophoresis, and (d) migration or sedimentation potential.
carry their water of hydration and exert a viscous drag on the water around them. Since there are more mobile cations than anions in a soil containing negatively charged clay particles, there is a net water flow toward the cathode. This flow is termed electroosmosis, and its magnitude depends on ke, the coefficient of electroosmotic hydraulic conductivity and the voltage gradient, as considered in more detail later. Streaming Potential
When water flows through a soil under a hydraulic gradient (Fig. 9.22b), double-layer charges are displaced in the direction of flow. This generates an electrical potential difference that is proportional to the hydraulic flow rate, called the streaming potential, between the opposite ends of the soil mass. Streaming potentials up to several tens of millivolts have been measured in clays. Electrophoresis
If a DC field is placed across a colloidal suspension, charged particles are attracted electrostatically to one
of the electrodes and repelled from the other. Negatively charged clay particles move toward the anode as shown in Fig. 9.22c. This is called electrophoresis. Electrophoresis involves discrete particle transport through water; electroosmosis involves water transport through a continuous soil particle network. Migration or Sedimentation Potential
The movement of charged particles such as clay relative to a solution, as during gravitational settling, for example, generates a potential difference, as shown in Fig. 9.22d. This is caused by the viscous drag of the water that retards the movement of the diffuse layer cations relative to the particles. Of the four electrokinetic phenomena, electroosmosis has been given the most attention in geotechnical engineering because of its practical value for transporting water in fine-grained soils. It has been used for dewatering, soft ground consolidation, grout injection, and the containment and extraction of chemicals in the ground. These applications are considered in a later section.
284
9
CONDUCTION PHENOMENA
9.13 TRANSPORT COEFFICIENTS AND THE IMPORTANCE OF COUPLED FLOWS
To assess conditions where coupled chemical, electrical, and hydraulic flows will be significant relative to direct flows, it is necessary to know the values of the Lij relative to the Lii. Estimates can be made by considering the probable values of the soil state parameters and the several flow and transport coefficients given in Eqs. (9.75) to (9.84). Typical ranges are given in Table 9.5. In Table 9.5 the diffusion coefficients and ionic mobilities for cations and anions are considered together since they lie within similar ranges for most species. Values of ionic mobility for specific ions in dilute solution are given in standard chemical references, for example, Dean (1973), and values of diffusion coefficients are given in Tables 9.3 and 9.4. Ionic mobility is related to the diffusion coefficient according to ui ⫽
Di兩zi兩F RT
(9.91)
in which zi is the ionic valence and F is Faraday’s constant. Similarly to the diffusion coefficients, the ionic mobilities are considerably less in a soil than in a free solution, especially in a fine-grained soil. The importance of coupled flows to fluid, electrical current, and chemical transport through soil under different conditions can be examined by study of the contributions of the different terms in Eqs. (9.71), (9.72), (9.87), and (9.88). For this purpose, the equations have been rewritten in one-dimensional form and in terms of the hydraulic, electrical, and chemical concentration gradients: ih ⫽ ⫺dh/dx, ie ⫽ ⫺dV/dx, and ic ⫽ ⫺dc/ dx, respectively. In addition, the chemical flows have been represented by a single equation. This assumes that all dissolved species are moving together. Terms involving the ionic mobility u do not exist in such a formulation because the cations and anions move together, with the effects of electrical fields assumed to accelerate the slower moving ions and to retard the faster moving ions. Thus there is no net transfer of electric charge due to ionic movement. The Lij coefficients have been replaced by the physical and chemical quantities that determine them, as given by Eqs. (9.74) through (9.85). The resulting equations are the following. For fluid flow: Jv ⫽
冋
册 冋册
冋
册
kh k2 k "kh ⫹ e w ih ⫹ e ie ⫹ RT ⫺ i n en n wn c
I⫽
冋 册 冋册
e ke w ih ⫹ i n n e
(9.93)
For chemical flow relative to the soil: Jc ⫽
冋
册 冋 册 冋 册
(1 ⫺ ")ckh ck2e w cke ⫹ ih ⫹ i n ne n e ⫹
D* ⫺
"ckh RT ic n w
(9.94)
Coupling Influences on Hydraulic Flow
In the absence of applied electrical and chemical gradients, flow under a hydraulic gradient is given by the first bracketed term on the right-hand side of Eq. (9.92). It contains the quantity k2e w /ne, which compensates for the electroosmotic counterflow generated by the streaming potential, which causes the measured value of kh to be slightly less than the true value of L11. As it is not usual practice to short-circuit between the ends of samples during hydraulic conductivity testing, the second bracketed term on the right-hand side of Eq. (9.92) is not zero. This term represents an electroosmotic counterflow that results from the streaming potential and acts in the direction opposite to the hydraulically driven flow. Analysis based on the values of properties in Table 9.5, as well as the results of measurements, for example, Michaels and Lin (1954) and Olsen (1962) show that this counterflow is negligible in most cases, but it may become significant relative to the true hydraulic conductivity for soils of very low hydraulic conductivity, for example, kh ⬍ 1 ⫻ 10⫺10 m/s. For example, for a value of ke of 5 ⫻ 10⫺9 m2 /s-V, an electrical conductivity of 0.01 mho/m, and a porosity of 35 percent, the counterflow term is 0.7 ⫻ 10⫺10 m/s. In the presence of an applied DC field the second bracketed term on the right-hand side of Eq. (9.92) can be very large relative to hydraulic flow in soils finer than silts, as ke, which typically ranges within only narrow limits, is large relative to kh; that is, kh is less than 1 ⫻ 10⫺8 m/s in these soils. The relative effectiveness of hydraulic and electrical driving forces for water movement can be assessed by comparing gradients needed to give equal flow rates. They will be equal if keie ⫽ khih
(9.95)
(9.92) For electrical current flow:
The hydraulic gradient required to balance the electroosmotic flow then becomes
TRANSPORT COEFFICIENTS AND THE IMPORTANCE OF COUPLED FLOWS
ih ⫽
ke i kh e
(9.96)
As the hydraulic conductivity of soils in which electroosmosis is likely to be used is usually of the order of 1 ⫻ 10⫺9 m/s or less, whereas ke is in the range of 1 ⫻ 10⫺9 to 1 ⫻ 10⫺8 m2 /s V, it follows that even small electrical gradients can balance flows caused by large hydraulic gradients. Because of this, and because ke is insensitive to particle size while kh decreases rapidly with decreasing particle size, electroosmosis is effective in fine-grained soils, as discussed further in Section 9.15. Chemically driven hydraulic flow is given by the last term on the right-hand side of Eq. (9.92). It depends primarily on the osmotic efficiency ". Osmotic efficiency has an important influence on the movement of chemicals through a soil, the development of osmotic pressure, and the effectiveness of clay barriers for chemical waste containment. Osmotic Efficiency The osmotic efficiency of clay, a slurry wall, a geosynthetic clay liner (GCL), or other seepage and containment barrier is a measure of the material’s effectiveness in causing hydraulic flow under an osmotic pressure gradient and of its ability to act as a semipermeable membrane in preventing the passage of ions, while allowing the passage of water. The osmotic pressure concept can be better appreciated by rewriting the last term in Eq. (9.92): "
kh k RT c 1 RTic ⫽ " h wn n w x
(9.97)
This form is analogous to Darcy’s law, with the quantity RT c/ w being the head difference. The osmotic efficiency is a measure of the extent to which this theoretical pressure difference actually develops. Theoretical values of osmotic pressure, calculated using the van’t Hoff equation, as a function of concentration difference for different values of osmotic efficiency are shown in Fig. 9.23. The van’t Hoff equation for osmotic pressure is ⫽ kT
冘 (n
iA
⫺ niB) ⫽ RT(ciA ⫺ ciB)
285
(9.98)
where k is the Boltzmann constant (gas constant per molecule), R is the gas constant per molecule, T is the absolute temperature, ni is concentration in particles per unit volume, and ci is the molar concentration. The van’t Hoff equation applies for ideal and relatively dilute solution concentrations (Malusis and Shackelford, 2002c). According to Fritz (1986) the error is low (⬍5%) for 1⬊1 electrolytes (e.g., NaCl, KCl) and concentrations 1.0 M.
Figure 9.23 Theoretical values of osmotic pressure as a function of concentration difference across a clay layer for different values of osmotic efficiency coefficient, ". (T ⫽ 20C).
Values of osmotic efficiency coefficient, ", or membrane efficiency (" expressed as a percentage), have been measured for clays and geosynthetic clay liners; for example, Kemper and Rollins (1966), Letey et al. (1969), Olsen (1969), Kemper and Quirk (1972), Bresler (1973), Elrick et al. (1976), Barbour and Fredlund (1989), and Malusis and Shackelford (2002b, 2002c). Values of membrane efficiency from 0 to 100 percent have been determined, depending on the clay type, porosity, and type and concentration of salts in solution. The results of many determinations were summarized by Bresler (1973) as shown in Fig. 9.24. The efficiency is shown as a function of a normalizing parameter, the half distance between particles b times the square root of the solution concentration 兹c. To put these relations into more familiar terms for use in geotechnical studies, the half spacings were converted to water contents on the assumption of uniform water layer thicknesses on all particles, using specific surface areas corresponding to different clay types and noting that volumetric water content equals surface area times layer thickness. The relationship between specific surface area and liquid limit (LL) obtained by Farrar and Coleman (1967) for 19 British clays LL ⫽ 19 ⫹ 0.56As (20%)
(9.99)
in which the specific surface area As is in square meters per gram, was then used to obtain the relationships shown in Fig. 9.25. The computed efficiencies shown in Fig. 9.25 should be considered upper bounds because the assumption of uniform water distribution over the full surface area underestimates the effective particle spacing in most cases. In most clays, espe-
286
9
CONDUCTION PHENOMENA
concentrations on the inside of a lined repository should be greater than on the outside, osmotically driven water flow should be directed from the outside toward the inside. The greater the osmotic efficiency the greater the driving force for this flow. Furthermore, if the efficiency is high, then outward diffusion of contained chemicals is restricted (Malusis and Shackelford, 2002b). In diffusion-dominated containment barriers, the effect of solute restriction on reducing solute diffusion is likely substantially more significant than the effect of osmotic flow (Shackelford et al., 2001). Coupling Influences on Electrical Flow
Figure 9.24 Osmotic efficiency coefficient as a function of b兹c where c is concentration of monovalent anion in nor-
Substitution of values for the parameters in Eq. (9.93) indicates, as would be expected, that electrical current flow is dominated completely by the electrical gradient ie. In the presence of an applied voltage difference, the other terms are of little importance, even if the movements of anions and cations are considered separately and the contributions due to ionic mobility are taken into account. On the other hand, when a soil layer behaves as an open electrical circuit, small electrical potentials, measured in millivolts, may exist if there are hydraulic and/or chemical flows. This may be seen by setting I ⫽ 0 in Eq. (9.93) and solving for ie, which must have value if ih has value. These small potentials and flows are important in such processes as corrosion and electroosmotic counterflow.
mality and 2b is the effective spacing between particle surfaces (from Bresler, 1973).
Coupling Influences on Chemical Flow
cially those with divalent adsorbed cations, individual clay plates associate in clusters giving an effective specific surface that is less than that determined by most methods of measurement. This means that the curves in Fig. 9.25 should in reality be displaced to the left. High osmotic efficiencies are developed at low water contents, that is, in very dense, low-porosity clays, and in dilute electrolyte systems. Malusis and Shackelford (2002a, 2002b, 2002c) found that the osmotic efficiency decreases with increasing solute concentration and attribute this to compression of the diffuse double layers adjacent to the clay particles. Water flow by osmosis can be significant relative to hydraulically driven water flow in heavily overconsolidated clay and clay shale, where the void ratio is low and the hydraulic conductivity is also very low. Such flow may be important in geological processes (Olsen 1969, 1972). Densely compacted clay barriers for waste containment, usually composed of bentonite, possess osmotic membrane properties. As the chemical
Equation (9.94) provides a description of chemical transport relative to the soil. It contains two terms that influence chemical flow under a hydraulic gradient; one for chemical transport under an electrical gradient, and one for transport of chemical under a chemical gradient. The first term in the first bracket of the righthand side of Eq. (9.94) describes advective transport. As would be expected, the smaller the osmotic efficiency, the more chemical flow through the soil is possible. The second term in the same bracket simply reflects the advective flow reduction that would result from electroosmotic counterflow caused by development of a streaming potential. As noted earlier, this flow will be small, and its contribution to the total flow will be small, except in clays of very low hydraulic and electrical conductivities. Advective transport is the dominant means for chemical flow for soils having a hydraulic conductivity greater than about 1 ⫻ 10⫺9 m/s. The importance of an electrical driving force for chemical flow depends on the electrical potential gradient. For a unit gradient, that is, 1 V/m, chemical flow
TRANSPORT COEFFICIENTS AND THE IMPORTANCE OF COUPLED FLOWS
287
Figure 9.25 Osmotic efficiency of clays as a function of water content.
quantities are comparable to those by advective flow under a unit hydraulic gradient in a clay having a hydraulic conductivity of about 1 ⫻ 10⫺9 m/s. Electrically driven chemical flow is relatively less important in higher permeability soils and more important in soils with lower kh. In cases where the electrically driven chemical transport is of interest, as in electrokinetic waste containment barrier applications, anion, cation, and nonionic chemical flows must be considered separately using expanded relationships such as given by Eqs. (9.87) and (9.88). The last bracketed quantity of Eq. (9.94) represents diffusive flow under chemical gradients. The quantity D*ic gives the normal diffusive flow rate. The second term represents a restriction on this flow that depends on the clay’s osmotic efficiency, "; that is, if the clay acts as an effective semipermeable membrane, diffusive flow of chemicals is restricted. However, even un-
der conditions where the value of " is low such that the second term in the bracket is negligible, chemical transport by diffusion is significant relative to advective chemical transport in soils with hydraulic conductivity values less than about 1 ⫻ 10⫺9 to 1 ⫻ 10⫺10 m/s for chemicals with diffusion coefficients in the range given by Table 9.7, that is, 2 ⫻ 10⫺10 to 2 ⫻ 10⫺9 m2 /s. This is illustrated by Fig. 9.26 from Shackelford (1988), which shows the relative importance of advective and diffusive chemical flows on the transit time through a 0.91-m-thick compacted clay liner having a porosity of 0.5 acted on by a hydraulic gradient of 1.33. A diffusion coefficient of 6 ⫻ 10⫺10 m2 /s was assumed. The transit time is defined as the time required for the solute concentration on the discharge side to reach 50 percent of that on the upstream side. For hydraulic conductivity values less than about 2 ⫻
288
9
CONDUCTION PHENOMENA
Figure 9.26 Transit times for chemical flow through a 0.91-
m-thick compacted clay liner having a porosity of 50 percent and acted on by a hydraulic gradient of 1.33 (from Shackelford, 1988).
10⫺9 m/s the transit time in the absence of diffusion would be very long. For diffusion alone the transit time would be about 47 years. Most compacted clay barriers and geosynthetic clay liners are likely to have hydraulic conductivity values in the range of 1 ⫻ 10⫺11 to 1 ⫻ 10⫺9 m/s, with the latter value being the upper limit allowed by the U.S. EPA for most waste containment applications. In this range, diffusion reduces the transit time significantly in comparison to what it would be due to advection alone. This is shown by the curve labeled advection– dispersion in Fig. 9.26. The calculations were done using the well-known advection–dispersion equation (Ogata and Banks, 1961) in which the dispersion term includes both mechanical mixing and diffusion. Mechanical mixing is negligible in low-permeability materials such as compacted clay. 9.14 COMPATIBILITY—EFFECTS OF CHEMICAL FLOWS ON PROPERTIES Chemical Compatibility and Hydraulic Conductivity
The compatibility between waste chemicals, especially liquid organics, and compacted clay liners and slurry wall barriers constructed to contain them must be considered in the design of waste containment barriers. Numerous studies have been done to evaluate chemical effects on clay hydraulic conductivity because of fears that prolonged exposure may compromise the integrity of the liners and barriers and because tests have shown that under some conditions clay can shrink and crack when permeated by certain classes of chemicals. Summaries of the results of chemical compatibility studies are given by Mitchell and Madsen (1987) and Quigley and Fernandez (1989), and factors controlling the long-
term stability of clay liners are discussed by Mitchell and Jaber (1990). Rigid wall, flexible wall, and consolidometer permeameters are used for compatibility testing in the laboratory. These three types of test apparatus are shown schematically in Fig. 9.27. Tests done in a rigid wall system overestimate hydraulic conductivity whenever chemical–clay interactions cause shrinkage and cracking; however, a rigid wall system is well suited for qualitative determination of whether or not there may be adverse interactions. In the flexible wall system the lateral confining pressure prevents cracks from opening; thus there is risk of underestimating the hydraulic conductivity of some soils. The consolidometer permeameter system allows for testing clays under a range of overburden stress states that are representative of those in the field and for quantitative assessment of the effects of chemical interactions on volume stability and hydraulic conductivity. More details of these permeameters are given by Daniel (1994). The effects of chemicals on the hydraulic conductivity of high water content clays such as used in slurry walls are likely to be much greater than on lower water content, high-density clays as used in compacted clay liners. This is because of the greater particle mobility and easier opportunity for fabric changes in a higher water content system. A high compactive effort or an effective confining stress greater than about 70 kPa can make properly compacted clay invulnerable to attack by concentrated organic chemicals (Broderick and Daniel, 1990). However, it is not always possible to ensure high-density compaction or to maintain high confining pressures, or eliminate all construction defects, so it is useful to know the general effects of different types of chemicals on hydraulic conductivity. The influences of inorganic chemicals on hydraulic conductivity are consistent with (1) their effects on the double-layer and interparticle forces in relation to flocculation, dispersion, shrinkage, and swelling, (2) their effects on surface and edge charges on particles and the influences of these charges on flocculation and deflocculation, and (3) their effects on pH. Acids can dissolve carbonates, iron oxides, and the alumina octahedral layers of clay minerals. Bases can dissolve silica tetrahedral layers, and to a lesser extent, alumina octahedral layers of clay minerals. Removal of dissolved material can cause increases in hydraulic conductivity, whereas precipitation can clog pores and reduce hydraulic conductivity. The most important factors controlling the effects of organic chemicals on hydraulic conductivity are (1) water solubility, (2) dielectric constant, (3) polarity, and (4) whether or not the soil is exposed to the pure organic or a dilute solution. Exposure of clay barriers
COMPATIBILITY—EFFECTS OF CHEMICAL FLOWS ON PROPERTIES
289
Figure 9.27 Three types of permeameter for compatibility testing: (a) rigid wall, (b) flexible wall, and (c) consolidometer permeameter (from Day, 1984).
to water-insoluble pure or concentrated organics is likely only in the case of spills, leaking tanks, and with dense non-aqueous-phase liquids (DNAPLs) or ‘‘sinkers’’ that accumulate above low spots in liners. Some general conclusions about the influences of organics on the hydraulic conductivity are: 1. Solutions of organic compounds having a low solubility in water, such as hydrocarbons, have no large effect on the hydraulic conductivity. This is in contrast to dilute solutions of inorganic compounds that may have significant effects as a result of their influence on flocculation and dispersion of the clay particles. 2. Water-soluble organics, such as simple alcohols and ketones, have no effect on hydraulic conductivity at concentrations less than about 75 to 80 percent.
3. Many water-insoluble organic liquids (i.e., nonaquoues-phase liquids, NAPLs) can cause shrinkage and cracking of clays, with concurrent increases in hydraulic conductivity. 4. Hydraulic conductivity increases caused by permeation by organics are partly reversible when water is reintroduced as the permeant. 5. Concentrated hydrophobic compounds (like many NAPLs) permeate soils through cracks and macropores. Water remains within mini- and micropores. 6. Hydrophilic compounds permeate the soil more uniformly than NAPLs, as the polar molecules can replace the water in hydration layers of the cations and are more readily adsorbed on particle surfaces. 7. Organic acids can dissolve carbonates and iron oxides. Buffering of the acid can lead to precip-
290
9
CONDUCTION PHENOMENA
itation and pore clogging downstream. However, after long time periods these precipitates may be redissolved and removed, thus leading to an increase in hydraulic conductivity. 8. Pure bases can cause a large increase in the hydraulic conductivity, whereas concentrations at or below the solubility limit in water have no effect. 9. Organic acids do not cause large-scale dissolution of clay particles. The combined effects of confining pressure and concentration, as well as permeant density and viscosity, are illustrated by Fig. 9.28 (Fernandez and Quigley, 1988). The data are for water-compacted, brown Sarnia clay permeated by solutions of dioxane in domestic landfill leachate. Increased hydrocarbon concentration caused a decrease in hydraulic conductivity up to concentrations of about 70 percent, after which the hydraulic conductivity increased by about three orders of magnitude for pure dioxane (Fig. 9.28a), for samples that were unconfined by a vertical stress (v ⫽ 0). On the other hand, the data points for samples maintained under a vertical confining stress of 160 kPa indicated no effect of the dioxane on hydraulic conductivity rel-
ative to that measured with water. The decreases in hydraulic conductivity for dioxane concentrations up to 70 percent can be accounted for in terms of fluid density and viscosity, as may be seen in Fig. 9.28b where the intrinsic values of permeability are shown. As noted earlier in this chapter, the intrinsic permeability is defined by K ⫽ k / . Although many chemicals do not have significant effect on the hydraulic conductivity of clay barriers, this does not mean that they will not be transported through clay. Unless adsorbed by the clay or by organic matter, the chemicals will be transported by advection and diffusion. Furthermore, the actual transit time through a barrier by advection, that is, the time for chemicals moving with the seepage water, may be far less than estimated using the conventional seepage velocity. The seepage velocity is usually defined as the Darcy velocity khih, divided by the total porosity n. In systems with unequal pore sizes the flow is almost totally through mini- and macropores, which comprise the effective porosity ne, which may be much less than the total porosity. Thus effective compaction of clay barriers must break down clods and aggregates to decrease the effective pore size and increase the propor-
Figure 9.28 (a) Hydraulic conductivity and (b) intrinsic permeability of compacted Sarnia clay permeated with leachate–dioxane mixtures. Initial tests run using water (●) followed by leachate–chemical solution (䉱). (from Fernandez and Quigley, 1988). Reproduced with per-
mission from the National Research Council of Canada.
ELECTROOSMOSIS
tion of the porosity that is effective porosity, thereby increasing the transit time. 9.15
ELECTROOSMOSIS
The coefficient of electroosmotic hydraulic conductivity ke defines the hydraulic flow velocity under a unit electrical gradient. Measurement of ke is made by determination of the flow rate of water through a soil sample of known length and cross section under a known electrical gradient. Alternatively, a null indicating system may be used or it may be deduced from a streaming potential measurement. From experience it is known that ke is generally in the range of 1 ⫻ 10⫺9 to 1 ⫻ 10⫺8 m2 /s V (m/s per V/m) and that it is of the same order of magnitude for most soil types, as may be seen by the values for different soils and a freshwater permeant given in Table 9.7. Several theories have been proposed to explain electroosmosis and to provide a basis for quantitative prediction of flow rates. Helmholtz and Smoluchowski Theory
charges of one sign on or near the surface of the wall and countercharges concentrated in a layer in the liquid a small distance from the wall, as shown in Fig. 9.29.10 The mobile shell of counterions is assumed to drag water through the capillary by plug flow. There is a high-velocity gradient between the two plates of the condenser as shown. The rate of water flow is controlled by the balance between the electrical force causing water movement and friction between the liquid and the wall. If v is the flow velocity and is the distance between the wall and the center of the plane of mobile charge, then the velocity gradient between the wall and the center of positive charge is v / ; thus, the drag force per unit area is dv /dx ⫽ v / , where is the viscosity. The force per unit area from the electrical field is E/
L, where is the surface charge density and E/ L is the electrical potential gradient. At equilibrium
v
E ⫽
L
10
A derivation using a Poisson–Boltzmann distribution of counterions adjacent to the wall gives the same result.
Coefficients of Electroosmotic Permeability
No.
Material
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
London clay Boston blue clay Kaolin Clayey silt Rock flour Na-Montmorillonite Na-Montmorillonite Mica powder Fine sand Quartz powder ˚ s quick clay A Bootlegger Cove clay Silty clay, West Branch Dam Clayey silt, Little Pic River, Ontario
(9.100)
or
This theory, based on a model introduced by Helmholtz (1879) and refined by Smoluchowski (1914), is one of the earliest and most widely used. A liquidfilled capillary is treated as an electrical condenser with
Table 9.7
291
Water Content (%)
ke in 10⫺5 (cm2 /s-V)
Approximate kh (cm/s)
52.3 50.8 67.7 31.7 27.2 170 2000 49.7 26.0 23.5 31.0 30.0 32.0 26.0
5.8 5.1 5.7 5.0 4.5 2.0 12.0 6.9 4.1 4.3 20.0–2.5 2.4–5.0 3.0–6.0 1.5
10⫺8 10⫺8 10⫺7 10⫺6 10⫺7 10⫺9 10⫺8 10⫺5 10⫺4 10⫺4 2.0 ⫻ 10⫺8 2.0 ⫻ 10⫺8 1.2 ⫻ 10⫺8 –6.5 ⫻ 10⫺8 2 ⫻ 10⫺5
ke and water content data for Nos. 1 to 10 from Casagrande (1952). kh estimated by authors; no. 11 from Bjerrum et al. (1967); no. 12 from Long and George (1967); no. 13 from Fetzer (1967); no. 14 from Casagrande et al. (1961).
292
9
CONDUCTION PHENOMENA
Figure 9.29 Helmholtz–Smoluchowski model for electrokinetic phenomena.
⫽ v
L
E
(9.101)
From electrostatics, the potential across a condenser is given by ⫽
D
(9.102)
where D is the relative permittivity, or dielectric constant of the pore fluid. Substitution for in Eq. (9.102) gives v⫽
冉 冊
D E L
(9.103)
The potential is termed the zeta potential. It is not the same as the surface potential of the double-layer 0 discussed in Chapter 6, although conditions that give high values of 0 also give high values of zeta potential. A common interpretation is that the actual slip plane in electrokinetic processes is located some small, but unknown, distance from the surface of particles; thus should be less than 0. Values of in the range of 0 to ⫺50 mV are typical for clays, with the lowest values associated with high pore water salt concentrations. For a single capillary of area a the flow rate is qa ⫽ va ⫽
D E a L
(9.104a)
and for a bundle of N capillaries within total crosssectional area A normal to the flow direction
qA ⫽ Nqa ⫽
D E Na L
(9.104b)
If the porosity is n, then the cross-sectional area of voids is nA, which must equal Na. Thus, qA ⫽
D E n A
L
(9.105)
By analogy with Darcy’s law we can write Eq. (9.105) as qA ⫽ keie A
(9.106)
in which ie is the electrical potential gradient E/ L and ke the coefficient of electroosmotic hydraulic conductivity is ke ⫽
D n
(9.107)
According to the Helmholtz–Smoluchowski theory and Eq. (9.107), ke should be relatively independent of pore size, and this is borne out by the values listed in Table 9.7. This is in contrast to the hydraulic conductivity kh, which varies as the square of some effective pore size. Because of this independence of pore size, electroosmosis can be more effective in moving water through fine-grained soils than flow driven by a hydraulic gradient. This is illustrated by the following simple example. Consider a fine sand and a clay of hydraulic conductivity kh of 1 ⫻ 10⫺5 m/s and 1 ⫻ 10⫺10 m/s, respectively. Both have ke values of 5 ⫻ 10⫺9 m2 /s V. For equal hydraulic flow rates khih ⫽ keie, so
ELECTROOSMOSIS
ih ⫽
ke i kh e
If an electrical potential gradient of 20 V/m is used, substitution in Eq. (9.108) shows that ih is 0.01 for the fine sand and 1000 for the clay. This means that a hydraulic gradient of only 0.01 can move water as effectively as an electrical gradient of 20 V/m in fine sand. However, for the clay, a hydraulic gradient of 1000 would be needed to offset the electroosmotic flow. However, it does not follow that electroosmosis will always be an efficient means to move water in clays because the above analysis does not take into account the power requirement to develop the potential gradient of 20 V/m or energy losses in the system. These points are considered further later. Schmid Theory
The Helmholtz–Smoluchowski theory is essentially a large-pore theory because it assumes a negligible extension of the counterion layer into the pore. Also, it does not account for an excess of ions over those needed to balance the surface charge. A model that overcomes the first of these problems was proposed by Schmid (1950, 1951). It can be considered a smallpore theory. The counterions are assumed to be distributed uniformly throughout the fluid phase in the soil. The electrical force acts uniformly over the entire pore cross section and gives the same velocity profile as shown by Fig. 9.29. The hydraulic flow rate through a single capillary of radius r is given by Poiseuille’s law: q⫽
r i 8 w h 4
(9.109)
The hydraulic seepage force per unit length causing flow is FH ⫽ r 2 wih
FE ⫽ A0 F0r 2
(9.108)
E
L
293 (9.112)
where A0 is the concentration of wall charges in ionic equivalents per unit volume of pore fluid, and F0 is the Faraday constant. Replacement of FH by FE in Eq. (9.111) gives qa ⫽
r 4
E F A A F ⫽ 0 0 r 2iea 8 0 0 L 8
(9.113)
so for a total cross section of N capillaries and area A qA ⫽
A0 F0r 2 nie A 8
(9.114)
This equation shows that ke should vary as r 2, whereas the Helmholtz–Smoluchowski theory leads to ke independent of pore size, as previously noted. Of the two theories, the Helmholtz gives the better results for soils, perhaps because most clays have a cluster or aggregate structure with electroosmotic flow controlled more by the larger pores than by the intracluster pores. Spiegler Friction Model
A completely different concept for electrokinetic processes takes into account the interactions of the mobile components (water and ions) on each other and of the frictional interactions of these components with pore walls (Spiegler, 1958). This theory provides insight into conditions leading to high electroosmotic efficiency. The assumptions include: 1. Exclusion of coions,11 that is, the medium behaves as a perfect perm-selective membrane, admitting ions of only one sign 2. Complete dissociation of pore fluid ions The following equation for electroosmotic transport of water across a fine-grained porous material containing adsorbed and free ions can be derived:
(9.110) ⫽ (W ⫺ H) ⫽
so
C3 C1 ⫹ C3(X34 /X13)
(9.115)
(9.111)
in which is the true electroosmotic water flow (moles/faraday), W is the measured water transport
The electrical force per unit length FE is equal to the charge times the potential, that is,
11 Ions of the opposite sign to the charged surface are termed counterions. Ions of the same sign are termed coions.
q⫽
r2 F 8 H
294
9
CONDUCTION PHENOMENA
(moles/faraday), H is the water transport by ion hydration (moles/faraday), C3 is the concentration of free water in the material (mol/m3), C1 is the concentration of mobile counterions m2, X34 is the friction coefficient between water and the solid wall, and X13 is the friction coefficient between cation and water. Concentrations C1 and C3 are hypothetical and probably less than values measured by chemical analysis because some ions may be immobile. Evaluation of X13 and X34 requires independent measurements of diffusion coefficients, conductance, transference numbers, and water transport. Thus Eq. (9.115) is limited as a predictive equation. Its real value is in providing a relatively simple physical representation of a complex process. From Eq. (9.115), ⫽ (W ⫺ H) ⫽
1 (C1 /C3 ⫹ X34 /X13)
(9.116)
At high water contents and for large pores, X34 /X13 → 0 because X34 becomes negligible. Then X34→0
⫽ C3 /C1
opposite sign. The greater the difference between the concentrations of cations and anions, the greater the net drag on the water in the direction toward the cathode. The efficiency and economics of the process depend on the volume of water transported per unit electrical charge passed. If the volume is high, then more water is transported for a given expenditure of electrical energy than if it is low. This volume may vary over several orders of magnitude depending on such factors as soil type, water content, and electrolyte concentration. In a low exchange capacity soil at high water content in a low electrolyte concentration solution, there is much more water per cation than in a high exchange capacity, low water content soil having the same pore water electrolyte concentration. This, combined with cation-to-anion ratio considerations, leads to the predicted water transport–water content–soil type–electrolyte concentration relationships shown schematically in Fig. 9.30, where increasing electrolyte concentration in the pore water results in a much
(9.117)
This relationship indicates that a high water-to-cation ratio implies a high rate of electroosmotic flow. At low water contents and for small pores, X34 will not be zero, thus reducing the flow. An increase in C1 reduces the flow of water per faraday of current passed because there is less water per ion. An increase in X13 increases the flow because there is greater frictional drag on the water by the ions. Ion Hydration
Water of hydration is carried along with ions in a direct current electric field. The ion hydration transport H is given by H ⫽ t⫹N⫹ ⫺ t N
(9.118)
where t⫹ and t are the transport numbers, that is, numbers that represent the fraction of current carried by a particular ionic species. The numbers N⫹ and N are the number of moles of hydration water per mole of cation and anion, respectively.
9.16
ELECTROOSMOSIS EFFICIENCY
Electroosmotic water flow occurs if the frictional drag between the ions of one sign and their surrounding water molecules exceeds that caused by ions of the
Figure 9.30 Schematic prediction of water transport by elec-
troosmosis in various clays according to the Donnan concept (from Gray, 1966).
ELECTROOSMOSIS EFFICIENCY
greater decrease in efficiency for inactive clay than more plastic, active clay. Tests on sodium kaolinite (inactive clay) and sodium illite (more active clay) gave the results shown in Fig. 9.31, which agree well with the predictions in Fig. 9.30. The slopes and locations of the curves can be explained more quantitatively in the following way. Alternatively to the double-layer theory given in Chapter 6, the Donnan (1924) theory can be used to describe equilibrium ionic distributions in fine-grained materials. The basis for the Donnan theory is that at equilibrium the potentials of the internal and external solutions are equal and that electroneutrality is required in both phases. It may be shown (Gray, 1966; Gray and Mitchell, 1967) that the ratio R of cations to anions in the internal phase for the case of a symmetrical electrolyte (z⫹ ⫽ z⫺) is given by R⫽ where
C⫹ 1 ⫹ (1 ⫹ y2)1 / 2 ⫽ C⫺ ⫺1 ⫹ (1 ⫹ y2)1 / 2
(9.119)
y⫽
2C0 A0
295 (9.120)
The concentration C0 is in the external solution, is the mean molar activity coefficient in the external solution, is the mean activity coefficient in the double layer, and A0 is the surface charge density per unit pore volume. The parameter A0 is related to the cation exchange capacity (CEC) by A0 ⫽
(CEC)w w
(9.121)
where w is the density of water and w is the water content. The higher R, the greater is the electroosmotic water transport, all other things equal. From Eqs. (9.119) to (9.121) it may be deduced that exclusion of anions is favored by a high exchange capacity (active clay), a low water content, and low salinity in the external solution. However, the concentration of anions in the double layer builds up more
Figure 9.31 Electroosmotic water transport versus concentration of external electrolyte solution for homoionic kaolinite and illite at various water content (from Gray, 1966).
296
9
CONDUCTION PHENOMENA
rapidly as the salinity of the external solution increases in inactive clays than in active clays. As a result the efficiency, as measured by volume of water per unit charge passed, decreases much more rapidly with increasing electrolyte concentration than in the more active clay. The results of electroosmosis measurements on a number of different materials are summarized in Fig. 9.32, which shows water flow rate as a function of water content. This figure may be used as a guide for prediction of electroosmotic flow rates. The flow rates shown are for open systems, that is, solution was admitted at the anode at the same time it was extracted from the cathode. Electrochemical effects (Section 9.18) and water content changes were minimized in these tests. Thus, the values can be interpreted as upper bounds on the flow rates to be expected in practice. Values of water content, electrolyte concentration in the pore water, and type of clay are required for electroosmosis efficiency estimation. Water content is readily measured, the electrolyte concentration is easily determined using a conductivity cell, and the clay type can be determined from plasticity and grain size information if mineralogical data are not available. Electroosmotic flow rates of 0.03 to 0.06 gal/h/amp are predicted using Fig. 9.32 for soils 11, 13, and 14 in Table 9.7. Electrical treatment for consolidation and ground strengthening was effective in these soils. For soil 12, however, a flow rate of 0.008 to 0.012 gal/h/ amp was predicted, and electroosmosis was not effective. Saxen’s Law Prediction of Electroosmosis from Streaming Potential
Streaming potential can be measured directly during a measurement of hydraulic conductivity by using a high-impedance voltmeter and reversible electrodes. Equivalence between streaming potential and electroosmosis may be derived. Expansion of Eq. (9.57) for coupled hydraulic and current flows gives qh ⫽ LHH P ⫹ LHE E
(9.122)
I ⫽ LEH P ⫹ LEE E
(9.123)
in which qh is the hydraulic flow rate, I is the electric current, LHH and LEE are the direct flow coefficients, LHE and LEH are the coupling coefficients for hydraulic flow due to an electrical gradient and electrical flow due to a hydraulic gradient, P is the pressure drop, and E is the electrical potential drop. In a usual hydraulic conductivity measurement, there is no electrical current flow, so I ⫽ 0, and E is the streaming potential. Equation (9.123) then becomes
E L ⫽ ⫺ EH
P LEE
(9.124)
In electroosmosis P ⫽ 0, so Eq. (9.122) is qh ⫽ LHE E
(9.125)
and Eq. (9.122) becomes I ⫽ LEE E
(9.126)
qh LHE ⫽ I LEE
(9.127)
so
By Onsager’s reciprocity theorem LEH ⫽ LHE so
冉冊 qh I
冉 冊
⫽⫺
P⫽0
E
P
(9.128) I⫽0
This equivalence between streaming potential and electroosmosis was first shown experimentally by Saxen (1892) and is known as Saxen’s law. It has been verified for clay–water–electrolyte systems. Care must be taken to ensure consistency in units. For example, the electroosmotic flow rate in gallons per hour per ampere is equal to 0.0094 times the streaming potential in millivolts per atmosphere. Energy Requirements
The preceding analysis leads to a prediction of the amount of water moved per unit charge passed, for example, gallons or cubic meters of water per hour per ampere or moles per faraday. If this quantity is denoted by ki, then qh ⫽ ki I
(9.129)
Unlike ke, ki varies over a wide range, as may be seen in Fig. 9.32. The power consumption P is P ⫽ E I ⫽
Eqh
ki
(in W)
(9.130)
for E in volts and I in amperes. The power consumption per unit volume of flow is P
E ⫽ ⫻ 10⫺3 qh ki
(in kWh)
(9.131)
Figure 9.32 Electroosmotic water transport as a function of water content, soil type, and electrolyte concentration: (a) homoionic kaolinite and illite, (b) illitic clay and collodion membrane, and (c) silty clay, illitic clay, and kaolinite.
297
298
9
CONDUCTION PHENOMENA
Relationship Between ke and ki
From Eqs. (9.108) and (9.129), the electroosmotic flow rate is given by
equations in place of Darcy’s law in consolidation theory. Assumptions
qh ⫽ ki I ⫽ ke
E A
L
(9.132)
The following idealizing assumptions are made: 1. There is homogeneous and saturated soil. 2. The physical and physicochemical properties of the soil are uniform and constant with time.12 3. No soil particles are moved by electrophoresis. 4. The velocity of water flow by electroosmosis is directly proportional to the voltage gradient. 5. All the applied voltage is effective in moving water.13 6. The electrical field is constant with time. 7. The coupling of hydraulic and electrical flows can be formulated by Eqs. (9.63) and (9.64). 8. There are no electrochemical reactions.
Because E/I is resistance and L/(resistance ⫻ A) is specific conductivity , Eq. (9.132) becomes ki ⫽
ke
(9.133)
As ke varies within relatively narrow limits, Eq. (9.133) shows that the electroosmotic efficiency, measured by ki, is a sensitive function of the electrical conductivity of the soil. For soils 11, 13, and 14 in Table 9.7, is in the range of 0.02 to 0.03 S. For soil 12, in which electroosmosis was not effective, is 0.25 S. In essence, a high value of electrical conductivity means that the current required to develop the voltage is too high for economical movement of water. In addition, if high current is used, the generation of gas, heat, and electrochemical effects become excessive.
Governing Equations
9.17
for the flow rate per unit area. For radial flow for the conditions shown in Fig. 9.33b and a layer of unit thickness
CONSOLIDATION BY ELECTROOSMOSIS
If, in a compressible soil, electroosmosis draws water to a cathode where it is drained away and no water is allowed to enter at the anode, then consolidation of the soil between the electrodes occurs in an amount equal to the volume of water removed. Water movement away from the anode causes consolidation in the vicinity of the anode. The effective stress must increase concurrently. Because the total stress in the vicinity of the anode remains essentially unchanged, the pore water pressure must decrease. Water drains at the cathode where there is no consolidation. Therefore, the total, effective, and pore water pressures at the cathode remain unchanged. As a result, hydraulic gradient develops that tends to cause water flow from cathode to anode. Consolidation continues until the hydraulic force that drives water back toward the anode exactly balances the electroosmotic force driving water toward the cathode. The usefulness of consolidation by electroosmosis as a means for soil stabilization was established by a number of successful field applications, for example, Casangrande (1959) and Bjerrum et al. (1967). Two questions are important: (1) How much consolidation will there be? and (2) How long will it take? Answers to these questions are obtained using the coupled flow
For one-dimensional flow between plate electrodes (Fig. 9.33a), Eq. (9.63) becomes k u V qh ⫽ ⫺ h ⫺ ke w x x
k u V qh ⫽ ⫺ h 2r ⫺ ke 2r w r r
(9.134)
(9.135)
Introduction of Eq. (9.134) in place of Darcy’s law in the derivation of the diffusion equation governing consolidation in one dimension leads to kh 2u 2V u ⫹ k ⫽ mv e 2 2 w x x t
(9.136)
and
12
Flow of water away from anodes toward cathodes causes a nonuniform decrease in water content along the line between electrodes. This leads to changes in hydraulic conductivity, electroosmotic hydraulic conductivity, compressibility, and electrical conductivity with time and position. To account for these effects, which are discussed by Mitchell and Wan (1977) and Acar et al. (1990), would greatly complicate the analysis because it would be highly nonlinear. Similar problems arise in classical consolidation theory, but the simple linear theory developed by Terzaghi is adequate for most cases. 13 In most cases some of the electrical energy will be consumed by generation of heat and gases at the electrodes. To account for those losses, an effective voltage can be used (Esrig and Henkel, 1968).
CONSOLIDATION BY ELECTROOSMOSIS
299
kh u V ⫽ ⫺ke w x x
(9.139)
k du ⫽ ⫺ e w dV kh
(9.140)
or
The solution of this equation is k u ⫽ ⫺ e w V ⫹ C kh
(9.141)
At the cathode, V ⫽ 0 and u ⫽ 0; therefore, C ⫽ 0, and the pore pressure at equilibrium at any point is given by k u ⫽ ⫺ e w V kh
Figure 9.33 Electrode geometries for analysis of consoli-
dation by electroosmosis: (a) one-dimensional flow and (b) radial flow.
2u ke 2V 1 u ⫹ ⫽ w 2 2 x kh x cv t
(9.137)
where mv is the compressibility and cv is the coefficient of consolidation. For radial flow, the use of Eq. (9.135) gives 2u ke 2V 1 ⫹ ⫹ w 2 2 r kh r r
冉
冊
u k V ⫹ e w r kh r
⫽
1 u cv t (9.138)
Both V and u are functions of position, as shown in Fig. 9.34; V is assumed constant with time, whereas u varies.
where the values of u and V are those at any point of interest. A similar result is obtained from Eq. (9.135) for radial flow. Equation (9.142) indicates that electroosmotic consolidation continues at a point until a negative pore pressure, relative to the initial value, develops that is proportional to the ratio ke /kh and to the voltage at the point. For conditions of constant total stress, there must be an equal and opposite increase in the effective stress. This increase in effective stress causes the consolidation. For the one-dimensional case, consolidation by electroosmosis is analogous to the loading shown in Fig. 9.35. For a given voltage, the magnitude of effective stress increase that develops depends on ke /kh. As ke only varies within narrow limits for different soils, the total consolidation that can be achieved depends largely on kh. Thus, the potential for consolidation by electroosmosis increases as soil grain size decreases because the finer grained the soil, the lower is kh. However, the amount of consolidation in any case depends on the soil compressibility as well as on the change in effective stress. For linear soil compression with increase in effective stress, the coefficient of compressibility av is
Amount of Consolidation
When the hydraulic gradient that develops in response to the differing amounts of consolidation between the anode and cathode generates a counterflow (kh / w)/ (u/ x) that exactly balances the electroosmotic flow ke(V/ x) in the opposite direction, consolidation is complete. As there then is no flow, qh in Eqs. (9.14) and (9.135) is zero. Thus Eq. (9.134) is
(9.142)
de de av ⫽ ⫺ ⫽ d du
(9.143)
de ⫽ av du ⫽ ⫺av d
(9.144)
or
in which d is the increase in effective stress.
300
9
CONDUCTION PHENOMENA
Figure 9.34 Assumed variation of voltage with distance during electroosmosis: (a) onedimensional flow and (b) radial flow.
Thus, the more compressible the soil, the greater will be the amount of consolidation for a given stress increase, just as in the case of consolidation under applied loads. It follows, also, that electroosmosis will be of little value in an overconsolidated clay unless the effective stress increases are large enough to bring the material back into the virgin compression range. The consolidation loading of any small element of the soil is isotropic, as it is done by increasing the effective stress through reduction in the pore water pressure. The entire soil mass being treated is not consolidated isotropically or uniformly, however, because the amount of consolidation varies with position, de-
pendent on the voltage at the point. Accordingly, properties at the end of treatment vary along a line between the anode and cathode, as shown, for example, by the posttreatment variations in shear strength and water content shown in Fig. 9.36. Values of these properties before treatment are also shown for comparison. More uniform property distributions between electrodes can be obtained if the polarity of electrodes is reversed after partial completion of consolidation (Wan and Mitchell, 1976). The results shown in Fig. 9.36 were obtained at a site in Norway where electroosmosis was used for the consolidation of quick clay (Bjerrum et al., 1967). The
CONSOLIDATION BY ELECTROOSMOSIS
301
Figure 9.35 Consolidation by electroosmosis and by direct loading, one-dimensional case: (a) electroosmosis and (b) direct loading.
variations in strength and water content after treatment are consistent with the patterns to be expected based on the predicted variation of pore pressure decrease and vertical strain stress increase with voltage and position shown in Fig. 9.35.
voltage, and TV is the time factor, defined in terms of the distance between electrodes L and real time t as
Rate of Consolidation
where cv is the coefficient of consolidation, given by
Solutions for Eqs. (9.137) and (9.138) have been obtained for several cases (Esrig, 1968, 1971). For the one-dimensional case, and assuming a freely draining (open) cathode and a closed anode (no flow), the pore pressure is u⫽
ke 2k V V(x) ⫹ e w 2 m kh w kh
n⫽0
n
冋冉 冊 册 1 2 2 TV 2
cvt L2
(9.146)
kh mv w
(9.147)
The average degree of consolidation U as a function of time is 4 3
冘 ⬁
n⫽0
冋冉 冊 册
(⫺1)n 1 exp ⫺ n ⫹ (n ⫹ 1/2)3 2
2
2TV
(9.148)
2
exp ⫺ n ⫹
cv ⫽
U⫽1⫺
x 冘 (n (⫹⫺1)1/2) sin冋(n ⫹ 1/2) 册 L ⬁
TV ⫽
(9.145)
where V(x) is the voltage at x, Vm is the maximum
Solutions for Eqs. (9.145) and (9.148) are shown in Figs. 9.37 and 9.38. They are applied in the same way as the theoretical solution for classical consolidation theory.
302
9
CONDUCTION PHENOMENA
˚ s, Norway Figure 9.36 Effect of electroosmosis treatment on properties of quick clay at A (from Bjerrum et al., 1967): (a) Undrained shear strength, (b) remolded shear strength, (c) water content, and (d) Atterberg limits.
ELECTROCHEMICAL EFFECTS
303
Figure 9.39 Average degree of consolidation as a function
of dimensionless time for radial consolidation by electroosmosis (from Esrig, 1968). Reprinted with permission of ASCE. Figure 9.37 Dimensionless pore pressure as a function of
dimensionless time and distance for one-dimensional consolidation by electroosmosis.
Figure 9.38 Average degree of consolidation versus dimen-
sionless time for one-dimensional consolidation by electroosmosis.
A numerical solution to Eq. (9.138) gives the results shown in Fig. 9.39 (Esrig, 1968, 1971). For the case of two pipe electrodes, a more realistic field condition than the radial geometry of Fig. 9.33b, Fig. 9.39 cannot be expected to apply exactly. Along a straight line between two pipe electrodes, however, the flow pattern is approximately the same as for the radial case for a considerable distance from each electrode. A solution for the rate of pore pressure buildup at the cathode for the case of no drainage (closed cathode) is shown in Fig. 9.40. This condition is relevant
to pile driving, pile pulling, reduction of negative skin friction, and recovery of buried objects. Special solutions for in situ determination of soil consolidation properties by electroosmosis measurements have also been developed (Banerjee and Mitchell, 1980). One of the most important points to be noted from these solutions is that the rate of consolidation depends completely on the coefficient of consolidation, which varies directly with kh, but is completely independent of ke. Low values of kh, as is the case in highly plastic clays, mean long consolidation times. Thus, whereas a low value of kh means a high value of ke /kh and the potential for a high effective consolidation pressure, it also means longer required consolidation times for a given electrode spacing. The optimum situation is when ke /kh is high enough to generate a large pore water tension for reasonable electrode spacings (2 to 3 m) and maximum voltage (50 to 150 V DC), but kh is high enough to enable consolidation in a reasonable time. The soil types that best satisfy these conditions are silts, clayey silts, and silty clays. Most successful field applications of electroosmosis for consolidation have been in these types of materials. As noted earlier, the electrical conductivity of the soil is also important; if it is too high, as in the case of high-salinity pore water, adverse electrochemical effects and unfavorable economics may preclude use of electroosmosis for consolidation. 9.18
ELECTROCHEMICAL EFFECTS
The measured strength increases in the quick clay at ˚ s, Norway (Fig. 9.36), were some 80 percent greater A
304
9
CONDUCTION PHENOMENA
Figure 9.40 Dimensionless pore pressure at the face of a cylindrical electrode as a function
of dimensionless time for the case of a closed cathode (a swelling condition) (from Esrig and Henkel, 1968).
than can be accounted for solely by reduction in water content. Also, the liquid and plastic limits were changed as a result of treatment. Consolidation alone should have no effect on the Atterberg limits because changes in mineralogy, particle characteristics, and/or pore solution characteristics are needed to do this. In addition to movement of water when a DC voltage field is applied between metal electrodes inserted into a wet soil, the following effects may develop: ion diffusion, ion exchange, development of osmotic and pH gradients, desiccation by heat generation at the electrodes, mineral decomposition, precipitation of salts or secondary minerals, electrolysis, hydrolysis, oxidation, reduction, physical and chemical adsorption, and fabric changes. As a result, continuous changes in soil properties that are not readily accounted for by the simplified theory developed previously must be expected. Some of them, such as electrochemical hardening of the soil that results in permanent changes in plasticity and strength, may be beneficial; others, such as heating and gas generation, may impair the efficiency of electroosmosis. For example, heat and gas generation were so great that a field test of consolidation by electroosmosis for foundation stabilization of the leaning Tower of Pisa was unsuccessful. A simplified mechanism for some of the processes during electroosmosis is as follows. Oxygen gas is evolved at the anode by hydrolysis 2H2O ⫺ 4e⫺ → O2 ↑ ⫹ 4H⫹
(9.149)
Anions in solution react with freed H⫹ to form acids.
Chlorine may also form in a saline environment. Some of the exchangeable cations on the clay may be replaced by H⫹. Because hydrogen clays are generally unstable, and high acidity and oxidation cause rapid deterioration of the anodes, the clay will soon alter to the aluminum or iron form depending on the anode material. As a result, the soil is usually strengthened in the vicinity of the anode. If gas generation at the anode causes cavitation and heat causes desiccation, cracking may occur. This will limit the negative pore pressure that can develop to a value less than 1 atm, and also the electrical resistance will increase, leading to a loss in efficiency. Hydrogen gas is generated at the cathode 4H2O ⫹ 4e⫺ → 2H2 ↑ ⫹ 4OH⫺
(9.150)
Cations in solution are drawn to the cathode where they combine with (OH)⫺ that is left behind to form hydroxides. The pH may rise to values as high as 12 at the cathode. Some alumina and silica may go into solution in the high pH environment. More detailed information about electrochemical reactions during electroosmosis can be found in Titkov et al. (1965), Esrig and Gemeinhardt (1967), Chilingar and Rieke (1967), Gray and Schlocker (1969), Gray (1970), Acar et al. (1990), and Hamed et al. (1991). Soil strength increases resulting from consolidation by electroosmosis and the concurrent electrochemical hardening have application for support of foundations on and in fine-grained soil. Pile capacity for a bridge
SELF-POTENTIALS
foundation in varved clay at a site in Canada was well below the design value and inadequate for support of the structure (Soderman and Milligan, 1961; Milligan, 1994). Electrokinetic treatment using the piles as anodes resulted in sufficient strength increase to provide the needed support. Recently reported model tests by Micic et al. (2003) on the use of electrokinetics in soft marine clay to increase the load capacity of skirt foundations for offshore structures resulted in increases in soil strength and supporting capacity of up to a factor of 3.
9.19
ELECTROKINETIC REMEDIATION
The transport of dissolved and suspended constituents into and out of the ground by electroosmosis and electrophoresis, as well as electrochemical, reactions have become of increasing interest because of their potential applications in waste containment and removal of contaminants from fine-grained soils. The electrolysis reactions at the electrodes described in the preceding section, wherein acid is produced at the anode and base at the cathode, are of particular relevance. After a few days of treatment the pH in the vicinity of the anode may drop to less than 2, and that at the cathode increase to more than 10 (Acar and Alshewabkeh, 1993). Toxic heavy metals are preferentially adsorbed by clay minerals and they precipitate except at low pH. Iron or aluminum cations from decomposing anodes can replace heavy-metal ions from exchange sites, the acid generated at the anode can redissolve precipitated material, and the acid front that moves across the soil can keep the metals in solution until removed at the cathode. Geochemical reactions in the soil pores impact the efficiency of the process. Among them are complexation effects that reverse ion charge and reverse flow directions, precipitation/dissolution, sorption, desorption and dissolution, redox, and immobilization or precipitation of metal hydroxides in the high pH zone near the cathode. Some success has been reported in the removal of organic pollutants from soils, at least in the laboratory, as summarized by Alshewabkeh (2001). However, it is unlikely that large quantities of non-aqueous-phase liquids can be effectively transported by electrokinetic processes, except as the NAPL may be present in the form of small bubbles that move with the suspending water. An in-depth treatment of the fundamentals of electrokinetic remediation and the practical aspects of its implementation are given by Alshewabkeh (2001) and the references cited therein.
9.20
305
SELF-POTENTIALS
Natural DC electrical potential differences of up to several tens of millivolts exist in the earth. These selfpotentials are generated by differing chemical conditions in adjacent soil layers, fluid flow, subsurface chemical reactions, and temperature differences. The self-potential (SP) method is one of the oldest geophysical methods for characterization of the subsurface (National Research Council, 2000). Self-potentials may be the source of phenomena of importance in geotechnical problems as well. The magnitude of self-potential between different soil layers depends on the contents of oxidizing and reducing substances in the layers (F. Hilbert, in Veder, 1981). These potentials can cause a natural electroosmosis in which water flows in the direction from the higher to the lower potential, that is, toward the cathode. The process is shown schematically in Fig. 9.41. An oxidizing soil layer is positive relative to a reducing layer, thus inducing an electroosmotic water flow toward the interface. If water accumulates at the interface, there can be swelling and loss of strength, leading ultimately to formation of a slip surface. Generation of Self-Potentials in Soil Layers
Soils in an oxidizing environment are usually yellow or tan to reddish brown and are characterized by oxides and hydrates of trivalent iron and a low pH relative to reducing soils, which are usually dark gray to bluegray in color and contain sulfides and oxides and hydroxides of divalent iron. The local electrical potential of the soil depends on the iron concentrations and can be calculated from Nernst’s equation:
Figure 9.41 Natural electroosmosis due to self-potential dif-
ferences between oxidizing and reducing soil layers. The oxidizing soil layer is positive relative to the reducing layer (redrawn from Hilbert, in Veder, 1981).
306
9
CONDUCTION PHENOMENA
⫽ 0.771 ⫹
冉 冊
RT c3⫹ ln Fe F c2⫹ Fe
(9.151)
in which the concentrations are of Fe in solution in moles/liter pore water. The difference in potentials between two layers gives the driving potential for electroosmosis. Values calculated using the Nernst equation are too high for actual soil systems because it applies for conditions of no current flow, and the flowing current also generates a diffusion potential acting in the opposite direction. Hilbert, in Veder (1981), gives the electrical potential as a function of the in situ pH, that is, ⫽ 0.186 ⫺ 0.059 pH
(9.152)
Reasonable agreement has been obtained between measured and calculated values of for different soil layers. The end result is that potential differences of up to 50 mV or so are developed between different layers. Potentials measured in a trench excavated in a slide zone are shown in Fig. 9.42. Excess Pore Pressure Generation by Self-Potentials
The pore pressure that may develop at an interface between two different soil layers is given by Eq. (9.142) in which V is the difference in self-potentials between the layers. For a given value of V, the magnitude of pore pressure depends directly on ke /kh. For example, if ke ⫽ 5 ⫻ 10⫺9 m2 /s V and kh ⫽ 1 ⫻ 10⫺10 m/s,
then ke /hh ⫽ 50 m/V. If the self-potential difference is 50 mV, then from Eq. (9.142) a pore pressure value of u ⫽ 50 ⫻ 9.81 ⫻ 0.05 ⬇ 25 kPa is generated, which is not an insignificant value. If water that is driven toward the interface cannot escape or be absorbed by the soil, then the effective stress will be reduced by this amount. If the water is absorbed into the clay layer, then softening will result. Either way, the resistance to sliding along the interface will be reduced. Landslide Stabilization Using Short-Circuit Conductors
If slope instability is caused by a slip surface between reducing and oxidizing soil layers, then a simple means for stabilization can be used (Veder, 1981). Shortcircuiting conductors, such as steel rods, are driven into the soil so that they extend across the slip surface and about 1 to 2 m into the soil below. The mechanism that is then established is shown in Fig. 9.43. Electric current generated by reduction reactions in the oxidizing soil layer and oxidizing reactions in the reducing layer flows through the conductors. Because of the presence of oxidizing agents such as ferric iron, oxygen, and manganese compounds, in the upper oxidizing layer that take up electrons, electrons pass from the metal conductor to the soil. That is, the introduction of electrons initiates reducing reactions. In the reducing layer, on the other hand, there is already a
Figure 9.42 Electrical potentials measured in a trench cut into a slide (from Veder, 1981). Reprinted with permission of Springer-Verlag.
THERMALLY DRIVEN MOISTURE FLOW
307
for use of short-circuiting conductors are (1) intact cohesive soils with a low hydraulic conductivity, (2) shear between oxidizing and reducing clay layers, and (3) a relatively thin, well-defined shear zone.
9.21
Figure 9.43 Mechanism for slide stabilization using shortcircuiting conductors (adapted from Veder, 1981).
surplus of electrons. If these pass into the conductor, then the environment becomes favorable for oxidation reactions. Thus, positive charges are generated in the reducing soil layer as the conductor carries electrons away. The oxidizing soil layer then takes up these electrons. Completion of the electrical circuit requires current flow through the soil pore water in the manner shown in Fig. 9.43, where adsorbed cations, shown as Na⫹, plus the associated water, flow away from the soil layer interface. This electroosmotic transport of water reduces the water content in the slip zone. Thus, shortcircuit conductors have three main effects (Veder, 1981): 1. Natural electroosmosis is prevented because the short-circuiting conductors eliminate the potential difference between the two soil layers. 2. Electrochemical reactions produce electroosmotic flow in the opposite direction, thus helping to drain the shear zone. 3. Corrosion of the conductors produces high valence cations that exchange for lower valence adsorbed cations, for example, iron for sodium, which leads to soil strengthening. Several successful cases of landslide stabilization using short-circuiting conductors have been described by Veder (1981) and the references cited therein. Typically, steel rods about 25 mm in diameter are used, spaced a maximum of 3 to 4 m apart in grid patterns covering the area to be stabilized. Conditions favorable
THERMALLY DRIVEN MOISTURE FLOW
Thermally driven flows in saturated soils are rather small. Gray (1969) measured thermoelectric currents on the order of 1 to 10 A/ C cm, with the warm side positive relative to the cold side. Thermoosmotic pressures of only a few tenths of a centimeter water head per degree Celsius were measured in saturated soil. Net flows in different directions have been measured in different investigations, evidently because of different temperature dependencies of chemical activity coefficients. These small thermoelectric and thermoosmotic effects in saturated soils may be of little practical significance in geotechnical problems. On the other hand, thermally driven moisture flows in partly saturated soils can be large, and that these flows can be very important in subgrade stability, swelling soils, and heat transfer and storage problems of various types. Theoretical representations of moisture flow through partly saturated soils based solely on the application of irreversible thermodynamics, such as developed by Taylor and Cary (1964), have not been completely successful. They underestimate the flows substantially, perhaps because of the inability to adequately represent all the processes and interactions. A widely used theory for coupled heat and moisture flow through soils was developed by Philip and De Vries (1957). It accounts for both liquid- and vaporphase flows. Vapor-phase flow depends on the thermal and isothermal vapor diffusivities and is driven by temperature and moisture content gradients. The liquidphase flow depends on the thermal and isothermal liquid diffusivities and is driven by the temperature gradient, the moisture content gradient, and gravity. The two governing equations are: For vapor-phase flow: qvap ⫽ ⫺DTV T ⫺ D V w
(9.153)
and for liquid-phase flow: qliq ⫽ ⫺DTL T ⫺ D L ⫺ k i w where qvap ⫽ vapor flux density (M/L2 /T) w ⫽ density of water (M/L3)
(9.154)
308
9
CONDUCTION PHENOMENA
T ⫽ temperature (K) ⫽ volumetric water content (L3 /L3) DTV ⫽ thermal vapor diffusivity (L2 /T/K) D V ⫽ isothermal vapor diffusivity (L2 /T) qliq ⫽ liquid flux density (M/L2 /T) DTL ⫽ thermal liquid diffusivity (L2 /T/K) D L ⫽ isothermal liquid diffusivity (L2 /T) k ⫽ unsaturated hydraulic conductivity (L/T) i ⫽ unit vector in vertical direction The thermal vapor diffusivity is given by DTV ⫽
冉冊
冉 冊
D0 d 0 v[a ⫹ ƒ(a) ]h w dT
(9.155)
The isothermal vapor diffusivity is given by D V ⫽
冉 冊 冉 冊冉 冊 hg D0 va 0 w RT
d d
(9.156)
where D0 ⫽ molecular diffusivity of water vapor in air (L2 /T) v ⫽ mass flow factor ⫽ P/(P ⫺ p) P ⫽ total gas pressure in pore space p ⫽ partial pressure of water vapor in pore space ⫽ tortuosity factor a ⫽ volumetric air content (L3 /L3) h ⫽ relative humidity of air in pores ⫽ ratio of average temperature gradient in the air-filled pores to the overall temperature gradient g ⫽ acceleration of gravity (L/T2) R ⫽ gas constant (FL/M/K) 0 ⫽ density of saturated water vapor (M/L3) ⫽ suction head of water in the soil (negative head) (L) ƒ(a) ⫽ a/ak for 0 ⬍ a ⬍ ak ⫽ 1 for a ak ak ⫽ a at which liquid conductivity is lost or at which the hydraulic conductivity falls below some arbitrary fraction of the saturated value The thermal liquid diffusivity is given by DTL ⫽ k
冉 冊冉 冊
d dT
(9.157)
The isothermal diffusivity is given by
冉冊
D L ⫽ k
d d
(9.158)
in which is the surface tension of water (F/L). Use of the above equations requires knowledge of four relationships to describe the properties of the soils in the system: 1. Hydraulic conductivity as a function of water content 2. Thermal conductivity as a function of water content 3. Volumetric heat capacity (see Table 9.2) 4. Suction head as a function of water content The hydraulic conductivity and suction relationships are hysteretic; that is, they depend on whether the soil is wetting or drying. Examples of the variations of the different properties needed for the analysis are shown in Fig. 9.44 as a function of degree of saturation and volumetric water content. The data are for a crushed limestone that is used for a trench backfill around buried electrical transmission cables. This material is used because of its low thermal resistivity, which makes it suitable for effective dissipation of heat from the buried cable, provided the saturation does not fall below about 40 percent. The vapor flow is made up of a flow away from the high-temperature side that is driven by a vapor density gradient and a return flow caused by variation in the pore vapor humidity as reflected by variations in soil suction. At moderate soil suction values, for example, a few meters for sand and several tens of meters for clay, the thermal vapor diffusivity predominates, and moisture is driven away from the heat source (McMillan, 1985). The isothermal diffusivity term only becomes important at very high suction levels. The liquid flow consists of a capillarity-driven flow toward the heat source and an outward liquid flow due to variations in water surface tension with temperature. McMillan’s analysis showed that for both sand and clay the isothermal liquid diffusivity term was 4 to 5 orders of magnitude greater than the thermal liquid diffusivity term. Thus capillarity-driven flow predominates for any significant gradient in the volumetric moisture content. The very small thermal liquid diffusivity is consistent with the observations noted earlier for saturated soils in which measured water flows under thermal gradients are small. The total water flow q in an unsaturated soil under the action of a temperature gradient and its resulting water content gradient equals the sum of the vaporphase and liquid-phase movements. Thus, from Eqs. (9.153) to (9.158),
THERMALLY DRIVEN MOISTURE FLOW
309
Figure 9.44 Examples of properties used for analysis of thermally driven moisture flow in a partially saturated, compacted, crushed limestone: (a) particle size distribution, (b) suction head as a function of volumetric water content, (c) hydraulic conductivity as a function of degree of saturation and volumetric water content, (d) isothermal liquid diffusivity as a function of degree of saturation and volumetric water content, (e) isothermal vapor diffusivity as a function of degree of saturation and volumetric water content, and (f) Thermal water diffusivity as a function of degree of saturation and volumetric water content. Thermal resistivity as a function of water content for this soil is shown in Fig. 9.14.
q ⫽ ⫺(DTV ⫹ DTL) T ⫺ (D V ⫹ D L ) ⫺ k i w ⫽ ⫺DT T ⫺ D ⫺ k i
(9.159)
in which D ⫽ DTV ⫹ DTL ⫽ thermal water diffusivity (9.160) and
Equation (9.159) is the governing equation for moisture movement under a thermal gradient in unsaturated soils as proposed by Philip and De Vries (1957). Differentiation of this equation and application of the continuity requirement gives the general differential equation for moisture flow: k ⫽ (DT T) ⫹ (D ) ⫹ t z
(9.162)
The heat conduction equation for the soil is
D ⫽ D V ⫹ D L ⫽ isothermal water diffusivity (9.161)
冉 冊
T k ⫽ t T t C
(9.163)
310
9
CONDUCTION PHENOMENA
Figure 9.44 (Continued )
where kt ⫽ thermal conductivity C ⫽ volumetric heat capacity The ratio of thermal conductivity to the volumetric heat capacity is the thermal diffusivity A. Both transient and steady-state temperature distributions computed using the Philip and De Vries theory incorporated into numerical models have agreed well with measured values in a number of cases. The actual moisture movements and distributions have not agreed as well, for example, Abdel-Hadi and Mitchell (1981) and Cameron (1986). The numerical simulations have been done using transform methods, finite difference methods, the finite element method, and the integrated finite difference method. Cameron (1986) reformulated the equations in terms of suction head rather than moisture content and incorporated them into the finite element model of Walker et al. (1981) for solution of two-dimensional problems. 9.22
GROUND FREEZING
Heat conduction in soils and rocks is discussed in Section 9.5, and values for thermal properties are given in
Table 9.2. Three topics are considered in this section: (1) the depth of frost penetration, which illustrates the application of transient heat flow analysis, (2) frost action in soils, a phenomenon of great practical importance that can be understood through consideration of interactions of the physical and physicochemical properties of the soil, and (3) some effects of freezing on the behavior and properties of the soil after thawing. These topics are also covered in some detail by Konrad (2001) and the references therein. Depth of Frost Penetration
Accurate estimation of the depth of ground freezing during the winter, the depth of thawing in permafrost areas during the summer, and the refrigeration and time requirements for artificial ground freezing for temporary ground stabilization are all problems involving transient heat flow analysis. They differ from the conduction analyses in the preceding sections in that the phase change of water to ice must be taken into account. Prediction of the maximum depth of frost penetration illustrates this type of problem. Theoretical solutions of this problem are based on a mathematical
GROUND FREEZING
analysis developed by Neumann in about 1860 (Berggren, 1943; Aldrich, 1956; Brown, 1964; Konrad, 2001). The relationship between thermal energy u and temperature T for a soil mass at constant water content is shown in Fig. 9.45. In the absence of freezing or thawing u ⫽C T
T 2T ⫽a 2 t z
311 (9.168)
where a ⫽ kt /C is the thermal diffusivity (L2 /T). Equation (9.168) is the one-dimensional, transient heat flow equation. At the interface between frozen and unfrozen soil, z ⫽ Z, and the equation of heat continuity is
(9.164) Ls
dZ ⫽ q ƒ ⫺ qu dt
(9.169)
The Fourier equation for heat flow is T qt ⫽ ⫺kt z
(9.165)
In the absence of freezing or thawing, thermal continuity and conservation of thermal energy require that the rate of change of thermal energy of an element plus the rate of heat transfer into the element equal zero, that is, for the one-dimensional case u q ⫹ ⫽0 t z
(9.166)
Using Eqs. (9.164) and (9.165), Eq. (9.166) may be written C
T 2T ⫽ kt 2 t z
(9.167)
or
where Ls is the latent heat of fusion of water and qƒ ⫺ qu is the net rate of heat flow away from the interface. Equation (9.169) can be written Ls
dZ T T ⫽ kƒ ƒ ⫺ ku u dt z z
(9.170)
where the subscripts u and f pertain to unfrozen and frozen soil, respectively. Simultaneous solution of Eqs. (9.168) and (9.170) gives the depth of frost penetration. Stefan Formula The simplest solution is to assume that the latent heat is the only heat to be removed during freezing and neglect the heat that must be removed to cool the soil water to the freezing point, that is, the thermal energy stored as volumetric heat is neglected. This condition is shown by Fig. 9.46. For this case Eq. (9.168) does not exist, and Eq. (9.170) becomes Ls
dZ T ⫽ kƒ s dt Z
(9.171)
where Ts is the surface temperature. The solution of this equation is
Figure 9.45 Thermal energy as a function of temperature
for a wet soil.
Figure 9.46 Assumed conditions for the Stefan equation.
312
9
CONDUCTION PHENOMENA
冉
2kƒ
Z⫽
冊
冕 T dt s
Ls
1/2
(9.172)
The integral of Ts dt is a measure of freezing intensity. It can be expressed by the freezing index F, which has units of degrees ⫻ time. Index F is usually given in degree-days. It is shown in relation to the annual temperature cycle in Fig. 9.47. Freezing index values are derived from meteorological data. Methods for determination of freezing index values are given by Linell et al. (1963), Straub and Wegmann (1965), McCormick (1971), and others. Maps showing mean freezing index values are available for some areas. It is important when using such data sources to be sure that there are not local deviations from the average values that are given. Different types of ground cover, local topography and vegetation, and solar radiation all influence the net heat flux at the ground surface. The Stefan equation can also be used to estimate the summer thaw depth in permafrost; that is, the thickness of the active layer. In this case the ground thawing index, also in degree-days and derived from meteorological data, is used in Eq. (9.172) in place of the freezing index (Konrad, 2001). Modified Berggren Formula The Stefan formula overpredicts the depth of freezing because it neglects the removal of the volumetric heats of frozen and unfrozen soil. Simultaneous solution of Eqs. (9.168) and
(9.170) has been made for the conditions shown in Fig. 9.48, assuming that the soil has a uniform initial temperature that is T0 degrees above freezing and that the surface temperature drops suddenly to Ts below freezing (Aldrich, 1956). The solution is
冉 冊
Z⫽
2kTst Ls
1/2
(9.173)
where k is taken as an average thermal conductivity for frozen and unfrozen soil. The dimensionless correction coefficient depends on the two parameters shown in Fig. 9.49. The thermal ratio is given by ⫽
T0 Ts
(9.174)
and the fusion parameter is ⫽
C T Ls s
(9.175)
An averaged value for the volumetric heats of frozen and unfrozen soil can be used for C in Eq. (9.175). In application, the quantity Tst in Eq. (9.173) is replaced by the freezing index, and Ts in (9.175) is given by F/t, where t is the duration of the freezing period. The coefficient corrects the Stefan formula for neglect of volumetric heat. For soils with high water content C is small relative to Ls; therefore, is small and
Figure 9.47 Freezing index in relation to the annual temperature cycle.
GROUND FREEZING
313
Figure 9.48 Thermal conditions assumed in the derivation of the modified Berggren for-
mula.
the Stefan formula is reasonable. For arctic climates, where T0 is not much above the freezing point, is small, is greater than 0.9, and the Stefan formula is satisfactory. However, in more temperate climates and in relatively dry or well-drained soils, the correction becomes important. A comparison between theoretical freezing depths and a design curve proposed by the Corps of Engineers is shown in Fig. 9.50 for several soil types. The theoretical curves were developed by Brown (1964) using the modified Berggren equation and the thermal properties given in Fig. 9.13. Consideration should be given to the effect of different types of surface cover on the ground surface temperature because air temperature and ground temperature are not likely to be the same, and the effects of thermal radiation may be important. Observed
depths of frost penetration may be misleading if estimates for a proposed pavement or other structure are needed because of differences in ground surface characteristics and because the pavement or foundation base will be at different water content and density than the surrounding soil. The solutions do not account for flow of water into or out of the soil or the formation of ice lenses during the freezing period. This may be particularly important when dealing with frost heave susceptible soils or when developing frozen soil barriers for the cutoff of groundwater flow. Methods for prediction of frost depth in soils susceptible to ice lens formation and the rate of heave are given by Konrad (2001). The initiation of freezing of flowing groundwater requires that the rate of volumetric and latent heat removal be high enough so that ice can form during the residence time
314
9
CONDUCTION PHENOMENA
Figure 9.49 Correction coefficients for use in the modified Berggren formula (from Aldrich,
1956).
of an element of water moving between the boundaries of the specified zone of solidification. Frost Heaving
Freezing of some soils is accompanied by the formation of ice layers or ‘‘lenses’’ that can range from a millimeter to several centimeters in thickness. These lenses are essentially pure ice and are free from large numbers of contained soil particles. The ground surface may ‘‘heave’’ by as much as several tens of centimeters, and the overall volume increase can be many times the 9 percent expansion that occurs when water freezes. Heave pressures of many atmospheres are common. The freezing of frost-susceptible soils beneath pavements and foundations can cause major distress or failure as a result of uneven uplift during freezing and loss of support on thawing, owing to the presence of large water-filled voids. Ordinarily, ice lenses are oriented normal to the direction of cold-front movement and become thicker and more widely separated with depth. The rate of heaving may be as high as several millimeters per day. It depends on the rate of freezing in
a complex manner. If the cooling rate is too high, then the soil freezes before water can migrate to an ice lens, so the heave becomes only that due to the expansion of water on freezing. Three conditions are necessary for ice lens formation and frost heave: 1. Frost-susceptible soil 2. Freezing temperature 3. Availability of water Frost heaving can occur only where there is a water table, perched water table, or pocket of water reasonably close to the freezing front. Frost-Susceptible Soils Almost any soil may be made to heave if the freezing rate and water supply are controlled. In nature, however, the usual rates of freezing are such that only certain soil types are frost susceptible. Clean sands, gravels, and highly plastic intact clays generally do not heave. Although the only completely reliable way to evaluate frost susceptibility is by some type of performance test during freezing, soils that contain more than 3 percent of their particles finer than 0.02 mm are potentially frost susceptible.
GROUND FREEZING
315
Figure 9.50 Predicted frost penetration depths compared with the Corps of Engineers’ de-
sign curve (Brown, 1964). Curve a—sandy soil: dry density 140 lb / ft3, saturated, moisture content 7 percent. Curve b—silt, clay: dry density 80 lb / ft3, unsaturated, moisture content 2 percent. Curve c—sandy soil; dry density 140 lb / ft3, unsaturated, moisture content 2 percent. Curve d—silt, clay: dry density 120 lb / ft3, moisture content 10 to 20 percent (saturated). Curve e—silt, clay: dry density 80 lb / ft3 saturated, moisture content 30 percent. Curve f—Pure ice over still water.
Frost-susceptible soils have been classified by the Corps of Engineers in the following order of increasing frost susceptibility:
Group (increasing susceptibility) F1 F2 F3
F4
Soil Types Gravelly soils with 3 to 20 percent finer than 0.02 mm Sands with 3 to 15 percent finer than 0.02 mm a. Gravelly soils with more than 20 percent finer than 0.02mm sands, except fine silt sands with more than 15 percent finer than 0.02 mm b. Clays with PI greater than 12 percent, except varved clays a. Silts and sandy silts b. Fine silty sands with more than 15 percent finer than 0.02 mm c. Lean clays with PI less than 12 percent d. Varved clays
A method for the evaluation of frost susceptibility that takes project requirements and acceptable risks and freezing conditions into account as well as the soil type is described by Konrad and Morgenstern (1983). Mechanism of Frost Heave The formation of ice lenses is a complex process that involves interrelationships between the phase change of water to ice, transport of water to the lens, and general unsteady heat flow in the freezing soil. The following explanation of the physics of frost heave is based largely on the mechanism proposed by Martin (1959). Although the Martin (1959) model may not be correct in all details in the light of subsequent research, it provides a logical and instructive basis for understanding many aspects of the frost heave process. The ice lens formation cycle involves four stages: 1. 2. 3. 4.
Nucleation of ice Growth of the ice lens Termination of ice growth Heat and water flow between the end of stage 3 and the start of stage 1 again
In reality, heat and water flows continue through all four stages; however, it is convenient to consider them separately. The temperature for nucleation of an ice crystal, Tn, is less than the freezing temperature, T0. In soils, T0 in
316
9
CONDUCTION PHENOMENA
pore water is less than the normal freezing point of water because of dissolved ions, particle surface force effects, and negative pore water pressures that exist in the freezing zone. The freezing point decreases with decreasing distance to particle surfaces and may be several degrees lower in the double layer than in the center of a pore. Thus, in a fine-grained soil, there is an unfrozen film on particle surfaces that persists until the temperature drops below 0C. The face of an ice front has a thin film of adsorbed water. Freezing advances by incorporation of water molecules from the film into the ice, while additional water molecules enter the film to maintain its thickness. It is energetically easier to bring water to the ice from adjacent pores than to freeze the adsorbed water on the particle or to propagate the ice through a pore constriction. The driving force for water transport to the ice is an equivalent hydrostatic pressure gradient that is generated by freezing point depression, by removal of the water from the soil at the ice front, which creates a higher effective stress in the vicinity of the ice than away from it, by interfacial tension at the ice–water interface, and by osmotic pressure generated by the high concentration of ions in the water adjacent to the ice front. Ice formation continues until the water tension in the pores supplying water becomes great enough to cause cavitation, or decreased upward water flow from below leads to new ice lens formation beneath the existing lens. The processes of freezing and ice lens formation proceed in the following way with time according to Martin’s theory. If homogeneous soil, at uniform water content and temperature T0 above freezing, is subjected to a surface temperature Ts below freezing, then the variation of temperature with depth at some time is as shown in Fig. 9.51. The rate of heat flow at any point is ⫺kt(dT/dz). If dT/dz at point A is greater than at point B, the temperature of the element will drop. When water goes to ice, it gives up its latent heat, which flows both up and down and may slow or stop changes in the value of dT/dz for some time period, thus halting the rate of advance of the freezing front into the soil. Ground heave results from the formation of a lens at A, with water supplied according to the mechanisms indicated above. The energy needed to lift the overlying material, which may include not only the soil and ice lenses above, but also pavements and structures, is available because ice forms under conditions of supercooling at a temperature T X ⬍ TFP, where TFP is the freezing temperature. The available energy is
F ⫽
L(TFP ⫺ T X) TFP
(9.176)
Figure 9.51 Temperature versus depth relationships in a
freezing soil.
The quantity L is the latent heat. Supercooling of 1C is sufficient to lift 12.5 kg a distance of 10 mm. Alternatively, the energy for heave may originate from the thin water films at the ice surface (Kaplar, 1970). As long as water can flow to a growing ice lens fast enough, the volumetric heat and latent heat can produce a temporary steady-state condition so that (dT/ dz)A ⫽ (dT/dz)B. For example, silt can supply water at a rate sufficient for heave at 1 mm/h. After some time the ability of the soil to supply water will drop because the water supply in the region ahead of the ice front becomes depleted, and the hydraulic conductivity of the soil drops, owing to increased tension in the pore water. This is illustrated in Fig. 9.52, where hydraulic conductivity data as a function of negative pore water pressure are shown for a silty sand, a silt, and a clay, all compacted using modified AASHTO effort, at a water content about 3 percent wet of optimum. A small negative pore water pressure is sufficient to cause water to drain from the pores of the silty sand, and this causes a sharp reduction in hydraulic conductivity. Because the clay can withstand large negative pore pressures without loss of saturation, the hydraulic conductivity is little affected by increasing reductions in the pore pressure (increasing suction). The small decrease that is observed results from the consolidation needed to carry the increased effective stress required to balance the reduction in the pore pressure. For the silt, water drainage starts when the suction reaches
GROUND FREEZING
317
which have now reduced the distance that water can be from a particle surface. The temperature drop must reach a depth where there is sufficient water available after nucleation to supply a growing lens. The thicker the overlying lens, the greater the distance, thus accounting for the increased spacings between lenses with depth. The greater the depth, the smaller the thermal gradient, as may be seen in Fig. 9.51, where (dT/dz)A ⬎ (dT/dz)A where A is on the temperature distribution curve for a later time t2. Because of this, the rate of heat extraction is slowed, and the temporary steady-state condition for lens growth can be maintained for a longer time, thus enabling formation of a thicker lens. More quantitative analyses of the freezing and frost heaving processes in terms of segregation potential, rates, pressures, and heave amounts are available. The Proceedings of the International Symposia on Ground Freezing, for example, Jones and Holden (1988), Nixon (1991), and Konrad (2001) provide excellent sources of information on these issues. Thaw Consolidation and Weakening
Figure 9.52 Hydraulic conductivity as a function of negative pore water pressure (from Martin and Wissa, 1972).
about 40 kPa; however, a significant continuous water phase remains until substantially greater values of suction are reached. In sand, the volume of water in a pore is large, and the latent heat raises the freezing temperature to the normal freezing point. Hence, there is no supercooling and no heave. Negative pore pressure development at the ice front causes the hydraulic conductivity to drop, so water cannot be supplied to form ice lenses. Thus sands freeze homogeneously with depth. In clay, the hydraulic conductivity is so low that water cannot be supplied fast enough to maintain the temporary steadystate condition needed for ice lens growth. Heave in clay only develops if the freezing rate is slowed to well below that in nature. Silts and silty soils have a combination of pore size, hydraulic conductivity, and freezing point depression that allow for large heave at normal freezing rates in the field. The freezing temperature penetrates ahead of a completed ice lens, and a new lens will start to form only after the temperature drops to the nucleation temperature. The nucleation temperature for a new lens may be less than that for the one before because of reduced saturation and consolidation from the previous flows,
When water in soil freezes, it expands by about 9 percent of its original volume. Thus a fully saturated soil increases in volume by 9 percent of its porosity, even in the absence of ice segregation and frost heave. The expansion associated with freezing disrupts the original soil structure. When thawed, the water returns to its original volume, the melting of segregated ice leaves voids, and the soil can be considerably more deformable and weaker that before it was frozen. Under drained conditions and constant applied overburden stress, the soil may consolidate to a denser state than it had prior to freezing. The lower the density of the soil, the greater is the amount of thaw consolidation. The total settlement of foundations and pavements associated with thawing is the sum of that due to (1) the phase change, (2) melting of segregated ice, and (3) compression of the weakened soil structure. Testing of representative samples under appropriate boundary conditions is the most reliable means for evaluating thaw consolidation. Samples of frozen soil are allowed to thaw under specified levels of applied stress and under defined drainage conditions, and the decrease in void ratio or thickness is determined. An example of the effects of freezing and thawing on the compression and strength of initially undisturbed Boston blue clay is shown in Fig. 9.53 from Swan and Greene (1998). These tests were done as part of a ground freezing project for ground strengthening to enable jacking of tunnel sections beneath operating rail lines during construction of the recently completed Central Artery/Tunnel Project in Boston. Detailed
318
9
CONDUCTION PHENOMENA
0 2 C1-UF e0 = 1.064
Vertical Strain, εv (%)
4 6 C4-FT e0 = 1.171
8 10 12 14 16 18 20 22 10
100 1000 Effective Stress, σc (kPa)
10000
(a) 120
Deviator Stress, σ1 – σ3 (kPa)
100 UUC1-UF (σ1–σ3)max = 109.6 kPa ε1 = 2.3% su/σ3cell = 0.36 e0 = 1.02; w = 37.5%
80
60
40 UUC4-FT (σ1– σ3)max = 42.4 kPa ε1 = 12.8% su/σ3cell = 0.14 e0 = 1.13; w = 43.2%
20
0
0
5
10
15
20
25
Axial Strain. % (b)
Figure 9.53 (a) Comparison between the compression behavior of unfrozen (C1-UF) and frozen then thawed (C4-FT) samples of Boston blue clay. (b) Deviator stress vs. axial strain in unconsolidated–undrained triaxial compression of unfrozen (UUC1-UF) and frozen and thawed (UUC4-FT) Boston blue clay (from Swan and Greene, 1998).
analysis of the thaw consolidation process and its analytical representation is given by Nixon and Ladanyi (1978) and Andersland and Anderson (1978). Ground Strengthening and Flow Barriers by Artificial Ground Freezing
Artificial ground freezing has applications for formation of seepage cutoff barriers in situ, excavation support, and other ground strengthening purposes. These appli-
cations are usually temporary, and they have the advantage that the ground is not permanently altered, except for such property changes as may be caused by the freeze–thaw processes. Returning the ground to its pristine state may be important for environmental reasons where alternative methods for stabilization could permanently change the state and composition of the subsoil. Freezing is usually accomplished by installation of freeze pipes and circulation of a refrigerant. For emer-
CONCLUDING COMMENTS
9.23
CONCLUDING COMMENTS
Conductivity properties are one of the four key dimensions of soil behavior that must be understood and quantified for success in geoengineering. The other three dimensions are volume change, deformation and strength, and the influences of time. They form the subjects of the following three chapters of this book. Water flows through soils and rocks under fully saturated conditions have been the most studied, and hydraulic conductivity properties, their determination and application for seepage studies of various types, construction dewatering, and the like are central to geotechnical engineering. One objective of this chapter has been to elucidate the fundamental factors that control
160
120 Second Stage
First Stage
Natural Strain, ε -%
gency and rapid ground freezing, expendable refrigerants such as liquid nitrogen or carbon dioxide in an open pipe can be used. The thermal energy removal and time requirements for freezing the ground can be calculated using the appropriate thermal conductivity, volumetric heat, and latent heat properties for the ground and heat conduction theory in conjunction with the characteristics of the refrigeration system (Sanger, 1968; Shuster, 1972; Sanger and Sayles, 1979). For many applications the energy required to freeze the ground in kcal/m3 will be in the range of 2200 to 2800 times the water content in percent (Shuster, 1972). However, if the rate of groundwater flow exceeds about 1.5 m/day, it may be difficult to freeze the ground without a very high refrigeration capacity to ensure that the necessary temperature decrease and latent heat removal can be accomplished within the time any element of water is within the zone to be frozen. The long-term strength and stress–strain characteristics of frozen ground depend on the ice content, temperature, and duration of loading. The short-term strength under rapid loading, which can be up to 20 MPa at low temperature, may be 5 to 10 times greater than that under sustained stresses. That is, frozen soils are susceptible to creep strength losses (Chapter 12). The deformation behavior of frozen soil is viscoplastic, and the stress and temperature have significant influence on the deformation at any time. The creep curves in Fig. 9.54 illustrate these effects. The onset of the third stage of creep indicates the beginning of failure. The evaluation of stability of frozen soil masses, the prediction of creep deformation, and the possibility of creep rupture are complex problems because of heterogeneous ground conditions, irregular geometries, and temperature and stress variations throughout the frozen soil mass. Design and implementation considerations for use of ground freezing in construction are given by Donohoe et al. (1998).
319
80
Third Stage
Pa
55
T
=
0
,σ °C
=
M
Temperature Effect
0.
40
T=
,σ= –2.2 °C
Pa
0.55 M
Stress effect
T = –2.2 °C, σ = 0.138 MPa 0 0
10
tf
20
30
Time, t (hr)
Figure 9.54 Creep curves for a frozen organic silty clay (from Sanger and Sayles, 1979).
the permeability of soils to water and how this property depends on soil type, especially gradation, and is sensitive to testing conditions, soil fabric, and environmental factors. The understanding of these fundamentals is important, not only because of the insights provided but also because many of the same considerations apply to the several other types of flows that are known to be important—chemical, electrical, and thermal. Knowledge of one is helpful in the understanding and quantification of the other because the mathematical descriptions of the flows follow similar force-flux relationships. At the same time it is necessary to take into account that the flows of fluids of different composition and the application of hydraulic, chemical, electrical, and thermal driving forces to soils can cause changes in compositions and properties, with differing consequences, depending on the situation. Furthermore, as examined in considerable detail in this chapter, flow coupling can be important, especially advective and diffusive chemical transport, electroosmotic water and chemical flow, and thermally driven moisture flow. Considerable impetus for research on these processes has been generated by geoenvironmental needs, including enhanced
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9
CONDUCTION PHENOMENA
and more economical waste containment and site remediation strategies. Ground freezing, in addition to its importance in engineering and construction in cold regions, is seeing new applications for temporary ground stabilization needed for underground construction in sensitive urban areas. QUESTIONS AND PROBLEMS
1. A uniform sand with rounded particles has a void ratio of 0.63 and a hydraulic conductivity, k, of 2.7 ⫻ 10⫺4 m/s. Estimate the value of k for the same sand at a void ratio of 0.75. 2. The soil profile at a site that must be dewatered consists of three homogeneous horizontal layers of equal thickness. The value of k for the upper and lower layers is 1 ⫻ 10⫺6 m/s and that of the middle layer is 1 ⫻ 10⫺4 m/s. What is the ratio of the average hydraulic conductivity in the horizontal direction to that in the vertical direction? 3. Consider a zone of undisturbed San Francisco Bay mud free of sand and silt lenses. Comment on the probable effect of disturbance on the hydraulic conductivity, if any. Would this material be expected to be anisotropic with respect to hydraulic conductivity? Why? 4. Assume the specific surface of the San Francisco Bay mud in Question 3 is 50 m2 /g and prepare a plot of the hydraulic conductivity in meters/second as a function of water content over the range of 100 percent decreased to 25 percent by consolidation using the Kozeny–Carman equation. Would you expect the actual variation in hydraulic conductivity as a function of water content to be of this form? Why? Sketch the variation you would expect and explain why it has this form. 5. At a Superfund site a plastic concrete slurry wall was proposed as a vertical containment barrier against escape of liquid wastes and heavily contaminated groundwater. The subsurface conditions consist of horizontally bedded mudstone and siltstone above thick, very low permeability clay shale. The cutoff wall was to extend into the slay shale, which has been shown to be able to serve as a very effective bottom barrier. For the final design and construction, however, a 3-ft-wide gravel trench was used instead of the slurry wall. Sumps and pumps placed in the bottom of the trench are used to collect liquids. Explain how this trench can serve as an effective cutoff and discuss the pros and cons of the two systems.
6. How can the effects of incompatibility between chemicals in a waste repository and a compacted clay liner best be minimized? 7. Two parallel channels, one with flowing water and the other with contaminated water, are 100 ft apart. The surface elevation of the contaminated channel is 99 ft, and the surface elevation of the clean water channel is at 97 ft. The soil between the two channels is sand with a hydraulic conductivity of 1 ⫻ 10⫺4 m/s, a dry unit weight of 100 pcf, and a specific gravity of solids of 2.65. Estimate the time it will take for seepage from the contaminated channel to begin flowing into the initially clean channel. Make the following assumptions and simplifications: a. Seepage is one dimensional. b. The only subsurface reaction is adsorption onto the soil particles. c. The soil–water partitioning coefficient is 0.4 cm3 /g. d. Hydrodynamic dispersion can be ignored. 8. For the compacted clay waste containment liner shown below and assuming steady-state conditions: a. What is the contaminant transport for pure molecular diffusion? b. What is the contaminant transport rate for pure advection? c. What is the contaminant transport rate for advection plus diffusion? d. Why don’t the answers to parts (a) and (b) add up to (c)?
NOTE: Advection and diffusion are in the same direction; therefore, J ⬎ 0, and the solution will be in the form c ⫽ a1ea2x ⫹ a3
QUESTIONS AND PROBLEMS
9. One-dimensional flow is occurring by electroosmosis between two electrodes spaced at 3.0 m with a potential drop of 100 V (DC) between them. What should the water flow rate be if the coefficient of electroosmotic permeability, ke, is 5 ⫻ 10⫺9 m2 /s V assuming an open system? If no water is resupplied at the anode, what maximum consolidation pressure should develop at a point midway between electrodes if the hydraulic conductivity of the soil is 1 ⫻ 10⫺8 m/s? 10. a. A soil has a coefficient of electroosmotic permeability equal to 0.3 ⫻ 10⫺8 m/s per V/m and a hydraulic conductivity of 6 ⫻ 10⫺9 m/s. Starting from the general relationship
321
Assume that the water pressure at the top of the leachate collection layer is atmospheric and that the only fluxes across the liner are water and electricity. The characteristics of the compacted clay liner are: Hydraulic conductivity
Ji ⫽ Lij Xj
kh ⫽ 1 ⫻ 10⫺7 m/s Electroosmotic coefficients
derive an expression for the pore water tension that may be developed under ideal conditions for consolidation of the clay by electroosmosis and compute the value that should develop at a point where the voltage is 25 V. Be sure to indicate correct units with your answers. b. In the absence of electrochemical effects or cavitation, would you consider your answer to part (a) to represent an upper or lower bound estimate of the pore water tension? Why? (HINT: Consider the influence of consolidation on the soil properties that are used to predict the pore water tension.) 11. In 1892 Saxen established that there is equivalence between electroosmosis and streaming potential such that the results of a hydraulic conductivity test in which streaming potential is measured can be used to predict the volume flow rate during electroosmosis in terms of the electrical current. Starting with the general equations for coupled electrical and hydraulic flow, derive Saxen’s law. What will be the drainage rate from a soil, in m3 /h amp, if the streaming potential is 25 mV/ atm? What will be the cost of electrical power per cubic meter of water drained if electricity costs $0.10 per kWh and a maximum voltage of 75 V is used? 12. It might be possible to prevent leakage of hazardous and toxic chemicals through waste impoundment and landfill clay or geosynthetic-clay liners by means of an electroosmosis counterflow barrier against hydraulically driven seepage. Consider the impoundment and liner system shown below.
ke ⫽ 2 ⫻ 10⫺9 m2 /s V ki ⫽ 0.2 ⫻ 10⫺6 m3 /s amp a. Wire mesh is proposed for use as electrodes. Where would you place the anode and cathode meshes? b. If the waste pond is to be filled to an average depth of 6 m, what voltage drop should be maintained between the electrodes? c. What will the power cost be per hectare of impoundment per year? Power costs $0.09 per kWh. d. Assume that the leachate collection layer is flushed continuously with freshwater and that the liquid waste contains dissolved salts. Write the complete set of equations that would be required to describe all the flows across the liner during electroosmosis. Define all terms. e. Will maintenance of a no hydraulic flow condition ensure that no leachate will escape through the clay liner? Why? 13. a. Estimate the minimum footing depths for structures in a Midwestern city where the freezing index is 750 degree-days and the duration of the freezing index is 100 days. The mean annual air temperature is 50F. The soil is silty clay with a water content of 20 percent and a dry unit weight of 110 lb/ft3. Assume no ice segregation and compare values according to the Stefan and modified Berggren formulas. b. What will be the depth of frost penetration below original ground surface level if a surface heave of 6 inches develops due to ice lens for-
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CONDUCTION PHENOMENA
mation? Assume a frozen ground temperature of 32F. c. If a pavement is to be placed over the soil, what thickness of granular base course should be used to prevent freezing of the subgrade? The base course will be compacted to a dry density of 125 lb/ft3 at a water content of 15 percent. If the pavement structure is to contain an 8inch-thick Portland cement concrete surface layer, will your result tend to overestimate or underestimate the base thickness required? Why? 14. A compacted fine-grained soil is to be used as a liner for a chemical waste storage area. Free liquid leachate and possibly some heavier than water free phase nonsoluble, nonpolar organic liquids (DNAPLs) may accumulate in some areas as a result of rupturing and corrosion of the drums in which they were stored. Two sources of soil for use in the liner are available. They have the following properties: Property
Soil A
Soil B
Unified class Liquid limit (%) Plastic limit (%) Clay size (%) Silt size (%) Sand size (%) Predominant clay mineral Cation exchange capacity (meg/100 g)
(CH) 90 30 50 30 20 Smectite
(CL) 45 25 30 40 30 Illite
60
20
a. Which of the two soils would be best suited for use in the liner? Why? b. What tests would you use to validate your choice? Why? c. Assume that you have confirmed that it will be possible to compact the soil to states that will have hydraulic conductivities in the range of 1 ⫻ 10⫺8 to 1 ⫻ 10⫺11 m/s. A liner thickness of 0.6 m is proposed. Leachate is likely to accumulate to a depth of 1.0 m above the top of the liner. A leachate collection layer will underlie the liner. d. If the concentration of dissolved salts in the leachate is 1.0 M and the average diffusion coefficient is 5 ⫻ 10⫺10 m2 /s, determine for the steady state the total amount of dissolved chemical per unit area per year that will escape
through the liner as a function of the hydraulic conductivity. Show in the same diagram the proportions of the total that are attributable to diffusion and advection. Assume that the leachate collection layer is fully drained, but for purposes of analysis the fluid level can be considered at the bottom of the clay. Determine the leakage rate through the liner per unit area as a function of the hydraulic conductivity and show it on a diagram. 15. The diagram below shows the cross section of a tunnel and underlying borehole in which waste canisters for spent nuclear fuel are located. Such an arrangement is proposed for deep (e.g., several hundred meters) burial of nuclear waste in crystalline rock. The surrounding rock can be assumed fully saturated, and the groundwater table will be within a few tens of meters of the ground surface. Thermal studies have shown that the temperature of the waste canister will rise to as high as 150C at its surface. A canister life of about 100 years is anticipated using either stainless steel or copper for the material. The surrounding environment must be safe against leakage of radionuclides from the repository for a minimum of 100,000 years.
QUESTIONS AND PROBLEMS
Clay or a mix of clay with other materials such as sand and crushed rock is proposed for use as the fill both around the canisters and in the tunnel. a. What are the most important properties that the backfill should possess to ensure isolation and buffering of the waste from the outside environment? b. What clay material would you propose for this application and under what conditions would you place it?
323
c. Assess the probable natures and directions of heat and fluid flows that will develop, if any. d. What alterations might occur in the material during the life of the repository if any? Consider the effects of groundwater from the surrounding ground, corrosion of the canister, and the prolonged exposure to high temperature. Would each of these alternations be likely to enhance or impair the effectiveness of the clay pack?
CHAPTER 10
Volume Change Behavior
10.1
INTRODUCTION
Volume changes in soils are important because they determine settlements due to compression, heave due to expansion, and contribute to deformations caused by shear stresses. Changes in volume cause changes in strength and deformation properties that, in turn, influence stability. Volume changes are induced by changes in applied stresses, chemical and moisture environments, and temperature. The effects of stress changes are generally the most important and have been the most studied. In this chapter, factors contributing to volume change are discussed, and their relative importance is considered. Emphasis is on consolidation and swelling. Shrinkage is a special case of consolidation, wherein the consolidation pressure is developed internally from capillary menisci and the surface tension of water. Reader familiarity with the phenomenological aspects of compression and swelling as ordinarily treated in geotechnical engineering is assumed, as described by the idealized void ratio–effective pressure relationships shown in Fig. 10.1. Unless otherwise noted, the discussion in this chapter is based on the behavior in one-dimensional deformation conditions. Although the mathematics and numerical analyses needed for quantification of volume changes in two or three dimensions are more complex, the phenomena and processes that control the behavior are the same.
10.2 GENERAL VOLUME CHANGE BEHAVIOR OF SOILS
Soil void ratio is normally in the range of about 0.5 to 4.0, as shown in Fig. 10.2. Although the range of pressures of interest in most cases (up to a few hundred kilopascals) is relatively small on a geological scale,
the void ratios encompass virtually the full range from fresh sediments to shale. Mechanical and chemical changes accompany and influence the densification process. In general, the void ratio–effective pressure relationship is related to grain size and plasticity in the manner shown by Fig. 10.2b. Particle size and shape, which together determine specific surface area, are the most important factors influencing both the void ratio at any pressure and the effects that physicochemical and mechanical factors have on consolidation and swelling (Meade, 1964). Particle size and shape are direct manifestations of composition, with increasing colloidal activity and expansiveness associated with decreasing particle sizes. Values of compression index, Cc, defined in Fig. 10.1, from less than 0.2 to as high as 17 for specially prepared sodium montmorillonite under low pressure have been measured, although values less than 2.0 are usual. The compression index for most natural clays is less than 1.0, with a value less than 0.5 in most cases. The swelling index, Cs, is less than the compression index, usually by a substantial amount, as a result of particle rearrangement during compression that does not recur during expansion. After one or more cycles of recompression and unloading accompanied with some irrecoverable volumetric strain, the reloading and swelling indices measured in the preyield region become nearly equal. Swelling index values for three clay minerals, muscovite, and sand are listed in Table 10.1. For undisturbed natural soils the swelling index values are usually less than 0.1 for nonexpansive materials to more than 0.2 for expansive soils. The compressibility of dense sands and gravels is far less than that of normally consolidated clays; nonetheless, volume changes under high pressures may be substantial in granular materials as shown in Fig. 10.3. At low stress levels, the compressibility of sand de325
326
10
VOLUME CHANGE BEHAVIOR
Figure 10.1 Idealized void ratio–effective stress relationships for a compressible soil.
Figure 10.2 Compression curves for several soils (redrawn from Lambe and Whitman,
1969).
PRECONSOLIDATION PRESSURE
Table 10.1
Mineral (1) Kaolinite
Illite
Smectite
Muscovite
327
Swelling Index Values for Several Minerals Pore Fluid, Adsorbed Cations, Electrolyte Concentration, in Gram Equivalent Weights per Liter (2)
Void Ratio at Effective Consolidation Pressure of 100 psf (5 kPa) (3)
Water, sodium, 1 Water, sodium, 1 ⫻ 10⫺4 Water, calcium, 1 Water, calcium, 1 ⫻ 10⫺4 Ethyl alcohol Carbon tetrachloride Dry air Water, sodium, 1 Water, sodium, 1 ⫻ 10⫺3 Water, calcium, 1 Water, calcium, 1 ⫻ 10⫺3 Ethyl alcohol Carbon tetrachloride Dry air Water, sodium, 1 ⫻ 10⫺1 Water, sodium, 5 ⫻ 10⫺4 Water, calcium, 1 Water, calcium, 1 ⫻ 10⫺3 Ethyl alcohol Carbon tetrachloride Water Carbon tetrachloride Dry air
0.95 1.05 0.94 0.98 1.10 1.10 1.36 1.77 2.50 1.51 1.59 1.48 1.14 1.46 5.40 11.15 1.84 2.18 1.49 1.21 2.19 1.98 2.29
Sand
Swelling Index (4) 0.08 0.08 0.07 0.07 0.06 0.05 0.04 0.37 0.65 0.28 0.31 0.19 0.04 0.04 1.53 3.60 0.26 0.34 0.10 0.03 0.42 0.35 0.41 0.01 to 0.03
From Olson and Mesri (1970). Reprinted with permission of ASCE.
pends on initial density. However, at higher stress levels, yielding is observed, and the compression curves for a given sand at different initial densities merge into a unique compression line. Particle crushing is the primary cause of the large volumetric strains that occur along the normal compression line. The yield stress is related to particle tensile strength (McDowell and Bolton, 1998; Nakata et al., 2001). Compressibility data for several sands, gravels, and rockfills are shown in Fig. 10.4. At a pressure of 700 kPa (100 psi) a compression of 3 percent is common, and values as high as 6.5 percent have been measured. Interestingly, the compacted shells of a rockfill dam are sometimes more compressible than the compacted clay core. 10.3 Figure 10.3 Compressibility of three sands under high pressure (from Pestana and Whittle, 1995).
PRECONSOLIDATION PRESSURE
Three different relationships between the present overburden effective stress v0 and the maximum past over-
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VOLUME CHANGE BEHAVIOR
Figure 10.4 Field compressibility of earth and rockfill materials (from Wilson, 1973). Re-
printed with permission from John Wiley & Sons.
burden effective stress vm are possible for the soil at a site: 1. vm ⬍ v0 —Underconsolidated The soil has not yet reached equilibrium under the present overburden owing to the time required for consolidation. Underconsolidation can result from such conditions as deposition at a rate faster than consolidation, rapid drop in the groundwater table, insufficient time since the placement of a fill or other loading for consolidation to be completed, and disturbance that causes a structure breakdown and decrease in effective stress. 2. vm ⫽ v0 —Normally Consolidated The soil is in effective stress equilibrium with the present overburden effective stress. Surprisingly few, if any, deposits have been encountered that are exactly normally consolidated. Most are at least very slightly overconsolidated as a result of processes of the type summarized in Table 10.2. Underconsolidated soil behaves as normally consolidated soil until the end of primary con-
solidation, and overconsolidated clays become normally consolidated clays when loaded beyond their maximum past pressure. 3. vm ⬎ v0 —Overconsolidated or Preconsolidated The soil has been consolidated, or behaves as if consolidated, under an effective stress greater than the present overburden effective stress. Characteristics, causes, and mechanisms of preconsolidation are summarized in Table 10.2. Cemented or structured soil may behave like an overconsolidated soil; the yield pressure is larger than the maximum past pressure even though the soil has not experienced a pressure greater than the present overburden stress. Accurate knowledge of the maximum past consolidation pressure is needed for reliable predictions of settlement and to aid in the interpretation of geologic history. If the recompression to virgin compression curve does not show a well-defined break, such as at point B in Fig. 10.1, the preconsolidation pressure is difficult to determine. Gentle curvature of the com-
329
PRECONSOLIDATION PRESSURE
Table 10.2
Preconsolidation Mechanisms for Horizontal Deposits Under Geostatic Stresses
Category A. Mechanical one dimensional
B. Desiccation
C. Drained creep (aging)
D. Physicochemical
Description 1. Changes in total vertical stress (overburden, glaciers, etc.) 2. Changes in pore pressure (water table, seepage conditions, etc.) 1. Drying due to evaporation, vegetation, etc. 2. Drying due to freezing 1. Long-term secondary compression
1. Natural cementation due to carbonates, silica, etc. 2. Other causes of bonding due to ion exchange, thixotropy, ‘‘weathering’’ etc.
Stress History Profile
In situ Stress Condition
Uniform with constant p ⫺ v0
Remarks/References
K0, but value at given OCR varies for reload versus unload
Most obvious and easiest to identify
Often highly erratic
Can deviate from K0, e.g., isotropic capillary stresses
Drying crusts found at surface of most deposits; can be at depth within deltaic deposits
Uniform with constant p / v0
K0, but not necessarily normally consolidated value
Leonards and Altschaeffl (1964); Bjerrum (1967)
(except with seepage)
Not uniform
No information
Poorly understood and often difficult to prove. Very pronounced in eastern Canadian clays, e.g., Sangrey (1972), Bjerrum (1973), and Quigley (1980)
After Jamiolkowski et al., 1985.
pression curve over the preconsolidation pressure range is characteristic of sands, weathered clays, heavily overconsolidated clays, and disturbed clays. The rate of loading and time have significant effects on the equilibrium void ratio–effective stress relationship, especially for sensitive structured clays as shown in Fig. 10.5. It is not surprising, therefore, that rate of loading and time influence also the measured preconsolidation pressure. The preconsolidation pressure decreases as the duration of load application increases and as the rate of deformation decreases, as shown by
Fig. 10.6 from Leroueil et al. (1990). The higher values of apparent preconsolidation pressure associated with the faster rates of loading reflect the influences of the viscous resistance of the soil structure. The ratedependent value of preconsolidation pressure, p can be approximated by (e.g., Leroueil et al., 1985) log( p) ⫽ A ⫹ B log(˙a)
(10.1)
where ˙ a is the vertical strain rate in one-dimensional consolidation, and A and B are fitting parameters. Typ-
330
10
VOLUME CHANGE BEHAVIOR
Preconsolidation Pressure (kPa)
100 90 80 70
Constant Rate of Strain Tests at 35 ° C
5 °C
Creep Tests at 25 °C
25 °C 35 °C
60 50 40 30 10 -9
Figure 10.5 Compression curves corresponding to different times after the completion of primary consolidation.
Constant Rate of Strain Tests at 5 °C Constant Rate of Strain Tests at 25 °C
Conventional Consolidation Test at 25 °C (After 24 Hours of Loading)
10 -8
Conventional Consolidation Test at 25 °C (At End of Primary Consolidation State)
10 -7 10 -6 10-5 Volumetric Strain Rate (s-1)
10-4
Figure 10.7 Effect of compression strain rate and temperature on measured preconsolidation pressure of Berthierville clay (from Leroueil and Marques, 1996).
dictions of field behavior are possible only if undisturbed samples or in situ tests are used for determination of properties. The following factors, several of which are treated in more detail in later sections, are important in determining resistance to volume change. Physical Interactions Between Particles Physical interactions include bending, sliding, rolling, and crushing of soil particles. Physical interactions are more important than physicochemical interactions at high pressures and low void ratios. Physicochemical Interactions Between Particles
Figure 10.6 Effect of load duration increment and deformation rate on compression curves (Leroueil et al., 1990). (a) Ottawa clay (data from Crawford, 1964). (b) Ba¨ckebol clay (data from Sa¨llfors, 1975).
ical examples of the fitting for the results of different types of compression tests on Berthierville clay are shown in Fig. 10.7 (Leroueil and Marques, 1996). The effect of temperature on preconsolidation pressure can also be seen, and this is further discussed in Section 10.12. The data in Figs. 10.6 and 10.7 also illustrate the difficulties and uncertainties in determining the true in situ conditions from the results of laboratory tests. 10.4 FACTORS CONTROLLING RESISTANCE TO VOLUME CHANGE
Both compositional and environmental factors influence volume change, so meaningful quantitative pre-
These interactions depend on particle surface forces that are responsible for double-layer interactions, surface and ion hydration, and interparticle attractive forces. Physicochemical interactions are most important in the formational stages of fine-grained soil deposits when they are at low pressures and high void ratios. Chemical and Organic Environment Chemical precipitates cement particles together. Organic matter influences surface forces and water adsorption properties, which, in turn, increase the plasticity and compressibility. Expansion of pyrite minerals in some shales and other earth materials as a result of oxidation caused by exposure to air and water has been the source of significant structural damage (Bryant et al., 2003). Temperature changes may cause changes in hydration states of some salts leading to volume changes. Mineralogical Detail Small differences in certain characteristics of expansive clay minerals can have major effects on the swelling of a soil. Fabric and Structure Compacted expansive soils with flocculent structures may be more expansive than those with dispersed structures. Figure 10.8 is an ex-
PHYSICAL INTERACTIONS IN VOLUME CHANGE
Figure 10.8 Effect of structure and electrolyte concentration
of absorbed solution on swelling of compacted clay (adapted from Seed et al. 1962a).
ample. At pressures less than the preconsolidation pressure, the soil with a flocculent structure was less compressible than the same soil with a dispersed structure. The reverse is generally true for pressures greater than the preconsolidation pressure. Stress History An overconsolidated soil is less compressible but more expansive than the same material initially at the same void ratio but normally consolidated. This is illustrated in Fig. 10.9. If anisotropic stress systems have been applied to a soil in the past, then anisotropic compression and swelling characteristics usually result. Temperature Increase in temperature usually causes a decrease in volume for a fully drained soil. If drainage is prevented, increase in temperature causes
Figure 10.9 Comparison of compressibility and swell characteristics for normally consolidated (compression curve) and overconsolidated (rebound and recompression curves) soil.
331
a decrease in effective stress. The responses of saturated soils to temperature change are analyzed in Section 10.12. Pore Water Chemistry Any change in the pore solution chemistry that depresses the double layers or reduces the water adsorption forces at particle surfaces reduces swell or swell pressure. An example of this is shown in Fig. 10.8, where increased electrolyte concentration in the water imbibed by a compacted clay resulted in reduced swelling. For soils containing only nonexpansive clay minerals, the pore water chemistry has relatively little effect on the compression behavior after the initial fabric has formed and the structure has stabilized under a moderate effective stress. This is in accordance with the principle of chemical irreversibility of clay fabric, discussed in Section 8.2. The leaching of normally consolidated marine clay at high water content, however, may be sufficient to cause a small reduction in volume owing to changes in interparticle forces (Kazi and Moum, 1973; Torrance, 1974). Stress Path The amount of compression or swelling associated with a given change in stress usually depends on the path followed. Loading or unloading from one stress to another in stages can give considerably different volume change behavior than if the stress change is done in one step. An example for swelling of a compacted sandy clay is shown in Fig. 10.10. Each sample was placed under water after compaction and allowed to swell under different surcharge pressures. Further discussion of the stress path dependency on volume change is given in Section 10.11 and Chapter 11.
10.5 PHYSICAL INTERACTIONS IN VOLUME CHANGE
Physical interactions between particles include bending, sliding, rolling, and crushing. In general, the coarser the gradation, the more important are physical particle interactions relative to chemically induced particle interactions. Deformation resistance developed by particle rolling and sliding is discussed in Chapter 11. Particle bending is important in soils with platy particles. Even small amounts of mica in coarse-grained soils can greatly increase the compressibility. Mixtures of a dense sand having rounded grains with mica flakes can even duplicate the form of the compression and swelling curves of clays, as shown in Fig. 10.11. Chattahoochie River sand with a mica content of 5 percent is twice as compressible as the same sand with no mica (Moore, 1971). On the other hand, a well-graded soil may be little affected in terms of compressibility by the addition of mica. Further discussion of the me-
332
10
VOLUME CHANGE BEHAVIOR
Figure 10.10 Effect of unloading stress path on swelling of a compacted sandy clay (Seed
et al. 1962a).
Figure 10.11 Comparison of compression and swelling curves for several clays and sand–
mica mixtures (from Terzaghi, 1931).
chanical behavior of mica–sand mixtures is given in Chapter 11. Cross-linking adds rigidity to soil fabric, especially clays containing platy particles. Particles and particle groups act as struts whose resistance depends both on their bending resistance and on the strengths of the junctions at their ends. According to van Olphen (1977), cross-linking is important even in ‘‘pure clay’’ systems, where the confining pressure is sometimes in-
terpreted, probably erroneously, as balanced entirely by interparticle repulsion. The importance of grain crushing increases with increasing particle size and confining stress magnitude. Particle breakage is a progressive process that starts at relatively low stress levels because of the wide dispersion of the magnitudes of interparticle contact forces. The number of contacts per particle depends on gradation and density, and the average contact force in-
PHYSICAL INTERACTIONS IN VOLUME CHANGE
creases greatly with particle size, as summarized in Table 10.3. Statistical analyses of the probable frequency distribution of contact forces show large deviations from the mean (Marsal, 1973). An example of this obtained from a numerical simulation of a particle assemblage is presented in Chapter 11. Unstressed, or idle particles, can occupy voids between larger particles or particle arches associated with strong force chains, as discussed in Chapter 7. The percentage of idle particles depends on gradation, fabric, void ratio, stress history, and stress level. In soils containing idle particles, particulate mechanics analyses of behavior that depend on such quantities as average number of particles per unit area or per unit volume, average number of contacts per particle, and the like lose their relevance unless the analyses allow for their existence. The resistance to grain crushing or breakage depends on the strength of the particles, which, in turn, depends on mineralogy and the soundness of the grains. Failure may be by compression, shear, or in a split tensile mode. Quartz grains are more resistant than feldspar, but there is greater variability in crushing and splitting resistance with changes in particle size for quartz than for feldspar. The amount of grain crushing to be expected for rockfills and gravels is summarized in Table 10.4. In this table, Bq is the proportion of the solid phase by weight that will undergo breakage, and qi is the concentration of solids [Vs /V ⫽ 1/(1 ⫹ e)].
Table 10.3 Soils
Studies of compressibility and grain crushing in sands and gravels under isotropic and anisotropic triaxial stresses up to 20 MPa showed the following (Lee and Farhoomand, 1967): 1. Coarse granular soils compress more and have more particle breakage than fine granular soils. A comparison of gradation curves before and after isotropic compression is shown in Fig. 10.12. 2. Soils with angular particles compress more and undergo more particle crushing than soils with rounded particles. 3. Uniform soils compress and crush more than well-graded soils with the same maximum grain size. 4. Under a given stress, compression and crushing continue indefinitely at a decreasing rate. 5. Volume change during compression depends primarily on the major principal stress and is independent of the principal stress ratio. 6. The higher the principal stress ratio (Kc ⫽ 1c / 3c) during consolidation, the greater the amount of grain crushing. Particle crushing results in increase in fines content with increasing confining pressure. An example of the change in particle size distribution curve with increasing confining pressure is shown in Fig. 10.13 (Fukumoto, 1992). Particle crushing can be quantified by Hardin’s (1985) relative breakage parameter Br, which
Contacts and Contact Forces in Granular
Soil Type Loose uniform gravel Dense uniform gravel Well-graded gravel, 0.8 mm ⬍ d ⬍ 200 mm Medium sand Gravel Rockfill, d ⫽ 0.7 m
Grain Contacts/ Particle (Range)
333
Grain Contacts/ Particle (Mean)
4–10
6.1
4–13
7.7
5–1912
5.9
Average Contact Force for ⫽ 1 atm (N)
10⫺2 10 104
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10
VOLUME CHANGE BEHAVIOR
Table 10.4
Grain Crushing in Rockfills and Gravels
Samples
Grain Size Distribution
Crushing Strength of Grains
Particle Breakage Bqqia
El infiernillo silicified conglomerate
Well-graded rockfills and gravels
High
0.02–0.10 for 5 1f 80 kg/cm2
Pinzandaran sand and gravel San Francisco basalt (gradations 1 and 2) El infiernillo diorite
Somewhat uniform rockfills
High
0.10–0.20 for 5 1f 80 kg/cm2
Well-graded rockfills
Low
Uniform rockfill produced by blasting metamorphic rocks (Cu ⬍ 5)
Low
El granero slate (gradation A) Mica granitic– gneiss (gradation X) Mica granitic– gneiss (gradation Y)
Increases with 1f ⬊ maximum value ⫽ 0.30
Bq is grain breakage parameter; qi is initial concentration of solids; 1f is major principal stress at failure. From Marsal, 1973. Reprinted with permission of John Wiley & Sons. a
Figure 10.12 Comparison of crushing of soils with different initial grain sizes for isotropic compression under 8 MPa (from Lee and Farhoomand, 1967). Reproduced with permission from the National Research Council of Canada.
FABRIC, STRUCTURE, AND VOLUME CHANGE
335
100
Percent Finer by Weight
Ottawa Sand : Initial Grading 0.42-0.82 mm 80 60
One dimensional consolidation to σ' v=14000 psi (97MPa) σ' v=8000 psi (55MPa) σ' v=5000 psi (34MPa)
40
σ' v=1000 psi (6.9MPa)
Initial
20 0 0.01
0.1
1
Grain Size (mm)
(a)
Percent Finer by Weight
100 80 60 40
Landstejin Sand : Initial Grading 4-7 mm Isotropically consolidated to 490 kPa and then sheared in triaxial compression to axial strain of 24% Isotropically consolidated to 98 kPa and then sheared in triaxial compression to axial strain of 24% Isotropically consolidated to 980 kPa
Initial
20 0 0.01
0.1
1
10
Grain Size (mm)
(b) Figure 10.13 Change in particle size distribution curve with increasing confining pressure:
(a) Ottawa sand and (b) Landstejn sand (from Fukumoto, 1992).
is defined in Fig. 10.14. The increase in Br with isotropic compression pressure is shown in Fig. 10.15 for Dog’s Bay carbonate sand (Coop and Lee, 1993). The figure also shows the increase in Br at critical-state failure (discussed further in Chapter 11). A unique particle breakage characteristic at failure is obtained irrespective of shearing conditions (i.e., undrained triaxial, drained triaxial, or constant mean pressure shearing). Aggregates of clay mineral particles are often observed in clays, and intact aggregate clusters of clay particles can be considered as the smallest units controlling the macroscopic mechanical behavior. These aggregate clusters behave in some ways similarly to granular particles (e.g., Barden, 1973, and Collins and McGown, 1974). It can be conceptualized that the con-
solidation of these clays is related to sequential breakage of clay aggregates into smaller aggregates as consolidation pressure increases (Bolton, 2000).
10.6 FABRIC, STRUCTURE, AND VOLUME CHANGE
Collapse, shrinkage, and compression are due to particle rearrangements from shear and sliding at interparticle contacts, disruption of particle aggregates, and grain crushing. Thus, both the arrangement of particles and particle groups and the forces holding them in place are important. Swelling depends strongly on physicochemical interactions between particles, but fabric also plays a role.
336
10
VOLUME CHANGE BEHAVIOR
An illustration of such differences is provided by the data in Table 10.5, where dry void ratios of several undisturbed and remolded clays are listed. In each case, the clay was dried from its natural water content either undisturbed or after thorough remolding. The substantially lower dry void ratios for the remolded samples indicate greater shrinkage than in the undisturbed samples. Structure anisotropy on a macroscale may be reflected by anisotropic shrinkage. For preferred orientation of platy particles parallel to the horizontal, vertical shrinkage on drying is greater than lateral shrinkage. For example, the vertical shrinkage of Seven Sisters clay was three times greater than the horizontal shrinkage (Warkentin and Bozozuk, 1961). Collapse Figure 10.14 Definition of relative breakage parameter Br
by Hardin (1985).
Collapse, as a result of wetting under constant total stress, is an apparent contradiction to the principal of effective stress discussed in Chapter 7. The addition of water increases the pore water pressure and reduces the effective stress; hence, expansion might be expected. The apparent anomaly of volume decrease under decreased effective stress is because of the application of continuum concepts to a phenomenon that is controlled by particulate behavior at contact levels for unsaturated soils. Collapse requires: 1. An open, low-density, partly unstable, partly saturated fabric 2. A high enough total stress that the structure is metastable 3. A strong enough clay binder or other cementing agent to stabilize the structure when dry
Figure 10.15 Increase in Br with confining pressure under
isotropic compression (NCL) and at critical state (CSL) achieved by standard triaxial compression shearing (both drained and undrained) and constant mean pressure shearing.
When water is added to a collapsing soil in which the silt and sand grains are stabilized by clay coatings or buttresses, the effective stress in the clay is reduced, the clay swells, becomes weaker, and contacts fail in shear, thereby allowing the coarser silt and sand particles to assume a denser packing. Thus, compatibility with the principle of effective stress is maintained on a microscale.
Shrinkage
Drying shrinkage of fine-grained soils is caused by particle movements resulting from pore water tensions developed by capillary menisci. If two samples of clay are at the same initial water content but have different fabrics, the one that is the more deflocculated and dispersed shrinks the most. This is because the average pore sizes are smaller in the deflocculated sample, thus allowing greater capillary stresses, and because of easier relative movements of particles and particle groups.
Compression Sands In Chapter 8 it was shown that the volume changes during the shear of samples of sand at the same void ratio but with different initial fabrics can be different. Different volume change tendencies for different fabrics developed resulting from different methods of sample preparation have also manifested themselves by differences in liquefaction behavior under undrained cyclic loading (see Fig. 8.22).
FABRIC, STRUCTURE, AND VOLUME CHANGE
337
Table 10.5 Void Ratios of Several Clays After Drying in the Undisturbed and Remolded States
Clay
Natural Water Content (%)
Boston blue Boston blue Fore River, Maine Goose Bay, Labrador Chicago Beauharnois, Quebec St. Lawrence
35.6 37.5 41.5 29.0 39.7 61.3 53.6
The compression behavior of a natural intact cemented calcarenite sand is shown in Fig. 10.16 (Cuccovillo and Coop, 1997). Similarly to structured clays, the initial compressibility before yielding is stiff due to cementation. If the cementation is stronger than the particle crushing strength, the compression line will lie to the right of the normal compression line of the uncemented reconstituted sand. If the cementation is weaker than the particle crushing strength, the compression curve will merge gradually toward that of the uncemented sand before yielding (Cuccovillo and Coop, 1999). This highlights the importance of relative
p (kPa) 100
2.20
1000
10000
Intact IB
2.00 1.80
10000 Intact Reconstituted
ν
NCL
1.60 2.40 1.20 4
5
6
7
8 9 In p(kPa)
10
11
12
Figure 10.16 Isotropic compression curves of intact and reconstituted calcarenite sand specimens (from Cuccovillo and Coop, 1997).
Sensitivity
Dry Void Ratio Undisturbed
Dry Void Ratio Remolded
6.8 5.8 4.5 2.0 3.4 5.5 5.4
0.69 0.75 0.65 0.60 0.65 0.76 0.79
0.50 0.53 0.46 0.55 0.55 0.70 0.66
strengths of cementation bonding and particles on the compression behavior of structured soils. Clays Compression curves obtained by odometer tests on undisturbed and remolded Leda (Champlain) clay, illite, and kaolinite are shown in Fig. 10.17. Liquidity index is used as an ordinate, and the sensitivity curves from Fig. 8.49 are superimposed. Curve A is for undisturbed Leda clay at an initial water content corresponding to a liquidity index of 1.82. Because the sensitivity contours were developed for normally consolidated clays, they cannot be used to estimate sensitivity for stresses less than the preconsolidation pressure. After the preconsolidation stress has been exceeded the curve cuts sharply across the sensitivity contours, indicating a large decrease in sensitivity as the structure is broken down by compression. Curve B is for kaolinite remolded at a liquidity index of 2.06. The early part of the consolidation curve is not shown in Fig. 10.17. Immediately after remolding at high water content the effective stress is very low, and the sensitivity is equal to 1. Curve B shows that consolidation results in an increase in sensitivity to a maximum of about 15 to 18, at an effective consolidation pressure of about 20 kPa. At this point, the interparticle and interaggregate shear stresses caused by the applied compressive stress begin to exceed the bond strengths, the degree of structural metastability decreases, and the sensitivity decreases. Curve D is for kaolinite remolded at a liquidity index of 0.98. It differs considerably from curve B. This is consistent with the results of other studies that show that the compression behavior, and therefore also the structure, are different for a given clay remolded at
338
10
VOLUME CHANGE BEHAVIOR
Figure 10.17 Change in sensitivity with consolidation for various clays.
different water contents, for example, Morgenstern and Tchalenko (1967b). Significantly lower sensitivity is developed in the kaolinite of curve D than that of curve B. These observations show that both the concentration of clay in suspension and the rate of sediment accumulation are important in determining the initial structure of clay deposits. At high pressures, both curves tend to merge together, indicating that the initial fabrics have been destroyed. Curve E is for a well-graded illitic clay remolded at a liquidity index of 1.36. The consolidation curve indicates a low sensitivity at all consolidation pressures. Results of strength tests showed that the actual sensitivity ranged from 1.0 to 2.6. Curve C is for Leda clay remolded at a liquidity index of 1.82. The sensitivity increases from 1 to about 8 with reconsolidation, indicating development of metastability after remolding and recompression. The sensitivity decreases at high pressures as convergence with curve A is approached. All of the above findings are consistent with the principles stated in Section 8.13.
Swelling
The structure influences swelling of fine-grained soils that is initiated by reduction of effective stress by unloading and/or addition of water. For example, an expansive soil that is compacted dry of optimum water content can swell more than if compacted to the same density wet of optimum (Seed and Chan, 1959). This difference cannot be accounted for in terms of differences in initial water content and, therefore, must be ascribed to differences in structure. A swell sensitivity has been observed in some clays wherein the swelling index for the remolded clay is higher than that of the same clay undisturbed. The increased swelling of the disturbed material can result both from the rupture of interparticle bonds that inhibit swelling in the undisturbed state and from differences in fabric. Old, unweathered, overconsolidated clays may be particularly swell sensitive. Swell sensitivities as high as 20 were measured in one case (Schmertmann, 1969).
OSMOTIC PRESSURE AND WATER ADSORPTION INFLUENCES ON COMPRESSION AND SWELLING
339
10.7 OSMOTIC PRESSURE AND WATER ADSORPTION INFLUENCES ON COMPRESSION AND SWELLING
Adsorption of cations on clays, the formation of double layers, and water adsorption on soil surfaces generate repulsive forces between particles as described in Chapters 6 and 7. Calculation of interparticle repulsions due to interacting double layers may be done in more than one way; the osmotic pressure concept is convenient and most widely used. By this approach, the pressure that must be applied to prevent movement of water either in or out of clay is determined as a function of particle spacings expressed in terms of void ratio or water content. The concept of osmotic pressure is illustrated by Fig. 10.18. The two sides of the cell in Fig. 10.18a are separated by a semipermeable membrane through which solvent (water) may pass but solute (salt) cannot. Because the salt concentration in solution is greater on the left side of the membrane than on the right side, the free energy and chemical potential of the water on the left are less than on the right.1 Because solute cannot pass to the right to equalize concentrations due to the presence of the membrane, solvent passes into the chamber on the left. The effect of this is twofold as shown by Fig. 10.18b. First, the solute concentration on the left is reduced and that on the right side is increased, which reduces the concentration imbalance between the two chambers. Second, a difference in hydrostatic pressure develops between the two sides. Since the free energy of the water varies directly with pressure and inversely with concentration, both effects reduce the imbalance between the two chambers. Flow continues through the membrane until the free energy of the water is the same on each side. It would be possible in a system such as that shown by Fig. 10.18a to completely prevent flow through the membrane by applying a sufficient pressure to the solution in the left chamber, as shown by Fig. 10.18c. The pressure needed to exactly stop flow is termed the osmotic pressure , and it may be calculated, for dilute solutions, by the van’t Hoff equation, which was introduced in Section 9.13: ⫽ kT
冘(n
iA
⫺ niB) ⫽ RT
冘(c
iA
⫺ ciB)
(10.2)
where k is the Boltzmann constant (gas constant per molecule), R is the gas constant per mole, T is the
1
Formal treatment of the concepts stated here and derivation of Eq. (10.1) are given in standard texts on chemical thermodynamics.
Figure 10.18 Osmotic pressure: (a) Initial condition: no
equilibrium, (b) final condition: equilibrium, and (c) osmotic pressure equilibrium.
absolute temperature, ni is the concentration (particles per unit volume), and ci is the molar concentration. Thus, the osmotic pressure difference between two solutions separated by a semipermeable membrane is directly proportional to the concentration difference. In a soil, there is no true semipermeable membrane separating regions of high- and low-salt concentration. The effect of a restrictive membrane is created, however, by the influence of the negatively charged clay surfaces on the adsorbed cations. Because of the attraction of adsorbed cations to particle surfaces, the cations are not free to diffuse, and concentration differences responsible for osmotic pressures are developed whenever double layers on adjacent particles
340
10
VOLUME CHANGE BEHAVIOR
overlap. The situation is shown schematically in Fig. 10.19. The difference in osmotic pressure midway between particles and in the equilibrium solution surrounding the clay is the interparticle repulsive pressure or swelling pressure Ps. It can be expressed in terms of midplane potentials according to the following equation (see Section 6.11): Ps ⫽ p ⫽ 2n0kT(cosh u ⫺ 1)
冘(c
ic
⫺ ci 0)
(10.3)
(10.4)
For single cation and anion species of the same valence ⫺ Ps ⫽ RT(cc ⫹ ca ⫺ c⫹ 0 ⫺ c0 )
cc ca ⫽ c0⫹ c0⫺ ⫽ c02
(10.6)
⫺ because c⫹ 0 ⫽ c0 . Thus Eq. (10.5) becomes
where n0 is the concentration in the external solution, and u is the midplane potential function. In terms of midplane cation and equilibrium solution concentrations cc and c0 (Bolt, 1956), Eq. (10.2) becomes Ps ⫽ ⫽ RT
where ca is the midplane anion concentration, and c⫹ 0 and c⫺ 0 are the equilibrium solution concentrations of cations and anions. At equilibrium in dilute solutions
(10.5)
Ps ⫽ RTc0
冉
冊
cc c0 ⫹ ⫺2 c0 cc
(10.7)
Midplane concentrations can be determined using the relationships in Chapter 6. Equation (10.7) assumes parallel flat plates and may be written in terms of void ratio for saturated clay. The water content w, in terms of weight of water per unit weight of soil solids, divided by the specific surface of soil solids As gives the average thickness of water layer, which is half the particle spacing or d. Thus,
Figure 10.19 Mechanism of osmotic swelling pressure generation in clay.
341
OSMOTIC PRESSURE AND WATER ADSORPTION INFLUENCES ON COMPRESSION AND SWELLING
d⫽
w w As
(10.8)
For saturated soil the void ratio is related to the water content by e ⫽ Gsw
e Gs w As
兩 兩 ⫻ 4 ⫻ 10⫺5
冘c
(10.9)
where Gs is the specific gravity of solids. Substituting Eq. (10.9) into Eq. (10.8) gives d⫽
systems that cover most of the moisture suction or overburden ranges of interest in soil mechanics or soil science are available (Collis-George and Bozeman, 1970). They are suitable for
(10.10)
⫻
冕
/2
⫽0
冉冊 c0 cc
1/2
d (1 ⫺ (c0 /cc)2 sin2 )1/2
兩 兩 ⫽
冘c ⫺ 冘c m
0
(10.14)
⫺5
4 ⫻ 10
For homovalent and dication/monoanion systems, 兺cm is found from (10.11)
in which v is the cation valence and distance x0 equals approximately 0.1/ v nm for illite, 0.2/ v nm for kaolinite, and 0.4/ v nm for montmorillonite. The parameter is given by ⫽ 2F 2 /DRT
(10.13)
where 兩 兩 is the swelling pressure or matric suction (see Section 7.12) measured in centimeters of water. Since the sum of the applied constraint 兩 兩 in concentration units and the external solution concentration must equal the midplane concentration, the pressure or suction is given by
Bolt (1955, 1956) showed that the double-layer equations (see Chapter 6) can be combined with Eq. (10.10) to give v(c0)1 / 2(x0 ⫹ d) ⫽ 2
20
0
(10.12)
in which F is the Faraday constant, R is the gas constant, and T is the temperature. Combinations of (Ps /RTc0) and v(c0)1/2(x0 ⫹ e/ Gs w As) that satisfy Eqs. (10.7) and (10.11) are given in Table 10.6. These values may be used to calculate theoretical curves of void ratio versus pressure for consolidation or swelling. For any value of log[Ps /(RTc0)] the swelling pressure may be calculated. The void ratio can be computed from the corresponding value of v(c0)1/2(x0 ⫹ e/Gs w As). For a given soil, Ps depends completely on cc and c0 and those factors that cause cc to be large relative to c0; for example, low c0, low valence of cation, and high dielectric constant, cause high interparticle repulsions, high swelling pressures, and large physicochemical resistance to compression. It is apparent from the values in Table 10.6 that the dominating influence on swelling pressure at any given void ratio is the specific surface area, which is determined mainly by mineralogy and particle size. The preceding relationships were developed for soils containing a single electrolyte, and they assume ideal behavior in accord with the DLVO theory as developed in Chapter 6. Approximate equations for mixed-cation
v()1/2
冉 冊
e ⫽ Gs As
冪冘c
⫺
2
冉
m
冘c 冊
1/2
–41 %2 ⫹
m
(10.15) where ⬇ 1.0 ⫻ 1015 cm/mmol at 20C and % is the double-layer charge in meq/cm2. For dilute concentrations in the external solution, Eqs. (10.14) and (10.15) reduce to 兩 兩 ⫽ 0.25 ⫻ 105
2 v2(e/Gs As)2
(10.16)
For mixed-cation heterovalent systems, 兺cm is given by v()1/2
冉 冊
e ⫽ Gs As
冉冘 冊 冉 再 冋冘 冒冉 1/2
cm
⫺cos⫺1 1/a 1⫺ ⫻
冘c 冊册
–14 %2⫹
cm
1/2
m
冎冊
1/2
cm (10.17)
The value of a in Eq. (10.17) is given by a⫽
⫹⫹ ⫹⫹ ⫹ ⫹⫹ 2 1/2 2cm ⫺ (c⫹ m ⫹ cm ) ⫹ [4c mcm ⫹ (cm ⫹ cm ) ] 2cm
(10.18)
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10
VOLUME CHANGE BEHAVIOR
Table 10.6 Relation Between the Distance Variable Expressed as a Function of the Void Ratio and the Swelling Pressure of Pure Clay Systema v(c0)1/2 (x0 ⫹ e/ Gs w As)
log Ps /(RTc0)
0.050 0.067 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.801 0.902
3.596 3.346 2.993 2.389 2.032 1.776 1.573 1.405 1.258 1.130 1.012
v(c0)1/2 (x0 ⫹ e/ Gs w As)
log Ps /(RTc0)
0.997 1.188 1.419 1.762 2.076 2.362 2.716 3.09 3.57 4.35
0.909 0.717 0.505 0.212 ⫺0.046 ⫺0.301 ⫺0.573 ⫺0.899 ⫺1.301 ⫺1.955
v is the cation valence; is 8F /1000 DRT ⬇ 1015 cm/mmol for water at normal T; c0 is the concentration in bulk solution (mmol/cm3); x0 ⫽ 4/ vT ˚ for illite, 2/ v A ˚ for kaolinite, and 4/ v A ˚ for montmorillonite; e is ⬇ 1/ v A the void ratio; Gs w is the density of solids, As is the specific surface area of a
clay; Ps is the swelling pressure; R is the gas constant; T is the absolute temperature; F is the Faraday constant; and D is the dielectric constant. Adapted from Bolt (1956).
where cm is the midplane anion concentration. Since evaluation of Eq. (10.18) requires knowledge of the midplane concentrations of the different ions separately, the application of Eq. (10.17) is not as straightforward as is the case of Eqs. (10.13) and (10.14). Applicability of Osmotic Pressure Concepts
A reasonably clear understanding of how well the osmotic pressure concept can account for the compression and swelling behavior of fine-grained soils has been developed. Homoionic Cation Systems
Early testing of the applicability of the osmotic pressure theory was done using ‘‘pure clays’’ consisting of specially prepared, very fine grained clay minerals. Good agreement between theoretical and experimental values of interparticle spacing and pressure for montmorillonite with particles finer than 0.2 m in 10⫺4 NaCl solution is shown in Fig. 10.20. The first compression curves are above decompression and recompression curves because of cross-linking and nonparallel particle arrangements, that is, fabric effects, which are eliminated during the first compression cycle. Theoretical and experimental compression
Figure 10.20 Relationship between particle spacing and pressure for montmorillonite (modified from Warkentin et al., 1957).
curves for sodium and calcium montmorillonite in 10⫺3 M electrolyte solutions are compared in Fig. 10.21. Agreement is fairly good as regards the influence of cation valence. However, the experimental curves are substantially above the theoretical curves. This may be caused by ‘‘dead’’ volumes of liquid resulting from terraced particle surfaces (Bolt, 1956).
OSMOTIC PRESSURE AND WATER ADSORPTION INFLUENCES ON COMPRESSION AND SWELLING
343
Figure 10.21 Compression curves of Na-montmorillonite and Ca-montmorillonite, fraction ⬍2 m, in equilibrium with
10⫺3 M NaCl and CaCl2, respectively. The dashed lines represent the theoretical curves for As ⫽ 800 m2 / g (Bolt, 1956).
Osmotic pressure theory was used successfully for prediction of swelling pressure developed in opalinum shale, a Jurassic clay rock (Madsen and Mu¨llerVonmoos, 1985, 1989). Swelling pressure was predicted using Eq. (10.2) and compared with the measured values, with the results shown in Fig. 10.22. Particle spacings were calculated from specific surface area and water content. Agreement between theory and experiment has not been good for clays containing particles larger than a few tenths of a micrometer. The coarse fraction (0.2 to 2.0 m) of two bentonites gave swelling pressures less than predicted, whereas the fine fraction (⬍0.2 m) gave values close to theoretical, even though the charge densities of the two fractions were the same (Kidder and Reed, 1972). Compression and swelling curves for three size fractions of sodium illite are shown in Fig. 10.23. The discrepancies between theory and experiment are fairly large for the ⬍0.2-m fraction; nonetheless, the experimental curves are in the predicted relative positions (Fig. 10.23a). However, for samples containing coarser particles (Figs. 10.23b and 10.23c), the curves are in reverse order to theoretical prediction. This is because the compression was controlled by initial particle orientations and physical interactions between the larger particles rather than by osmotic repulsive pressures. The concentration of CaCl2 or MgCl2 has essentially no influence on the swelling of a 2-m fraction of illite, and the consolidation is influenced only by how the changes in concentration change the initial structure (Olson and Mitronovas, 1962). Factors in addition to clay particle size may also contribute to failure of the theory in natural soils. The DLVO theory that serves as the basis for determination
Figure 10.22 Predicted and measured swelling pressures for
Opalinum shale (Madsen and Mu¨ller-Vonmoos, 1989).
of the midplane concentrations suffers from several deficiencies, as discussed in Chapter 6. In addition, physical particle interactions and the effects of interparticle short- and long-range forces such as van der Waals forces are neglected. Mixed-Cation Systems
Most soils contain mixtures of sodium, potassium, calcium, and magnesium in their adsorbed cation complex. Therefore, modifications of the double-layer and osmotic pressure equations for homoionic clays are required. The extent to which the resulting equations may be suitable depends on the structural status of the clay as well as on the particle size. Equations for mixed-cation systems are derived on the assumption that ions of all species are distributed uniformly over the clay surfaces in proportion to the amounts present. However, sodium and calcium ions may separate into distinct regions. This is termed demixing (Glaeser and Mering, 1954; McNeal et al., 1966; McNeal, 1970; Fink et al., 1971).
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10
VOLUME CHANGE BEHAVIOR
Figure 10.23 Influence of NaCl concentration and particle size on compression and swelling
behavior of Fithian illite.
Observed behavior was good for several cases examined using a demixed ion model (5 out of 6) for values of exchangeable sodium percentage (ESP) less than about 50 (McNeal, 1970). Based on X-ray determinations of interplate spacings in montmorillonite (Fink et al., 1971) it appears that for 1. ESP ⬎ 50 percent, there is random mixing of Na⫹ and Ca2⫹ and unlimited swelling between all plates on addition of water. 2. 10 percent ⬍ ESP ⬍ 50 percent, there is demixing on interlayer exchange sites, with progres˚ sively more sets of plates collapsing to a 20-A repeat spacing with decrease in ESP. 3. ESP ⬍ 10 to 15 percent the interlayer exchange complex is predominantly Ca saturated, with Na ions on external planar and edge sites. Summary
Osmotic pressure (double-layer) theory fails to explain the first compression of most natural clays of the type encountered in geotechnical practice because of phys-
ical particle interference and fabric factors related to particle size. The behavior is consistent with the principle of chemical irreversibility of clay fabric (Bennett and Hurlbut, 1986), which is discussed in Section 8.2. Nonetheless, when the physical and chemical influences of cation type on fabric and effective specific surface are taken into account, the behavior can be better understood, as illustrated, for example, by Di Maio (1996). For those cases in which fabric changes and interparticle interactions are small, such as swelling from a precompressed state, or for clays with very high specific surface area (very small particles) such as bentonite, the theory gives a reasonable description of swelling, at least qualitatively. Water Adsorption Theory of Swelling
An alternative to the osmotic pressure theory for clay swelling is that swelling is caused by surface hydration (Low, 1987, 1992). Interaction of water with clay surfaces reduces the chemical potential of the water, thereby generating a gradient in the chemical potential that causes additional water to flow into the system.
INFLUENCES OF MINERALOGICAL DETAIL IN SOIL EXPANSION
The general relationships that describe the water properties as a function of water layer thickness and water content are given in Section 6.5. The swelling pressure (in atmospheres) for pure clays follows the following empirical relationship (Low, 1980): ( ⫹ 1) ⫽ B exp[ /w] ⫽ B exp[ki /(tw)]
(10.19)
in which B and are constants characteristic of the clay, w is the water content, w is the density of water, t is the average thickness of water layers, and ki ⫽ / ( w As), where As is the specific surface. Equation (10.19) shows, as would be expected, that the lower the water content and, therefore, the smaller the water layer thickness, the higher is the swelling pressure. Whereas this approach can explain the swelling of pure clays accurately, the osmotic pressure theory cannot (Low, 1987, 1992). On the other hand, the influences of surface charge density, cation valence, electrolyte concentration, and dielectric constant, which have profound influences on swelling and swelling pressure, as shown in the previous section, are not directly accounted for by the hydration theory unless appropriate adjustments can be made for the influences of these factors on B, , and ki. An explanation that is consistent with both the influences of the double-layer/osmotic pressure theory and the water adsorption theory is as follows. Charge density and cation type influence the relative proportions of fully expandable and partially expandable layers in swelling clay. For example, calcium montmorillonite does not swell to interplate distances greater than about 0.9 nm where the particles stabilize by attractive interactions between the basal planes of the unit layers as influenced by exchangeable cations and adsorbed water (Norrish, 1954; Blackmore and Miller, 1962; Sposito, 1984). In the presence of high electrolyte concentrations or pore fluids of low dielectric constant, interlayer swelling is suppressed, and the effective specific surface is greatly reduced relative to that for the case where interlayer swelling occurs. The amount of water required to satisfy surface hydration is reduced greatly. A hydration water layer thickness on smectite surfaces of about 10 nm is needed to reach a distance beyond which the water properties are no longer influenced by surface forces (see Fig. 6.9), and Low (1980) indicates that the swelling pressure of montmorillonite is about 100 kPa for a water layer thickness of about 5 nm. For a fully expanding smectite having a specific surface area of 800 m2 /g, this latter water layer thick-
345
ness would correspond to a water content of 400 percent. Thus, a material such as sodium montmorillonite (bentonite) with its very high specific surface would be expected to be expansive over a wide range of water contents, and experience shows clearly that it is. On the other hand, consider an illite or a smectite made up of quasi-crystals so that interlayer swelling is negligible. As both materials have surface structures that are essentially the same, it would be expected that the hydration forces should be similar. Thus, an adsorbed water layer of 5 nm would also be reasonable. However, the specific surface areas of pure illite and nonexpanded smectite are only about 100 m2 /g, which corresponds to a water content of 50 percent. For a pure kaolinite having a specific surface of 15 m2 /g, the water content would be only 7.5 percent for a 5-nmthick adsorbed layer. It is evident, therefore, that the specific surface dominates the amount of water required to satisfy forces of hydration. Except for very heavily overconsolidated clays and those soils that contain large amounts of expandable smectite, there is sufficient water present even at low water contents to satisfy surface hydration forces, and swelling is small. On the other hand, when the clay content is high and particle dissociation into unit layers is extensive, the effective specific surface area is large and swelling can be significant. The tendency for smectite dissociation into unit layers can be evaluated through consideration of double-layer interactions, with those conditions that favor the development of high repulsive forces, as discussed in Chapter 6, leading to greater dissociation.
10.8 INFLUENCES OF MINERALOGICAL DETAIL IN SOIL EXPANSION
In soils where swelling is attributable solely to the clay content, smectite or vermiculite are the most likely minerals because only these minerals have sufficient specific surface area so that there are unsatisfied water adsorption forces at low water contents. Details of structure and the presence of interlayer materials may have significant effects on the swelling properties of these minerals. In addition, the presence of certain other minerals in soils and shales, such as pyrite and gypsum, as well as geochemical and microbiological factors, may lead to significant amounts of swelling and heave. Details of all the phenomena go well beyond the scope of this book; however, a few examples are given in this section to illustrate their nature and importance.
346
10
VOLUME CHANGE BEHAVIOR
Crystal Lattice Configuration Effects
Greatest swelling is observed for charge deficiencies in silicate layer structures of about one per unit cell as indicated in Table 10.7. Evidently, for layer silicates with sufficient isomorphous substitution to give charge deficiencies greater than 1.0 to 1.5 per unit cell, the balancing cations are so strongly held and organized in the interlayer regions that interlayer swelling is prevented. Within the range of charge deficiencies where swell is observed, there is no consistent relationship between charge, as measured by the cation exchange capacity, and the amount of swell (Foster, 1953, 1955). This finding is more consistent with the surface hydration model for clay swelling than with the osmotic pressure theory. An inverse correlation exists between free swell and the b dimension of the montmorillonite crystal lattice (Davidtz and Low, 1970). Differences in b dimension, which may be caused by differences in isomorphous substitution, evidently cause changes in water hydration forces. Furthermore, as the water content increases, so also does the b dimension, as shown in Fig. 6.5. Swelling ceases when the b dimension reaches 0.9 nm. Hydroxy Interlayering
The occurrence, formation, and properties of hydroxyl–cation interlayers (Fe–OH, Al–OH, Mg–H) have been studied regarding their effects on physical
Table 10.7 Influence of Lattice Charge on Expansion
Mineral
Negative Charge per Unit Cell Tendency to Expand
Margarite Muscovite
4
Biotite Paragonite Hydrous mica and illite Vermiculite Montmorillonite Beidellite Nontronite Hectorite Pyrophyllite
2
None Only with drastic chemical treatment, if at all
⬎1.2
1.4–0.9
Expanding
1.0–0.6
Readily expanding
0
None
From Brindley and MacEwen (1953).
properties of expansive clays, for example, Rich (1968). Some aspects of interlayering between the basic sheets in the expansive clay minerals are: 1. Optimum conditions for interlayer formation are: a. Supply of A13⫹ ions b. Moderately acid pH (⬇5) c. Low oxygen content d. Frequent wetting and drying 2. Hydroxyaluminum is the principal interlayer material in acid soils, but Fe–OH layers may be present. 3. Mg(OH)2 is probably the principal interlayer component in alkaline soils. 4. Randomly distributed islands of interlayer material bind adjacent layers together. The degree of interlayering in soils is usually small (10 to 20 percent), but this is enough to fix the basal spac˚. ing of montmorillonite and vermiculite at 14 A 5. The cation exchange capacity is reduced by interlayer formation. 6. Swelling is reduced. Salt Heave
Some saline soils with high contents of salts can undergo changes in volume associated with hydration– dehydration phenomena. One example is the swelling of some soils containing large amounts of sodium sulfate (Na2SO4) found in and around the Las Vegas area of Nevada. When the temperature falls from above about 32C to below about 10C, the salt hydrates to Na2SO4 10H2O with accompanying increase in volume. This salt heave has been responsible for damage to light structures and is described in more detail by Blaser and Scherer (1969) and Blaser and Arulanandan (1973). Impact of Pyrite
Sulfur occurs in rock and soil as sulfide (S⫺ or S2⫺), sulfate (SO42⫺), and organic sulfur. The sulfide minerals, of which pyrite is one of the most common and easily oxidized (Burkart et al., 1999), are of greatest concern. The amount of sulfide sulfur is a good indicator of the potential for oxidation reactions and weathering that can result in expansion. Sulfideinduced heave has occurred in materials containing as little as 0.1 percent sulfide sulfur (Belgeri and Siegel 1998). Products of pyrite oxidation include sulfate minerals, insoluble iron oxides such as goethite (FeOOH) and hematite (Fe2O3), and sulfuric acid (H2SO4). Sulfuric acid can dissolve other sulfides, heavy metals, carbonates, and the like that are present in the oxidation zone, thus allowing the effects of oxidation to increase as the process builds upon itself.
INFLUENCES OF MINERALOGICAL DETAIL IN SOIL EXPANSION
The relative proportion of sulfate sulfur is indicative of the degree of weathering or oxidation that has already occurred. Sulfate crystals develop in the capillary zone and tend to localize along discontinuities due to reduced stress in these regions. The increase in volume resulting from the growth of sulfate minerals along bedding planes is a dominant factor in the vertical heave that occurs in shales and other materials that have subhorizontal fissility (Kie, 1983; Hawkins and Pinches, 1997). The production of sulfates by pyrite oxidation also increases the potential for further deleterious reactions, such as the formation of gypsum and expansive sulfate minerals (e.g., ettringite). Gypsum (CaSO4 2H2O) is considered to be the primary cause of heave resulting from sulfate expansion. Volume increases associated with several sulfidic chemical weathering reactions are given in Table 10.8. For comparative purposes, these percentages are based on the assumption that the altered rock was initially composed of 100 percent of the original mineral. Sulfide oxidation reactions are usually catalyzed by microbial activity. Gypsum forms when sulfate ions react with calcium in the presence of water, resulting in very large volume increases. The products of pyrite oxidation reactions are significantly less dense than the initial sulfide product (pyrite); for example, the specific gravity of pyrite is 4.8 to 5.1, whereas that of gypsum is only 2.3, and that of calcium is 2.6. Acidity produced by pyrite oxidation can also result in significant quantities of acid mine and rock drainage. Bacterially Generated Heave—Case History
About 1000 wooden houses founded on mudstone sediments in Iwaki City, Fukushima Prefecture, Japan, were damaged by heaving of their foundations (Oyama
Table 10.8 Volume Increases of Selected Mineral Transformations Mineral Transformation Original Mineral Illite Illite Calcite Pyrite Pyrite Pyrite
New Mineral Alunite Jarosite Gypsum Jarosite Anhydrous ferrous sulfate Melanterite
Volume Increase of Crystalline Solids (%) 8 10 60 115 350 536
Data from Fasiska et al. (1974), Shamburger et al. (1975), and Taylor (1988).
347
et al., 1998; Yohta, 1999, 2000). The amount of heave was as much as 480 mm. The cost for repairs was estimated at 10 billion yen (Yohta, 2000). The mudstone at the site contained 5 percent pyrite. Whereas the pH of the sediment was initially 7 to 8 before heave, the pH of the heaved ground was about 3, and it contained acidophilic iron-oxidizing bacteria (Oyama et al., 1998). Yamanaka et al. (2002) further confirmed the presence and effects of sulfate-reducing, sulfur-oxidizing, and acidophilic iron-oxidizing bacteria by means of several series of laboratory culture experiments. Test results presented by Yamanaka et al. (2002), which include electron photomicrographs of the bacteria, showed consistent variations of hydrogen sulfide concentration, pH, Fe3⫹ concentration, Fe2⫹ ⫹ Fe3⫹ concentration, and SO42⫺ concentration over time periods up to 50 days for both the natural mudstone and the mudstone after heat treatment to 121C. The heat treatment prevented or greatly slowed the bacterial activity, whereas very significant changes in concentrations and pH were measured for tests done at 28C. For example, the concentration of H2S increased from 0.3 to 2.2 mM in 20 days, the pH decreased from about 6.5 to 1.3 in 47 days, the concentration of Fe3⫹ increased from about 6 to 125 in 5 days, and the concentration of SO42⫺ increased from less than 1 to about 15 mM in 25 days. Based on their results and observations, Yamanaka et al. (2002) developed the following explanation for the processes leading to the foundation heave. The ground temperature, which had been about 18C at depth, increased to about 25C in the summer after excavation. Initial anaerobic, high water content conditions and the stimulation of sulfate-reducing bacteria generated H2S. As the ground dried and became permeable to air, sulfate-oxidizing bacteria grew and stimulated production of H2SO4, the lowering of pH, and pyrite oxidation. The reaction of H2SO4 with the calcium carbonate present in the mudstone led to formation of gypsum and, with potassium and ferric ions, to formation of jarosite. The foundation heave was associated with the volume increase that accompanied the formation of both gypsum and jarosite crystals. Sulfate-Induced Swelling of Cement- and LimeStabilized Soils
Some fine-grained soils, especially in arid and semiarid areas, contain significant amounts of sulfate and carbonate. Sodium sulfate, Na2SO4, and gypsum, Ca SO4 2H20, are the common sulfate forms, and calcium carbonate, CaCO3, and dolomite, MgCO3, are the usual carbonate forms. The dominant clay minerals in these soils are expansive smectites. Delayed expansion fol-
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VOLUME CHANGE BEHAVIOR
lowing admixture stabilization of these soils using Portland cement and lime has developed at several sites (Mitchell, 1986). Although test programs showed suppression of swelling and substantial strength increase at short times (days) as a result of the incorporation of the stabilizer, subsequent heave of magnitude sufficient to destroy pavements developed after of exposure to water at some later time. The mechanism associated with this process appears to be as follows. When cement or lime is mixed with soil and water, there is a pH increase to about 12.4, some calcium goes into solution and exchanges with sodium on the expansive clay. This ion exchange, along with light cementation by carbonate and gypsum, if present, suppresses the swelling tendency of the clay. The mixed and compacted soil is nonexpansive and has higher strength than the untreated material. If sodium sulfate is present, then available lime is depleted according to Ca(OH)2 ⫹ Na2SO4 → CaSO4 ⫹ 2NaOH Silica (SiO2) and alumina (Al2O3) dissolve from the clay in the high pH environment and/or they may be present in amorphous form initially. These compounds can then combine with calcium, carbonate, and sulfate to form ettringite, Ca6[Si(OH)6]2(SO4)3 26H2O, and/ or thaumasite, Ca6[Si(OH)6]2(SO4)2(CO3)2 24H2O, which are very expansive materials (Mehta and Hu, 1978). In addition, in the case of lime-treated soil, if the available lime is depleted, the pH will drop and the further dissolution of SiO2 from the clay will stop. As silica is needed for formation of the cement (CSH) that is the desired end product of the pozzolanic lime stabilization reaction, long-term strength gain is prevented. Consequently, when the treated material is given access to water, a large amount of swell may occur. Further details concerning lime–sulfate heave reactions in soils are given in Dermatis and Mitchell (1992).
10.9
CONSOLIDATION
fective stress is linear, and properties of the soil do not change during the consolidation process. Deformations in only one dimension, usually vertical, are considered since determinations of settlements caused by loadings from structures or fills are common applications of the theory. In such a case, the relationship between void ratio and vertical stress is as shown in Fig. 10.24a for a normally consolidated clay layer, and that in Fig. 10.24b applies for an overconsolidated clay layer.2 As shown in any basic text on soil mechanics, the amount of vertical settlement H that a homogeneous clay layer of thickness H will undergo if subjected to a vertical stress increase at the surface is given by
H ⫽
e H 1 ⫹ e0
(10.20)
in which e0 is the initial void ratio and e is the decrease in void ratio due to the stress increase from v0 to v1 . For convenience, the change in void ratio is often written in terms of compression index or coefficient of compressibility and change in effective stress as defined in Fig. 10.1. The rate at which consolidation under the stress increases from v0 to v1 is determined using Terzaghi’s solution to the one-dimensional diffusion equation applied to the transient state water flow from the consolidating clay layer. It is assumed in this theory that the rate of volume decrease is controlled totally by hydrodynamic lag, that is, the time required for water to flow out of the consolidating soil under the gradients generated by the applied pressures. The governing equation is u 2u ⫽ cv 2 t z
(10.21)
in which u is the excess pore pressure, t is time, z is distance from a drainage surface, and cv is the coefficient of consolidation. The coefficient is given by cv ⫽
kh(1 ⫹ e) av w
(10.22)
Introduction and Simple One-Dimensional Theory
Terzaghi’s (1925b) quantitative description of soil compression and its relation to effective stress and the rate at which it occurs marked the beginning of modern soil mechanics. An ideal homogeneous clay layer is assumed to follow the paths shown in Fig. 10.1 when subjected to compression, unloading, and reloading. Key assumptions for analysis of the consolidation rate according to the Terzaghi theory are that the soil is saturated, the relationship between void ratio and ef-
where kh is the hydraulic conductivity, av ⫽ ⫺de/d v is the coefficient of compressibility, and w is the unit weight of water.
2 In engineering practice compression and swelling curves are often plotted using settlement ratio, H / H as ordinate rather than void ratio, e, for convenience in settlement computations. Void ratio is used herein because it is more indicative of the state and properties of the soil.
CONSOLIDATION
349
Figure 10.24 Idealized compression curves for clay layers: (a) normally consolidated and (b) overconsolidated.
Solutions for Eq. (10.22) for different boundary conditions are given in standard soil mechanics texts in terms of a dimensionless depth z/H (where H is the maximum distance to a drainage boundary) and a dimensionless time factor T ⫽ cvt/H 2 for different boundary conditions. The solution for u ⫽ ƒ(z/H, T) for a layer of thickness 2H that is initially at equilibrium and subjected to a rapidly applied uniform surface loading is shown in Fig. 10.25a. The average degree of consolidation U over the full depth of the clay layer as a function of T for this case is shown in Fig. 10.25b. Ranges of Compressibility and Consolidation Parameters
The curves in Fig. 10.2, as well as the fact that the void ratio of a soil cannot decrease without limit under increasing pressure, mean that the assumption of a linear relationship between void ratio and log of effective consolidation pressure that defines the compression index Cc is simply a useful engineering approximation that applies over a range of stresses and void ratios of practical interest.3 Values for compression index less than 0.2 represent soils of slight to low compressibility; values of 0.2 to 0.4 are for soils of moderate to intermediate compressibility; and a compression index
3 Compression index Cc or swelling index Cs and the coefficient of compressibility av are related as follows:
de C av ⫽ ⫺ ⫽ ln 10 c or d v v
ln 10
Cs v
Hence, av is both stress level and stress history dependent.
greater than 0.4 indicates high compressibility. Correlations between compression index and compositional and state parameters have been proposed by a number of investigators. Several such relationships for cohesive soils were summarized by Djoenaidi (1985) and quoted by Kulhawy and Mayne (1990), and these relationships are shown in Fig. 10.26. A simple correlation between the compression ratio, defined as Cc /(1 ⫹ e0), where e0 is the initial void ratio, and the natural water content is shown in Fig. 10.27. The large increase in compressibility that occurs when sensitive clay is loaded beyond its maximum prior effective consolidation pressure is shown in Fig. 8.44. Values of compression index for the steepest part of the compression curve as a function of in situ void ratio and sensitivity are shown in Fig. 10.28. The profound influence of structure metastability as represented by high sensitivity is clearly evident. Usual ranges of coefficient of consolidation for finegrained soils are given in Fig. 4.19. Owing to the direct dependence of the coefficient of consolidation cv on hydraulic conductivity and its inverse proportionality to coefficient of compressibility, reliable determination of a representative value in any case is difficult. Both hydraulic conductivity and compressibility are changed by sample disturbance and by consolidation itself. Most settlement predictions are done using average values for coefficient of consolidation. Shortcomings of Simple Theory for Predicting Volume Change and Settlements
In many cases, predictions of the volume changes and settlements and the rates at which they develop, which
350
10
VOLUME CHANGE BEHAVIOR
Figure 10.25 Solution to the one-dimensional consolidation equation: (a) distribution of excess pore water pressures as a function of dimensionless time and depth for a doubly drained clay layer and (b) average degree of consolidation as a function of time factor.
are based on the above simple theory, are poor. Among the types of deviations between the observed and predicted settlement and pore pressure responses are the following (Crooks et al., 1984; Becker et al., 1984; Tse, 1985; Mitchell, 1986; Duncan, 1993): 1. Differences in predicted and observed initial pore pressure development upon load applications 2. Continued pore pressure buildup after completion of loading 3. Differences between field consolidation rates and those predicted based on the results of laboratory tests
4. Changes in pore pressure dissipation rates during and following construction 5. Apparent lack of strength gain with consolidation following load application There are two types of reasons for deviations from the simple theory. In the first category are those that relate to soil behavior and the fact that in general the simple relationships between effective stress shown in Figs. 10.1 and 10.24 are neither unique nor time independent. In the second category are those that relate to the constitutive models and their application and the fact that the simplifying assumptions that may be required are not representative of the real conditions.
CONSOLIDATION
351
Figure 10.26 Representative values of compression index Cc for cohesive soils (Djoenaidi,
1985).
Soil Behavior Factors Characteristics of the real behavior of fine-grained soils that are important in determining the amount and rate of consolidation include:
Figure 10.27 Compression ratio as a function of natural water content (from Lambe and Whitman, 1969). Reprinted with permission from John Wiley & Sons.
1. Fabric and Structure Resistance to compression is determined by both effective stress and structure. Structural influences that must be considered relate to the initial state, the effects of sample disturbance, structural breakdown associated with consolidation under pressures greater than the maximum past consolidation pressure, and the effects of anisotropic loading. 2. Time and Rate of Loading The relationship between void ratio and effective consolidation pressure is not unique for a fine-grained soil but is influenced by rate of loading and time under a constant load as well. That is, e ⫽ e( , t)
(10.23)
In differential form, Eq. (10.23) can be written
冉 冊
e de ⫽ dt
Figure 10.28 The influence of sensitivity and in situ void ratio on compression index (from Leroueil et al., 1983). Reproduced with permission of the National Research Council of Canada.
t
冉冊
d e ⫹ dt t
(10.24)
According to this relationship, the total void ratio change at any time is the sum of two components: (1) that due to change in effective stress, or effective stress related compressibility, given by the first term on the right-hand side of Eq. (10.24) and (2) that due to time, or time-related compressibility, given by the second term on the right. The rate at which the total void ratio decreases as a function of time after application of
352
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VOLUME CHANGE BEHAVIOR
a stress increase may be controlled by either how rapidly the water can escape under a hydraulic gradient or by how fast the structure of the soil can deform or creep under a given magnitude of effective stress. Component (1) compression is commonly referred to as primary consolidation. Component (2) compression is commonly referred to as secondary compression. In addition, aging phenomena during time under sustained stress generate additional resistance to further compression. 3. Temperature Owing to differential thermal expansions of soil solids and the pore fluid and changes in interparticle bond strength and resistance to sliding that can result from changes in temperature, temperature-induced changes in effective stress and volume are possible. These effects are considered further in Section 10.12. Modeling Factors The commonly used constitutive models for soil compression and consolidation may not give suitable representations of actual behavior for the following reasons:
1. The relationship between void ratio and effective consolidation pressure is not linear, as is assumed for the Terzaghi consolidation theory. In fact, the use of compression index and swelling index to characterize soil compression and swelling recognize the nonlinear nature of the void ratio– effective stress relationship. 2. Changes in void ratio, compressibility, and hydraulic conductivity during consolidation are neglected or not properly taken into account. 3. Secondary compression, which is creep of the soil skeleton, is often neglected, and models for taking it into account are of uncertain validity. 4. Soil properties differ among the strata making up the soil profile and within the individual strata themselves. 5. Boundary conditions are uncertain or unknown, especially the drainage boundaries. Given that the time for primary consolidation varies as the square of the distance to a drainage layer, errors in definition and location of drainage boundaries have a major impact on settlement rate predictions. 6. Although one-dimensional analyses are often used, two- and three-dimensional effects may be important. 7. The stress increments may not be known with certainty. Analysis of modeling factors of the type listed above is outside the scope of this book; however, additional
information about them and about how to account for them can be found in Gibson et al. (1981), Tse (1985), Mesri and Castro (1987), Leroueil et al. (1990), Scott (1989), Duncan (1993), and elsewhere. Generalization of Terzaghi’s one-dimensional consolidation theory to three dimensions was made by Biot (1941). At present, there are finite element and finite difference codes that solve Biot’s consolidation equation incorporating nonlinear stress–stress relationships as well as anisotropic hydraulic conductivity. The hydraulic conductivity can also be a function of void ratio or effective stress. Further details can be found in Lewis and Schrefler (1997) and Coussy (2004). Soil behavior factors are considered further in the remainder of this section. Effects of Sample Disturbance
The effects of sample disturbance on the compression curve of sensitive or structured clay are shown in Fig. 8.44 and include: 1. A lower void ratio under any effective stress. 2. Higher values of recompression index and lower values of the compression index for a disturbed clay than for the undisturbed soil. 3. Less clearly defined stress history; determination of the maximum past consolidation pressure may be difficult and uncertain. Several methods to estimate the influences of sample disturbance on measured compression properties and strength have been proposed. Among them, Schmertmann’s (1955) procedure is useful for determination of a corrected maximum past pressure and for estimation of more representative values of swelling and recompression indices. The SHANSEP (stress history and normalized soil engineering properties) method (Ladd and Foott, 1974) was developed for more accurate determination of the strength of soft clay. By this method, samples are consolidated beyond the maximum past pressure into the virgin compression range. Provided the structure of the consolidated clay does not differ extensively from that of the undisturbed clay, the relationships between the ratios of shear stress divided by effective consolidation pressure versus strain and pore pressure divided by effective consolidation pressure versus strain are the same for both the original undisturbed clay and the consolidated samples. An uncertainty in this method, however, is the extent of breakdown of a structured soil from its initial state when it is consolidated past its prior maximum past pressure. Evidence indicates that it works well for clays of low-to-medium sensitivity.
SECONDARY COMPRESSION
10.10
SECONDARY COMPRESSION
According to the simple consolidation theory, which assumes uniqueness between void ratio and effective stress, consolidation ends when excess hydrostatic pressures within a clay layer are fully dissipated. On this basis, the relationship between degree of consolidation and dimensionless time is as shown in Fig. 10.25b. In reality, however, most soils continue to compress in the manner shown in Fig. 10.29. The reason for secondary compression is that the soil structure is susceptible to a viscous or creep deformation under the action of sustained stress as the fabric elements adjust slowly to more stable arrangements. The rate of secondary compression is controlled by the rate at which the structure can deform, as opposed to the rate of primary consolidation, which is controlled by Darcy’s law, which determines how rapidly water can escape from the pores under a hydraulic gradient.4 The mechanism of secondary compression involves sliding at interparticle contacts, expulsion of water from microfabric elements, and rearrangement of adsorbed water molecules and cations into different positions. The observed behavior is consistent with that of a thermally activated rate process, which involves mechanisms that are discussed in more detail in Section 12.4. The relationship between void ratio and log of time during secondary compression is linear for most soils over the time ranges of interest following primary con-
Figure 10.29 Idealized relationship between void ratio and logarithm of time showing primary consolidation and secondary compression.
4
It is commonly assumed that there are no excess hydrostatic pressures during secondary compression. However, water is expelled during secondary compression, and water flow is driven by hydrostatic head differences, so there must be some small hydrostatic pressure difference between the interior and a drainage boundary.
353
solidation.5 Thus, it is convenient to define a coefficient of secondary compression, Ce, according to Ce ⫽ ⫺de/d(log t)
(10.25)
The value of Ce is usually related to the compression index Cc as shown in Table 10.9, where values are listed for a number of different natural soils. Average values for Ce /Cc are 0.04 0.01 for inorganic clays and silts, 0.05 0.01 for organic clays and silts, and 0.075 0.01 for peats. Similar behavior for a number of clean sands is shown in Fig. 10.30, where it may be seen that Ce /Cc falls in the range of 0.015 to 0.03. A general relationship between void ratio, effective consolidation pressure, and time is shown in Fig. 10.31, with slopes Ce and Cc indicated. When the curves corresponding to different times after the end of primary consolidation are projected onto the void ratio–log effective stress plane, Fig. 10.5 is obtained for the assumption of linearity between void ratio and log . Algebraic manipulation of the secondary compression equation and the primary compression equation shows that the preconsolidation pressure is rate dependent (Soga and Mitchell, 1996), consistent with the data presented in Fig. 10.7. Both laboratory tests and field measurements, as well as theoretical arguments, have been made to establish whether or not (1) the relationship between the end-of-primary consolidation void ratio and effective consolidation pressure is unique and independent of load increment ratio or deformation rate, and (2) whether or not both primary consolidation and secondary compression can occur together or if all primary consolidation must be completed before secondary compression begins. The answers to these questions are important as they impact the usefulness of laboratory odometer test results on thin samples with short drainage paths, in which consolidation times are short, for prediction of the consolidation of thick layers in the field wherein consolidation times are often very long. Detailed discussion of these issues is outside the scope of this book. Among the many important references on these points are Taylor (1942), Murayama and Shibata (1961), Bjerrum (1967), Walker (1969),
5 There is no reason to believe that secondary compression should continue indefinitely because a final equilibrium of the structure should ultimately develop under a given stress state. In nature, chemical, biological, and climate changes also develop over long time periods. These changes can accelerate the establishment of equilibrium or create new conditions of disequilibrium. However, the assumption of linearity between void ratio and log of time after the end of primary consolidation is sufficiently accurate for most practical cases.
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10
VOLUME CHANGE BEHAVIOR
Table 10.9 Values of the Ratio of Coefficient of Secondary Compression to Compression Index for Natural Soils Grouping
Soil Type
Ce / Cc
Inorganic clays and silts
Whangamarino clay Leda clay Soft blue clay Portland sensitive clay San Francisco Bay mud New Liskeard varved clay Silty clay C Near-shore clays and silts Mexico City clay Hudson River silt Norfolk organic silt Calcareous organic silt Postglacial organic clay Organic clays and silts New Haven organic clay silt Amorphous and fibrous peat Canadian muskeg Peat Peat Fibrous peat
0.03–0.04 0.025–0.06 0.026 0.025–0.055 0.04–0.06 0.03–0.06 0.032 0.055–0.075 0.03–0.035 0.03–0.06 0.05 0.035–0.06 0.05–0.07 0.04–0.06 0.04–0.075 0.035–0.083 0.09–0.10 0.075–0.085 0.05–0.08 0.06–0.085
Organic clays and silts
Peats
From Mesri and Godlewski (1977).
Figure 10.30 C / Cc values for clean sands (from Mesri et
al., 1990). Reprinted with permission of ASCE.
Figure 10.31 General relationship among void ratio, effective stress, and time (from Mesri and Godlewski, 1977). Reprinted with permission of ASCE.
IN SITU HORIZONTAL STRESS (K0)
Aboshi (1973), Mesri (1973), Mesri and Godlewski (1977), Jamiolkowski et al. (1985), Leroueil et al. (1985, 1988), Mesri and Choi (1985), Leroueil (1988), Mesri et al. (1995), Leroueil (1995), and Mesri (2003). In spite of these uncertainties, conventional practice has been to assume that secondary compression does not begin until completion of primary consolidation. This has the advantage of simplicity in that settlement estimates can be made on the basis of degree of consolidation according to the simple theory during times up to the end of primary consolidation. For longer times, the total settlement is taken as the consolidation settlement increased by an amount of secondary compression derived from Eq. (10.25). This is undoubtedly an oversimplification of real behavior, as from the perspective of the soil, there should be no difference between the two types of compression. It compresses just sufficiently to withstand the applied stresses at any time, and the rate at which it occurs in any element depends on whether or not the rate of water flow from the element at that time is controlled by a preexisting hydrostatic excess pressure gradient (primary consolidation) or by the time-dependent generation of small pore pressures owing to structural readjustment (secondary compression). On this basis, it would seem most likely that within a clay layer both primary consolidation and secondary compression may be occurring concurrently in different elements. The major difficulty has been in the formulation of a constitutive model to describe both the hydrodynamic and viscous components of the soil response that is both accurate and that can be readily implemented into analytical or numerical solutions. With recent advances in theory and programs that can be run on personal computers, it is now possible to more properly describe the actual soil response and to make improved settlement rate predictions (Duncan, 1993).
10.11
IN SITU HORIZONTAL STRESS (K0)
Terzaghi’s consolidation theory considers compression only in one dimension. The soil model relates the vertical strain to the change in vertical stress, and this defines the volume change under zero horizontal displacement conditions. There is no need to consider the change in horizontal stress to calculate the deformation, even though the actual horizontal stress changes during loading and unloading. However, once soil deformation departs from the one-dimensional condition, it is necessary to consider the state and changes of the stresses in the other directions and the associated volume change behavior.
355
In most cases, the horizontal stress in the ground does not equal the vertical overburden stress. The minimum and maximum possible values can be calculated on the basis of plasticity theories for earth pressure. The actual value, which must fall somewhere between these limiting values, is a proportion of the vertical overburden stress that depends primarily on soil type and stress history. It is often determined (or estimated) on the basis of these two factors using empirical correlations, and, sometimes the results of in situ tests such as the self-boring pressuremeter (Mair and Wood, 1987). The main limitation of in situ measurements is that they invariably cause disturbance and allow lateral deformations of the ground that change the stress being measured. The general ranges of in situ lateral stress for different soil types are summarized, and factors influencing lateral stress are reviewed in this section. Development of Horizontal Stress
The relationship between the horizontal effective stress and the vertical effective stress depends on the lateral deformation that accompanies changes in vertical stress. If the vertical stress and strain increase without any deformation in the horizontal directions (i.e., onedimensional compression, as would be the case for an accumulating sediment), the soil is said to be in an atrest state, and the horizontal stress associated with this condition is termed the at-rest pressure. The ratio between the horizontal and vertical effective stresses during initial compression of a soil is a constant, defined by the coefficient of earth pressure at rest K0 (⫽ h / v). Values of K0 for normally consolidated soils are generally in the range of 0.3 to 0.75. Jaky’s equation has been found to give a good estimate for many soils: K0 ⫽ 1 ⫺ sin
(10.26)
in which is the effective stress friction angle measured in triaxial compression tests. Although correlations have been published that suggest unique relationships between K0 and liquid limit or plasticity index, a comprehensive set of data for 135 clay soils indicates little correlation, as shown in Fig. 10.32. This is not surprising since the Atterberg limits depend only on composition, and K0 is a state parameter that is dependent on composition, structure, and stress history. When the vertical stress on a normally consolidated soil is reduced, the horizontal stress does not decrease in the same proportion as the vertical stress. Thus, the value of at-rest earth pressure coefficient for an overconsolidated soil (K0)oc is greater than that for the normally consolidated soil (K0)nc, and it varies with the
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VOLUME CHANGE BEHAVIOR
Figure 10.32 Lack of correlation between coefficient of
earth pressure at rest and plasticity index for normally consolidated soils (from Kulhawy and Mayne, 1990). Reprinted with permission from EPRI.
amount of overconsolidation, as shown schematically in Fig. 10.33, and in Fig. 10.34 for 48 clays. The data in Fig. 10.34 can be approximated by the equation K0 ⫽ (1 ⫺ sin )(OCR)sin
(10.27)
Kulhawy and Mayne (1990) give additional useful correlations for estimation of K0. The complicated stress paths associated with onedimensional compression of four clays are illustrated in Fig 10.35. In the upper plot for each clay the deviator stress is shown as a function of the mean effective stress during one-dimensional compression. Before yielding, the stress path shows larger stress ratios than the K0 ⫽ 1 ⫺ sin line. As the stress state approaches the preconsolidation pressure, the stress path moves to the K0 ⫽ 1 ⫺ sin line. The curvature
Figure 10.33 Variation of horizontal effective stress with
vertical effective stress for loading and unloading.
Figure 10.34 Dependence of (K0)oc on overconsolidation ratio (from Kulhawy and Mayne, 1990). Reprinted with permission from EPRI.
toward the K0 line coincides with the region of largest compression index (steepest slope on the volumetric strain versus effective mean stress diagrams), implying structural degradation. Effect of Lateral Yielding on the Coefficient of Earth Pressure
If an element of soil initially under an at-rest stress condition is allowed to yield by compressing in a vertical direction while spreading laterally, for example, triaxial or plane strain compression, then the horizontal earth pressure coefficient decreases until a failure condition is reached. If, on the other hand, the element is compressed in the horizontal direction while being allowed to expand in the vertical direction, triaxial or plane strain extension, then the horizontal earth pressure increases until failure develops. These two conditions and the associated variations in K are shown in Fig. 10.36. The two failure conditions are termed active and passive, respectively, and the corresponding earth pressure coefficients are the coefficient of active earth pressure Ka and the coefficient of passive earth pressure Kp. According to classical theories of earth pressure based on limiting equilibrium of a plastic material hav-
100
(σa – r)/2(kPa)
(σa – r)/2(kPa)
IN SITU HORIZONTAL STRESS (K0)
50
0
0
50
100 150 (σa + r)/2(kPa)
1000 ure
l fai ak
500
200
Pe
0
0
500
d ture g) truc therin s e a d K o( by we
1000 1500 (σa + r)/2(kPa)
2000
0
0
e0 = 0.69 εv(%)
e0 = 1.97 εv(%)
357
10
4 8
20 12 (b) Unweathered Keuper marl
200
(σa – r)/2(kPa)
(σa – r)/2(kPa)
(a) Sensitive Canadian clay ilure k fa Pea
100
d)
ture
uc estr
d
K o(
0 0
100 100 100 (σa + r)/2(kPa)
50
25
0 0
100
0
25 50 75 (σa + r)/2(kPa)
0 e0 = 1.04
5
e0 = 0.69 εv(%)
εv (%)
100
10
5 10
15
15 (d) Chalk
(c) Artificially bonded soil
Figure 10.35 Variation in lateral stress with mean stress during one-dimensional consolidation of four clays (from Leroueil and Vaughan, 1990).
ing a friction angle and a cohesion c, the limiting minimum and maximum values of the earth pressure coefficients are
冉 冉
冊 冊
冉 冉
冊 冊
Ka ⫽ tan2 45 ⫺
2c ⫺ tan 45 ⫺ 2 v 2
(10.28)
Kp ⫽ tan2 45 ⫹
2c ⫹ tan 45 ⫹ 2 v 2
(10.29)
These limiting values are for isotropic soil and a horizontal ground surface. Standard soil mechanics texts should be consulted for further details on limiting earth pressure coefficients under sloping ground and the influences of changes in applied loads on in situ lateral stress.
Under one-dimensional conditions, compression is usually plotted on the e–log v plane, as shown in Fig. 10.1. For three-dimensional stress and deformation conditions, however, the volumetric behavior is often plotted on the e–ln p plane (or v –ln p plane), where p is the mean effective pressure and v is the specific volume (⫽1 ⫹ e). When a specimen is consolidated isotropically, the slope of the normal compression line is defined as ⫽ ⫺de/d ln p(⫽ ⫺dv /d ln p) (Schofield and Wroth, 1968).6 Figure 10.37 shows the change in void ratio with mean effective stress (p) for reconstituted kaolin clay specimens consolidated isotropically at constant stress The swelling (or recompression) line is often called the ! line on e–ln p plane and the slope is defined as the recompression index !(⫽ ⫺de / d ln p) 6
358
10
VOLUME CHANGE BEHAVIOR
1.9
q
Stress Paths
1 2
1.7 Void Ratio
3
p⬘
1.5 Stress Path 1: q/p⬘ = 0.375
1.3
Stress Path 2: q/p⬘ = 0.288 Stress Path 3: q/p⬘ = 0
70
100
200
300
500
1000
Mean Pressure p⬘ (kPa)
Figure 10.37 Effect of stress ratio ( 1 / 3 or q / p) on vol-
umetric compression behavior of reconstituted kaolin clay. Figure 10.36 Variation of lateral earth pressure coefficient
with deformation of a soil element.
ratios ( 1 / 3 or q/p) as shown by the stress paths in the insert diagram. The compression lines are parallel to each other and therefore they will have the same compression index . Similar behavior is observed in sands; the isotropic compression line and the one-dimensional compression line are parallel to each other. Assuming that K0 is constant during loading, the value of isotropically consolidated specimens will be the same as that of one-dimensionally consolidated specimens.7 Examination of Fig. 10.37 indicates that the volumetric behavior of soils can be separated into two components: (i) one due to compression or swelling by the increase or decrease in mean effective pressure p and (ii) the other due to dilation or contraction by shearing of the soil by the increase in q. Further discussion of deformation behavior under combined volumetric and deviatoric stress loading conditions is given in Chapter 11. Anisotropy
Unless the horizontal earth pressure coefficient is equal to 1.0, which is not the usual case, the stress condition In one dimensional consolidation condition, p ⫽ (1 ⫹ 2K0) v. The relationship between Cc (⫽ ⫺de / d log v) and (⫽ ⫺de / d ln p) is Cc ⫽ ln 10: Cc ⫽ ⫺de / d log v ⫽ ⫺ln 10[de / d(ln v)] ⫽ ⫺ln 10de / {d ln p ⫺ d[ln(1 ⫹ 2K0)]} ⫽ ⫺ln 10de / d ln p) (K0 is constant in normally consolidated state, hence d[ln(1 ⫹ 2K0)] ⫽ 0). On the other hand, it is not possible to relate Cs obtained from the onedimensional consolidation test to ! obtained from the isotropic unloading test. This is because the K0 value changes as the specimen is unloaded and therefore the d[ln(1 ⫹ 2K0)] term in the above equation does not become zero. 7
in the ground is anisotropic. Furthermore, although it is usually assumed that the in situ stresses are the same in all directions beneath level ground, there are some conditions in which this may not be true. These include situations wherein there is a directional component to the soil fabric that formed during deposition, as might be the case, for example, for an alluvial or beach deposit. Directional variability has been measured at some sites by means of pressure cells, pressure meters that contain multiple sensing arms, and flat plate dilatometers. With the development of new shear wave and tomography methods for the nondestructive and nonintrusive testing of soil layers, it is possible to obtain much more data on the actual lateral stress state and its variability, thus providing new insights into geologic and soil formational history, as well as quantitative values for use in the analysis and prediction of behavior. Time Dependence of Lateral Earth Pressure at Rest
It is usually assumed in conventional geotechnical analyses that the coefficient of lateral earth pressure atrest K0 is a time-invariant constant. Whether or not this is indeed the case is not known with certainty, and there is no clear consensus on how K0 should be expected to vary with time (Schmertmann, 1983). However, if a soil is assumed to remain under a constant effective stress state following consolidation and there are no changes in the compositional or environmental conditions, then slow changes in lateral pressure should occur in any material that is susceptible to creep and stress relaxation. Creep and stress relaxation are analyzed in Section 12.7.
TEMPERATURE–VOLUME RELATIONSHIPS
As long as a deviator stress is acting K0 ⫽ 1.0, and a soil element will tend to distort. If the vertical stress is greater than the horizontal stress (K0 ⬍ 1.0), then the element will try to expand laterally, but under onedimensional conditions it cannot, and the horizontal stress increases to restrain it. Conversely, if the horizontal stress is initially greater than the vertical stress (K0 ⬎ 1.0), then the element will try to compress laterally, but under one-dimensional conditions it cannot, so the horizontal stress decreases. Thus, over long periods of time, the coefficient of horizontal earth pressure at rest in normally consolidated soil should increase toward 1.0 and that in heavily overconsolidated soil should decrease toward 1.0. Values of K0 as a function of time, as determined in triaxial cells by Lacerda (1976), for undisturbed samples of soft San Francisco Bay mud, are shown in Fig. 10.38. Also shown is a theoretical relationship between K0 and time that was developed using the general stress–strain–time equations developed in Section 12.9. Thus, both theory and experiment support the above reasoning that K0 should increase with time when K0 is less than 1.0.
10.12 TEMPERATURE–VOLUME RELATIONSHIPS
Temperature changes generate volume and/or effective stress changes in saturated soils. For example, the percentage of the original pore water volume that is drained from a saturated specimen of illite subjected to a temperature increase from 18.9 to 60C followed by cooling to 18.9C while maintaining an isotropic effective stress of 200 kPa is shown in Fig. 10.39. The variation in effective stress 3 under the same temperature changes but with drainage prevented is shown in
359
Figure 10.39 Volume of pore water drained from saturated
illite under an isotropic effective stress of 200 kPa as a function of temperature change.
Fig. 10.40. Temperature effects such as these must be considered relative to their influences on deformation and stability both in the laboratory and the field. Theoretical Analysis Drained Conditions Increase in temperature causes thermal expansion of mineral solids and pore water. In addition, there can be changes in soil structure. For a temperature change T, the volume change of the pore water is
( Vw) T ⫽ wVw T
(10.30)
where w is the thermal expansion coefficient of soil water, and Vw is the pore water volume. The change in volume of mineral solids is ( Vs) T ⫽ sVs T
(10.31)
where s is the thermal coefficient of cubical expansion of mineral solids, and Vs is the volume of solids. The thermal coefficient of water is approximately 15 times greater than that of the solids (Cui et al., 2000). If a saturated soil is free to drain due to a change in temperature while under constant effective stress, the volume of water drained is Figure 10.38 K0 as a function of time for San Francisco Bay
mud. The theoretical curve was developed by Kavazanjian and Mitchell (1984) using the general stress–strain–time Eq. (12.43) adapted for zero lateral strain.
( VDR) T ⫽ ( Vw) T ⫹ ( Vs) T ⫺ ( Vm) T
(10.32)
in which ( Vm) T is the change in total volume due to
T, with volume increases considered positive.
360
10
VOLUME CHANGE BEHAVIOR
Figure 10.40 Effect of temperature changes on the effective stress in saturated illite under constant confining pressure.
In a soil mass with all grains in contact, and assuming the same coefficient of thermal expansion for all soil minerals, the soil grains and the soil mass undergo the same volumetric strain s T. In addition, the change in temperature induces a change in interparticle forces, cohesion, and/or frictional resistance that necessitates some particle reorientations to permit the soil structure to carry the same effective stress. If the volume change due to this effect is ( VST) T , then ( Vm) T ⫽ sVm T ⫹ ( VST ) T
(10.33)
and ( VDR) T ⫽ wVw T ⫹ s Vs T ⫺ [s Vm T ⫹ ( VST ) T]
(10.34)
Undrained Conditions The governing criterion for
undrained conditions is that the sum of the separate volume changes of the soil constituents due to both temperature and pressure changes must equal the sum of the volume changes of the soil mass due to both temperature and pressure changes; that is ( Vw) T ⫹ ( Vs) T ⫹ ( Vw) P ⫹ ( Vs) P ⫽ ( Vm) T ⫹ ( Vm) P
(10.35)
where the subscripts T and P refer to temperature and pressure changes, respectively. If mw, ms, and ms refer to the compressibility of water, the compressibil-
ity of mineral solids under hydrostatic pressure, and the compressibility of mineral solids under concentrated loadings, respectively, then ( Vw) P ⫽ mwVw u
(10.36)
( Vs) P ⫽ msVs u ⫹ msVs
(10.37)
where u is the change in pore water pressure and is the change in effective stress. The term ms Vs is the change in volume of mineral solids due to a change in effective stress, which also manifests itself by changes in forces at interparticle contacts. Also ( Vm) P ⫽ mv Vm
(10.38)
where mv is the compressibility of the soil structure. From Eqs. (10.30), (10.31), (10.36), (10.37), and (10.38), Eq. (10.35) becomes wVw T ⫹ s Vs T ⫺ ( Vm) T ⫽ Mv Vm ⫺ mwVw u ⫺ Vs(ms u ⫹ ms )
(10.39)
For constant total stress during a temperature change
⫽ ⫺ u
Thus, Eq. (10.39) becomes
(10.40)
TEMPERATURE–VOLUME RELATIONSHIPS
w Vw T ⫹ sVs T ⫺ ( Vm) T ⫽ mv Vm ⫺ mwVw u ⫺ u Vs(ms ⫺ ms)
(10.41)
Since ms and ms are not likely to be significantly different, and both are much less than mv and mw , little error results from assuming ms ⫺ ms ⫽ 0, so Eq. (10.41) can be written wVw T ⫹ sVs T ⫺ ( Vm) T ⫽ ⫺mv Vm u ⫺ mwVw u
(10.42)
The left side of Eq. (10.42) is equal to ( VDR) T , and the right side is an equivalent volume change caused entirely by a change in pore pressure. Because Vm ⫽ Vw ⫹ Vs
(10.43)
Eq. (10.42) may be written, after substitution for ( Vm) T by Eq. (10.33), w Vw T ⫺ sVw T ⫺ ( VST) T ⫽ ⫺mv Vm u ⫺mwVw u
(10.44)
Rearrangement of Eq. (10.44) gives the pore pressure change accompanying a temperature change:
u ⫽ ⫽
n T(s ⫺ w) ⫹ ( VST ) T /Vm mv ⫹ nmw n T(s ⫺ w) ⫹ ST T mv ⫹ nmw
(10.45)
in which n is the porosity, and ST is the physicochemical coefficient of structural volume change defined by ST ⫽
( VST ) T /Vm
T
(10.46)
Thus, the factors controlling pore pressure changes are the magnitude of T, porosity, the difference between thermal expansion coefficients for soil grains and water, the volumetric strain due to physicochemical effects, and the compressibility of the soil structure. For most soils (but not rocks) mv » mw , so
u ⫽
n(s ⫺ w) T ⫹ ST T mv
(10.47)
Consistency in algebraic signs is required for the application of the above equations. Both s and w are positive and indicate volume increase with increasing
361
temperature. The compressibilities mv and mw are negative because an increase in pressure causes a decrease in volume, and ST is negative if an increase in temperature causes a decrease in volume of the soil structure. Volume Change Behavior
Permanent volume decreases occur when the temperature of normally consolidated clay is increased under drained conditions, as shown by Fig. 10.41. Temperature changes in the order indicated were carried out on a sample of saturated, remolded illite after initial consolidation to an effective stress of 200 kPa. Water drains from the sample during increase in temperature and is absorbed during temperature decrease. The shape of the curves is similar to normal consolidation curves for volume changes caused by changes in applied stresses. When the temperature is increased, two effects occur. If the increase is rapid, a significant positive pore pressure develops due to greater volumetric expansion of the pore water than of the mineral solids. The lower the hydraulic conductivity of the soil, the longer the time required for this pore pressure to dissipate. Dissipation of this pressure accounts for the parts of the curves in Fig. 10.41 that resemble primary consolidation. The second effect results because increase in temperature causes a decrease in the shearing resistance at individual particle contacts. As a consequence, there is partial collapse of the soil structure and decrease in void ratio until a sufficient number of additional bonds are formed to enable the soil to carry the stresses at the higher temperature. This effect is analogous to secondary compression under stress increase. When the temperature drops, differential thermal contractions between the soil solids and the pore water cause pressure reduction in the pore water. The soil then absorbs water, as shown by the temperature decrease curves in Fig. 10.41. No secondary volume change effect is observed because the temperature decrease causes a strengthening of the soil structure and no further structural adjustment is required to carry the effective stress. On subsequent temperature increases, the secondary effect is negligible because the structure has already been strengthened in prior cycles. The final height changes and volumes of water drained associated with each temperature change shown in Fig. 10.41 are plotted as a function of temperature in Fig. 10.42, and clay structure volume changes are shown in Fig. 10.43. The forms of these plots are similar to conventional compression curves involving virgin compression, unloading, and reload-
362
10
VOLUME CHANGE BEHAVIOR
Figure 10.41 Volume of water drained from a saturated clay as a function of time as a result of temperature changes.
ing. An irrecoverable volume reduction after each temperature cycle is noted. Again, the effect of temperature increase is analogous to a pressure increase. The slope of the curves in Fig. 10.43 is the coefficient of thermal expansion for the soil structure
ST , defined previously by Eq. (10.46). For the cases shown, ST has a value of about ⫺0.5 ⫻ 10⫺4 C⫺1. The effect of temperature on clay compression depends on the pressure range (Campanella and Mitchell, 1968; Plum and Esrig, 1969). Weaker structure at low
TEMPERATURE–VOLUME RELATIONSHIPS
363
Figure 10.42 Effect of temperature variations on the height and volume change of saturated
illite.
stresses caused by increased temperature causes consolidation to a lower void ratio in order to carry the stress. The weakening effect of higher temperature is compensated by the strengthening effect of lower void ratio. As shown in Fig. 10.44, the compression index Cc is found to be approximately independent of temperature. On the other hand, the isothermal swelling index ! (⫽ ⫺de/d ln p) of reconstituted samples of an illitic clay measured under isotropic confining stress conditions is found to be temperature dependent as shown in Fig. 10.45. The preconsolidation pressure of a natural soft clay depends on temperature as illustrated in Fig. 10.7. Figure 10.46 shows the normalized preconsolidation pressure (⫽ preconsolidation pressure at temperature T/ preconsolidation pressure at 20C) with temperature
(Leroueil and Marques, 1996). The data show that there is approximately 1 percent decrease in preconsolidation pressure per one 1C temperature increase between 5 and 40C and somewhat less at higher temperatures (Leroueil and Hight, 2002). Stress history or overconsolidation ratio has a major influence on the volume change caused by increase in temperature (Hueckel and Baldi, 1990). For normally consolidated to moderately overconsolidated clay, irrecoverable volume reduction was observed by structure degradation and the shear strength increased. Volume expansion was observed in heavily overconsolidated clay, and the expansion rate increased with OCR. The effect of heating followed by cooling at two stages in a consolidation test is shown in Fig. 10.47.
364
10
VOLUME CHANGE BEHAVIOR
0.08
κT
0.06
0.04 䉭 䉭 䉭
0.02
0.00 10
䉭 䉭
20
40
60 80 100
200
Figure 10.45 Effect of temperature on swelling index of isotropically consolidated illitic clay specimens. The clay contained small amounts of Kaolin, chlorite and quartz and had a liquid limit of 30 percent (after Graham et al., 2001).
Figure 10.43 Volume changes in clay structure caused by
temperature change.
Figure 10.46 Effect of temperature on preconsolidation
pressure. The preconsolidation pressure at temperature T is normalized by the preconsolidation pressure at 20C (after Leroueil and Marques, 1996).
The effect is remarkably similar to the development of an apparent precompression due to aging and creep under a sustained stress as discussed in Chapter 12. Pore Pressure Behavior
Figure 10.44 Effect of temperature on isotropic consolida-
tion behavior of saturated illite (Campanella and Mitchell, 1968).
Pore pressure changes in saturated soils caused by temperature changes are reasonably well predicted by Eq. (10.47). The most important factors are the thermal expansion of the pore water, the compressibility of the soil structure, and the initial effective stress. The appropriate value of the compressibility mv depends on the rebound and recompression characteristics of the soil. When temperature increases, pore pressure increases, and effective stress decreases, which is a condition analogous to unloading. When temperature decreases, pore pressure decreases, and effective stress
CONCLUDING COMMENTS
Figure 10.47 Effect of heating and cooling on void ratio versus pressure relationship of illite (Plum and Esrig, 1969).
pore water pressure and effective stress than for the buckshot clay. The parameter F is approximately the same for different clays (Table 10.10). Knowledge of F values allows determination of laboratory temperature control to assure accurate pore pressure measurements in undrained testing of soil samples. For example, if it were desired to keep pore pressure fluctuations within 5 kPa for one of the clays in Table 10.10, the required temperature control would be about 0.5C for a sample at an effective stress of 500 kPa. The preceding analyses indicate that the overall volume changes that result from changes in temperature may not be large. However, the structural weakening and pore pressure changes that occur may be significant in terms of their influences on shear deformation and strength.
10.13
increases. As the previous temperature history caused permanent volume decrease at the higher temperature, the condition is analogous to recompression. Thus, the appropriate value of mv is based on the slope of the rebound or recompression curves, both of which are approximately the same, and can be defined by (mv)R ⫽
Vm /Vm 0.435 Cs ⫽
(1 ⫹ e0)
(10.48)
where Cs is the swelling index, e0 is the initial void ratio, and is the effective stress at which (mv)R is to be evaluated. A pore pressure–temperature parameter F may be defined as the change in pore pressure per unit change in temperature per unit effective stress, or alternatively, the change in unit effective stress per unit change in temperature, that is, F⫽
u/ T
/ e [( ⫺ w) ⫹ ST /n] ⫽⫺ ⫽ 0 s
T 0.435Cs
(10.49) Some values of F are given in Table 10.10. The values listed for are averages for the indicated temperature ranges. The influence of effective stress on change in pore pressure can be seen for the data for Vicksburg buckshot clay and for the saturated sandstone. The greater change in pore pressure for a given T for a higher initial effective stress is predicted by this theory. Also, the much lower compressibility of the sandstone is responsible for a much higher temperature sensitivity of
365
CONCLUDING COMMENTS
Knowledge of volume changes to be expected in a soil mass as a result of changes in confinement, loading, exposure to water and chemicals, changes in temperature and the like is one of the four dimensions of soil behavior that must be understood for success in geoengineering, the other three being fluid and energy conduction properties, deformation and strength properties, and the influences of time. The nature and influences of different factors on volume change have been the subject of this chapter. Soil compression and consolidation under applied stress have been the most studied owing to their essential role in estimation of settlements, and this was one of the first motivations for development of soil mechanics. The mechanical aspects of compression and swelling are far better understood and quantified than are those generated by physicochemical, geochemical, and microbiological factors, although interest and research on the latter is intensifying. Although analysis of volume change is typically done through consideration of a soil mass as a continuum, the processes that determine it are at the particulate level and involve discreet particle movements required to produce a new equilibrium following changes in stress and environmental conditions. Important aspects of colloidal type interactions involving interparticle forces, water adsorption phenomena, and soil fabric effects were analyzed in this chapter. Discreet particle movements and their relationships to macroscopic volumetric and deviatoric behavior are discussed in more detail in Chapters 11 and 12. Soil swelling, sometimes referred to as ‘‘the hidden disaster’’ owing to the very large economic, but unspectacular, damages (several billion dollars in the
366
10
VOLUME CHANGE BEHAVIOR
Table 10.10 Temperature-Induced Pore Pressure Changes Under Undrained Condtions
Soil Type Illite (grundite) San Francisco Bay mud Weald Claya Kaolinite Vicksburg buckshot clayb Saturated sandstone (porous stone) a b
(kN/m2)
T (C)
u (kN/m2)
F ( u/ T) (C⫺1)
200 150
21.1–43.4 21.1–43.4
⫹58 ⫹50
0.013 0.015
710 200 100 650
25.0–29.0 21.1–43.4 20.0–36.0 20.0–36.0
⫹51 ⫹78 ⫹28 ⫹190
0.018 0.017 0.017 0.018
250 580
5.3–15.0 5.3–15.0
⫹190 ⫹520
0.079 0.092
From Henkel and Sowa (1963). From Ladd (1961) Fig. VIII-6.
U.S.) to pavements, structures, and utilities each year, is attributable to both double layer repulsions and water adsorption in soils that contain significant amounts of high plasticity clay minerals. Other causes of soil and rock expansion have been identified as well, such as pyrite related mineral transformations and sulfate reactions, often mediated by microorganisms. QUESTIONS AND PROBLEMS
1. What is the single most important property or characteristic controlling the consolidation and swelling behavior of a soil? Why? 2. If two samples of the same sand have the same relative density and are confined under the same effective stress, can they have different volume change properties? Why? 3. In what soil types and under what conditions do physical particle interactions dominate in determining the compression and swelling behavior? In what soil types and under what conditions do physicochemical factors dominate? 4. Provide an explanation for the differences in amount of swelling associated with expansion following the different stress paths shown in Fig. 10.10. 5. Consider the following soil profile beneath a level ground surface:
Depth Range (m)
Soil Type
Unit Weight (kN/m3)
0–5 5–10 10–18 18–30 ⬎30
Surcharge fill Rubble fill Clean sand Soft clay Bedrock
19.0 17.0 18.0 16.0 —
The water table is at a depth of 8 m. a. Show profiles of vertical total, effective, and water pressure as a function of depth below the ground surface before placement of the surcharge fill. Assume that each layer is normally consolidated. b. Show profiles of vertical total, effective, and water pressure as a function of depth immediately after placement of the surcharge fill. Indicate if the clay layer is normally consolidated, overconsolidated, or underconsolidated at this time. c. Show profiles of vertical total, effective, and water pressure as a function of depth at a long time after the placement of the surcharge fill. Are the sand and clay layers normally consolidated, underconsolidated, or overconsolidated? d. Show profiles of vertical total, effective, and water pressure as a function of depth immediately after removal of the surcharge fill. Are the sand and clay layers normally consolidated, underconsolidated, or overconsolidated?
QUESTIONS AND PROBLEMS
e. Show profiles of vertical total, effective, and water pressure as a function of depth at a long time after removal of the surcharge fill. Are the sand and clay layers normally consolidated, under-consolidated, or overconsolidated? f. Show depth profiles and approximate values of the horizontal coefficient of earth pressure at rest for the conditions in parts (a) through (e). 6. Two near-surface strata of the same soft clay are to be consolidated. In one the consolidation is to be done by placement of a surcharge fill at the ground surface. In the other, the consolidation is to be effected by lowering the water table to the bottom of the clay layer and evaporation of water from the ground surface, which will cause shrinkage of the clay. The ground water table is initially at the top of the clay stratum. Show profiles of effective stress and water pressure versus depth for each stratum corresponding to the condition where the vertical effective stress is the same in each at middepth. Will the clay structure be the same in each stratum at this depth at this time? Why? 7. Describe and contrast the compression, consolidation, and swelling potential properties of the following soil types. Assume their initial states (water content, overburden pressure, environmental chemistry) to be representative of the indicated soil type as ordinarily encountered in nature. a. Loess b. Varved clay c. Carbonate sand d. Quick clay e. Tropical andisol f. Glacial moraine g. Torrential stream deposit or mudflow h. Sand hydraulic fill i. Compacted clay liner of an earth dam 8. Prepare a schematic diagram of liquidity index versus log effective consolidation pressure. Show the positions of normally consolidated and heavily overconsolidated samples of a given clay on this diagram. 9. Discuss the strengths and weaknesses of the osmotic pressure and water adsorption theories for clay swelling in terms of their adequacy to explain the influences of mineralogical and compositional factors on the swelling of fine-grained soils. 10. Calculate the equilibrium void ratios at a pressure of 1.0 atm for the following systems assuming that the DLVO and osmotic pressure theories are valid:
367
a. Sodium montmorillonite in 0.002 M NaCl b. Sodium montmorillonite in 0.2 M NaCl c. Sodium illite in 0.002 M NaCl d. Sodium illite in 0.2 M NaCl Assume any quantities needed but not stated. 11. Consider the real behavior of sediments formed from montmorillonite and illite in waters of the above concentrations. Approximately what void ratios would you expect to find after normal consolidation to a pressure of 1.0 atm? If different than the values you calculated in the preceding problem, state why? 12. A normally consolidated, saturated marine clay is sampled without structural disturbance from beneath the seafloor and sealed to prevent water movement in or out. The temperature of the clay in situ is 5C. The effective stress at the time of sampling is 200 kPa and the void ratio of the clay is 0.90. The sealed sample is taken immediately to the shipboard laboratory where the original in situ confining stress is immediately reapplied. a. What will be the subsequent effective stress in the laboratory at a temperature of 20C? The clay has a compression index of 0.5 and a swelling index of 0.05. Other properties are as follows: • Compressibility of water ⫽ ⫺4.83 ⫻ 10⫺5 cm2 /kg • Coefficient of thermal expansion of solid mineral particles ⫽ 0.35 ⫻ 10⫺4 C⫺1 • Coefficient of thermal expansion of water ⫽ 2.07 ⫻ 10⫺4C⫺1 • Coefficient of thermal expansion of the soil structure ⫽ 0.5 ⫻ 10⫺4C⫺1 b. How does the change in effective stress computed in part (a) compare with the value estimated on the basis of Table 10.10 in the text? c. If the same confining stress is maintained but drainage of the sample is then allowed, how much water, expressed as a percentage of the original sample volume, will move in or out of the clay? d. Illustrate the changes accompanying the operation in parts (a) and (c) on a diagram of void ratio versus log effective consolidation pressure. 13. Identify and discuss some possible consequences of seawater intrusion into a freshwater sand aquifer overlying a compressible clay stratum which, in turn, overlies another freshwater aquifer.
368
10
VOLUME CHANGE BEHAVIOR
14. What is a collapsing soil? What conditions can initiate collapse? What factors determine the magnitude and rate of collapse? Is the process compatible with the principle of effective stress? Why?
(consolidating) a highly plastic clay slurry that is initially at a liquidity index considerably greater than 1.0. Explain how each of the methods that you have identified works.
15. Volume and temperature stability over long periods of time (thousands of years) is a very important consideration in the utilization of earth materials as containment barriers for various types of chemical and radioactive waste. What mineral types, gradations, and placement conditions would you specify for this application? Why?
17. Comment on the mechanisms of primary consolidation and secondary compression in terms of the rate-controlling factors, influences of and effects on soil structure, whether they occur sequentially or concurrently, and the suitability of our usual procedures for quantifying them for geoengineering analysis.
16. Suggest possible methods other than direct loading using surcharge fills for reducing the water content
18. Suggest possible methods for preventing or reducing swelling on the exposure of expansive soil to water and explain the mechanisms involved.
CHAPTER 11
Strength and Deformation Behavior
11.1
INTRODUCTION
All aspects of soil stability—bearing capacity, slope stability, the supporting capacity of deep foundations, and penetration resistance, to name a few—depend on soil strength. The stress–deformation and stress– deformation–time behavior of soils are important in any problem where ground movements are of interest. Most relationships for the characterization of the stress–deformation and strength properties of soils are empirical and based on phenomenological descriptions of soil behavior. The Mohr–Coulomb equation is by far the most widely used for strength. It states that ff ⫽ c ⫹ ff tan
(11.1)
ff ⫽ c ⫹ ff tan
(11.2)
where ff is shear stress at failure on the failure plane, c is a cohesion intercept, ff is the normal stress on the failure plane, and is a friction angle. Equation (11.1) applies for ff defined as a total stress, and c and are referred to as total stress parameters. Equation (11.2) applies for ff defined as an effective stress, and c and are effective stress parameters. As the shear resistance of soil originates mainly from actions at interparticle contacts, the second equation is the more fundamental.
In reality, the shearing resistance of a soil depends on many factors, and a complete equation might be of the form Shearing resistance ⫽ F(e, c, , , C, H, T, , ˙ , S) (11.3) in which e is the void ratio, C is the composition, H is the stress history, T is the temperature, is the strain, ˙ is the strain rate, and S is the structure. All parameters in these equations may not be independent, and the functional forms of all of them are not known. Consequently, the shear resistance values (including c and ) are determined using specified test type (i.e., direct shear, triaxial compression, simple shear), drainage conditions, rate of loading, range of confining pressures, and stress history. As a result, different friction angles and cohesion values have been defined, including parameters for total stress, effective stress, drained, undrained, peak strength, and residual strength. The shear resistance values applicable in practice depend on factors such as whether or not the problem is one of loading or unloading, whether or not short-term or long-term stability is of interest, and stress orientations. Emphasis in this chapter is on the fundamental factors controlling the strength and stress–deformation behavior of soils. Following a review of the general characteristics of strength and deformation, some re369
370
11
STRENGTH AND DEFORMATION BEHAVIOR
lationships among fabric, structure, and strength are examined. The fundamentals of bonding, friction, particulate behavior, and cohesion are treated in some detail in order to relate them to soil strength properties. Micromechanical interactions of particles in an assemblage and the relationships between interparticle friction and macroscopic friction angle are examined from discrete particle simulations. Typical values of strength parameters are listed. The concept of yielding is introduced, and the deformation behavior in both the preyield (including small strain stiffness) and post-yield regions is summarized. Time-dependent deformations and aging effects are discussed separately in Chapter 12. The details of strength determination by means of laboratory and in situ tests and the detailed constitutive modeling of soil deformation and strength for use in numerical analyses are outside the scope of this book.
11.2 GENERAL CHARACTERISTICS OF STRENGTH AND DEFORMATION Strength
1. In the absence of chemical cementation between grains, the strength (stress state at failure or the ultimate stress state) of sand and clay is approximated by a linear relationship with stress: ff ⫽ ff tan
(11.4)
or
Shear Stress τ or Stress Ratio τ/σ
) ⫽ (1ff ⫹ 3ff )sin (1ff ⫺ 3ff
(11.5)
where the primes designate effective stresses 1ff and 3ff are the major and minor principal effective stresses at failure, respectively. 2. The basic contributions to soil strength are frictional resistance between soil particles in contact and internal kinematic constraints of soil particles associated with changes in the soil fabric. The magnitude of these contributions depends on the effective stress and the volume change tendencies of the soil. For such materials the stress–strain curve from a shearing test is typically of the form shown in Fig. 11.1a. The maximum or peak strength of a soil (point b) may be greater than the critical state strength, in which the soil deforms under sustained loading at constant volume (point c). For some soils, the particles align along a localized failure plane after large shear strain or shear displacement, and the strength decreases even further to the residual strength (point d). The corresponding three failure envelopes can be defined as shown in Fig. 11.1b, with peak, critical, and residual friction angles (or states) as indicated. 3. Peak failure envelopes are usually curved in the manner shown in Fig. 4.16 and schematically in Fig. 11.1b. This behavior is caused by dilatancy suppression and grain crushing at higher stresses. Curved failure envelopes are also observed for many clays at residual state. When
Secant Peak Strength Envelope
Peak
b
Shear Stress τ c
At Large Strains
Critical state Strength Envelope
Tangent Peak Strength Envelope Peak Strength
φpeak
d
φcritical state
b, c
Critical State b
Residual Strength Envelope
φ residual
c
Residual
d d
a
a Normal effective stress σ
a
Strain
Dense or Overconsolidated
(a)
Loose or Normally Consolidated
(b)
Figure 11.1 Peak, critical, and residual strength and associated friction angle: (a) a typical
stress–strain curve and (b) stress states.
GENERAL CHARACTERISTICS OF STRENGTH AND DEFORMATION
expressed in terms of the shear strength normalized by the effective normal stress as a function of effective normal stress, curves of the type shown in Fig. 11.2 for two clays are obtained.
371
4. The peak strength of cohesionless soils is influenced most by density, effective confining pressures, test type, and sample preparation methods. For dense sand, the secant peak friction angle (point b in Fig. 11.1b) consists in part
Figure 11.2 Variation of residual strength with stress level (after Bishop et al., 1971): (a) Brown London clay and (b) Weald clay.
372
11
STRENGTH AND DEFORMATION BEHAVIOR
resistance depends only on composition and effective stress. The basic concept of the critical state is that under sustained uniform shearing at failure, there exists a unique combination of void ratio e, mean pressure p, and deviator stress q.1 The critical states of reconstituted Weald clay and Toyoura sand are shown in Fig. 11.4. The critical state line on the p –q plane is linear,2 whereas that on an e-ln p (or e-log p) plane tends to be linear for clays and nonlinear for sands. 7. At failure, dense sands and heavily overconsolidated clays have a greater volume after drained shear or a higher effective stress after undrained shear than at the start of deformation. This is due to its dilative tendency upon shearing. At failure, loose sands and normally consolidated to moderately overconsolidated clays (OCR up to about 4) have a smaller volume after drained shear or a lower effective stress after undrained shear than they had initially. This is due to its contractive tendency upon shearing. 8. Under further deformation, platy clay particles begin to align along the failure plane and the shear resistance may further decrease from the critical state condition. The angle of shear resistance at this condition is called the residual friction angle, as illustrated in Fig. 11.1b. The postpeak shearing displacement required to cause a reduction in friction angle from the critical state value to the residual value varies with the soil type, normal stress on the shear plane, and test conditions. For example, for shale mylonite3 in contact with smooth steel or other polished hard surfaces, a shearing displacement of only 1 or 2 mm is sufficient to give residual strength.4 For soil against soil, a slip along the
Void Ratio e Water Content w
of internal rolling and sliding friction between grains and in part of interlocking of particles (Taylor, 1948). The interlocking necessitates either volume expansion (dilatancy) or grain fracture and/or crushing if there is to be deformation. For loose sand, the peak friction angle (point b in Fig. 11.1b) normally coincides with the critical-state friction angle (point c), and there is no peak in the stress–strain curve. 5. The peak strength of saturated clay is influenced most by overconsolidation ratio, drainage conditions, effective confining pressures, original structure, disturbance (which causes a change in effective stress and a loss of cementation), and creep or deformation rate effects. Overconsolidated clays usually have higher peak strength at a given effective stress than normally consolidated clays, as shown in Fig. 11.3. The differences in strength result from both the different stress histories and the different water contents at peak. For comparisons at the same water content but different effective stress, as for points A and A, the Hvorslev strength parameters ce and e are obtained (Hvorslev, 1937, 1960). Further details are given in Section 11.9. 6. During critical state deformation a soil is completely destructured. As illustrated in Fig. 11.1b, the critical state friction angle values are independent of stress history and original structure; for a given set of testing conditions the shearing
Normally Consolidated Virgin Compression
A
A
e ff
Shear Stress τ
Rebound Overconsolidated
τ
σff
In three-dimensional stress space ⫽ ( x, y, z, xy, yz, zx) or the equivalent principal stresses ( 1, 2, 3), the mean effective stress p, and the deviator stress q is defined as 1
σe
p ⫽ (x ⫹ y ⫹ z) / 3 ⫽ (1 ⫹ 2 ⫹ 3) / 3
Peak Strength Envelope
φcrit
2 2 2 兹(x ⫺ y)2 ⫹ (y ⫺ z)2 ⫹ (z ⫺ x)2 ⫹ 6 xy ⫹ 6 yz ⫹ 6 zx
Overconsolidated
A
A
φe
Hvorslev Envelope
ce
Normally Consolidated
0
σff
Normal Effective Stress σ
Figure 11.3 Effect of overconsolidation on effective stress
strength envelope.
q ⫽ (1 / 兹2) ⫽ (1 / 兹2)兹(1 ⫺ 2)2 ⫹ (2 ⫺ 3)2 ⫹ (3 ⫺ 1)2
For triaxial compression condition ( 1 ⬎ 2 ⫽ 3), p ⫽ ( 1 ⫹ 2 2) / 3, q ⫽ 1 ⫺ 2 2 The critical state failure slope on p–q plane is related to friction angle , as described in Section 11.10. 3 A rock that has undergone differential movements at high temperature and pressure in which the mineral grains are crushed against one another. The rock shows a series of lamination planes. 4 D. U. Deere, personal communication (1974).
373
GENERAL CHARACTERISTICS OF STRENGTH AND DEFORMATION
4 Critical State Line
Deviator Stress q (MPa)
Deviator Stress q (kPa)
500 400 300 200
Overconsolidated Normally Consolidated
100 0
0
100
Critical State Line 3
2
1
0
200 300 400 500 600 Mean Pressure p(kPa)
0
(a-1) p versus q
Critical State Line 0.95
Isotropic Normal Compression Line
0.5
0.4 Overconsolidated 0.3
Initial State
0.90
Void ratio e
Void ratio e
0.6
4
(b-1) p versus q
Critical State Line
0.7
1 2 3 Mean Pressure p(MPa)
0.85 0.80 0.75
Normally Consolidated 100
200
300 400 500
Mean Pressure p (kPa) (a-2) e versus lnp (a)
0.02
0.05 0.1 0.5 1 Mean Pressure p(MPa)
5
(b-2) e versus logp (b)
Figure 11.4 Critical states of clay and sand: (a) Critical state of Weald clay obtained by drained triaxial compression tests of normally consolidated () and overconsolidated (●) specimens: (a-1) q–p plane and (a-2) e–ln p plane (after Roscoe et al., 1958). (b) Critical state of Toyoura sand obtained by undrained triaxial compression tests of loose and dense specimens consolidated initially at different effective stresses, (b-1) q–p plane and (b-2) e– log p plane (after Verdugo and Ishihara, 1996).
shear plane of several tens of millimeters may be required, as shown by Fig. 11.5. However, significant softening can be caused by strain localization and development of shear bands, especially for dense samples under low confinement. 9. Strength anisotropy may result from both stress and fabric anisotropy. In the absence of chemical cementation, the differences in the strength
of two samples of the same soil at the same void ratio but with different fabrics are accountable in terms of different effective stresses as discussed in Chapter 8. 10. Undrained strength in triaxial compression may differ significantly from the strength in triaxial extension. However, the influence of type of test (triaxial compression versus extension) on the effective stress parameters c and is relatively
374
11
STRENGTH AND DEFORMATION BEHAVIOR
Figure 11.5 Development of residual strength with increasing shear displacement (after
Bishop et al., 1971).
small. Effective stress friction angles measured in plane strain are typically about 10 percent greater than those determined by triaxial compression. 11. A change in temperature causes either a change in void ratio or a change in effective stress (or a combination of both) in saturated clay, as discussed in Chapter 10. Thus, a change in temperature can cause a strength increase or a strength decrease, depending on the circumstances, as illustrated by Fig. 11.6. For the tests on kaolinite shown in Fig. 11.6, all samples were prepared by isotropic triaxial consolidation at 75F. Then, with no further drainage allowed, temperatures were increased to the values indicated, and the samples were tested in unconfined compression. Substantial reductions in strength accompanied the increases in temperature. Stress–Strain Behavior
1. Stress–strain behavior ranges from very brittle for some quick clays, cemented soils, heavily overconsolidated clays, and dense sands to ductile for insensitive and remolded clays and loose sands, as illustrated by Fig. 11.7. An increase in
Figure 11.6 Effect of temperature on undrained strength of kaolinite in unconfined compression (after Sherif and Burrous, 1969).
375
GENERAL CHARACTERISTICS OF STRENGTH AND DEFORMATION
(a) Typical Strain Ranges in the Field
Stiffness G or E
Retaining Walls Foundations Tunnels
Linear Elastic Nonlinear Elastic Preyield Plastic
Full Plastic
10-4
10-3
10-2
Figure 11.7 Types of stress–strain behavior.
10-1
100
101
Strain % Dynamic Methods Local Gauges
confining pressure causes an increase in the deformation modulus as well as an increase in strength, as shown by Fig. 11.8. 2. Stress–strain relationships are usually nonlinear; soil stiffness (often expressed in terms of tangent or secant modulus) generally decreases with increasing shear strain or stress level up to peak failure stress. Figure 11.9 shows a typical stiffness degradation curve, in terms of shear modulus G and Young’s modulus E, along with typical strain levels developed in geotechnical construction (Mair, 1993) and as associated with different laboratory testing techniques used to measure the stiffness (Atkinson, 2000). For example, Fig. 11.10 shows the stiffness degradation of sands and clay subjected to increase in shear strain. As illustrated in Fig. 11.9, the stiffness degradation curve can be separated into
Figure 11.8 Effect of confining pressure on the consolidated-drained stress–strain behavior of soils.
Conventional Soil Testing (b) Typical Strain Ranges for Laboratory Tests
Figure 11.9 Stiffness degradation curve: stiffness plotted
against logarithm of strains. Also shown are (a) the strain levels observed during construction of typical geotechnical structures (after Mair, 1993) and (b) the strain levels that can be measured by various techniques (after Atkinson, 2000).
four zones: (1) linear elastic zone, (2) nonlinear elastic zone, (3) pre-yield plastic zone, and (4) full plastic zone. 3. In the linear elastic zone, soil particles do not slide relative to each other under a small stress increment, and the stiffness is at its maximum. The soil stiffness depends on contact interactions, particle packing arrangement, and elastic stiffness of the solids. Low strain stiffness values can be determined using elastic wave velocity measurements, resonant column testing, or local strain transducer measurements. The magnitudes of the small strain shear modulus (Gmax) and Young’s modulus (Emax) depend on applied confining pressure and the packing conditions of soil particles. The following empirical equations are often employed to express these dependencies: Gmax ⫽ AG FG(e)pnG
(11.6)
Ei(max) ⫽ AE FE(e)i nE
(11.7)
where FG(e) and FE(e) are functions of void ratio, p is the mean effective confining pressure, i is the effective stress in the i direction, and the other parameters are material constants.
11
STRENGTH AND DEFORMATION BEHAVIOR
Secant Shear Modulus G (MPa)
TC
140 120
Confining Pressure
PSC
78.4 kPa
Toyoura Sand
49 kPa
Ticino Sand
100 80 60 40 20 10-4
10-3
10-2
10-1
100
Secant Shear Modulus G (MPa)
376
Confining Pressures
120
σc = 400 kPa
100
σc = 200 kPa
80 60
σc = 100 kPa
40
σc = 30 kPa
20 10-5
10-4
10-3
10-2
10-1
100
Shear Strain (%)
Shear Strain (%) (a)
(b)
Figure 11.10 Stiffness degradation curve at different confining pressures: (a) Toyoura and
Ticino sands (TC: triaxial compression tests, PSC: plain strain compression tests) (after Tatsuoka et al., 1997) and (b) reconstituted Kaolin clay (after Soga et al., 1996).
plastic soils at low confining pressure conditions to greater than 5 ⫻ 10⫺2 percent at high confining pressure or in soils with high plasticity (Santamarina et al., 2001). 5. Irrecoverable strains develop in the pre-yield plastic zone. The initiation of plastic strains can be determined by examining the onset of permanent volumetric strain in drained conditions or residual excess pore pressures in undrained conditions after unloading. Available experi-
104 103 102
Undisturbed Remolded Remolded with CaCO3 nG = 0.13
nG = 0.65 nG = 0.63
101 100 100
101 102 103 104 Confining pressure, p⬘ (kPa) (a)
Vertical Young's Modulus Evmax/FE(e) (MPa)
Shear Modulus,Gmax MPa
Figure 11.11 shows examples of the fitting of the above equations to experimental data. 4. The stiffness begins to decrease from the linear elastic value as the applied strains or stresses increase, and the deformation moves into the nonlinear elastic zone. However, a complete cycle of loading, unloading, and reloading within this zone shows full recovery of strains. The strain at the onset of the nonlinear elastic zone ranges from less than 5 ⫻ 10⫺4 percent for non-
500
At each vertical effective stress, horizontal effective stress σh⬘ (kPa) was varied between 98 kPa and 196 kPa
450 400
nE = 0.49
350 300 250
100
150 200
250
300
Vertical Effective Stress,σv⬘ (kPa) (b)
Figure 11.11 Small strain stiffness versus confining pressure: (a) Shear modulus Gmax of cemented silty sand measured by resonant column tests (from Stokoe et al. 1995) and (b) vertical Young’s modulus of sands measured by triaxial tests (after Tatsuoka and Kohata, 1995).
GENERAL CHARACTERISTICS OF STRENGTH AND DEFORMATION
mental data suggest that the strain level that initiates plastic strains ranges between 7 ⫻ 10⫺3 and 7 ⫻ 10⫺2 percent, with the lower limit for uncemented normally consolidated sands and the upper limit for high plasticity clays and cemented sands. 6. A distinctive kink in the stress–strain relationship defines yielding, beyond which full plastic strains are generated. A locus of stress states that initiate yielding defines the yield envelope. Typical yield envelopes for sand and natural clay are shown in Fig. 11.12. The yield envelope expands, shrinks, and rotates as plastic strains develop. It is usually considered that expansion is related to plastic volumetric strains; the surface expands when the soil compresses and shrinks when the soil dilates. The two inner envelopes shown in Fig. 11.12b define the boundaries between linear elastic, nonlinear elastic, and pre-yield zones. When the stress state moves in the pre-yield zone, the inner envelopes move with the stress state. This multienvelope concept allows modeling of complex deformations observed for different stress paths (Mroz, 1967; Pre´vost, 1977; Dafalias and Herrman, 1982; Atkinson et al., 1990; Jardine, 1992). 7. Plastic irrecoverable shear deformations of saturated soils are accompanied by volume
changes when drainage is allowed or changes in pore water pressure and effective stress when drainage is prevented. The general nature of this behavior is shown in Figs. 11.13a and 11.13b for drained and undrained conditions, respectively. The volume and pore water pressure changes depend on interactions between fabric and stress state and the ease with which shear deformations can develop without overall changes in volume or transfer of normal stress from the soil structure to the pore water. 8. The stress–strain relation of clays depends largely on overconsolidation ratio, effective confining pressures, and drainage conditions. Figure 11.14 shows triaxial compression behavior of clay specimens that are first normally consolidated and then isotropically unloaded to different overconsolidation ratios before shearing. The specimens are consolidated at the same confining pressure p0, but have different void ratios due to the different stress history (Fig. 11.14a). Drained tests on normally consolidated clays and lightly overconsolidated clays show ductile behavior with volume contraction (Fig. 11.14b). Heavily overconsolidated clays exhibit a stiff response initially until the stress state reaches the yield envelope giving the peak strength and volume dilation. The state of the
Yield State Pre-yield State
Initial Condition q = σ⬘a-σ⬘r MPa Failure Line 0.8
Yield State Stress Path
q = σ⬘a-σ⬘r
Initial State Surrounded by Linear Elastic Boundary
MPa 0.6
Yield Envelope
Yield Envelope
0.6
0.4 Preyield Boundary
0.4 0.2 0.2
Linear Elastic Boundary
MPa 0.0
0.2
0.4
0.6
-0.2 -0.4
0.8
1.0 p = (σa + 2σr)/3
0.0
0.2
MPa 0.4
0.6 p = (σa + 2σr)/3
-0.2 Failure Line
(a)
377
(b)
Figure 11.12 Yield envelopes: (a) Aoi sand (Yasufuku et al., 1991) and (b) Bothkennar clay (from Smith et al., 1992).
378
11
STRENGTH AND DEFORMATION BEHAVIOR
Same Initial Confining Pressure
Same Initial Confining Pressure
Dense Soil
Critical State Dense Soil
Metastable Fabric
Deviator Stress
Deviator Stress
Cavitation
Critical State Loose Soil
Loose Soil
Critical State
Metastable Fabric Axial or Deviator Strain
Axial or Deviator Strain
Dense Soil
Dense Soil +ΔV/V0
-Δu
0
0
Cavitation
Loose soil
Loose Soil +Δu
-ΔV/V0 Metastable Fabric
Metastable Fabric
(a)
(b)
Figure 11.13 Volume and pore pressure changes during shear: (a) drained conditions and (b) undrained conditions.
Initial State Failure at Critical State (D: Drained, U: Undrained)
Void Ratio
Deviator Stress
3 Heavily Overconsolidated Deviator 2 Lightly Stress Overconsolidated
U3 2 Lightly Overconsolidated U2
D Critical State
Virgin Compression Line
3 Heavily Overconsolidated
1 Normally Consolidated U1
1 Normally Consolidated
1 Normally consolidated
U1 Axial or Deviatoric Strain
Axial or Deviatoric Strain 2 Lightly Overconsolidated U2 D U3
+ΔV/V0
3 Heavily Overconsolidated
-Δu
3 Heavily Overconsolidated
3 Heavily Overconsolidated Critical State Line p0
-ΔV/V0
2 Lightly Overconsolidated
2 Lightly Overconsolidated +Δu 1 Normally Consolidated
log p 1 Normally Consolidated (a)
(b)
(c)
Figure 11.14 Stress–strain relationship of normally consolidated, lightly overconsolidated,
and heavily overconsolidated clays: (a) void ratio versus mean effective stress, (b) drained tests, and (c) undrained tests.
FABRIC, STRUCTURE, AND STRENGTH
soil then progressively moves toward the critical state exhibiting softening behavior. Undrained shearing of normally consolidated and lightly overconsolidated clays generates positive excess pore pressures, whereas shear of heavily overconsolidated clays generates negative excess pore pressures (Fig. 11.14c). 9. The magnitudes of pore pressure that are developed in undrained loading depend on initial consolidation stresses, overconsolidation ratio, density, and soil fabric. Figure 11.15 shows the undrained effective stress paths of anisotropically and isotropically consolidated specimens (Ladd and Varallyay, 1965). The difference in undrained shear strength is primarily due to different excess pore pressure development associated with the change in soil fabric. At large strains, the stress paths correspond to the same friction angle. 10. A temperature increase causes a decrease in undrained modulus; that is, a softening of the soil. As an example, initial strain as a function of stress is shown in Fig. 11.16 for Osaka clay
Figure 11.16 Effect of temperature on the stiffness of Osaka clay in undrained triaxial compression (Murayama, 1969).
Failure Line in Triaxial Compression
(MPa) 0.3
tested in undrained triaxial compression at different temperatures. Increase in temperature causes consolidation under drained conditions and softening under undrained conditions.
σr/σa = 0.54
Deviator Stress q = σa + σrσ
0.2
0.1
11.3
0.0
Fabric Changes During Shear of Cohesionless Materials
0.1
0.2
0.3
0.4
(MPa)
Mean Pressure p = (σa + 2σr )/3
-0.1
-0.2 σr/σa = 1.84 -0.3 Initial
Failure Line in Triaxial Extension
At Failure Anisotropically Consolidated σr/σa = 0.54 Isotropically Consolidated Anisotropically Consolidated σr/σa = 1.84
Figure 11.15 Undrained effective stress paths of anisotrop-
ically and isotropically consolidated specimens (after Ladd and Varallyay, 1965).
379
FABRIC, STRUCTURE, AND STRENGTH
The deformation of sands, gravels, and rockfills is influenced by the initial fabric, as discussed and illustrated in Chapter 8. As an illustration, fabric changes associated with the sliding and rolling of grains during triaxial compression were determined using a uniform sand composed of rounded to subrounded grains with sizes in the range of 0.84 to 1.19 mm and a mean axial length ratio of 1.45 (Oda, 1972, 1972a, 1972b, 1972c). Samples were prepared to a void ratio of 0.64 by tamping and by tapping the side of the forming mold. A delayed setting water–resin solution was used as the pore fluid. Samples prepared by each method were tested to successively higher strains. The resin was then allowed to set, and thin sections were prepared. The differences in initial fabrics gave the markedly different stress–strain and volumetric strain curves shown in Fig. 11.17, where the plunging method refers to
380
11
STRENGTH AND DEFORMATION BEHAVIOR
Figure 11.17 Stress–strain and volumetric strain relationships for sand at a void ratio of
0.64 but with different initial fabrics (after Oda, 1972a). (a) Sample saturated with water and (b) sample saturated with water–resin solution.
tamping. There is similarity between these curves and those for Monterey No. 0 sand shown in Fig. 8.23. A statistical analysis of the changes in particle orientation with increase in axial strain showed: 1. For samples prepared by tapping, the initial fabric tended toward some preferred orientation of long axes parallel to the horizontal plane, and the intensity of orientation increased slightly during deformation. 2. For samples prepared by tamping, there was very weak preferred orientation in the vertical direction initially, but this disappeared with deformation. Shear deformations break down particle and aggregate assemblages. Shear planes or zones did not appear until after peak stress had been reached; however, the distribution of normals to the interparticle contact planes E() (a measure of fabric anisotropy) did change with strain, as may be seen in Fig. 11.18. This figure shows different initial distributions for samples prepared by the two methods and a concentration of contact plane normals within 50 of the vertical as deformation progresses. Thus, the fabric tended toward greater anisotropy in each case in terms of contact plane orientations. There was little additional change in E() after the peak stress had been reached, which implies that particle rearrangement was proceeding without significant change in the overall fabric.
As the stress state approaches failure, a direct shearinduced fabric forms that is generally composed of regions of homogeneous fabric separated by discontinuities. No discontinuities develop before peak strength is reached, although there is some particle rotation in the direction of motion. Near-perfect preferred orientation develops during yield after peak strength is reached, but large deformations may be required to reach this state. Compaction Versus Overconsolidation of Sand
Specimens at the same void ratio and stress state before shearing, but having different fabrics, can exhibit different stress–strain behavior. For example, consider a case in which one specimen is overconsolidated, whereas the other is compacted. The two specimens are prepared in such a way that the initial void ratio is the same for a given initial isotropic confining pressure. Coop (1990) performed undrained triaxial compression tests of carbonate sand specimens that were either overconsolidated or compacted, as illustrated in Fig. 11.19a. The undrained stress paths and stress– strain curves for the two specimens are shown in Figs. 11.19b and 11.19c, respectively. The overconsolidated sample was initially stiffer than the compacted specimen. The difference can be attributed to (i) different soil fabrics developed by different stress paths prior to shearing and (ii) different degrees of particle crushing prior to shearing (i.e., some breakage has occurred dur-
FABRIC, STRUCTURE, AND STRENGTH
381
Figure 11.18 Distribution of interparticle contact normals as a function of axial strain for sand samples prepared in two ways (after Oda, 1972a): (a) specimens prepared by tapping and (b) specimens prepared by tamping.
ing the preconsolidation stage for the overconsolidated specimen). Therefore, overconsolidation and compaction produced materials with different mechanical properties. However, at large deformations, both specimens exhibited similar strengths because the initial fabrics were destroyed. Effect of Clay Structure on Deformations
The high sensitivity of quick clays illustrates the principle that flocculated, open microfabrics are more rigid but more unstable than deflocculated fabrics. Similar behavior may be observed in compacted fine-grained soils, and the results of a series of tests on structuresensitive kaolinite are illustrative of the differences (Mitchell and McConnell, 1965). Compaction conditions and stress–strain curves for samples of kaolinite compacted using kneading and static methods are shown in Fig. 11.20. The high shear strain associated with kneading compaction wet of optimum breaks down flocculated structures, and this accounts for the
much lower peak strength for the sample prepared by kneading compaction. The recoverable deformation of compacted kaolinite with flocculent structure ranges between 60 and 90 percent, whereas the recovery of samples with dispersed structures is only of the order of 15 to 30 percent of the total deformation, as may be seen in Fig. 11.21. This illustrates the much greater ability of the braced-box type of fabric that remains after static compaction to withstand stress without permanent deformation than is possible with the broken-down fabric associated with kneading compaction. Different macrofabric features can affect the deformation behavior as illustrated in Fig. 11.22 for the undrained triaxial compression testing of Bothkennar clay, Scotland (Paul et al., 1992; Clayton et al., 1992). Samples with mottled facies, in which the bedding features had been disrupted and mixed by burrowing mollusks and worms (bioturbation), gave the stiffest response, whereas samples with distinct laminated features showed the softest response.
382
11
STRENGTH AND DEFORMATION BEHAVIOR 1.0 Overconsolidated 0.8
Normal Compression Line
q (MPa)
2
0.6 0.4 Compacted 0.2
Overconsolidated Sample
0
Void 1.5 Ratio
0
0.2 0.4 p (MPa)
0.6
(b) q (MPa)
Compacted Sample
1.0
1
Compacted 0.75 0.5
0.1 1 Mean Pressure p
Overconsolidated
(MPa) 0.25
(a) 0
0
4
8 12 16 Axial strain ε a (%)
20
(c)
Figure 11.19 Undrained response of compacted specimen and overconsolidated specimen
of carbonate sand: (a) stress path before shearing, (b) undrained stress paths during shearing, and (c) stress–strain relationships (after Coop, 1990).
If slip planes develop at failure, platy and elongated particles align with their long axes in the direction of slip. By then, the basal planes of the platy clay particles are enclosed between two highly oriented bands of particles on opposite sides of the shear plane. The dominant mechanism of deformation in the displacement shear zone is basal plane slip, and the overall thickness of the shear zone is on the order of 50 m. Fabrics associated with shear planes and zones have been studied using thin sections and the polarizing microscope and by using the electron microscope (Morgenstern and Tchalenko, 1967a, b and c; Tchalenko, 1968; McKyes and Yong, 1971). The residual strength associated with these fabrics is treated in more detail in Section 11.11. Structure, Effective Stresses, and Strength
The effective stress strength parameters such as c and are isotropic properties, with anisotropy in undrained strength explainable in terms of excess pore pressures developed during shear. The undrained strength loss associated with remolding undisturbed
clay can also be accounted for in terms of differences in effective stress, provided part of the undisturbed strength does not result from cementation. Remolding breaks down the structure and causes a transfer of effective stress to the pore water. An example of this is shown in Fig. 11.23, which shows the results of incremental loading triaxial compression tests on two samples of undisturbed and remolded San Francisco Bay mud. In these tests, the undisturbed sample was first brought to equilibrium under an isotropic consolidation pressure of 80 kPa. After undrained loading to failure, the triaxial cell was disassembled, and the sample was remolded in place. The apparatus was reassembled, and pore pressure was measured. Thus, the effective stress at the start of compression of the remolded clay at the same water content as the original undisturbed clay was known. Stress–strain and pore pressure–strain curves for two samples are shown in Figs. 11.23a and 11.23b, and stress paths for test 1 are shown in Fig. 11.23c. Differences in strength that result from fabric differences caused by thixotropic hardening or by different compaction methods can be explained in the same
383
FRICTION BETWEEN SOLID SURFACES
Figure 11.21 Ratio of recoverable to total strain for samples of kaolinite with different structure.
Stress-Strain Relationships
Stress Paths 0.6
0.4
Facies Mottled Bedded Laminated
0.2
0.0
Figure 11.20 Stress–strain behavior of kaolinite compacted
by two methods.
(σa – σr)/2 σao
(σa – σr)/2 σao
0.6
0.4
0.0 0
2
4
Facies Mottled Bedded Laminated
0.2
0.4
0.6
0.8
1.0
(σa + σr)/2σao
Axial Strain (%)
Figure 11.22 Effect of macrofabric on undrained response
way. Thus, in the absence of chemical or mineralogical changes, different strengths in two samples of the same soil at the same void ratio can be accounted for in terms of different effective stress.
11.4
FRICTION BETWEEN SOLID SURFACES
The friction angle used in equations such as (11.1), (11.2), (11.4), and (11.5) contains resistance contributions from several sources, including sliding of grains in contact, resistance to volume change (dilatancy), grain rearrangement, and grain crushing. The
of Bothkennar clay in Scotland (after Hight and Leroueil, 2003).
true friction coefficient is shown in Fig. 11.24 and is represented by ⫽
T ⫽ tan N
(11.8)
where N is the normal load on the shear surface, T is the shear force, and , the intergrain sliding friction angle, is a compositional property that is determined by the type of soil minerals.
384
11
STRENGTH AND DEFORMATION BEHAVIOR
Figure 11.23 (a) and (b) Effect of remolding on undrained strength and pore water pressure in San Francisco Bay mud. (c) Stress paths for triaxial compression tests on undisturbed and remolded samples of San Francisco Bay mud.
Basic ‘‘Laws’’ of Friction
Two laws of friction are recognized, beginning with Leonardo da Vinci in about 1500. They were restated by Amontons in 1699 and are frequently referred to as Amontons’ laws. They are: 1. The frictional force is directly proportional to the normal force, as illustrated by Eq. (11.8) and Fig. 11.24. 2. The frictional resistance between two bodies is independent of the size of the bodies. In Fig.
11.24, the value of T is the same for a given value of N regardless of the size of the sliding block. Although these principles of frictional resistance have long been known, suitable explanations came much later. It was at one time thought that interlocking between irregular surfaces could account for the behavior. On this basis, would be given by the tangent of the average inclination of surface irregularities on the sliding plane. This cannot be the case, however, because such an explanation would require that de-
FRICTION BETWEEN SOLID SURFACES
385
Figure 11.23 (Continued )
contacting surfaces. He observed that the actual area of contact is very small because of surface irregularities, and thus the cohesive forces must be large. The foundation for the present understanding of the mobilization of friction between surfaces in contact was laid by Terzaghi (1920). He hypothesized that the normal load N acting between two bodies in contact causes yielding at asperities, which are local ‘‘hills’’ on the surface, where the actual interbody solid contact develops. The actual contact area Ac is given by Ac ⫽ where y is the shearing strength assumed to have force that can be
N y
(11.9)
yield strength of the material. The of the material in the yielded zone is a value m. The maximum shearing resisted by the contact is then T ⫽ Acm
Figure 11.24 Coefficient of friction for surfaces in contact.
(11.10)
The coefficient of friction is given by T/N, crease as surfaces become smoother and be zero for perfectly smooth surfaces. In fact, the coefficient of friction can be constant over a range of surface roughness. Hardy (1936) suggested instead that static friction originates from cohesive forces between
⫽
T Acm m ⫽ ⫽ N Acy y
(11.11)
This concept of frictional resistance was subsequently further developed by Bowden and Tabor (1950,
386
11
STRENGTH AND DEFORMATION BEHAVIOR
1964). The Terzaghi–Bowden and Tabor hypothesis, commonly referred to as the adhesion theory of friction, is the basis for most modern studies of friction. Two characteristics of surfaces play key roles in the adhesion theory of friction: roughness and surface adsorption. Surface Roughness
The surfaces of most solids are rough on a molecular scale, with successions of asperities and depressions ranging from 10 nm to over 100 nm in height. The slopes of the nanoscale asperities are rather flat, with individual angles ranging from about 120 to 175 as shown in Fig. 11.25. The average slope of asperities on metal surfaces is an included angle of 150; on rough quartz it may be over 175 (Bromwell, 1966). When two surfaces are brought together, contact is established at the asperities, and the actual contact area is only a small fraction of the total surface area. Quartz surfaces polished to mirror smoothness may consist of peaks and valleys with an average height of about 500 nm. The asperities on rougher quartz surfaces may be about 10 times higher (Lambe and Whitman, 1969). Even these surfaces are probably smoother than most soil particles composed of bulky minerals. The actual surface texture of sand particles depends on geologic history as well as mineralogy, as shown in Fig. 2.12. The cleavage faces of mica flakes are among the smoothest naturally occurring mineral surfaces. Even in mica, however, there is some waviness due to rotation of tetrahedra in the silica layer, and surfaces usually contain steps ranging in height from 1 to 100 nm, reflecting different numbers of unit layers across the particle. Thus, large areas of solid contact between grains are not probable in soils. Solid-to-solid contact is through asperities, and the corresponding interparticle contact stresses are high. The molecular structure and composition in the contacting asperities determine the magnitude of m in Eq. (11.11).
Figure 11.25 Contact between two smooth surfaces.
Surface Adsorption
Because of unsatisfied force fields at the surfaces of solids, the surface structure may differ from that in the interior, and material may be adsorbed from adjacent phases. Even ‘‘clean’’ surfaces, prepared by fracture of a solid or by evacuation at high temperature, are rapidly contaminated when reexposed to normal atmospheric conditions. According to the kinetic theory of gases, the time for adsorption of a monolayer tm is given by
tm ⫽
1 SZ
(11.12)
where is the area occupied per molecule, S is the fraction of molecules striking the surface that stick to it, and Z is the number of molecules per second striking a square centimeter of surface. For a value of S equal to 1, which is reasonable for a high-energy surface, the relationship between tm and gas pressure is shown in Fig. 11.26. The conclusion to be drawn from this figure is that adsorbed layers are present on the surface of soil particles in the terrestrial environment,
Figure 11.26 Monolayer formation time as a function of atmospheric pressure.
FRICTION BETWEEN SOLID SURFACES
and contacts through asperities involve adsorbed material, unless it is extruded under the high pressure.5 Adhesion Theory of Friction
The basis for the adhesion theory of friction is in Eq. (11.10), that is, the tangential force that causes sliding depends on the solid contact area and the shear strength of the contact. Plastic and/or elastic deformations determine the contact area at asperities. Plastic Junctions If asperities yield and undergo plastic deformation, then the contact area is proportional to the normal load on the asperity as shown by Eq. (11.9). Because surfaces are not clean, but are covered by adsorbed films, actual solid contact may develop only over a fraction of the contact area as shown in Fig. 11.27. If the contaminant film strength is c, the strength of the contact will be T ⫽ Ac[m ⫹ (1 ⫺ )c]
(11.13)
Equation (11.13) cannot be applied in practice because and c are unknown. However, it does provide a possible explanation for why measured values of friction angle for bulky minerals such as quartz and feldspar are greater than values for the clay minerals and other platy minerals such as mica, even though the surface structure is similar for all the silicate minerals. The small particle size of clays means that the load per particle, for a given effective stress, will be small relative to that in silts and sands composed of the bulky minerals. The surfaces of platy silt and sand size particles are smoother than those of bulky mineral parti-
cles. The asperities, caused by surface waviness, are more regular but not as high as those for the bulky minerals. Thus, it can be postulated that for a given number of contacts per particle, the load per asperity decreases with decreasing particle size and, for particles of the same size, is less for platy minerals than for bulky minerals. Because should increase as the normal load per asperity increases, and it is reasonable to assume that the adsorbed film strength is less than the strength of the solid material (c ⬍ m), it follows that the true friction angle () is less for small and platy particles than for large and bulky particles. In the event that two platy particles are in face-to-face contact and the surface waviness is insufficient to cause direct solid-tosolid contact, shear will be through the adsorbed films, and the effective value of will be zero, again giving a lower value of . In reality, the behavior of plastic junctions is more complex. Under combined compression and shear stresses, deformation follows the von Mises–Henky criterion, which, for two dimensions, is 2 ⫹ 3 2 ⫽ y2
sorbed surface films.
5
Conditions may be different on the Moon, where ultrahigh vacuum exists. This vacuum produces cleaner surfaces. In the absence of suitable adsorbate, clean surfaces can reduce their surface energy by cohering with like surfaces. This could account for the higher cohesion of lunar soils than terrestrial soils of comparable gradation.
(11.14)
For asperities loaded initially to ⫽ y, the application of a shear stress requires that become less than y. The only way that this can happen is for the contact area to increase. Continued increase in leads to continued increase in contact area. This phenomenon is called junction growth and is responsible for cold welding in some materials (Bowden and Tabor, 1964). If the shear strength of the junction equals that of the bulk solid, then gross seizure occurs. For the case where the ratio of junction strength to bulk material strength is less than 0.9, the amount of junction growth is small. This is the probable situation in soils. Elastic Junctions The contact area between particles of a perfectly elastic material is not defined in terms of plastic yield. For two smooth spheres in contact, application of the Hertz theory leads to d ⫽ (NR)1 / 3
Figure 11.27 Plastic junction between asperities with ad-
387
(11.15)
where d is the diameter of a plane circular area of contact; is a function of geometry, Poisson’s ratio, and Young’s modulus6; and R is the sphere radius. The contact area is
6
For a sphere in contact with a plane surface ⫽ 12(1 ⫺ 2) / E.
388
11
STRENGTH AND DEFORMATION BEHAVIOR
Ac ⫽
(NR)2 / 3 4
(11.16)
If the shear strength of the contact is i, then T ⫽ i Ac
(11.17)
and ⫽
T ⫽ i (R)2 / 3 N⫺1 / 3 N 4
(11.18)
According to these relationships, the friction coefficient for two elastic asperities in contact should decrease with increasing load. Nonetheless, the adhesion theory would still apply to the strength of the junction, with the frictional force proportional to the area of real contact. If it is assumed that the number of contacting asperities in a soil mass is independent of particle size and effective stress, then the influences of particle size and effective stress on the frictional resistance of a soil with asperities deforming elastically may be analyzed. For uniform spheres arranged in a regular packing, the gross area covered by one sphere along a potential plane of sliding is 4R 2. The normal load per contacting asperity, assuming one asperity per contact, is N ⫽ 4R2
(11.19)
Using Eq. (11.16), the area per contact becomes Ac ⫽
(4R3)2 / 3 4
(11.20)
and the total contact area per unit gross area is (Ac)T ⫽
冉 冊
1 2 R (4)2 / 3 ⫽ (4)2 / 3 4R2 4 16
(11.21)
The total shearing resistance of is equal to the contact area times i, so ⫽
(4)2 / 3 i ⫽ iK()⫺1 / 3 16
(11.22)
where K ⫽ (4)2 / 3 /16. On this basis, the coefficient of friction should decrease with increasing , but it should be independent of sphere radius (particle size). Data have been obtained that both support and contradict these predictions. A 50-fold variation in the normal load on assemblages of quartz particles in contact with a quartz block was found to have no effect on
frictional resistance (Rowe, 1962). The residual friction angles of quartz, feldspar, and calcite are independent of normal stress as shown in Fig. 11.28. On the other hand, a decreasing friction angle with increasing normal load up to some limiting value of normal stress is evident for mica and the clay minerals in Fig. 11.28 and has been found also for several clays and clay shales (Bishop et al., 1971), for diamond (Bowden and Tabor, 1964), and for solid lubricants such as graphite and molybdenum disulfide (Campbell, 1969). Additional data for clay minerals show that frictional resistance varies as ()⫺1 / 3 as predicted by Eq. (11.22) up to a normal stress of the order of 200 kPa (30 psi), that is, the friction angle decreases with increasing normal stress (Chattopadhyay, 1972). There are at least two possible explanations of the normal stress independence of the frictional resistance of quartz, feldspar, and calcite: 1. As the load per particle increases, the number of asperities in contact increases proportionally, and the deformation of each asperity remains essentially constant. In this case, the assumption of one asperity per contact for the development of Eq. (11.22) is not valid. Some theoretical considerations of multiple asperities in contact are available (Johnson, 1985). They show that the area of contact is approximately proportional to the applied load and hence the coefficient of friction is constant with load. 2. As the load per asperity increases, the value of in Eq. (11.13) increases, reflecting a greater proportion of solid contact relative to adsorbed film contact. Thus, the average strength per contact increases more than proportionally with the load, while the contact area increases less than proportionally, with the net result being an essentially constant frictional resistance. Quartz is a hard, brittle material that can exhibit both elastic and plastic deformation. A normal pressure of 11 GPa (1,500,000 psi) is required to produce plastic deformation, and brittle failure usually occurs before plastic deformation. Plastic deformations are evidently restricted to small, highly confined asperities, and elastic deformations control at least part of the behavior (Bromwell, 1965). Either of the previous two explanations might be applicable, depending on details of surface texture on a microscale and characteristics of the adsorbed films. With the exception of some data for quartz, there appears to be little information concerning possible variations of the true friction angle with particle size. Rowe (1962) found that the value of for assemblages of quartz particles on a flat quartz surface de-
FRICTIONAL BEHAVIOR OF MINERALS
389
Figure 11.28 Variation in friction angle with normal stress for different minerals (after
Kenney, 1967).
creased from 31 for coarse silt to 22 for coarse sand. This is an apparent contradiction to the independence of particle size on frictional resistance predicted by Eq. (11.22). On the other hand, the assumption of one asperity per contact may not have been valid for all particle sizes, and additionally, particle surface textures on a microscale could have been size dependent. Furthermore, there could have been different amounts of particle rearrangement and rolling in the tests on the different size fractions. Sliding Friction
The frictional resistance, once sliding has been initiated, may be equal to or less than the resistance that had to be overcome to initiate movement; that is, the coefficient of sliding friction can be less than the coefficient of static friction. A higher value of static friction than sliding friction is explainable by timedependent bond formations at asperity junctions. Stick–slip motion, wherein varies more or less erratically as two surfaces in contact are displaced, appears common to all friction measurements of minerals involving single contacts (Procter and Barton, 1974). Stick–slip is not observed during shear of assemblages of large numbers of particles because the slip of individual contacts is masked by the behavior of the mass as a whole. However, it may be an important mechanism of energy dissipation for cyclic loading at very small strains when particles are not moving relative to each other.
11.5
FRICTIONAL BEHAVIOR OF MINERALS
Evaluation of the true coefficient of friction and friction angle is difficult because it is very difficult to
do tests on two very small particles that are sliding relative to each other, and test results for particle assemblages are influenced by particle rearrangements, volume changes, surface preparation factors, and the like. Some values are available, however, and they are presented and discussed in this section. Nonclay Minerals
Values of the true friction angle for several minerals are listed in Table 11.1, along with the type of test and conditions used for their determination. A pronounced antilubricating effect of water is evident for polished surfaces of the bulky minerals quartz, feldspar, and calcite. This apparently results from a disruptive effect of water on adsorbed films that may have acted as a lubricant for dry surfaces. Evidence for this is shown in Fig. 11.29, where it may be seen that the presence of water had no effect on the frictional resistance of quartz surfaces that had been chemically cleaned prior to the measurement of the friction coefficient. The samples tested by Horn and Deere (1962) in Table 11.1 had not been chemically cleaned. An apparent antilubrication effect by water might also arise from attack of the silica surface (quartz and feldspar) or carbonate surface (calcite) and the formation of silica and carbonate cement at interparticle contacts. Many sand deposits exhibit ‘‘aging’’ effects wherein their strength and stiffness increase noticeably within periods of weeks to months after deposition, disturbance, or densification, as described, for example, by Mitchell and Solymar (1984), Mitchell (1986), Mesri et al. (1990), and Schmertmann (1991). Increases in penetration resistance of up to 100 percent have been measured in some cases. The relative importance of chemical factors, such as precipitation at
390
11
Table 11.1 Mineral Quartz
STRENGTH AND DEFORMATION BEHAVIOR
Values of Friction Angle () Between Mineral Surfaces Type of Test Block over particle set in mortar
Conditions
(deg)
Dry
6
Moist Water saturated Water saturated
24.5 24.5 21.7
Dry Water saturated Water saturated
7.4 24.2 22–31
Quartz
Three fixed particles over block
Quartz
Block on block
Quartz Quartz
Particles on polished block Block on block
Quartz
Particle–particle
Saturated
26
Feldspar
Particle–plane Particle–plane Block on block
Saturated Dry Dry Water saturated Water saturated
Feldspar Feldspar
Free particles on flat surface Particle–plane
Calcite
Block on block
Muscovite
Along cleavage faces
Phlogopite
Biotite
Chlorite
Along cleavage faces
Along cleavage faces
Along cleavage faces
Comments
Reference
Dried over CaCl2 before testing
Tschebotarioff and Welch (1948)
Normal load per particle increasing from 1 to 100 g Polished surfaces
Hafiz (1950)
Horn and Deere (1962)
decreasing with increasing particle size Depends on roughness and cleanliness Single-point contact
Rowe (1962)
22.2 17.4 6.8 37.6 37
Polished surfaces
Horn and Deere (1962)
25–500 sieve
Lee (1966)
Saturated
28.9
Single-point contact
Dry Water saturated Dry
8.0 34.2 23.3
Polished surfaces
Procter and Barton (1974) Horn and Deere (1962)
Oven dry
Horn and Deere (1962)
Dry Saturated Dry
16.7 13.0 17.2
Air equilibrated
Dry Saturated Dry
14.0 8.5 17.2
Air equilibrated
Dry Saturated Dry
14.6 7.4 27.9
Air equilibrated
Dry Saturated
19.3 12.4
Air equilibrated
Variable
interparticle contacts, changes in surface characteristics, and mechanical factors, such as time-dependent stress redistribution and particle reorientations, in causing the observed behavior is not known. Further details of aging effects are given in Chapter 12.
0–45
Oven dry
Oven dry
Oven dry
Bromwell (1966) Procter and Barton (1974)
Horn and Deere (1962)
Horn and Deere (1962)
Horn and Deere (1962)
As surface roughness increases, the apparent antilubricating effect of water decreases. This is shown in Fig. 11.29 for quartz surfaces that had not been cleaned. Chemically cleaned quartz surfaces, which give the same value of friction when both dry and wet,
FRICTIONAL BEHAVIOR OF MINERALS
391
Figure 11.29 Friction of quartz (data from Bromwell, 1966 and Dickey, 1966).
show a loss in frictional resistance with increasing surface roughness. Evidently, increased roughness makes it easier for asperities to break through surface films, resulting in an increase in [Eq. (11.13) and Fig. 11.27]. The decrease in friction with increased roughness is not readily explainable. One possibility is that the cleaning process was not effective on the rough surfaces. For soils in nature, the surfaces of bulky mineral particles are most probably rough relative to the scale in Fig. 11.29, and they will not be chemically clean. Thus, values of ⫽ 0.5 and ⫽ 26 are reasonable for quartz, both wet and dry. On the other hand, water apparently acts as a lubricant in sheet minerals, as shown by the values for muscovite, phlogopite, biotite, and chlorite in Table 11.1. This is because in air the adsorbed film is thin, and surface ions are not fully hydrated. Thus, the adsorbed layer is not easily disrupted. Observations have shown that the surfaces of the sheet minerals are scratched when tested in air (Horn and Deere, 1962). When the surfaces of the layer silicates are wetted, the mobility of the surface films is increased because of their increased thickness and because of greater surface ion hydration and dissociation. Thus, the values of listed in Table 11.1 for the sheet minerals under saturated conditions (7 –13) are probably appropriate for sheet mineral particles in soils.
Clay Minerals
Few, if any, directly measured values of for the clay minerals are available. However, because their surface structures are similar to those of the layer silicates discussed previously, approximately the same values would be anticipated, and the ranges of residual friction angles measured for highly plastic clays and clay minerals support this. In very active colloidal pure clays, such as montmorillonite, even lower friction angles have been measured. Residual values as low as 4 for sodium montmorillonite are indicated by the data in Fig. 11.28. The effective stress failure envelopes for calcium and sodium montmorillonite are different, as shown by Fig. 11.30, and the friction angles are stress dependent. For each material the effective stress failure envelope was the same in drained and undrained triaxial compression and unaffected by electrolyte concentration over the range investigated, which was 0.001 N to 0.1 N. The water content at any effective stress was independent of electrolyte concentration for calcium montmorillonite, but varied in the manner shown in Fig. 11.31 for sodium montmorillonite. This consolidation behavior is consistent with that described in Chapter 10. Interlayer expansion in calcium montmorillonite is restricted to a c-axis spacing of 1.9 nm, leading to formation of domains or layer aggregates of several unit layers. The interlayer spac-
392
11
STRENGTH AND DEFORMATION BEHAVIOR
Figure 11.30 Effective stress failure diagrams for calcium and sodium montmorillonite (af-
ter Mesri and Olson, 1970).
Figure 11.31 Shear and consolidation behavior of sodium
montmorillonite (after Mesri and Olson, 1970).
ing of sodium montmorillonite is sensitive to doublelayer repulsions, which, in turn, depend on the electrolyte concentration. The influence of the electrolyte concentration on the behavior of sodium montmorillonite is to change the water content, but not the strength, at any effective consolidation pressure. This suggests that the strength generating mechanism is independent of the system chemistry. The platelets of sodium montmorillonite act as thin films held apart by high repulsive forces that carry the effective stress. For this case, if it is assumed that there is essentially no intergranular contact, then Eq. (7.29) becomes i ⫽ ⫹ A ⫺ u0 ⫺ R ⫽ 0
(11.23)
Since ⫺ u0 is the conventionally defined effective stress , and assuming negligible long-range attractions, Eq. (11.23) becomes ⫽ R
(11.24)
This accounts for the increase in consolidation pressure required to decrease the water content, while at
the same time there is little increase in shear strength because the shearing strength of water and solutions is essentially independent of hydrostatic pressure. The small friction angle that is observed for sodium montmorillonite at low effective stresses can be ascribed mainly to the few interparticle contacts that resist particle rearrangement. Resistance from this source evidently approaches a constant value at the higher effective stresses, as evidenced by the nearly horizontal failure envelope at values of average effective stress greater than about 50 psi (350 kPa), as shown in Fig. 11.30. The viscous resistance of the pore fluid may contribute a small proportion of the strength at all effective stresses. An hypothesis of friction between fine-grained particles in the absence of interparticle contacts is given by Santamarina et al. (2001) using the concept of ‘‘electrical’’ surface roughness as shown in Fig. 11.32. Consider two clay surfaces with interparticle fluid as shown in Fig. 11.32b. The clay surfaces have a number of discrete charges, so a series of potential energy wells exists along the clay surfaces. Two cases can be considered: 1. When the particle separation is less than several nanometers, there are multiple wells of minimum energy between nearby surfaces and a force is required to overcome the energy barrier between the wells when the particles move relative to each other. Shearing involves interaction of the molecules of the interparticle fluid. Due to the multiple energy wells, the interparticle fluid molecules go through successive solidlike pinned states. This stick–slip motion contributes to frictional resistance and energy dissipation. 2. When the particle separation is more than several nanometers, the two clay surfaces interact only by the hydrodynamic viscous effects of the interparticle fluid, and the frictional force may be estimated using fluid dynamics.
PHYSICAL INTERACTIONS AMONG PARTICLES
393
disorder of particles, (i.e., local spatial fluctuations of coordination number, and positions of neighboring particles) produce packing constraints and disorder. This leads to inhomogeneous but structured force distributions within the granular system. Deformation is associated with buckling of these force chains, and energy is dissipated by sliding at the clusters of particles between the force chains. Discrete particle numerical simulations, such as the discrete (distinct) element method (Cundall and Strack, 1979) and the contact dynamics method (Moreau, 1994), offer physical insights into particle interactions and load transfers that are difficult to deduce from physical experiments. Typical inputs for the simulations are particle packing conditions and interparticle contact characteristics such as the interparticle friction angle . Complete details of these numerical methods are beyond the scope of this book; additional information can be found in Oda and Iwashita (1999). However, some of the main findings are useful for developing an improved understanding of how stresses are carried through discrete particle systems such as soils and how these distributions influence the deformation and strength properties.
Figure 11.32 Concept of ‘‘electrical’’ surface roughness ac-
cording to Santamarina et al., (2001): (a) electrical roughness and (b) conceptual picture of friction in fine-grained particles.
The aggregation of clay plates in calcium montmorillonite produces particle groups that behave more like equidimensional particles than platy particles. There is more physical interference and more intergrain contact than in sodium montmorillonite since the water content range for the strength data shown in Fig. 11.30 was only about 50 to 97 percent, whereas it was about 125 to 450 percent for the sodium montmorillonite. At a consolidation pressure of about 500 kPa, the slope of the failure envelope for calcium montmorillonite was about 10, which is in the middle of the range for nonclay sheet minerals (Table 11.1).
11.6 PHYSICAL INTERACTIONS AMONG PARTICLES
Continuum mechanics assumes that applied forces are transmitted uniformly through a homogenized granular system. In reality, however, the interparticle force distributions are strongly inhomogeneous, as discussed in Chapter 7, and the applied load is transferred through a network of interparticle force chains. The generic
Strong Force Networks and Weak Clusters
Examples of the computed normal contact force distribution in a granular system are shown in Figs. 11.33a for an isotropically loaded condition and 11.33b for a biaxial loaded condition (Thornton and Barnes, 1986). The thickness of the lines in the figure is proportional to the magnitude of the contact force. The external loads are transmitted through a network of interparticle contact forces represented by thicker lines. This is called the strong force network and is the key microscopic feature of load transfer through the granular system. The scale of statistical homogeneity in a two-dimensional particle assembly is found to be a few tens of particle diameters (Radjai et al., 1996). Forces averaged over this distance could therefore be expected to give a stress that is representative of the macroscopic stress state. The particles not forming a part of the strong force network are floating like a fluid with small loads at the interparticle contacts. This can be called the weak cluster, which has a width of 3 to 10 particle diameters. Both normal and tangential forces exist at interparticle contacts. Figure 11.34 shows the probability distributions (PN and PT) of normal contact forces N and tangential contact forces T for a given biaxial loading condition. The horizontal axis is the forces normalized by their mean force value (⬍N⬎ or ⬍T⬎), which depend on particle size distribution (Radjai et al., 1996). The individual normal contact forces can be as great
394
11
STRENGTH AND DEFORMATION BEHAVIOR
tric compression of a dense granular assembly (Thornton, 2000). The strong force network carries most of the whole deviator load as shown in Fig. 11.36 and is the load-bearing part of the structure. For particles in the strong force networks, the tangential contact forces are much smaller than the interparticle frictional resistance because of the large normal contact forces. In contrast, the numerical analysis results show that the tangential contact forces in the weak clusters are close to the interparticle frictional resistance. Hence, the frictional resistance is almost fully mobilized between particles in the weak clusters, and the particles are perhaps behaving like a viscous fluid. Buckling, Sliding, and Rolling
Figure 11.33 Normal force distributions of a twodimensional disk particle assembly: (a) isotropic stress condition and (b) biaxial stress condition with maximum load in the vertical direction (after Thornton and Barnes, 1986).
as six times the mean normal contact force, but approximately 60 percent of contacts carry normal contact forces below the mean (i.e., weak cluster particles). When normal contact forces are larger than their mean, the distribution law of forces can be approximated by an exponentially decreasing function; Radjai et al. (1996) show that PN ( ⫽ N/ ⬍N⬎) ⫽ ke1.4(1⫺ ) fits the computed data well for both two-and three-dimensional simulations. The exponent was found to change very slightly with the coefficient of interparticle friction and to be independent of particle size distributions. Simulations show that applied deviator load is transferred exclusively by the normal contact forces in the strong force networks, and the contribution by the weak clusters is negligible. This is illustrated in Fig. 11.35, which shows that the normal contact forces contribute greater than the tangential contact forces to the development of the deviator stress during axisymme-
As particles begin to move relative to each other during shear, particles in the strong force network do not slide, but columns of particles buckle (Cundall and Strack, 1979). Particles in the strong force network collapse upon buckling, and new force chains are formed. Hence, the spatial distributions of the strong force network are neither static nor persistent features. At a given time of biaxial compression loading, particle sliding is occurring at almost 10 percent of the contacts (Kuhn, 1999) and approximately 96 percent of the sliding particles are in the weak clusters (Radjai et al., 1996). Over 90 percent of the energy dissipation occurs at just a small percentage of the contacts (Kuhn, 1999). This small number of sliding particles is associated with the ability of particles to roll rather than to slide. Particle rotations reduce contact sliding and dissipation rate in the granular system. If all particles could roll upon one another, a granular assembly would deform without energy dissipation.7 However, this is not possible owing to restrictions on particle rotations. It is impossible for all particles to move by rotation, and sliding at some contacts is inevitable due to the random position of particles (Radjai and Roux, 1995).8 Some frictional energy dissipation can therefore be considered a consequence of disorder of particle positions. As deformation progresses, the number of particles in the strong force network decreases, with fewer particles sharing the increased loads (Kuhn, 1999). Figure
7 This assumes that the particles are rigid and rolling with a singlepoint contact. In reality, particles deform and exhibit rolling resistance. Iwashita and Oda (1998) state that the incorporation of rolling resistance is necessary in discrete particle simulations to generate realistic localized shear bands. 8 For instance, consider a chain loop of an odd number of particles. Particle rotation will involve at least one sliding contact.
PHYSICAL INTERACTIONS AMONG PARTICLES
395
Figure 11.34 Probability distributions of interparticle contact forces: (a) normal forces and
(b) tangential forces. The distributions were obtained for contact dynamic simulations of 500, 1024, 1200 and 4025 particles. The effect of number of particles in the simulation on probability distribution appears to be small (after Radjai et al., 1996).
forces to the evolution of the deviator stress during axisymmetric compression of a dense granular assembly (after Thornton, 2000).
Figure 11.36 Contributions of strong and weak contact forces to the evolution of the deviator stress during axisymmetric compression of a dense granular assembly (after Thornton, 2000).
11.37 shows the spatial distribution of residual deformation, in which the computed deformation of each particle is subtracted from the average overall deformation (Williams and Rege, 1997). A group of interlocked particles that instantaneously moves as a rigid body in a circular manner can be observed. The outer
boundary of the group shows large residual deformation, whereas the center shows very small residual deformation. The rotating group of interlocked particles, which can be considered as a weak cluster, becomes more apparent as applied strains increase toward failure. The bands of large residual deformation [termed
Figure 11.35 Contributions of normal and tangential contact
396
11
STRENGTH AND DEFORMATION BEHAVIOR
Stress Ratio q/p
A B C
Triaxial Compression
Contact Plane Normals in Initial State: 1.5 More in Vertical Direction 1.0 Same in All Directions More in Horizontal Direction
0.5
-8
-6
-4
-2
2 -0.5
4
6 8 10 Axial Strain (%)
-1.0
Triaxial Extension
(a) Fabric Anisotropy A
A B C
Contact Plane Normals in Initial State: 0.4 More in Vertical Direction 0.3 Same in All Directions 0.2 More in Horizontal Direction
0.1
-8
Figure 11.37 Spatial distribution of residual deformation observed in an elliptic particle assembly at an axial strain level of (a) 1.1%, (b) 3.3%, (c) 5.5%, (d) 7.7%, (e) 9.8%, and (ƒ ) 12.0% (after Williams and Rege, 1997).
microbands by Kuhn (1999)] are where particle translations and rotations are intense as part of the strong force network. Kuhn (1999) reports that their thicknesses are 1.5D50 to 2.5D50 in the early stages of shearing and increase to between 1.5D50 and 4D50 as deformation proceeds. This microband slip zone may eventually become a localized shear band. Fabric Anisotropy
The ability of a granular assemblage of particles to carry deviatoric loads is attributed to its capability to develop anisotropy in contact orientations. An initial isotropic packing of particles develops an anisotropic contact network during compression loading. This is because new contacts form in the direction of compression loading and contacts that orient along the direction perpendicular to loading direction are lost. The initial state of contact anisotropy (or fabric) plays an important role in the subsequent deformation as illustrated in Fig. 11.18. Figure 11.38 shows results
-6
-4
-2
2 -0.1 -0.2 -0.3 -0.4 -0.5
4
6 8 10 Axial Strain (%)
(b)
Figure 11.38 Discrete element simulations of drained triaxial compression and extension tests of particle assemblies prepared at different initial contact fabrics: (a) stress–strain relationships and (b) evolution of fabric anisotropy parameter A (after Yimsiri, 2001).
of discrete particle simulations of particle assemblies prepared at different states of initial contact anisotropy under an isotropic stress condition (Yimsiri, 2001). The initial void ratios are similar (e0 ⬇ 0.75 to 0.76) and both drained triaxial compression and extension tests were simulated. Although all specimens are initially isotropically loaded, the directional distributions of contact forces are different due to different orientations of contact plane normals (sample A: more in the vertical direction; sample B: similar in all directions; sample C: more in the horizontal direction). As shown in Fig. 11.38a, both samples A and C showed stiffer response when the compression loading was applied in the preferred direction of contact forces, but softer response when the loading was perpendicular to the preferred direction of contact forces. The response of sample B, which had an isotropic fabric, was in between the two. Dilation was most intensive when the contact forces were oriented preferentially in the di-
PHYSICAL INTERACTIONS AMONG PARTICLES
rection of applied compression; and experimental data presented by Konishi et al. (1982) shows a similar trend. Figure 11.38b shows the development of fabric anisotropy with increasing strain. The degree of fabric anisotropy is expressed by a fabric anisotropy parameter A; the value of A increases with more vertically oriented contact plane normals and is negative when there are more horizontally oriented contact plane normals.9 The fabric parameter gradually changes with increasing strains and reaches a steady-state value as the specimens fail. The final steady-state value is independent of the initial fabric, indicating that the inherent anisotropy is destroyed by the shearing process. The final fabric anisotropy after triaxial extension is larger than that after triaxial compression because the additional confinement by a larger intermediate stress in the extension tests created a higher degree of fabric anisotropy. Close examination of the contact force distribution for the strong force network and weak clusters gives interesting microscopic features. Figure 11.39 shows the values of A determined for the subgroups of contact
Fabric Anisotropy Parameter A
0.1
397
forces categorized by their magnitudes when the specimen is under a biaxial compression loading condition (Radjai, 1999). The direction of contact anisotropy of the weak clusters (N/ ⬍N⬎ less than 1) is orthogonal to the direction of compression loading, whereas that of the strong force network (N/⬍ N⬎ more than 2) is parallel. Figure 11.40 shows an example of fabric evolution with strains in biaxial loading (Thornton and Antony, 1998). The fabric anisotropy is separated into that in the strong force networks (N/⬍ N⬎ of more than 1) and that in the weak clusters (N/ ⬍N⬎ less than 1). Again the directional evolution of the fabric in the weak clusters is opposite to the direction of loading. Therefore, the stability of the strong force chains aligned in the vertical loading direction is obtained by the lateral forces in the surrounding weak clusters. Changes in Number of Contacts and Microscopic Voids
At the beginning of biaxial loading of a dense granular assembly, more contacts are created from the increase in the hydrostatic stress, and the local voids become smaller. As the axial stress increases, however, the local voids tend to elongate in the direction of loading as shown in Fig. 11.41. Consequently particle contacts are lost. As loading progresses, vertically elongated local voids become more apparent, leading to dilation in
0.05
0.0 1
2
3
4
5
6 N/
-0.05
-0.1
Figure 11.39 Fabric anisotropy parameter A for different levels of contact force when the specimen is under biaxial compression loading conditions (after Radjai et al., 1996).
9 The density of contact plane normals E( ) with direction is fitted with the following expression (Radjai, 1999):
E( ) ⫽
c {1 ⫹ A cos 2( ⫺ c)}
where c is the total number of contacts, c is the direction for which the maximum E is reached, and the magnitude of A indicates the amplitude of anisotropy. When the directional distribution of contact forces is independent of , the system has an isotropic fabric and A ⫽ 0.
Figure 11.40 Evolution of the fabric anisotropy parameters of strong forces and weak clusters when the specimen is under biaxial compression loading conditions (after Thornton and Antony, 1998).
398
11
STRENGTH AND DEFORMATION BEHAVIOR
Figure 11.41 Simulated spatial distribution of local microvoids under biaxial loading (after Iwashita and Oda, 2000): (a) 11 ⫽ 1.1% (before failure), (b) 11 ⫽ 2.2% (at failure), (c) 11 ⫽ 4.4% (after failure), and (d ) 11 ⫽ 5.5% (after failure).
terms of overall sample volume (Iwashita and Oda, 2000). Void reduction is partly associated with particle breakage. Thus, there is a need to incorporate grain crushing in discrete particle simulations to model the contractive behavior of soils (Cheng et al., 2003). Normal contact forces in the strong force network are quite high, and, therefore, particle asperities, and even particles themselves, are likely to break, causing the force chains to collapse. Local voids tend to change size even after the applied stress reaches the failure stress state (Kuhn, 1999). This suggests that the degrees of shearing required for the stresses and void ratio to reach the critical state are different. Numerical simulations by Thornton (2000) show that at least 50 percent axial
strain is required to reach the critical state void ratio. Practical implication of this is discussed further in Section 11.7. Macroscopic Friction Angle Versus Interparticle Friction Angle
Discrete particle simulations show that an increase in the interparticle friction angle results in an increase in shear modulus and shear strength, in higher rates of dilation, and in greater fabric anisotropy. Figure 11.42 shows the effect of assumed interparticle friction angle on the mobilized macroscopic friction angle of the particle assembly (Thornton, 2000; Yimsiri, 2001). The macroscopic friction angle is larger than the interparticle friction angle if the interparticle friction angle is smaller than 20. As the interparticle friction becomes
PHYSICAL INTERACTIONS AMONG PARTICLES
399
50
Macroscopic Friction Angle (degrees)
40
30
20
Drained (Thornton, 2000) Drained Triaxial Compression (Yimsiri, 2001) Undrained Triaxial Compression (Yimsiri, 2001)
10
Drained Triaxial Extension (Yimsiri, 2001) Undrained Triaxial Extension (Yimsiri, 2001) Experiment (Skinner, 1969)
0 0
10
20
30
40
50
60
70
80
90
Interparticle Friction Angle (degrees) Figure 11.42 Relationships between interparticle friction angle and macroscopic friction
angle from discrete element simulations. The macroscopic friction angle was determined from simulations of drained and undrained triaxial compression (TC) and extension (TE) tests. The experimental data by Skinner (1969) is also presented (after Thornton, 2000, and Yimsiri, 2001).
more than 20, the contribution of increasing interparticle friction to the macroscopic friction angle becomes relatively small; the macroscopic friction angle ranges between 30 and 40, when the interparticle friction angle increases from 30 to 90.10 The nonproportional relationship between macroscopic friction angle of the particle assembly and interparticle friction angle results because deviatoric load is carried by the strong force networks of normal forces and not by tangential forces, whose magnitude is governed by interparticle friction angle. Increase in interparticle friction results in a decrease in the percentage of sliding contacts (Thornton, 2000). The interparticle friction therefore acts as a kinematic constraint of the strong force network and not as the direct source of macroscopic resistance to shear. If the interparticle friction were zero, strong force chains could not develop, and the particle assembly will be-
Reference to Table 11.1 shows that actually measured values of for geomaterials are all less than 45. Thus, numerical simulations done assuming larger values of appear to give unrealistic results.
have like a fluid. Increased friction at the contacts increases the stability of the system and reduces the number of contacts required to achieve a stable condition. As long as the strong force network can be formed, however, the magnitude of the interparticle friction becomes of secondary importance. The above findings from discrete particle simulations are partially supported by the experimental data given by Skinner (1969), which are also shown in Fig. 11.42. He performed shear box tests on spherical particles with different coefficients of interparticle friction angle. The tested materials included glass ballotini, steel ball bearings, and lead shot. Use of glass ballotini was particularly attractive since the coefficient of interparticle friction increases by a factor of between 3.5 and 30 merely by flooding the dry sample. Skinner’s data shown in Fig. 11.42 indicate that the macroscopic friction angle is nearly independent of interparticle friction angle. Effects of Particle Shape and Angularity
10
A lower porosity and a larger coordination number are achieved for ellipsoidal particles compared to spherical
400
11
STRENGTH AND DEFORMATION BEHAVIOR
particles (Lin and Ng, 1997). Hence, a denser packing can be achieved for ellipsoidal particles. Ellipsoid particles rotate less than spherical particles. An assembly of ellipsoid particles gives larger values of shear strength and initial modulus than an assemblage of spherical particles, primarily because of the larger coordination number for ellipsoidal particles. Similar findings result for two-dimensional particle assemblies. Circular disks give the highest dilation for a given stress ratio and the lowest coordination number compared to elliptical or diamond shapes (Williams and Rege, 1997). An assembly of rounded particles exhibits greater softening behavior with fabric anisotropy change with strain, whereas an assembly of elongated particles requires more shearing to modify its initial fabric anisotropy to the critical state condition (Nouguier-Lehon et al., 2003).
Deviator Stress
σa
Clays
The basic concept of the critical state is that, under sustained uniform shearing, there exists a unique relationships among void ratio ecs (or specific volume vcs ⫽ 1 ⫹ ecs), mean effective pressure pcs, and deviator stress qcs as shown in Fig. 11.43. An example of the critical state of clay was shown in Fig. 11.4a. The critical state of clay can be expressed as qcs ⫽ Mpcs
(11.25)
vcs ⫽ 1 ⫹ ecs ⫽ % ⫺ cs ln pcs
(11.26)
where qcs is the deviator stress at failure, pcs is the mean effective stress at failure, and M is the critical
M (triaxial compression)
σr
σr
Mean Pressure p Critical State Line
M (triaxial extension)
(a) Specific Volume v
Compression Lines of Constant Stress Ratio q/p
Γ
11.7 CRITICAL STATE: A USEFUL REFERENCE CONDITION
After large shear-induced volume change, a soil under a given effective confining stress will arrive ultimately at a unique final water content or void ratio that is independent of its initial state. At this stage, the interlocking achieved by densification or overconsolidation is gone in the case of dense soils, the metastable structure of loose soils has collapsed, and the soil is fully destructured. A well-defined strength value is reached at this state, and this is often referred to as the critical state strength. Under undrained conditions, the critical state is reached when the pore pressure and the effective stress remain constant during continued deformation. The critical state can be considered a fundamental state, and it can be used as a reference state to explain the effect of overconsolidation ratios, relative density, and different stress paths on strength properties of soils (Schofield and Wroth, 1968).
Critical State Line
q = σa – σr
λ λ cs
Isotropic Compression Line
Critical State Line ln p
1
(b) Figure 11.43 Critical state concept: (a) p–q plane and (b) v–ln p plane.
state stress ratio. The critical state on the void ratio (or specific volume)–mean pressure plane is defined by two material parameters: cs, the critical state compression index and %, the specific volume intercept at unit pressure (p ⫽ 1). The compression lines under constant stress ratios are often parallel to each other, as shown in Fig. 11.43b. Parameter M in Equation (11.25) defines the critical state stress ratio at failure and is similar to for the Mohr–Coulomb failure line. However, Equation (11.25) includes the effect of intermediate principal stress 2 because p ⫽ 1 ⫹ 2 ⫹ 3, whereas the Mohr–Coulomb failure criterion of Eq. (11.4) or (11.5) does not take the intermediate effective stress into account. In triaxial conditions, a ⬎ r ⫽ r and r ⫽ r ⬎ a for compression and extension, respectively (see Fig. 11.43).11 Hence, Eqs. (11.4) and (11.25) can be related to each other for these two cases as follows:
11
a is the axial effective stress and r is the radial effective stress.
CRITICAL STATE: A USEFUL REFERENCE CONDITION
M⫽
6 sin crit for triaxial compression 3 ⫺ sin crit
(11.27)
M⫽
6 sin crit for triaxial extension 3 ⫹ sin crit
(11.28)
These equations indicate that the correlation between M and crit is not unique but depends on the stress conditions. Neither is a fundamental property of the soil, as discussed further in Section 11.12. Nonetheless, both are widely used in engineering practice, and, if interpreted properly, they can provide useful and simple phenomenological representations of complex behavior. The drained and undrained critical state strengths are illustrated in Figs. 11.44a and 11.44b for normally consolidated clay and heavily overconsolidated clay, respectively. The initial mean pressure–void ratio state of the normally consolidated clay is above the critical state line, whereas that of the heavily overconsolidated clay is below the critical state line. When the initial state of the soil is normally consolidated at A (Fig. 11.44a), the critical state is B for undrained loading
Critical State Line
Deviator Stress q
M
and C for drained triaxial compression. Hence, the deviator stress at critical state is smaller for the undrained case than for the drained case. On the other hand, when the initial state of the soil is overconsolidated from D (Fig. 11.44b), the critical state becomes E for undrained loading and F for drained triaxial compression. The deviator stress at critical state is smaller for the drained case compared to the undrained case. It is important to note that the soil state needs to satisfy both state equations [Eqs. (11.25) and (11.26)] to be at critical state. For example, point G in Fig. 11.44b satisfies pcs and qcs, but not ecs; therefore, it is not at the critical state. Converting the void ratio in Eq. (11.26) to water content, a normalized critical state line can be written using the liquidity index (see Fig. 11.45). LIcs ⫽
wcs ⫺ wPL ln(pPL /p) ⫽ wLL ⫺ wPL ln(pPL /pLL)
Deviator Stress q
Critical State Line M
Drained Peak Strength Undrained Strength
C
E
Drained Strength
F
G 3
B
3
1 A
D
1 Mean pressure p
Specific Volume v
D
Mean pressure p
Specific Volume v
Γ
Γ B
A
F Isotropic Compression Line
C
G D
D
ln p (a)
Isotropic Compression Line λ
λ cs
Critical State Line 1
E
λ
λ cs
(11.29)
where wcs is the water content at critical state when the effective mean pressure is p. pLL and pPL are the
Drained Strength
Undrained Strength
401
Critical State Line 1
ln p (b)
Figure 11.44 Drained and undrained stress–strain response using the critical state concept:
(a) normally consolidated clay and (b) overconsolidated clay.
402
11
STRENGTH AND DEFORMATION BEHAVIOR
Water Content
Critical State Line
Liquidity Index
Isotropic Compression Line
Liquid Limit wLL
Critical State Line
LI = 1 (ln(p), w)
(ln(p’), LI)
LI
w
LIeq-1
wcs
LICS
Plastic Limit wPL
LI = 0
ln(pLL)
ln(p) ln(pPL)
ln(pLL)
Mean pressure
(a)
ln(p) ln(pPL) Mean Pressure (b)
Figure 11.45 Normalization of the critical state line: (a) water content versus mean pressure and (b) liquidity index versus mean pressure.
mean effective pressure at liquid limit (wLL) and plastic limit (wPL), respectively; pLL ⬇ 1.5 to 6 kPa and pPL ⬇ 150 to 600 kPa are expected considering the undrained shear strengths at liquid and plastic limits are in the ranges suLL ⫽ 1 to 3 kPa and suPL ⫽ 100 to 300 kPa, respectively12 (see Fig. 8.48). Using Eq. (11.29), a relative state in relation to the critical state for a given effective mean pressure (i.e., above or below the critical state line) can be defined as (see Fig. 11.45) LIeq ⫽ LI ⫺ LIcs ⫹ 1 ⫽ LI ⫹
log(p /pLL) log(pPL /pLL )
(11.30)
where LIeq is the equivalent liquidity index defined by Schofield (1980). When LIeq ⫽ 1 (i.e., LI ⫽ LIcs) and q/p ⫽ M, the clay has reached the critical state. Figure 11.46 gives the stress ratio when plastic failure (or fracture) initiates at a given water content. When LIeq ⬎ 1 (the state is above the critical state line), and the soil in a plastic state exhibits uniform contractive behavior. When LIeq ⬍ 1 (the state is below the critical state line), and the soil in a plastic state exhibits localized dilatant rupture, or possibly fracture, if the stress ratio reaches the tensile limit (q/p ⫽ 3 for triaxial compression and ⫺1.5 for triaxial extension; see Fig. 11.46b). Hence, the critical state line can be used as a reference to characterize possible soil behavior under plastic deformation.
Sands
The critical state strength and relative density of sand can be expressed as qcs ⫽ Mpcs DR,cs ⫽
emax ⫺ ecs 1 ⫽ emax ⫺ emin ln(c /p)
A review by Sharma and Bora (2003) gives average values of suLL ⫽ 1.7 kPa and suPL ⫽ 170 kPa.
(11.32)
where ecs is the void ratio at critical state, emax and emin are the maximum and minimum void ratios, and c is the crushing strength of the particles.13 The critical state line based on Eq. (11.32) is plotted in Fig. 11.47. The plotted critical state lines are nonlinear in the e– ln p plane in contrast to the linear relationship found for clays. This nonlinearity is confirmed by experimental data as shown in Fig. 11.4b. At high confining pressure, when the effective mean pressure becomes larger than the crushing strength, many particles begin to break and the lines become more or less linear in the e–ln p plane, similar to the
13
Equation (11.32) is derived from Eq. 11.36 proposed by Bolton (1986) with IR ⫽ 0 (zero dilation). Bolton’s equation is discussed further in Section 11.8. Other mathematical expressions to fit the experimentally determined critical state line are possible. For example, Li et al. (1999) propose the following equation for the critical state line (ecs versus p): ecs ⫽ e0 ⫺ s
12
(11.31)
冉冊 p pa
where e0 is the void ratio at p ⫽ 0, pa is atmospheric pressure, and s and are material constants.
CRITICAL STATE: A USEFUL REFERENCE CONDITION
Fracture
Ductile Plastic and Contractive
Dilatant Rupture
q
Tensile Fracture
q/p
403
Triaxial Compression
3 MTC
3
Triaxial Compression
MTC
MTE
1
0.5 Triaxial Extension
1.0
LIeq
p 2
-1.5
MTE
3
Fracture
Dilatant Rupture (a)
Tensile Fracture
Ductile Plastic and Contractive
Triaxial Extension
(b)
Figure 11.46 Plastic state of clay in relation to normalized liquidity index: (a) stress ratio
when plastic state initiates for a given LIeq and (b) definition of stress ratios used in (a) (after Schofield, 1980).
DR,cs =
emax – ecs 1 emax – emin = In (σc/p)
0.2
0.2 Relative Density Dr
emax 0
Relative Density Dr
e max 0
0.4 0.6 0.8
e min 1 1.2 0.001
0.4 0.6 0.8
emin 1 1.2 p/σc
0.2 0.3 p/σc
(a)
(b)
0.01
0.1
1
0
0.1
0.4
0.5
Figure 11.47 Critical state line derived from Eq. (11.32): (a) e–log p plane and (b) e–p
plane.
behavior of clays. Coop and Lee (1993) found that there is a unique relationship between the amount of particle breakage that occurred on shearing to a critical state and the value of the mean normal effective stress. This implies that sand at the critical state would reach a stable grading at which the particle contact stresses
would not be sufficient to cause further breakage. Coop et al. (2004) performed ring shear tests (see Section 11.11) on a carbonate sand to find a shear strain required to reach the true critical state (i.e., constant particle grading). They found that particle breakage continues to very large strains, far beyond those
404
11
STRENGTH AND DEFORMATION BEHAVIOR
reached in triaxial tests. Figure 11.48a shows the volumetric strains measured for a selection of their tests, which were carried out at vertical stress levels in the range of 650 to 860 kPa. A constant volumetric strain is reached at a shear strain of around 2000 percent. For specimens at lower stress levels, more shear strains (20,000 percent or more) were required. Similar findings were made for quartz sand (Luzzani and Coop, 2002). Figure 11.48b shows the degree of particle breakage with shear strains in the logarithmic scale. The amount of breakage is quantified by Hardin’s (1985) relative breakage parameter Br defined in Fig. 10.14. At very large strains, the value of Br finally stabilizes. The strain required for stabilization depends on applied stress level. Interestingly, less shear strain was needed for the mobilized friction angle to reach the steady-state value (Fig. 11.48c) than for attainment of the constant volume condition, (Fig. 11.48a). The critical state friction angle was unaffected by the particle breakage. In summary, the critical state concept is very useful to characterize the strength and deformation properties of soils when it is used as a reference state. That is, a soil has a tendency to contract upon shearing when its state is above the critical state line, whereas it has a tendency to dilate when it is below the critical state line. Various normalized state parameters have been proposed to characterize the difference between the actual state and the critical state line, as illustrated in Fig. 11.49. These parameters have been used to characterize the stiffness and strength properties of soils. Some of them are introduced later in this chapter.
11.8
STRENGTH PARAMETERS FOR SANDS
Many factors and phenomena act together to determined the shearing resistance of sands, for example, mineralogy, grain size, grain shape, grain size distribution, (relative) density, stress state, type of tests and stress path, drainage, and the like [see Eq. (11.3)]. In this section, the ways in which these factors have become understood and have been quantified over the last several decades are summarized. Several correlations are given to provide an overview and reference for typical values and ranges of strength parameters for sands and the influences of various factors on these parameters.14
14
A number of additional useful correlations are given by Kulhawy and Mayne (1990).
Early Studies
The important role of volume change during shear, especially dilatancy, was recognized by Taylor (1948). From direct shear box testing of dense sand specimens, he calculated the work at peak shear stress state and showed that the energy input is dissipated by the friction using the following equation: peak dx ⫺ n dy ⫽ n dx
(11.33)
where peak is the applied shear stress at peak, n is the confining normal (effective) stress on the shear plane, dx is the incremental horizontal displacement at peak, dy is the incremental vertical displacement (expansion positive) at peak stress, and is the friction coefficient. The energy dissipated by friction (the component in the right-hand side) is equal to the sum of the work done by shearing (first component in the left-hand side) and that needed to increase the volume (the second component in the left-hand side). The latter component is referred to as dilatancy. Rearranging Eq. (11.33),
冉冊
peak dy ⫽ tan m ⫽ ⫹ dx
(11.34)
Thus, the peak shear stress ratio or the peak mobilized friction angle m consists of both interlocking (dy/dx) and sliding friction between grains (). This equation that relates stress to dilation is called the stress– dilatancy rule, and it is an important relationship for characterizing the plastic deformation of soils, as further discussed in Section 11.20. Rowe (1962) recognized that the mobilized friction angle m must take into account particle rearrangements as well as the sliding resistance at contacts and dilation. Particle crushing, which increases in importance as confining pressure increases and void ratio decreases, should also be added to these components. The general interrelationships among the strength contributing factors and porosity can be represented as shown in Fig. 11.50. In this figure, f is the friction angle corrected for the work of dilation. It is influenced by particle packing arrangements and the number of sliding contacts. The denser the packing, the more important is dilation. As the void ratio increases, the mobilized friction angle decreases. The critical state is defined as the condition when there is no volume change by shearing [i.e., (dy/dx) ⫽ 0 in Eq. (11.34)]. The corresponding mobilized friction angle m is crit . The ‘‘true friction’’ in the figure is associated with the resistance to interparticle sliding.
STRENGTH PARAMETERS FOR SANDS
Shear Strain (%) 50,000 100,000
Volumetric strain (%)
0
150,000
RS3
0
RS5 RS7 RS8 20
(a)
RS13 RS15
40 Luzzani & Coop, 805 kPa 650-930 kPa
1.0
248-386 kPa 60-97 kPa
Relative Breakage
0.8 RS7
0.6
RS8
(b)
0.4 0.2
?
0.0
800 kPa unsheared
10
100
1000
10,000
100,000 1,000,000
Shear Strain
Mobilized Friction Angle (degrees)
50 40
RS3
30
RS7 20
RS8
(c)
RS9 10
RS10 RS15
0 1
10
100
1000
10,000
100,000
Shear Strain (%)
Figure 11.48 Ring shear test results of carbonate sand: (a) volumetric strain versus shear
strain, (b) the degree of particle breakage with shear strains, and (c) mobilized friction angle versus shear strains (after Coop et al., 2004).
405
406
11
STRENGTH AND DEFORMATION BEHAVIOR
1. State parameter (Been and Jefferies, 1985)
Void ratio e
Ψ = e – ec
Critical state line (pc , e c)
Loose Sand
ecD
Loose sand Ψ = eL – ecL (>0)
( pL, eL )
2. State index (Ishihara et al., 1998)
Ψ<0 Ψ>0 Dense sand
ecL
Dense sand Ψ = eD – ecD (<0)
Is = (e 0 – ec )/(e0 – e) Loose sand Is = (e0 – ecL)/(e0 – eL) (>1) Dense sand Is = (e 0 – e cD)/(e0 – e0) (<1)
( pD, e D)
3. State pressure index (Wang et al., 2002) Ip = p/pc
pcL
pcD
Log (Mean pressure p)
Loose sand Ip = pL/pcL (>1) Dense sand Ip = pD/pcD (<1)
Figure 11.49 Various parameters that relate the current state to the critical state.
1990; Yasufuku et al., 1991). This is demonstrated in the ring shear test results shown in Figs. 11.48b and 11.48c; with increasing shear strains, the critical state strength is reached well before particle crushing ceases.
46 φm
42 38
Peak Friction Angle
Dilation Interlocking
φcrit
φ 34
φf Rearrangement, Fabric Development Crushing (estimated)
30 26 Densest Packing
Critical Void Ratio
True Friction To Zero
26
30
The peak friction angle can be considered as the sum of interparticle friction, rearrangement, crushing, and the dilation contribution. For plane strain conditions, Bolton (1986) proposed the following empirical equation that relates the mobilized friction angle at a given stress state to the critical state friction angle crit and dilation angle : ⫽ crit ⫹ 0.8
34
38
(11.35)
42
Porosity n (%)
Figure 11.50 Contributions to shear strength of granular
soils (modified from Rowe, 1962).
Critical State Friction Angle
The specific value of the critical state angle of internal friction crit depends on the uniformity of particle sizes, their shape, and mineralogy and is developed at large shear strains irrespective of initial conditions. Typical values are 40 for well-graded, angular quartz or feldspar sands, 36 for uniform subangular quartz sand, and 32 for uniform rounded quartz sand. Particle crushing appears to have little effect on crit (Coop,
where dilation angle is the ratio of volumetric strain increment dv to the axial strain da at the stress state of interest. This is similar to Taylor’s equation (Eq. (11.34)). However, in Eq. (11.34) changes with shear, whereas crit is a constant material property. The relative density Dr is a convenient index to characterize the interlocking characteristics packing structure. The effects of relative density, grain size, and gradation on the peak friction angle of cohesionless soils are illustrated by Fig. 11.51. Similar information in terms of void ratio, unit weight, and Unified Soil Classification is given in Fig. 11.52. The peak values of friction angle for quartz sands range from about 30 to more than 50, depending on gradation, relative density, and confining pressure.
407
Secant Friction Angle at Peak Failure (degree)
STRENGTH PARAMETERS FOR SANDS
Figure 11.51 Dependence of the friction angle of cohesion-
less soils on relative density and gradation (after Schmertmann, 1978).
50
Uniformly Graded Cambria Sand Initial Relative Density = 89.5%
45 Triaxial Extension 40 35 Triaxial Compression 30
20 0.1
Contraction at Peak Failure
Dilation at Peak Failure
25
0.2
0.5 1 2 5 10 20 50 Effective Mean Pressure at Peak Failure (kPa)
100
Figure 11.53 Effect of confining pressure on peak friction angle (after Yamamuro and Lade, 1996).
To take effective confining pressure into account, Bolton (1986) proposed the normalized dilatancy index IR, defined as
冉冊
IR ⫽ Dr(Q ⫺ ln p) ⫺ R ⫽ Dr ln
Figure 11.52 Dependence of friction angle of cohesionless soils on unit weight and relative density (after NAVFAC, 1982).
Although the values of interparticle friction angle and the critical state friction angle crit are essentially constant for a given mineral, the magnitudes of the dilation angle in Eq. (11.35) vary with effective confining pressure; that is, Figs. 11.51 and 11.52 apply for a particular value of confining pressure. In general, the contribution of dilation increases with increasing density and decreases with increasing confining pressure. The effect of confining pressure on peak friction angle is shown in Fig. 11.53 (Yamamuro and Lade, 1996). Up to confining pressures of 5 to 10 MPa, the peak friction angle decreases with increasing confining pressure due to suppressed dilation and particle crushing. At pressures greater than about 10 MPa, the friction angle remains approximately constant, but the values in triaxial extension are smaller than those in triaxial compression.
c ⫺R p
(11.36)
where Dr is the relative density, and p is the mean effective confining pressure. The empirical parameter Q is related to the crushing strength of the soil particles; that is, Q ⫽ ln c, where c is the crushing strength (same dimensions as p). The Q values (using kPa) are 10 for quartz and feldspar, 8 for limestones, 7 for anthracite, and 5.5 for chalk. Bolton (1986) found that R ⫽ 1 fits the available data well. The critical state is achieved when IR ⫽ 0, and this is given as Eq. (11.32). Index IR increases as the soil density increases. The parameter characterizes the state of the soil in relation to the critical state, similarly to the ones illustrated in Fig.11.49. Using IR (between 0 and 4), Bolton (1986) deduced the following correlations for the peak friction angle and critical state friction angle (in degrees) from the plots shown in Fig. 11.54. m ⫺ crit ⫽ 3IR
for triaxial compression conditions (11.37)
m ⫺ crit ⫽ 5IR
for plane strain conditions (11.38)
The dilatancy contribution to sand strength, represented by the difference between the peak triaxial compression friction angle and the critical state friction
408
11
STRENGTH AND DEFORMATION BEHAVIOR
20
φmax – φcrit (degrees)
Plane Strain Tests Triaxial Compression Tests 16
Eq.(11.38)
Data for p ≈ 300 kPa Eq.(11.37)
12
8
4
0 0.0
0.2
0.4
0.6
0.8
1.0
Relative Density Dr
Figure 11.54 Difference between peak friction angle and critical state friction angle for triaxial compression and plain strain compression data on sands (after Bolton, 1986).
angle crit, as determined by Bolton (1986), is shown in Fig. 11.55. The values shown are appropriate for quartz sands (Q ⫽ 10). Other forms to characterize the peak friction angle in relation to the initial state of a sand are available. For example, Been and Jefferies (1986) relate the peak friction angle to the state parameter defined in Fig. 11.49, as shown in Fig. 11.56.
As shown in Fig. 11.54 and by Eqs. (11.37) and (11.38), the critical state and peak friction angles vary depending on test conditions. The difference is related to the magnitude of the intermediate principal stress in relation to the major and minor principal stresses. Further details are given in Section 11.12. Undrained Strengths
In most cases, the deformation of sands occurs under drained conditions. However, the undrained behavior of sands is important when flow slides or earthquakes are of concern. These events are very rapid, and rapid deformation of loose to medium dense cohesionless soils can generate excess pore water pressures resulting in loss of strength or liquefaction. The stress-strain relationship in undrained triaxial tests of Toyoura sand at different densities are shown in Fig. 11.57a, and the corresponding effective stress paths are shown in Fig. 11.57b (Yoshimine et al., 1998). A sudden flow failure can occur in loose sand deposits by the drop in strength with increase in shear strain. Typical undrained responses of sand specimens at different densities are illustrated in Fig. 11.58a. Loose sand exhibits peak strength and then softens. The peak state on the p –q plane is termed the collapse surface (Sladen et al., 1985),15 and the slope increases with increase in initial density and decrease in confining pressure, as illustrated in Fig. 11.58b. In triaxial compression, the slope for many sandy soils ranges from 0.62 to 0.90 with an upper bound of 1.0 (Olson and Stark, 2003). Once the soil softens, large shear deformation is generated by moderate shear stresses. The softened soil eventually leads to the steady state, in which there is no further contraction tendency. The pore pressures and stresses remain constant as the soil continues to shear in a steady state of deformation (Castro, 1975; Poulos, 1981). The steady state occurs when the soil continuously deforms at constant volume, constant stress, and constant velocity.16 It develops under stress-controlled conditions because of the flowing nature of softened soil. When the soil is very loose, the effective stress becomes zero, indicating a static liquefaction condition, which is the transformation of a granular material from a solid to a liquefied state (Youd et al., 2001).
15
Figure 11.55 Dilatancy component as a function of mean
effective stress at critical state and relative density (modified from Bolton, 1986).
Similar concepts are proposed by others. For example, the critical stress ratio (Vaid and Chern, 1985), the instability line (Lade, 1992), and the yield strength ratio (Olson and Stark, 2003). 16 The basic concept of the steady state is essentially the same as the critical state defined for clay by Schofield and Wroth (1969).
STRENGTH PARAMETERS FOR SANDS
409
Figure 11.56 Peak friction angle versus state parameter (after Been and Jefferies, 1986).
Even dense sands exhibit positive excess pore pressures at the beginning of deformation up to small strain. However, after a certain stress ratio is reached, the undrained stress path reverses its direction indicating contractive to dilative behavior as shown in Fig. 11.58c, and the stress reversal is called the state of phase transformation (Ishihara et al., 1975). The stress–strain response thereafter is strain hardening and does not exhibit any peak. The soil eventually reaches the ultimate steady state or the critical state as long as the pore water does not cavitate. Medium dense specimens initially soften after the stress state passes the collapse line as illustrated in Fig. 11.58c. The stress state then reaches a point of minimum strength, which is called the quasi-steady state (Alarcon-Guzman et al., 1988) or flow with limited liquefaction (Ishihara, 1993). At this stage, the soil is in the state of phase transformation, and the mobilized strength then increases gradually with further shear strain due to increase in effective stress by negative pore water pressure development. As shearing continues, the soil shows a strain-hardening behavior, climbing along the critical state line, and the stress state finally reaches the critical or ultimate steady state at very large strains. Reported data indicate that the slope of the critical state on the p –q plane is approximately the same as that of the phase transformation line (Been et al., 1991; Ishihara, 1993; Zhang and Garga, 1997; Vaid and Sivathayalan, 2000); at least, these lines are difficult to distinguish from each other.
For loose sand, the steady state is the minimum undrained shear strength associated with a rapid collapsing of soil structure. As discussed in Section 11.7, it has been suggested that the stress state of the steady state is a function of void ratio, so a unique critical state line exists on the e–log p plane as shown in Fig. 11.4b (Castro, 1975; Poulos et al., 1985, and others). The shape depends on grain angularity and fines content (Zlatovic and Ishihara, 1995). At a given initial void ratio, the steady state strength can be determined from the critical state line. For a relatively small confining pressure, a small change in void ratio can give dramatic difference in undrained shear strength because the critical state line on e–log p plane is very flat at this stress level. For medium dense sand, the quasi-steady state can be considered as the minimum undrained shear strength. As the soil continues to deform, the shearing resistance increases. Although the stress ratios at quasi-steady state, and critical state are similar on the p –q plane, the quasi-steady state on e–log p plane lies below the critical state line as shown in Fig. 11.59. For a given initial void ratio, therefore, the stress state of quasi-steady state is smaller than that of the critical state. The location of the quasi-steady state line on e–log p plane is influenced by shear mode and sample preparation method (i.e., soil fabric) (Konrad, 1990; Ishihara, 1993; Yoshimine and Ishihara, 1998). Figure 11.60 shows the undrained shear behavior of Toyoura
Next Page
410
11
STRENGTH AND DEFORMATION BEHAVIOR
Figure 11.57 Undrained stress–strain response of Toyoura sand specimens prepared at dif-
ferent densities by dry pluviation (after Yoshimine et al., 1998).
sand in triaxial compression, triaxial extension, and simple shear (Yoshimine et al., 1999). The specimens were prepared to similar void ratios, and an initial confining pressure of 100 kPa was applied. The minimum undrained shear strength and the quasi-steady state vary significantly depending on the mode of shearing, which in turn leads to different quasi-steady state lines on the e–p plane as shown in Fig. 11.61. Hence, large variation of minimum undrained shear strengths is often observed depending on shear mode, which is pri-
marily due to the anisotropic soil fabric. Further details are given in Section 11.12. The slope of the collapsing surface and the minimum undrained strength are related to both initial density and confining pressure. Typical values of the collapse surface stress ratio obtained from triaxial compression tests are plotted against state parameter in Fig. 11.62 (Olson and Stark, 2003). Although the data are scattered, a general trend for a given sand is that the slope decreases with decreasing state param-
Previous Page STRENGTH PARAMETERS FOR CLAYS
Deviator Stress (σ1 – σ3)
Phase Transformation
Dense Dilative Medium Dense Quasi-steady State Critical State
Critical State Line Collapse Surface for Loose Sand
Steady State
Collapse Surface for Very Loose Sand
Liquefaction Loose Very Loose
Mean Pressure p Steady State
(b)
Loose
Liquefaction (σ3 = 0) Very Loose Deviator Strain
Deviator Stress (σ1 – σ3)
Excess Pore Pressure Δu
Deviator Stress (σ1 – σ3)
Critical State
411
Very Loose Loose Medium Dense
Dense
Critical State Critical State Line Phase Transformation Lines Collapse Surface for Medium Dense Sand Dense Medium Dense Mean Pressure p
Phase Transformation
(a)
(c)
Figure 11.58 Typical undrained responses of sand specimens with different densities: (a) stress–strain–pore pressure response, (b) stress paths for loose and very loose specimens, and (c) stress paths for medium dense and dense specimens.
Toyoura Sand
0.95
eter. Similarly, the minimum undrained strength normalized by the initial confining pressure can be related to state parameter as shown in Fig. 11.63 (Olson and Stark, 2003). For a given soil, the strength ratio decreases with increasing state parameter and is larger in triaxial compression than in triaxial extension.
Void Ratio e
0.90
11.9 0.85
Quasi-steady State Line
Friction Angles
0.80 0.75 0.02
Quasi-steady State Initial State
STRENGTH PARAMETERS FOR CLAYS
Critical State Line from Fig.11.4(b)
0.05 0.1 0.2 0.5 1.0 Effective Mean Pressure p (kPa)
2.0
Figure 11.59 Quasi-steady state line and critical state line on e–log p plane (after Ishihara, 1993).
The peak value of for clays decreases with increasing plasticity index and activity as shown in Fig. 11.64. Similarly, the critical state friction angle of normally consolidated kaolin clays ranges from 20 to 25, whereas that of montmorillonite clays is approximately 20. However, as the shearing continues, the friction angle of normally consolidated montmorillonite clays decreases to a value between 5 and 10. This is called the residual state and further details are given in Sec-
412
11
STRENGTH AND DEFORMATION BEHAVIOR
Figure 11.61 Quasi-steady state line in triaxial compression, triaxial extension, and simple shear on e–p plane (after
Yoshimine et al., 1999).
ce ⫽ hce
Figure 11.60 Undrained shear behavior of Toyoura sand in
triaxial compression, triaxial extension, and simple shear (after Yoshimine et al., 1999).
tion 11.11. The friction angle of kaolin clays tends to remain near the above values even at large strains. Failure Envelope for Overconsolidated Clays
The differences in effective stress failure envelopes between normally consolidated and overconsolidated clays were illustrated in Fig. 11.3, and Hvorslev (1960) proposed the following relationship to model the strength characteristics of overconsolidated clays: ff ⫽ ce ⫹ ff tan e
(11.40)
where hc is a material constant. Substituting Eq. (11.40) into Eq. (11.39) gives ff ⫽ hc ⫹ ff tan e e e
(11.41)
Reported values of hc and e range from 0.034 to 0.145, and from 9.9 to 18.8, respectively (Wood, 1990).17 Rearranging Eq. (11.41) gives tan m ⬅
ff ⫽ hc e ⫹ tan e ff ff
(11.42)
(11.39)
where e is an equivalent friction angle and ce is the cohesion intercept. These are called the Hvorslev parameters. If e is constant, ce becomes a linear function of e, which is the equivalent consolidation pressure as determined from the void ratio at failure eff as shown in Fig. 11.3.
17
For general stress conditions, Schofield and Wroth (1968) modified the Hvorslev equation to the following:
冉 冉
冊 冊
q 6 sin e p ⫽ c cot ⫹ pe 3 ⫺ sin e pe pe
for triaxial compression
q 6 sin e p ⫽ c cot ⫹ pe 3 ⫹ sin e pe pe
for triaxial extension
STRENGTH PARAMETERS FOR CLAYS
Figure 11.62 Relationship between the slope of the instability line and state parameter
(after Olson and Stark, 2003).
Figure 11.63 Relationship between the undrained shear strength ratio and state parameter (after Olson and Stark, 2003).
413
414
11
STRENGTH AND DEFORMATION BEHAVIOR
Figure 11.64 Relationship between sin and plasticity index for normally consolidated
soils (adapted from Kenny, 1959). Data for pure clays from Olsen, 1974.
where m is the mobilized friction angle at failure. For normally consolidated clay, (e / ff) ⫽ 1 and tan m ⫽ tan crit ⫽ hc ⫹ tan e. Substituting this into Eq. (11.42) gives tan m ⫽ hc
冉
冊
e ⫺ 1 ⫹ tan crit ff
(11.43)
Hence the peak friction angle m for overconsolidated clays depends on the overconsolidation (e / ff) (the first term in the right-hand side) and the critical state friction angle crit. The form of this equation is similar to Eqs. (11.34) and (11.35) derived for sands. The Hvorslev parameters, e and ce, have been termed true friction angle and true cohesion, and are considered by some to reflect the mechanism of shear strength in terms of interparticle forces and friction. Such an interpretation is questionable, however, because, as shown in Chapter 8, two samples at the same water content but different effective stresses must have different structures. Thus, during deformation, there will be differences in volume change under drained conditions or differences in pore water pressure for deformation under undrained conditions. Furthermore, Eq. (11.40) shows that ce is an effective stressdependent property. Present evidence is that true cohesion is negligible in the absence of chemical bonding between particles caused by cementation.
Undrained Shear Strength
Undrained shear strength su coupled with total stress analysis [c ⫽ su and ⫽ 0 in Eq. (11.1)] is often used to examine the failure state of geotechnical structures under undrained conditions. The undrained shear strength of saturated normally consolidated clay determined using isotropically consolidated specimens as a function of liquidity index is shown in Fig. 8.43. The undrained strength for a given initial void ratio eini can be obtained using the critical state Eqs. (11.25) and (11.26): su ⫽
冉
冊
M % ⫺ 1 ⫺ eini exp 2
(11.44)
The above equation applies to both normally consolidated and overconsolidated clays. For a given soil, the initial void ratio eini can be related to the current stress state and the overconsolidation ratio. The relationship between undrained strength normalized by the effective overburden stress after isotropic consolidation i has been deduced from critical state soil mechanics by Wroth and Houlsby (1985) as su / i ⫽ 0.129 ⫹ 0.00435PI
(11.45)
BEHAVIOR AFTER PEAK AND STRAIN LOCALIZATION
in which PI is the plasticity index. Alternatively, the following relationship can be used for normally consolidated to slightly overconsolidated clays with lowto-moderate plasticity (Jamiolkowski et al., 1985): su / vp ⫽ 0.23 0.04
(11.46)
where vp is the vertical preconsolidation stress, and su is for direct simple shear. The influence of overconsolidation on the undrained strength of clays is shown by Figs. 11.65 and 11.66. In Fig. 11.65, the undrained strength is normalized by
415
the initial effective overburden pressure. In Fig. 11.66, the normalized strength of the overconsolidated clay is further normalized to the normalized strength of the normally consolidated clay. That normalization of undrained shear strength leads to unique relationships, such as those in these figures, forms the basis of the SHANSEP (stress history and normalized soil engineering properties) method of design in soft clays (Ladd and Foott, 1974) that is widely used in practice:
冉 冊
su su ⫽ v0 v0
(OCR)m
(11.47)
NC
where (su / v0)NC is the strength ratio of normally consolidated clay, m is a material constant, and OCR is the overconsolidation ratio, defined as the ratio of the vertical preconsolidation stress vp to the current vertical stress v. Typical values of m range between 0.7 and 0.9. This method is particularly well suited for use with clays of low-to-medium sensitivity, that is, clays that do not suffer large structural breakdown when consolidated beyond their preconsolidation pressure. It is also important to note that the strength ratio depends largely on the mode of shearing as shown in Fig. 11.67 (Ladd, 1991) and the values given in Eqs. (11.45) and (11.46) are at the lower range (or the conservative side) in the figure. Further details of the effect of shearing mode on undrained strength are given in Section 11.12.
Figure 11.65 Effect of overconsolidation on the normalized undrained shear strength of several clays (after Ladd et al., 1977).
11.10 BEHAVIOR AFTER PEAK AND STRAIN LOCALIZATION
When laboratory tests are done on soils exhibiting peak strength, strains at a certain location in a soil specimen often localize after the peak, leading to
Figure 11.66 Normalized undrained strength ratio as a func-
Figure 11.67 Effect of shear modes on undrained shear
tion of overconsolidation ratio (after Ladd et al., 1977).
strength ratios of different plasticity soils (after Ladd, 1991).
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11
STRENGTH AND DEFORMATION BEHAVIOR
(a)
(b)
Figure 11.68 Shear bands observed in plane strain compression tests: axial strain of (a) 9.6 percent and (b) 19 percent (after Alshibli and Sture, 2000).
‘‘shear band’’ formation in a direction diagonal to the principal stress directions. Examples of shear bands observed in the laboratory are shown in Fig. 11.68 (Alshibli and Sture, 2000). The deformation is localized, and the two soil bodies on opposite sides of the shear band act as rigid bodies. Strain localization tends to occur in soils that exhibit strain-softening behavior, such as overconsolidated clay and dense sand under low confining pressure. This observation illustrates the difficulty in obtaining the material behavior from experimental measurements at the specimen boundaries, as these strains are different from the strains in the shear band where the actual shearing is occurring. The peak strength and the associated strain are specimen size dependent because of the progressive nature of shear band development. The direction of shear banding is influenced by particle size (Arthur et al., 1982; Vermeer, 1990). In plane strain conditions, the direction of shear band with respect to the loading direction is bounded by /4 ⫹ /2 and /4 ⫹ crit /2, where is the dilation angle at the peak stress and crit is the critical state friction angle. Experimental data indicate that the shear band direction is close to /4 ⫹ crit /2 for small diameter particles (D50 ⫽ 0.2 mm), but the inclination decreases toward /4 ⫹ /2 for larger diameter particles (Oda and Iwashita, 1999). The thickness of the shear band depends on particle size as shown in Fig. 11.69. It increases with increasing displacement, but then reaches a constant value between 7 to 10 particle diameters when the displace-
Figure 11.69 Thickness of shear band as a function of par-
ticle size (after Oda and Iwashita, 1999).
ment is more than 20 particle diameters (Scarpelli and Wood, 1982; Oda and Kazama, 1998). However, this does not mean that more particles are involved in the shear band. It is more likely that the local void ratio in the shear band is growing. Examination of resinimpregnated specimens with shear bands shows that this local void ratio is larger than the maximum void ratio for a stable load-carrying structure (Oda and Kazama, 1998, Frost and Jang, 2000) and the very loose structure in the shear band is shown in Fig. 11.70 using X-ray CT. Discrete particle simulations by Iwashita and Oda (1998) show that the very large void ratios
RESIDUAL STATE AND RESIDUAL STRENGTH
Figure 11.70 Large local voids observed along the shear
zone using microfocus X-ray computed tomography (after Oda et al., 2004).
inside the shear band (see Fig. 11. 41d) are associated with particle rotation inside and near the shear band. The particles inside the shear band tend to rotate, whereas the particles outside the shear band remained in their original positions. A high gradient of particle rotation is developed at the boundary of shear bands, and the rotational resistance at this high rotational gradient zone was able to transfer loads even at void ratios larger than the maximum void ratio. Possible situations where strain localization is likely to occur are listed in Table 11.2. Distinct failure planes are often observed in both the laboratory and the field. Figure 11.72 is an X-ray photograph of shear bands observed in a model of a retaining wall failure (Milligan, 1974 and interpretation by Les´niewska and Mroz, 2000). Shear bands are observed in the field as slip planes. The practical implication of strain localization is that there can be significant differences between the continuum-based assumptions and analyses used in common geotechnical design (such as friction angle and critical state) and the actual conditions. Accordingly, careful interpretation of experimental and field data, as well as the relevance of analytical and numerical models is necessary. More detailed theoretical considerations of strain localization and shear band formation are outside the scope of this book; however, other references are available (Chambon et al., 1994; Vardoulakis and Sulem, 1995).
11.11 RESIDUAL STATE AND RESIDUAL STRENGTH
The drop in drained strength after peak is reached in intact overconsolidated clay can be attributed to (1) an
417
increase in water content owing to dilatancy and (2) reorientation of clay particles along the shear plane. These processes transform the material to its residual state. A postpeak drop in strength also occurs in normally consolidated clays if the strength loss due to breakdown of structure and particle reorientation exceeds the strength gain due to consolidation during shear. The strength of the soil once the residual state has been reached is a minimum and is termed the residual strength. The deformation at this stage becomes localized, and the residual state is developed within a shear band, as described in the previous section. The residual strength-determining factors for a given test type and strain rate are reduced to the effective stress, composition, and friction angle. The friction angle corresponding to this strength is the residual friction angle r . Its value depends on the mineralogy, gradation, bulky particle characteristics, and rate of shear. The relationships between stress and shear displacement for soils with low and high clay fractions sheared under constant effective stress on the failure plane are shown in Fig. 11.73. A residual condition can also be developed under undrained conditions. In this case, the effective stress on the shear plane at the residual state will differ from that initially or at peak stress. As a result of the rearrangement contributions to the residual strength of soils with low clay contents, as in Fig. 11.73b, the loss of strength, under drained conditions, between peak and residual is small. This is illustrated by Fig. 11.74, which shows the critical and residual friction angles for sand–bentonite mixtures tested in ring shear. Three zones are identified in Fig. 11.74 and termed rolling shear, transitional shear, and sliding shear. The shear displacements required to reach the residual strength can be large, as indicated by the values in Table 11.3. Because the shear displacements required to reach the residual state are large, the stability of embankments and slopes is only controlled by residual strength when there are preexisting slide surfaces. For first-time slides the stability is controlled by an average strength that lies between the peak and residual with a value that is influenced by the amount of progressive failure along the shear surface. Owing to the large displacements required to develop a full residual condition, special testing methods have been developed. For example, a ring shear device was developed by Bishop et al. (1971), which can be used to shear specimens through large displacements that are always in the same direction. The values of residual friction angle shown in Fig. 11.28 were obtained by shearing samples in direct shear back and
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11
Table 11.2
STRENGTH AND DEFORMATION BEHAVIOR
Possible Occurrences of Strain Localization
1. Dilative Material Subjected to Drained Shear Localization occurs after the deviator stress reaches its peak as the soil dilates. This type of localization occurs in dense sand under low confinement and in heavily overconsolidated clay. Some examples are given in Desrues et al. (1996) and Saada et al. (1999). 2. Contractive Material Subjected to Undrained Shear Shear of loose sand at high confinement causes softening after the effective stress state passes the collapse line (see Section 11.8) due to generation of excess pore pressures. In some cases, shear bands are hidden by bulging (Santamarina and Cho, 2003). Some examples are given in Finno et al. (1998) and Mokni and Desrues (1999). 3. Dilative Material Subjected to Undrained Shear Cavitation Shear of dense sand at low confinement generates large reductions in pore pressure. If the pore pressure becomes less than the vapor pressure (⫺100 kPa) of water, cavitation occurs. The effective stress drops at locations where cavitation occurs, and, therefore, the soil softens. Some examples are given in Schrefler et al. (1996), Roger et al. (1998), and Mokni and Desrues (1999). 4. Alignment of Platy Particles If soil particles are platy, they align at a certain angle and this reduces the shearing resistance. The residual friction angle discussed in Section 11.11 is a good example of this type of strain localization behavior. 5. Lightly Cemented Soils When cemented sands are sheared under low confinement, interparticle cementation breaks at low strain levels, and the shear resistance drops. Examples are given in Santamarina and Cho (2003) for artificially cemented soils and Cuccovillo and Coop (1999) for naturally structured sands. 6. Unsaturated Soils For soils at low degree of saturation, menisci form at the particle contacts, and this increases interparticle attractions by surface tension. When the soil is sheared, some of the menisci break, and this additional contribution to strength is lost, at least temporarily, until new menisci are formed. The loss of menisci causes local decrease in interparticle attraction, and, therefore, the soil may undergo softening. 7. Particle Breakage When particle breakage occurs, there is a change in particle size distribution, particle shape, and textures. The collapse of soil structure by particle breakage leads to contractive behavior upon shearing. 8. Heterogeneous Soil If a soil has a layer of loose material sandwiched between denser materials, strain localizes in the loose layer. Microlayering is observed in many natural soils due to their depositional conditions. For moist tamped compacted soil, thin looser zones exist between tamping layers, and these can initiate localized failure. 9. Other Cases The degree of localization can be influenced significantly by experimental conditions. Influencing factors include nonuniform specimen shape, friction at end platens, high length-to-diameter specimens, and tilted platens. The occurrence of localization also depends on applied loading rate. Figure 11.71 shows failed samples of kaolin clay after unconfined compression tests at two different loading rates (Atkinson, 2000). Sample A, which was loaded slowly, exhibited strain localization due to local fluid migration in the dilating shear zone. Sample B, which was loaded more rapidly, did not show distinct shear bands, as the pore fluid did not have time to migrate within the specimen. Modified from Santamarina and Cho (2003).
forth through displacements of 2 to 2.5 mm each side of center until minimum values were obtained. As Table 11.3 indicates that many tens of millimeters in the same direction may be required, some of the values in Fig. 11.28 may be high, especially for the layer silicates, where the protrusion of particle edges across the shear surface could give increased resistance. A preferred method of testing, if a ring shear device is not available, is to separate and reset the two halves of a
direct shear box to enable continued deformation always in the same direction. Nonclay Minerals
The residual strength of nonclay minerals is not much different than the critical state strength, as noted above. Quartz, feldspar, and calcite all have the same value of r ⫽ 35, as shown in Fig. 11.28, even though the
RESIDUAL STATE AND RESIDUAL STRENGTH
419
Figure 11.71 Samples of kaolin clay after unconfined com-
pression tests: (a) slower loading and (b) faster loading (courtesy of J. H. Atkinson, 2000).
Figure 11.73 Stress–shear displacement curves under con-
stant effective normal stress on the shear plane (Skempton, 1985): (a) high clay fraction (⬎40 percent and (b) low clay fraction (⬍20 percent).
(a)
(b)
Figure 11.72 Shear bands observed in centrifuge modeling of retaining wall failure: (a) Xray photograph (after Milligan, 1974) and (b) interpretation of the photography by Le´sniewska and Mroz (2000).
420
11
STRENGTH AND DEFORMATION BEHAVIOR
Figure 11.74 Influence of clay fraction on the peak and re-
sidual friction angles for sand–bentonite mixtures as determined by ring shear tests (after Lupini et al., 1981).
Table 11.3 Displacements Corresponding to Various Stages of Shear in Clays with a Clay Size Fraction Greater Than 30 Percenta Displacement (mm) Stage Peak Volume change rate ⬇ 0 At r ⫹ 1 Residual r
Normally Overconsolidated Consolidated 0.5–3
3–6
4–10 30–200 100–500
Intact clays with ⬍ 600 kPa. Data from Skempton (1985). a
to sliding shear at high contents of clay size particles. The more active the clay fraction, the lower the residual friction angle at a given clay size fraction percentage. A composite relationship showing the residual friction angle as a function of clay size fraction, derived from Kenney (1967), Lupini et al. (1981), Skempton (1985), and others is shown in Fig. 11.75. There is a sharp drop in the residual friction angle when PI exceeds 30 percent. This is attributed to a transition from turbulant shear to sliding shear. Other correlations are available for certain soil types (Mesri and CepedaDiaz, 1986; Colotta et al., 1989; Stark and Edit, 1994). Highly plastic soils of volcanic origin are an exception to the general relationship shown in Fig. 11.75. These soils, which may have clay size fractions well above 50 percent, exhibit residual friction angles that are several degrees higher than those shown in the figure. Both particle morphology and structural factors have been suggested as possible causes (Sitar, 1991; Wesley, 1992). As volcanic clays often contain large amounts of allophane, which consists of bulky shaped particles rather than platy particles, rolling shear may continue to make a major contribution. Alternatively, or in addition, physicochemical attractive forces between particles may be sufficiently strong to prevent the development of parallel orientations of platy particles and basal plane shear. For soils with liquid limits more than 50, Wesley (2003) shows that the position on the plasticity chart in relation to the A-line [i.e.,
PI ⫽ PI ⫺ 0.73(LL ⫺ 20)] is a good indicator to give good correlations for residual friction angle for both clays and volcanic ashes as shown in Fig. 11.76.
interparticle friction angles are different (see Table 11.1). This is because the critical state friction angle becomes approximately independent of interparticle friction when the interparticle friction angle becomes more than 25 ( ⫽ 0.47), as illustrated in Fig. 11.42. The shape and roughness of particles are important features that influence the critical state friction angle. Influence of Increasing Clay Content
As the proportion of clay increases, the residual friction angle decreases as a result of the reduced contribution from silt and sand particle rearrangement and the lower sliding friction angle of the clay minerals in comparison to the nonclay minerals. The influence of clay fraction is indicated through the transition from rolling shear for soils composed mainly of bulky grains
Figure 11.75 Composite relationship showing dependence of residual friction angle on soil composition as represented by activity and clay size fraction.
RESIDUAL STATE AND RESIDUAL STRENGTH
Figure 11.76 Residual friction angle of volcanic clays and
clays in relation to their location on the plasticity chart relative to the A-line (from Wesley, 2003).
Clay Minerals
Basal plane slip is the dominant deformation mechanism at large strain in the clay minerals and other layer silicates. Compression textures with basal planes approximately perpendicular to the normal load direction are formed in the shear zone, and most of the deformation takes place in this zone as well as in zones of high particle orientation that enclose it. The behavior
Table 11.4
421
of the layer silicates and solid lubricants such as graphite and molybdenum disulfide (MoS2) is similar. The type and number of bonds along the cleavage planes are important for basal plane slip, as may be seen by the values in Table 11.4. Of the materials listed, only attapulgite does not fit the pattern of decreased r with decreased interlayer bond strength. The high residual strength of attapulgite is because the lathlike particles occur as intermeshed aggregates, and the crystal structure gives a stair-step mode of cleavage. As a result, attapulgite behaves more like a massive mineral than a platy mineral in shear (Chattopadhyay, 1972). For many clays, the residual friction angle decreases with increasing confining pressure, that is, the failure envelopes are curved. The values in Fig. 11.28 for several clay minerals, as well as the data for brown London clay and Weald clay in Fig. 11.2, show significant stress dependency of the residual friction angle, that is, the failure envelope is curved. One possible reason for this curvature is that under low normal stresses less work is required to shear the clay in the absence of perfect orientation of clay particles in the shear zone than would be required to develop parallelism during shear. An alternative explanation of the stress dependency of r for clays can be based on the elastic junction theory developed in Section 11.4. If deformations at particle contacts are elastic, then the area of real contact between sliding surfaces increases less than pro-
Bonding Along Cleavage Planes, Cleavage Mode, and Residual Strength
Mineral
Mode of Cleavage
Quartz Attapulgite
No definite cleavage Along (110) plane
Mica
Good basal (001)
Kaolinite
Basal (001)
Illite
Basal (001)
Montmorillonite
Excellent basal (001)
Talc Graphite MoS2
Basal (001) Basal (001) Basal (001)
Adapted from Chattopadhyay (1972).
Bonding Along Cleavage Planes Si–O–Si, weak Secondary valence (0.5–5 kcal/mol) ⫹ K linkages Secondary valence (0.5–5 kcal/mol) ⫹ H bonds (5–10 kcal/mol) Secondary valence (0.5–5 kcal/mol) ⫹ K linkages Secondary valence (0.5–5 kcal/mol) ⫹ exchangeable ion linkages Secondary valence (0.5–5 kcal/mol) van der Waal’s Weak interlayer
r (deg)
35 30
Particle Shape
17–24
Bulky Fibrous and needle-shaped Sheet
12
Platy
10.2
Platy
4–10
Platy–filmy
6 3–6 2
Platy Sheet Sheet
422
11
STRENGTH AND DEFORMATION BEHAVIOR
portionally with increase in normal effective stress; and according to Eq. (11.22), tan r should vary as (n)⫺1 / 3. Data for several clays are shown in Fig. 11.77, which show agreement with this theory in the lowpressure range (up to 200 kPa), but at higher stresses, r is independent of stress, indicating that the solid contact area varies in direct proportion to effective normal stress. Both hypotheses appear tenable, and evidence is not available to favor one over the other. Nonetheless, for practical purposes it is clear that determinations of values of residual strength to be used for analysis of specific problems should be made under stress conditions approximating those in the field. Other important considerations include the structural features and lithological details in the field. Examples of the former are presheared surfaces generated by old landslides and tectonic and glacial deformation, whereas those for the latter are horizontal bedding planes, laminations, and weak seams (Mesri and Shahien, 2003). They all can contribute in dropping to the residual condition after relatively small displacements.
(1990) show from their database of past studies that the friction angle deduced from triaxial extension tests is 10 to 20 percent larger than that from triaxial compression tests. Similar differences have been observed between plane strain friction angle and triaxial compression friction angle for both sands and clays. The peak friction angles of sands determined from plane strain tests are 0.5 to 4 larger than those from triaxial compression tests (Cornforth, 1964). The Mohr– Coulomb friction angle is based only on the major and minor principal stresses [i.e., Eq. (11.5)]. Under triaxial compression conditions, the intermediate principal stress, 2, equals the minor principal stress, whereas under plane strain loading it is greater. The higher confinement under plane strain loading can account for the higher measured friction angle. The stress states at failure in the field differ from triaxial compression/extension and plane strain conditions. The effect of intermediate principal stress can be expressed by a b value, defined by b⫽
11.12 INTERMEDIATE STRESS EFFECTS AND ANISOTROPY
The friction angles shown in Fig. 11.51 and Fig. 11.52 are for triaxial compression. Kulhawy and Mayne
2 ⫺ 3 1 ⫺ 3
(11.48)
where 1, 2, and 3 are maximum, intermediate, and minor principal stresses, respectively; b ⫽ 0 for triaxial compression conditions (1 ⬎ 2 ⫽ 3), whereas b ⫽
Figure 11.77 Residual friction angle as a function of normal effective stress on the shear plane raised to the minus one-third power (replotted from data in Chattopadhyay, 1972).
INTERMEDIATE STRESS EFFECTS AND ANISOTROPY
1 for triaxial extension conditions (1 ⫽ 2 ⬎ 3). The value of b for plane strain conditions depends on material properties but is approximately 0.3 to 0.4.
423
in triaxial extension than in triaxial compression, as observed in Fig. 11.38b. Greater shear resistance is expected for conditions that give a larger degree of fabric anisotropy.
Sands
The intermediate stress effect can be measured using true triaxial apparatus or hollow cylinder torsional shear apparatus. The influence of intermediate principal stress (2) on measured friction angle of sands is illustrated by Fig. 11.78. In general, the peak friction angle increases 10 to 15 percent from b ⫽ 0 (triaxial compression) to b ⫽ 0.3 to 0.4 (plane strain), and it stays constant or slightly decreases as b reaches 1 (triaxial extension). The variation of measured friction angle with changes in intermediate principal stress can be attributed to the effects of different mean stress and stress anisotropy on the dilatancy and particle rearrangement contributions to the total strength. For given maximum and minimum principal stresses, the triaxial extension conditions have the largest mean effective stress, whereas the triaxial compression conditions have the smallest mean effective stress. The higher confinement for triaxial extension and plane strain conditions contributes to the increasing friction angle for these conditions. Fabric anisotropy also contributes to differences between triaxial and plane strain strengths. Discrete particle simulations by Thornton (2000) show that the average ratio of sliding contacts to the coordination number at failure were both independent of b. However, a larger degree of fabric anisotropy was observed
Figure 11.78 Effect of intermediate principal stress on fric-
tion angle (from Kulhawy and Mayne, 1990). Reprinted with permission from EPRI.
Clays
Effective stress friction angles for normally consolidated clays measured in plane strain compression are compared with those determined in triaxial compression in Fig. 11.79. The added confinement in plane strain yields a friction angle that is about 10 percent higher than measured in triaxial compression. The measured friction angle in triaxial extension is about 20 percent greater than in triaxial compression, as shown in Fig. 11.80. These results are consistent with the data presented in Fig. 11.78 for sands. The undrained shear strength su in triaxial compression is approximately twice as large as that of triaxial extension for normally consolidated clay as shown in Fig. 11.67. This large variation is primarily due to the difference in the excess pore pressures generated and is very much related to the initial bedding structure, as discussed later. Failure Envelopes
Various models fit the experimental data showing the intermediate stress effect. Among them are I1I2 ⫽ const. I3
(Matsuoka and Nakai, 1985) (11.49)
Figure 11.79 Comparative values of effective stress friction angle of normally consolidated clays in triaxial compression and plane strain compression (from Kulhawy and Mayne, 1990). Reprinted with permission from EPRI.
424
11
STRENGTH AND DEFORMATION BEHAVIOR
60
Triaxial compression 40°
Friction Angle
50 40
Triaxial compression 30°
30
Triaxial compression 20°
20
Lade and Duncan (1975) 10 0
Matsuoka and Nakai (1985) 0
0.2
Triaxial Compression
0.4 0.6 b-Value
Plane Strain
0.8
1
Triaxial Extension
Figure 11.81 Failure criterion models that include the intermediate stress effect.
Figure 11.80 Comparative values of effective stress friction angle of normally consolidated clays in triaxial extension and triaxial compression (from Kulhawy and Mayne, 1990). Reprinted with permission from EPRI.
I31 ⫽ const. I3
(Lade and Duncan, 1975)
(11.50)
where I1, I2, and I3 are the first, second and third stress invariants.18 The models are plotted in Fig. 11.81. Matsuoka and Nakai’s model gives the same friction angle for compression and extension, whereas Lade and Duncan’s model gives the ratio of the triaxial extension friction angle (TE) to the triaxial compression friction angle (TC) to be 1.08 at TC ⫽ 20 to 1.15 at TC ⫽ 40. Given the large scatter in the published experimental data (see Fig. 11.78), it is not possible to conclude that one model is better than the other. Fabric Anisotropy
The soil fabric created during depositional and postdepositional processes contributes to mechanical anisotropy. For example, nonspherical particles tend to
18
The three stress invariants are defined as
I1 ⫽ 1 ⫹ 2 ⫹ 3
I2 ⫽ 12 ⫹ 23 ⫹ 31
where 1, 2, and 3 are the principal stresses.
I3 ⫽ 123
deposit with their long axis in the direction perpendicular to gravity, and, therefore, the assembly will be inherently stiffer in the depositional (vertical) direction than in the horizontal direction. This is inherent or fabric anisotropy. The effect of inherent anisotropy on strength is controlled by how rapidly the fabric changes during shearing (called induced anisotropy). If the fabric created by deformation-induced anisotropy destroys the inherent anisotropy, the strength will not be affected by the inherent anisotropy (even though the deformations prior to failure will be affected). Details of the effects of fabric on mechanical property anisotropy were given in Section 8.9. Positive loading in triaxial compression tests is usually in the direction perpendicular to the bedding plane, whereas that in triaxial extension tests tends to be radially inward in the bedding plane direction. Figure 11.82 shows the undrained shearing responses of Toyoura sand specimens in triaxial compression and extension tests (Yoshimine et al., 1998). The specimens sheared in extension showed 100 percent excess pore pressure development leading to static liquefaction, whereas the specimens sheared in compression showed small softening at the beginning but then hardening at large strains due to large dilative behavior. Similar variations in undrained shear strength of clays were shown in Fig. 11.67. From these data, it is not clear whether the difference is due to the intermediate stress (b value) effect or to the initial anisotropic fabric generated during dry pluviation. Figure 11.83 shows different cases of variation in b value and the major principal stress direction in relation to initial cross-anisotropic soil fabric. A direc-
RESISTANCE TO CYCLIC LOADING AND LIQUEFACTION
425
bedding plane, more sand particles had to move to provide more stable soil fabric, and a larger magnitude of excess pore pressure was therefore developed. Examination of Figs. 11.82 and 11.84 indicates that conventional triaxial compression can give higher undrained shear strength with less softening compared to other shear modes. Similar data were presented by Kirkgard and Lade (1993) for normally consolidated San Francisco Bay mud. These findings have practical significance since the use of triaxial compression data may result in unconservative evaluation of flow liquefaction potential or undrained shear strength.
11.13 RESISTANCE TO CYCLIC LOADING AND LIQUEFACTION
Figure 11.82 Undrained response of dry plluviated Toyoura
Repeated or cyclic loading of soils can be caused by a number of natural phenomena or human activities, including earthquakes, wind, waves, vehicular traffic, and reciprocating machinery. Cyclic loads cause stresses and deformations in much the same manner as do slowly applied loads; however, their relatively short duration and repetitive and dynamic nature are responsible for several unique aspects of soil behavior. Attention is given in this section primarily to saturated cohesionless soils and clays because these materials are particularly susceptible to strength degradation and/or failure during earthquakes. Soils of the type encountered as pavement subgrades or as used in pavement subbases and bases are usually relatively dense and not susceptible to large strength and stiffness losses if properly prepared and compacted.
sand specimens in triaxial compression and extension: (a) stress–strain relationships and (b) undrained stress paths (after Yoshimine et al., 1998).
Drained Behavior
tional parameter is defined as the angle between the direction perpendicular to the bedding plane and the major principal stress direction. The conventional triaxial compression will be case A (b ⫽ 0 and ⫽ 0) in Fig. 11.83, whereas the triaxial extension will be case B (b ⫽ 1 and ⫽ 90) in Fig. 11.83. Ideally, therefore, the investigation of b-value effects on strength should be performed with the same value or vice versa (e.g., cases A, C, and D or cases C, E, and F in Fig. 11.83). Using a hollow cylinder torsional shear apparatus, Yoshimine et al. (1998) examined the effects of b value and the loading direction separately on undrained behavior of Toyoura sand, and some test results are shown in Fig. 11.84. For sands with relative density between 30 and 41 percent, the effect of inherent anisotropy appears to be more significant than the effect of b. When the loading direction was in parallel to the
Repeated cyclic shear straining of sand under drained conditions is shown in Figs. 11.85a and 11.85b for loose and dense Toyoura sand specimens, respectively. The cyclic loading usually causes densification. Figures 11.85(a-2) and 11.85(b-2) show development of volumetric strain with increasing number of loading cycles. For the loose sand specimen (Fig. 11.85a), the volumetric strain increases more or less monotonically. Although there is a decreasing trend of void ratio with increasing number of cycles, it is also interesting to note that, for a given cyclic shear application on the dense sand specimen, the volumetric strain does not increase monotonically but fluctuates with cyclic loading, as illustrated in Fig. 11.85(b-2). Shear-induced dilation is observed as the applied shear displacement reaches its maximum in the loading stage. During unloading, there is shear-induced volume contraction. The combination of dilation during loading and contraction during unloading leads to overall contraction.
426
11
STRENGTH AND DEFORMATION BEHAVIOR
σv
σv σh1 σh2
σh1
σσh2 σh1v= σh2 > σv
σh1v> σh2 > σv
α = 90°
v
B
F Parallel to the Bedding Plane
α
Loading Direction of Major Principal Stress in Relation to the Bedding Plane
α
σ11 α σσ3
σσ22 σ1v> σ2 > σ3
E
σv
σv
σv
v
σh1 Perpendicular to the Bedding Plane α = 0°
σh1
σh2 σvv> σh1 = σh2 0 A Triaxial Compression
σh1 σh2 σvv> σh1 > σh2
σh2
σh1
σvv= σh1 > σh2
C b - Value
D 1 Triaxial Extension
Figure 11.83 Effects of inherent anisotropy and the intermediate stress.
The influences of shear strain magnitude and number of load cycles are shown in Fig. 11.86. The densification results from the disruption of the initial soil fabric caused by the repeated shear strains followed by repositioning of the soil grains into more efficient packing. The higher the initial void ratio and the greater the number of cycles, the greater the effect. Undrained Behavior
When saturated soil is subjected to repeated cycles of loading, and provided the shear stresses are of sufficient magnitude, the structure begins to break down, and part of the confining stress is transferred to the pore water, with a concurrent reduction of effective stress and strength. This, in turn, leads to increase in shear strain under constant stress cyclic loading or a decrease in the cyclic stress required to cause a given value of cyclic strain. The deformation and failure behavior of sands in undrained cyclic loading depends on initial void ratio, initial effective stress state, and the cyclic shear stress amplitude. The results of an undrained cyclic simple shear test on Monterey sand are shown in Fig. 11.87. Develop-
ment of shear strains with cyclic loading is called cyclic mobility. Liquefaction is said to have occurred when the pore water pressure has increased to the magnitude of the initial effective confining pressure, at which point the strains become very large. Similar to the undrained response in monotonic loading, the undrained response of sand under cyclic loading depends on density, confining pressure, and soil fabric. The effect of density on cyclic behavior of Toyoura sand under triaxial loading conditions is shown in Fig. 11.88. All sands exhibit increase in pore pressure with increase in number of loading cycles, but the shear strain development for a given number of cycle is smaller for denser specimens. In the loose sand (Fig. 11.88a), when the stress state reaches the collapse surface, the soil softens leading to sudden liquefaction. The medium dense sand (Fig. 11.88b) exhibits quasi-steady state as the stress state reaches the phase transformation line. Some cycles with large stress–strain loops are observed and the specimen finally reaches liquefaction. The dense sand (Fig. 11.88c) never liquefies. Once the stress state reaches the phase transformation line, the stress–strain curve moves back and forth
RESISTANCE TO CYCLIC LOADING AND LIQUEFACTION
427
Figure 11.84 Effect of and b values on undrained response of dry plluviated Toyoura sand: (a) effect of when b ⫽ 0.5 and (b) effect of b when ⫽ 45 (after Yoshimine et al., 1998).
along and below the steady-state line and shear strain develops gradually. Beneath gently sloping to flat ground, liquefaction may lead to ground oscillation or lateral spread as a consequence of either flow deformation or cyclic mobility (Youd et al., 2001). The liquefaction susceptibility of different types of natural and artificial sedimentary soil deposits is summarized in Table 11.5. As the excess pore pressure developed during liquefaction dissipates, ground settlement is observed. Sand boils can develop through overlying less permeable soils in order to dissipate the excess pore pressures from liquefied soil below. The magnitude of the cyclic shear strains that develop following initial liquefaction decreases with increasing initial relative density and increases with increasing cyclic shear stress. The general relationship
between cyclic shear stress and number of load cycles to initial liquefaction depends on the relative density, and is of the form shown in Fig. 11.89. In this figure the cyclic shear stress applied by a simple shear apparatus is normalized by dividing by the initial effective confining pressure 0, and the ratio is often called the cyclic resistance ratio (CRR). Methods for determination of the liquefaction susceptibility of a specific site are given by Kramer (1996) and by Youd et al. (2001). In reality, generation of pore pressure is a result of the breakdown of soil structure and a tendency for the soil to densify, and this is caused by shear deformations, so liquefaction is more fundamentally controlled by shear strain than by shear stress. Furthermore, there is a level of shear strain, or threshold shear strain below which no pore pressure is generated. This is illus-
428
11
STRENGTH AND DEFORMATION BEHAVIOR
Stress Ratio q/p Toyoura Sand 2 Air Pluviated Initial Void Ratio = 0.845 p = 98 kPa = constant
_2
Stress Ratio q/p Toyoura Sand 2 Air Pluviated Initial Void Ratio = 0.653 p = 98 kPa = constant
2 Shear Strain γ (%)
_2
2 Shear Strain γ (%) _1.2
_1.2
(a-1) Stress Ratio – Shear Strain Relation
(b-1) Stress Ratio – Shear Strain Relation Volumetric Strain εv 0.6
Volumetric Strain εv 3
_2
_2
0
2 Shear Strain γ (%)
(a-2) Volumetric Strain – Shear Strain Relation
(a)
0
2 Shear Strain γ (%)
_0.6
(b-2) Volumetric Strain – Shear Strain Relation
(b)
Figure 11.85 Cyclic behavior of Toyoura sand in drained conditions: (a) loose sand and (b) dense sand (after Pradhan and Tatsuoka, 1989).
Figure 11.86 Effect of shear strain and number of load cycles on the reduction in void ratio of Ottawa sand (from Youd, 1972). Reprinted with permission of ASCE.
trated by Fig. 11.90 in which the pore pressure ratio as a function of cyclic shear strain is shown for Monterey No. 0 sand at three relative densities. The mechanics of pore pressure generation during cyclic loading can be understood by reference to Fig. 11.91 from Seed and Idriss (1982) and by Fig. 8.20. In Fig. 11.91, point A represents a soil specimen in its initial state. Under cyclic loading it would, if allowed to drain and compress, decrease in void ratio to point B in order to be able to continue to sustain effective pressure 0. However, since the soil cannot drain, the collapsing soil structure generates a pore pressure denoted in Fig. 11.91 by u. The magnitude of the pore pressure depends on the slope of the rebound curve B– C, as discussed below. From laboratory cyclic simple shear tests on several sands, the general relationship between pore pressure ratio (i.e., the generated pore pressure divided by the initial effective confining pressure) and the cycle ratio as shown in Fig. 11.92 has been determined. The cycle ratio is defined by the number of load cycles Ne divided by the number of load cycles to cause liquefaction Nl.
RESISTANCE TO CYCLIC LOADING AND LIQUEFACTION
429
mined from testing at different densities under the same confining stress condition, whereas the constant density contour lines move downward if the confining pressure increases, as illustrated in Fig. 11.93 for Aio sand samples prepared at the same relative density. This is because a soil at a given void ratio behaves as if relatively looser or more compressible at higher confining pressure. There are many other factors that impact the actual value of CRR to use in practice; the major ones are the confining pressure, the initial shear stresses under static condition, sample preparation methods, and the mode of shearing (Seed, 1979; Seed and Harder, 1990). Additional information and data can be found in Youd et al. (2001), Vaid et al. (2001), Boulanger (2003), and Hosono and Yoshimine (2004). Residual Strength after Liquefaction
Figure 11.87 Results of an undrained cyclic simple shear test on loose Monterey sand (Seed and Idriss, 1982): (a) pore water pressure response, (b) shear strain response, and (c) applied cyclic shear stress.
Using the slope of the rebound curve (Fig. 11.91) and the densification that would occur if drainage was permitted, it is possible to compute the induced pore pressure by
u ⫽ Er rd
(11.51)
where Er is the rebound modulus and rd is the volumetric strain that would occur if drainage were permitted. Martin et al. (1975) give procedures to evaluate these two parameters from the results of static rebound tests in a consolidation ring and cyclic load tests on dry sand, respectively. Finn (1981) reported good agreement between predicted and measured values using the proposed method. The liquefaction resistance depends not only on cyclic stress amplitude and density but also on the initial effective stress state. For example, Fig. 11.89 is deter-
The residual strength of sands, silty sands, and silts following liquefaction is a subject of continuing study owing to its importance in the analysis of postearthquake stability and deformation of embankments, dams, and structures. Detailed discussion of this topic is outside the scope of this book; however, two approaches have been used to estimate the residual strength, one based on steady state strength determined by laboratory tests as described in Section 11.8 and the other on the Standard Penetration Test (SPT) N value (Seed, 1987; Seed and Harder, 1990). A correlation between the residual strength and the preearthquake SPT N value is shown in Fig. 11.94. The strength values shown in this figure were determined by back analysis of liquefaction-induced slides; thus, they avoid problems related to sampling disturbance effects on strength and are representative of known field behavior. However, there is some uncertainty relating to how well the measured N values are representative of the zone in which the failure developed. The selection of a particular value within the range of strengths shown for any given N value, and variability in the N values that are measured, add additional uncertainty. Excess pore pressures can be generated either internally as described above or externally by transient seepage flow from an adjacent liquefied region. For example, if there is a less permeable layer above a sand layer, excess pore pressures can develop under the impermeable layer leading to softening of the soil. Hence, local heterogeneity plays an important role in liquefaction-induced soil deformation and failure, which requires careful site investigation to identify any low permeable layers. The strength degradation of clays due to cyclic loading follows similar patterns to that of sand, but it is much less for clays than for cohesionless and slightly
430
11
STRENGTH AND DEFORMATION BEHAVIOR
Liquefaction Failure
100 80
Initial Cyclic Loops Before Failure
20 10 0
-15
-10
-5
-10 0 -2 0
Reaching Collapse -30 Surface after Several -40 Cycles
5
10
15
Liquefaction Failure
60
Deviator Stress q (MPa)
Deviator Stress q (MPa)
50
Dr = 30% 40 Initial p = 200 kPa Cyclic Stress Δq = 40 kPa 30
Reaching Collapse Surface after Several Cycles
40 20 0 -20 0
50
100
150
200
250
-40 -60
Initial State
Liquefaction
-80
-50 Axial Strain (%)
-100 Mean Pressure p(MPa)
(a) 100
Phase Transformation
80
40
Liquefaction Failure
20 0
-1 5
-10
-5
-20 0
5
10
15
-40 -60
Reaching Collapse Surface after Several Cycles
Deviator Stress q (MPa)
Deviator Stress q (MPa)
100
Dr = 50% 80 Initial p = 200 kPa 60 Cyclic Stress Δq = 60 kPa
-80
Initial State
40 20 0 -20 0
50
100
150
200
250
-40 -60 -80
-100 Axial Strain (%)
Phase Transformation
60
Reaching Collapse Surface after Several Cycles
Liquefaction
-100
Mean Pressure p(MPa)
(b)
50
Increasing Cycles
20 10 0 -15
-10
Increasing Cycles
-5
-10 0 -20 -30
Phase Transformation
40
5
10
15
Deviator Stress q (MPa)
Deviator Stress q (MPa)
50
Dr = 70% 40 Initial p = 100 kPa Cyclic Stress Δq = 40 kPa30
-40
30 20 10 0 -10 0
40
60
80
100
120
-20 -30 -40
-50 Axial Strain (%)
20
-50
Initial State Phase Transformation Mean Pressure p(MPa)
(c) Figure 11.88 Cyclic behavior of Toyoura sand in undrained conditions: (a) loose sand, (b) medium dense sand, and (c) dense sand (after Yamamoto, 1998).
431
RESISTANCE TO CYCLIC LOADING AND LIQUEFACTION
Table 11.5
Liquefaction Susceptibility of Soil Deposits
Type of Deposit (1) River channel Floodplain Alluvial fan and plain Marine terraces and plains Delta and fan-delta Lacustrine and playa Colluvium Talus Dunes Loess Glacial till Tuff Tephra Residual soils Sabka
Likelihood That Cohesionless Sediments, When Saturated, Would Be Susceptible to Liquefaction (by Age of Deposit)
General Distribution of Cohesionless Sediments in Deposits (2)
⬍500 yr
Holocene (4)
Pleistocene (5)
a. Continental Deposits Locally variable Very High Locally variable High Widespread Moderate Widespread —
High Moderate Low Low
Low Low Low Very low
Very Very Very Very
Widespread Variable Variable Widespread Widespread Variable Variable Rare Widespread Rare Locally variable
Moderate Moderate Moderate Low Moderate High Low Low High Low Moderate
Low Low Low Very low Low High Very low Very low ? Very low Low
Very low Very low Very low Very low Very low Unknown Very low Very low ? Very low Very low
High Moderate Low Moderate Moderate Moderate
Low Low Very low Low Low Low
Very Very Very Very Very Very
— —
— —
(3)
High High High Low High High Low Low High Low High
Prepleistocene (6) low low low low
b. Coastal Zone Delta Esturine Beach high wave energy Low wave energy Lagoonal Fore shore
Widespread Locally variable Widespread Widespread Locally variable Locally variable
Very high High Moderate High High High
low low low low low low
c. Artificial Uncompacted fill Compacted fill
Variable Variable
Very high Low
— —
(From Youd and Perkins (1978); reprinted from the Journal of Geotechnical Engineering, ASCE, Vol. 104, No. 4, pp. 433–446. Copyright 1978. With permission of ASCE.
cohesive soils that are susceptible to liquefaction as shown in Fig. 11.95 (Hyodo et al., 1994). An assumption of a strength loss of about 20 percent is sometimes used in practice. Figure 11.96 shows the undrained cyclic shear stress ratio cy /su that brings normally consolidated clays to failure after 10 loading cycles (Andersen, 2004). The data include eight clays with different plasticity indices. In the direct shear tests (Fig. 11.96a), the undrained cyclic shear stress ratio at failure decreases with increase in initial static shear stress a /su and increases with plasticity index. In the
triaxial tests (Fig. 11.96b), the initial static shear is defined as a /su ⫽ (ac ⫺ rc )/2su, where ac and rc are the axial and radial consolidation stresses, respectively. The values of cy /su ⫽ (a ⫺ r)/2su show peaks at a /su ⫽ 0.2 to 0.3, indicating that the small initial anisotropy gave increased cyclic resistance. However, the undrained cyclic shear stress ratio at failure decreases when the initial static shear stress is higher or in triaxial extension conditions. Evidently in normal clays the magnitude of cyclic shear strain is less than that required to cause complete remolding.
432
11
STRENGTH AND DEFORMATION BEHAVIOR
Figure 11.89 Cyclic stress ratio and number of load cycles to cause initial liquefaction of
a sand at different initial relative densities (from De Alba et al., 1976). Reprinted with permission of ASCE.
Figure 11.90 Pore pressure as a function of cyclic shear
strain illustrating a threshold strain of about 0.01 percent, below which no excess pore pressures are developed (from Dobry et al., 1981). Reprinted with permission of ASCE.
Complete remolding would define an absolute lower bound, and its value is defined by the clay sensitivity. Cyclic stresses could cause sufficient deformations in quick clay to initiate a liquefaction-type flow failure. Some examples are given in Andersen et al. (1988). 11.14
STRENGTH OF MIXED SOILS
The presence of fines in sands can significantly influence the strength behavior. Differing effects can be obtained depending on particle size, shapes, and sample
Figure 11.91 Mechanism of pore pressure generation during
cyclic loading (Seed and Idriss, 1982).
preparation methods. Figure 11.97 shows different scenarios of intergranular matrix of two different size particles (Thevanayangam and Martin, 2002). Initially the maximum and minimum void ratios of a sand–silt mixture decrease with increase in silt content, but then the
STRENGTH OF MIXED SOILS
Figure 11.93 Effect of confining pressure on cyclic resis-
Itukaichi clay and Toyoura sand (Hyodo et al., 1994).
Cyclic Shear Strength / Static Undrained Shear Strength (τcy / su)
tance ratio (Hyodo et al., 2002).
Figure 11.95 Comparison of the cyclic resistance ratios of
Cyclic Shear Strength / Static Undrained Shear Strength (τcy / suDSS)
Figure 11.92 Rate of pore pressure buildup in cyclic simple shear tests (from Seed et al., 1976). Reprinted with permission of ASCE.
433
Direct Simple Shear Tests - Strength at 10 Cycles OCR = 1 1.2 Offshore Africa, PI=80 -100% Marlin IIa, PI=50%
1.0
Troll I, PI=37%
0.8
Troll II, PI=20%
Marlin IIb+, PI=45%
0.6 Drammen, PI=27%
0.4 0.2
North Sea GC, PI=16-27% Storebælt, PI=7-12%
0.0 0.0 0.2 0.4 0.6 0.8 1.0 Initial Shear Stress / Static Undrained Shear Strength (τa / s uDSS )
1.0 0.8
Triaxial Tests - Strength at 10 Cycles OCR = 1 Offshore Africa, PI=80-100% Troll II, PI=20%
Marlin IIb+, PI=45%
Troll I, PI=37%
Marlin IIa, PI=50%
0.6 0.4 Drammen, PI=27%
0.2 Storebælt, PI=7-10%
0.0 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Initial Shear Stress / Static Undrained Shear Strength (τa / s u)
Figure 11.94 Postliquefaction residual strength as a function
Figure 11.96 Normalized shear stresses that give undrained
of Standard Penetration Test N values (Seed and Harder, 1990).
failure after 10 cycles in (a) direct shear tests and (b) triaxial tests (Andersen, 2004).
434
11
STRENGTH AND DEFORMATION BEHAVIOR
Figure 11.97 Granular mix classification (Thevanayangam and Martin, 2002).
void ratios increase when the silt becomes the host soil as shown in Fig. 4.4. In case (i), the fine particles fit in the void space formed by the coarse particles. The mechanical behavior is little affected by the presence of fines because the external forces are transferred through the contacts between coarse particles. In cases (ii) and (iii), the fine particles start to fully occupy some void space and separate the coarse particles and prevent them from touching each other. These fine particles may reinforce the skeleton of coarse particles or they may make the skeleton unstable. As the proportion of fine particles increases, the coarse particles float inside the matrix of fine particles as illustrated as case (iv). The fine grains then dominate the mechanical behavior of the mixed soils, and the coarse grains may or may not contribute to shear resistance as a reinforcing element. Once the mixing scenario reaches case (iv), the void ratio increases with increasing fines content due to increasing specific surface of the mixture. The threshold value to become case (iv) depends on the specific mixture but is usually in the range of 25 to 45 percent fines in most cases (Polito and Martin, 2001). For cases (i) to (iii), the granular void ratio eG defined in Chapter 4 is a useful index for consideration of the effect of fines. If two mixed soils with different
fines content have the same granular void ratio and the same mechanical properties, the fines are just occupying the void space and are not influencing shear resistance. Most reported cases show that, for a given granular void ratio, the undrained strength and cyclic shear resistance are either independent of or increase with silt content (Shen et al., 1977; Vaid, 1994; Polito and Martin, 2001; Carraro et al., 2003). The undrained response of sand mixed with equidimensional silt particles is shown in Fig. 11.98 (Kuerbis et al., 1988). Specimens of the mixture were created by slurry deposition, and the density was controlled in such a way that all specimens had relatively similar granular void ratios eG, even though the actual void ratio decreased with increasing silt content. Both undrained triaxial compression and extension tests were performed following isotropic consolidation. Increased silt content gave stiffer response in triaxial compression. Apparently, the silts filled the void space and stabilized the soil as shown in Fig. 11.99a. However, the effect was small in triaxial extension. Liquefaction resistance increases with relative density as shown in Fig. 11.89. However, increasing silt content gives scattered relationships between relative density and the CRR at 20 loading cycles, as shown in
Silt Content %
(σa – r)/2 (kPa)
200
0 4 7.5 13.3 22.3
e
eG
0.764 0.728 0.669 0.547 0.448
0.764 0.802 0.805 0.784 0.863
Cyclic Resistance Ratio
STRENGTH OF MIXED SOILS
100
0.8
435
0% fines 5% fines 10% fines 15% fines
0.6 0.4 0.2 0.0 0.0
0
100
200
300
0.2
400
tests on silty sand with different mixing ratios (Kuerbis et al., 1988).
0.8 Cyclic Resistance Ratio
Figure 11.98 Undrained triaxial compression and extension
0.8
1.0
0.4
0.3
(a)
(σa + r)/2 (kPa) –100
0.4 0.6 Relative Density
0% fines 5% fines 10% fines 15% fines
0.6 0.4 0.2 0.0 0.8
0.7
0.6 0.5 Void Ratio
(a)
(b)
Cyclic Resistance Ratio
(b) 0.8
0% fines 5% fines 10% fines 15% fines
0.6 0.4 0.2 0.0 0.8
0.7
0.6 0.5 Granular Void Ratio
0.4
(c ) Figure 11.100 Cyclic resistance ratios of silty sands plotted
against (a) relative density, (b) void ratio, and (c) granular void ratio (from Carraro et al., 2003). (c)
(d)
Figure 11.99 Schematic diagrams of how fine particles are
placed inside coarse-grain matrix: (a) sand–silt mixture with silt filling the void, (b) sand–silt mixture with silts between sands and granular void ratio larger than emax, (c) sand–clay mixture, and (d ) sand–mica mixture.
Fig. 11.100a due to variations in maximum and minimum void ratios with increasing silt content. If the CRR values are plotted in terms of void ratio and cyclic resistance as shown in Fig. 11.100b, the liquefaction resistance at a given void ratio decreases with
increasing silt content. If the CRR values are plotted as a function of the granular void ratio eG, as shown in Fig. 11.100c, the sand–silt mixtures give higher liquefaction resistance than clean sand, but the resistance of these mixtures was independent of silt content. The above results are applicable when the granular void ratio eG is smaller than the maximum void ratio emax of the host medium (without fines). When fines are added, it is possible to create specimens that have eG larger than emax even though the overall void ratio is smaller than emax (Lade and Yamamuro, 1997; Thevanayagam and Mohan, 2000). This condition can be
436
11
STRENGTH AND DEFORMATION BEHAVIOR
achieved if some fines are placed between the coarser particles as shown in Fig. 11.99b. In this case, the structure is metastable, and the strength of the mixed soil is reduced due to fewer sand grain contacts. When smaller particles such as clays are added instead of silt-size particles, the clay fines act as a lubricator at sand particle contacts as shown in Fig. 11.99c and make the soil unstable. Undrained responses of Ham river sand mixed with different kaolin contents are shown in Fig. 11.101 (Georgiannou et al., 1991). Samples were prepared by pluviating the sand into distilled water with suspended kaolin particles so that similar granular void ratios were achieved. Both undrained triaxial compression and triaxial extension tests were performed after consolidating the samples under K0 stress conditions. In triaxial compression, the increase in clay content did not affect the peak stress, but the strain-softening behavior was more pronounced. After the specimen passed the phase transformation line, the stress increased toward the critical state. In triaxial extension, addition of clay led to total liquefaction. The friction angle did not change for clay fractions up to 20 percent. This delayed the development of anisotropic fabric needed to resist the increasing load. The shape of fine particles also influences the stability of the mixed soil. Hight et al. (1998) report the behavior of micaceous sands in connection with flow slides that occurred during construction of the Jamuna Bridge in Bangladesh. The large and platy mica flakes
(MPa) 0.3
(σ’a+ σ’ r)/2
0.2
Triaxial Compression Tests Clay Content = 0%, eG = 0.77 Clay Content = 4.6%, eG = 0.80 Clay Content = 7.6%, eG = 0.80
bridged between the host sand particles (Fig. 11.99d), and increased the overall void ratio as shown in Fig. 11.102. On the other hand, inclusion of smaller silt and clay particles decreased the overall void ratio, as also shown in Fig. 4.4. The open fabric of a sand–mica mixture can give complicated soil deformation and strength properties depending on mica particle orientation and shear mode (Hight et al., 1998). Further increase in fines content leads to sand particles floating in clay or silt as shown by case (iv) in Fig. 11.97. The mixed soil then behaves more like pure clay or silt. The deformation behavior then becomes more clay/silt dominated, and the coarser particles may or may not contribute to the strength properties. For example, Fig. 11.103 shows that the liquefaction resistance of mixtures with fines content greater than 35 percent was independent of silt content and granular void ratio (Polito and Martin, 2001).
11.15
COHESION
True cohesion is shear strength in excess of that generated by frictional resistance to sliding between particles, the rearrangement of particles, and particle crushing. That is, true cohesion must result from adherence between particles in the absence of any externally applied or self-weight forces. The existence of tensile or shear strength in the absence of effective compressive stress in the soil skeleton or on the failure plane might be considered true cohesion. However, the particulate nature of soil and the fact that most interparticle contacts are not oriented in the plane of shear mean that the application of directional shear stress will induce normal forces at most interparticle contacts. These forces will, in turn, generate a resistance
Initial Stress State 0.1
(σ’a+ σ’r)/2 0.0
-0.1
0.1
0.5 0.3 0.4 (MPa) Triaxial Extension Tests Clay Content = 0%, e G = 0.77 Clay Content = 3.5%, e G = 0.80
0.2
Clay Content = 7.5%, e G = 0.80
Figure 11.101 Undrained triaxial compression and extension test stress paths of clay–sand mixtures with different mixing ratios but at similar granular void ratios (Georgiannou et al., 1991).
Figure 11.102 Effect of fines (mica, silt, and kaolin) on void
ratio of a sand (Hight et al. 1998).
COHESION
0.30
× Yatesville Sand with 50% Silt 夽 Yatesville Sand with 75% 䊉 Silt 100% Silt
䉬 Monterey
Sand with 35% Silt 䊏 Monterey Sand with 50% Silt 䉱 Monterey Sand with 75% Silt
Cyclic Resistance Ratio CRR
0.25
0.20
0.15
0.10
437
䊉 × 䊉 䉬䉬 䊉
䊏
×
×
×
1.40
1.60
䉱
夽 夽 夽
0.05
0.00 0.80
1.00
1.20
1.80
2.00
2.20
Granular Void Ratio eG
Figure 11.103 Variation of cyclic resistance ratio with granular void ratio with silt content
above the threshold value (Polito and Martin, 2001).
to sliding at the contact provided the value of is greater than zero. Confirmation of the existence of a true cohesion and determination of its value from strength tests is difficult because projection of the failure envelope back to ⫽ 0 is uncertain, owing to the curvature of most failure envelopes, unless tests are done at very low effective stresses. Tensile tests cannot be made on most soils. Harison et al. (1994) performed various types of tensile tests on compacted clay specimens but found that the tensile strengths decreased with increase in specimen size due to increase in the number of internal flaws. There is no convenient way to run a triaxial compression test while maintaining the effective stress equal to zero on the potential failure plane. Strength can be measured by direct shear with no applied normal stress . Some examples are given in Bishop and Garga (1969), Graham and Au (1985), and Morris et al. (1992); however, for the reason given in the previous paragraph, the measured strength cannot be attributed specifically to true cohesion. Possible Sources of True Cohesion
Three possible sources for true cohesion between soil particles have been proposed: 1. Cementation Chemical bonding between particles by cementation by carbonates, silica, alumina, iron oxide, and organic compounds is possible. Cementing materials may be derived from the soil minerals themselves as a result of
solution–redeposition processes, or they may be taken from solution. An analysis of the strength of cemented bonds was given by Ingles (1962) and is summarized in Section 7.4 and Eqs. (7.2) to (7.8). Cohesive strengths of as much as several hundred kilopascals (several tens of pounds per square inch) may result from cementation. Stress–strain curves and peak failure envelopes for cemented sands are shown in Fig. 11.104. These curves show that even relatively small amounts of cement can have very large effects on the deformation properties. Small values of cohesion have a large effect on the stability of a soil and its ability to stand unsupported on steep slopes. However, at large strains when the cementation breaks down, the strengths become similar irrespective of the degree of cementation as shown in Fig. 11.104a. 2. Electrostatic and Electromagnetic Attractions Electrostatic and electromagnetic attractions between small particles are discussed in Sections 6.12 and 7.4. Electrostatic attractions become significant (⬎ 7 kPa or 1 psi) for separation distances ⬍2.5 mm. Electromagnetic attractions or van der Waals forces are a source of tensile strength only between closely spaced particles of very small size (⬍1 m). 3. Primary Valence Bonding and Adhesion When normally consolidated clay is unloaded, thus becoming overconsolidated, the strength does not decrease in proportion to the effective
438
11
STRENGTH AND DEFORMATION BEHAVIOR
Figure 11.104 Stress–strain curves and failure envelopes for cemented and uncemented sand at a relative density of 74 percent: (a) stress–strain curves and (b) failure envelopes based on peak strength (from Clough et al., 1981). Reprinted with permission of ASCE.
stress reduction, but a part is retained as shown in Fig. 11.3. Whether or not the higher strength in the overconsolidated clay is because of the lower void ratio or due to the formation of interparticle bonds is not known. However, a ‘‘cold welding’’ or adhesion may be responsible for some of it. This could result from the formation of primary valence bonds at interparticle contacts. Apparent Cohesion
An apparent cohesion can be generated by capillary stresses. Water attraction to particle surfaces combined with surface tension causes an apparent attraction between particles in a partly saturated soil. Equation (7.9) can be used to estimate the magnitude of tensile strength that can be developed by capillary stresses in a soil. This is not a true cohesion; instead, it is a frictional strength generated by the positive effective stress created by the negative pore water pressure. Summary
Several contributions to cohesion are summarized in Fig. 11.105 in terms of the potential tensile strengths that can be generated by each mechanism as a function of particle size. For all the mechanisms except chemical cementation, cohesion is a consequence of normal
stresses between particles generated by internal attractive forces. The mechanism of shear resistance resulting from these attractions should be the same as if the contact normal stresses were derived from effective compression stresses carried by the soil. It is convenient, therefore, to think of cohesion (except for cementation) as due to interparticle friction derived from interparticle attractions, whereas the friction term in the Mohr–Coulomb equation is developed by interparticle friction caused by applied stresses. Essentially the same concept was suggested by Taylor (1948) where cohesion was attributed to an ‘‘intrinsic pressure.’’ Similarly, Trollope (1960) attributed shear strength to the Terzaghi and Bowden–Tabor adhesion theory, with both applied stresses and interparticle forces contributing to the effective stress that developed the frictional resistance. Present evidence indicates that cohesion due to interparticle attractive forces is quite small in almost all cases, whereas that due to chemical cementation can be significant. 11.16
FRACTURING OF SOILS
Soil fracturing is often observed in geotechnical practice. Tensile cracks develop when there is external tension stress such as at the crest of a landslide or vertical cuttings. In some cases, water can fill the cracks, lead-
FRACTURING OF SOILS
439
Figure 11.105 Potential contributions of several bonding mechanisms to soil strength
(Ingles, 1962).
ing to further instability. Soil piping can occur in a dam from water flow through cracks causing internal erosion. Hydraulic fracturing results from increase in the pressure at the crack tips. Hydraulic fractures can be created by injecting fluids, grouts, or chemicals and used to control settlements caused by underground construction, to determine the in situ horizontal stress state, to create an impermeable hydraulic barrier, or to inject ground treatment chemicals for soil reinforcement and contaminated ground remediation. Desiccation also causes the development of tensile cracks as the suction in the soil increases by evaporation and causes shrinkage of the soil by increase in effective stresses. Resistance to fracturing depends on tensile strength (or true cohesion) of the material, which is often small in geomaterials except when they are cemented. Fracturing can occur in clays in undrained conditions by rapid increase in external pressure or in sands and clays by fluid permeation. Various mechanisms for fracture initiation are described below.
principal effective stress is equal to the negative value of the tensile strength (t ).19 This criterion can be written as 3 ⫽ ⫺t
(11.52)
When a tensile force is applied to a saturated soil in the direction of minor principal stress, it will be sheared in undrained conditions and the soil cracks if Eq. (11.52) is satisfied. The tensile total stress 3 then becomes 3 ⫽ u0 ⫹ u ⫺ t ⫽ u0 ⫹ ( 3 ⫹ A( 1 ⫺ 3)) ⫺ t
(11.53)
where u0 is the initial pore pressure, u is the excess pore pressure generated during the shearing process leading to fracture, A is Skempton’s pore pressure parameter (Section 8.9), and 1 and 3 are the changes
Fracture under Undrained Conditions
If particle contacts cannot carry tension, it is often assumed that the tensile cracking occurs when the minor principal effective stress 3 becomes zero. If the soil is cemented, cracking is generated when the minor
19
Note that the tensile strength of a soil is defined in terms of effective stress. Unfortunately, many tensile strength values are written in total stress since pore pressure is not measured.
440
11
STRENGTH AND DEFORMATION BEHAVIOR
in major and minor principal total stresses, respectively.20 Rearrangement of Eq. (11.53) gives 1 A
3 ⫽ ⫺ (3i ⫹ t) ⫹ 1
increases, but the circumferential stress initially decreases as long as the soil behaves linear elastically and does not fail in shear (see Fig. 11.106a). Cracks develop in the radial direction when the effective circumferential stress becomes zero for uncemented soils and equal to the negative value of the tensile strength for cemented soils. Assuming that the clay behaves linear elastically,21 the change in the radial total stress
r (⫽ 1) at the cavity is equal to the negative of the change in the circumferential stress (⫽ 3);
r ⫽ ⫺ . Substituting this condition in Eq. (11.54) under plane strain conditions (A ⬇ –12 )22 gives
(11.54)
where 3i is the initial minor principal effective stress prior to applying the tensile force. Injection of fluid into a cylindrical cavity surrounded by a clay formation can lead to fracture by increase in cavity pressure. Examples of this mechanism are fracture grouting and soil fracturing around driven piezometers (Lefebvre et al., 1981, 1991). According to cavity expansion theory, the radial total stress at the cavity
Pf ⫺ 3i ⫽ r ⫽ 3i ⫹ t or Pf ⫽ 23i ⫺ u0 ⫹ t
A more general case can be written as 3 ⫽ u0 ⫹ ( p ⫹ a q) ⫺ t, where p and q are the changes in mean pressure and deviator stress, and a is the modified pore pressure parameter defined by Wood (1990).
(11.55)
20
21
For simplicity, the undrained behavior of clays is assumed to be linear elastic-perfectly plastic. 22 No change of intermediate principal stress ( 2 ⫽ 0) is assumed.
Tension crack
σr = Pf
σθ Pf σθ -σθ = σt
σ0
σr
σ’0
σθ
−σ t
σθ
Cavity Displacement
Solid Line: Total Stresses Dotted Line: Effective Stresses
Pf (a)
σr = Pf
Plastic Deformation
σ0
σθ
σ0
Pf
σθ 2s σr u
σθ
σθ Crack
Plastic Instability
2su
Cavity Displacement
Solid Line: Total Stresses Dotted Line: Effective Stresses
(b) Figure 11.106 Fracture mechanisms of injection fluids into a cavity: (a) tensile fracture in
undrained conditions and (b) shear failure in undrained conditions.
FRACTURING OF SOILS
where Pf is the injection pressure that causes the clay to fracture. The above mechanism assumes that the tensile fracture occurs when Eq. (11.53) is satisfied in a uniform displacement field at the injection cavity. The fracture pressure Pf increases linearly with the initial total confining pressure 3i with a slope of 2. In reality, deformation around the cavity is not uniform and fracture can initiate at a localized zone at a pressure smaller than the prediction. This leads the slope between Pf and 3i to be smaller than 2. Other considerations for this fracture mechanism include the effect of shear-induced pore pressure and a nonlinear stress– strain relationship (Andersen et al., 1994). As injection pressure increases, the clay at the surface of the cavity may reach undrained shear failure before the circumferential effective stress becomes zero in uncemented soils or reaches the tensile strength in cemented soils. In such cases, the changes in the stress state at the cavity boundary with increasing cavity strain are shown in Fig. 11.106b). Upon shear failure, the difference between the radial and circumferential stresses (both total and effective) remains equal to 2su, and, therefore, the minimum principal effective stress never reaches zero. In such circumstance, it is difficult to see how plastic yielding initiates a fracture. However, there is much field and experimental evidence suggesting that fracture has indeed occurred even though plastic deformation was observed at the cavity due to the low undrained shear strength of the soil (Mori and Tamura, 1987; Panah and Yanagisawa, 1989; Au et al., 2003). A possible explanation is that the increase in plastic shear failure zone created shear bands or an unstable state around the cavity. This leads to a localized microscale crack and the injected fluid can penetrate into the crack to produce local tensile stresses at the crack tips, as illustrated in Fig. 11.106b. A simple cylindrical cavity expansion analysis shows that the cavity pressure required for the cavity boundary to reach the plastic state is Pf ⫽ 3i ⫹ su
(11.56)
where 3i is the initial total stress prior to shearing and su is the undrained shear strength. The fracture pressure Pf increases with initial confining pressure in direct proportion (i.e., slope of 1). If the plastic zone around the expanding cavity increases before fracture initiates or su increases with initial confining pressure, the fracture pressure Pf would increase from the value given in Eq. (11.56) and, therefore, the linear proportion between Pf and 3i is expected to be larger than 1. Empirical equations to estimate soil fracture under undrained conditions are available (Jaworski et al.,
441
1981; Yanagisawa and Panah, 1989), and they can be generalized by the following equation: Pf ⫽ m3i ⫹ n
(11.57)
where m and n are material constants. Experimental data give values of m varying between 1.5 and 1.8 (Jaworski et al., 1981), whereas data indicating shearinduced fracture give values of m ⫽ 1.05 to 1.085 (Panah and Yanagisawa, 1989). Reported values of fracture pressure as a function of confining pressure for various soils are plotted in Fig. 11.107. The m values of individual data sets are in general bounded by Eqs. (11.55) and (11.56). Fracture under Drained Conditions
Forced seepage flow into a cavity in permeable soil leads to soil fracture if the effective stress reduces to the negative sign of the tensile strength of the soil. Practical applications of this situation are in situ permeability testing and bore hole stability. To interpret the fracture conditions around a driven piezometer, Bjerrum et al. (1972) developed the following conditions for the initiation of fracture in soils using the equilibrium equation with the assumptions of steady state pore fluid flow from a cylindrical cavity and elastic soil material. Horizontal cracks may develop if the injection pressure exceeds the initial total vertical stress: Pinj ⫽ u0 ⫹ v0
(11.58)
where Pinj is the injection pressure, u0 is the initial pore pressure, and v0 is the initial vertical effective stress. Vertical cracks in the radial direction from the piezometer develop when the circumferential effective stress becomes smaller than the tensile strength of the material. Bjerrum et al. (1972) consider two cases: (i) the piezometer is in contact with the surrounding soil and (ii) the piezometer moves away from the surrounding soil (called ‘‘blow off’’). For the former case, cracks develop when the following condition is satisfied: Pinj ⫽ u0 ⫹
冉 冊
1 ⫺ 1 [t ⫹ (1 ⫺ )h0 ]
(11.59)
where is Poisson’s ratio, t is the tensile strength, h0 is the initial horizontal effective stresses; is a disturbance factor that considers the change in circumferential effective stress due to piezometer installation. Typical values of are given in Table 11.6.
442
11
STRENGTH AND DEFORMATION BEHAVIOR
Figure 11.107 Increase in fracture pressure with initial confining pressure of different soils.
Table 11.6
Typical Values of Disturbance Factors ␣ and 
Soil Type
Range of Compressibility Ratio E/ h0(1 ⫹ v)
High compressibility Medium compressibility Low compressibility
1–3 3–10 10–70
0.4–0.2 0.2 to ⫺0.2 ⫺0.2 to ⫺1.1
0.5–1.1 1.1–2.0 2.0–4.2
From Bjerrum et al. (1972).
FRACTURING OF SOILS
In some cases, the radial effective stress in the soil next to the piezometer becomes zero and the soil separates from the piezometer. This occurs when the injection pressure becomes larger than the total radial effective stress: Pinj ⫽ u0 ⫹ h0(1 ⫹ )
443
al., 1992). Soil shrinks by the decrease in pore pressure and increase in effective stress. This decrease in volume generates vertical cracks. On the other hand, the tensile strength that provides the resistance to crack formation increases with increased negativity of pore water pressure.
(11.60) Fracture Propagation
where is a disturbance factor that considers the change in radial effective stress during piezometer installation. Typical values of are given in Table 11.6. Further increase in injection pressure leads to development of vertical cracks in the radial direction, which occurs when the following condition is satisfied: Pinj ⫽ u0 ⫹ (1 ⫺ )[t ⫹ (2 ⫹ ⫺ )h0 ]
Limited knowledge is available concerning fracture orientation and propagation. Some examples of fractures developed by injection of different fluids are shown in Fig. 11.109. When fluid is injected into the
(11.61)
Desiccation Cracks
Reduction in moisture by surface evaporation from clays leads to increase in interparticle contact forces by suction. Soil then shrinks and desiccation cracks may develop. The generation of cracks changes the hydraulic properties from Darcy’s-type homogeneous flow to fracture-dominated flow. This can cause some environmental problems, such as unexpected poor performance of contaminant barrier systems. Figure 11.108 shows the crack patterns observed after desiccation of sensitive clays (Konrad and Ayad, 1997). The cracks can be pentagonal and heptagonal in shape, and their size appears to be uniform. Morris et al. (1992) report that crack depths from 0.5 to 6.0 m are observed in natural soils in Australia and Canada. Unfortunately, the available knowledge for prediction of crack depth and spacing is limited. The decrease in matrix suction resulting from evaporation leads to two counteracting effects (Morris et
(a)
(b) Figure 11.109 Different fracture patterns observed in laboFigure 11.108 Photos of desiccation cracks (Konrad and
Ayad, 1997).
ratory: (a) vertical and radial fractures hardened by epoxy and (b) horizontal fracture by cement bentonite mixture injection.
444
11
STRENGTH AND DEFORMATION BEHAVIOR
soil to create hydraulic fracture, a rule of thumb is that vertical fractures are formed when K0 is less than 1 [as given Eq. (11.59)] and horizontal fractures develop when K0 is more than 1 [as given in Eq. (11.60) with ⫽ 0]. However, this assumes injection into a linear elastic infinite soil medium. When multiple grout injections are performed at close distance, horizontal fractures can be observed even though K0 is less than 1 (Soga et al., 2004). Natural bedding also affects fracture orientation. In shallow formations, fractures are often horizontally oriented or gradually dipped (Murdoch and Slack, 2002). Simple criteria presented as Eqs. (11.56) to (11.61) are applied for global stress conditions, where microscale cracks often develop by local tensile stresses at the crack tips. Fracture mechanics have been used with some success to characterize the cracking resistance of the soils and to examine possible crack propagation (Morris et al., 1992; Harison et al., 1994; Murdoch and Slack, 2002). The actual mechanisms of fracture development in a fluid–soil system are more complicated than in the above analyses, as illustrated in Fig. 11.110. They may involve plastic deformation at the crack tip, soil rate effects, penetration of injection fluid into the cracks, and permeation of injection fluid from cracks into the soil medium. If the clay is overconsolidated and saturated, the negative pore pressure generated by shearing in front of the crack could possibly lead to cavitation and dry cracks may develop in front of penetrating injection fluid.
well before failure. A good example is the onedimensional compression behavior discussed in Chapter 10. After the stress state becomes larger than the preconsolidation pressure, the soil has yielded and plastic strains develop. This leads to the concept of yield envelope (sometimes referred as yield surface or limit state curve), which differentiates the state of the soil between elastic and plastic. Examples of the yield envelope of sands and clays were shown in Fig. 11.12. When the stress state reaches the yield envelope, the total strain is governed by the development of plastic strain increments. Unfortunately, for soils, there is no distinct transition from elastic to plastic behavior. Plastic strains do develop inside the yield envelope and the stiffness degrades even at very small strain levels. Figure 11.111 shows a schematic nonlinear stress–strain relationship for a soil subjected to monotonic and cyclic deviator loads. Some experimental data are shown in Figs. 11.85 and 11.88. Under cyclic loading, the relationships are hysteretic, which indicates energy absorption, or damping, during each complete cycle of stress reversal. The shear modulus G and damping ratio are used to characterize the curves in Fig. 11.111, and they are defined by
Secant Stiffness
DEFORMATION CHARACTERISTICS Shear Stress
11.17
Strains are often decomposed into elastic (recoverable) and plastic (irrecoverable) parts. Conventional soil mechanics assumes that plastic strains develop only when the stress state satisfies some failure criterion (e.g., the Mohr–Coloumb criterion). Otherwise, the soil behaves elastically. However, plastic strains usually develop
Permeation
Injection Fluid
Localized Shearing with Dilation and Rate Effect
Cavitation?
G1
G2
τ2 Monotonic loading curve
τ1
Cyclic loading curves
γ1
γ2 Shear Strain
Monotonic loading curve
Fluid Penetration Into Crack
Figure 11.110 Possible fracture propagation mechanisms in
Figure 11.111 Monotonic and cyclic load stress–strain re-
soils.
lationships at different strain amplitudes.
DEFORMATION CHARACTERISTICS
G⫽
c c
mation parameters usually cannot be determined accurately by conventional triaxial testing. With the use of local strain measurement systems (Jardine et al., 1984; Goto et al., 1991; Scholey et al., 1995; Cuccovillo and Coop, 1997; Lo Presti et al., 2001; Yimsiri and Soga, 2002), however, it is now possible to measure the development of stresses from very small strains, which can then be used for accurate prediction of deformations in the field. To characterize nonlinear deformation inside the yield envelope, it is convenient to define four zones in the p –q plane as shown in Figs. 11.112b, 112c and 112d. The initial stress state is considered to be at point O, and the boundaries of the zones are determined by stress probe testing in different stress path directions. The boundaries often associated with strain levels (axial or shear strains), and the corresponding secant stiffness values are illustrated in Fig. 11.112a.
(11.62)
in which c is the applied shear stress and c is the corresponding shear strain, and ⫽
1 E 2 G 2c
(11.63)
dεp/dεt
Stiffness G or E
in which E is the energy dissipated per cycle per unit volume, given by the area within the hysteresis loop. Understanding this pre-yield deformation behavior is very important, as most strains observed in geotechnical construction practice are indeed small (less than 0.1 percent) (Burland, 1989). Site response under earthquake loading is influenced by stiffness degradation and damping characteristics that are associated with relatively small strain levels (Seed and Idriss, 1982). This was illustrated in Fig. 11.9, which shows typical strains observed in various types of geotechnical construction and shows that the necessary defor-
1
I
II
III
State A
IV
1. Zone 1 (True Elastic Region) Soil particles do not slide relative to each other under a small
Critical-State Line
q
Y3 Envelope
State B State C
IVIV Y2 Envelope III
II dεp Plastic Strain Increment dεt Total Strain Increment
Strain O Y1 Envelope Initial State I p
Strain ’ p
0 (a)
(c) State B
Critical State Line
q
q
Critical State Line Expanded Y3 Envelope
Y3 Envelope
IV
II III I
Y2 Envelope
II
Y1 Envelope
III O Initial State
Y2 Envelope
Y1 Envelope I p
(b) State A
445
(d) State C
Figure 11.112 Four zones of deformation characterization: (a) stiffness degradation and
plastic strain development, (b), (c), and (d) are the stress conditions and the location of the four zones associated with three successive states (modified from Jardine, 1992).
446
11
STRENGTH AND DEFORMATION BEHAVIOR
stress increment, and the stiffness is at its maximum. The soil stiffness is determined from contact interactions, particle packing arrangement, and elastic stiffness of the solids. The soil stiffness values can be obtained from elastic wave velocity measurements, resonant column testing, and very accurate local strain transducers. Cyclic loading produces only very small hysteresis by stick–slip motions at particle contacts and other mechanisms, producing very small energy dissipation less than 1 percent. The strains at which the stress state reaches the outer boundary of zone 1 (called Y1 envelope) are usually described as elastic limit strains or elastic threshold strains. This state is illustrated as state A in Fig. 11.112b. The elastic limit axial strain depends on soil type, solid stiffness, and confining pressure as shown in Table 11.7 for different geomaterials. Micromechanics analysis by Santamarina et al. (2001) shows that it increases from less than 5 ⫻ 10⫺6 strain, for nonplastic soils at low confining pressure conditions, to greater than 5 ⫻ 10⫺4 strain at high confining pressure conditions or in soils with high plasticity. 2. Zone 2 (Nonlinear Elastic Region) Soil particles start to slide or roll relative to each other in this zone. The stress–strain behavior becomes nonlinear, and the stiffness begins to decrease from the true elastic value as the applied strains or stresses increase. However, a complete cyclic loading (unloading and reloading) shows full recovery of strains and therefore the zone is called
Table 11.7
elastic even though microscopically soil particles may not be back to their original locations after the cyclic loading. When the stress state reaches the outer boundary of zone 2 (called the Y2 envelope), plastic strains start to develop. The initiation of plastic strains can be determined by examining the onset of permanent volumetric strain in drained conditions or residual excess pore pressures in undrained conditions after unloading. Hence the strain level that defines the Y2 envelope is called volumetric threshold strain.23 The value of the volumetric threshold strain is generally one order of magnitude higher than that of the elastic threshold strains. The available experimental data suggest that it ranges between 7 ⫻ 10⫺5 and 7 ⫻ 10⫺4 (the lower limit for uncemented normally consolidated sands and the upper limit for high plasticity clays and cemented sands). At this strain level, the stiffness degrades to 60 to 85 percent of the true elastic value (Ishihara, 1996).
23 Other definitions of the Y2 surface are available. For example, (a) perform undrained cyclic loading test and find the linear relationship between max and p / max, where max is the maximum strain for each cycle and p is the residual strain (Smith et al., 1992); (b) the strain level when excess pore pressures start to accumulate in a sequence of undrained cyclic tests at different strain levels (Vucetic, 1994); (c) change in the direction of strain path in the vol–s space in drained tests (Kuwano, 1999); and (d) change in the slope of the excess pore pressure–vertical effective stress in undrained triaxial compression test (Kuwano, 1999).
Elastic Limit Strain for Various Geomaterials from Triaxial Tests
Material
Elastic Limit Axial Strain
Dogs Bay sand Leighton Buzzard sand Kaolinite Berthieville clay Bothkennar clay Queenborough clay Osaka Bay clay London clay Vallericca clay Calcarenite Sandstone High-density chalk Low-density chalk Cement-treated sandy soil Samamihara mudstone
⬍1 ⫻ 10⫺5 2 ⫻ 10⫺5 ⬍2 ⫻ 10⫺5 ⬍2 ⫻ 10⫺5 ⬍2 ⫻ 10⫺5 –3 ⫻ 10⫺5 ⬍2 ⫻ 10⫺5 1 ⫻ 10⫺5 2 ⫻ 10⫺5 ⬍1 ⫻ 10⫺4 1 ⫻ 10⫺4 2 ⫻ 10⫺4 5 ⫻ 10⫺5 2 ⫻ 10⫺5 –4 ⫻ 10⫺4 1 ⫻ 10⫺4 2 ⫻ 10⫺4
After Matthews et al. (2000).
Soil Description Uniform, angular biogenetic carbonate sand Uniform, subround, quzartz sand Reconstituted clay Soft silty clay Soft marine clay Soft silty clay Overconsolidated marine clay Stiff overconsolidated, fissured clay Weakly cemented overconsolidated clay Weak rock, carbonate sand cemented with calcite Weak rock, quartz grain weakly bonded bny iron oxide Dry density ⫽ 1.94 g/cm3 Dry density ⫽ 1.35 g/cm3 Hard soil/weak rock Weak rock
LINEAR ELASTIC STIFFNESS
3. Zone 3 (Preyield Plastic Region) As the stress state approaches the yield envelope (Y3 envelope), the ratio of plastic to total strain increases, approaching values close to 1.0 at the yield envelope. This state is illustrated as state B in Figs. 11.112a and 11.112c. Soil particles slide relative to one another, with strong force chains breaking and reforming continuously to accommodate the changing stress conditions. 4. Zone 4 (Full Plastic Region) Once the stress state reaches the Y3 yield envelope, there is a distinct kink in the stress–strain relationship and plastic strains develop fully. This state is illustrated as state C in Figs. 11.112a and 11.112d. The yield envelope expands or shrinks depending on the plastic increments; in general, the yield envelope expands if positive plastic volumetric strain (contraction) develops, whereas it shrinks if negative plastic volumetric strain (dilation) develops. The sizes of Y1 and Y2 surfaces may change with the enlargement or shrinkage of Y3 surface. If the stress state reaches the critical state, the soil is considered to have reached failure. Examples of experimentally determined boundaries are shown in Fig. 11.12b for Bothkennar clay and Fig. 11.113 for Ham River sand. These zones are not fixed in space when the stress state moves inside the Y3 yield
0.3 Y3 Envelope 0.2
q = σa – σr
0.1
0.0
Initial Stress State
Y1 Envelope
0.1
0.2
Y2 Envelope 0.3
0.4
p = (σa + 2σr )/3 -0.1
-0.2
envelope as illustrated in Figs. 11.112c and 11.112d. If a stress state is probed in a certain direction within zone 2, the Y1 envelope is dragged with the stress state. When the stress path is reversed inside the Y1 envelope, the soil behaves as truly elastic. Once the stress state reaches the other side of the Y1 envelope, the Y1 envelope is again dragged with the stress state. When the stress state is in zone 3, both Y1 and Y2 envelopes are dragged with the stress state. The movement of these surfaces is therefore kinematic. The stiffness and its degradation are controlled by the new stress path direction in relation to the previous stress path direction (Atkinson et al., 1990). If the soil is allowed to age at a fixed effective stress point, the Y1 and Y2 envelopes may grow in size.
11.18
LINEAR ELASTIC STIFFNESS
Knowledge of soil stiffness in the linear elastic region is important for evaluating soil response under dynamic loadings such as earthquakes, mechanical vibration, and vehicle vibration. It also provides indirect information regarding the state and natural soil structure, and, therefore, stiffness values can be used to assess the quality of soil samples (i.e., the degree of soil disturbance). The linear elastic stiffness of soils is evaluated from measurements of elastic wave velocities or use of local displacement transducers. Theoretical analysis of elastic waves in a particulate assembly is outside the scope of this book, but details can be found in Richart et al. (1970) and Santamarina et al. (2001), among others. The small strain shear modulus (Gmax) depends on the applied confining pressure and packing conditions of soil particles. The following empirical equation (Hardin and Black, 1966) is often used for isotropic stress conditions24: Gmax ⫽ AF(e)pn
Stress Path to Initial State
Y3 Envelope
-0.3
Figure 11.113 Y1, Y2, and Y3 envelopes for Ham River sand
(Jardine et al., 2001).
447
(11.64)
where F(e) is a void ratio function, p is the mean effective stress, and A and n are material constants. An example of the fitting was shown in Fig. 11.11, and Table 11.8 summarizes some experimental data for different types of soils. Equation (11.64) is dimensionally inconsistent, except when n ⫽ 1. Various theoretical solutions such as the Hertz–Mindlin contact theory are available to re-
24 In practice, Gmax and pare often normalized by pa (reference pressure such as atmospheric pressure) so that the equation appears to be dimensionally consistent. However, there is no physical meaning to this.
448
11
Table 11.8
STRENGTH AND DEFORMATION BEHAVIOR
Coefficients Used in Eq. (11.64)
Soil Type
A
F(e)
n
Void Ratio Range
Test Method a
Reference
Sand 6,900
(2.174 ⫺ e)2 1⫹e
0.5
0.3–0.8
RC
Hardin and Richart (1963)
Angular-grain crushed 3,270 quartz Several sands 9,000
(2.973 ⫺ e)2 1⫹e (2.17 ⫺ e)2 1⫹e
0.5
0.6–1.3
RC
0.4
0.6–0.9
RC
Hardin and Richart (1963) Iwasaki et al. (1978)
Toyoura sand
8,000
(2.17 ⫺ e)2 1⫹e
0.5
0.6–0.8
Cyclic TX
Kokusho (1980)
Several cohesionless and cohesive soils
4,500– 140,000
1 0.3 ⫹ 0.7e2
0.5
NA
RC
Hardin and Blandford (1989)
Ticino sand
7,100
(2.27 ⫺ e)2 1⫹e
0.43
0.6–0.9
RC and TS
Lo Presi et al. (1993)
Reconstituted NC kaoline
3,270
(2.973 ⫺ e)2 1⫹e
0.5
0.5–1.5
RC
Hardin and Black (1968)
Several undisturbed NC clays
3,270
(2.973 ⫺ e)2 1⫹e
0.5
0.5–1.7
RC
Hardin and Black (1968)
Reconstituted NC kaolin
4,500
(2.973 ⫺ e)2 1⫹e
0.5
1.1–1.3
RC
Marcuson and Wahls (1972)
Reconstituted NC bentonite
450
(4.4 ⫺ e)2 1⫹e
0.5
1.6–2.5
RC
Marcuson and Wahls (1972)
Several undisturbed silts and clays
893–1,726
(2.973 ⫺ e)2 1⫹e
0.46–0.61
0.4–1.1
RC
Kim and Novak (1981)
Undisturbed NC clay
90
(7.32 ⫺ e)2 1⫹e
0.6
1.7–3.8
Cyclic TX
Kokusho et al. (1982)
Undisturbed Italian clays
4,400–8,100
0.40–0.58
0.6–1.8
RC and BE
Jamiolkowski et al. (1995)b
Several soft clays
5,000
e⫺1.3(average from e⫺x: x ⫽ 1.11–1.43) e⫺1.5
Several soft clays
18,000– 30,000
Round-grain Ottawa sand
Clays
a
1
0.5
1–5
SCPT
Shibuya and Tanaka (1996)c
0.5
1–6
SCPT
Shibuya et al. (1997)c
(1 ⫹ e)2.4
RC: resonant column test, TX: triaxial test, TS: torsional shear test, BE: bender element test, SCPT: seismic cone test. From anisotropic stress condition. c Using v instead of p. After Yimsiri (2001). b
449
LINEAR ELASTIC STIFFNESS
Table 11.9
Some Analytical Solutions for Shear Modulus Under Isotropic Loading of pⴕ Coordination Number
Packing
Shear Modulus
冉冊 冉冊 冉冊 冉
1/3
冉冊 冉冊
(1 ⫺ g)1 / 3 p 2 ⫺ g Gg
Simple cubic
6
Gmax 3 ⫽ Gg 2
Body-centered cubic
8
Gmax 1 ⫽9 Gg 6
Face-centered cubic
12
Gmax 1 3 ⫽ Gg 2 2
Random packing
Cn
兹3cn Gmax 1 ⫽ Gg 5 兹2(1 ⫹ e)
1/3
(1 ⫺ g)1 / 3 p 6 ⫺ 5g Gg
1/3
1/3
1/3
冉冊
(4 ⫺ 3g) p 2/3 (2 ⫺ g)(1 ⫺ g) Gg
冊
2/3
1/3
冉冊
(5 ⫺ 4g) p (2 ⫺ g)(1 ⫺ g)2 / 3 Gg
1/3
After Santamarina and Cascante (1996).
Cn ⫽ 13.28 ⫺ 8e
(11.65)
By varying compaction effort, sand samples can be prepared to different densities for a given applied confining stress. In this case, a smaller void ratio implies that the number of particle contacts is larger, and, therefore, the small strain stiffness increases. This effect is taken into account in the void ratio function
F(e). Several expressions are available for the void ratio function as listed in Table 11.8. These functions are empirical and apply for specific ranges of void ratios and, therefore, should be used with caution. Equation (11.64) is derived assuming isotropic stress conditions. Anisotropic stress conditions as well as anisotropic soil fabric give stiffness values that depend on the direction of loading. The shear modulus is a function of the principal effective stresses in the directions of wave propagation and particle motion and is relatively independent of the out-of-plane principal stress. This is shown in Fig. 11.114, in which the variations of measured shear wave velocities propagating in three different directions (Vsxy, Vsyz, and Vszx) are shown as the vertical effective stress z was increased
σz Change in Vertical Effective Stress S-wave Velocity, Vs (m/s)
late the global elastic stiffness to microscopic properties such as particle stiffness and Poisson’s ratio, number of contacts, void ratio, and contact force directions (see Table 11.9). These solutions suggest that the pressure p and Gmax could be normalized by the shear modulus of the particle itself (Gg). It is noted from Table 11.8 that the values of the exponent n range from 0.4 to 0.6. As shown in Table 11.9, however, classical contact mechanics solutions using the Hertz–Mindlin contact theory predict n ⫽ –13 . This is because the soil particles are assumed to be smooth elastic spheres. If the contacts are considered to be an interaction of rough surfaces, the modification of theory leads to increases in the exponent to values that are closer to the experimental observations given in Table 11.8 (Yimsiri and Soga, 2000). By comparing Eq. (11.64) with the micromechanical model listed at the bottom of Table 11.9, it is possible to relate the void ratio function F(e) to number of contacts per particle (i.e., coordination number) and A to the elastic properties of particle itself. From the analysis of uniform grain fabrics, the coordination number Cn can be related to the porosity n by Eq. (5.1) or to the void ratio e by the following equation. (Chang et al., 1991).
400
Direction of Wave Propagation Particle Motion
Vs-zx Vs-xy
300
Vs-xy
Vs-yz
Vs-yz Vs-zx
200 20
40
60
80
100
200
300
Vertical Effective Stress, σ z (kPa)
Figure 11.114 Variation of shear wave velocities in different
directions as a function of anisotropic stresses (Stokoe et al., 1995).
11
STRENGTH AND DEFORMATION BEHAVIOR
with the horizontal effective stresses x and y being held constant (Stokoe et al., 1995). The shear wave Vsxy, which propagates and has the particle motion in the out-of-plane directions, shows no change in its velocity. This leads to the following empirical equation for stiffness under anisotropic stress conditions (Roesler, 1979; Yu and Richart, 1984; Stokoe et al., 1985, 1991; Hardin and Blandford, 1989): Gij(max) ⫽ AGFGi rGj sG OCRk
(11.66)
where i is the effective normal stress in the direction of wave propagation, j is the effective normal stress in the direction of particle motion, and AG, rG, sG, and k are material constants. Experimental evidence suggests that rG ⬇ sG. Hence, an alternative equation that relates the stiffness to the mean state of stress on the plane of particle motion is also available:
冉
Gij(max) ⫽ AGFG
冊
i ⫹ j 2
nG
OCRk
(11.67)
Equations (11.66) and (11.67) include the effect of overconsolidation ratio (OCR). Hardin and Black (1968) found that k is a function of plasticity index (k increasing from 0 to 0.5 as PI increases from 0 to more than 100). Viggiani and Atkinson (1995) report k ⫽ 0.3 for reconstituted kaolin and k ⫽ 0.35 for reconstituted and undisturbed London clay. It can be argued that the void ratio function is a redundant factor since the void ratio is a unique function of present effective stress, stress history (OCR), and soil compressibility. However, this argument should be restricted to reconstituted clays and not applied to natural clays. Similar empirical equations are proposed for other elastic constants. P-wave velocity is a function only of the effective stress in the coaxial direction as shown in Fig. 11.115 (Stokoe et al., 1995). Hence, the small strain constrained modulus Mi(max) in the i direction can be expressed as Mi(max) ⫽ AMF(e)inM
(11.68)
where AM and nM are material constants. Similarly to the constrained modulus, the small strain Young’s modulus Ei(max) in the i direction (e.g., vertical or horizontal) is a function of the effective stress in the coaxial direction (i direction) only. The increase in Young’s modulus with stress in the coaxial direction is shown in Fig. 11.116a, whereas no change in the modulus with the increase in the stresses in orthogonal direction is shown in Fig. 11.116b (Hoque
σz Change in Vertical Effective Stress Direction of Wave Propagation Particle Motion Vp-zz Vp-xx Vp-xx
600
P-wave Velocity, Vp (m/s)
450
500
400
300 20
Vp-zz
Vp-yy Vp-yy
40 60 80 100 200 Vertical Effective Stress, σz (kPa)
300
Figure 11.115 Variation of P-wave velocities in different directions as a function of anisotropic stresses (Stokoe et al., 1995).
and Tatsuoka, 1998). This leads to the following empirical equation for small strain Young’s modulus: Ei(max) ⫽ AEF(e)i nE
(11.69)
where AE and nE are material constants. Micromechanics analysis by Yimsiri and Soga (2000) supports this relation when the change in contact fabric anisotropy with applied stress is considered. Limited data are available with respect to Poisson’s ratio, and it is often assumed to be a constant value. The data by Hoque and Tatsuoka (1998) shown in Fig. 11.117 indicate that Poisson’s ratio vh (i.e., horizontal expansion by vertical load) increases with vertical effective stress and decreases with increase in horizontal stress. The following empirical equations are proposed by Horque and Tatsuoka (1998) for Poisson’s ratios: vh ⫽ AvhF(e)(v / h)nvh
(11.70)
hv ⫽ AhvF(e)(h / v)nhv
(11.71)
where Avh, Ahv, nvh, and nhv are material constants. Hoque and Tatsuoka (1998) report the values of nvh and nhv can be assumed to be half of nE given in Eq. (11.69). Small strain stiffness anisotropy originates from (i) anisotropic stress conditions and (ii) anisotropic soil fabric. The former is considered in Eqs. (11.66) to (11.71). For the latter, the material constant A should be directionally dependent reflecting a given anisotropic fabric. The effect of soil fabric on small strain stiffness of reconstituted London clay specimens is shown in Fig. 11.118 where the shear wave velocities in different directions are measured under the same confining pressures, and three different values of stiffness (Gvh, Ghv, and Ghh) are obtained. Results indicate
LINEAR ELASTIC STIFFNESS
5000
Ev SLB Sand
Ev/(F(e)Pa) or Eh/(F(e)Pa)
Eh SLB Sand
451
Ev Toyoura Sand E Ehv Toyoura Toyoura sand Sand
4000
3000
2000
1000
For Ev (or Eh) measurement, σv/Pa (or σh/Pa) is varied between 1.0 and 2.0 at each σv (or σh)
1.0
1.5 σv/Pa or σh/Pa
2.0
Figure 11.117 Poission’s ratio as a function of anisotropic
stresses (Hoque and Tatsuoka, 1998).
(a) Ev versus σv and Eh versus σh
Ev/(AEF(e)σv)
Eh SLB Sand
Eh Toyoura Sand
1.2
1.0
0.8
0.0
1.0
2.0 3.0 σ’h/P a
4.0
(b) E v versus σh Figure 11.116 Vertical and horizontal Young’s modulus as
Figure 11.118 Stiffness anisotropy of undisturbed London
a function of anisotropic stresses for Toyoura sand (Hoque and Tatsuoka, 1998).
clay under isotropic stress conditions (Jovicic and Coop, 1998).
that, for a given confining pressure, the values of Ghh are larger than those of Gvh ⬇ Ghv. Hence, the soil is inherently stiffer horizontally than vertically due to its soil fabric. The reported data on clay under isotropic stress conditions consistently show that Ghh is approximately 50 percent larger than Gvh, indicating inherent anisotropic characteristics caused by orientation of platy clays (Pennington et al., 1997; Jovicic and Coop, 1998). The ratios of Ghh /Gvh for six Italian clays measured in onedimensional consolidation tests were between 1.3 and 2.0, and the ratio increased with overconsolidation ratio (Jamiolkowski et al., 1995).
For sands, most studies show that the ratio Ghh /Gvh is greater than 1 (e.g., Lo Presti and O’Neill, 1991; Stokoe et al., 1991; Bellotti et al., 1996). However, reported values for the ratio of Ev /Eh are inconclusive; some sands are stiffer in the vertical direction (Hoque and Tatsuoka, 1998), whereas the others are stiffer in the horizontal direction (Stokoe et al., 1991). Anisotropic properties are related to fabric (contact) anisotropy, and therefore the mixed results obtained may be due to the differences in sample preparation procedures. The experimental data show that the small strain stiffness is rather insensitive to the strain rate and number of loading cycles as long as the loading is within
11
STRENGTH AND DEFORMATION BEHAVIOR
the true elastic range but that the elastic limit strain increases with strain rate (Shibuya et al., 1992; Tatsuoka et al., 1997). Resonant column tests on clays and sands show that the small strain shear modulus is independent of frequency in the range of 0.05 to 2500 Hz (e.g., Hardin and Richart, 1963; Hardin and Drnevich, 1972; Stokoe et al., 1995). Although conservation of energy may be an issue for true elastic response, experimental evidence indicates that energy is dissipated even at this strain level and damping values are typically 0.35 to 1 percent for sands and 1.0 to 1.5 percent for clays. Similar to the small strain stiffness, the damping at very small strain also depends on confining pressure and the following empirical form is proposed (Hardin, 1965): ⫽ Bpm
(11.72)
where B and m are material constants. The reported values of the exponent m range from ⫺0.05 to ⫺0.22 (Santamarina and Cascante, 1996; Stokoe et al., 1999). Although the particles in contact are not moving relative to each other, some microscopic proportion of the contact area can slide or slip, which is known as the stick–slip frictional contact loss. Micromechanical analysis considering the energy dissipation by this behavior gives m ⫽ ⫺–23 . Santamarina and Cascante (1996) attribute the difference to other attenuation mechanisms available in soils. These include chemical interaction of adsorbed layers at contacts, wave scattering, thermal relaxation, and other forms of energy coupling (e.g., mechanoelectromagnetic, mechanoacoustic). The damping is also affected by loading frequency, which is further described in Chapter 12. It has been argued that the use of the empirical equations presented above may produce nonconservative ‘‘elastic’’ response in terms of energy conservation (i.e., it may generate energy during a closed stress loop) (Zytynski et al., 1978). To be thermomechanically consistent, theoretical models for the pressuredependent stiffness of soils are available (e.g., Houlsby, 1985; Hueckel et al., 1992; Borja et al., 1997; Einav and Puzrin, 2004). They show that, if both shear and bulk moduli are to be mean pressure dependent, the stiffness needs to be anisotropic and stress induced. This is important in deformation analysis since the anisotropic stiffness in turn leads to cross dependence between shear behavior and volumetric behavior (Graham and Houlsby, 1983).
analysis. For instance, assume that the true elastic axial stiffness of a soil is 100 MPa. Considering that the elastic threshold axial strain is of the order of 10⫺5, the axial stress increment required to reach to this strain level is only 1 kPa. Hence, errors in stiffness of 100 percent result in small differences in the associated stress increments (a few kilopascals). Typical strain levels under working loads are usually in an intermediate level between linear elastic and plastic deformation, and, therefore, the knowledge of nonlinear (zone 2) and irreversible (zone 3) deformation characteristics is more important for evaluating ground movements accurately. Stiffness degradation from small strains to intermediate strains has been recognized in resonant column testing since the 1960s when the soil was subjected to cyclic loading (Hardin and Drnevich, 1972). Nowadays, detailed characterization of deformation properties at intermediate strain levels is possible with the use of local strain measurement systems, as described previously. The shear modulus decreases and the damping increases as the shear strain increases because of structural breakdown that results in a decreasing proportion of elastic deformation and an increasing proportion of plastic strain with increasing shear strain. The shear modulus degradation curves of Ticino sand, obtained by monotonic and cyclic loadings using various testing apparatus (triaxial compression, torsional shear, and resonant column) are shown in Fig. 11.119 (Tastuoka et al., 1997). The small strain stiffness is nearly independent of the test type, but at larger strains, the cyclic loading gives consistently larger shear modulus com-
Monotonic Triaxial Monotonic Torsional Shear Cyclic Triaxial Cyclic Torsional shear Resonant Column
100
Secant Shear Modulus G G
452
80 60
40
20
Ticino Sand σ’0 = 49 kPa e = 0.640
0 10-4
11.19 TRANSITION FROM ELASTIC TO PLASTIC STATES
In some cases, accurate evaluation of stiffness values at very small strains may not be crucial in geotechnical
10-3
10-2
10-1
100
Shear Strain γ (%) Figure 11.119 Stiffness degradation of Ticino sand obtained by monotonic and cyclic loadings using various testing apparatus (Tatsuoka et al., 1997).
TRANSITION FROM ELASTIC TO PLASTIC STATES
pared to the monotonic loading at a given strain level. This is because the soil densifies during cyclic loading and the number of loading cycles has an effect on stiffness. As noted earlier, the shear strain level that gives an onset of permanent volumetric strain in drained conditions or residual excess pore pressures in undrained conditions after unloading is called the volumetric threshold strain. The stiffness degradation curve is influenced by many factors such as stress state, stress path, soil type, and soil fabric (i.e., anisotropy). For example, Fig. 11.10 shows the stiffness degradation of sands and clays subjected to increase in shear stress at different confining pressures. The effect of stress path directions on the stiffness degradation curve is shown in Fig. 11.120 (Atkinson et al., 1990). Triaxial tests were performed on reconstituted overconsolidated London clay specimens in such a way as to maintain a constant mean pressure. Different stiffness degradation curves were obtained even though they were sheared along the same stress path (OX in Fig. 11.120a). This is be-
453
cause the specimens had different stress path histories prior to shearing (AO, BO, CO, and DO) [termed recent stress history by Atkinson et al. (1990)], and stiffer response was obtained when the stress path was reversed (D → O → X). The use of the multisurface concept described in Section 11.17 conveniently explains this complex deformation behavior. Since the small strain elastic stiffness is also influenced by the same factors, the stiffness degradation curves are sometimes normalized by the small strain stiffness; G/Gmax versus log or E/Emax versus log a. A summary of normalized shear modulus degradation curves for a variety of soils are shown in Fig. 11.121 (Kokusho, 1987). The curve for modulus degradation with increasing strain may be somewhat flatter for gravels than that for sands and clays. The curves tend to move to the right as the confining pressure increases; it is possible that the degradation curve at very high confining pressure (in the megapascal range) may lie beyond the bands given in Fig. 11.121 (Laird and Stokoe, 1993).
Deviator stress q (kPa)
Sands and Gravels
The following relationship can be used for the dynamic shear modulus of sands and gravels at different strain levels (Seed et al., 1984):
X 100
D
0
C
O
100
200
400 Mean Pressure p (kPa)
B
-100
冉冊
G p ⫽ 22.1K2 pa pa
A
1/2
(11.73)
where p is the mean effective principle stress, pa is the atmospheric pressure, and K2 is a coefficient that depends primarily on grain size, relative density, and shear strain. The coefficient K2 is generally greater by a factor from about 1.35 to 2.5 for gravels than for sands. Values of K2 vary with relative density and shear
(a)
40
(A➝)O➝X 20 (C➝)O➝X 10 (B➝)O➝X 0 10-2
10-1 100 Deviator strain γ (%)
101
(b)
Figure 11.120 Recent stress history effect on stiffness deg-
radation: (a) stress paths and (b) stiffness degradation on OX stress path (from Atkinson et al., 1990).
Shear Modulus Ratio G/Gmax
Shear Modulus G (MPa)
(D➝)O➝X 30 1.0
Clay, 100 kPa
0.5
Sand, 50 kPa Gravel, 50 ~ 830 kPa 0.0 10-4
10-3
10-2
10-1
100
Shear Strain γ (%)
Figure 11.121 Normalized stiffness degradation curves of various types of soils (Kokusho, 1987).
454
11
STRENGTH AND DEFORMATION BEHAVIOR
strain approximately as shown in Fig. 11.122 and with void ratio and shear strain as shown in Fig. 11.123. Equation (11.73) assumes that the exponent is –12 . Experimental evidence suggests that the exponent increases with strain level as shown in Fig. 11.124 and reaches 0.8 to 0.9 at a strain level of 1 percent (Jovicic and Coop, 1998; Yamashita et al., 2000). Values of the damping ratio for sands and gravels are about the same, and they are only slightly influenced by grain size and density. The ranges of values as a function of cyclic shear strain are shown in Fig. 11.125. The damping value decreases with increasing number of loading cycles and confining pressure, and much of the decrease occurs in the first 10 cycles (Stokoe et al., 1999). Clays
Although the variation of shear moduli and damping ratio with shear strain is relatively independent of composition for sands and gravels, the same is not the case for cohesive soils. Curves of the type shown in Figs. 11.121 and 11.125 are displaced to the right for clays with increasing plasticity, as shown by Fig. 11.126. These relationships were developed by Vucetic and
Dobry (1991) based on the results of a review of available cyclic load data from 16 different studies. The influences of various compositional and environmental factors on shear modulus and damping ratio of normally consolidated and moderately overconsolidated clays are listed in Table 11.10. Vucetic and Dobry (1991) hypothesized that increasing plasticity influences the degradation curves in the following manner. Increasing plasticity index reflects decreasing particle size and increasing specific surface area. The number of interparticle contacts becomes large, and interparticle electrical and chemical bonding and repulsive forces become large relative to the particle weights in comparison with sands. The many bonds within the microstructure act as a system of relatively flexible linear springs that can resist larger shear strains (up to 0.1 percent before they are broken) than is the case for sands, wherein particle elasticity is practically the only source of linear behavior, and interparticle sliding at contacts may start at strains as low as percent with the onset of plastic deformations. To these ideas might be added the fact that the thin, platy morphology of most clay particles make them able to deform elastically to considerably greater levels
Figure 11.122 Shear modulus factor K2 for sands as a function of relative density and shear
strain (Seed et al., 1984).
TRANSITION FROM ELASTIC TO PLASTIC STATES
455
Figure 11.123 Shear modulus factor K2 for sands as a function of void ratio and shear strain (Seed et al., 1984).
Figure 11.124 Variation of the shear modulus n exponent
value with strains on Dogs Bay sand (Jovicic and Coop, 1997).
Figure 11.125 Damping ratios for sands and gravels (Seed
et al., 1984).
456
11
STRENGTH AND DEFORMATION BEHAVIOR
Figure 11.126 Normalized modulus and damping ratio as a function of cyclic shear strain showing the influence of soil composition as measured by plasticity index (from Vucetic and Dobry, 1991). Reprinted with permission of ASCE.
of strain than is possible for the bulky, stiff granular particles. Furthermore, the several orders-of-magnitude smaller size and greater number of interparticle contacts per unit volume for the cohesive materials mean that even minute elastic distortions at interparticle contacts can give a cumulative strain that is large. For a cohesionless soil to develop such large shear deformations would require much greater displacements at intergrain contacts than could be accommodated without sliding.
11.20
PLASTIC DEFORMATION
Irrecoverable plastic strain initiates at a shear strain level of approximately 10⫺2 percent, and the amount of plastic strain increases with further deformation. A
fully plastic state is obtained when the stress state reaches the yield envelope as discussed in Section 11.17. As long as the stress state during and after geotechnical construction is within the yield envelope, the strain generated is elastic dominated. Hence, in order to control ground deformation in overconsolidated clays, it is useful to keep the construction-induced stress paths within the yield envelope. Once the stress state reaches the yield envelope, the generated strain will be plastic dominated. Generation of plastic strains is often unavoidable in normally and lightly overconsolidated clays because the initial stress state is either already on or near the yield envelope. The most important mechanical feature of soil in the plastic state is dilatancy, in which there is coupling between shear and volumetric deformations. That is, dense sands and heavily overconsolidated clays exhibit volume dilation in drained conditions and negative excess pore pressure generation in undrained conditions, whereas loose sands and normally consolidated and lightly overconsolidated clays exhibit volume contraction in drained conditions and positive excess pore pressure generation in undrained conditions. The rule that governs the generation of plastic volumetric strain associated with plastic deviator strain is called the dilatancy (or flow) rule. Some examples of this for dense sands were already presented in Eqs. (11.34) and (11.35), in which the degree of dilatancy [dy/dx in Eq. (11.34) and in Eq. (11.35)] is related to the applied principal stress ratio (or the mobilized friction angle) and the internal friction angle. These observations are important because the incorporation of stress–dilatancy into plasticity theory can lead to a useful form of constitutive modeling for soils. The development of plastic strains is often characterized by the following three aspects of soil behavior: (a) yield envelope, (b) dilatancy rule, and (c) hardening rule, which relates the change in the size of yield envelope to plastic strain increments. By assigning mathematical functions to these three aspects of soil behavior, a plastic constitutive model can be developed. Detailed review and development of all recent plasticity theories and proposed constitutive soil models are beyond the scope of this book. However, some essential aspects of soil behavior observed during plastic deformation are summarized here. Yield Envelope and Hardening
The yield envelope defines the stress state when there is full development of plastic strains. Typical yield envelopes measured for a natural clay consolidated at different confining pressures are shown in Fig. 11.127.
457
PLASTIC DEFORMATION
Table 11.10 Effect of Various Compositional and Environmental Factors on Maximum Shear Modulus Gmax, Modulus Ratio G /Gmax, and Damping Ratio of Normally Consolidated and Moderately Overconsolidated Clays Increasing Factor (1) Confining pressure, 0 (or vc) Void ratio, e Geologic age, tg Cementation, c Overconsolidation, OCR Plasticity index, PI
Cyclic strain, c Strain rate, ˙ (frequency of cyclic loading)
Number of loading cycles, N
Gmax (2) Increases with 0 Decreases with e Increases with tg Increases with c Increases with OCR Increases with PI if OCR ⬎ 1; stays about constant if OCR ⫽ 1 — Increases with ˙
Decreases after N cycles of large c but recovers later with time
(4)
G/ Gmax (3) Stays constant or increases with 0 Increases with e May increase with tg May increase with c Not affected
Stays constant or decreases with 0 Decreases with e Decreases with tg May decrease with c Not affected
Increases with PI
Decreases with PI
Decreases with c G increases with ˙ ; G/ Gmax probably not affected if G and Gmax are measured at same ˙ Decreases after N cycles of large c (Gmax measured before N cycles)
Increases with c Stays constant or may increase with ˙
Not significant for moderate c and N
From Dobry and Vucetic (1987).
Some observations can be made from this figure as follows: 1. The yield envelope is a function of stress and its size is controlled by stress history variables such as preconsolidation pressure. This is often expressed mathematically as F(, pc, ) ⫽ 0
Figure 11.127 Yield surfaces of Winnipeg clay at different
confining pressures (Graham et al., 1983b).
(11.74)
where is the effective stresses, pc is the preconsolidation pressure, and is the rotation angle of the yield envelope with respect to the mean pressure axis. The yield envelopes of intact samples are larger than those of remolded (or destructured) samples; geological aging processes and cementation produce large yield envelopes for intact clays as shown in Fig. 11.128. When the cementation bonding breaks down and the soil becomes destructured, the yield envelope can become smaller.
458
11
STRENGTH AND DEFORMATION BEHAVIOR
0.6
tions [i.e., (a) triaxial compression, (b) isotropic, and (c) triaxial extension]. A mathematical form that describes the change in with generation of plastic strains is called the rotational hardening rule.
Intact State
(σa – σr)/2σp
Destructured State 0.4
Magnitude of Plastic Strains and Stress–Dilatancy 0.2
0 0
0.2
0.4 0.6 (σa+ σr)/2σp
0.8
1.0
0.8
1.0
(a) 0.6
Intact State
(σa – σr)/2σp
Destructured State 0.4
0.2
0 0
0.2
0.4
0.6
(σa+σr)/2σp
Once the stress state is on the yield envelope, the soil is in the fully plastic state. The arrows in Fig. 11.129 show the vector magnitude of plastic strains measured for a given stress increment. The vertical component of the arrows is the deviator plastic strain increment d ps (or d p), whereas the horizontal component is the volumetric plastic strain increment dpv.25 Similarly, the plastic strain vectors measured in Winnipeg clay are shown in Fig. 11.130 (Graham et al., 1983b). The vector of the plastic strain increment appears to be a function of the current stress state. This observation leads to the concept of stress–dilatancy. Dilatancy during plastic deformation can be expressed as the ratio of plastic volumetric strain increment dpv to plastic deviatoric increment dsp; D ⫽ dpv /dsp. For clays, the value of D can be expressed as a function of stress ratio and material constants. For instance, the following stress–dilatancy equation can be proposed based on Taylor’s equation (11.34)26: dpv q ⫽M⫺ ⫹ 0 p ds p
(b) Figure 11.128 Yield surfaces of intact and destructured soft
clays: (a) Saint Alban clay and (b) Ba¨ckebol clay (Leroueil and Vaughan, 1990).
2. The yield envelope increases in size with increasing preconsolidation pressure pc, which is often associated with the generation of plastic volumetric strain. The size increases as the soil is more densely packed along the normal consolidation line. A mathematical form that describes the change in pc with generation of plastic strains is called the hardening rule. 3. The shape of the yield envelope is often an inclined ellipse in the p –q plane. The inclination is related to the anisotropic consolidation history as well as the anisotropic fabrics. Some yield envelopes of sands are shown in Fig. 11.129 (Yasufuku et al., 1991). The yield envelopes were determined by applying different stress paths and connecting the stress state when the plastic strains initiate for a given stress path. The shape of the yield envelopes resembles a tear drop, and the inclinations of the yield envelopes are clearly affected by the initial anisotropic stress condi-
(11.75)
where 0 is the initial anisotropy (e.g., Sekiguchi and Ohta, 1977). When 0 ⫽ 0, the equation becomes the stress–dilatancy rule used in the Cam-clay model (Roscoe and Schofield, 1963). Soil exhibits contractive behavior when the dilation angle is negative and q/p is less than M ⫹ 0, whereas the soil exhibits dilative behavior when the dilation angle is positive and q/p is more than M ⫹ 0. Figure 11.131 shows the stress– dilatancy relationship for the data presented in Fig. 11.130. The data follow a similar trend to Eq. (11.75). Other stress–dilatancy rules that are used to derive constitutive models for clays are available. Experimental evidence suggests that the stress– dilatancy relationship for sand depends on confining pressure and density as well as soil fabric, compared to a simpler form used in clays such as Eq. (11.75). Rowe (1962) derived the following stress–dilatancy
In triaxial condition, dpv ⫽ dpa ⫹ 2drp, dsp ⫽ (–23 )(dpa ⫺ dpr ), and d p ⫽ dpa ⫺ dpr , where dpa is the axial plastic strain and dpr is the radial plastic strain. 26 Note that Taylor’s expression was for the peak state only. This equation is applied to all stress state conditions under plastic deformation for both loose and dense cases. 25
459
PLASTIC DEFORMATION
q (MPa)
q (MPa)
q (MPa)
0.8
0.8
0.8
0.6
0.6
0.4
0.4
0.6 Initial State
0.4
0.2
0.2 0.0
Initial State
(MPa) 0.2
0.4 0.6
0.8
0.0
1.0 p’
0.2
0.2
(MPa)
0.4 0.6
0.8
(MPa)
0.0
1.0 p’
-0.2
-0.2
-0.2
-0.4
-0.4
-0.4
(a)
Initial State
0.2
0.4 0.6
(b)
0.8
1.0 p’
(c)
Figure 11.129 Yield surfaces of sands with different initial stress histories. Initial states (a) compression, (b) isotropic, and (c) extension (Yasufuku et al., 1991).
dε p
Cam-clay (Roscoe and Schofield, 1963) dε pv/dε ps = M - q/p
dεsp Stress Ratio q/p'
dε vp 0.6
q/σp
0.4
1.4
1.2 Modified Cam-clay (Roscoe and Burland, 1968) dε pv/dε ps = [M2 - (q/p)2]/ 2(q/p) 1 0.8 Modified Cam-clay
Data from Graham et al. (1983). See Fig 11.130
0.6 0.4
0.2
0.2 Cam-clay
0 0
0.2
0.4
0.6
0.8
1.0
-2.5
-2
-1.5
-0.5
0 0
0.5
1
1.5
2
2.5
p
Plastic Strain Ratio (-dε pv/dε s)
p/σp
Figure 11.130 Plastic strain vectors at yielding of natural
-1
Figure 11.131 Stress dilatancy relations of natural Winnipeg
Winnipeg clay (Graham et al., 1983b).
clay (Wood, 1991).
rule for sand in triaxial loading based on his experimental data as well as theoretical analysis:
respectively. Equations (11.76) and (11.77) have a similar form to Eq. (11.75), in which the dilation depends on stress ratio and material constants.27 However, Rowe (1962) noted that the material constant c used in Eqs. (11.76) and (11.77) is influenced by the density. Different initial anisotropic stress states give different
冉 冊 冉
冊
a ⫺2dpr c ⫽ tan2 ⫹ p r da 4 2
in triaxial compression
冉 冊 冉
r ⫺dap c ⫽ tan2 ⫹ a 2drp 4 2
in triaxial extension
(11.76)
冊
Equations (11.76) and (11.77) can be rewritten in terms of p, q, d pv, and d p (Pradhan and Tatsuoka, 1989): 27
(11.77)
where dpa and dpr are the axial and radial strain increments, c is the ‘‘characteristic friction angle’’ and a and r are the axial and radial effective stresses,
冋 冋
册 册
q 3 (2K ⫹ 1)(⫺d pv / d p) ⫹ 2(K ⫺ 1) ⫽ p 2 (K ⫺ 1)(⫺d vp / d p) ⫹ (K ⫹ 2) q 3 (K ⫹ 2)(⫺d pv / d p) ⫺ 2(K ⫺ 1) ⫽ p 2 (1 ⫺ K)(⫺d vp / d p) ⫹ (2K ⫹ 1) where K ⫽ (1 ⫹ sin c) / (1 ⫺ sin c).
for d pa ⬎ 0 for d pa ⬍ 0
460
11
STRENGTH AND DEFORMATION BEHAVIOR
stress–dilatancy curves as shown in Fig. 11.132. The curves were derived from the data presented in Fig. 11.129 and are presented in terms of stress ratio q/p and plastic strain increment ratio d pv /d p. Hence, the stress–dilatancy relationship of a sand depends not only on stress ratio but also on density, confining pressure and initial anisotropic stress conditions. As noted in Eqs. (11.75) to (11.77) and Figs. 11.131 and 11.132, the development of plastic increments is governed by the current stress state. This is in contrast to elastic deformation, which is related directly to stress increments. For example, for an isotropic elastic model, dev dp G ⫽3 e ds dq K
(11.78)
where G is the shear modulus, K is the bulk modulus and dev and dse are the elastic volumetric and deviatoric strains, respectively. The physical mechanisms of elastic deformation and plastic deformation are fundamentally different, that is, stress increment dependent versus stress dependent. Because of this, the same stress increment may give very different strain increments. Careful selection of elastic and/or plastic models is therefore necessary in ground deformation analysis.
Stress Ratio q/p Case (a)
2.0
Case (b) Case (c)
1.5
in Fig.11.129 1.0
Compression
0.5
-4
-3
-2
-1
0
1
?
-0.5
2
3 4 Strain Increment ratio -dεvp/dγ p
?
-1.0
Extension
Figure 11.132 Stress dilatancy relations of sands with dif-
ferent initial anisotropic stress conditions (Yasufuku et al., 1991).
11.21
TEMPERATURE EFFECTS
The average ground temperature varies between 7 and 10, whereas laboratory conditions are between 18 and 23. In some situations, the soil can undergo large temperature change, for example, ground freezing, heating of nuclear waste repositories, underground storage reservoirs, and the like. It can be important to recognize the significance of temperature when evaluating strength and model parameters. In general, increase in temperature will result in thermal expansion of soil grains as well as pore fluid. The particle contact properties will also be modified. A change in temperature, therefore, causes either a change in void ratio or a change in effective stress (or a combination of both) in a saturated clay, as described in Section 10.12. In this section some effects of temperature on shear resistance of soils are considered. A change in temperature can cause a strength increase or a strength decrease depending on the circumstances (e.g., temperature variation during initial consolidation or during shearing in drained or undrained conditions), as illustrated by Fig. 11.133. The higher the consolidation temperature, the greater the shear strength at any given test temperature because of the greater decrease in void ratio at the higher consolidation temperatures.28 In Fig. 11.133, Tc represents the temperature at consolidation and Ts the temperature of shear for consolidated undrained direct shear tests on highly plastic alluvial clay. For a given consolidation temperature Tc, the undrained strength decreases in a regular manner with the increasing test temperature. From tests such as these, it has been established that for given initial conditions the undrained strength of normally consolidated saturated clay may decrease by about 10 percent for a temperature increase from 0 to 40C. For overconsolidated clays, the undrained shear strength is less influenced by temperature (Marques et al., 2004). The relative insensitivity of overconsolidated clay to temperature may be due to the compensating effects of increase stiffness and softening of soil structure by volume expansion as described in Section 10.12. Similar to the strain rate effect, the preconsolidation pressure, and hence the size of the yield envelope, decreases with increase in temperature, as illustrated in Fig. 10.46 and Fig. 11.134 for natural clay specimens tested between 10 and 50. Hence, the weakening of
For all tests, Ts Tc to prevent further consolidation under a higher temperature, which would result in the strength being about the same as if it had been consolidated under the higher temperature initially.
28
TEMPERATURE EFFECTS
461
Figure 11.133 Effect of consolidation and test temperatures on the strength of alluvial clay
in direct shear (Noble and Demirel, 1969).
Figure 11.134 Influence of temperature on yield surface of a St-Roch-de-l’Achigan clay, Quebec (Marques et al., 2004).
soil structure by increase in temperature is apparent. On the other hand, the critical state friction angle is found to be independent of temperature (Hueckel and Baldi, 1990; Graham et al., 2001; Marques et al., 2004). Drainage conditions during heating prior to shear are important, as illustrated in Fig. 11.133. If drainage is prevented, the expansion of water controls the expan-
sion of soil volume because thermal expansion of water is much larger than that of soil particles. This results in generation of positive excess pore pressure and, as a consequence, undrained stiffness and shear strength decrease as shown in Fig. 11.16. If drainage is allowed, the expanding water is free to drain and hence the volume change of the soil is governed by the expansion of soil particles and the
462
11
STRENGTH AND DEFORMATION BEHAVIOR
change in particle contact conditions. Normally consolidated clays often result in decrease in void ratio, and hence the initial stiffness generally increases with temperature. However, it has been reported that the decrease in void ratio in normally consolidated clays cannot be solely accounted for the increase in stiffness (Tsuchida et al., 1991; Kuntiwattanakul et al., 1995). This observation is similar to the aging effect discussed in Chapter 12. Hence, it can be considered that temperature is one of the driving forces in time-dependent deformation of soils, and the rate process theory described in the next chapter conveniently explains much of the observed temperature–time–effective stress behavior of soils.
11.22
CONCLUDING COMMENTS
Limit equilibrium and plasticity analyses, as done, for example, in studies of slope stability, lateral pressure, and bearing capacity, depend on accurate representation of soil strength. So also does soil resistance against failure due to earthquakes or other cyclic loadings. The stresses and deformations under subfailure loading conditions depend on stress–strain properties. The factors responsible for and influencing strength have been identified and analyzed. The strength of most uncemented soils is provided by interparticle sliding, dilatancy, particle rearrangements, particle crushing, and true cohesion. Frictional resistance is developed by adhesion between contacting asperities on opposing particle surfaces. Values of true friction angle () range from less than 4 for sodium montmorillonite to more than 30 for feldspar and calcite. In the absence of cementation, true cohesion in soils is small. Results from discrete particle simulations indicate that the deviatoric load applied to a particle assembly is transferred exclusively by the normal contact forces in the strong force networks. The interparticle friction therefore acts as a kinematic constraint of the strong force network and not as the direct source of macroscopic resistance to shear. The residual friction angle depends on gradation, mineralogical composition, and effective stress. The value of residual friction angle for clay may decrease by several degrees for increases in effective stress on the shear surface from 0 to 400 kPa (0 to 60 psi). The shear displacements in one direction required to develop residual strength may be several tens of millimeters. These factors should be taken into account when analyzing stability problems. Loose sands behave like normally consolidated clays. The behavior of dense sand appears to be similar to that of overconsolidated clays. However, for clays,
a dense state (below critical state) can only be achieved by unloading, and, therefore, the preconsolidation pressure can be used to characterize the peak strength and deformation. For sands, on the other hand, the difference in strength and deformation behavior of normally consolidated dense sand and overconsolidated sand is noted even when they are at the same void ratio and confining pressure. This is because of possible different soil fabrics. The critical friction angle of cohesionless soils contains contributions from particle crushing, particle rearrangement by rolling, as well as from interparticle sliding. The critical state concept can be used to characterize the density effect on peak strength for normally consolidated sand. Rearrangement and rolling are unimportant when the clay content is high enough to prevent granular particle interference. Ideally, the critical state strength or friction angle should be used for design of simple geotechnical structures. Otherwise, a careful selection of safety factor is needed when the peak strength or peak friction angle is used. However, whether it is possible to find the true critical state from conventional triaxial and torsional shear tests is questionable, especially for sands. Because of the great diversity of soil types and the range of environmental conditions to which they may be subjected, evaluations of deformation and strength, their characterization for analyses, and prediction of future behavior will continue as major components of any project. In the majority of geotechnical engineering projects and problems, correct site characterization and property evaluation are the two most critical elements. If they are not done reasonably and reliably, then there cannot be understanding or confidence from subsequent soil mechanics analyses, no matter how sophisticated they may be or how powerful the computer that provides the numerical solutions.
QUESTIONS AND PROBLEMS
1. Based on the descriptions given in Section 11.3 and 11.6, summarize microscopic interpretation of overconsolidation, compaction, dilation, peak friction angle, and critical state friction angle. 2. A clay has liquid and plastic limits of 80 and 25, respectively. For the following conditions, find possible plastic failure mechanisms at different confining pressures using Eq. (11.30) and Fig. 11.46. Discuss any practical implications. a. The clay is consolidated to a water content of 65 percent. b. The clay is heavy compacted to a water content of 25 percent.
QUESTIONS AND PROBLEMS
3. A quartz sand has minimum and maximum void ratios of 0.35 and 0.75, respectively. The critical state friction angle is 35. a. Using Eqs. (11.31) and (11.32), plot the critical state line on the p –q plane and on the e–log p plane. b. Find the undrained shear strengths at critical state when the void ratios are 0.4 and 0.7. Does the initial effective stress state matter to the computed values? How about the values of excess pore pressure generated during undrained tests? c. Draw the effective stress path of a drained triaxial compression test on the p –q plane. The initial effective isotropic confining pressure is 100 kPa. Find the drained strength and void ratio at critical state. d. Sketch possible stress–axial strain and axial strain–void ratio curves of the drained triaxial compression test considered in part (c). Consider two different initial void ratios: (i) e ⫽ 0.4 and (ii) e ⫽ 0.7. Comment on the results. e. Repeat the calculations of parts (c) and (d) when the initial confining pressure is 1 MPa. Comment on the results. 4. Using the critical state of the sand defined in Question 3, plot void ratio versus peak friction angle at three different confining pressures: (i) 5 kPa, (ii) 500 kPa, and (iii) 5 MPa. To develop the plot, try (i) Eq. (11.37) or (ii) Fig. 11.56. Comment on the results by discussing the relative importance of confining pressure and void ratio on friction angle of soils. 5. A clay was isotropically normally consolidated and the isotropic compression line was found to be e ⫽ 1.5 ⫺ 0.35 ln p. The clay was then unloaded isotropically and the slope of unloading line on a e–ln p diagram was found to be ! ⫽ 0.05. A series of undrained triaxial compression tests were performed on the clay, and the critical state was found to be q ⫽ 0.8p and ecs ⫽ 1.3 ⫺ 0.35 ln p. Plot the stress and state paths on the p –q plane and the e–ln p plane for the following conditions: a. The clay is isotropically consolidated to 400 kPa along the isotropic compression line. b. The clay at state (a) is sheared in undrained conditions to the critical state. Also, sketch a possible stress–strain relationship. c. The clay at state (a) is unloaded isotropically to 200 kPa (OCR ⫽ 2).
463
d. The clay at state (c) is sheared in undrained conditions to the critical state. Also, sketch a possible stress–strain relationship. e. Repeat parts (c) and (d) for other OCR conditions. Comment on the results. 6. The virgin compression curve of a clay was found to be e ⫽ 1.3 ⫺ 0.6 log v from one-dimensional consolidation tests. The swelling index Cs was 0.1. The clay was preconsolidated to v ⫽ 100 kPa prior to shearing. a. Using the Hvorslev parameters of hc ⫽ 0.1 and e ⫽ 15, plot the failure envelope on the – plane. b. Plot shear strength f / v as a function of OCR and compare the results to the data shown in Fig. 11.65. 7. Why does a sample with shear bands give different strengths depending on sample size? 8. Find a case study that describes the importance of knowing the residual friction angle of clay. Explain (a) the geologic and hydrogeologic conditions, (b) the possible peak, critical, and residual friction angles, and (c) microscopic interpretation of decrease in friction angle at residual state. 9. Consider two saturated samples of the same soil having exactly the same water content, density, temperature, and structure are initially at equilibrium under the same effective stress states. Compare and explain differences in strength, if any, that you would expect if a. One is loaded in triaxial compression and the other in plane strain. b. One is tested in triaxial compression and the other is tested in plane stress. c. One is tested as is and the other is tested after heating with (i) no drainage allowed and (ii) full drainage is allowed. d. One is tested in triaxial compression and the other is tested in triaxial extension. 10. An embankment is to be constructed on a soft clay, and a potential failure surface is shown in the figure below. The clay possesses anisotropic fabric. Considering the intermediate stress effect and anisotropy effects described in Section 11.12, consider possible stress paths from the stress before the construction and discuss what strength values should be used in design for the following locations in the clay: (i) location A, which is located underneath the embankment, (ii) location B, which is at some depth near the toe of the embankment,
464
11
STRENGTH AND DEFORMATION BEHAVIOR
and (iii) location C, which is located some distance away from the embankment.
11. Find a paper that describes the effects of soil fabric on liquefaction resistance of sands. Give the microscopic interpretation of why a sample with a certain soil fabric generates more excess pore pressures than others. 12. Provide physical explanations of how and why the following factors can affect the cyclic resistance ratio (CRR) of sands: a. Confining pressure b. Initial K0 stress condition c. Static shear stress along the sloping ground d. Shear modes (triaxial compression and extension, simple shear, etc.) e. Sample preparation and soil fabric f. Silt fines and clay fines 13. Water is injected into overconsolidated clay with an OCR of approximately 3. Using the correlations and data presented throughout the book, estimate the injection pressure required to fracture the clay
at a depth of 20 m. Consider both fracturing in (i) undrained conditions assuming that the injected fluid has not permeated into the ground and (ii) drained conditions assuming the injection is in a steady state seepage state. 14. Convert some of the stiffness degradation curves plotted in Figs. 11.10 and 11.119 to shear stress versus logarithm of strain. Identify the shear stresses required to reach the boundaries of different zones described in Section 11.17. Discuss which zones are important for what type of geotechnical activities. 15. Give physical microscopic explanations of different stiffness degradation curves presented in Fig. 11.120. Why can the multisurface concept presented in Section 11.17 be used to model this complex behavior? 16. Discuss the differences between elastic and plastic deformations of soils as microscopic behavior and macroscopic behavior. 17. The data showing volume reduction with increasing temperature at a given pressure were presented in Fig. 10.44 (Campanella and Mitchell, 1968). If we consider the normal compression curve at 76.5F to be the reference state, the compression curves at the other temperatures can be interpreted to have exhibited temperature-induced creep behavior and hence reached the quasioverconsolidated state. Can the data presented in Fig. 11.133 be explained in such a way using the Hvoslev strength concept for overconsolidated clays?
CHAPTER 12
Time Effects on Strength and Deformation
12.1
INTRODUCTION
Virtually every soil ‘‘lives’’ in that all of its properties undergo changes with time–some insignificant, but others very important. Time-dependent chemical, geomicrobiological, and mechanical processes may result in compositional and structural changes that lead to softening, stiffening, strength loss, strength gain, or altered conductivity properties. The need to predict what the properties and behavior will be months to hundreds or thousands of years from now based on what we know today is a major challenge in geoengineering. Some time-dependent changes and their effects as they relate to soil formation, composition, weathering, postdepositional changes in sediments, the evolution of soil structure, and the like are considered in earlier chapters of this book. Emphasis in this chapter is on how time under stress changes the structural, deformation, and strength properties of soils, what can be learned from knowledge of these changes, and their quantification for predictive purposes. When soil is subjected to a constant load, it deforms over time, and this is usually called creep. The inverse phenomenon, usually termed stress relaxation, is a drop in stress over time after a soil is subjected to a particular constant strain level. Creep and relaxation are two consequences of the same phenomenon, that is, time-dependent changes in structure. The rate and magnitude of these time-dependent deformations are determined by these changes.
Time-dependent deformations and stress relaxation are important in geotechnical problems wherein longterm behavior is of interest. These include long-term settlement of structures on compressible ground, deformations of earth structures, movements of natural and excavated slopes, squeezing of soft ground around tunnels, and time- and stress-dependent changes in soil properties. The time-dependent deformation response of a soil may assume a variety of forms owing to the complex interplays among soil structure, stress history, drainage conditions, and changes in temperature, pressure, and biochemical environment with time. Timedependent deformations and stress relaxations usually follow logical and often predictable patterns, at least for simple stress and deformation states such as uniaxial and triaxial compression, and they are described in this chapter. Incorporation of the observed behavior into simple constitutive models for analytical description of time-dependent deformations and stress changes is also considered. Time-dependent deformation and stress phenomena in soils are important not only because of the immediate direct application of the results to analyses of practical problems, but also because the results can be used to obtain fundamental information about soil structure, interparticle bonding, and the mechanisms controlling the strength and deformation behavior. Both microscale and macroscale phenomena are discussed because understanding of microscale processes can provide a rational basis for prediction of macroscale responses. 465
466 12.2
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
GENERAL CHARACTERISTICS
1. As noted in the previous section soils exhibit both creep1 and stress relaxation (Fig. 12.1). Creep is the development of time-dependent shear and/or volumetric strains that proceed at a rate controlled by the viscouslike resistance of soil structure. Stress relaxation is a timedependent decrease in stress at constant deformation. The relationship between creep strain and the logarithm of time may be linear, concave upward, or concave downward as shown by the examples in Fig. 12.2. 2. The magnitude of these effects increases with increasing plasticity, activity, and water content 3.
4.
5.
Figure 12.1 Creep and stress relaxation: (a) Creep under
constant stress and (b) stress relaxation under constant strain.
1
The term creep is used herein to refer to time-dependent shear strains and / or volumetric strains that develop at a rate controlled by the viscous resistance of the soil structure. Secondary compression refers to the special case of volumetric strain that follows primary consolidation. The rate of secondary compression is controlled by the viscous resistance of the soil structure, whereas, the rate of primary consolidation is controlled by hydrodynamic lag, that is, how fast water can escape from the soil.
6.
of the soil. The most active clays usually exhibit the greatest time-dependent responses (i.e., smectite ⬎ illite ⬎ kaolinite). This is because the smaller the particle size, the greater is the specific surface, and the greater the water adsorption. Thus, under a given consolidation stress or deviatoric stress, the more active and plastic clays (smectites) will be at higher water content and lower density than the inactive clays (kaolinites). Normally consolidated soils exhibit larger magnitude of creep than overconsolidated soils. However, the basic form of behavior is essentially the same for all soils, that is, undisturbed and remolded clay, wet clay, dry clay, normally and overconsolidated soil, and wet and dry sand. An increase in deviatoric stress level results in an increased rate of creep as shown in Fig. 12.1. Some soils may fail under a sustained creep stress significantly less (as little as 50 percent) than the peak stress measured in a shear test, wherein a sample is loaded to failure in a few minutes or hours. This is termed creep rupture, and an early illustration of its importance was the development of slope failures in the Cucaracha clay shale, which began some years after the excavation of the Panama Canal (Casagrande and Wilson, 1951). The creep response shown by the upper curve in Fig. 12.1 is often divided into three stages. Following application of a stress, there is first a period of transient creep during which the strain rate decreases with time, followed by creep at nearly a constant rate for some period. For materials susceptible to creep rupture, the creep rate then accelerates leading to failure. These three stages are termed primary, secondary, and tertiary creep. An example of strain rates as a function of stress for undrained creep of remolded illite is shown in Fig. 12.3. At low deviator stress, creep rates are very small and of little practical importance. The curve shapes for deviator stresses up to about 1.0 kg/cm2 are compatible with the predictions of rate process theory, discussed in Section 12.4. At deviator stress approaching the strength of the material, the strain rates become very large and signal the onset of failure. A characteristic relationship between strain rate and time exists for most soils, as shown, for example, in Fig. 12.4 for drained triaxial compression creep of London clay (Bishop, 1966)
GENERAL CHARACTERISTICS
467
Figure 12.2 Sustained stress creep curves illustrating different forms of strain vs. logarithm
of time behavior.
and Fig. 12.5 for undrained triaxial compression creep of soft Osaka clay (Murayama and Shibata, 1958). At any stress level (shown as a percentage of the strength before creep in Fig. 12.4 and in kg/cm2 in Fig. 12.5), the logarithm of the strain rate decreases linearly with increase in the
logarithm of time. The slope of this relationship is essentially independent of the creep stress; increases in stress level shift the line vertically upward. The slope of the log strain rate versus log time line for drained creep is approximately ⫺1. Undrained creep often results in a slope be-
468
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
Figure 12.3 Variation of creep strain rate with deviator stress for undrained creep of re-
molded illite.
tween ⫺0.8 and ⫺1 for this relationship. The onset of failure under higher stresses is signaled by a reversal in slope, as shown by the topmost curve in Fig. 12.5. 7. Pore pressure may increase, decrease, or remain constant during creep, depending on the volume change tendencies of the soil structure and whether or not drainage occurs during the deformation process. In general, saturated soft sensitive clays under undrained conditions are most susceptible to strength loss during creep due to reduction in effective stress caused by increase in pore water pressure with time. Heavily overconsolidated clays under drained con-
ditions are also susceptible to creep rupture due to softening associated with the increase in water content by dilation and swelling. 8. Although stress relaxation has been less studied than creep, it appears that equally regular patterns of deformation behavior are observed, for example, Larcerda and Houston (1973). 9. Deformation under sustained stress ordinarily produces an increase in stiffness under the action of subsequent stress increase, as shown schematically in Fig. 12.6. This reflects the time-dependent structural readjustment or ‘‘aging’’ that follows changes in stress state. It is analogous to the quasi-preconsolidation effect
GENERAL CHARACTERISTICS
469
Figure 12.4 Strain rate vs. time relationships during drained creep of London clay (data
from Bishop, 1966).
due to secondary compression discussed in Section 8.11; however, it may develop under undrained as well as drained conditions. 10. As shown in Fig. 12.7, the locations of both the virgin compression line and the value of the preconsolidation pressure, p, determined in the laboratory are influenced by the rate of loading during one-dimensional consolidation (Graham et al., 1983a; Leroueil et al., 1985). Thus, estimations of the overconsolidation ratio of clay deposits in the field are dependent on the loading rates and paths used in laboratory tests for determination of the preconsolidation pressure. If it is assumed that the relationship between strain and logarithm of time during compression is linear over the time ranges of interest and that the secondary compression index Ce is constant regardless of load, the rate-dependent preconsolidation pressure p at ˙ 1 can be related to the axial strain rate as follows (Silvestri et al, 1986; Soga and Mitchell, 1996; Leroueil and Marques, 1996):
冉 冊
p ˙ 1 ⫽ p(ref) ˙ 1(ref)
Ce / (Cc⫺Cr)
⫽
冉 冊 ˙ 1
˙ 1(ref)
(12.1)
where Cc is the virgin compression index, Cr is the recompression index and p(ref) is the preconsolidation pressure at a reference strain rate ˙ 1(ref). In this equation, the rate effect increases with the value of ⫽ Ce /(Cc ⫺ Cr). The variation of preconsolidation pressure with strain rate is shown in Fig. 12.8 (Soga and Mitchell, 1996). The data define straight lines, and the slope of the lines gives the parameter . In general, the value of ranges between 0.011 and 0.094. Leroueil and Marques (1996) report values between 0.029 and 0.059 for inorganic clays. 11. The undrained strength of saturated clay increases with increase in rate of strain, as shown in Figs. 12.9 and 12.10. The magnitude of the effect is about 10 percent for each order of magnitude increase in the strain rate. The strain rate
470
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
Figure 12.5 Strain rate vs. time relationships during undrained creep of Osaka alluvial clay
(Murayama and Shibata, 1958).
effect is considerably smaller for sands. In a manner similar to Eq. (12.1), a rate parameter can be defined as the slope of a log–log plot of deviator stress at failure qƒ at a particular strain rate ˙ 1 relative to qƒ(ref), the strength at a reference strain rate ˙ 1(ref), versus strain rate. This gives the following equation: qƒ qƒ(ref)
⫽
冉 冊 ˙ 1
˙ 1(ref)
(12.2)
The value of ranges between 0.018 and 0.087, similar to the rate parameter values used to define the rate effect on consolidation pressure in Eq. (12.1). Higher values of are associated with more metastable soil structures (Soga and Mitchell, 1996). Rate dependency decreases with increasing sample disturbance, which is consistent with this finding.
12.3 TIME-DEPENDENT DEFORMATION–STRUCTURE INTERACTION Figure 12.6 Effect of sustained loading on (a) stress–strain
and strength behavior and (b) one-dimensional compression behavior.
In reality, completely smooth curves of the type shown in the preceding figures for strain and strain rate as a function of time may not exist at all. Rather, as dis-
TIME-DEPENDENT DEFORMATION–STRUCTURE INTERACTION
Figure 12.7 Rate dependency on one-dimensional compression characteristics of Batiscan
clay: (a) compression curves and (b) preconsolidation pressure (Leroueil et al., 1985).
471
472
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
Figure 12.8 Strain rate dependence on preconsolidation pressure determined from onedimensional constant strain rate tests (Soga and Mitchell, 1996).
Figure 12.9 Effect of strain rate on undrained strength (Kulhawy and Mayne 1990). Re-
printed with permission from EPRI.
cussed by Ter-Stepanian (1992), a ‘‘jump-like structure reorganization’’ may occur, reflecting a stochastic character for the deformation, as shown in Fig. 12.11 for creep of an undisturbed diatomaceous, lacustrine, overconsolidated clay. Ter-Stepanian (1992) suggests that there are four levels of deformation: (1) the molecular level, which consists of displacement of flow units by
surmounting energy barriers, (2) mutual displacement of particles as a result of bond failures, but without rearrangement, (3) the structural level of soil deformation involving mutual rearrangements of particles, and (4) deformation at the aggregate level. Behavior at levels 3 and 4 is discussed below; that at levels 1 and 2 is treated in more detail in Section 12.4.
TIME-DEPENDENT DEFORMATION–STRUCTURE INTERACTION
473
Figure 12.10 Strain rate dependence on undrained shear strength determined using constant
strain rate CU tests (Soga and Mitchell, 1996).
Figure 12.11 Nonuniformity of creep in an undisturbed, diatomaceous, lacustrine, overconsolidated clay (from TerStepanian, 1992).
Time-Dependent Process of Particle Rearrangement
Creep can lead to rearrangement of particles into more stable configurations. Forces at interparticle contacts have both normal and tangential components, even if the macroscopic applied stress is isotropic. If, during the creep process, there is an increase in the proportion of applied deviator stress that is carried by interparticle normal forces relative to interparticle tangential forces, then the creep rate will decrease. Hence, the rate at which deformation level 3 occurs need not be uniform owing to the particulate nature of soils. Instead it will reflect a series of structural readjustments as particles move up, over, and around each other, thus leading to
the somewhat irregular sequence of data points shown in Fig. 12.11. Microscopically, creep is likely to occur in the weak clusters discussed in Section 11.6 because the contacts in them are at limiting frictional equilibrium. Any small perturbation in applied load at the contacts or time-dependent loss in material strength can lead to sliding, breakage or yield at asperities. As particles slip, propped strong-force network columns are disturbed, and these buckle via particle rolling as discussed in Section 11.6. To examine the effects of particle rearrangement, Kuhn (1987) developed a discrete element model that considers sliding at interparticle contacts to be viscofrictional. The rate at which sliding of two particles relative to each other occurs depends on the ratio of shear to normal force at their contact. The relationship between rate and force is formulated in terms of rate process theory (see Section 12.4), and the mechanistic representations of the contact normal and shear forces are shown in Fig. 12.12. The time-dependent component in the tangential forces model is given as a ‘‘sinhdashpot’’.2 The average magnitudes of both normal and 2 Kuhn (1987) used the following equation for rate of sliding at a contact:
X˙ ⫽
冉 冊 冉
冊
2kT
F ƒt exp ⫺ sinh h RT 2kTn1 ƒn
where n1 is the number of bonds per unit of normal force, ƒt is the tangential force and ƒn is the normal force. The others are parameters related to rate process theory as described in Section 12.4.
474
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
Figure 12.12 Normal and tangential interparticle force mod-
els according to Kuhn (1987).
tangential forces at individual contacts can change during deformation even though the applied boundary stresses are constant. Small changes in the tangential and normal force ratio at a contact can have a very large influence on the sliding rate at that contact. These changes, when summed over all contacts in the shear zone, result in a decrease or increase in the overall creep rate. A numerical analysis of an irregular packing of circular disks using the sinh-dashpot representation gives creep behavior comparable to that of many soils as shown in Fig. 12.13 (Kuhn and Mitchell, 1993). The creep rate slows if the average ratio of tangential to normal force decreases, whereas it accelerates and may ultimately lead to failure if the ratio increases. In some cases, the structural changes that are responsible for the decreasing strain rate and increased stiffness may cause the overall soil structure to become more metastable. Then, after the strain reaches some limiting value, the process of contact force transfer from decreasing tangential to increasing normal force reverses. This marks the onset of creep rupture as the structure begins to collapse. A similar result was obtained by Rothenburg (1992) who performed discrete particle simulations in which smooth elliptical particles were cemented with a model exhibiting viscous characteristics in both normal and tangential directions.
Figure 12.13 Creep curves developed by numerical analysis
of an irregular packing of circular disks (from Kuhn and Mitchell, 1993).
Particle Breakage During Creep
Particle breakage can contribute to time-dependent deformation of sands (Leung et al., 1996; Takei et al., 2001; McDowell, 2003). Leung et al. (1996) performed one-dimensional compression tests on sands, and Fig.
TIME-DEPENDENT DEFORMATION–STRUCTURE INTERACTION
100
夹 䊉
Percentage Passing (%)
80 Dry sand RD = 75% Pressure = 15.4 MPa 60
40
夹
20
䊉 0夹 0
After 5 days After Before 290 s Test 䊉 夹 䊉
100
200 Sieve Size (μm)
300
400
Figure 12.14 Changes in particle size distribution of sand before loading and after two different load durations (from Leung, et al., 1996).
12.14 shows the particle size distribution curves for samples before loading and after two different load durations. The amount of particle breakage increased with load duration. Microscopic observations revealed that angular protrusions of the grains were ground off, producing fines. The fines fill the voids between larger particles and crushed particles progressively rearranged themselves with time. Aging—Time-Dependent Strengthening of Soil Structure
The structural changes that occur during creep that is continuing at a decreasing rate cause an increase in soil stiffness when the soil is subjected to further stress increase as shown in Fig. 12.6. Leonards and Altschaeffl (1964) showed that this increase in preconsolidation pressure cannot be accounted for in terms of the void ratio decrease during the sustained compression period. Time-dependent changes of these types are a consequence of ‘‘aging’’ effects, which alter the structural state of the soil. The fabric obtained by creep may be different from that caused by increase in stress, even though both samples arrive at the same void ratio. Leroueil et al. (1996) report a similar result for an artificially sedimented clay from Quebec, as shown in Fig. 12.15a. They also measured the shear wave velocities after different times during the tests using bender elements and computed the small strain elastic shear modulus. Figure 12.15b shows the change in shear modulus with void ratio.
475
Additional insight into the structural changes accompanying the aging of clays is provided by the results of studies by Anderson and Stokoe (1978) and Nakagawa et al. (1995). Figure 12.16 shows changes in shear modulus with time under a constant confining pressure for kaolinite clay during consolidation (Anderson and Stokoe, 1978). Two distinct phases of shear modulus–time response are evident. During primary consolidation, values of the shear modulus increase rapidly at the beginning and begin to level off as the excess pore pressure dissipates. After the end of primary consolidation, the modulus increases linearly with the logarithm of time during secondary compression. The expected change in shear modulus due to void ratio change during secondary compression can be estimated using the following empirical formula for shear modulus as a function of void ratio and confining pressure (Hardin and Black, 1968): G⫽A
(2.97 ⫺ e)2 0.5 p 1⫹e
(12.3)
where A is a unit dependant material constant, e is the void ratio, and p is the mean effective stress. The dashed line in Fig. 12.16 shows the calculated increases in the shear modulus due to void ratio decrease using Eq. (12.3). It is evident that the change in void ratio alone does not provide an explanation for the secondary time-dependent increase in shear modulus. This aging effect has been recorded for a variety of materials, ranging from clean sands to natural clays (Afifi and Richart, 1973; Kokusho, 1987; Mesri et al., 1990, and many others). Further discussion of aging phenomena is given in Section 12.11. Time-Dependent Changes in Soil Fabric
Changes in soil fabric with time under stress influence the stability of soil structure. Changes in sand fabric with time after load application in one-dimensional compression were measured by Bowman and Soga (2003). Resin was used to fix sand particles after various loading times. Pluviation of the sand produced a horizontal preferred particle orientation of soil grains, and increased vertical loading resulted in a greater orientation of particle long axes parallel to the horizontal, which is in agreement with the findings of Oda (1972a, b, c), Mitchell et al. (1976), and Jang and Frost (1998). Over time, however, the loading of sand caused particle long axes to rotate toward the vertical direction (i.e., more isotropic fabric). Experimental evidence (Bowman and Soga, 2003) showed that large voids became larger, whereas small voids became smaller, and particles group or cluster
476
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
A
A
Normal Consolidation Line
2.6
B
2.4 Void Ratio e
Stiffness Change During the Primary Consolidation Between B and C B
Quasipreconsolidation Pressure 2.2
C
Creep for 120 days
C
D
D
Increase in Stiffness during Creep (C-D)
E
Destructuring State
2.0
E
F
F 1.8
4
6
8
10
20
Vertical Effective Stress σv (kPa)
(a )
0.5
1
2
5
Small-strain Stiffness G0 (MPa)
(b )
Figure 12.15 (a) Compression curve and (b) variation of the maximum shear modulus G0
with void ratio for artificially sedimented Jonquiere clay (from Leroueil et al., 1996).
together with time. Based on these particulate level findings, it appears that the movements of particles lead to interlocking zones of greater local density. The interlocked state may be regarded as the final state of any one particle under a particular applied load, due to kinematic restraint. The result, with time, is a stiffer, more efficient, load-bearing structure, with areas of relatively large voids and neighboring areas of tightly packed particles. The increase in stiffness is achieved by shear connections obtained by the clustering. Then, when load is applied, the increased stiffness and strength of the granular structure provides greater resistance to the load and the observed aging effect is seen. The numerical analysis in Kuhn and Mitchell (1993) led to a similar hypothesis for how a more ‘‘braced’’ structure develops with time. For load application in a direction different to that during the aging period, however, the strengthening effect of aging may be less, as the load-bearing particle column direction differs from the load direction. Time-Dependent Changes in Physicochemical Interaction of Clay and Pore Fluid
A portion of the shear modulus increase during secondary compression of clays is believed to result from
a strengthening of physicochemical bonds between particles. To illustrate this, Nakagawa et al. (1995) examined the physicochemical interactions between clays and pore fluid using a special consolidometer in which the sample resistivity and pore fluid conductivity could be measured. Shear wave velocities were obtained using bender elements to determine changes in the stiffness characteristics of the clay during consolidation. Kaolinite clay mixed with saltwater was used for the experiment, and changes in shear wave velocities and electrical properties were monitored during the tests. The test results showed that the pore fluid composition and ion mobility changed with time. At each load increment, as the effective stress increased with pore pressure dissipation, the shear wave velocities, and therefore the shear modulus, generally increased with time as shown in Fig. 12.17. It may be seen, however, that in some cases, the shear wave velocities at the beginning of primary consolidation decreased slightly from the velocities obtained immediately before application of the incremental load, probably as a result of soil structure breakdown. During the subsequent secondary compression stage, the shear wave velocity again increased. As was the case for the results in Fig.12.16, the increases in shear wave velocity dur-
Sample Height Change (mm)
Shear Modulus of less than γ = 10-3% (MPa)
TIME-DEPENDENT DEFORMATION–STRUCTURE INTERACTION
50
40
477
Ball Kaolinite
IG = ΔG per log time = 6.2 MPa
30
20
Possible Change in G by Void Ratio Decrease Only Estimated Using Eq. (12.3)
10 Primary Consolidation 0
10 1
Secondary Compression
10 2 Time (min)
10 3
10 4
0.5
1.0
1.5 Initial Consolidation Pressure = 70 kPa Initial Void Ratio e 0 = 1.1 2.0 10 0
10 1
10 2
10 3
10 4
Time (min)
Figure 12.16 Modulus and height changes as a function of time under constant confining pressure for kaolinite: (a) shear modulus and (b) height change (from Anderson and Stokoe, 1978). Figure 12.17 Changes in shear wave velocity during primary consolidation and secondary compression of kaolinite. Consolidation pressures: (a) 11.8 kPa and (b) 190 kPa (from Nakagawa et al., 1995).
ing secondary compression are greater than can be accounted for by increase in density. The electrical conductivity of the sample measured by filter electrodes increased during the early stages of consolidation, but then decreased continuously thereafter as shown in Fig. 12.18. The electrical conductivity is dominated by flow through the electrolyte solution in the pores. During the initial compression, a breakdown of structure releases ions into the pore water, increasing the electrical conductivity. With time, the conductivity decreased, suggesting that the released ions are accumulating near particle surfaces. Some of these released ions are expelled from the specimen as consolidation progressed as shown in Fig. 12.18b. A slow equilibrium under a new state of effective stress is hypothesized to develop that involves both small particle rearrangements, associated with decrease in void ratio during secondary compression, and development of increased contact strength as a result of pre-
cipitation of salts from the pore water and/or other processes. Primary consolidation can be considered a result of drainage of pore water fluid from the macropores, whereas secondary compression is related to the delayed deformation of micropores in the clay aggregates (Berry and Poskitt, 1972; Matsuo and Kamon, 1977; Sills, 1995). The mobility of water in the micropores is restricted due to small pore size and physicochemical interactions close to the clay particle surfaces. Akagi (1994) did compression tests on specially prepared clay containing primarily Ca in the micropores and Na in the macropores. Concentrations of the two ions in the expelled water at different times after the start of consolidation were consistent with this hypothesis.
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TIME EFFECTS ON STRENGTH AND DEFORMATION
sen and Wu (1964), Mitchell (1964), Mitchell et al. (1968, 1969), Murayama and Shibata (1958, 1961, 1964), Noble and Demirel (1969), Wu et al. (1966), Keedwell (1984), Feda (1989, 1992), and Kuhn and Mitchell (1993). Concept of Activation
The basis of rate process theory is that atoms, molecules, and/or particles participating in a timedependent flow or deformation process, termed flow units, are constrained from movement relative to each other by energy barriers separating adjacent equilibrium positions, as shown schematically by Fig. 12.19. The displacement of flow units to new positions requires the acquisition of an activation energy F of sufficient magnitude to surmount the barrier. The potential energy of a flow unit may be the same following the activation process, or higher or lower than it was initially. These conditions are shown by analogy with the rotation of three blocks in Fig. 12.20. In each case, an energy barrier must be crossed. The assumption of a steady-state condition is implicit in most applications to soils concerning the at-rest barrier height between successive equilibrium positions. The magnitude of the activation energy depends on the material and the type of process. For example, values of F for viscous flow of water, chemical reactions, and solid-state diffusion of atoms in silicates are about 12 to 17, 40 to 400, and 100 to 150 kJ/mol of flow units, respectively. Figure 12.18 Changes in electrical conductivity of the pore
water during primary consolidation and secondary compression of kaolinite. Consolidation pressures: (a) 95 kPa and (b) 190 kPa (from Nakagawa et al., 1995).
12.4 SOIL DEFORMATION AS A RATE PROCESS
Deformation and shear failure of soil involve timedependent rearrangement of matter. As such, these phenomena are amenable for study as rate processes through application of the theory of absolute reaction rates (Glasstone et al., 1941). This theory provides both insights into the fundamental nature of soil strength and functional forms for the influences of several factors on soil behavior. Detailed development of the theory, which is based on statistical mechanics, may be found in Eyring (1936), Glasstone et al. (1941), and elsewhere in the physical chemistry literature. Adaptations to the study of soil behavior include those by Abdel-Hady and Herrin (1966), Andersland and Douglas (1970), Christen-
Activation Frequency
The energy to enable a flow unit to cross a barrier may be provided by thermal energy and by various applied potentials. For a material at rest, the potential energy– displacement relationship is represented by curve A in Fig. 12.21. From statistical mechanics it is known that
Figure 12.19 Energy barriers and activation energy.
SOIL DEFORMATION AS A RATE PROCESS
Figure 12.20 Examples of activated processes: (a) steady-state, (b) increased stability, and
(c) decreased stability.
Figure 12.21 Effect of a shear force on energy barriers.
479
480
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
the average thermal energy per flow unit is kT, where k is Boltzmann’s constant (1.38 ⫻ 10⫺23 J K⫺1) and T is the absolute temperature (K). Even in a material at rest, thermal vibrations occur at a frequency given by kT/h, where h is Planck’s constant (6.624 ⫻ 10⫺34 J s⫺1). The actual thermal energies are divided among the flow units according to a Boltzmann distribution. It may be shown that the probability of a given unit becoming activated, or the proportion of flow units that are activated during any one oscillation is given by
冉 冊
F p( F) ⫽ exp ⫺ NkT
(12.4)
where N is Avogadro’s number (6.02 ⫻ 1023), and Nk is equal to R, the universal gas constant (8.3144 J K⫺1 mol⫺1). The frequency of activation then is ⫽
冉 冊
⫺ F kT exp h NkT
(12.5)
In the absence of directional potentials, energy barriers are crossed with equal frequency in all directions, and no consequences of thermal activations are observed unless the temperature is sufficiently high that softening, melting, or evaporation occurs. If, however, a directed potential, such as a shear stress, is applied, then the barrier heights become distorted as shown by curve B in Fig. 12.21. If ƒ represents the force acting on a flow unit, then the barrier height is reduced by an amount (ƒ /2) in the direction of the force and increased by a like amount in the opposite direction, where represents the distance between successive equilibrium positions.3 Minimums in the energy curve are displaced a distance from their original positions, representing an elastic distortion of the material structure. The reduced barrier height in the direction of force ƒ increases the activation frequency in that direction to →⫽
冉
冊
kT
F/N ⫺ ƒ /2 exp ⫺ h kT
(12.6)
The net frequency of activation in the direction of the force then becomes ( →) ⫺ ( ←) ⫽ 2
(12.8) Strain Rate Equation
At any instant, some of the activated flow units may successfully cross the barrier; others may fall back into their original positions. For each unit that is successful in crossing the barrier, there will be a displacement . The component of in a given direction times the number of successful jumps per unit time gives the rate of movement per unit time. If this rate of movement is expressed on a per unit length basis, then the strain rate ˙ is obtained. Let X ⫽ F (proportion of successful barrier crossings and ) such that ˙ ⫽ X[( →) ⫺ ( ←)]
冉
冊
˙ ⫽ 2X
冉 冊 冉 冊
kT
F ƒ exp ⫺ sinh h RT 2kT
(12.10)
The parameter X may be both time and structure dependent. If (ƒ /2kT) ⬍ 1, then sinh(ƒ /2kT) ⬇ (ƒ /2kT), and the rate is directly proportional to ƒ. This is the case for ordinary Newtonian fluid flow and diffusion where ˙ ⫽
1
(12.11)
where ˙ is the shear strain rate, is dynamic viscosity, and is shear stress. For most solid deformation problems, however, (ƒ /2kT) ⬎ 1 (Mitchell et al., 1968), so
冉 冊
sinh
冉 冊
ƒ 1 ƒ ⬇ exp 2kT 2 2kT
(12.12)
and (12.7)
Work (ƒ / 2) done by the force ƒ as the flow unit drops from the peak of the energy barrier to a new equilibrium position is assumed to be given up as heat.
3
(12.9)
Then from Eq. (12.8)
and in the opposite direction, the increased barrier height decreases the activation frequency to
F/N ⫹ ƒ /2 kT ←⫽ exp ⫺ h kT
冉 冊 冉 冊
kT
F ƒ exp ⫺ sinh h RT 2kT
˙ ⫽ X
冉 冊 冉 冊
kT
F ƒ N exp ⫺ exp h RT 2RT
(12.13)
Equation (12.13) applies except for very small stress intensities, where the exponential approximation of the hyperbolic sine is not justified. Equations (12.10) and
481
BONDING, EFFECTIVE STRESSES, AND STRENGTH
(12.13) or comparable forms have been used to obtain dashpot coefficients for rheological models, to obtain functional forms for the influences of different factors on strength and deformation rate, and to study deformation rates in soils. For example, Kuhn and Mitchell (1993) used this form as part of the particle contact law in discrete element modeling as described in the previous section. Puzrin and Houlsby (2003) used it as an internal function of a thermomechanical-based model and derived a rate-dependent constitutive model for soils.
12.5 BONDING, EFFECTIVE STRESSES, AND STRENGTH
Using rate process theory, the results of timedependent stress–deformation measurements in soils can be used to obtain fundamental information about soil structure, interparticle bonding, and the mechanisms controlling strength and deformation behavior. Deformation Parameters from Creep Test Data
If the shear stress on a material is and it is distributed uniformly among S flow units per unit area, then
Soil Deformation as a Rate Process
S
Although there does not yet appear to be a rigorous proof of the correctness of the detailed statistical mechanics formulation of rate process theory, even for simple chemical reactions, the real behavior of many systems has been substantially in accord with it. Different parts of Eq. (12.13) have been tested separately (Mitchell et al., 1968). It was found that the temperature dependence of creep rate and the stress dependence of the experimental activation energy [Eq. (12.14)] were in accord with predictions. These results do not prove the correctness of the theory; they do, however, support the concept that soil deformation is a thermally activated process.
Displacement of a flow unit requires that interatomic or intermolecular forces be overcome so that it can be moved. Let it be assumed that the number of flow units and the number of interparticle bonds are equal. If D represents the deviator stress under triaxial stress conditions, the value of ƒ on the plane of maximum shear stress is
Arrhenius Equation
so Eq. (12.13) becomes
ƒ⫽
ƒ⫽
Equation (12.13) may be written
冉 冊
kT E ˙ ⫽ X exp ⫺ h RT
˙ ⫽ X
(12.14)
where E ⫽ F ⫺
ƒ N 2
(12.15)
is termed the experimental activation energy. For all conditions constant except T, and assuming that X(kT/h) ⬇ constant ⫽ A, ˙ ⫽ A exp
冉 冊 ⫺
E RT
(12.16)
Equation (12.16) is the same as the well-known empirical equation proposed by Arrhenius around 1900 to describe the temperature dependence of chemical reaction rates. It has been found suitable also for characterization of the temperature dependence of processes such as creep, stress relaxation, secondary compression, thixotropic strength gain, diffusion, and fluid flow.
D 2S
冉 冊 冉 冊
kT
F D exp ⫺ exp h RT 4SkT
(12.17)
(12.18)
(12.19)
This equation describes creep as a steady-state process. Soils do not creep at constant rate, however, because of continued structural changes during deformation as described in Section 12.3, except for the special case of large deformations after mobilization of full strength. Thus, care must be taken in application of Eq. (12.19) to ensure that comparisons of creep rates and evaluations of the influences of different factors are made under conditions of equal structure. The time dependency of creep rate and the possible time dependencies of the parameters in Eq. (12.19) are considered in Section 12.8. Determination of Activation Energy From Eq. (12.14) ln(˙ /T) E ⫽⫺ (1/T) R
(12.20)
provided strain rates are considered under conditions of unchanged soil structure. Thus, the value of E can be determined from the slope of a plot of ln(˙ /T) versus (1/T). Procedures for evaluation of strain rates for
482
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TIME EFFECTS ON STRENGTH AND DEFORMATION
soils at different temperatures but at the same structure are given by Mitchell et al. (1968, 1969). Determination of Number of Bonds For stresses large enough to justify approximating the hyperbolic sine function by a simple exponential in the creep rate equation and small enough to avoid tertiary creep, the logarithm of strain rate varies directly with the deviator stress. For this case, Eq. (12.19) can be written ˙ ⫽ K(t) exp(D)
known, /S is calculated as a measure of the number of interparticle bonds.4 Activation Energies for Soil Creep
Activation energies for the creep of several soils and other materials are given in Table 12.1. The free energy of activation for creep of soils is in the range of about 80 to 180 kJ/mol. Four features of the values for soils in Table 12.1 are significant:
(12.21)
1. The activation energies are relatively large, much higher than for viscous flow of water. 2. Variations in water content (including complete drying), adsorbed cation type, consolidation pressure, void ratio, and pore fluid have no significant effect on the required activation energy. 3. The values for sand and clay are about the same. 4. Clays in suspension with insufficient solids to form a continuous structure deform with an activation energy equal to that of water.
where K(t) ⫽ X ⫽
冉 冊
kT
F exp ⫺ h RT
4SkT
(12.22) (12.23)
Parameter is a constant for a given value of effective consolidation pressure and is given by the slope of the relationship between log strain rate and stress. It is evaluated using strain rates at the same time after the start of creep tests at several stress intensities. With
Table 12.1
A procedure for evaluation of from the results of a test at a succession of stress levels on a single sample is given by Mitchell et al. (1969).
4
Activation Energies for Creep of Several Materials
Material 1. Remolded illite, saturated, water contents of 30 to 43% 2. Dried illite: samples air-dried from saturation, then evacuated 3. San Francisco Bay mud, undisturbed 4. Dry Sacramento River sand 5. Water 6. Plastics 7. Montmorillonite–water paste, dilute 8. Soil asphalt 9. Lake clay, undisturbed and remolded 10. Osaka clay, overconsolidated 11. Concrete 12. Metals 13. Frozen soils 14. Sault Ste. Marie clay, suspensions, discontinuous structures 15. Sault Ste. Marie clay, Li⫹, Na⫹, K⫹ forms, in H2O and CCl4, consolidated
Activation Energy (kJ/ mol)a
Reference
105–165
Mitchell, et al. (1969)
155
Mitchell, et al. (1969)
105–135 ⬃105 16–21 30–60 84–109 113 96–113 120–134 226 210⬃ 393 Same as water 117
Mitchell, et al. (1969) Mitchell, et al. (1969) Glasstone, et al. (1941) Ree and Eyring (1958) Ripple and Day (1966) Abdel-Hady and Herrin (1966) Christensen and Wu (1964) Murayama and Shibata (1961) Polivka and Best (1960) Finnie and Heller (1959) Andersland and Akili (1967) Andersland and Douglas (1970) Andersland and Douglas (1970)
The first four values are experimental activation energies, E. Whether the remainder are values of F or E is not always clear in the references cited. a
BONDING, EFFECTIVE STRESSES, AND STRENGTH
Number of Interparticle Bonds
Evaluation of S requires knowledge of , the separation distance between successive equilibrium positions in the interparticle contact structure. A value of 0.28 nm ˚ ) has been assumed because it is the same as the (2.8 A distance separating atomic valleys in the surface of a silicate mineral. It is hypothesized that deformation involves the displacement of oxygen atoms along contacting particle surfaces, as well as periodic rupture of bonds at interparticle contacts. Figure 12.22 shows this interpretation for schematically. If the above assumption for is incorrect, calculated values of S will still be in the same correct relative proportion as long as remains constant during deformation. Normally Consolidated Clay Results of creep tests at different stress intensities for different consolidation pressures enable computation of S as a function of consolidation pressure. Values obtained for undisturbed San Francisco Bay mud are shown in Fig. 12.23. The open point is for remolded bay mud. An undisturbed specimen was consolidated to 400 kPa, rebounded to
483
50 kPa, and then remolded at constant water content. The effective consolidation pressure dropped to 25 kPa as a result of the remolding. The drop in effective stress was accompanied by a corresponding decrease in the number of interparticle bonds. Tests on remolded illite gave comparable results. A continuous inverse relationship between the number of bonds and water content over a range of water contents from more than 40 percent to air-dried and vacuum-desiccated clay is shown in Fig. 12.24. The dried material had a water content of 1 percent on the usual oven-dried basis. The very large number of bonds developed by drying is responsible for the high dry strength of clay. Overconsolidated Clay Samples of undisturbed San Francisco Bay mud were prepared to overconsolidation ratios of 1, 2, 4, and 8 following the stress paths shown in the upper part of Fig. 12.25. The sample represented by the triangular data point was remolded after consolidation and unloading to point d, where it had a water content of 52.3 percent. The undrained compressive strength as a function of consolidation pressure is shown in the middle section of Fig. 12.25, and the number of bonds, deduced from the creep tests, is shown in the lower part of the figure. The effect of overconsolidation is to increase the number of interparticle bonds over the values for normally consolidated clay. Some of the bonds formed during consolidation are retained after removal of much of the consolidation pressure. Values of compressive strength and numbers of bonds from Fig. 12.25 are replotted versus each other in Fig. 12.26. The resulting relationship suggests that strength depends only on the number of bonds and is independent of whether the clay is undisturbed, remolded, normally consolidated, or overconsolidated. Dry Sand Creep tests on oven-dried sand yielded results of the same type as obtained for clay, as shown in Fig. 12.27, suggesting that the strength-generating and creep-controlling mechanisms may be similar for both types of material. Composite Strength-Bonding Relationship Values of S and strength for many soils are combined in Fig. 12.28. The same proportionality exists for all the materials, which may seem surprising, but which in reality should be expected, as discussed further later. Significance of Activation Energy and Bond Number Values
Figure 12.22 Interpretation of in terms of silicate mineral
surface structure.
The following aspects of activation energies and numbers of interparticle bonds are important in the understanding of the deformation and strength behavior of uncemented soils.
484
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TIME EFFECTS ON STRENGTH AND DEFORMATION
Figure 12.23 Number of interparticle bonds as a function of consolidation pressure for normally consolidated San Francisco Bay mud.
Figure 12.24 Number of bonds as a function of water con-
tent for illite.
1. The values of activation energy for deformation of soils are high in comparison with other materials and indicate breaking of strong bonds. 2. Similar creep behavior for wet and dry clay and for wet and dry sand indicates that deformation is not controlled by viscous flow of water. 3. Comparable values of activation energy for wet and dry soil indicate that water is not responsible for bonding. 4. Comparable values of activation energy for clay and sand support the concept that interparticle bond strengths are the same for both types of material. This is supported also by the uniqueness of the strength versus number of bonds relationship for all soils. 5. The activation energy and presumably, therefore, the bonding type are independent of consolidation pressure, void ratio, and water content. 6. The number of bonds is directly proportional to effective consolidation pressure for normally consolidated clays. 7. Overconsolidation leads to more bonds than in normally consolidated clay at the same effective consolidation pressure. 8. Strength depends only on the number of bonds. 9. Remolding at constant water content causes a decrease in the effective consolidation pressure, which means also a decrease in the number of bonds. 10. There are about 100 times as many bonds in dry clay as in wet clay.
BONDING, EFFECTIVE STRESSES, AND STRENGTH
485
Figure 12.25 Consolidation pressure, strength, and bond numbers for San Francisco Bay
mud.
Although it may be possible to explain these results in more than one way, the following interpretation accounts well for them. The energy F activates a mole of flow units. The movement of each flow unit may involve rupture of single bonds or the simultaneous rupture of several bonds. Shear of dilute montmorillonite–water pastes involves breaking single bonds (Ripple and Day, 1966). For viscous flow of water, the activation energy is approximately that for a single hydrogen bond rupture per flow unit displacement, even though each water molecule may form simultaneously
up to four hydrogen bonds with its neighbors. If the single-bond interpretation is also correct for soils, then consistency in Eq. (12.10) requires that shear force ƒ pertain to the force per bond. On this basis, parameter S indicates the number of single bonds per unit area. In the event activation of a flow unit requires simultaneous rupture of n bonds, then S represents 1/nth of the total bonds in the system. That the activation energy for deformation of soil is well into the chemical reaction range (40 to 400 kJ/ mol) does not prove that bonding is of the primary
486
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TIME EFFECTS ON STRENGTH AND DEFORMATION
Figure 12.26 Strength as a function of number of bonds for San Francisco Bay mud. Figure 12.28 Composite relationship between shear strength
valence type because simultaneous rupture of several weaker bonds could yield values of the magnitude observed. On the other hand, the facts that (1) the activation energy is much greater than for flow of water, (2) it is the same for wet and dry soils, and (3) it is essentially the same for different adsorbed cations and
and number of interparticle bonds (from Matsui and Ito, 1977). Reprinted with permission from The Japanese Society of SMFE.
Figure 12.27 Strength as a function of number of bonds for dry Antioch River sand.
BONDING, EFFECTIVE STRESSES, AND STRENGTH
pore fluids (Andersland and Douglas, 1970) suggest that bonding is through solid interparticle contacts. Physical evidence for the existence of solid-to-solid contact between clay particles has been obtained in the form of photomicrographs of particle surfaces that were scratched during shear (Matsui et al., 1977, 1980) and acoustic emissions (Koerner et al., 1977). Activation energy values of 125 to 190 kJ/mol are of the same order as those for solid-state diffusion of oxygen in silicate minerals. This supports the concept that creep movements of individual particles could result from slow diffusion of oxygen ions in and around interparticle contacts. The important minerals in both sand and clay are silicates, and their surface layers consist of oxygen atoms held together by silicon atoms. Water in some form is adsorbed onto these surfaces. The water structure consists of oxygens held together by hydrogen. It is not too different from that of the silicate layer in minerals. Thus, a distinct boundary between particle surface and water may not be discernable. Under these conditions, a more or less continuous solid structure containing water molecules that propagates through interparticle contacts can be visualized. An individual flow unit could be an atom, a group of atoms or molecules, or a particle. The preceding arguments are based on the interpretation that individual atoms are the flow units. This is consistent with both the relative and actual values of S that have been determined for different soils. Furthermore, by using a formulation of the rate process equation that enabled calculation of the flow unit volume from creep test data, Andersland and Douglas (1970) obtained a value ˚ 3, which is of the same order as that of of about 1.7 A individual atoms. On the other hand, Keedwell (1984) defined flow units between quartz sand particles as consisting of six O2⫺ ions and six Si4⫹ ions and between two montmorillonite clay particles as consisting of four H2O molecules. If particles were the flow units, not only would it be difficult to visualize their thermal vibrations, but then S would relate to the number of interparticle contacts. It is then difficult to conceive how simply drying a clay could give a 100-fold increase in the number of interparticle contacts, as would have to be the case according to Fig. 12.27. A more plausible interpretation is that drying, while causing some increase in the number of interparticle contacts during shrinkage, causes mainly an increase in the number of bonds per contact because of increased effective stress. At any value of effective stress, the value of S is about the same for both sand and clay. The number of interparticle contacts should be vastly different; how-
487
ever, for equal numbers of contacts per particle, the number per unit volume should vary inversely with the cube of particle size. Thus, the number of clay particles of 1-m particle size should be some nine orders of magnitude greater than for a sand of 1-mm average particle size. Each contact between sand particles would involve many bonds; in clay, the much greater number of contacts would mean fewer bonds per particle. The contact area required to develop bonds in the numbers indicted in Figs. 12.23 to 12.27 is very small. For example, for a compressive strength of 3 kg/cm2 (⬇ 300 kPa) there are 8 ⫻ 1010 bonds/cm2 of shear surface. Oxygen atoms on the surface of a silicate mineral have a diameter of 0.28 nm. Allowing an area 0.30 nm on a side for each oxygen gives 0.09 nm2, or 9 ⫻ 10⫺16 cm2, per bonded oxygen for a total area of 9 ⫻ 10⫺16 ⫻ 8 ⫻ 1010 ⫽ 7.2 ⫻ 10⫺5 cm2 /cm2 of soil cross section. Hypothesis for Bonding, Effective Stress, and Strength
Normal effective stresses and shear stresses can be transmitted only at interparticle contacts in most soils.5 The predominant effects of the long-range physicochemical forces of interaction are to control the initial soil fabric and to alter the forces transmitted at contact points from what they would be due to applied stresses alone. Interparticle contacts are effectively solid, and it is likely that both adsorbed water and cations in the contact zone participate in the structure. An interparticle contact may contain many bonds that may be strong, approaching the primary valence type. The number of bonds at any contact depends on the compressive force transmitted at the contact, and the Terzaghi–Bowden and Tabor adhesion theory of friction presented in Section 11.4, can account for strength. The macroscopic strength is directly proportional to the number of bonds. For normally consolidated soils the number of bonds is directly proportional to the effective stress. As a result of particle rearrangements and contacts formed during virgin compression, an overconsolidated soil at a given effective stress has a greater number of bonds and higher strength than a normally consolidated soil. This effect is more pronounced in clays than in sands because the larger and bulky sand grains tend to re-
5 Pure sodium montmorillonite may be an exception since a part of the normal stress can be carried by physicochemical forces of interaction. The true effective stress may be less than the apparent effective stress by R ⫺ A as discussed in Chapter 7.
488
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TIME EFFECTS ON STRENGTH AND DEFORMATION
cover their original shapes when unloaded, thus rupturing most of the bonds in excess of those needed to resist the lower stress. The strength of the interparticle contacts can vary over a wide range, depending on the number of bonds per contact. The unique relationship between strength and number of bonds for all soils, as indicted by Fig. 12.28, reflects the fact that the minerals comprising most soils are silicates, and they all have similar surface structures. In the absence of chemical cementation, interparticle bonds may form in response to interparticle contact forces generated by either applied stresses, physicochemical forces of interaction, or both. Any bonds existing in the absence of applied effective stress, that is, when ⫽ 0, are responsible for true cohesion. There should be no difference between friction and cohesion in terms of the shearing process. Complete failure in shear involves simultaneous rupture or slipping of all bonds along the shear plane.
12.6 SHEARING RESISTANCE AS A RATE PROCESS
Deformation at large strain can approach a steady-state condition where there is little further structural change with time (such as at critical state). In this case, Eq. (12.19) can be used to describe the shearing resistance as a function of strain rate and temperature. If the maximum shear stress is substituted for the deviator stress D, then ⫽
1 ⫺ 3 2
冉 冊 冉 冊
kT
F exp ⫺ exp h RT 2SkT
冉 冊
kT
F ⫺ ⫹ h RT 2SkT
冉冊
2S 2SkT ˙
F ⫹ ln N B
where a and b are constants and ƒ is the effective normal stress on the shear plane. Thus, Eq. (12.27) becomes ⫽
冉
冊
2a F 2akT ˙ 2b F 2bkT ˙ ⫹ ln ⫹ ⫹ ln ƒ N B N B (12.29)
Equation (12.29) is of the same form as the Coulomb equation for strength: ⫽ c ⫹ ƒ tan
(12.30)
By analogy, c⫽
2a F 2akT ˙ ⫹ ln N B
(12.31)
tan ⫽
2b F 2bkT ˙ ⫹ ln N B
(12.32)
These equations state that both cohesion and friction depend on the number of bonds times the bond strength, as reflected by the activation energy, and that the values of c and should depend on the rate of deformation and the temperature.
(12.25)
All other factors being equal, the shearing resistance should increase linearly with the logarithm of the rate of strain. This is shown to be the case in Fig. 12.9, which contains data for 26 clays. Additional data for several clays are shown in Fig. 12.29, where shearing resistance as a function of the speed of vane rotation in a vane shear test is plotted. Analysis of the relationship between shearing stress and angular rate of vane rotation " shows that / log " decreases with an increase in water content. This follows directly from Eq. (12.29) because
(12.26)
By assuming X(kT/h) is a constant equal to B (Mitchell, 1964), Eq. (12.26) can be rearranged to give ⫽
(12.28)
Strain Rate Effects
Taking logarithms of both sides of Eq. (12.25) gives ln ˙ ⫽ ln X
S ⫽ a ⫹ bƒ
(12.24)
and ˙ ⫽ X
From the relationships in Section 12.5, the following relationship between bonds per unit area and effective stress is suggested.
(12.27)
d 2akT 2bkT 2kT ⫽ ⫹ ƒ ⫽ (a ⫹ bƒ) d ln(˙ /B) (12.33) that is, d /d ln (˙ /B) is proportional to the number of bonds, which decreases with increasing water content.
CREEP AND STRESS RELAXATION
489
Figure 12.29 Effect of rate of shear on shearing resistance of remolded clays as determined by the laboratory vane apparatus (prepared from the data of Karlsson, 1963).
This interpretation of the data in Figs. 12.9 and 12.29 assumes that the effective stress was unaffected by changes in the strain rate, which may not necessarily be true in all cases. Effect of Temperature
Assumptions of reasonable values for parameters show that the term (˙ /B) is less than one (Mitchell, 1964). Thus the quantity ln(˙ /B) in Eq. (12.29) is negative, and an increase in temperature should give a decrease in strength, all other factors being constant. That this is the case is demonstrated by Fig. 12.30, which shows deviator stress as a function of temperature for samples of San Francisco Bay mud compared under conditions of equal mean effective stress and structure. Other examples of the influence of temperature on strength are shown in Figs. 11.6 and 11.133.
12.7
CREEP AND STRESS RELAXATION
Although the designation of a part of the strain versus time relationship as steady state or secondary creep may be convenient for some analysis purposes, a true steady state can exist only for conditions of constant structure and stress. Such a set of conditions is likely only for a fully destructured soil, and a fully destructured state is likely to persist only during deformation at a constant rate, that is, at failure. This state is often called ‘‘steady state,’’ in which the soil is deforming continuously at constant volume under constant shear and confining stresses (Castro, 1975; Castro and Poulos, 1977). Otherwise, bond making and bond breaking occur at different rates as a result of different internal timeand strain-dependent phenomena, which might include thixotropic hardening, viscous flows of water and ad-
490
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TIME EFFECTS ON STRENGTH AND DEFORMATION
Figure 12.30 Influence of temperature on the shearing resistance of San Francisco Bay mud. Comparison is for samples at equal mean effective stress and at the same structure.
sorbed films, chemical, and biological transformations, and the like. Furthermore, distortions of the soil structure and relative movements between particles cause changes in the ratio of tangential to normal forces at interparticle contacts that may be responsible for large changes in creep rate. Because of these time dependencies some of the parameters in Eq. (12.19) may be time dependent. For example, Feda (1989) accounted for the time dependency of creep rate by taking changes in the number of structural bonds into account. Therefore, application of Eq. (12.19) for the determination of the bonding and effective stress relationships discussed in Section 12.5 required comparison of creep rates under conditions of comparable time and structure. The influence of creep stress magnitude on the creep rate at a given time after the application of the stress to identical samples of a soil was shown in Fig. 12.3. At low stresses the creep rates are small and of little practical importance. The curve shape is compatible with the hyperbolic sine function predicted by rate process theory, as given by Eq. (12.10). In the midrange of stresses, a nearly linear relationship is found between logarithm of strain rate and stress, also as predicted by Eq. (12.10) for the case where the argument of the hyperbolic sine is greater than 1. At stresses approaching the strength of the material, the strain rate becomes very large and signals the onset of failure. Other examples of the relationships between logarithm of strain rate and creep stress corresponding to different times after the application of the creep stress are given in Fig. 12.31 for drained tests on London clay
Figure 12.31 Variation of creep strain rate with deviator
stress for drained creep of London clay (data from Bishop, 1966).
and Fig. 12.32 for undrained tests on undisturbed San Francisco Bay mud. Only values for the midrange of stresses are shown in Figs. 12.31 and 12.32. Effect of Composition
In general, the higher the clay content and the more active the clay, the more important are stress relaxation and creep, as illustrated by Figs. 4.22 and 4.23, where creep rates, approximated by steady-state values, are related to clay type, clay content, and plasticity. Timedependent deformations are more important at high water contents than at low. Deviatoric creep and secondary compression are greater in normally consolidated than overconsolidated soils. Although the magnitude of creep strains and strain rates may be small in sand or dry soil, the form of the
491
CREEP AND STRESS RELAXATION
creep tests on sands. The conflicting evidence may be due to the presence or absence of impurities that may lubricate or cement the soil in the presence of water (Human, 1992; Bowman, 2003). Volume Change and Pore Pressures
Due to the known coupling effects between shearing and volumetric plastic deformations in soils, an increase in either mean pressure or deviator stress can generate both types of deformations. Creep behavior is no exception. Time-dependent shear deformations are usually referred to as deviatoric creep or shear creep. Time-dependent deformations under constant stress referred to as volumetric creep. Secondary compression is a special case of volumetric creep. Deviatoric creep is often accompanied by volumetric creep. The ratio of volumetric to deviatoric creep fol-
E
Drained Triaxial Test
1
2820 min
Volumetric Strain (%)
Confining Pressure σ3 = 414 kPa 0.8
Deviator Stress from 344 to 377 kPa
0.6 D 90 min
0.4 0.2
Figure 12.32 Variation of creep strain rate with deviator
stress for undrained creep of normally consolidated San Francisco Bay mud.
1450 min
20 min C
2 min
0
A B
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Deviator strain (%)
(a) 1.0
Stress ratio q/p
behavior conforms with the patterns described and illustrated above. This is to be expected, as the basic creep mechanism is the same in all inorganic soils.6 Water may ‘‘lubricate’’ the particles and possibly increase the creep rate even though the basic mechanism of creep is the same for dry and wet materials (Losert et al., 2000). Takei et al. (2001) showed that the development of creep strains due to time-dependent breakage of talc specimens increased more for saturated specimens than dry ones. However, a negligible effect of water on creep rate was reported by Ahn-Dan et al. (2001) who performed creep tests on unsaturated and saturated crushed gravel and by Leung et al. (1996) who performed one-dimensional compression
0.8 0.6 0.4 0.2 0
0 1 2 3 4 Strain increment ratio dεv/dεs during creep
(b) Figure 12.33 Dilatancy relationship obtained from drained
6
Volumetric creep and secondary compression of organic soils, peat, and municipal waste fills can develop also as a result of decomposition of organic matter.
creep tests on kaolinite: (a) development of volumetric and deviatoric strains with time and (b) effect of stress ratio on strain increment ratio d / ds (from Walker, 1969).
492
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
lows a plastic dilatancy rule. Walker (1969) investigated the time-dependent change of these two components from incremental drained triaxial creep tests on normally consolidated kaolinite. The increase in shear strains with increase in volumetric strains at different times is shown in Fig. 12.33a. At the beginning of the triaxial test, the deviator stress was instantaneously increased from 344 to 377 kPa and kept constant. After an immediate increase in shear strains at constant volume (AB in Fig. 12.33a), section BD corresponds to primary consolidation that is controlled by the dissipation of pore pressures. After point D, creep occurred, and the ratio of volumetric to deviatoric strains was independent of time. This ratio decreased with increasing stress ratio as shown in Fig. 12.33b. This observation led to the time-dependent flow rule, which is similar to the dilatancy rule described in Section 11.20. Sand deforms with time in a similar manner. Under progressive deviatoric creep, the volumetric creep response is highly dependent on density, the stress level, and the stress path before creep. The rate of both volumetric and deviatoric creep increases with confining pressure, particularly after particle crushing becomes important at high stresses (Yamamuro and Lade, 1993). For dense sand under high deviator stress, dilative creep is observed (Murayama et al., 1984; Mejia et al., 1988). The volumetric response of dense sand and gravel with time is a highly complex function of stress
history, with some samples contracting or dilating (Lade and Liu, 1998; Ahn-Dan et al., 2001). Some dense sand samples contract initially but then dilate with time (Bowman and Soga, 2003). Further discussion of the creep behavior of sands in relation to mechanical aging phenomena is given in Section 12.11. The fundamental process of creep strain development is therefore similar to that of time-independent plastic strains, and the same framework of soil plasticity can possibly be used. It can be argued whether it is necessary to separate the deformation into time-dependent and independent components. Rateindependent behavior can be considered as the limiting case of rate-dependent behavior at a very slow rate of loading. Volumetric-deviatoric creep coupling implies that rapid application of a stress or a strain invariably results in rapid change of pore water pressures in a saturated soil under undrained conditions. For a constant total minor principal stress, the magnitude of the pore pressure change depends on the volume change tendencies of the soil when subjected to shear distortions. These tendencies are, in turn, controlled by the void ratio, structure, and effective stress, and can be quantified in terms of the pore pressure parameter A as discussed in Chapters 8 and 10. An example showing pore pressure increase with time for consolidated undrained creep tests on illite at several stress intensities is shown in Fig. 12.34. Figure 12.35 shows a slow decrease in
Figure 12.34 Pore pressure development with time during undrained creep of illite.
CREEP AND STRESS RELAXATION
493
Figure 12.35 Normalized pore pressure vs. time relationships during creep of kaolinite.
An increase in temperature decreases effective stress, increases pore pressure, and weakens the soil structure. Creep rates ordinarily increase and the relaxation stresses corresponding to specific values of strain decrease at higher temperature. These effects are illustrated by the data shown in Figs. 12.38 and 12.39.
Although the general form of the stress–strain–time and stress–strain rate–time relationships are similar to those shown above for triaxial loading conditions, the actual values may differ considerably. For example, undisturbed Haney clay, a gray silty clay from British Columbia, with a sensitivity in the range of 6 to 10, was tested both in triaxial compression and plane strain (Campanella and Vaid, 1974). Samples were normally consolidated both isotropically and under K0 conditions to the same vertical effective stress. Samples consolidated isotropically were tested in triaxial compression. Coefficient K0 consolidation was used for both K0 triaxial and plane strain tests. The results shown in Fig. 12.40 indicate that the precreep stress history had a significant effect on the deformations. The plane strain and K0 consolidated triaxial samples gave about the same creep behavior under the same deviatoric stress, which suggests that preventing strain in one horizontal direction and/or the intermediate principal stress were not factors of major importance for this soil under the test conditions used.
Effects of Test Type, Stress System, and Stress Path
Interaction Between Consolidation and Creep
Most measurements of time-dependent deformation and stress relaxation in soils have been done on samples consolidated isotropically and tested in triaxial compression or by measurement of secondary compression in oedometer tests. However, most soils in nature have been subjected to an anisotropic stress history, and deformation conditions conform more to plane strain than triaxial compression in many cases. Some investigations of these factors have been made.
Experimental evidence suggests that creep occurs during primary consolidation (Leroueil et al., 1985; Imai and Tang, 1992). Following the initial large change following load application, the pore pressure may either dissipate, with accompanying volume change if drainage is allowed, or change slowly during creep or stress relaxation, if drainage is prevented. The development of complete effective stress and void ratio equilibrium may take a long time. One illustration of
pore pressure during the sustained loading of kaolinite. Similar behavior was demonstrated in the measured stress paths of undrained creep test on San Francisco Bay mud (Arulanandan et al., 1971). As shown in Fig. 12.36, the effective stress states shifted toward the failure line. At higher stress levels, the specimens eventually underwent creep rupture. However, soil strength in terms of effective stresses does not change unless there are chemical, biological, or mineralogical changes during the creep period. This is illustrated by the stress paths shown schematically in Fig. 12.37, where the pre- and postcreep strengths fall on the same failure envelope. Effects of Temperature
TIME EFFECTS ON STRENGTH AND DEFORMATION
Normal Undrained Triaxial Compression Test: Effective Stress Path
50 Possible Critical State Line Deviator Stress q (kPa)
12
Total Stress Path of 3 Triaxial Compression Test
40
1
30 Effective Stress State After 1,000 min Creep
20
After 20,000 min Creep Effective Stress Path of Undrained Creep
10
0 0
10
20
30
40
50
60
70
80
Mean Pressure p (kPa)
(a)
400 Possible Critical State Line
Normal Undrained Triaxial Compression Test: Effective Stress Path Total Stress Path of Triaxial Compression Test 3
320 Deviator Stress q (kPa)
494
1 240 Effective Stress State After 1,000 min Creep 160
After 20,000 min Creep Effective Stress Path of Undrained Creep
80
0
0
80
160
240 320 400 480 Mean Pressure p (kPa)
560
640
(b) Figure 12.36 Measured stress paths of undrained creep tests of San Francisco Bay mud.
Initial confining pressure: (a) 49 kPa and (b) 392 kPa (from Arulanandan et al., 1971).
CREEP AND STRESS RELAXATION
495
Figure 12.37 Effects of undrained creep on the strength of normally consolidated clay.
Figure 12.38 Creep curves for Osaka clay tested at different temperatures—undrained tri-
axial compression (Murayama, 1969).
this is given by Fig. 10.5, where it is shown that the relationship between void ratio and effective stress is dependent on the time for compression under any given stress. Another is given by Fig. 12.41, which shows pore pressures during undrained creep of San Francisco Bay mud. In each sample, consolidation under an effective confining pressure of 100 kPa was allowed for 1800 min prior to the cessation of drainage and the start of a creep test. The consolidation period was greater than that required for 100 percent primary consolidation. The curve marked 0 percent stress level refers to a specimen maintained undrained but not subject to a deviator stress. This curve indicates that each
of the other tests was influenced by a pore pressure that contained a contribution from the prior consolidation history. The magnitude and rate of pore pressure development if drainage is prevented following primary consolidation depend on the time allowed for secondary compression prior to the prevention of further drainage. This is illustrated by the data in Fig. 12.42, which show pore pressure as a function of time for samples that have undergone different amounts of secondary compression. In summary, creep deformation depends on the effective stress path followed and any changes in stress
496
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
Figure 12.39 Influence of temperature on the initial and final stresses in stress relaxation
tests on Osaka clay—undrained triaxial compression (Murayama, 1969).
Figure 12.40 Creep curves for isotropically and K0-consolidated samples of undisturbed
Haney clay tested in triaxial and plane strain compression (from Campanella and Vaid, 1974). Reproduced with permission from the National Research Council of Canada.
RATE EFFECTS ON STRESS–STRAIN RELATIONSHIPS
497
Figure 12.41 Pore pressure development during undrained creep of San Francisco Bay mud
after consolidation at 100 kPa for 1800 min (from Holzer et al., 1973). Reproduced with permission from the National Research Council of Canada.
Figure 12.42 Pore pressure development under undrained conditions following different periods of secondary compression (from Holzer et al., 1973). Reproduced with permission from the National Research Council of Canada.
with time. Furthermore, time-dependent volumetric response is governed both by the rate of volumetric creep and by the rate of consolidation. The latter is a complex function of drainage conditions and material properties, especially the permeability and compressibility. Because the effective stress path is controlled by the rate of loading and drainage conditions, the separation of consolidation and creep deformations can be difficult in the early stage of time-dependent deformation as given by section BD in Fig. 12.33a. In some cases, a fully coupled analysis of soil–pore fluid interaction with an appropriate time-dependent constitutive model
is necessary to reconcile the time-dependent deformations observed in the field and laboratory.
12.8 RATE EFFECTS ON STRESS–STRAIN RELATIONSHIPS
An increase in strain rate during soil compression is manifested by increased stiffness, as was noted in Section 12.3. In essence, the state of the soil jumps to the stress–strain curve that corresponds to the new strain rate. Commonly, this rate-dependent stress–strain
498
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
curve, noted by S˘uklje (1957), is the same as if the soil had been loaded from the beginning at the new strain rate. This phenomenon is often observed in clays. Examples are given in Fig. 12.43a for undrained triaxial compression tests of Belfast and Winnipeg clays (Graham et al., 1983a) and Fig. 12.43b for onedimensional compression tests of Batiscan clay (Leroueil et al., 1985).
0.6 5% /h R 0.5 R 0.5% /h
The undrained shear strength and apparent preconsolidation pressure of soils decrease with decreasing strain rate or increasing duration of testing. Preconsolidation pressures obtained from one-dimensional consolidation tests and undrained shear strengths obtained from triaxial tests are just two points on a soil’s yield envelope in stress space. For a given metastable soil structure, the degree of rate dependency of preconsolidation pressure is similar to that of undrained shear strength (Soga and Mitchell, 1996). If the apparent preconsolidation pressure depends on the strain rate at which the soil is deforming, then the same analogy can be expanded to the assumption that the size of the entire yield envelope is also strain rate dependent (Tavenas and Leroueil, 1977). Figure 12.44 shows a family of strength envelopes corresponding to constant strain rates7 obtained from drained and undrained creep tests on stiff plastic Mascouche clay from Quebec (Leroueil and Marques, 1996). The effective stress failure line of soil is uniquely defined regardless of the magnitude of the strain rate applied in undrained compression. Figure 12.45a shows the failure line of Haney clay (Vaid and Campanella, 1977). The line represents the stress conditions at the maximum ratio of 1 / 3. The data were obtained by various undrained tests, and a unique failure line can be observed. Figure 12.45b shows the undrained stress paths and the critical state line of reconstituted mixtures of sand and clay with plasticity indices ranging from 10 to 30 (Nakase and Kamei, 1986). A unique critical state line can be observed although the rates of shearing are different. The change in undrained shear strength with strain rate results from a difference in generation of excess pore pressures. A decrease in strain rate leads to larger excess pore pressures at failure due to creep deformation.
The strain rate is defined as ˙ vs ⫽ 兹˙ 2v ⫹ ˙ s2, where ˙ v is the volumetric strain rate and ˙ s is the deviator strain rate (Leroueil and Marques, 1996). Whether the use of this strain rate measure is appropriate or not remains to be investigated. 7
0.05% /h Belfast Clay 4 m σ1c = σv0
0.3
R 16%/h
0.2 1%/h 0.25%/h Winnipeg Clay 11.5 m σ1c > σv0
0.1
CAU Triaxial Compression Tests Relaxation Tests (R) 0
0
4
8
12
16
20
Axial Strain
0
0
50
Effective Stress σv (kPa) 100 150 200
.
εv2 5
10
Strain εv (%)
Yield and Strength Envelopes of Clays
(σ1 – σ3)/2σ1c
0.4
.
εv2
.
εv1
.
εv1
.
.
εv2
εv1
.
15
εv1
.
20
25
250
εv2 SP1 test SP2 test . εv1 = 2.70 & 10–6 s–1 . εv2 = 1.05 & 10–7 s–1 . εv3 = 1.34 & 10–5 s–1
.
εv3
.
εv1
.
εv1
30
Figure 12.43 Rate-dependent stress–strain relations of clays: (a) undrained triaxial compression tests of Belfast and Winnipeg clay (Graham et al., 1983a) and (b) onedimensional compression tests of Batiscan clay (Leroueil et al., 1985).
RATE EFFECTS ON STRESS–STRAIN RELATIONSHIPS
499
Figure 12.44 Influence of strain rate on the yield surface of Masouche clay (from Leroueil and Marques, 1996).
Excess Pore Pressure Generation in Normally Consolidated Clays
Excess pore pressure development depends primarily on the collapse of soil structure. Accordingly, strain is the primary factor controlling pore pressure generation. This is shown in Fig. 12.46 by the undrained stress– strain–pore pressure response of normally consolidated natural Olga clay (Lefebvre and LeBouef, 1987). The natural clay specimens were normally consolidated under consolidation pressures larger than the field overburden pressure and then sheared at different strain rates. Although the deviator stress at any strain increases with increasing strain rate, the pore pressure versus strain curves are about the same at all strain rates. At a given deviator stress, the pore pressure generation was larger at slower strain rates as a result of more creep under slow loading. This is consistent with the observation made in connection with undrained creep of clays as discussed in Section 12.7. Straindriven pore pressure generation was also suggested by Larcerda and Houston (1973) who showed that pore pressure does not change significantly during triaxial
stress relaxation tests in which the axial strain is kept constant. Overconsolidated Clays
Rate dependency of undrained shear strength decreases with increasing overconsolidation, since there is no contraction or collapse tendency observed during creep of heavily overconsolidated clays. Sheahan et al. (1996) prepared reconstituted specimens of Boston blue clay at different overconsolidation ratios and sheared them at different strain rates in undrained conditions. Figure 12.47 shows that the undrained stress path and the strength were much more strain rate dependent for lightly overconsolidated clay (OCR ⫽ 1 and 2) than for more heavily overconsolidated clay (OCR ⫽ 4 and 8). The results also show that the strength failure envelope is independent of strain rate as discussed earlier. The strain rate effects on stress–strain–pore pressure response of overconsolidated structured Olga clays are shown in Fig. 12.48 (Lefebvre and LeBouef, 1987). The natural samples were reconsolidated to the field
500
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
0.4 Const. Stress Creep Const. Rate of Strain Shear Const. Rate of Loading Shear Aged Samples Const. Load Creep Step Creep Thixotropic Hardened
(σ1 – σ3)/2σ1c
0.3
0.2
0.1
0 0
0.1
0.2
0.3
0.4 (σ1 + σ3)/2σ1c
0.5
0.6
0.7
0.8
(a) 1.0
0.8
0.8
al-
St
0.2
itic
M-15. ε(%/min) . 7&10-1: ε. 1 -2 7&10 : ε2 . 7&10-3: ε3
0.4
0
Cr
Cr
e
in
-L
K0
q/σvc
St itic
al-
q/σvc
0.4
ate
0.6
ate
0.6
Lin
Lin
e
e
1.0
M-10 . ε(%/min) . 7&10-1: ε. 1 7&10-2: ε2 . 7&10-3: ε3
0.2 0 Cr
Cr
0
0.2
e
e
Lin
–0.4
Lin
–0.4
ate
ate
St
St
al-
al-
itic
–0.2
itic
–0.2
–0.6
e
in
-L
K0
–0.6 0.4
0.6 p/σvc
0.8
1.0
M15 Soil (Plasticity Index = 15)
(b)
0
0.2
0.4
0.6 p/σvc
0.8
1.0
M10 Soil (Plasticity Index = 10)
Figure 12.45 Strain rate independent failure line: (a) Haney clay (from Vaid and Campa-
nella, 1977) and (b) reconstituted mixtures of sand and clay (from Nakase and Kamei, 1986).
overburden pressure. The deformation is brittle, with strain softening indicating development of localized shear failure planes. Up to the peak stress, the response follows what has been described previously, that is the stress–strain response is rate dependent and the pore pressure generation is strain dependent but independent of rate. However, after the peak, the pore pressure
generation becomes rate dependent. This is due to local drainage within the specimens as the deformation becomes localized. As the time to failure increased, there is more opportunity for local drainage toward the dilating shear band and the measured pore pressure may not represent the overall behavior of the specimens. The difference in softening due to swelling at the fail-
501
RATE EFFECTS ON STRESS–STRAIN RELATIONSHIPS
100 80 60 Axial Strain Rate 0.1 %/hr 0.5 %/hr 2.6 %/hr 12.3 %/hr
40
Excess Pore Pressure Δu (kPa)
20 0 140
1
2
3
4
5
6
7 8 Axial Strain (%)
120 100 80
Axial Strain Rate 0.1 %/hr 0.5 %/hr 2.6 %/hr 12.3 %/hr
60 40 20 0
1
2
3
4
5
6
7 8 Axial Strain (%)
(σa – σr)/2σvm
Figure 12.46 Stress–strain and pore pressure–strain curves for normally consolidated Olga clay (from Lefebvre and LeBouef, 1987).
0.4
Effective Stress State at Peak for Axial Strain Rate = 0.051 %/hr Axial Strain Rate = 0.50 %/hr Axial Strain Rate = 5.0 %/hr Axial Strain Rate = 49 %/hr
Initial K0 Consolidation State Effective Stress Path for Axial Strain Rate = 0.50 %/hr
OCR=1 Large Rate Effect
0.3
0.2
OCR=8 Negligible Rate Effect
OCR=4
OCR=2 OCR=1
0.1 OCR=2 OCR=4 0.0
0.2 OCR=8
0.4
0.6
0.8 (σa + σr)/2σvm
-0.1
Figure 12.47 Rate dependency stress path and strength of overconsolidated Boston blue clay (from Sheahan et al., 1996).
Overconsolidated Olga Clay Undrained Triaxial Compression Tests Initial Isotropic Confining Pressure = 17.6 kPa
70
Deviator Stress q (kPa)
Deviator Stress q (kPa)
120
Excess Pore Pressure Δu (kPa)
Normally Consolidated Olga Clay Undrained Triaxial Compression Tests Initial Isotropic Confining Pressure =137 kPa
60 50 40 30
Axial Strain Rate 0.1 %/hr 0.5 %/hr 2.5 %/hr 12.3 %/hr
20 10 0
1
2
3
4
5
6
7
8
Axial Strain (%) 20
Axial Strain Rate 0.1 %/hr 0.5 %/hr 2.6 %/hr 12.3 %/hr
10
0
1
2
3
4
5
6
7
8
Axial Strain (%)
Figure 12.48 Stress–strain and pore pressure–strain curves for overconsolidated Olga clay (from Lefebvre and LeBouef, 1987).
ure plane results in apparent rate dependency at large strains. Similar observations were made by Atkinson and Richardson (1987) who examined local drainage effects by measuring the angles of intersection of shear bands with very different times of failure. Rate Effects on Sands
Similar rate-dependent stress–strain behavior is observed in sands (Lade et al., 1997), but the effects are quite small in many cases (Tatsuoka et al., 1997; Di Benedetto et al., 2002). An example of time dependency observed for drained plane strain compression tests of Hostun sand is shown in Fig. 12.49 (Matsushita et al., 1999). The stress–strain curves for three different strain rates (1.25 ⫻ 10⫺1, 1.25 ⫻ 10⫺2, and 1.25 ⫻ 10⫺3 %/min) are very similar, indicating very small rate effects when the specimens are sheared at a constant strain rate. On the other hand, the change from one rate to another temporarily increases or decreases the resistance to shear. The influence of acceleration rather than the rate is reflected by the significant creep deformation and stress relaxation of this rateinsensitive material as shown the figure. This is differ-
12
6.0
TIME EFFECTS ON STRENGTH AND DEFORMATION
Variation of Stress-strain curve by Constant Strain Rate Tests at Axial Strain Rates = 0.125, 0.0125 and 0.00125 %/min. A Very Small Rate Effect Is Observed for Continuous Loading.
Creep
Stress Ratio σa /σr
5.5
CRS at 0.125%/min
300
CRS at 0.00125%/min
CRS at 0.125%/min
5.0
Creep Stress Relaxation CRS at 0.00125%/min
4.5 Creep
4.0
CRS at 0.125%/min
3.5
Creep
Accidental Pressure Drop Followed by Relaxation Stage
CRS at 0.125%/min
3.0 0
1
2
3
4
5
6
7
Young's Modulus, Esec or Eeq (MPa)
502
Esec = Δq/εa, Eeq = (Δq)SA / (εa)SA NSF-Clay Isotropically Consolidated Emax = 239 MPa p0 = 300 kPa
200
100
8
Shear Strain γ = εa – εr (%)
0
10-3
10-2
10-1
100
Axial Strain, εa or Single Amplitude of Cyclic Axial Strain, (εa)SA (%)
Figure 12.49 Creep and stress relaxation of Hostun sand
(from Matsushita et al., 1999).
Figure 12.50 Clay stiffness degradation curves at three
strain rates (from Shibuya et al., 1996).
ent from the observations made for clays as shown in Fig. 12.43 in which a unique stress–strain–strain rate relationship was observed. Hence, the modeling of stress–strain–rate behavior of sands appears to be more complicated than that of clays, and further investigation is needed, as time-dependent behavior of sands can be of significance in geotechnical construction as discussed further in Section 12.10.
Although the magnitude is small, the strain rate dependency of the stress–strain relationship is observed even at small strain levels for clays. The stiffness increases less than 6 percent per 10-fold increase in strain rate (Leroueil and Marques, 1996). The rate dependency on stiffness degradation curves measured by monotonic loading of a reconstituted clay is shown in Fig. 12.50 (Shibuya et al., 1996). At different strain levels, the increase in the secant shear modulus with shear strain rate ˙ is often expressed by the following equation (Akai et al., 1975; Isenhower and Stokoe, 1981; Lo Presti et al., 1996; Tatsuoka et al., 1997): G( ) ⫽
G
log ˙ G( , ˙ ref)
(12.34)
where G is the increase in secant shear modulus with increase in log strain rate log ˙ , and G( , ˙ ref) is the secant shear modulus at strain and reference strain rate ˙ ref. The magnitude is large in clays, considerably less in silty and clayey sands, and small in clean sands (Lo Presti et al., 1996; Stokoe et al., 1999). The variation of G with strain is shown in Fig. 12.51 for dif-
Coefficient of Strain Rate, (γ)
Stiffness at Small and Intermediate Strains
Shear Strain, γ (%)
Figure 12.51 Strain rate parameter G and strain level for
several clays (from Lo Presti et al., 1996).
MODELING OF STRESS–STRAIN–TIME BEHAVIOR
ferent plasticity clays (Lo Presti et al., 1996). The magnitude of rate dependency increases with strain level, especially for strain levels larger than 0.01 percent, which is within the preplastic region zone 3 described in Section 11.17. Rate Effects During Cyclic Loading
The frequencies of cyclic loading to which a soil is subjected can vary widely. For example, the frequency of sea and ocean waves is in the range of 10⫺2 to 10⫺1 Hz, earthquakes are in the range of 0.1 to a few hertz, and machine foundations are in the range of 10 to 100 Hz. Similarly to monotonic loading, the effect of loading frequency on shear modulus degradation is small in clean, coarse-grained soils (Bolton and Wilson, 1989; Stokoe et al., 1995), but the effect becomes more significant in fine-grained soils (Stokoe et al., 1995; d’Onofrio et al., 1999; Matesic and Vucetic, 2003; Meng and Rix, 2004). An example of frequency effects on a shear modulus degradation curve for a clay obtained from cyclic loading is shown in Fig. 12.50 along with the monotonic data. Figure 12.52 shows the effect of frequency on shear modulus of several soils at very small shear strains (less than 10⫺3 percent) measured by torsional shear and resonant column apparatuses (Meng and Rix, 2004). The effect is 10 percent increase per log cycle at most. At a given frequency of cyclic loading, the strain rate applied to a soil increases with applied shear strain as shown by the equation below: ˙ ⫽ 4ƒ c
(12.35)
where ƒ is the frequency and c is the cyclic shear strain amplitude. Using Eq. (12.35), Matesic and Vucetic (2003) report values of G of 2 to 11 percent for clays and 0.2 to 6 percent for sands as the strain rate increases 10-fold. The values of G in general decreased when the applied cyclic shear strain increased from 5 ⫻ 10⫺4 percent to 1 ⫻ 10⫺2 percent. It should be noted that the strain range examined is within the non-linear elastic range (zone 1 to zone 2 in Section 11.17). The monotonic loading data presented in Fig. 12.51 show that the rate effect becomes more pronounced at larger strain, that is, as plastic deformations become more significant. Hence, it is possible that the fundamental mechanisms of rate dependency are different at small elastic strain levels than at larger plastic strains. Small strain damping shows more complex frequency dependency, as shown in Fig. 12.53 (Shibuya et al., 1995; Meng and Rix, 2004). At a frequency of more than 10 Hz, the damping ratio increases with increased frequency, possibly due to pore fluid viscosity effects. As the applied frequency decreases, the damping ratio decreases. However, at a frequency less than 0.1 Hz, the damping ratio starts to increase with decreasing frequency. This may result from creep of the soil (Shibuya et al., 1995). 12.9 MODELING OF STRESS–STRAIN–TIME BEHAVIOR
Constitutive models are needed for the solution of geotechnical problems requiring the determination of de-
250
Shear Modulus G (MPa)
Vallencca Clay
200 Sandy Elastic Silt
150 100
Kaolin Kaolin
Sandy Lean Clay
50
Sandy Silty Clay Kaolin Subgrade Fat Clay
0
10-2
10-1
100 Frequency (Hz)
101
102
Figure 12.52 Rate dependency of cyclic small strain stiffness of a sandy elastic silt (from
Meng and Rix, 2004).
503
504
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
6
Clayey Subgrades
5 Damping (%)
Augusta Clay Sandy Lean Clay
4 Pisa Clay Vallencca Clay
3
Fat Clay Sandy Silty Clay
2 Sandy Elastic Silt
1 Kaolin
10-2
10-1
100
101
102
Frequency (Hz) Figure 12.53 Effect of strain rate of damping ratio of soils (from Shibuya et al., 1995 and
Meng and Rix, 2004).
formations, displacements, and strength and stability changes that occur over time periods of different lengths. Various approaches have been used, including empirical curve fitting, extensions of rate process theory, rheological models, and advanced theories of viscoelasticity and viscoplasticity. Owing to the complexity of stress states, the many factors that influence the creep and stress relaxation properties of a soil, and the difficulty of accounting for concurrent volumetric and deviatoric deformations in systems that are many times undergoing consolidation as well as secondary compression or creep, it is not surprising that development of general models that can be readily implemented in engineering practice is a challenging undertaking. Nonetheless, some progress has been made in establishing functional forms and relationships that can be applied for simple analyses and comparisons, and one of these is developed in this section. A complete review and development of all recent theories and proposed relationships for creep and stress relaxation is beyond the scope of this book. Comprehensive reviews of many models for representation of the timedependent plastic response of soils are given in Adachi et al. (1996). General Stress–Strain–Time Function Strain Rate Relationships between axial strain rate ˙ and time t of the type shown in Figs. 12.4 and 12.5
冉冊
ln ˙ ⫽ ln ˙ (t1,D) ⫺ m ln
or
˙ ˙ (t1,D)
冉冊
⫽ ⫺m ln
t t1
(12.36)
(12.37)
where ˙ (t1,D) is the axial strain rate at unit time and is a function of stress intensity D, m is the absolute value of the slope of the straight line on the log strain rate versus log time plot, and t1 is a reference time, for example, 1 min. Values of m generally fall in the range of 0.7 to 1.3 for triaxial creep tests; lower values are reported for undrained conditions than for drained conditions. For the development shown here, the stress intensity D is taken as the deviator stress (1 ⫺ 3). A shear stress or stress level could also be used. The same data plotted in the form of Figs. 12.3, 12.31, and 12.32 can be expressed by
冋 册 ˙ ˙ (t,D0)
ln
⫽ D
(12.38)
or ln ˙ ⫽ ln ˙ (t,D0) ⫹ D
(12.39)
in which ˙ (t,D0) is a fictitious value of strain rate at D ⫽ 0, a function of time after start of creep, and is the slope of the linear part of the log strain rate versus stress plot. From Eqs. (12.37) and (12.39)
can be expressed by ln
t t1
冉冊
ln ˙ (t1,D) ⫺ m ln For D ⫽ 0,
t ⫽ ln ˙ (t,D0) ⫹ D t1
(12.40)
冉冊
ln ˙ (t,D0) ⫽ ln ˙ (t1,D0) ⫺ m ln
t t1
MODELING OF STRESS–STRAIN–TIME BEHAVIOR
(12.41)
in which ˙ (t1,D0) is the value of strain rate obtained by projecting the straight-line portion of the relationship between log strain rate and deviator stress at unit time to a value of D ⫽ 0. Designation of this value by A and substitution of Eq. (12.41) into Eq. (12.39) gives
冉冊
ln ˙ ⫽ ln A ⫹ D ⫺ m ln
t t1
vided the variation of strength with water content is known. Since normal strength tests are considerably simpler and less time consuming than creep tests, the uniqueness of the quantity Dmax can be useful because the results of a limited number of tests can be used to predict behavior over a range of conditions. A further generalization of Eq. (12.43) then is
冉冊
˙ ⫽ Ae
冉冊 t1 t
(12.42)
(12.44)
where ⫽ Dmax
m
(12.43)
This simple three-parameter equation has been found suitable for the description of the creep rate behavior of a wide variety of soils. The parameter A is shown in Fig. 12.54. Since it reflects an order of magnitude for the creep rate under a given set of conditions, it is in a sense a soil property. A minimum of two creep tests are needed to establish the values of A, , and m for a soil. If identical specimens are tested using different creep stress intensities, a plot of log strain rate versus log time yields the value of m, and a plot of log strain rate versus stress for different values of time can be used to find and A from the slope and the intercept at unit time, respectively. The parameter has units of reciprocal stress. If stress is expressed as the ratio of creep stress to strength at the beginning of creep, D/Dmax, then the dimensionless quantity Dmax should be used. For a given soil and test type, values of Dmax do not vary greatly for different water contents, as the change in with water content is compensated by a change in Dmax. Thus the strain rate versus time behavior for any stress at any water content can be predicted from the results of creep tests at any other water content, pro-
Figure 12.54 Influence of creep stress magnitude on the
creep rate at a given time after stress application.
m
t ˙ ⫽ A exp(D) 1 t
which may be written D
505
D⫽
D Dmax
(12.45)
Strain A general relationship between strain and time is obtained by integration of Eq. (12.43). Two solutions are obtained, depending on the value of m. If ⫽ 1 at t ⫽ t1 ⫽ 1, then ⫽ 1 ⫹
A 1⫺m
exp (D)(t1⫺m ⫺ 1)
when m ⫽ 1 (12.46)
and ⫽ 1 ⫹ A exp (D)ln t
when m ⫽ 1
(12.47)
Creep curve shapes corresponding to these relationships are shown in Fig. 12.55. These curves encompass the variety of shapes shown in Fig. 12.2. A similar equation to Eq. (12.46) was developed by Mesri et al. (1981) from Eq. (12.43). The initial time-independent strain was neglected, and the resulting equation is At1
冉冊
t ⫽ exp(D) 1⫺m t1
1⫺m
(12.48)
It may be seen in Fig. 12.56 that this equation describes the uniaxial creep behavior of three clays very well. Data for both drained and undrained creep are shown. Stress Relaxation Stress decay during stress relaxation is approximately linear with logarithm of time until it levels off at some residual stress after a long time. There is equivalency between creep and stress relaxation in that a general phenomenological model that predicts one can be used to predict the other, as shown by Akai et al. (1975), Lacerda (1976), Borja (1992), and others. For example, Eq. (12.44) takes the following form when stress relaxation is started after deformation at constant rate of strain (Lacerda and Houston, 1973):
506
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
Figure 12.55 Creep curve shapes predicted by the general stress–strain–time function of Eqs. (12.46) and (12.47).
D D t ⫽ ⫽ 1 ⫺ s log D0 D0 t0
(t ⬎ t0)
where s is the slope of the stress relaxation curve, and the zero subscript refers to conditions at the start of stress relaxation. Also s⫽
#
D
t0 ⫽
(12.49)
(12.50)
h0 ˙
(12.52)
where h0 is the strain rate to give a delay time of t0 ⫽ 1 min before stresses begin to relax. The data presented by Lacerda and Houston (1973) indicate that the values of # and h0 increase with increasing plasticity of the soil. Constitutive Models
where #⫽
2.3(1 ⫺ m)
(12.51)
The validity of this equation has been established for m ⬍ 1.0. Pore pressures decrease slightly during undrained stress relaxation. Stresses may not begin to relax immediately after the strain rate is reduced to zero. The time t0 between the time that the strain rate is reduced to zero and the beginning of relaxation is a variable that depends on the soil type and the prior strain rate. This is shown schematically in Fig. 12.57. The greater the initial rate of strain to a given deformation, the more quickly relaxation begins. This is a direct reflection of the relative differences in equilibrium soil structures during and after deformation. Values of t0 as a function of prior strain rate are shown in Fig. 12.58 for several soils. These curves can be described empirically by
Different rheological models have been proposed for the mathematical description of the stress–strain–time behavior of soils that are made up of combinations of linear springs, viscous dashpots, and sliders. In the Murayama and Shibata (1958), Christensen and Wu (1964), and Abdel-Hady and Herrin (1966) models, the dashpots are nonlinear, with stress–flow rate response governed by rate process theory. Rheological models are useful conceptually to aid in recognition of elastic and plastic components of deformation. They are helpful for visualization by analogy of viscous flow that accompanies time-dependent change of structure to a more stable state. Mathematical relationships can be developed in a straightforward manner for the description of creep, stress relaxation, steady-state deformation, and the like in terms of the model constants. In most cases, these relationships are complex and necessitate the evaluation of several parameters that may not be valid for different stress intensities or soil states. Only one-dimensional stresses and deformations are
MODELING OF STRESS–STRAIN–TIME BEHAVIOR
Figure 12.56 Correspondence between creep strain predicted by Eq. (12.48) and measured
values. Diagrams are from Mesri et al. (1981), which were based on analyses by Semple (1973).
507
508
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
12.10
CREEP RUPTURE
As discussed in Section 12.2 and shown in Fig. 12.6, the strength of a soil and the stress–strain curve may be changed as a result of creep. In some cases, such as the drained creep of a compressive soil, the strength may be increased. Changes in strength may be as much as 50 percent or more of the strength measured in normal undrained tests prior to creep. Causes of Strength Loss During Creep Figure 12.57 Influence of prior strain rate on stress relaxa-
tion.
Figure 12.58 Influence of prior strain rate on the time to start of stress relaxation (adapted from Lacerda and Houston, 1973).
considered. None appears to exist that has the generality and simplicity of the three-parameter creep Eqs. (12.43), (12.46), and (12.47). Both plasticity and creep are controlled by the motion of dislocations or breakage among soil particles, so it may be physically more correct to predict both plastic and creep deformations with one equation. Two particularly promising approaches are based on an extension of the Cam-clay model to take into account time-dependent volumetric and deviatoric deformations (Kavazanjian and Mitchell, 1980; Borja and Kavazanjian, 1985; Kaliakin and Dafalias, 1990; Borja, 1992; Al-Shamrani and Sture, 1998; Hashiguchi and Okayasu, 2000) and on an elasto-viscoplastic equation developed using flow surface theory (Sekiguchi, 1977, 1984; Matsui and Abe, 1985, 1986, 1988; Matsui et al., 1989; Yin and Graham, 1999) and overstress theory (Adachi and Oka, 1982; Katona, 1984: Kutter and Sathialingham, 1992; Rocchi et al., 2003).
Loss of strength during creep is particularly important in soft clays deformed under undrained conditions and heavily overconsolidated clays in drained shear. Both of these conditions are pertinent to certain types of engineering problems: the former in connection with stability of soft clays immediately after construction, and the latter in connection with problems of long-term stability. The loss of strength as a result of creep may be explained in terms of the following principles of behavior: 1. If a significant portion of the strength of a soil is due to cementation, and creep deformations cause failure of cemented bonds, then strength will be lost. 2. In the absence of chemical or mineralogical changes the strength depends on effective stresses. If creep causes changes in effective stress, then strength changes will also occur. 3. In almost all soils, shear causes changes in pore pressure during undrained deformation and changes in water content during drained deformation. 4. Water content changes cause strength changes. These processes are illustrated by the stress paths and effective stress envelope shown schematically in Fig. 12.37. Strength loss in saturated, heavily overconsolidated clays tested under undrained conditions has also been reported, for example, Casagrande and Wilson (1951), Goldstein and Ter-Stepanian (1957), and Vialov and Skibitsky (1957). This may be explained as follows. Shear deformations cause dilation and the development of negative pore pressures, which do not develop uniformly throughout the sample but concentrate along planes where the greatest shearing stresses and strains develop. With time during sustained loading, water migrates into zones of high negative pore pressures leading to softening and strength decrease relative to the strength in ‘‘normal’’ undrained strength tests. This leads to shear band formation.
CREEP RUPTURE
This process is shown in Fig. 12.59 with reference to an effective stress failure envelope for a heavily overconsolidated clay. The effective stress path is represented by AB, and AC represents the total stress path in a conventional consolidated-undrained (CU) test. The negative pore pressure at failure is CB. If a creep stress DE is applied to the same clay, a negative pore pressure EF is induced. This negative pore pressure dissipates during creep, and the clay in the shear zone swells. At the end of the creep period, the effective stress will be as represented by point E. Further shear starting from these conditions leads to strength G, which is less than the original value at B. It is evident also that if the negative pore water pressure is large enough, and the sustained load is applied long enough, then point E could reach the failure envelope. This appears to have been the conditions that developed in several cuts in heavily overconsolidated brown London clay, which failed some 40 to 70 years after excavations were made (Skempton, 1977).
509
in turn, a function of deformation rates, the hydraulic conductivity, and the surrounding water pressure and drainage conditions. The time to failure of heavily overconsolidated clays in which negative pore water pressures develop as a result of unloading is best estimated on the basis of drained strengths, effective stresses, and consideration of the rate of swelling that is possible for the particular clay and ambient stress and groundwater conditions. An exception would be when strength loss results from the time-dependent rupture of cementing bonds. In this case, sustained load creep tests in the laboratory may allow establishment of a stress level versus time-to-failure relationship. For soils subject to failure during undrained creep, the time to failure is usually a negative exponential function of the stress, for stresses greater than some limiting value below which no failure develops even after very long times.8 The relationship between deviator stress, normalized to the pretest major principal effective stress, and time to failure for Haney clay is shown in Fig. 12.60. These and similar data define cer-
Time to Failure
The time to failure of soils susceptible to strength loss under sustained stresses depends on the rates at which pore pressures develop and at which water can migrate into or out of the critical shear zone. These rates are,
8 This critical stress below which creep rupture does not occur has been termed the upper yield, the lower yield being the stress below which deformations are elastic (Murayama and Shibata 1958, 1964).
Figure 12.59 Stress paths for normal undrained shear and drained creep of heavily overconsolidated clay.
510
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
tain principles relating to the probability of creep rupture and the time to failure: 1. Values of the parameter m less than 1.0 in Eqs. (12.43) through (12.46) are indicative of a high potential strength loss during creep and eventual failure (Singh and Mitchell, 1969). 2. The minimum strain rate ˙ min prior to the onset of creep rupture decreases, and the time to failure increases, as the stress intensity decreases, as shown in Fig. 12.61 for Haney clay. The relationship is unique, as may be seen in Fig. 12.62, which shows that tƒ ⫽ Figure 12.60 Time to rupture as a function of creep stress
for Haney clay (Campanella and Vaid, 1972).
C ˙ min
(12.53)
Values of the constant C accurate to about 0.2 log cycles are given in Table 12.2. 3. The strain at failure is a constant independent of stress level, as shown in Fig. 12.63. The failure
Figure 12.61 Creep rate behavior of K0-consolidated, undisturbed Haney clay under axisymmetric loading (Campanella and Vaid, 1972).
511
SAND AGING EFFECTS AND THEIR SIGNIFICANCE
ƒ ⫽ constant ⫽
1 1⫺m
˙ mintƒ ⫽
C 1⫺m
(12.56)
Thus, the constant in Eq. (12.53) is defined by C ⫽ (1 ⫺ m)ƒ
Figure 12.62 Relationship between time to failure and min-
imum creep rate (from Campanella and Vaid, 1974). Reproduced with permission from the National Research Council of Canada.
Values of ƒ for Haney clay tested in three ways are shown in Fig. 12.63, and values of C and m are in Table 12.3. The agreement between predicted and measured values of C is reasonable. Predictions of the time to failure under a given stress may be made in the following way. Strain at failure can be determined by either a creep rupture test or by a normal shear or compression test. If a normal strength test is used, then the rate of strain must be slow enough to allow pore pressure equalization or drainage, depending on the conditions of interest, and the stress history and stress system should simulate those in the field. Parameter m can be established from a creep test, and then C can be computed from Eq. (12.57). Values of A and are established from creep tests at two stress intensities. Then, for t1 ⫽ 1, C ⫽ ˙ mintƒ ⫽ A exp(D)t1⫺m ƒ
strain is taken as the strain corresponding to the minimum strain rate. For the case of undrained creep rupture, this is consistent with the concept that pore pressure development is uniquely related to strain and independent of the rate at which it accumulates (Lo, 1969a, 1969b). The relationship expressed by Eq. (12.53) results directly from the fact that the strain at the point of minimum strain rate is a constant independent of stress or strain rate. The general stress–strain rate–time function [see Eq. (12.43)] describes the strain rate–time behavior until ˙ min is reached. For t1 ⫽ 1 and ⫽ 0 at t ⫽ 0, the corresponding strain–time equation is ⫽
A 1⫺m
exp(D)t1⫺m
1 1⫺m
˙ t mt1⫺m
(12.58)
and corresponding values of D and tƒ can be calculated using Eq. (12.58) rewritten as ln tƒ ⫽
1 1⫺m
冋 冉冊 册 ln
C ⫺ D A
(12.59)
Other constitutive models are available to model the complex time-dependent behavior under various loading conditions. For example, Sekiguchi (1977) developed a viscoplastic model that gives excellent representations of strain rate effects on undrained stress–strain behavior, stress relaxation, and creep rupture of normally consolidated clays. Other models listed in Section 12.9 are able to simulate timedependent behavior in a similar manner.
(12.54)
By setting ⫽ 0 at t ⫽ 0, the assumption is made that there is no instantaneous deformation. Substitution for A exp(D) in Eq. (12.54) gives ⫽
(12.57)
(12.55)
which at the point of minimum strain rate becomes
12.11 SAND AGING EFFECTS AND THEIR SIGNIFICANCE
Over geological time, lithification and chemical reactions can change sand into sandstone or clay into mudstone or shale. However, even over engineering time, behavior of soils can alter as stresses redistribute after construction (Fookes et al., 1988). As discussed in the previous sections, it is well established that finegrained soils and clays have properties and behavior that change over time as a result of consolidation,
512
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
Table 12.2
Creep Rupture Parameters for Several Clays
Soil Undisturbed Haney clay, N.C.b Undisturbed Haney clay, N.C.b Undisturbed Haney clay, N.C.b Undisturbed Seattle clay, O.C.c Undisturbed Tonegawa loamc Undisturbed Redwood City clay, N.C.c Undisturbed Bangkok mudc Undisturbed Osaka clayc
Test Typea
Creep Rate Parameter, m
C ⫽ (˙min tƒ) (0.2 log cycles)
ICU
0.7
1.2
ACU
0.4
0.2
ACU-PS
0.5
0.3
ICU
0.5
0.6
U
0.8
1.6
ICU
0.75
2.8
ICU
0.70
1.4
1.0
0.07
a
ICU, isotropic consolidated, undrained triaxial; ACU, K0 consolidated, undrained triaxial; ACU-PS, K0 consolidated, plane strain; and U, compression test. b Data from Campanella and Vaid (1974). c Data from Singh and Mitchell (1969).
Figure 12.63 Axial strain at minimum strain rate as a function of creep stress for undisturbed Haney clay (from Campanella and Vaid, 1974). Reproduced with permission from the National Research Council of Canada.
SAND AGING EFFECTS AND THEIR SIGNIFICANCE
Test Condition
Creep Rate Parameter m (from Table 12.2)
(from Fig. 12.63)
C Predicted by Eq. (12.57)
C Measured
ICUa ACUb ACU-PSc
0.7 0.4 0.5
2.8 0.3 0.5
0.84 0.18 0.25
1.2 0.20 0.30
ƒ
a
Isotropic consolidated, undrained triaxial. Anisotropic, consolidated, undrained triaxial. c Anisotropic consolidated, undrained, plane strain. Data from Campanella and Vaid (1974). b
shear, swelling, chemical and biological changes, and the like. Until recently it has not been appreciated that cohesionless soils exhibit this behavior as well. Much recent field evidence of the changing properties of granular soils over time is now available and these data suggest that recently disturbed or deposited granular soils gain stiffness and strength over time at constant effective stress—a phenomenon called aging. The evidence includes the time-dependent increase in stiffness and strength of densified sands as measured by cone penetration resistance (Mitchell and Solymer, 1984; Thomann and Hryciw, 1992; Ng et al., 1998) and the setup of displacement piles in granular materials (Astedt et al., 1992; York et al., 1994; Chow et al., 1998; Jardine and Standing, 1999; Axelsson, 2000). Hypotheses to explain this phenomenon include both creep processes and chemical and biological cementation processes. The discussion in this section is focused primarily on granular soils as the relevant aspects for clays are treated in detail throughout other sections of the book. Increase in Shear Modulus with Time
As discussed in Section 12.3, the shear modulus at small strain is known to increase with time under a confining stress, and this is considered to be the consequence of aging. This behavior can be quantified by a coefficient of shear modulus increase with time using the following formula (Anderson and Stokoe, 1978):
idation, t2 is some time of interest thereafter, G is the change in small strain shear modulus from t1 to t2, G1000 is the shear modulus measured after 1000 min of constant confining pressure, which must be after completion of primary consolidation, and NG is the normalized shear modulus increase with time. Large increase in stiffness due to aging is represented by large values of IG or NG. In general, the measured NG value for clays ranges between 0.05 and 0.25. The aging effect also increases with an increasing plasticity index as shown in Fig. 12.64 (Kokusho, 1987). The data in the figure have been supplemented by values of G/G for several sands compiled by Jamiolkowski (1996). Mesri et al. (1990) report that NG for sands varies between 0.01 and 0.03 and increases as the soil becomes finer. Jamiolkowski and Manassero (1995) give values of 0.01 to 0.03 for silica sands, 0.039 for sand with 50 percent mica, and 0.05 to 0.12 for carbonate sand. Experimental results show that the rate of increase in stiffness with time for very loose carbonate sand increases as the stress level increases (Howie et al., 2002). Isotropic stress state resulted in a slower rate of increase in stiffness. There is only limited field data that shows evidence of aging effects on stiffness. Troncoso and Garces (2000) measured shear wave velocities using downhole ΔG : Modulus Increase in Every 10-fold Time Increase G1000 : Modulus at 1,000 min
0.30
ΔG/G1000 = 0.03PI 0.5
Modulus Increase Ratio ΔG/G1000
Table 12.3 Predicted and Measured Values of C for Haney Clay
0.25
0.20 Clay Marcuson et al. (1972) Afifi et al. (1973) Trudeau et al. (1973) Anderson et al. (1973) Zen et al. (1978) Kokusho et al. (1982) Umehara et al. (1985) Sand Jamiolkowski (1996)
0.15 f
0.10
0.05
a = Ticino Sand (Silica) b = Hokksund Sand (Silica) c = Messina Sand and Gravel (Silica) d = Glauconite Sand (Quartz/Glauconite) e = Quiou Sand (Carbonate) f = Kenya Sand (Carbonate)
e d c a, b
IG ⫽ G/log(t2 /t1) NG ⫽ IG /G1000
(12.60) (12.61)
where IG is the coefficient of shear modulus increase with time, t1 is a reference time after primary consol-
513
0.00
0
20
40
60
80
100
Plasticity Index PI Figure 12.64 Modulus increase ratio for clays (from Kokusho, 1987), supplemented by the data for sands (from Jamiolkowski, 1996).
514
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
wave propagation tests in low-plasticity silts with fines contents from 50 to 99 percent at four abandoned tailing dams in Chile. The shear modulus normalized by the vertical effective stress is plotted against the age of the deposit in Fig. 12.65. The age of the deposits is expressed as the time since deposition. Although the soil properties vary to some degree at the four sites,9 very significant increase in stiffness at small strains can be observed after 10 to 40 years of aging. The degree to which secondary compression could have contributed to this increase is not known. Time-Dependent Behavior after Ground Improvement
Stiffness and strength of sand increase with time after disturbance and densification by mechanical processes such as blasting and vibrocompaction. Up to 50 percent or more increase in strength has been observed over 6 months (Mitchell and Solymer, 1984; Thomann and Hryciw, 1992; Charlie et al., 1992; Ng et al., 1998; Ashford, et al., 2004) as measured by cone penetration testing. The Jebba Dam project on the Niger River, Nigeria, was an early well-documented field case where aging effects in sands were both significant and widespread (Mitchell and Solymer, 1984). The project involved the treatment of foundation soils beneath a 42-m-high dam
and seepage blanket. Due to large depths of the loose sand deposit requiring densification, a two-stage densification program was performed. The upper 25 m of sand (and a 5- to 10-m-thick sand pad placed by hydraulic filling of the river) was densified using vibrocompaction. Deposits between depths of 25 to 40 m were densified by deep blasting. During the blasting operations, it was observed that the sand exhibited both sensitivity—that is, strength loss on disturbance—and aging effects. A typical example of the initial decrease in penetration resistance after blasting densification and subsequent increase with time is shown in Fig. 12.66. Initially after improvement, there was in some cases a decrease in penetration resistance, despite the fact that surface settlements ranging from 0.3 to 1.1 m were measured. With time (measured up to 124 days after improvement), however, the cone penetration resistance was
Figure 12.65 Normalized shear modulus as function of aging of tailings (from Troncoso and Garces, 2000).
9
The four sites identified by Troncoso and Garces (2000) are called Barahona, Cauquenes, La Cocinera, and Veta del Agua and the aging times between abandonment and testing were 28, 19, 5, and 2 years, respectively. The tailing deposits at Barahona had a liquid limit of 41 percent and a plastic limit of 14 percent, whereas those at the other three sites had liquid limits of 23 to 29 percent and plastic limits of 2 to 6 percent.
Figure 12.66 Effect of time on the cone penetration resistance of sand following blast densification at the Jebba Dam site.
SAND AGING EFFECTS AND THEIR SIGNIFICANCE
found to increase by approximately 50 to 100 percent of the original values. Similar behavior was found following blast densification of hydraulic fill sand that had been placed for construction of Treasure Island in San Francisco Bay more than 60 years previously (Ashford et al., 2004). Aging effects were also observed after placement of hydraulic fill working platforms in the river at the Jebba Dam site and after densification by vibrocompaction as shown in Figs. 12.67 and 12.68. In the case of vibrocompaction, however, there was considerable variability in the magnitude of aging effects throughout the site. Because of the greater density increase caused by vibrocompaction than by blast densification, no initial decrease in the penetration resistance was observed at the end of the compaction process. Charlie et al. (1992) found a greater rate of aging after densification by blasting for sands in hotter climates than in cooler climates and suggested a correlation between the rate of aging and mean annual air temperature for available field data as shown in Fig. 12.69. In the figure, the increase in the CPT tip resistance (qc) with time is expressed by the following equation:
Figure 12.68 Effect of time on the cone penetration resistance of hydraulic fill sand after placement at the Jebba Dam site.
(12.62)
where N is the number of weeks since disturbance and K expresses the rate of increase in tip resistance in logarithmic time.
Mitchell and Solymer (1984)
1.0
Empirical Constant K
qc (N weeks) ⫽ 1 ⫹ K log N qc (1 week)
515
Schmertmann (1987) and Fordham et al. (1991) Charlie et al. (1992)
0.1
Jefferies et al. (1988) 0.02 -10
0
10
20
30
40
Temperature (°C) Figure 12.69 Rate of increase of normalized CPT tip resis-
tance against temperature for different cases of reported aging effects after blasting (by Charlie et al., 1992).
Figure 12.67 Effect of time on the cone penetration resistance of sand following vibrocompaction densification at the Jebba Dam site.
Schmertmann (1991) postulated that a ‘‘complicated soil structure’’ is present in freshly deposited soil. The structure then becomes more stable by ‘‘drained dispersive movements’’ of soil particles. He suggests that stresses would arch from softer, weaker areas to stiffer zones with time, leading to an increase in K0 with time. Mitchell and Solymar (1984) suggested that the cementation of particles may be the mechanism of aging
516
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
of sands, similar to diagenesis in locked sands and young rocks (Dusseault and Morgenstern, 1979; Barton, 1993) in which grain overgrowth has been observed. However, others have questioned whether significant chemical reactions can occur over the short time of observations. In addition, there is some evidence of aging in dry sands wherein chemical processes would be anticipated to be very slow. Setup of Displacement Piles
Much field data indicates that the load-carrying capacity of a pile driven into sand may increase dramatically over several months, long after pore pressures have dissipated (e.g., Chow et al., 1998; Jardine and Standing, 1999). The amount of increase is highly variable, ranging from 20 to 170 percent per log cycle of time as shown in Fig. 12.70 (Chow et al., 1998; Bowman, 2002). Most of the increase in capacity occurs along the shaft of the pile as the radial stress at rest increases
with time (Axelsson, 2000). Evidence suggests that piles in silts and find sands set up more than those in coarse sands and gravels (York et al., 1994). Both driven and jacked piles exhibit setup, whereas bored piles do not. Hence, the stress–strain state achieved during the construction processes of pile driving have an influence on this time-dependent behavior and various mechanisms have been suggested to explain this (Astedt et al., 1992; Chow et al., 1998; Bowman, 2002). Unfortunately, at present, there is no conclusive evidence to confirm any of the proposed hypotheses. Despite the many field examples and laboratory studies on aging effects, there is still uncertainty about the mechanism(s) responsible for the phenomenon. Understanding the mechanism(s) that cause aging is of direct practical importance in the design and evaluation of ground improvement, driven pile capacity, and stability problems where strength and deformation properties and their potential changes with time are important. Mechanical, chemical, and biological factors have been hypothesized for the cause of aging. Biological processes have so far been little studied; however, mechanical and chemical phenomena have been investigated in more detail, and some current understanding is summarized below.
12.12
Figure 12.70 Increase in total and shaft capacity with time
for displacement piles in sand (from Chow et al., 1998 and Bowman, 2003).
MECHANICAL PROCESSES OF AGING
Creep is hypothesized as the dominant mechanism of aging of granular systems on an engineering timescale by Mesri et al. (1990) and Schmertmann (1991). Increased strength and stiffness does not occur solely from the change in density that occurs during secondary compression. Rather, it is due to a continued rearrangement of particles resulting in the increased macrointerlocking of particles and the increased microinterlocking of surface roughness. This is supported by the existence of locked sands (Barton, 1993; Richards and Barton, 1999), which exhibit a tensile strength even without the presence of binding cement. Some micromechanical explanations of the process are given in Section 12.3. Although no increase in stiffness was detected when glass balls were loaded isotropically (Losert et al., 2000), sand has been found to increase in strength and stiffness under isotropic stress conditions (Daramola, 1980; Human, 1992). These increases develop even under isotropic confinement because the angular particles can lock together in an anisotropic fabric. It has been shown that more angular particles produce materials more susceptible to creep deformations (Mejia et al., 1988, Human, 1992, Leung et al., 1996). Isotropic
CHEMICAL PROCESSES OF AGING
12.13
CHEMICAL PROCESSES OF AGING
Chemical processes are a possible cause of aging. Historically, the most widespread theory used to explain aging effects in sand has involved interparticle bond-
Stress State at Creep: p = 600 kPa and q = 800 kPa All Samples Were Prepared With Relative Density of Approximately 70%.
Deviatoric Strain (%)
0.25 0.20 Montpellier Natural Sand
0.15 Glass Ball
0.10
Leighton Buzzard Uniform Silica Sand
0.05 0.00 10 1 0.05
Volumetric Strain (%)
compression tests by Kuwano (1999) showed that radial creep strains were greater than axial strains in soils with angular particles than in soils with rounded particles due to a more anisotropic initial fabric. Angular particles can result in longer duration of creep and a greater aging effect since they have a larger range of stable contacts and the particles can interlock. As spherical particles rearrange more easily than elongated ones (Oda, 1972a), rounder particles initially creep at a higher rate before settling into a stable state. Hence, any aging effect on rounded particles tends to disappear quickly when the soil is subjected to new stress state. When a constant shear stress is applied to loose sand, large creep accompanied by volumetric contraction is observed (Bopp and Lade, 1997). Higher contact forces due to loose assemblies contribute to increased particle crushing, contributing to contraction behavior. Hence, decrease in volume by soil crushing leads to increase in stiffness and strength. Field data suggest that displacement piles in medium-dense to dense sands set up more than those in loose sand (York et al., 1994). Dense granular materials may dilate with time depending on the applied stress level during creep as shown in Fig. 12.71 (Bowman and Soga, 2003). Initially, the soil contracts with time, but then at some point the creep vector rotates and the dilation follows. Similar observations were made by Murayama et al. (1984) and Lade and Lui (1998). This implies that sands at a high relative density will set up more as more interlock between particles may occur (Bowman, 2002). The laboratory observation of initial contraction followed by dilation conveniently explains the field data of dynamic compaction where the greater initial losses and eventual gains in stiffness and strength of sands are found close to the point of application where larger shear stresses are applied to give dilation (Dowding and Hryciw, 1986; Thomann and Hryciw, 1992; Charlie et al., 1992). Increased strength and stiffness due to mechanical aging occurs predominantly in the direction of previously applied stress during creep (Howie et al., 2002). No increase was observed when the sand was loaded in a direction orthogonal to that of the applied shear stress during creep (Losert et al., 2000).
517
10 2
10 3
10 4
10 5
Montpellier Natural Sand
0.00
-0.05 -0.10
Dilation Glass Ball
-0.15 Leighton Buzzard Uniform Silica Sand
-0.20 -0.25 -0.30 10 0
10 1
10 2
10 3
10 4
10 5
Time (s) Figure 12.71 Dilative creep observed in triaxial creep tests
of dense fine sand (by Bowman and Soga, 2003).
ing. Terzaghi originally referred to a ‘‘bond strength’’ in connection with the presence of a quasipreconsolidation pressure in the field (Schmertmann, 1991). Generally, this mechanism has been thought of as type of cementation, which would increase the cohesion of a soil without affecting its friction angle. Denisov and Reltov (1961) showed that quartz sand grains adhered to a glass plate over time. They placed individual sand grains on a vibrating quartz or glass plate and measured the force necessary to move the grains as shown in Fig. 12.72. The dry grains were allowed to sit on the plate for varying times and then the plate was submerged, also for varying times, before vibrating began. It was found that the force required to move the sand grains continued to increase up to about 15 days of immersion in water. The cementating agent was thought to be silica-acid gel, which has an amorphous structure and would form a precipitate at
518
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
(1) Glass or Quartz Plate (2) To the Oscillation Generator 2
1
䉭
f ––– 3.0 f0
2.0
(1) Without Soaking (2) 42-hour Soaking (3) 6-day Soaking (4) 14-day Soaking
䊊
䉭
4
䉭 䊊
3
1.0
0
10 min
䉭
䊊
&
&
2 1
&
䊊
&
2h
20h
Time
Figure 12.72 Results of vibrating plate experiment from
Denisov and Reltov (1961). Term ƒ / ƒ0 is a measure of the bonding force between sand and glass or quartz plate.
particle contacts (Mitchell and Solymer, 1984). The increased strength is derived from crystal overgrowths caused by pressure solution and compaction. Strong evidence of a chemical mechanism being responsible for some aging was obtained by Joshi et al. (1995). A laboratory study was made of the effect of time on penetration resistance of specimens prepared with different sands (river sand and sea sand) and pore fluid compositions (air, distilled water, and seawater). After loading under a vertical stress of 100 kPa, the values of penetration resistance were obtained after different times up to 2 years. Strength and stiffness increases were observed in all cases, and a typical plot of load–displacement curves at various times is shown in Fig. 12.73. The effects of aging were greater for the submerged sand than for the dry specimens. Scanning electron micrographs of the aged specimens in distilled water and seawater showed precipitates on and in between sand grains. For the river sand in distilled water, the precipitates were composed of calcium (the soluble fraction of the sand) and possibly silica. For the river sand in seawater, the precipitates were composed of sodium chloride. However, there are several reported cases in which cementation was an unlikely mechanism of aging, at least in the short term. For example, dry granular soils can show an increase in stiffness and strength with time (Human, 1992; Joshi et al., 1995; Losert et al., 2000). Cementation in dry sand is unlikely, as moisture is required to drive solution and precipitation reactions involving silica or other cementation agents. Mesri et al. (1990) used the triaxial test data from Daramola (1980) to argue against a chemical mecha-
Figure 12.73 Effect of aging on the penetration resistance of River sand (from Joshi et al.,
1995).
CHEMICAL PROCESSES OF AGING
nism responsible for aging effects in sands. Figure 12.74 shows the effects of aging on both the stiffness and shear strength of Ham River sand. Four consolidated drained triaxial tests were performed on samples with the same relative density and confining pressure (400 kPa) but consolidated for different periods of time (0, 10, 30, and 152 days) prior to the start of the triaxial tests. The results showed that the stiffness increased and the strain to failure decreased with increasing time of consolidation. Although increased values of modulus were observed, the strain at failure is approximately 3 percent. Mesri et al. (1990) argue that this large strain would destroy any cementation, and therefore another less brittle mechanism must be responsible for the increase in stiffness. In summary, experimental evidence indicates that mechanical aging behavior is enhanced by shear stress
application in denser materials. It is also associated with the microinterlocking occurring during the generation of creep strain. The increase in stiffness and strength is observed in the direction of the applied stresses, but the aging effect disappears rather quickly when loads are applied in other directions. Chemical aging can also occur within days depending on such factors as chemical environment and temperature. Some conditions in natural deposits are not replicated in small-scale laboratory testing. Most laboratory tests are done using clean granular materials, whereas in the field there will be impurities, biological activity, and heterogeneity of void ratio and fabric. Furthermore, the introduction of air and other gases during ground improvement may have consequences that have so far not been fully evaluated. Arching associated with dissipation of blast gases and the redistribution of
Figure 12.74 Effect of aging on stress–strain relationship of Ham River sand (from Dara-
mola, 1980).
519
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
stresses through the soil skeleton may also play a role (Baxter and Mitchell, 2004). The boundary conditions associated with penetration testing in rigid-wall cylinders in the laboratory may prevent detection of timedependent increases in penetration resistance that are measured under the free-field conditions in the field.
12.14
CONCLUDING COMMENTS
With exception of settlement rate predictions, most soil mechanics analyses used in geotechnical engineering assume limit equilibrium and are based on the assumption of time-independent properties and deformations. In reality, time-dependent deformations and stress changes that result from the time-dependent or viscous rearrangement of the soil structure may be responsible for a significant part of the total ground response. Rate process theory has proven a particularly fruitful approach for the study of time-dependent phenomena in soils at consistencies of most interest in engineering problems, that is, at water contents from about the plastic limit to the liquid limit. From an analysis of the influences of stress and temperature on deformation rates and other evidence, it has been possible to deduce that interparticle contacts are essentially solid and that clay strength derives from interatomic bonding in these contacts. The strength depends on the number of bonds per unit area, and the constant of proportionality between number of bonds and strength is essentially the same for all silicate minerals, probably because of their similar surface structures. Recognition of the fact that any macroscopic stress applied to a soil mass induces both tangential and normal forces at the interparticle contacts is essential to the understanding of rheological behavior. The results of discrete particle simulations show that changes in creep rate with time can be explained by changes in the tangential and normal force ratio at interparticle contacts that result from particle rearrangement during deformation. The change in microfabric in relation to strong particle networks and weak clusters leads to possible explanation of the mechanical aging process. Time-dependent deformations and stress relaxation follow predictable patterns that are essentially the same for all soil types. Simple constitutive equations can reasonably describe time-dependent behavior under limited conditions. Much remains to be learned, however, about the influences of combined stress states, stress history and transient drainage conditions on creep, stress relaxation, and creep rupture before reliable
analyses and predictions can be made for large and complex geotechnical structures.
QUESTIONS AND PROBLEMS
1. Find an article about a problem, project, or issue that involves some aspect of the long-term behavior of a soil as an important component. The article may be from a technical journal or magazine or elsewhere. The only requirement is that it involves consideration of time-dependent ground behavior in some way. a. Prepare a one-page informative abstract of the article. b. Summarize the important geotechnical issues in the article and write down what you believe you would need to know to understand them well enough to solve the problem, resolve the issue, advise a client, and so forth. Do not exceed two pages. c. Identify topics, figures, equations, and other material in Chapter 12, if any, that might be useful in addressing the problems. 2. The figure below shows relationships between (1) number of interparticle bonds and effective consolidation pressure and (2) compressive strength and number of interparticle bonds for three soils as determined using rate process theory. Determine the angle of internal friction in terms of effective stresses (as determined from CU tests with pore pressure measurements), for each soil. Assume Aƒ ⫽ 0, 0.3, and 0.3 for the sand, illite, and Bay mud, respectively, in the range 0 ⬍ (1 ⫺ 3)ƒ ⬍ 500 kPa, where Aƒ is the ratio of pore pressure at failure to the deviator stress at failure (1 ⫺ 3)ƒ. 40
Number of Bonds - 1010 cm-2
520
30 Sand 20 Illite 10
Bay Mud
0 0
100 200 300 400 σc = Effective Consolidation Pressure (kPa)
500
QUESTIONS AND PROBLEMS
1000
0
5
10
15
20
521
90
25
-2
Number of Bonds - 1010 cm
80
Water Content (%)
(σ1 – σ3)max(kPa)
800
600 Sand, Illite, Bay Mud 400
70
60
50
40
200
30 20
0
3. Equation (12.43) is a simple three-parameter equation for strain rate during constant stress creep of soils. a. Show the meaning of , D, and m on a clearly labeled sketch. b. Modify Eq. (12.43) and indicate the information needed to permit prediction of creep rates for a given soil at any value of water content and stress intensity from a knowledge of creep rates at a single water content corresponding to different stress intensities. c. Develop a relationship between stress intensity and time to failure for a soil subject to strength loss under the application of a sustained stress. 4. The results of triaxial compression creep tests on samples of overconsolidated Bay mud at three stress
XRupture
40
80 100 200 Compressive Strength (kPa)
400
intensities are shown below, as is the variation of compressive strength with water content. A temporary excavation is planned that will create a slope with an average factor of safety of 1.5. The average water content of the clay in the vicinity of the cut is 50 percent. The excavation is planned to remain open for a period of 4 months. Prepare a plot of strain rate versus time for an element of clay and assess the probability of a creep rupture failure occurring during this period. 5. Given that a. The creep rate of a soil, for times up to the onset of failure, can be expressed by Eq. (12.43), in which D is the deviator stress, and b. The time to failure by creep rupture, tƒ, can be taken as the time corresponding to minimum strain rate, ˙ min, prior to acceleration of deformation and failure, and tests have shown that ˙ mintƒ ⫽ constant
Axial Strain (%)
50 40
Water Content = 60% Dmax = 125 kPa
D = 100 kPa
30
D = 85 kPa
20 D = 68 kPa
0 1
10
100 Time (min)
1000
10,000
If a test embankment designed at a factor of safety of 1.05 based on shear strength determined in a short-term test fails in creep rupture after 3 months, how long should it be before failure of a prototype embankment having a factor of safety of 1.3? From a plot of deformation rate versus time for the test embankment, it has been found that m ⫽ 0.75. The results of shortterm creep tests have shown also that Dmax ⫽ 6.0. The factor of safety is defined as the strength available divided by the strength that must be mobilized for stability.
522
12
TIME EFFECTS ON STRENGTH AND DEFORMATION
6. Would you expect that creep and stress relaxation will be significant contributors to the stress– deformation and long-term strength of soils on the Moon? Why? 7. List possible causes of sand aging wherein the stiffness and strength (usually as determined by pene-
tration tests) can increase significantly over time periods as short as weeks or months following deposition and/or densification. Outline a test program that might be done to test the validity of one of these causes.
List of Symbols
a a a a a a a ac am at av A A A A A A A A A A A A0 A0 Ac Aƒ Aƒ Ah Ai Ai A0i
area coefficient for harmonics cross-sectional area of a tube crystallographic axis direction or distance effective cluster contact area volumetric air content thermal diffusivity effective area of interparticle contact coefficient of compressibility with respect to changes in water content coefficient of compressibility with respect to changes in ( ⫺ ua) coefficient of compressibility in one dimensional compression activity area creep rate parameter cross section area normal to the direction of flow Hamaker constant long-range interparticle attractions Skempton’s pore pressure parameter thermal diffusivity van der Waal’s constant short-range attractive stress pore pressure parameter ⫽ u/
(1 ⫺ 3) concentration of charges on pore wall surface charge density per unit pore volume solid contact area area of flow passages pore pressure parameter at failure Hamaker constant state parameter in disturbed state total surface area of the ith grain state parameter at equilibrium
As ˚ A b b b B B Bq Br c c c c c c c c c0 c0⫹ c0⫺ ca ce, ce cec cic, cc ci 0 cm cm cu cv cw C C C C
specific surface area per unit weight of solids Angstrom unit ⫽ 1 ⫻ 10⫺10 m coefficient of harmonics crystallographic axis direction or distance intermediate stress parameter parameter in rate process equation ⫽ X(kT/h) Bishop’s pore water pressure coefficient grain breakage parameter Hardin’s relative breakage parameter cohesion cohesion intercept in total stress concentration molar concentration crystallographic axis direction or distance undrained shear strength velocity of light cohesion intercept in effective stress equilibrium solution concentration, bulk solution concentration cation equilibrium solution concentration anion equilibrium solution concentration mid-plane anion concentration Hvorslev’s cohesion parameter cation exchange capacity mid-plane cation concentration equilibrium solution concentration mid-plane concentration mid-plane anion concentration undrained shear strength coefficient of consolidation concentration of water capacitance chemical concentration clay content by weight composition 523
524 C C C C C C Cc C* c Cl Cn CR CRR Cs Cs Cs Cu Cu CW C, Ce d d d10 d60 dx dy D D D D D D0 D0 D50 Deƒƒ DeV Dmax DR, Dr Ds DTV D* e e e0 e* 100 ec
LIST OF SYMBOLS
electrical capacitance short-range repulsive force between contacting particles soil compressibility speed of light in vacuum or in air, 3 ⫻ 108 m/sec volumetric heat volumetric heat capacity compression index intrinsic compression index compressibility of pore fluid coordination number compression ratio cyclic resistance ratio compressibility of a solid shape coefficient swelling index coefficient of uniformity compressibility of soil skeleton by pore pressure change compressibility of water coefficient of secondary compression diameter distance sieve size that 10% of the particles by weight pass through sieve size that 60% of the particles by weight pass through incremental horizontal displacement at peak incremental vertical displacement at peak diameter of particle dielectric constant, relative permittivity diffusion coefficient deviator stress stress level ⫽ D/Dmax molecular diffusivity of water vapor in air self-diffusion coefficient sieve size that 50% of the particles by weight pass through effective diameter isothermal vapor diffusivity strength at the beginning of creep relative density characteristic grain size thermal vapor diffusivity effective diffusion coefficient electronic charge ⫽ 4.8029 ⫻ 10⫺10 esu ⫽ 1.60206 ⫻ 10⫺10 coulomb void ratio initial void ratio intrinsic void ratio under effective vertical stress of 100 kPa intracluster void ratio
ecs eƒƒ eg, eG eini eL emax emin ep eT E E E E E50 Emax Er ESP E( ) ƒ ƒ ƒi ƒn ƒt F F F F F F F, F0 F Fd
F FE FH
FI F⬁ g G G G1000 Gg Gmax Gs Gs GSC GSG
void ratio at critical state void ratio at failure void ratio of the granular phase, granular void ratio initial void ratio void ratio at liquid limit maximum void ratio minimum void ratio intercluster void ratio total void ratio experimental activation energy potential energy Young’s modulus voltage, electrical potential secant modulus at 50 percent of peak strength small strain Young’s modulus rebound modulus exchangeable sodium percentage distribution function for interparticle contact plane normals force acting on a flow unit frequency fraction of particles between two sizes normal force tangential force force of electrostatic attraction formation factor free energy freezing index pressure-temperature parameter tensile strength Faraday constant ⫽ 96,500 coulombs partial molar free energy on adsorption free energy of the double layer per unit area at a plate spacing of 2d free energy of activation electrical force per unit length hydraulic seepage force per unit length causing flow fabric index free energy of a single non-interacting double layer acceleration due to gravity shear modulus source-sink shear modulus measured after 1000 minutes of constant confining pressure shear modulus of grains small strain shear modulus secant shear modulus specific gravity of soil solids specific gravity of clay particles specific gravity of the granular particles
LIST OF SYMBOLS
h h h hm hs H H H H H H i i ic ie ih it I I I1, I2, I3 IG IR Iv Jc JD Ji Ji Js Jv Jw J 0i k k k k k k k0 kc ke kh ki kr ks k(S) kt k K K
head or head loss relative humidity of air in pores Planck’s constant ⫽ 6.624 ⫻ 10⫺27 erg sec matrix or capillary head osmotic or solute head maximum distance to drainage boundary stress history thickness total head water transport by ion hydration partial molar heat content gradient unit vector chemical gradient electrical gradient hydraulic gradient thermal gradient electrical current intensity stress invariants coefficient of shear modulus increase with time dilatancy index void index chemical flow rate chemical flow rate flux of constituent i value of property i in clay-water system flow rate of salt relative to fixed soil layer volume flow rate of solution flow rate of water value of property i in pure water Boltzmann’s constant ⫽ 1.38045 ⫻ 10⫺23 J/ K hydraulic conductivity, hydraulic permeability mean coordination number of a grain selectivity coefficient thermal conductivity true cohesion in a solid pore shape factor osmotic conductivity electro-osmotic conductivity hydraulic conductivity constant characteristic of a property relative permeability saturated conductivity saturation dependent hydraulic conductivity thermal conductivity unsaturated hydraulic conductivity absolute permeability or intrinsic permeability bulk modulus
K K K K0 Ka Kc Kc Kd Kp Kso K l l l L L Lij LI LIeq LL Ls m m m mc ms ms mv mw mw M M M n n n n n n n n0 n1 ne ni N
525
double-layer parameter ⫽ (8n0e2v2 /DRT)1 / 2 pore shape factor rate of increase in tip resistance in logarithmic time coefficient of lateral earth pressure at rest coefficient of active earth pressure principal stress ratio principal stress ratio during consolidation distribution coefficient coefficient of passive earth pressure stress-optical material constant wavelengths of monochromatic radiation length material thickness total number of pore classes latent heat of fusion length coupling coefficient or conductivity coefficient liquidity index equivalent liquidity index liquid limit latent heat of fusion of water slope of relationship between log creep strain rate and log time total mass per unit total volume total number of pore classes mass of clay compressibility of mineral solids under hydrostatic pressure compressibility of mineral solids under concentrated loadings compressibility compressibility of water mass of water constrained modulus or coefficient of volume change metal cations monovalent cation concentration concentration, ions per unit volume harmonic number integer number of grains in an ideal breakage plane porosity total number of pore classes unspecified atomic ratio concentration in external solution number of bonds per unit of normal force effective porosity Refractive index in i direction Avogadro’s number ⫽ 6.0232 ⫻ 1023 mole⫺1
526 N N N N N N N N1 Ne NG Ns Nw OCR p p p p p p p po pa pc pcs ps pz P P P P P P P Pc Pˆ c Pƒ PI Pinj PL PN PR Ps PT
LIST OF SYMBOLS
coordination number monovalent cation concentration normal load or force number of moles of hydration water per mole of ion number of particles per cluster in a cluster structure number of weeks since disturbance total number of harmonics number of load cycles to cause liquefaction number of load cycles normalized shear modulus increase with time moles of water per unit volume of sediment moles of salt per unit volume of sediment overconsolidation ratio constant that accounts for the interaction of pores of various sizes hydrostatic pressure matrix or osmotic pressure pressure partial pressure of water vapor in pore space vertical consolidation pressure mean effective pressure present overburden pressure atmospheric pressure preconsolidation pressure mean effective pressure at critical state osmotic or solute pressure gravitational pressure area bond strength per contact zone concentration of divalent cations power consumption total gas pressure in pore space total pressure wetted perimeter capillary pressure capillary pressure at air entry injection pressure that causes clay to fracture plasticity index injection pressure plastic limit probability distribution of normal contact force peak ratio swelling pressure probability distribution of tangential contact force
q q q q qc qcs qƒ qh qhc qhe qi qt qvap qw Q Q r r rk rp rp R R R R R R R R Rd RH Rp R( ) s su S S S S S S S S S S0 SAR
degree of connectivity between waterconducting pores deviator stress flow rate hydraulic flow rate CPT tip resistance deviator stress at critical state deviator stress at failure hydraulic flow rate osmotic flow rate electro-osmotic flow rate concentration of solids heat flow rate vapor flux density water flow rate electrical charge quantity of heat pore radius radius ratio of horizontal to vertical hydraulic conductivities pore size tube radius coefficient of roundness electrical resistance gas constant ⫽ 1.98726 cal/ K-mole 8.31470 joules/ K-mole 82.0597 cm3 atm/ K-mole long-range repulsion pressure ratio of cations and anions source or sink mass transfer term sphere radius tube radius retardation factor hydraulic radius average particle radius radius at angle slope of stress relaxation curve undrained shear strength entropy fraction of molecules striking a surface that stick to it number of flow units per unit area partial molar entropy saturation specific surface area per unit volume of solids structure swell partial molar entropy specific surface per unit volume of soil particles sodium adsorption ratio
LIST OF SYMBOLS
St Su Sw Sx, Sy, Sz t t t t t1 tƒ tm T T T T T0 Tc Tc TFP Ts Ts TV u u u u u u u u* u0 u0 Uƒ U v v v v v vave vc0 vcs vh
V V V V V V
sensitivity undrained shear strength water saturation ratio projected areas of interparticle contact surfaces average thickness tetrahedral coordinations time transport number reference time time to failure time for adsorption of a monolayer intercluster tortuosity shear force temperature time factor initial temperature intracluster tortuosity temperature at consolidation freezing temperature surface temperature temperature of shear for consolidated undrained direct shear tests time factor excess pore pressure ionic mobility midplane potential function pore water pressure pore water pressure in the interparticle zone pressure thermal energy effective ionic mobility initial pore pressure pore water pressure remote from the interparticle zone pore pressure at failure average degree of consolidation flow velocity frequency of activation ionic valance settling velocity specific volume ⫽ 1 ⫹ e average flow velocity specific volume of the pure clay specific volume at critical state apparent water flow velocity area difference in self-potentials electrical potential speed valence voltage
V V0 VA VDR VGS Vm Vp VR Vs Vs Vw Vw w wL, wl wP, wp W W W W W x X X Xi y z z z z Z Z Z G s ST w
527
volume initial volume attractive energy volume of water drained volume of granular solids total volume of soil mass compression wave velocity repulsive energy shear wave velocity volume of solids partial molar volume of water volume of water water content liquid limit plastic limit water content width fluid volume water transport weight distance from the clay surface distance friction coefficient driving force potential function ⫽ ve /kT direction of gravity distance from drainage surface electrolyte ionic valence elevation or elevation head number of molecules per second striking a surface potential function ⫽ 'e 0 /kT angle between b and c crystallographic axes directional parameter disturbance factor geometrical packing parameter inclination of failure plane to horizontal plane slope of the relationship between logarithm of creep rate and creep stress thermal ratio tortuosity factor normalized strain rate parameter thermal expansion coefficient of soil solids thermal expansion coefficient of soil structure thermal expansion coefficient of water angle between a and c crystallographic axes birefringence ratio
528 0, i p ˙ 0 1 ˙ a ƒ ˙ min rd s ˙ s v ˙ v
E
b c crit e, e ƒ m r repose v , #
LIST OF SYMBOLS
disturbance factor geometrical packing parameter rotation angle of yield envelope constant characteristic of the property and the clay Bishop’s unsaturated effective stress parameter clay plate thickness measured between centers of surface layer atoms deformation parameter in Hertz theory displacement, distance solid fraction of a contact area relative retardation particle eccentricity distance dielectric constant, permittivity porosity strain strain rate permittivity of vacuum, 8.85 ⫻ 10⫺12 C2 /(Nm2) axial strain vertical strain rate in one dimensional consolidation strain at failure minimum strain rate volumetric strain that would occur if drainage were permitted deviator strain deviator strain rate volumetric strain volumetric strain rate energy dissipated per cycle per unit volume friction angle local electrical potential friction angle in effective stress angle defining the rate of increase in shear strength with respect to soil suction characteristic friction angle friction angle at critical state Hvorslev friction parameter friction angle corrected for the work of dilation peak mobilized friction angle residual friction angle angle of repose apparent specific volume of the water in a clay/water system of volume V intergrain sliding friction angle dissipation function activity coefficient angle between a and b crystallographic axes unit weight
˙ c d % % 0 ! ! !ⴖ cs ( b m r s d T w W
shear strain rate applied shear strain or cyclic shear strain amplitude dry unit weight double layer charge specific volume intercept at unit pressure dynamic viscosity fraction of pore pressure that gives effective stress initial anisotropy swelling index real relative permittivity polarization loss, imaginary relative permittivity compression index correction coefficient for frost depth prediction equation damping ratio decay constant pore size distribution index separation distance between successive positions in a structure wave length of X ray wave length of light critical state compression index chemical potential coefficient of friction dipole moment fusion parameter Poisson’s ratio viscosity critical state stress ratio Poisson’s ratio Poisson’s ratio of soil skeleton osmotic or swelling pressure angle of bedding plane relative to the maximum principal stress direction contact angle geometrical packing parameter liquid-to-solid contact angle orientation angle volumetric water content volumetric water content at full saturation residual water content volumetric water content at full saturation bulk dry density charge density mass density bulk dry density resistivity of saturated soil density of water resistivity of soil water area occupied per absorbed molecule on a surface
LIST OF SYMBOLS
0 1 1 1 1c 1ƒ 1ƒƒ 2 3 3 3c 3ƒƒ a ac as aw c c e e eƒƒ ƒ ƒ ƒƒ ƒƒ h h0 i i i iso max min n p r r rc s s s T T , t
double-layer charge electrical conductivity entropy production normal stress surface tension of water surface charge density total stress effective stress initial effective confining pressure major principal total stress tensile strength of the interface bond major principal effective stress major principal stress during consolidation major principal stress at failure major principal effective stress at failure intermediate principal effective stress minor principal total stress minor principal effective stress minor principal stress during consolidation minor principal effective stress at failure axial effective stress axial consolidation stress interfacial tension between air and solid interfacial tension between air and water crushing strength of particles tensile strength of cement electrical conductivity equivalent consolidation pressure effective AC conductivity partial stress increment for fluid phase effective normal stress on shear plane normal total stress on failure plane normal effective stress on failure plane electrical conductivity due to hydraulic flow initial horizontal effective stress effective stress in the i-direction intergranular stress isotropic consolidation isotropic total stress maximum principal stress minimum principal stress effective normal stress preconsolidation pressure radial total stress radial effective stress radial consolidation stress conductivity of soil surface partial stress increment for solid phase tensile strength of the sphere electrical conductivity of saturated soil tensile strength of cemented soil
v v v0 v0 vm vp W ws y a c c cy d ƒƒ i i m peak ' ' 0 d 0 s m p s " " "
529
vertical stress vertical effective stress overburden vertical effective stress overburden effective stress maximum past overburden effective stress vertical preconsolidation stress electrical conductivity of pore water interfacial tension between water and solid yield strength circumferential stress shear strength shear stress surface tension swelling pressure or matric suction undrained shear strength apparent tortuosity factor applied shear stress contaminant film strength undrained cyclic shear stress drained shear strength shear stress at failure on failure plane shear strength shear strength of contact shear strength of solid material in yielded zone applied shear stress at peak initial static shear stress mass flow factor cation valence distance function ⫽ Kx, double-layer theory ratio of average temperature gradient in air filled pores to overall temperature gradient dilation angle electrical potential intrinsic friction angle matric suction surface potential of double layer displacement pressure electrical potential state parameter total potential of soil water electrical potential at the surface gravitational potential matrix or capillary potential gas pressure potential osmotic or solute potential angular velocity frequency osmotic efficiency true electroosmotic flow zeta potential
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