SMIG 2016

PRIMERA CONFERENCIA EULALIO JUÁREZ BADILLO

ELASTIC SETTLEMENT OF SHALLOW FOUNDATION DUE TO RISE OF WATER TABLE IN GRANULAR SOIL – A STRAIN INFLUENCE FACTOR APPROACH

BRAJA M. DAS

2016 SOCIEDAD MEXICANA DE INGENIERÍA GEOTÉCNICA, A. C.

Copyright, México, 2016 Sociedad Mexicana de Ingeniería Geotécnica, A.C. Valle de Bravo No. 19 Col. Vergel de Coyoacán, 14340 Ciudad de México, MÉXICO Tel. +(52)(55)5677-37-30, +(52)(55)5677-37-30, Fax+(52)(55)5679-36-76 Fax+(52)(55)5679-36-76 Página web: www.smig.org.mx Correo electrónico: [email protected] [email protected] ISBN: En trámite Editado por: Miguel Angel Figueras Corte Prohibida la reproducción parcial o total de esta publicación, por cualquier medio, sin la previa Autorización escrita de la Sociedad Mexicana de Ingeniería Geotécnica, A.C. Total or partial reproduction of this book by any medium requires prior written consent of the Sociedad Mexicana de Ingeniería Geotécnica, A.C.

Las opiniones expresadas en este volumen son responsabilidad exclusiva exclusiva del autor. !"#$#%$& ()"*(&&(+ #$ ,-#& .%/01( 2*( ,-( &%/( *(&"%$#/#,4 %5 #,& 20,-%*6

CONSEJO DE HONOR Leonardo Zeevaert Wiechers † Raúl J. Marsal Cordoba † Alfonso Rico Rodríguez † Enrique Tamez González Guillermo Springall Caram Edmundo Moreno Gómez Carlos Jesús Orozco y Orozco † Luis Vieitez Utesa Gabriel Moreno Pecero Raúl Flores Berrones Luis Miguel Aguirre Menchaca Gabriel Auvinet Guichard Luis Bernardo Rodríguez González Raúl Vicente Orozco Santoyo Alberto Jaime Paredes Mario Jorge Orozco Cruz Juan Jacobo Schmitter M. del Campo Héctor M. Valverde Landeros CONSEJO CONSULTIVO José Francisco Fernández Romero Rigoberto Rivera Constantino Walter Iván Paniagua Zavala Juan de Dios Alemán Velásquez David Yáñez Santillán MESA DIRECTIVA 2015-2016 Raúl Aguilar Becerril Presidente

Norma Patricia López Acosta Vicepresidente

Carlos Roberto Torres Álvarez Secretario

Celestino Valle Molina Tesorero

María del Carmen Suárez Galán Nilson Contreras Pallares Miguel Figueras Corte Aristoteles Jaramillo Rivera Vocales

Ysamar Libertad Pino

SOCIEDAD MEXICANA DE INGENIERÍA GEOTÉCNICA, A. C.

COMITÉ ORGANIZADOR XIX RNPIG

Araceli Aguilar Mora Rosemberg Reyes Ramírez Raúl Aguilar Becerril Zenón Medina Domínguez Miguel Angel Figueras Corte

Sociedad Mexicana de Ingeniería Geotécnica Braja M. Das

Conferencia Eulalio Juárez Badillo

vii

ELASTIC SETTLEMENT OF SHALLOW FOUNDATION DUE TO RISE OF WATER TABLE IN GRANULAR SOIL – A STRAIN INFLUENCE FACTOR APPROACH

Contenido

PREFACIO ……………………………………………………………………………………. viii SEMBLANZA DEL PROFESOR EULALIO JUÁREZ BADILLO ……………………… ix SEMBLANZA DEL DR. BRAJA M. DAS ………………………………………………..... xi RESUMEN ……………………………………………………………………………………. 2 1. INTRODUCTION ………………………………………………………………………… 3 2. FACTORS ASSOCIATED WITH SETTLEMENT CAUSED BY GROUNDWATER TABLE FLUCTUATION …………………………………………………………………… 3 3. EMPIRICAL RELATIONSHIPS FOR LOSS OF SOIL STIFFNESS ……………….. 4 4. RESULTS OF LABORATORY MODEL TESTS ……………………………………… 7 5. RECENT DEVEVLOPMENTS ………………………………………………………….. 9 6. NUMERICAL MODELING ……………………………………………………………... 9 7. A MODEL FOR DETERMINATION OF C w ………………………………………….. 11 8. CONCLUSIONS ………………………………………………………………………….. 15 ACKNOWLEDGMENTS …………………………………………………………………… 16 REFERENCES ………………………………………………………………………………. 17

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Sociedad Mexicana de Ingeniería Geotécnica viii

XIX Reunión Nacional de Profesores de Ingeniería Geotécnica

PREFACIO En 1962, años después de concluir sus estudios en la Universidad de Harvard bajo la guía de Arthur Casagrande, Eulalio Juárez Badillo es el primero en obtener el grado de Doctor en Ingeniería otorgado por la Universidad Nacional Autónoma de México (UNAM). En esa época, con la coautoría de Alfonso Rico Rodríguez, escribe los tres tomos clásicos del conocido libro: “Mecánica de Suelos”. Fue uno de los fundadores del Instituto de Ingeniería de la UNAM en 1956 y de la Sociedad Mexicana de Mecánica de Suelos en 1957. Desde 1959 y hasta hace muy poco tiempo, el Dr. Juárez Badillo se dedicó a la impartición de clases y a la investigación en la División de Estudios de Posgrado de la UNAM. La destacada labor del Dr. Juárez Badillo en la investigación y en las aulas ha dejado una huella en todos sus alumnos, donde además de adquirir los conocimientos de los fundamentos de la mecánica de suelos, escuchamos sus pasajes filosóficos, su conceptualización de la vida y sus siempre interesantes acertijos. A todas estas aportaciones se suma su permanente disposición, ejemplo de trabajo y, especialmente, su calidad humana. La Mesa Directiva actual, con la aprobación del Consejo de Honor y del Consejo Consultivo de la SMIG, presenta la Primer Conferencia “Eulalio Juárez Badillo” en el marco del XIX Reunión Nacional de Profesores de Ingeniería Geotécnica (RNPIG), rindiendo así un merecido homenaje a tan ilustre ingeniero mexicano por sus distinguidos logros, contribuciones y dedicación a la formación de generaciones de ingenieros interesados en la geotecnia. Se ha invitado a otro distinguido especialista a impartir la Primer Conferencia Juárez Badillo: al Profesor Braja M. Das, decano emérito de la Facultad de Ingeniería y Ciencias de la Computación de la Universidad de California. Es autor de numerosos artículos técnicos, textos y libros de consulta de ingeniería geotécnica, entre los que destacan “Fundamentos de Ingeniería de Cimentaciones” y “Fundamentos de Ingeniería Geotécnica”, empleados en diversas universidades del mundo. Nuestro sincero agradecimiento al Profesor Das por aceptar ser el primer ponente de la conferencia principal de la XIX RNPIG y aportar este valioso material. Mi reconocimiento y aprecio al Dr. Raúl Vicente Orozco Santoyo por sumarse a esta labor y preparar la semblanza del Dr. Juárez Badillo, al Dr. Rosemberg Reyes Ramírez por contribuir amablemente con la semblanza del Profesor Braja Das y, en especial, al M en I. Miguel Ángel Figueras Corte por ser el responsable de la coordinación de la Primer Conferencia Eulalio Juárez Badillo. Raúl Aguilar Becerril Presidente, SMIG

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SEMBLANZA DEL PROFESOR EULALIO JUÁREZ BADILLO Raúl Vicente Orozco Santoyo

Cuando la SMIG me invitó a participar en este evento magno y trascendente, intitulado: PRIMER CONFERENCIA “EULALIO JUÁREZ BADILLO”, sentí un gran honor y una profunda emoción, motivados por este importante personaje, mi mentor principal, quien ha influido en mi proceder profesional y afectivo de mi vida, en cuestiones aún ajenas a la mecánica de suelos, uno de sus "juguetes" favoritos. Desde que lo conocí, en 1961, durante un curso de especialización en Vías Terrestres de la UNAM, me transmitió muchos conocimientos de mecánica de suelos en la materia denominada geotecnia. Desde entonces unificó los criterios básicos de esta disciplina, que abarca la geología, la mecánica de suelos, la mecánica de rocas y otras afines, para entender y "sentir" el comportamiento de lo que él ha denominado como geomateriales. Sus teorías se aplican a cualquiera de éstos, sean suelos o concretos (de cemento Portland, asfálticos, alquitránicos, etc.), con expresiones de la física sencillas de entender, basadas en la observación de la naturaleza y comprobadas con experimentos reales. Recuerdo que durante la Maestría en Vías Terrestres, Eulalio nos impartió un curso básico de geología aplicada, y nos enseñó a entender y amar a la naturaleza, en todo su esplendor, para lograr que nos "sintiéramos" suelo transportado o residual, roca o cualquier otro geomaterial. Durante los seminarios y las materias afines a la geotécnica, en los estudios de postgrado, nos inculcó a que constantemente se debe estudiar, observar y actualizar los conocimientos, y aprender de los éxitos y fracasos. Muchas anécdotas se pueden contar sobre lo que sus discípulos vivimos con Eulalio, nuestro maestro y amigo, con enfoques "fuera de serie", fundamentalmente en su manera de pensar y establecer de inmediato los criterios básicos de ingeniería, para dar soluciones sólidas a sus problemas, así como los de actuar en la vida, principalmente en situaciones difíciles de carácter mental y espiritual. Aparte de ser un hombre de primera magnitud, su nobleza, generosidad y disciplina como ingeniero, profesor, investigador, científico y filósofo, son cualidades muy notables que nos conducen en todo momento a pensar y actuar en forma positiva. Por eso su NOMBRE en esta conferencia que será perdurable dentro y fuera de esta querida Sociedad Mexicana de Ingeniería Geotécnica, antes Sociedad Mexicana de Mecánica de Suelos, en que fue socio fundador y la presidió en 1957. Siendo yo estudiante de ingeniería civil en Guadalajara, Jal., se grabó en mi mente un comentario que me hizo mi padre (Ing. Ernesto Orozco y Orozco, representante federal de la SCOP): "una eminencia resolvió un gran problema de estabilidad de taludes en la carretera Guadalajara - Ixtlahuacán del Río, en la barranca del Río Santiago”. Era precisamente el Dr. Eulalio Juárez Badillo. Durante los estudios geotécnicos para el proyecto de terracerías y obras de drenaje, en el Libramiento a Pto. Vallarta. Jal., Eulalio efectuó una visita de supervisión y nos enseñó que en el campo debemos "sentir" la estabilidad de los taludes, sobre todo a largo plazo, y el “sentir” de otros conceptos básicos. Nos llamó la atención su salud física y la mental, así como sus estados anímico y afectivo en toda su extensión; en el sitio practicaba profundamente el yoga y la meditación.

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Sociedad Mexicana de Ingeniería Geotécnica x


El Dr. Eulalio Juárez Badillo ha producido y presentado diferentes e innumerables obras nacionales y extranjeras: artículos, publicaciones, libros, conferencias, pláticas, etc., por lo cual ha recibido muchos nombramientos y reconocimientos. Entre sus principales obras destacadas, está la elaboración del primer libro de texto, en español, sobre mecánica de suelos, realizado en conjunto con el M.I. Alfonso Rico Rodríguez (†). Los tres tomos que se editan son famosos en los países de habla hispana. También fue uno de los fundadores del Instituto de Ingeniería-UNAM, en 1957; además, en 2005 recibió la medalla de Profesor Emérito al cumplir 50 años de catedrático en la UNAM, directamente del rector (Juan Ramón de la Fuente). En noviembre de 1926, el Dr. Eulalio Juárez Badillo nació en Cd. Victoria, Tamaulipas y después estudió ingeniería civil y matemáticas en la Escuela Nacional de Ingeniería. Su maestría la recibió en la Universidad de Harvard y el doctorado en la UNAM. Por otro lado, es académico de honor en la Academia de Ingeniería. Cabe destacar el apoyo que ha recibido de su esposa, sus hijos, sus nietos y familia en general. ¡ENHORABUENA!

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xi

SEMBLANZA DEL PROFESOR BRAJA M. DAS Rosemberg Reyes Ramírez Braja Mohan Das, nació en la India el 2 de marzo de 1941, realizó sus estudios de posgrado en Estados Unidos obteniendo su M.S. en Ingeniería Civil en la Universidad de Iowa y su Ph. D en Ingeniería Geotécnica por parte de la Universidad de Wisconsin, Madison. El Profesor Das es autor de más de 250 artículos técnicos en el área de ingeniería geotécnica y ha escrito un importante número de textos y libros de referencia en ingeniería geotécnica. Sus principales áreas de investigación incluyen cimentaciones superficiales, anclajes de tierra y geosintéticos. Es miembro vitalicio de la Sociedad Americana de Ingenieros Civiles, miembro vitalicio de la Sociedad Americana de Educación en Ingeniería y miembro emérito del Comité de Estabilización Química y Mecánica de la Junta de Investigación de Transporte del Consejo Nacional de Investigación (Washington DC). El Profesor Das ha participado en los comités de Cimentaciones Superficiales de la ASCE, en el Comité de Cimentaciones Profundas y en el Comité de Muros de Concreto. También fue miembro del comité editorial de la ASCE para el Journal of Geotechnical Engineering . de 2000 a 2006, fue co-editor de Geotechnical and Geological Engineering an International Journal publicado por Springer en los Países Bajos, donde fungió como presidente de comité desde 1995 hasta 2001. Actualmente es editor en jefe de la revista - International Journal of Geotechnical Engineering - publicado por Taylor y Francis (Reino Unido). El primer número de la revista fue publicado en octubre de 2007. El Dr. Das ha recibido numerosos premios por excelencia en la enseñanza, entre ellos el Premio de la Fundación AMOCO, el Premio AT & T a la Excelencia Pedagógica de la Sociedad Americana de Educación en Ingeniería, el Premio “Ralph Teetor” de la Sociedad de Ingenieros Automotrices y el “Distinguished Achievement Award” a la excelencia académica de la Universidad de Texas en El Paso. El Dr. Braja Das es Decano Emérito del Colegio de Ingeniería y Ciencias de la Computación de la Universidad Estatal de California, en Sacramento, en 2006 después de 12 años como decano el Profesor Das se jubila y actualmente reside en Las Vegas, Nevada, EUA.

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PRIMERA CONFERENCIA EULALIO JUÁREZ BADILLO 2016

ELASTIC SETTLEMENT OF SHALLOW FOUNDATION DUE TO RISE OF WATER TABLE IN GRANULAR SOIL – A STRAIN INFLUENCE FACTOR APPROACH ASENTAMIENTO ELÁSTICO DE CIMIENTACIÓN SUPERFICIAL DEBIDO A LA ELEVACIÓN DEL NIVEL DE AGUA SUBTERRANEA EN SUELO GRANULAR – APPROXIMACION BASADA EN LA INFLUENCIA DEL FACTOR DE DEFORMACION BRAJA M. DAS Dean Emeritus, California State University, Sacramento

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Sociedad Mexicana de Ingeniería Geotécnica 2


ABSTRACT Increase in the elastic settlement of shallow foundation supported by granular soil due to the rise of groundwater table may be due to several factors, such as the presence of soluble salt, presence of fines, and loss of capillary tension effect in the soil. However, the most important factor contributing to the increase in settlement is the loss of soil stiffness due to submergence. Terzaghi (1943) suggested that the stiffness of granular soil is generally reduced by about 50% after saturation which induces additional settlement. Several empirical relationships are presently available in the literature for estimating the settlement of shallow foundations on granular soil caused by the rise of ground water table. These relationships are based on the assumption of the loss of soil stiffness as suggested by Terzaghi (1943). A comparison of these relationships shows that there is a wide variation in the water table correction factor. The empirical relationships have been summarized in this paper. In addition, the results of a limited number of laboratory tests that are presently available in the literature are also included. In order to provide a more rational procedure for estimating the settlement correction factor due to the rise in water table, a recently developed concept based on the strain influence factor has been elaborated upon. The strain influence factor diagrams for a circular and rectangular foundation used for this study were developed using FLAC and FLAC3D with soil modulus of elasticity of 30 MPa, Poisson’s ratio of 0.2, and load intensity of 100 kPa per unit area of the foundation. These parameters are generally consistent with most of the shallow foundations constructed in the field. Laboratory model test results compare well with the strain influence factor approach.

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1. INTRODUCTION Elastic settlement of shallow foundations supported by granular soil has been the subject of study by geotechnical engineers over the past several years. These studies can generally be grouped into two major categories: A. Methods Based on Observed Settlement of Structures and Full Scale Prototypes: These methods are empirical or semi-empirical in nature and are correlated with the results of the standard in situ test such as the standard penetration test (SPT), the cone penetration test (CPT), the flat dilatometer test (DMT), and the pressuremeter test (PMT). B. Methods Based on Theoretical Relationships Derived from the Theory of Elasticity. The relationships for settlement calculation available in this category contain the term modulus of elasticity (Es). A review of most of these methods can be found in Das and Sivakugan (2007), and Das, Atalar and Shin (2009). Generally speaking, in the case of shallow foundations supported by granular soil, the elastic settlement is primarily a function of (a) applied pressure; (b) stiffness of the soil (i.e., the modulus of elasticity, Es); (c) length-to-width ratio of the foundation; and (d) the depth of embedment. One other factor that also may play an important role in the development of elastic settlement of shallow foundations is the variation of groundwater table if located close to the foundation. The groundwater table can rise up to or beyond the foundation level due to flooding or rain. This can cause substantial additional unforeseen settlement that can exceed the tolerable limit provided in the building code. At the present time, there is no widely accepted procedure to quantify the increase in settlement due to the rise of groundwater table. Various researchers have, in the past, proposed correction factors to account for water table depth. These factors differ from each other in magnitude and also vary with water table depth. A few field observations and some small-scale laboratory model tests have been reported in the literature. These will be reviewed in this paper. In addition, a recently developed rational procedure to quantify the additional settlement of shallow foundations due to the rise in water table by use of the strain influence factor will be discussed in detail.

2. FACTORS ASSOCIATED WITH SETTLEMENT CAUSED BY GROUNDWATER TABLE FLUCTUATION Figure 1 shows a shallow foundation on a granular soil deposit. The width and the depth of embedment of the foundation are B and Df , respectively. The groundwater table is located at a depth of Dw measured from the ground surface. Following are various factors associated with the increase in foundation settlement due to the rise in the groundwater table: •

Some soil will have soluble salt which, due to their ionic nature, create strong bonding with the soil grains when dry. The rise in water table causes the salt to dissolve and the bonding is lost. This might create large additional settlement in loose granular soil (U.S. Army Corps of Engineers, 1990).

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Figure 1. Shallow foundation in a granular soil. Presence of fines in granular soil mass may induce additional settlement when the water table rises. These fines create bonding with coarse grains in dry state, which is lost when they are saturated. Moreover, the lubrication mechanism of soil grains by water can result in additional settlement (US Army Corps of Engineers, 1990). • Capillary tension exists in partially saturated soil above the water table. This causes an apparent cohesion in the granular soil mass increasing the effective stress and hence the shear strength. When the water table rises, the capillary suction is lost and additional settlement occurs (US Army Corps of Engineers, 1990). • The most important factor, however, for settlement increase is the loss of soil stiffness due to submergence. Terzaghi (1943) intuitively predicted that submergence of granular soil from a dry state will approximately reduce the effective unit weight ( γ′) by 50%. This, in effect, will reduce the confining stress in soil located below the foundation by about 50% and hence the soil stiffness (i.e., the modulus of elasticity, E s). As a result, when the water table rises from very deep and reaches the foundation level, the elastic settlement will increase by 100%. •

3. EMPIRICAL RELATIONSHIPS FOR LOSS OF SOIL STIFFNESS Based on the rationale provided by Terzaghi (1943), several empirical relations have been proposed in the past by various investigators to account for additional elastic settlement arising from the loss of soil stiffness due to the rise of groundwater table. Now, a nondimensional parameter can be defined as:

 !  

"#$%&' %$)*&+

",+

where Cw = settlement correction factor, Se(water table) = total settlement with water table rising, S e = elastic settlement in dry sand Most of the empirical relationships found in literature are summarized in Table 1. It is important to point out that Cw proposed by Bazaraa (1967) shown in Table 1 is based on the effective unit weight of soil at a depth of D f + B/2 in dry state compared to when water is present. He used the dry and saturated unit weights of soil as 17.29 kN/m and 19.65 kN/m , respectively. !

!

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Table 1. Empirical Relationships for C w .

Author(s)

Year

Teng

1962

Alpan

1964

Terzaghi and Peck

1967

Bazaraa

1967

Equation for

 !

,

1 2. −    -./ 0 -./     ! 2.- − -./  "34'  !  +  ! 2 − 2 5 ,.- "34' 67'3$8& 3479:$%;496+ γ′ 02   !  0  γ′  94 #$%&'

2

Peck, Hanson, and Thornburn

1974

Bowles

1977

NAVFAC

1982

Cw

 !

#$%&' <'&6&9%

,

5 ,.  -./ 0 -./   0   ! 2 −  0  5 ,. ! 2 − ,./− 5 ,.-

Figures 2, 3 and 4 show comparisons of Cw obtained from the relationships given in Table 1. It can be seen from these figures that, for given values of Df /B and Dw/B, the magnitude of Cw varies over a wide range. For example, for Df /B = 0 and D w/B = 0.5, the magnitude of C w can vary from about 1.0 to 1.75. The general trend of the variation of Cw with Dw/B is linear or convex upwards (for a given Df /B). However the main differences are • •

The maximum value of Cw = Cw(max), and The magnitude of Dw/B at which the water table starts inducing additional settlement. It can vary from 0.4 to 2.

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Figure 2. Plot of Dw/B vs. Cw for Df /B = 0.

Figure 3. Plot of Dw/B vs. Cw for Df /B = 0.5.

Only a few laboratory field test results are presently available in the literature to compare the applicability of the empirical relationships. In the following section, some useful laboratory test results obtained from the studies of Agarwal and Rana (1987); Murtaza, Athar and Khan (1995); and Morgan, Shukla and Sivakugan (2010) are summarized. """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""


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Figure 4. Plot of Dw/B vs. Cw for Df /B = 1.0.

4. RESULTS OF LABORATORY MODEL TESTS Agarwal and Rana (1987) evaluated Cw by conducting a number of model tests on three square model foundations with Df /B = 0. The size (B × B) of the model foundations were 200 mm × 200 mm, 150 mm × 150 mm, and 100 mm × 100 mm. The dry unit weight of sand for the test varied from 15.5 kN/m to 15.7 kN/m . The results of Cw obtained from this study are shown in Figure 5. From this study, Cw can be expressed by the relation: !

!

 ! ,.=/ − -./> 

"2+

Equation (2) shows that Cw is 1.95 at Dw/B = 0, 1.38 at D w/B = 0.5, and 1.0 at D w/B = 1.0. Hence, the groundwater table has no effect on settlement if it is located at a depth equal to or greater than B below the foundation. Murtaza, Athar and Khari (1995) conducted tests with model foundations with dimensions of 60 mm × 60 mm, 80 mm × 80 mm, and 100 mm × 100 mm resting on dense, medium and loose sand. First, tests were conducted to determine the ultimate bearing capacity in dry sand at various degrees of compaction with Df /B = 0 (i.e. surface foundation). Following that, allowable loads for each case were determined with factor of safety, FS = 1.5, 2 and 3. Settlements of the model foundation at allowable load were determined in dry and fully saturated conditions (D f /B = 0). Figure 6 shows the settlement of the 60 mm × 60 mm model foundation at various applied pressures in dry and saturated conditions of the sand. The results of these tests showed that settlement increased significantly in the order of 8 to 12 times in wet sand. In submerged condition, settlement increased eight times for a factor of safety of 3 and twelve times for a factor of safety of 1.5 when compared to the dry condition. """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""



Figure 5. Variation of Cw vs. Dw/B from the laboratory model tests of Agarwal and Rana (1987).

Figure 6. Laboratory model test results of Murtaza et al. (1995) on 60 mm × 60 mm model foundation. Morgan, Shukla and Sivakugan (2010) conducted some laboratory tests on a square model foundation measuring 100 mm × 100 mm (Df /B = 0) supported by two types of granular soil at very loose state (relative density, Dr = 0%) and very dense state (Dr = 100%). Additional settlement by increasing Dw/B and applied pressure were measured (Figure 7). The results from these tests indicated that the magnitude of Cw can be as high as 5.3. """""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""


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Figure 7. Additional settlement due to water table rise obtained from laboratory experiments by Morgan et al. (2010).

5. RECENT DEVEVLOPMENTS From the previous discussions in Sections 3 and 4, it was shown that the magnitude of Cw may be substantially higher than 2 (a value that was originally postulated by Terzaghi, 1943). The variation of Cw with Dw/B appears to be a function of the length-to-width ratio of the foundation, embedment ratio (Df /B), type of soil, level of pressure applied to the foundation, among others. During the last five years or so some systematic, but limited, studies to understand the problem under consideration —both numerical modeling and laboratory experimentation—have been undertaken. The results of these studies are summarized in the following section.

6. NUMERICAL MODELING Shahriar, Sivakugan and Das (2013) have provided a numerical modeling approach to estimate Cw by using the explicit finite difference code FLAC. The analysis was done by assuming the soil behavior as (a) linear elastic, (b) hyperbolic non-linear elastic, and (c) Mohr-Coulomb elastoplastic. For the study, the following parameters were used (Df /B = 0): • • • • • • •

Young’s modulus Es (in dry soil) = 30 MPa Young’s modulus of soil in submerged soil = 15 MPa Poisson’s ratio, = 0.2 Dry unit weight of soil = 17.2 kN/m Saturated unit weight of soil = 20.1 kN/m Submerged (effective) unit weight of soil = 10.3 kN/m Foundation width B = 1 m



!

!

!

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Figure 8 shows the variation of Cw with Dw/B for circular and strip foundations based on linear elastic constitutive model. For this case C w = 2 for circular and strip foundations at Dw/B = 0 as postulated by Terzaghi (1943).

Figure 8. Variation of Cw with D w/B based on linear elastic constitutive model (after Shahriar, Sivakugan and Das, 2013). Figure 9 shows the results of the variation of Cw with D w/B for a circular foundation (Df /B = 0) using a hyperbolic non-linear elastic model, where the stiffness decreases with the increase in stress, for soil friction angle, ϕ = 40°. The hyperbolic non-linear elastic model in FLAC is used to predict two important aspects of soil behavior: non-linearity and stress dependency. This model is based on the stress-strain relationship proposed by Kondner and Zelasko (1963), "

1 − 3+ ! ,    0 "1 − 3+

?$@

ϵ

where (σ1 – σ3)max is the asymptotic value of stress difference, is the axial strain, and Ei is the initial tangent modulus which is also the slope of σ – curve. The plots of Cw vs. Dw/B show that, for the foundation, the variation of Cw is a function of pressure applied to the foundation. At Dw/B = 0, the magnitude of C w can be about 2.5 when the pressure on the foundation is ⅔q u (q u = ultimate bearing capacity).

ϵ

Figure 10 shows a comparison of Cw obtained for a circular foundation (Dw/B = 0) based on MohrCoulomb model, hyperbolic model and linear elastic model. For this part of the study, the foundation was subjected to a working load. The working load is defined as the one that gives a factor of safety of 3 against bearing capacity failure which was estimated through FLAC runs. Note that when the Mohr-Coulomb model is used, the additional settlement due to submergence is much larger, which may explain the high additional settlement found in the literature.

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11


Figure 9. Variation of Cw for a circular foundation based on hyperbolic non-linear elastic model for ϕ = 40° (after Shahriar, Sivakugan and Das, 2013).

Figure 10. Settlement corrections for circular foundation with water table rise based on three different soil models under working loads— = 0.3, ϕ = 35° (after Shahriar, Sivakugan and Das, 2013).



7. A MODEL FOR DETERMINATION OF Cw Keeping in mind the wide variation of the water table correction factor (C w) obtained from limited model test results (Section 4) and the results obtained from numerical modeling (Section 6), Shahriar et al. (2015) proposed a model for estimation of Cw with Dw/B based on the strain influence factor concept. This can be explained with reference to Figure 11 which shows the nature of variation of the strain influence factor and C w with depth under a foundation.

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Figure 11. Schematic diagram of: (a) shallow foundation with rising groundwater table; (b) strain influence factor under the foundation; (c) groundwater table correction factor, Cw.

The total area of the strain influence factor diagram is A t, and Aw is the area of the submerged strain influence factor diagram. The maximum value of Cw is Cw(max) when the strain influence diagram is fully submerged. The magnitude of Cw when the water table is located at a depth Z below the foundation may be expressed as:

 ! , 0 �

"?$@+

   − ,  

"A+

The strain influence factor diagram recommended for use in Equation (3) was given by Shahriar, Sivakugan and Das (2012). This was obtained using FLAC and FLAC3D with soil modulus of elasticity, Es = 30 MPa; Poisson’s ratio, = 0.2; and load per unit area of the foundation, q = 100 kPa. Vertical and horizontal stresses were obtained at various depths along the centerline below the foundation, which were then used to calculate the vertical strain using the constitutive relationship of Hooke’s Law:



ϵ

ϵ ! , � −  0  

"B+

where z and Cs are the vertical normal strain and elastic modulus, respectively, at a depth z below the centerline of the foundation, and x , y , and z are the stresses along x, y and z directions.

σ σ

σ

The strain influence factor (Dz + was then obtained as:

 ! 

"/+

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13


The variations of Dz vs. z/B thus obtained for circular foundations and rectangular foundations with B/L = 1, 0.75, 0.5, 0.25 and 0 are given in Figure 12.

Figure 12. Strain influence factor diagrams obtained from linear elastic analysis (after Shahriar, Sivakugan and Das, 2012).

Based on several laboratory model tests with circular and rectangular model foundations (B = 100 mm) conducted on loose sand at a relative density of 38% and dense sand at a relative density of 77%, Shahriar et al. (2015) have reported the following average values: • •

Cw(max) = 6.3 and n = 0.85 (for loose sand) Cw(max) = 3.4 and n = 1.1 (for dense sand)

Substituting the above values in Equation (3) gives:

0 85    ! , 0 /.A   

"34' *446& 6$9:+

"E+

11    ! , 0 2.B   

"34' :&96& 6$9:+

">+

.

and .

Table 2 gives the variation of Aw/At for various values of Dw/B and B/L.

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Table 2. Aw/At values at different depths for various foundation shapes (after Shahriar, 2015)

Water table depth, Dw/B

Foundation shape Rectangular Rectangular Rectangular (B/L = 0.75) (B/L = 0.50) (B/L = 0.25)

Circular

Square (B/L = 1)

0

1

1

1

1

1

1

0.5

0.573

0.612

0.658

0.703

0.757

0.785

1

0.33

0.368

0.416

0.475

0.562

0.314

2

0.149

0.171

0.2

0.241

0.327

0.399

3

0.08

0.094

0.11

0.135

0.196

0.264

4

0.044

0.051

0.06

0.075

0.113

0.163

5

0.019

0.023

0.027

0.034

0.051

0.078

6

0

0

0

0

0

0

Strip (B/L = 0)

Figures 13 and 14 show a comparison of Equations (6) and (7) with the laboratory model test results (B = 100 mm) for circular and rectangular foundations with B/L = 0.5 in loose and dense sand. The agreement is good.

Figure 13. Comparison of Equation (6) with laboratory model test results: (a) circular foundation in loose sand; (b) rectangular foundation (B/L = 0.5) in loose sand (after Shahriar et al., 2015).

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15


Figure 14. Comparison of Equation (7) with laboratory model test results: (a) circular foundation in dense sand; (b) rectangular foundation (B/L = 0.5) in dense sand; (after Shahriar et al., 2015).

8. CONCLUSIONS The studies presently available on the subject of elastic settlement of shallow foundations resting on granular soil due to the rise of ground water table have been summarized. Based on this review, the following general conclusions can be drawn: There is a wide variation in the water table correction factor (C w) at a given Dw/B obtained from the empirical relationships presently available. • The magnitude of Cw at D w/B = 0 can be substantially larger than 2 and commonly believed. It is a function of several factors, such as type of soil, stress level on the foundation, and the length-to-width ratio of the foundation. • Numerical modeling assuming soil behavior as linear elastic, hyperbolic non-linear elastic, and Mohr-Coulomb elastoplastic illustrates the fact mentioned above. • A new model for predicting Cw using strain influence factor has been presented along with some laboratory model test results which shows good agreement. •

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ACKNOWLEDGMENTS I would like to thank the Mexican Society for Geotechnical Engineering and the National Meeting of the Professors in Geotechnical Engineering for providing me the forum to deliver the First Eulalio Juárez Badillo Lecture. It is truly a great honor. • Thanks are due to Professor N. Sivakugan of James Cook University, Queensland, Australia, for involving me as the Associate Supervisor for the Ph.D. work of Mohammad A. Shahriar during which the present strain influence factor method was developed. • My wife, Janice Das, has been a constant source of inspiration for all of my scholarly work for the past 47 years. She helped prepare this paper in its final form. • Cengage Learning, the publisher of most of my major books, for translating the books into Spanish, which introduced me to a number of Spanish-speaking engineers around the work, including Mexico. •

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REFERENCES Agarwal, K. G.; Rana, M. K. (1987). Effect of Ground Water on Settlement of Footing in Sand, Proceedings, Ninth European Conference on Soil Mechanics and Foundation Engineering, Dublin, A. A. Balkema, 2, 751-754. Alpan, I. (1964). Estimating the Settlement of Foundations on Sand, Civil Engineering and Public Works Review, 59(700), 1415-1418. Bazaraa, A. R. (1967). Use of the Standard Penetration Test for Estimating Settlements of Shallow Foundations on Sand, Ph.D. Dissertation, Department of Civil Engineering, University of Illinois, Champaign-Urbana. Berardi, R.; Lancellotta, R. (1991). Stiffness of Granular Soil from Field Performance, Geotechnique, 41(1), 149-157. Bowles, J. E. (1977). Foundation Analysis and Design, 2nd Ed., McGraw-Hill , New York Das, B. M.; Sivakugan, N. (2007). Settlement of Shallow Foundations on Granular Soil—An Overview, International Journal of Geotechnical Engineering , 1(1), 19-29. Das, B. M.; Atalar, C.; Shin, E. C. (2009). Developments in Elastic Settlement Estimation Procedures for Shallow Foundations on Granular Soil, 3rd Geotechnik Symposium, Çukurova Üniversitesi, Adana, Turkey, 43-75. Kondner, R. L. A.; Zelasko, J. S. (1963). A Hyperbolic Stress-strain Formulation of Sands. Proceedings, Second. Pan-American Conference on Soil Mechanics and Foundation Engineering, Sao Paulo, Brazil, 1, 289-324. Morgan, A. B.; Shukla, S. K..; Sivakugan, N. (2010). An Experimental Study on the Additional Settlement of Footings Resting on Granular Soils by Water Table Rise, Soils and Foundations, 50 (2), 319-324. Murtaza, G.; Athar, M.; Khan, S.M. (1995). Influence of Submergence on Settlement of Footing on Sand, Journal of the Institution of Engineers (India), 76 (5), 51-54. NAVFAC (1982). Soil Mechanics Design Manual 7.1, Department of the Navy, Navy Facilities Engineering Command , Alexandria, Virginia. Peck, R. B., Hanson, W. E., and Thornburn, T. H. (1974). Foundation Engineering, 2nd Ed., John Wiley and Sons, New York. Shahriar, M. (2015). Settlement of Shallow Foundations Due to Rise of Water Table in Granular Soil, Ph.D. Dissertation, James Cook University, Australia, 164 p. Shahriar, M. A.; Sivakugan, N.; Das, B. M. (2012). Strain Influence Factors for Footings on an Elastic Medium, Proceedings, 11th Australia-New Zealand Conference on Geomechanics, Melbourne, Australian Geomechanics Society and the New Zealand Geotechnical Society, 131-136.

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Shahriar, M. A.; Sivakugan, N.; Das, B. M. (2013). Settlement Correction for Future Water Table Rise in Granular Soils: A Numerical Modelling Approach, International Journal of Geotechnical Engineering , 7(2), 214–217. Shahriar, M. A.; Sivakugan, N.; Das, B. M.; Urquhart, A.; Tapiolas. M. (2015). Water Table Correction Factors for Settlements of Shallow Foundations in Granular Soils, International Journal of Geomechanics, ASCE , 15(1), 7p. Teng, W. C. (1962). Foundation Design, Prentice-Hall Inc., New Jersey. Terzaghi, K. (1943). Theoretical Soil Mechanics, John Wiley and Sons, New York. Terzaghi, K.; Peck, R. B. (1948). Soil Mechanics in Engineering Practice, 1st Ed., John Wiley and Sons, New York. U. S. Army Corps of Engineers (1990). Engineering and Design—Settlement Analysis, http://www.usace.army.mil/publications/eng-manuals/em.htm , Washington, D.C.

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SMIG 2016

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