US. Department of Transportation
Publication No. FHWA-HI-94-021 February 1994
Federal Highway Administration
NHI Course No. 13127
Pavement Deflection Analysis Participant Workbook
National Highway Institute
Contents Section 1- Course Introduction 1.1 1.2
Deflecti on Measur ements and The ir Uses 1.1.1 Surf ace deflections 1.1.2 Deflection Uses Objectives Course
Page 1-1 1-1 1-1 1-3
Section2 - Materials Characterization 2.1
Introd uctio n 2.1.1 General 2.1.2 Need for Elas tic Moduli
2-1 2-1 2-2
2.2
Elast ic Moduli in Pav ement Systems 2.2.1 Elas tic Modulus 2.2.2 Modulus Strength of Elastic ity — Not a Measu re of 2.2.3 Determ ination of Ela stic Modulus 2.2.4 Labora tory vs. Field Moduli 2.2.5 Diffe rent Types of Moduli 2.2.6 Differen ce Between Modulus of Elas ticity and Resilient Modulus 2.2.7 Poisson's Ratio 2.2.8 Nom enclature and Symbols 2.2.9 Stre ss Sensitivity of Moduli
2-4 2-4 2-5 2-5 2-7 2-8 2-8 2-10 2-13 2-13
Lab orato ry Determina tion of Elas tic Moduli
2-13
2.3.1 2.3.2 2.3.3 2.3.4
Introduc Dia metraltionResilient Modulus Triax ial Resilient Modulus Fle xura l Modulus
2-13 2-17 2-21
SH RP Resilient Modulus Laboratory Tests [2.3] 2.4.1 Aspha lt Concrete — SHRP Protocol P07 2.4.2 Aspha lt Treated Base and Subbase 2.4.3 Unstabilized Mater ials — SHRP Protocol P46
2-21 2-21 2-21 2-23
2.3
2.4
Page 2.5
2. 6
Typ ical Valu es of Ela stic Modu li 2.5. 1 Typic al valu es of m odulu s of elast icity for vario us mat eri als 2.5. 2 Typi cal Pa vement Ma ter ials
2-24 2-24
Est ima ting Elastic Mo duli of Pa vement Mat erials
2-25
2.6.1 2.6. 2 2.6. 3
2-25 2-26
2.6.4
Section
Asph alt Conc ret e Modu li Port land Cement Concrete Moduli Sta bil iz ed Mat erials Moduli (includes base, subba se an d subgr ad e) Un sta bili zed
2-24
2-27 2-27
2.7
Var iat ion s in Modulus 2.7.1 Gener al 2.7. 2 Temper at ur e 2.7.3 Moi stu re 2.7.4 F reeze-Tha w Con ditions 2.7.5 Time of Loadin g 2.7.6 Str ess Level 2.7.7 Ma ter ial Den sity
2-41 2-41 2-41 2-42 2-43 2-44 2-45 2-46
2.8
P oisson's Rat io
2-4 7
3 - Fu n da m ent als of Mechan
is tic -Em pirical Desi
gn
3.1
In tr oductio n 3.1. 1 Overview of H istoric al Developme n t 3.1. 2 Reasons for Using Mecha nist ic-Em piric al Proc edures (rath er th an empiric al)
3-1 3-1 3-1
3.2
La yered Elast ic Systems
3-7
3. 2. 1 3.2. 2
3-7
3.2.3 3.2.4 3.2.5 3.2. 6
Assump tio ns and Inpu t Requirement s One-l ayer System Wi th Point Loading (Boussinesq) O dem ar k's Met hod i3 .181 Two- layer System (Burm ister ) Mu lti-l a yer System Elast ic Layer Co mpu ter Pr ogra ms
3-10 3-16 3-20 3-24 3-24
Page 3. 3
Ana lysis of Rigi d Pa vemen ts 3.3. 1 In tr oduction 3.3. 2 Continu ously Su pport ed Slab Models 3.3.3 Ela stic La yer Model 3.3. 4 Finite E lemen t Models 3.3.5 Coupled Models
3- 36 3-36 3-36 3-38 3-39 3-39
3.4
Des ign P rocess 3.4. 1 Flexi ble Pa vemen ts 3.4. 2 Rigi d Pa vemen ts
3-40 3-40 3-58
3.5
E xistin g Overlay an d Mechan istic -Em piric al Design Procedures 3.5. 1 In tr oduction 3.5.2 New design Pr ocedu res 3.5.3 Over lay design Pr ocedu r es
3.6
Exa m ple 3.6. 1 3.6. 2 3.6. 3 3.6.4 3.6. 5
3.7
Section
In tr oduction Aspha lt Inst itut e Eff ective Thickness Procedure Aspha lt Ins titu te Def lec tion P roc edu re WSDOT Mec h an istic -Em piric al Su mm ar y
Us e of Ela stic Analysis Sof twa re 3.7. 1 In tr oduction 3.7. 2 Sof twa re Demonst ra tio n 3.7.3 Descript ion of "Sta nd ar d" Sections 3.7.4 Classr oom Exer cise
4 - Nond estru ctiv e Testing Devi 4.1
4.2
In tr oduction 4.1.1 4.1.2
3-63 3-63 3-63 3-72 3-88 3-88 3-89 3-91 3-92 3-94 3-94 3-9 4 3-96 3-102 3-102
ces
Types of Da ta Col lec ted Benefits
Su r face Def lec tion Mea su rem ent s (NDT for Str uctur al Evalua tio n) 4.2. 1 Def lec tion Measu rem ent Uses 4.2. 2 Cat ego ries of Nond estr uctive Testing equipment 4.2. 3 Typic al ND T Pa tt ern s
4-1 4-1 4-3
4-3 4-3 4-4 4-5
Page 4.3
St at ic or Slo w Moving Def lec tion Equ ipmen t 4.3. 1 Benk elma n Beam 4.3. 2 Plat e Bea rin g Test 4.3.3 Aut oma ted Beam s [4.31 4.3.4 Cur vatu re Meter s [4.3] 4.3.5 Typical Applic a tions 4.3 .6
4.4
4.5
4. 6
4.7
Advant ages/ Disadvan ta ges of Sta tic or Slo w Moving Lo ad Def lec tion E qu ipm en t
4-6 4-6 4-8 4-9 4-9 4-9 4-9
Dyn am ic Vibra tory Load (Stea dy Sta te Defl ec tions) 4.4. 1 Gen era l 4.4.2 Dyn aflect 4.4. 3 Road Rat er 4.4.4 WES H ea vy Vibr at or [4.21 4.4.5 F H WA Cox Van (Thu m per ) f4.21 4.4 .6 Typi cal Uses of Steady Sta te Pa vemen t Su rfa ce Deflec tions
4-10 4-10 4-11 4- 14 4-17 4-17
Im pa ct (Im pulse) Lo ad 4.5.1 Gen era l Response Devic es 4.5. 2 Dyna test F alling Wei ght Defl ec tomet er (FWD) 4.5.3 KUAB F alling Weig ht Defl ec tomet er f4.5. 4J5, 4 J ] 4.5. 4 Foun dat ion Mec ha nic s Fa ll ing Weight Deflectom et er [4. 12] 4.5 .5 Ph onix FWD [M , 4J £] 4.5.6 SASW Appr oaches 4.5.7 Typic al Uses of Impu lse Pa vemen t Su rfa ce Deflec tion 4.5 .8 Adv an ta ges an d Disadvanta ges of Impu lse Lo ad Equ ipment
4-18 4-18
Co mp ar iso ns and Co rr el ations Betwe en FWD an d Oth er Devic es 4.6. 1 Int roduction 4.6.2 Comp ar isons Between Devic es 4.6.3 Corr elat ion s Betw een Defl ectio n Measu ring Equipment Calibra tion of Load Cel l an d Def lec tio n Sen sors
4-1 8
4-21 4-25 4-26 4-27 4-27 4-28 4-28
4-29 4-29 4-30 4-37 4-45
Page Section è - Deflection Analysis Techniques 5-1
Introduction 5.1.1 5.1.2 5.1.3 5.1.4 5.1.5 5.1.6 5.1.7 5.1.8 5.1.9 5.1.10
General Basin Para meters (Including Deflection Maximum Deflections) Regression Equations for Predicting Moduli Surface Moduli Backcalculation Combining Indices for Project Analysis Jo int Evaluation in Rigi d Pavements Void Detection in Rigid Pavements Class Exercise A - Deflection Basin Parameters Class Exercise B - Load Transfer Efficiency
5-1 5-4 5-12 5-15 5-15 5-26 5-42 5-51 5-56
Manual Backcalculation Initial E stimat es 5.2.1 Class Exercise 5.2.2 Problem Summary 5.2.3
5-58 5-63 5-66 5-73
Automated Backcalculation Introduction 5.3.1 TypicalFlowchart 5.3.2 Measur es of Deflection Basin 5.3.3 Convergence
5-74 5-74 5-74 5-76
5.3.4 5.3.5 5.3.6 5.3.7 5.3.8
Class Exercise — Convergence Error Me asure of Modulus Convergenc e Convergence Techniques Summary of Backcalculation Programs Verification of Backcalcula tion Res ults
Backc alculation of Rigid Pavemen ts Introduction 5.4.1 Backcalculation Methods for Rigid 5.4.2 Pavements Backcalculation of C omposite Pav em ents 5.4.3
5-83 5-84 5-85 5-90 5-95 5-101 5-101 5-103 5-109
5.5
Critical Sen sitivity Issues in Backcalc ulation 5.5.1 Input Data 5.5.2 Compensating La yer and N on-Linearity Effects 5.5.3 Subgrade "Stiff' Layers 5.5.4 Pavem ent Layer Thickness Effect s
5.5.5 5.5.6 5.5.7 5.5.8 5.6
5.7
Relative Stiffness Effects Season alLayer Effects Fixing Layer Moduli Rules of Thumb
Page 5-112 5-114 5-114
5-115 5-135 5-140 5-142 5-144 5-145
Reliability and Errors in Deflection Analysis 5.6.1 Introduction 5.6.2 Types of Measurem ent E rrors 5.6.3 Sources of Erro rs in Backcalculation 5.6.4 Effects of Erro rs on Ba ckcalculated Moduli 5.6.5 Procedures to Minimize Errors
5-151 5-151 5-151 5-155 5-156
Exp ert Syste m
5-159
5-159
Section 6 - Backcalculation Programs 6.1
Overview 6.1.1 6.1.2
Computer Programs for Backcalculation Selection of a Backcalculation Com puter Program
6-1 6-1 6-6
6.2
Specific Programs 6.2.1 BOUSDEF 6.2.2 EVERCALC MODULUS 6.2.3 6.2.4 MODCOMP
6-13 6-14 6-22 6-35 6-48
6.3
Class Project Description Perform Backcalcula tion 6.3.1 6.3.2 Perform a Basic Mechanistic-Empirical Analysis
6-49 6-49 6-65
6.4
Add itional Proje ct Data 6.4.1 Data File Format 6.4.2 Project Data
6-66 6-66 6-67
Page Se ctio n 7 - Course W rap-U p 7.1 7.2 7.3 7.4
Summ ary and Review Fut ure Tren ds in Pave men t Deflection Analysis Question s and Answers Course Eva luatio n
7-1 7-2 7-3 7-3
SECTION 1.0 COURSE INTRODUCTION 1.1 DEFLEC TION MEASUR EMENTS AND THEIR USES 1.1.1 Surface Deflections A simple and convenient method to assess the structural integrity of pavements is to apply a load to the pavement surface and mea sure the resulting deflectio ns. In this course, a variety of methods for utilizing pavement deflections to obtain information regarding the structural conditi on and load carryi ng capacity o f pavement syste ms will be presented. Pavement deflection measurement techniques are numer ous and can be categorized according to the characteris tics of load appli ed to the pavem ent sur face. Static or slow moving load deflection measurements represent the first generation approach which basically srcinated with the development of the Benkelman Beam at the WASHO Ro ad Tes t in the early 50's. The next generation involved application of a dynamic vibratory load, exemplified by the Dynaf lect a nd Road Rater. These pieces of equipment are more mobile and productive than the static equipment, and led to deflection measurements becoming a routine pavem ent condition survey task. Falli ng weigh t deflectometers can be considered third generation deflection equipment and measure deflections resulting from a dy namic impulse load which attempts to simulate the effect o f a moving wheel l oad. Fu ture equipm ent will likely measure deflections caused by an actual wheel load mov ing at highway speeds. 1.1.2 Deflection Use s Early use of deflection data typically involved considera tion of maximum deflection directly under the load, rela tive to empir ical standards. Usually some st atisti cal measu re o f deflect ions on a pavement section i s compared with a "tolerable" deflection level for that section under the expected tr affic. If the measured val ue exceeds t he
1-1
tolerable deflection then an empirical procedure deter mines the corrective measure required, usually an overlay, to reduce the measured deflections to the tolerable level. Examples of this approach include The Asphalt Institute's MS -17 and CalTrans' Test Method 356. In so me stat es maximum deflections are monitored during spring thaw and load restrictions are placed when the thawing pave ment's deflection reaches a certain l evel. Empirical use of deflection basin data usually involves one of the "basin pa rameters" which combine some o r all o f the measu red basin deflections into a single number. With a trend towards mechanistic pavement analysis and design, which is based on fundamental engineering prin ciples, the use o f deflec tion data has become more sophis ticated. Com plete defl ection basins are used, in a pro ce dure known as backcalculation, to estimate in-situ elastic moduli for each pavem ent layer. Know ledge o f the exist ing layer thicknesses are typically necessary for this pro cedure. A typical deflection b asin i s shown in Fi gu re 1.1. The backcalculated moduli themselves provide an indica tion o f layer condi tion. They are also used in an e lasti c layer or finite element program to calculate stresses and strains resulting from applied loads. These stresses and strains are used with fatigue or distress relationships to evaluate damage accumulation under traffic and predict pavem ent failure. They can also be used to evaluate cor rective measures such as overlays, rehabilitation or recons truction. It is these mechanistic analyses o f pave ment deflection that this course is intended to address. The backcalculation procedure is covered in detail in sub seque nt secti ons. Brief ly, however, it involves calculation of theoretical deflections under the applied load using assume d pavem ent layer moduli . These theoretical deflections are compared with measured deflections such as those shown in Fi gu re 1.1. The assumed moduli are then adjusted in an iterative procedure until theoretical and measured deflection basins match acceptably well. The moduli derived in this way are considered represen tative of t he pavem ent response to load, and can be used to calculate stresses or strains in the pavement structure for analysis purposes. 1-2
TYPICAL DEFLECTION BASIN ) s il m ro s n o r c i (m N O I T C E L F E D
Figure 1.1 - A Typical Deflection Basin
1.2 COU RSE OBJECT IVES The specific course objectives are to familiarize participants with: (a)
Empirical and mechanistic-empirical pavem ent deflec tion based design procedures, with emphasis on the latter.
(b)
Materials characterizati on for these procedures, with emphasis on elastic modulus.
(c)
Selection o f deflection test equipm ent - strengths & weaknesses 1-3
(d)
Bac kcalcula tion proce dures for flexible and rigid pavements—theory and application.
(e)
Deflection measu remen ts and factors affecting them, including unusual field conditions.
(f)
Err ors in deflection data and how they affect backc al culation procedures.
(g)
Practical applications o f backcalcu lation result s.
1-4
SECTION 2.0 MATERIALS CHARACTERIZATION 2.1 INTRODUCTION 2.1.1
General Backcalculation is an iterative process that uses a theo retical model, pavement layer thickness, Poisson's ratio, and estimated moduli, adjusted during the backcalcula tion procedure, to produce theoretical deflections that match field measured deflections within a specified tol erance. The end result of the backcalculation process is a modulus value for e ach pavement l ayer. SEC TION 2 concentrates on materials characterization, with the intent of ensuring that course participants are familiar with typical moduli for common pavement materials. In particular, a participant should be able to deduce whether any particular modulus produced by back calculation is reasonable, and, if outside typical expected values, the possible reasons for the deviation. Typical pavement materials will range from poor qual ity, unstabilized, natural, in-situ subgrades to high qual ity manufactured materials such as Portland Cement Con crete (PCC ) and asphal t concrete (AC). It should be kept in mind that, although one of the primary objectives o f pavem ent con struction specifications i s to ensure material consistency, significant material vari ability is common and will be reflected in the surface deflection measurem ents. In particular, subgrade response is likely to show the greatest variability, and subgrade response typically accounts for up to 90% of the measure d deflecti on for some pavements. This will be demonstrated through the use of layered elastic pro grams to be introduced later in this course.
2-1
2.1.2
Nee d for Elastic Moduli Much of the structural deterioration of a pavement structure is caused by the stresses or strains in the indi vidual materials of the pavement. Strains at the bottom of an asphalt layer are related to cracking of the asphalt, whil e stresses or st rains on top o f the subgrad e may cause rutting or roughness. These stresses or strains are not related in any simple wa y to the overall deflection of the pavement. Stresses, strains and deflections are all pavement response parameters and it may be tempting to assume that sim ple relationships exist between different types of response. The relationships are. simple in a semi-infinite half space, but they are no t in a layered system. That deflection is a poor substitute for strain, may be illustrated by an example. In Fi gu re 2.1 the pavements are loaded by a 50 kN (11.3 kip) dua l wheel load. The tire pressure is 0.7 MPa (102 psi) and the distance betw een the tire centers is 350 mm (13.75 in.). In Case I, at the center point between tires, the applied load results i n a deflection o f 0.464 mm (18.3 mil) and a maximum compressive strain on top of the subgrade o f 476 (^strain (10 -6 mm/mm ), These deflections and strains, as well as those described subsequently, were calculat ed with the elast ic layer program ELSY M5. Case II is identical to Case I, excep t that the subgrade modu lus is only half the value used for Ca se I. In Case II, at the same l ocations considered for Case I, the same load results in a deflection of 0.705 mm (27.8 mil) and a subgrade strain o f 659 (^st rain. Clearly the pav e ment in case II has a poorer "bearing capacity" than Case I, exhibiting higher stresses and strains under the same load level.
2-2
AC 150 mm, 2000 MPa
50 kN (Pressure = .7 MPa)
Base 300 mm, 300 MPa OVERLAYS : Deflection Compressive strain AC
185 mm 65 mm
V ///
Base
ubgraá^"
40 MPa C ase 1
C a s e II
D e f l. ( m m ) 0 . 4 6 4 Strain 4 7 6 (*10A6)
0 .7 0 5 659
C a s eIII
C a s eIV
0 .5 9 4 4 76
0 .4 6 3 285
Figure 2.1(a)
AC 6 in., 290,000 psi 11250 lb. (Pressure = 10 2 psi) Base 1 2 ¡„ 4 3 50Q psj OVERLAYS :
Deflection / ComDressive
ubgrac^)
5 , 8 0 0 ps i
5,800 psi
Case I
Case II
Case III
0.018
0 .0 2 8
0 .0 2 3
4 7 3
659
4 76
' 1 1 , 6 0 0 p si Defl. (in.) Strain (*10A6)
7.3 in.
Figure 2.1(b)
2-3
iubgrac^'') 5,800 psi Case IV 0.018 28 5
To red uce deflections and strains in Case II, an addi tional layer o f asphalt concrete (AC) (modulus 2000 M Pa or 290 KS I) could be ad ded. To reduce the sub grad e strain to the same l evel as Case I , 65 mm (2.6 in.) of AC should be added. However to reduce the deflec tion . to the level for Case I , 185 mm (7.3 in.), almost three times as much AC is required. The use of deflections as a direct measure of the struc tural capacity of a pavement should, therefore, be avoided. Instead the deflections should be used to determine the pavement layer moduli, and the moduli then used to compute stresses or strains which can be used to evaluate structural capacity or remaining life.
2.2
ELASTIC MOD ULI IN PAVEM ENT SYSTE MS
2.2. 1
Elastic M odulus Elasticity refers to the ability of a substance or object to return to its src inal state after undergoing deformation due to the appli cati on o f force . Elasti c modulus is simply the stiff ness o f a materi al w ithin its elastic range. Elastic modulus has been adopted in the 1986 AASH TO Guide for the Desi gn o f Pavement Struct ures for ch aracterizing paving materials [2. 61 Elastic modulus is sometimes called Young's modulus since Thomas Young published the concept of elastic modulus in 1807. Essentially, elastic modulus can be determined for any solid material and represents a constan t ratio o f stres s (a) and strain (e). E = stress/ strain Thus, the "flexibility" of any object (be it pavement or airplane or bridge or whatever) depends on its elastic modulus and geometri cal sha pe. In fact , the produc t of modulus (E) and moment of inertia (I) is a common measure of structural stiffness.
2-4
(Eq. 2.1)
A material is elastic if it is able to return to its srcinal shape or size immediately after being elongated or com pressed. Almost all materials are elastic to some degree as long as the load placed on a material does not cause it to deform permanently. How ever, in the case of highway ma terials t his often is no t the case. 2.2.2
Modu lus o f Elasti city — No t a Mea sure o f Strengt h It is important to remember that a measure of a mate rial's modulus of elasticity or the resilient modulus is not a measure of strength. Strength is the stress needed Figu re to break or rupture a material (as illustrated in 2.2 ), whereas elasticity means that the material returns to its srcin al shape and size. How ever, mod ulus o f elasticity is a measure of material stiffness, and may provide an indication o f material condition o r quali ty.
2.2. 3
Determination o f Elastic Modulus Elastic moduli are generally determined by the follow ing two methods: 1. Lab Procedures Direct lab measurement o f resi lient modulus can be p er formed using AASHTO Method T292 and T294 for non-plastic subgrade and unbound materials and ASTM D4123 for asphalt concrete and other stabilized mate rials. These experienced tests are fairly sophisticated and them cos tly, and require lab personnel to run reliably. 2. Non Destructive Testing (NDT) NDT techniques are being used more than ever to assess the structural condition of existing pavement systems. This assessmen t requires calculat ion of pave ment layer moduli.
2-5
strengrth
s s e r t S
>
Strain
Figu re 2 .2 Sketch of Stress vs. Strain of a Materia] in Compression
2-6
§?
In general, two types of NDT procedures may be used. These include: □
deflec based methods that util(FWD), ize devic as the tion falling weight deflectometer thees such dynaflect, road rater, etc., and
□
wave propagat ion tec hnique s suc h as spe ctral analysis o f surface waves (SAS W) method (brief ly covered in Appendix E).
In the deflection based methods the deflection basin data is analyzed, usually using elastic theory, to backcalculate moduli of pavement layers and an average modu lus o f underlying soils. Wave propagation techniques employ high frequency waves of extremely low magnitude to determine elastic properties o f the pavement ers. SASW methods not yet automated and requirelaysignificant effort, and as are a result, are generally not utilized for production work. 2.2.4
Labo ratory vs. Field Moduli Comparison of moduli obtained from standardized laboratory tests with those backcalculated from field deflection measurements often produce varying results. This is not surprising, since it is fairly unlikely that cond itions of temp erature, stress, moisture, loading rate, load duration, material volume and density, amongst others, are likely to be the same for laboratory and field tests. M ost pavem ent materi als are sensiti ve to one or more of these factors in terms of apparent modulus response, so that resultsany maycomparisons. need signifi As cant adjustm ent prior to test making an example, a typical impulse load from a fallin g weight deflectometer has a duration of 25 - 30 ms, while dy namic load pulses of 100 ms or more are fairly common for laboratory tests, with many tests using 100 ms as a standard. Asphalt concrete would show a modulus of up to about 50% or more higher for the FWD load duration than the laboratory test at 25° C (77° F), all other factors being equa l. This vari es with tempera ture, and the range is about 25% at 5° C (40° F); based on the Asphalt Institute equation [2.121. A. few degrees difference in temperature can have the same effect as this difference in load duration.
2-7
The intent of this brief discussion is to emphasize that comparisons should be made only if conditions are essentiall y the same for field and laboratory t ests. If this is not the adjustments provided should beinmade Section to "normalize" the case, tests (information 2. 6 should assist in doing this). 2.2 .5
Different Types o f Modu li Discussions about moduli can be complicated by the nume rous kinds o f mod uli such as : ♦ Modu lus o f elas ticity ♦ Diam etral resili ent modulus ♦ Triaxial resili ent modulus ♦ Bulk modul us ♦ Mo dulus o f resi lience ♦ Mo dulus o f rigidity ♦ Modulus of rupt ure ♦ ♦ ♦ ♦ ♦
Modulus of roug hness Secant modulus Tangent modul us Young's modul us Shear modulus Fineness modulus ...etc.
We are only interested in the modulus of elasticity and resilient modulus and throughout these notes, we will use the term "modulus" to mean the same. 2.2.6
Differ ence Betwee n Modulus of Elasti city and Resilient Modulus What is the difference between modulus of elasticity and resi lient modulus? The modu of elastici plot ty for a material is basically the slope of itslus stress-strain within the elastic range (as shown in Fig ure 2.2). Fi gure 2.3 shows a stress versus strain curve for steel. The initial straight-line portion of the curve is the elastic range fo r the steel . I f the material is loaded to any value of stress in this part of the curve, it will return to its srcinal shape. Thus, the modulus of elasticity is the slope of this part of the curve and is equal to about 207,000 MPa (30,000 ksi) for steel. On the other hand, resilient modulus is usually based on stress and strain measurements from rapidly applied loads — more like those that pavement materials experience from wheel loads.
2-8
Stress
Strain
Figure 2.3 - Stress-Strain Diagram for Steel
2-9
Many pavement materials exhibit a significant amount of plastic or permanent deformation under applied loads, as well as an elastic or recoverable deformation. Resilient modulus is the ratio of the applied stress to the recoverable (elastic) strain, i.e. resilient modulus relates to the elastic component of the response only. It is an estimate o f the modulus o f elast icity. This is illustrated in Figu re 2.4. 2.2.7
Poisson's Ratio The other material parameter used in elastic analysis of pavement systems is Poisson's ratio. This is defined as the ratio o f transverse to longi tudi nal strains o f a loaded specimen. This concept is illustrated in Figure 2.5. In realistic terms, Poisson's ratio can vary from 0 to 0.5 (assuming no specimen volume increase occurs after loading). Generally, "stiffer" materials will have lower Poisson's ratios than "softer" materials. You might see Poisson's ratios larger than 0.5 reported in the literature; however, this implies that the material wa s stressed to cracking, experimental error, etc. This can also occur in granular materials if applied stresses cause particle re-orientation which results in a volume increase. Poisson 's ratio varies f rom .15 for Portlan d cem ent concrete to .45 for subgrade soi ls. Typical val ues are shown i n Section 2.8. Poisson 's ratio i s tem perature sensitive but for backcalculation purposes it is always assumed to be constant.
2-10
Mr= a d/er
Figure 2.4 - Resilient Modulus
2-11
(Mr ) for a Plasti c M aterial
V
.
U2 £L
Where
H-
Poisson's ratio
eD1
— - strain along the diametrical (horizontal) axis
AD
— « strain along the longitudinal (vertical) axis
Figure 2 . 5 Illustration of Po isson’s Rato
2-12
2.2.8
No men clature and Symbol s The nomenclature and symbols from the 1986 AASHTO Guide [2.6] will be used in referring to pavement moduli. For example: (a)
Ea C
asphalt concrete elastic modulus
(b)
Eb S
base course resilient modulus
(c)
Esb
subbase course resilient modulus
(d)
M r (o r E s g )=
roadbed soil (subgrade) resilient modulus
The only exception is that interchangeably. 2.2.9
M r and E s g will be used
Stress Sensit ivity o f Moduli Changes in stress can have a large impact on resilient modulus for certain types of pavement construction materials. "Typical" relationships are shown in Fig ures 2. 6 an d 2.7, and are discussed in more detail later in this section. As shown i n Fig ure s 2.6 an d 2.7, coarse grained materials tend to show stress stiffening behav ior and fine grained materials are likely to be stress softening.
2.3 LABO RATO RY DETER MINAT ION OF ELASTIC MODULI 2.3.1
Introduction Moduli can be measured in the laboratory using the diametral or split tensile tests for bound materials such as AC or PCC, and the triaxial test for unbound mate rials. Mo duli can also be measured using a flexural test. PCC m odul i are often correlated to compressive or split tensile strength test results.
2.3.2
Diametral Resili ent Modulus Diametral resilient modulus is the stiffness of a material subjected to a repeated, dynamic pulse-type loading.
2-13
(6= 0,
+2 a3 )
Figu re 2 . 6Resilient Modulus vs. BuUc Stress for Unstabilized Coarse Grained Materials
(od = o 1 -C 3 )
Figure 2 . 7 Resil ient M odulus vs. Dev iat or Str ess for Unstabilized Fine Grained Materials
2-14
Diametral de formation is measured along the horizontal diameter (in fact, the term "diametral" simply means "diamete r" — or measured across a diameter ). This test is most commonly used for AC materials. One standard method for this test is ASTM D4123 Indirect Tension Test for Resilient Modulus of Bitumi nous Mixtures. It generally takes about 10 minutes to test one samp le. A com pressive l oad (to pro duce tensile stress) is applied to an AC core or laboratory com pacted sample, typically 100 mm (4 in.) in diameter and 63.5 mm (2.5 in.) thick or 150 mm (6 in.) in diameter and 75 mm (3 in.) thick. The AC sample is loaded ver tically in compression (Figure 2.8) which produces a relatively uniform tensile stress across the vertical diameter {Figure 2.9). The horizontal deformation is measured with LVDTs across the diamet er o f the sam ple as shown in Figu re 2.10. The formula below can be used to calculate the resilient modulus:
EAr = P ^ + ° 27) where
Ea
c
(t)(AH) = asphalt concrete resil ient modulus, psi ,
P
= repeated load, lb.,
H
= Poi sson' s ratio (usually assumed ),
t
= thickness o f the sample, in.,
AH = recoverable horizon tal deformation, in. [To convert to MPa use MPa = psi/145]
2-15
(Eq. 2.2)
Load
Figur e 2 . 8Ver tical Loading of ^ AC Core or Laboratory Prepared Specimen for Determining Diametral Resilient Modulus
I
Figure 2 . 9 Vertica l Loading P roduces a Rela tive ly Unif orm T en sil e Stress Acro ss the Vertical Diameter
Figure 2 . 1 0 Measurement of Ho rizontal Def orma tio n in th e Diametral Resilient Modulus Test
2-16
To c ondu ct thi s type o f test, the needed test equipment incl udes (after ASTM D4123): □ Testing machiof ne capab le load of apply ing a and l oadload pulse over a range frequencies, durations, levels (t ypical load du ration is 0. Is at 1 H z w ith load ranges 4 to 35 N/mm (20 to 200 lb./i n.) o f speci men thickness (10 to 50 percent of the AC tensile strength). □ Tem perature contr ol system capabl e o f contr olli ng temperatures from 5 to 40°C (41 to 104°F). Typi cally, moduli are determined at 5, 25, 40°C (41, 77, and 104°F). □ M easurement and recording s ystem. The horizont al measurements are made with linear variable differ ential transformers (LVDTs) capable of measuring deformations of 0.00025 mm (0.00001 in.). Loads are measured with an electronic load cell. Due to possible creep effects at the higher tempera tures, caution is warranted for such resilient moduli results. 2.3.3
Triaxial Resilient M odulus One commonly used triaxial standard test method is AASHTO T292 and T294 (currently under revision). consists of a cylindrical 4Thein.specimen (100 mm) in diameter by 8 sample in. (200normally mm) high (Figure 2.11). The sample is generally compacted in the laboratory; however, undisturbed samples are pre ferred if available (which is rare). The specimen is enclosed vertically by a thin "rubber" membrane and on both ends by rigid surfaces (platens) as sketched in Figu re 2.12 . The sample is placed in a pressure cham ber and a confining pressure is applied (a3) as sketched in Fig ure 2.13. The sample then undergoes repeated pulses of an axial stress referred to as "deviator stress." This deviator stress is designated and it equals the total vertical stress applied by the testing apparatus (a^)
2-17
(100 mm)
F igu re 2 .1 1 Basic TriaxiaJ Specimen Co nfiguration
-Platen f c-—
-M
*■ £ ■
X - Sample »
V
♦
«
V
- 4;
V
'
*
*
5
Membrane
L
—
. ___
^
'Pialen
Fig ure 2¿ 12 Encl osur e of Triaxial Speci men
o3 ■ confining stress °3 -
- r.; «. F
•
—
r ' •
Chamber
«>
.
Figu re 2 . 13Triaxial Specimen in Pressure Chamber
2-18
minus the confining stress ( 0 3 ). In other words, the deviator stress is the repeated stress applied to the sample. These stresses are further illustrated in Figure 2.14 . The resulting strains are calculated over a gauge length, which is designated by "L" (refer to Figu re 2.15 ). As illustrated in Figu re 2.1 5, the initial condition
o f the sample is unloaded (no induced stres s). W hen the deviator stress is applied, the sample deforms, changing in length as shown in Figu re 2.16. This change in sam ple length is directly proportional to the stiffness. The following equation can be used to calculate the resili ent m odulus: MR (orER) = ^
(Eq. 2.3) e.
Mr (o r Er ) = resilient modulus,
where a j
= deviat or stress, = P/A
P
= repeated load ,
A
=
cross secti onal area o f the samp le,
er
=
recove rable axial strain,
= AL/L L
=
gauge lengt h over which the sampl e deformation is measured,
AL
=
change in sample lengt h over the gauge length due to applied load.
If the material is relatively strongly bound then the confining pressure is not necessary and the modulus can be measured in uniaxial compression.
2-19
c , > total axial stress
o^» deviator stress c 3 - confining stress
*=0
or
od *=o,-C
Figure 2.14
3
StressesActing on Triaxia] Specimen
No Load
L • length over which repe ate d deformation Is measured
Fi gur e 2 . 1 5 Gage Length for Measurem ent o f Strain o n Triaxia] Specimen
Fig ur e 2 . 1 6 Deformation of Triaxia! Specimen U nd er Lo ad 2-20
2.3.4
Flexural M odulus Flexural t ests are m ost commonly used to
determine t he
modulus o f rupture o f PCC. They are als o used ofwith cyclic loading to determine the fatigue characteristics bound materials, particularly AC. Data from flexural tests can provide a flexural modulus . Mod ulus o f rup ture (MR) is defined as the maximum tensile stress in the beam sample at failure. Typical ly third-po int load ing is used as in AASHTO T97-86 Flexural Strength of Concrete (using simple Beam with Third-Point Load ing). PC C beams are usuall y 150 mm x 150 mm (6 in. x 6 in.) in cross section, with length more than three times the depth. AC fatigue tests have been performed on samples with cross-sections varying from 38 mm x 38 mm (1 X A in. x VA in.) through 150 mm x 150 mm (6 in. x 6 in.). The sample i s loaded at the third point as shown in Figu re 2.17 . Note that modulus of rupture (MR) is the tensile strength in bending for PCC and is different from modulus of elasticity (E) or resilient modulus (Mr).
2.4 SHRP RESILIENT MODU LUS LABORATOR Y TESTS [ 11]
2.4.1
Asphalt Concrete — SHRP Protoco l P07 ( current ly under revision): Uses the repetitive indirect tensile test (similar to AST M D4123). The precondi tioni ng, ap plied stress and seating loads are shown in Tab le 2.1.
2.4.2
Asphalt Treated Base and Subbase SHR P Pro toco l P33 has been eli minate d. Fo r materials with sufficient cohesion SHRP Protocol P07 should be used. Otherwise use SHRP Pro tocol P46.
2-21
P/2
P/2
b = Thickness A = Deflection
77
^
23 PU 1296/ A b
h
3
12 Figure 2.17 - Flexural Testing in Third Point Loading
2-22
2.4.3
Unstabilized Materials — SHRP Proto col P46: Uses a triaxial compression test conceptually similar to AA SHT O T294 ( which is under r evisi on). The test sequence for granular materials is shown and fine-grained (cohesive) materials in in Table Table 2.3, 2.2
Table 2.1.
SHRP Resili ent M odulus Test Requireme nts — Asphalt Concrete, Protocol P07.
Test Temp. (°F)
Applied Stress*
Seating Stress*
Min. Load Applications
41
30
3.0
30
77
15
1.5
30
104
5
0.5
30
* as a percen tage o f tensi le strength at 77° F
Table 2.2.
Confining Press., psi
SHRP Resilien t Modu lus Test Requirements — Non-Cohesive (Unbound) Granular, (Base or Subbase) Protocol P46 — Type 1 or Type 2 Repet. Appi. Dev. Stress, psi 15
15
Min. Load Applications
Comment
500
Pre.
3
6 3, ,9
100
Test
5
5, 10, 15
100
Test
10
10, 20, 30
100
Test
15
10, 15, 30
100
Test
20
15, 20, 40
100
Test
2-23
Table 2.3.
SHRP Resili ent Mo dulus Test Requirements — Subgrade Soils (Fine Grai ned), Protocol P 46 — Type 1 or Type 2
Confining Press., psi
Repet. Appi. Dev. Stress, psi
Min. Load Applications
Comment
6
4
500
Pre.
6, 4,2
2, 4, 6, 8, 10
100
Test
2.5 TYPICAL VALUES OF ELASTIC MODU LI 2.5.1
Typical values o f mod ulus o f elasti city for various materials include E Material o Rubber o Wood
(MPa)
(psi)
1,000 1,000,0002,000,000 10,000,000 30,000,000 170,000,000
o Aluminum o Steel o Diamond
7 7,000-14,000 70,000 200,000 1,200,000
Typical pavement materials E o
Material Asphalt Concrete
(32°F (0°C)) o Asphalt Concrete (70°F (21°C)) o Asphalt Concrete (120°F (49°Q) o C rushed Stone o S andySoils o SiltySoils o Clayey Soils o Stabilized Soils o Portland Cement Concrete
2-24
(psi)
(MPa)
3,000,000
21,000
500,000
3,500
20,000
150
20,000-100,000 5,000-30,000 5,000-20,000 5,000-15,000 5,000-3,000,000
150-750 35-210 35-150 35-100 35-21,000
3,000, 000 -8, 000, 000
20, 000 -56,000
2.6 ESTIMA TING ELASTIC MODULI O F PAVEMENT MATERIALS Introduction In most cases it will be fairly obvious whether backcalculated moduli are reasonable for the type of material in a given pavement laye r. Howe ver, in some cases, a backcalculated modulus may be significantly different than expected, yet be feasible and consistent with the conditions at the time the deflecti on data was obt ained. This sect ion attempts to identify factors most likely to affect material response, and provides some guidelines in estimat ing moduli from information other than that used in the backcalculation procedure. 2.6.1
Asphalt Conc rete Moduli (Range Approx. 345 MPa to 20,700 MPa (20,000 to 3,000,000 psi.)) i.
Lab orato ry tests for resilient modulus
ii.
Shell method i.e. Van der Poel's nomogra ph (or McLeod's modification)
iii.
The Asphalt Institute regression equation [2.12] (which is eas ily programmed into a spreadsheet): log
|E*| = 5.553833 +
0.028829 (P
200
/ f 0 17033) - 0.034 76 Vv +
0.070377 ^70°^ 10
6
+ 0.000005 X -
0.0018 9 (X/f u ) + 0 .931757 (1 /f 0.02 774)
(Eq. 2.4)
where |E *| = dynamic modulus (psi) X
- tp (1-3 +0.49825 logf)pac0.5
2-25
(Eq. 2.5)
and P 2 0 0 = % ° f aggregat e passing f
#200
sieve
= load frequency (Hz)
V y = % air voids in mix T170°F, 10° = absolute viscosity of asphalt cement at 70°F, in poises (.3 x 10 6 to 5 x 106) Pac
= % asphalt (by weight of mix)
tp
= temperature (°F)
This equation is "highly satisfactory" for densegraded crushed stone and gravel mixes, but needs to be corrected for different mixes such as sandasphalt or slag asphalt [ 2 . 1 1 ]. iv.
2.6.2
Emulsion Mixes a.
Unc ured - treat as unboun d material
b.
Cur ed - use (i), (ii) or (iii)
Portland Ce ment Concrete Moduli (Range Approx. 14,000 to 56,000 MPa ( 2 to 8 x 106 psi.)) i. ii.
Lab orato ry tests E = 33 p 1 5 fc 0 5 (psi)
(Eq. 2.6)
p = unit weight of concrete (pcf) fc = compressive strength at 28 days (psi) or
E = 57,000 f c0
-5
2-26
for normal weight PCC (psi)
(Eq. 2.7)
2.6.3
Stabilized Materials Modu li (includes base, subbase and subgrade) (Range Approx. 35 MPa to 14,000 MPa (5 x 10 3 to 2 x 10 6 psi.)) i.
Lab orato ry tests (all)
ii.
Lime stabilized.
Compression Ec (i n ksi) = 1 0 + 0.124 UC , [2 J] UC
(Eq. 2.8)
= unconfmed compressive strength (psi)
Flexure (Eq. 2.9)
E f = 4.6 MR - 139 (ksi) , [ 2 J \ M R = modulus of rupture (psi) iii.
Cem ent Stabilized. Some gener al inform ation is shown in Table 2.4. (Eq. 2.10)
E = fc + 500 (ksi) [2.131 fc = compressive strength (psi) iv. 2.6.4
Asp halt stabilized. Similar to AC.
Unstabil ized (Range Approx. 35 to 690+ MPa (5,000 to i.
, + psi.)) Lab orato ry tests.
1 0 0 0 0 0
ii.
Mr=k
or
M r=k
where
10^2
(psi)
(Eq. 2.11)
(psi)
(Eq. 2.12)
ad
= deviator stress
0
= bulk stress = a ! +
2-27
+ CJ3
Table 2.4 - Summary of the properti es of Cement-Stabilized Soil. f2.81
(UC = unconfined compressive strength; P roperty Density
Unconfined Compressive Strength
G r a n u l a r S o ils 1.6-2.2 t/m 2
UC = (90 to 150) C UC = (0.5 to 1.0) C (UC)„ = (UC )d 0 k = 70 C (p si ) k * 0.5 C (MN/m 2)
Cohesion
Friction A ngle Flexural and Tensile Strength Strength under combined stress states
C = cemen t content, percent by weight)
F in e -G ra i n e d S o ils 1.4-2.0 t/m 3
UC = (40 to 80) C UC = (0.3 to 0.6) C + k log (k /do0) k = 10 C (psi) k = 0.7 C (MN/m 2)
To a few hundred psi To a few hundred psi c = 7.0 +0.2 25 (UC) ps i To a few MN/m2 To a few MN/m2 c = 0.05 + 0.225 (UC MN/m2) 44-50° 430-0° Tensile Strength = (1/5 to 1/3) compressive strength (ct, - ct3)2 = UC(a 1+ a 3) for a 3/UC < 0.1 a, = UC + 5a c for a 3/UC > 0.1 (compression positives)
CBR
CBR = 0.55 (UC)1431
2-28
Notes May be higher or lower than untreated soil. Delay between mixing and compaction causes density reduction. UC in psi UC in MN/m2 d * age (days) (d > d0 ) (UC)d0 = UC strength at age of d0 days Depends on C, d
May decrease at high confining pressures. Need 1 - 3% cement to develop. Relationships developed using Griffith crack theory UC in psi
Table 2.4 (continued) [2.81 Property Modulus-Compression
G r a n u la r S o ils
F i n e - G r a i n e d S o i ls
1 x 10s - 5 x 10s psi
10* -1 0 s psi
7 - 35 GN/m2
0.7 - 7 GN/m 2
0 . 7 5 ( 1 - s in ♦ )( «,- *, n 2 E
r E, _ [
2c cos <|> + 2CT3 sin
J
N ote s Depends on stress level E, = initial tangent modules E* = tangent modulus
1
cj 3
= confining pressure
pa = atmospheric pressure n =0.1 -0.5
Ei = Kpa(a3/pa)n
k =1,000-10,000 4 = internal friction angle
Modulus - tension and Flexure
Same order of magnitude as in compression MRc = Kc(a1 - a 3)^ l( a3)''2(UC)"
Resilient Modulus Compression Resilient Modulus - Flexure
Mr f = Kf(10)m- UC
Ec > E* (usually) k, = 0.2 to 0.6 k2 = 0.25 to 0.7 n = 1.0 + 0.18C m = 0.04(10)-186C Effect of confining pressure not known
No fatigue for F/T( < 0.50 Ti= initial tensile strength
Fatigue Behavior
F=
8 (°,+ °s)
F =
0.1-0.2
2-29
for a. + 3o j > 0 ct1
+ 3ct3 < 0
0.15-0.35
Table 2.4 - (Concluded) [2jy P ro p e rty
G r a n u l a r S o il s
Shrinkage
F i n e - G r a i n e d S o i ls
A few ten ths of 1%
Up to 1%
Notes Shrinkage cracks generally inevitable
Thermal Properties (a) conductivity
k = 0.6
k = 0.3
k = 1.0
k = 0.55
(b) Heat Capacity
C = 0.82
(c) Thermal Expansion
1 psi = 6.89 1 1
BTU - ft/hr * ft2 * #F w/m * °K
C = 8.40
BTU/ lb * #F J/kg * 0
e = 5 x 10-*
•F-1
s = 9 x 10-6
•c-1
PA = 6.89 x 10-J MN/mm2
iii.
See Table 2.5 Hicks & McHattie [2.10]. Table 2.6 and Figu re 2. 18 Rada & Witczak [2.7].
iv.
CBR estimates (subgrade). Generally these relationships were developed for CBR values of less than 15-20% (see Figur e 2.1 9).
Shell: E(MPa) = 10 CBR [E (psi) = 1500 CBR]
(Eq. 2.13)
WES:E(MPa)= 37.3 CBR0-™ [E(psi)=5409CBR°-711]
(Eq. 2.14)
TRRL: E(MPa)=17.6 CBR
(Eq. 2.15)
2-30
0 -64
[E(psi)=2550 CBR0-64]
Table 2.5 - Selected Measured Dynamic Moduli for Pavement Material [2.101 Unbound Cranular Base Colorado; standard Base, V' max and 8.7% < No. 200; standard subbas e, 2 V and 7 .9 \ < No. 200 California; well-graded and subrounded gravel 3/4" max; class 2 aggregate base
Frequency & Duration
Load Repetition
Dynamic Modulus
120 cpm, 0.2 sec
10,000
lO ^ I S a ^ 1*1*7, 2.4% w-c 10.019O3*1 *65, 6 .3 \ **-c 8,687a3*‘496, 8.2% w-c
m x
100
30 cpm, 0.1 sec
California; well-graded and angular crushed stone 3/4" max; class 2 aggregate base
30 cpm, 0.1 sec
So i1-aggr egate of 1 7% s il ty sand and 83% crushed granite; 100% T-180; w-c » 5.1% California; well-graded and subrounded gravel 3/4" max; class 2 aggregate base (dry) S i l t y f i n e sand 100% AASHO T -9 9 ; <»0% < No. 200 w-c * 13 .*»%
33 cpm, 0.1 sec
10,000
30 cpm, 0.2 sec
10,000
100
Dry 10.000 to 13,000 8.000 to 9,000 p Partially saturated 7.000 to 10,000 5.000 to 7,000 p Ory 11.000 to 12,000 14.000 t o 15,000 Partially saturated 9,000 to 7,500 to 3,8360*
p s i, 3% < No. 200, C 3* 53 s i, 8% <.No. 200 , o3*^9 p s i, 3% < No. 200, 03*55 s i, 8% < No. 200, a3*60 p s i, 3% < No. 200, 03* 57 p s i, 10% < No. 200, O 3*S0
10,000p ps i,i i , 10% 3% << No. No. 200, 200, o3* o3*5757 9,500
3,use*55
33 cpm. 10,000 0.1 sec
7,000o3*55
1.8560*81 3.1260*37
Subgrade AASH0 class A- 6 s il ty cla y; w-c * 14 to 18 percent; y * 110 to 114 pcf Micaceous s ilty sand s ubg rad e S il ty cla y (AASHO Te st) ; O • 5 to 10 p s i; o 3 < 3 p s i; v * 110 to 115 pcf d
Hi ghl y plastic cl ay (P I ■ 36. 5) and s ilt y clay (P I - 25 .5) AASHO clas s A-7-6 s il ty cla y; w- c = 11 to 20% y * 102 to 105 pc f AA^HO class A-6 to A-7-6 silty clay
120 cpm, 0.2 sec
10,000
33 cpm, 0.1 sec 20 cpm. 0.25 sec
10,000
30 cpm, 0.1 sec 120 cpm, 0.2 sec
10,000
30 cpm. 0.1 sec
2-31
10,000
100
3, 000 to 4, 000 p s i, 18% w-c 7,0 00 to 8,00 0 p s i, 16% w-c 15,000 to 20,000 psi , 14% w-c wet season 3,000 to 4,000 psi. dry season 1,500 to 2,000 psi. 13,000 p s i, 13% w-c 10,000 p s i, 14% w-c 8,000 p s i, 15% w-c 7.000 p s i, 16% w-c 17% w-c 2.000 to 5,000 psi. 2,000 p s i. 18% w-c 4,150o 3,200o 5*2 20% w-c 7,000 to 10,000 psi. , V8% w-c 15,000 to 16,000 psi , 16% w-c 14,000 to 15,000 psi 10, 000 p si, 1 at m (so il m oist ure suct ion during test) 100,000
p s i. 10 atm
Table 2.6 - From Rada & Witczak Ì2.71
(a)
Typical values for k1and k2for unbound base and subbase materials (MR= k.,0 k2 ). (a) Base Moisture Condition
k/
k2*
Dry Damp Wet
6,000 - 10,000 4,000 - 6,000 2,000 - 4,000
0.5 - 0.7 0.5 - 0.7 0.5 - 0.7
(b) Subbase Dry
6,000 - 8,000
0.4 - 0.6
Damp Wet
4,000 1,500-4- ,6,000 0 00
00.4 .4-0.6- 0.6
2-32
Table 2.6 (cont'd) - From Rada & Witczak [2.71
(b) Dry, Sr < 60 Percent Standard CE k2 ki
Aggregate DGA - limestone - 1a DGA Limestone - 2a CR-6-crushed stone3 CR-6-slaga Sand-aggregate blendsb Bank-run gravelb
Modified CE ki
k2
8,500
0.5
10,500
0. 5
11,500
0. 3
15,000
0.3
6 ,0 0 0
0.5
9,000
0.5
12,500
0.35
20,000
0.35
3,800
0.5
6,000
0.5
5,000
0 .4
8 ,0 0 0
0.4
ak1-k2 values are typical for fines percentage (no. 200) of less than 15-18 percent. bk1value should be decreased and and k2 value increased if fines percentage is greater than 10 percent. (CE = Compactive Effort )
2-33
Table 2.6 (cont'd) - From Rada & Witczak [2.71
(b), (cont’d) Wet, Sr > 85 Percent Standard CE k2 ki
Aggregate DGA - limestone - 1a DGA Limestone - 2a CR-6-crushed stone3 CR-6-slag3 Sand-aggregate blendsb Bank-run gravelb
Modified CE ki
k2
7 ,0 0 0
0.4
9,000
0.4
6,000
0.5
7 ,50 0
0.5
3 ,5 0 0
0 .7
5,000
0 .7
5 ,6 0 0
0 .35
9 ,0 0 0
0 .3 5
1,900
0.7
3,000
0.7
1,250
0.7
2 ,0 0 0
0 .7
ak1-k2 values are typical for fines percentage (no. 200) of less than 15-18 percent. than bk1value 10 percent. should be decreased and and k2 value increased if fines percentage is greater (CE = Compactive Effort)
2-34
) i s p ( e u l a V
0.0
0.2
0.4
0
K 2 Value
Figure 2.18 (Rada & Witczak Î2.7])
2-35
.6
0.8
1.0
1.2
Danish Road Laborator y: E(MPa) = 10 CBR
0 73
[E(psi) =1500 CBR
0 -73
]
(Eq. 2.16)
where CB R = Californi a Bearing Ratio (%) N ote : Method also uses Eg = modulus of granular layer on subgrade where Eg = K E sg
(Eq. 2.17)
K = factor varying between 1.5 and 4.8 depending on who is using method (Shell, TAI, Kentucky, etc.) Shell also suggests that K is a function of the thickness of the granular layer so that Eg = 0.2hg whe re
hg
E sg
0 -45
ESg for hg in inches]
(Eq. 2.19)
A relationship between R-value and modulus is: E Sg =1 15 5 + 555R whe re R = Hveem stabilometer R-value.
vi.
(Eq. 2.18)
= granular layer thickness in (mm)
[Eg = 0.86hg v.
°-45
Genera l corre lation relationships , e.g., Table 2.7 Yo der & Witczak [2,9] Table 2.8 Hicks & McH attie i2.101
2-36
(Eq. 2.20)
FIG. 2-19 : CBR-MODULUS RELATIONSHIPS
) a P M ( S U L U D O M
CBR « ----- SHELL
2-37
----- □ ----- W ES
------ ♦ ----- TRRL
----- ©----- DK
Table 2.7 - Characteristics Pertinen t to Road and Runw ay Foun dation [2.91
Major Divisions (1) (2)
Gravel and gravelly soils
Coarse grained soils
Sand an d sandy soils
Low c o m p r e s s i bility L5
Letter (3)
High c o m p r e s s i bility LL>50 Peat and other fib ro u so r g a n ic soils
Value as Base Directly Under Wearing Surfac e (6)
Potential Frost Action (7)
GW
Gravel or sandy gravel, well gTaded
E x c e l le n t
Go o d
None to very slight
GP
Gravel or sandy gravel, poorly graded
G o od t o excellent
Poor to fair
None to very slight
GU
Gravel or sandy gravel, uniformly graded
Good
Poor
None to very slight
GM
S ilty gravel or silty sandy gravel
G o o d to e x c e ll e n t
Fair to good
Slight to mediu m
GC
C layey gravel or clayey sangrdayvel
Good
Poor
sw
Sand or gravelly sand, well graded
Good
Poor
None to very slight
SP
San dorgravellysand, poorly graded
Fairtogood
Poortonot suitable
None to very slight
su
Sand or gravelly sand, uniformlygraded
Fair to good
Not suitable
None to ve ry slight
SM
Silty sand or silty gravelly sand
Good
Poor
Slight to high
SC
C layey sand or clayey gravelly sand
Fair to good
Not suitable
Slight to high
ML
S ilts ,sandysilts, gravelly silts, or
Fairtopoor
CL
Lediatomaceous anclays, sandysoils clays, or gravelly c la y s O r g a n i c s i l t s or l e a n organic clays
Fairtopoor
OL Fine grained soils
Name (4)
Value as Foundation When Not Subject to Frost Action (5)
MH CH OH Pt
M ica ceo u s clays or diatomaceous soils Fatclays Fat organic clays Peat, humus, and other
2-38
N o tsuitable
N otsuitable
Slight to medium
M ed iu mto very high Medium to high
Poor
Not suitable
Medium to high
Poor
Not suitable
Poortovery poor Poor to very poor
N o tsuitable
Medium to very high M ed iu m
Not suitable
Not suitable
Medium
Not suitable
Slight
Table 2.7 (cont'd.) - Characteristics Pertinent to Road and Runway Foundation f2.91 Compressi bility and Ex p a ns io n
(8)
Gravel and gravelly soils
LL > 50 P e a t a nd o t h e r
Crawler-type tractor, 125- 140 rubber tired equipment, steel-wheeled roller Crawler-ty pe tractor, 120- 130 rubber-tired equipment, steel-wheeled roller Crawler-type tractor, 115-12 5 rubber-tired equipment Rubber-tired equipment, 130-1 45 sheepsfoot roller, close control of moisture Rubber-tired equipment, 120- 140 sheepsfoot roller
60 -80
30 0 o r more
3 5 -6 0
3 0 0 or more
2 5 -5 0
3 0 0 o r m or e
4 0 -8 0
3 0 0 or more
20-40
200-300
Crawler-type tractor, 11 0- 13 0 rubber-tired equipment Crawler-type tractor, 105 -12 0 rubber-tire equipment Crawler-type tractor, 100-1 15 rubber-tired equipment Rubber-tired equipment, 120-1 35 sheepsfoot roller, close control of moisture Rubber-tired equipment, 105- 130 sheepsfoot roller
20 -4 0
20 0- 30 0
15 -2 5
2 0 0 -3 0 0
10-20
200-300
2 0 -4 0
2 0 0 -3 0 0
1 0 -2 0
2 00-300
Rubber-tired equipment, 100-1 25 sheepsfoot roller, close control of moisture Rubber-tired equipment 100-1 25 sheepsfoot roller Rubber-tired equipment 90-1 05 sheepsfoot roller
5-15
100-200
5-15
100-200
4-8
100-200
4 -8
1 0 0 -2 0 0
3 -5
5 0 -1 0 0
3-5
50-100
Ch ar ac t e r is ti c s Co mp a c t io n Eq u ipm e n t (10) (9)
(p c f ) (11)
E x c e l le n t
GP
A l m o s t n on e
E xc ellen t
GU
A l m o s t n on e
E x c e ll e n t
GM
Very slight
Fair to Poor
GC
S ligh t
Poor to practically impervious
SW
Almost none
Excellent
SP
A lm o s t n o n e
Excellent
su
Almost none
Excellent
SM
V erysligh t
SC
S lig h tto medium
Poor to practically impervious
ML
S ligh tto medium
Fair to poor
CL
M e d iu m
OL
Medium to high
Practically impervious Poor
MH
H ig h
Fair to poor
CH
H igh
OH
H ig h
Practically impervious Practically impervious
Rubber-tired equipment, 80-100 sheepsfoot roller Rubber-tired equipment, 90-110 sheepsfoot roller Rubber-tired equipment, 80-105 sheepsfoot roller
Fairtopoor
Compaction not practical
Fairtopoor
LL < 50
Fine grained 1 soils High compressi bility
Subgrade Modulus, k (pci) (13)
A lm o s t n o n e
Low
compressi bility
F i e ld CBR (12)
GW
Coarse grained soils Sand and sandy soils
Unit Dry W ei g h t
Drain age
Pt
V e ry h i g h
fibrous organic soils
2-39
Table 2.8 - Crude Empirical Relationships Between Resilient Modulus and Other Test Data [2.101
p a i
5K
10K
20K
50 K .
Kg/cm2
10 OK
1
,
|
DYNAMIC MODULUS
200
500
I
IK
. 1
■
2K
1
.
5K
1
1
10K .
1
CBR 2
3
4
5
1
I I
1
6
8
1. 1 . 1
Bea rin g Value, pai 20
J
___
25
30
40
L J ___ I
_ _
10
20 .
1
30
40
50
1
1
1
80 ,
.
10 0
1 ,
1
(12" sia. plate, 0.2" deflection, 80
u_J
__
100
200
,_ | ___ i
___
300
10 repetitions)
400
1__ i_
General Soil Rating as Subgrade, Sub-Base or Base Very Poor Poor Fair Med. Good Med. Good Med. Good Subgrade Sub Sub Sub Sub Sub Sub Base Base grade grade grade grade base base
A.A.S.H.O. SOIL CLASSIFICATION I I I I_____I___ A-l-b A-1-a A-2-7 A-2-6 A-2-5 A-2-4 A3 A4 T^~ _____
A5 A6 A-7-6
Excellent Base
I___ I
A-7-5
T
I
I
I I
I I
UNIFIED SOIL CLASSIFICATION
2-40
2.7 VARIATIONS IN MODULUS 2.7.1
General To some extent, the preceding approaches for estimat ing moduli from material and loading characteristics have explicitly included specified ranges or values of the temp erature, loading frequency, et c. How ever, it is of interest to summarize these effects below, with some indic ation o f the relative importa nce of each parameter or condition in affecting the modulus.
2.7.2
Temperature i.
Asph alt bou nd materials Temperature is theofmost significant affect as ing the modulus asphalt treatedfactor materials illustrated by The Asphalt Institute (TAI) modu lus equation. At low tempe ratures (below about 0-5° C [30-40° F]) the modulus tends towards a value of 14,000 to 20,000 MPa (2 to 3 million psi). At high tempe ratures (above about 45-50° C [110° to 120° F]) the modulus tends to a rela tively low value, usually less than about 700 MPa ( 100,000 psi), with the actual value related to the modulus o f the untreated aggregat e.
ii.
Cementitious bound material These comments relate to materials stabilized to the point of exhibiting an unconfined compres sive strength, such as soil cement or cement stabilized subbases. Other cement- or limetreated materials would exhibit behavior similar to unbound granular materials with a similar gra dation. Cement bound materi als show l ittle tem perature effect in terms of modulus at normal pavemen t temp erature ranges. How ever, defl ec tion data may be affected by temperature due to expansion or contraction movement at joints or cracks, or due to shape effects resulting from temperature gradients. 2-41
iii.
Unbound materials Tem peratu re has little effect on the modulus of unbound materials, except in the way that mois ture in the material is affected by temperature. Below freezing (0° C or 32° F), modulus is sig nificantly increased due to cementing action of ice. Otherwise, no effec t is expected excep t if temperature causes moisture content changes, which is not a direct load-related response effect during the deflection test, but a longer term material condition effect.
2.7.3
Moisture i.
Asphalt boun d materials Moisture has little or no direct response effects on deflection data for asphalt boun d materials. If the asphaltic material is moisture sensitive and subject to stripping, the reduction in modulus will reflect the extent to which stripping has occurred at any given time, but, again, the moisture does not show a direct response effect.
ii.
Cement bound material s The presence or absence of moisture will have no effect on the direct response of cement bound materials during deflecti on testing. Mo isture wi ll have a long term effect on modulus similar to the effect it has on strength.
iii.
Unbou nd materials At a given density and stress level, moisture content is probably the most significant factor affecting the modulus of unbound materials, as illustrated by the relationships shown in Table 2.6. Mod ulus can increase by a factor o f five or more for a mat erial as it dries out. This is true for coarse grained and fine grained materials, although the effect of drainage conditions may be 2-42
more significant for coarse grained materials. Reduction in modulus with increased moisture content is usually related to decreased inter particle friction due to increased lubrication for cohe sionles s materials. In cohesiv e soils, modulus changes are usually related to the soil fabric effects associated with clay-waterelectrolyte systems, which are fairly complex. Under saturated conditions applied loading may result in excess pore water pressures which can dramatical ly affect apparent structural response. 2.7.4
Freeze-Thaw Conditi ons This usually refers to the spring thaw period in areas where significant seasonal frost penetration of the pavemen t occurs during winter. Thawing occurs from the surface down, resulting in thawed material under lain by frozen material until the structure is completely thawed. There is usually an excess of surface wa ter present, so that the thawed zone is often saturated and unable to drain due to underl ying ice. This combination of low temperatures and saturated conditions results in material modulus combinations that are particularly susceptible to load associated damage. i.
Asph alt bou nd materials The direct response effect on asphaltic materials during spring thaw is governed by temperature conditions at this time. Typically tempera tures are low, resulting in high asphalt moduli and relatively brittle behavior for these materials. Damaging conditions under load are com pounded by the lack of support from unbound, saturated materials in the thaw zone.
ii.
Cement boun d materials Deflection of cementitious materials is independ ent of temperature or moisture conditions. Cement bound materials may be damaged by
2-43
freeze-thaw or wet-dry cycles, resulting in low ered modul i and strengths. This damage ma y be reflected by increased deflections. Freez e-thaw effects are more of a factor for stabilized bases or subgrades than the pavement surface. iii.
Unbou nd materials The m odulus o f unbound materials in t he thawed zone are generally at their lowest level, particu larly in the area close to the thawing front, where they are likely to be saturated and subject to excess pore pressures under a dynamic load due to lack of drainage. Moduli may be as low as 2 0 % or less of the modulus that would be exhib ited by the material in a dry condi tion. Fo r frost susceptible materials the response may be perma nently affected if ice lenses form causing frost heave during the freezing process, which results in a loss in density on thawing.
2.7.5
Time o f Loading i.
Asph alt bou nd materials At any given temperature, the modulus of asphaltic materials is strongly influenced by time of loading due to the visco-elastic nature of the material. This effect is reduced at low temp era tures. The Asphalt Institute equation i n Section 2.6 .1 can be used to illustrate the effect . The dif ference in time of loading between laboratory tests (typically 0.1 sec.) and FWD tests (typically .025 to .035 sec) can result in a 50% difference in moduli, with the higher modulus exhibited for the shorter load pulse on the FWD.
ii.
Ceme nt bou nd materials Dynamic moduli for cementitious materials can be approximately twice the static moduli. (Neville, 2.4) How ever, thi s effect reduces as the modulus increases, with good quality PCC 2-44
moduli in the 28,000-35,000 MPa (4 to 5 million psi) range showing similar moduli for dynamic or static loading conditions, according to Neville. Some practitioners suggest that tests dynamic PCC moduli determined from FWD will show significantly higher values than laboratory (static) measured moduli.
iii.
Unb oun d materials The effect of time of loading on the modulus of unbound materials is generally small compared with stress level and moisture content effects.
2.7.6
Stress Level i. Asphalt boun d materials Within typical ranges of stress level encountered in pavement structures, the effect on asphaltic material modulus is insignificant. ii.
Cem ent bou nd materials Generally speaking, stress level does not signifi cantly affect modulus for strongly bound ce mented materials, although Table 2.4 (Ref. 2.8) shows a relationship between stress state and compressive modulus for cement stabilized soil. For cement or lime modified materials showing little or no cohesion, stress level effects would be similar to those exhibited by unbound materials.
iii.
Unb ound materials Many unbound materials are extremely stresssensitive with moduli very significantly affected by stress level. Gran ular materials will often show stress-stiffening behavior, as described in Section 2.2.7 and 2.5.4, with the apparent modulus increasing as the applied stress level 2-45
increases. Fine-gr ained materials often exhibit stress-softening behavior, showing a decreasing modu lus as the stress level increases. This has a significant bearing an on alyses. deflection measurements and the associated If deflections are measured with an FWD, unbound material stress levels are very different for the center sensor compared with outer sensors which may be 1.8m (6 ft.) or more away from the load plate. This means that the material response would be differ ent at these locations which needs to be recog nized in the analysis. Stress level effects should also be considered if the deflection test load is different from the ex pected design wheel loa d. 2.7.7
Material Density Density is considered to be an indicator of the quality o f constructed pavement layers and is typi cally ref lected by the material modulus . i.
Asphalt boun d materials For a typical adequate quality asphalt concrete material, modulus will vary somewhat with den sity, and this variation can be illustrated with the Asphalt Institute modulus equation in Section 2.6 .1. The variation is minor compared with temp erature and time of loading effects. Ho w ever, significant variations will occur if densities are significantly lowered due to poor compac tion, for instance.
ii.
Ceme nt boun d materials Cementitious bound materials show some modulus variation with density as illustrated by the PCA modulus equation in Section 2.6.2. The modulus of light weight concrete [1600kg/m3 (100 lb./ft3)] may be 50% to 60% that of normal weight PCC.
2-46
iii.
Unb ound materials Density effects are relatively minor for unbound materials arelevels. compacted typical pavement structural that layer Theto modulus does in crease with increased density, as illustrated by Rada & Witczak's data in Table 2.6 and Figu re 2.1 9, or by the relationship between CBR and modulus (Fig 2.20). Stress level and moisture effects are more significant than density effects for unbou nd materials.
2.8 POISSO N'S RATIO Poisson's ratio was defined and described in
Section 2.2.5.
Typical values o f Poisson's ratio (n) include: o o o o
Material Steel Aluminum PCC Flexible Pavement o Asphalt Concrete o Crushed Stone o Soils (fine-grained)
Poisson'sRatio 0.25-0.30 0.33 0.15-0.20*
0.35 (±) 0.40 (±) 0.45 (±)
*Dynamic determination o f n could approach 0.25 for PCC [Neville (1.4)] The particular significance of Poisson's ratio lies in the fact that it essentially defines the three dimensional state of stress or strain in the material, as illustrated by the general Figu re ized Hooke's law for multiaxial loading i.e., (see 2 . 21 ),
8x
= Y '
E ( °y + az )=
2-47
i [ ° * - ^ ( a y+ a z)]
(E q . 2 .2 1 )
%
= ^
§ K + °z) = ^ [a y-^ (a x+a 2)]
(Eq. 2.22) (Eq. 2.23)
where
e = strain a = stress E = elastic modulus = Poisson's ratio
As example, the uniaxial load case with Oy = aza =simple 0 which resultsconsider in:
(Eq. 2.24) (Eq. 2.25) i.e. response along the y and z axes are directly related to Poisson's ratio. It is obvious from t his that the magnitude o f Poisson's ratio is important to mechanisti c pavement anal yses. Fortunately large variations in Poisson's ratio for a given pavement material are unlikely. Since it is very difficult to me asure Poisso n's ratio the value is usually assumed. It is believed that the analysis is fairly insensitive to this value.
2-48
a.
a,
Figure 2.20 - Three Dimensional Stress Diagram
2-49
2.9
C l ass
E xerci
se
Objecti ve : To f an i l i ari ze t h e stud e n t w i t h the t yp i ca l r an ge o f va l ue s of »od ul i t hat are com ao n to hi gh w ay pa ve ce nt sater i al s. fart A Di al of sa
rect i on s: U si ng t he i nfor mat i on con t ai ne d in t his »a nu al , on g w i t h you r persona l ex pe ri en ce , en t er a "r ea so na ble" val ue t he no du l us o f el ast i ci t y a nd P oisso n's rati o f o r a ac h o f t h e t eri als des cri be d.
1 . A new asphal t concr de gree s Fa hr enhe i t ) .
et e s urf ace at 2 5 de grees
¡P o i ss o n ' a R at i o
2.
A new pont
l and
e slab .
P oi sson' a R at i o
3.
A cl ea n, cr ushed Poi sson' a Ea ii- e
o f E l as t i ci t y l Ei l l
fH Pa )
cenent concret
C el si us {77
Mod ul us o f E l as t i ci t y fM P a ) Itill
st one ba se l a ye r, we l l drai m
H c *3 u l u s m
el
ned.
Elasticity
lE ill
4 . A cem ent - st abi l i zed ba se, w i t h 40 »a (1 1 /2 in ) » axi sua pa rt i cl e size , an d a 28-day con pres si ve str en gth o f ap proxi 70 00 kP a ( >1 00 0 ps i ) . P oi sson'
a
Eg tig
Mod ul us p f E l as t i ci t y fMPa)
5 . A si l t y sand subg r ade , su bject to in lat e sp ri ng o f t he ye a r. Poi ss on ' s Rfi ti fl
satel
*
se as on al f ros t p en etr ati on ,
H adii li li -fi l— J k l Afi lA SLi lX I KE A1
2-50
y
6 . Th e sa ne si l t y «and s fal l o f t h e ye ar. P oiR atsso i on' »
u b -gra d e «• i n prob l en 5 , but
i n l et*
(M Mod Pa ) ul us o f E l as t i ci l t EyS l )
7 . A recycled bi t um i nous s urf a ce , vel C el si us (1 0 4 degr ees F ah r enh ei t ) . P oi sso n' » Eat I p
l - co*pa
Mod ulus 1
ct ed , et 4 0 de gree s
o f E l as t i ci t y l £i i i
1 M£ a
I. A 1 i ae - st abi l i zed subg r ade w i t h an un co nfi ne d co ap ressi st r eng t h of 1000 kP a ( - 15 0 ps i ). P oi sso n' s
Mod ul us o f Elasti
P at i o A p oo rl y drai R at i o o f 3 . 9.
vs
ci t y
I MP A l ned d
a y su bg rad e h av i ng a C al i f orni
P oi sso n' . L at i g
Mod ulus (MPa)
a B e ari ng
o f E l as t i ci t y Ids!)
1 0 . A clea n , cr ushed 9 rave l b a se , se p a rated f ro» t he « ^ r a d e i n prob l en 9 b y e l aye r of f i l t er f a b ri c, an d co ve red b y e t hin bi t um i no us surf ace (eg . , • chi p se a l ). P oi sson ' s
Rat i o
Mod ulus
1K P&1
2-51
o f E l asti
ci t y
F art
I
Di rect i on s: B ased upon t he de scri pti on o f e ac h pavem ent systea w ri t e do w n an expect ed ao dul us o f el a sti ci t y a n d P oi sson ' * rati o f t he mat i alands a iaan t he xi p aauvemmeprobn t. ab Al le soval i nd aifor ni eamumch probabl e val er ue ue fi cate or t he a cx Ju l u s o f each l ayer .
, o
a
Pave r cen t Ko . 1 - New C on c r et e Pavem ent A ne w l y const r uct ed j oi nt ed, rei nforced co ncrete pa vem ent has a a 20 0 a m (8 i n ) ceD ent t r eat ed ba se 15 0 K m (6 i n ) sur f ace ov er a count y r oa d w hi ch ser ves 5500 A DT . (C T B) . I t i s l ocat ed on T he sub grade so i l i s a pl ast i c c l ay , a n d un de r drai ns h ave be en pl ace d al on g bot h si des of t he pa ve men t a t a d ep t h o f 1.1 ae t era (42 i n ) . L a ye r Wuftfre r
Mat er i al
1
P C Concr
2
CTB
3
P l asti
et e
P oi sson' » R at i o
Mod ulus i K Fa I
of E l ast i ci t y
____ _ _ _ _ _ _ _ _ _ _
____ ___ ___
I bsII __ __ __ __ __ __ __
c C l ay
P ave r en t No . 2 - A gi ng Asphal
t P av ese nt
A fl ex i bl e pavem ent w as con st r uct ed 2 0 ye ars ag o on s st at e pri mary r oa d w hi ch cur r ent l y se r ves 1 2 , 0 00 A DT . Th e pave ment i s a com po sed of a 110 us ( 4. 5 i n ) aspha l t con cret e sur f ace over 40 0 an (16 i n ) cr ushe d st one ba se co urse . Th e subgr ade i s a a n ort he rn cl i na t e w he r e the si l t y sa n d . Th e r oad i s l oca t ed i n f rost pe ne t r at i on i s t ypi cal l y a b ou t 1 a eter ( 4 0 i n ) each wi n t e r. Du e t o w ea t he r an d t r af f i c, t h e a sp h a l t su rf ac e i s se verel y all i ga t o r cr acke d and sl i gh t l y rutt e d in the w he e l pa t h s. L a ye r
al
po i sson ' s R ati o
1
Agi ng HM AC
___ ___ ___ _
___ _ ___________
_______________
2
Cr.
____ ___ ___
_
_______________
3
S i l t y S an d*
__ _ _ _ _ _ _ _ _ _ ________ -
4
S i l t y S and
_ _________
Materi
VliEbSI
St one
’i n t he zon e o f f r ost pe
Mo d u l u s o f E l asti X£ £ i i
______________
________
n e t rati
2-52
on
ci t y l £ Si l
SECTION 2.0 REFERENCES Bu-bushait, A. A., "Development of a Flexible Pavement Fatigue Model for Washington State," Ph.D. Dissertation, Department of Civil Engineering, University of Washington, Seattle, Washington, 1985. Southgate, H. F., and Deen, R. C., "Temperature Distributions in Asphalt Concrete Pave ments," Hig hw ay Res earc h R ec or d No. 549, Highway Research Board, Washington, D.C., 1975, pp. 39-46. Hadley, W. O., “Laboratory Techniques for Resilient Modulus Testing,” Pr oce edi ng s, Strategic Highway Research Program Products Spe cialty Conference, American Society of Civil Engineers, Denver, Colorado, April 8-10, 1991. Neville, A.M., Properties of Concrete, John Wiley and Sons, New York, 1975, p. 320. Houston, W.N., Mamlouck, M.S., Perera, R.W.S., "Laboratory versus Nondestructive Testing Pavement Design ", ASC E J our nal o f Transpo rta tio n Eng inee ring Vol. 118 No. 2, Mar/Apr 1992, New York, pp 207-222. AASHTO, "Guide for Design of Flexible Pavement Structures", 1986. Rada, G. and Witczak, M.W. "Comprehensive Evaluation of Laboratory Resilient Moduli Results for Granular Material", TRB, TRR 810, 1981. Terrel, R.L., Epps, J.A., Barenberg, E.J., Mitchell, J.K. and Barenberg, E.J., "Soil Stabilization in Pavement Structures: A User's Manual" Volumes I and II. US FHWAIP802, 1979. Yoder, E.J. and Witczak, M.W., "Principles of Pavement Design", John Wiley & Sons, 1975.
2-53
2.10
Hicks, R.G. and McHattie, R.L., "Use of Layered Theory in the Design and Evaluation of Pavement Systems", Alaska DOT Re po rt UFHWAADRD838, 1982.
2.11
Miller,
2.12
The Asphalt Insititute, "Research and Develop ment the Asphalt Institute's Thickness Design Manual (M S-1) Ninth Edition, Research Report No. 82-2, 1982
2.13
Thompson, M R., "A Propo sed Thickness Design Procedu re for High Strength Stabi lized Base (HSSB) Pavements", Transp ortation Engineering Series No. 48, Illinois Cooperative Highway and Transpo rtation Series No. 216, University o f Illinois, Champaign, Illinois, 1988.
J.S., Uzan, J. and Witczak, M.W., "Modification of the Asphalt Institute Bitu minous Mix Modulus Predictive Equation", TRB TRR 911, Washington D.C.
2-54
SECTION 3.0 FUNDAMENTALS OF MECHANISTIC-EMPIRICAL DESIGN 3.1 INTRODUCTION 3.1.1 Overview o f Histori cal Development a. b. c. d. e. f. gh. i. jk. 1. m.
1848 Kelvin - elastic hal f space 1885 Boussinesq - elastic half space (point load) 1926 W estergaard - two l ayers 1928 Love - elastic half space (circular load) 1943 Burmister - two layers 1948 Fox - solutions two layers 1949 Odemark - transformed section (equivalent thickness) 1951 Acum and Fo x - s olutions three layers Early 50's - finite element method 1961 Jones and Peattie - three layers 1963 Comm ercial progr ams >five layers 1970's - Wi despread u se of layered theo ry (main frame) 1980's - Mic roc ompu ters used a s tools
3.1.2 Reasons for Using Mechanistic-Empirical Procedures (rather than empirical) Mechanics is the science of motion and the action of forces on bodies. Whe n we refer to a mechanistic ap proach in engineering, we are talking about the applica tion of elementary physics to determine the reaction of struc tures to loading. The primary concern in pavements is how the structure distributes vehicle loads to the under lying soil layers. Weak pavements concen trate the load over a smalle r area o f the subgrade than strong pavements resulting in higher stresses as shown in Figu re 3.1. In fundamental order to quantify properties how theofload the is materials being distributed, must be known certain along with the thicknesses of the pavement layers and the load characteristics. These will be discussed lat er. An empirical approach is one which is based on the results o f experiments or experience. Generall y, it requires a number of observations to be made in order to ascertain the relationships between the variables and outcomes of trials. It is not nece ssary to firmly establish the scientific basis for the relationships as long as the limitations are recognized. In some cases, i t is much more expedient to rely on experience than to try to quantify the exact cause and effect of certain phenomena.
3-1
Strong Pavement
W e a k P av e m e n t
Load
Load
V ____________________I
_____________________ I
__________________
Surface Base
r r r TTTTr > _ Subgrade
Figure 3.1 - Load Distributi on Characteri stics of Strong ver sus We ak Pavement
Most of the pavement design procedures used in the past have been empirical in that their failure criteria were based on a set of given set of conditions, i.e., traffic, materials, layer configurations, and environment. The equation for the thickness of cover (total pavement structure) for asphal t pavements developed by Hveem and Carmany [3.1] for California highways is an example of empirical pavement design: T = K'(TI)(90 - R)/(c)° where
2
T = thickness o f cover, (ft.) K 1 = 0.095 (coeff icient depending on design wheel load and tire pressure with a factor of safety), TI = traffic index, R = resistance value, and c
= cohes iometer value.
Although the above equation encompasses parameters for the bound materials (c-value) and the underlying unbound materials (R-value) as well as the traffic volume (TI), it is based on a 22 kN (5000 lb.) wheel load with a tire pres sure of 480 k Pa (70 psi). This approach is s till used by CalTrans, but the equation has been adjusted to the cur rent form which no longer involves c, for instance. Yo der [3.2] noted that it is unlikely that this design proce dure could be successfully adapted to a region with severe frost problems or different r ainfall characteri stics. Another illustration of an empirical design procedure is the AASHTO process. The fundamental information for developing the design procedure came from the AASHO Road Test which was constructed and tested during the late 1950s and early 1960s. The most recent version of this flexible pavement design process is illustrated in Fi gure 3.2. This figure shows the basic design nomograph which was developed from the following empirically de rived performance equation: [3.16]
3-3
(Eq. 3.1)
logi o W is = (Z r ) (S o ) + (9.36)(log (SN + 1)) - 0.20
°® 10
0.40 +
f APSI 4 2 - 15
J - +(2 .32) (l ogi 0 MR) - 8.07
1094
(SN + 1) 5.19
wher e W is = 18,000 lb. (80 kN) equivalent single axle loads predicted to pt, Zr
= Z-stati sti c associated wit h the selected level o f design r eliabilit y,
So
=
SN
= Structural Num ber (essentially a "Thickness Index"),
overall standard deviation o f norma l dis tribution of errors associated with traffic prediction and pavement performance,
APSI = overall serviceability loss = po - Pt, p0
= initial serviceability index following con struction,
Pt
= terminal serviceability index, and
Mr
= resilient modulus o f the roadbed soil(s ). (psi)
The various constants in the above equation were ob tained from regress ion anal ysis o f the A ASHO R oad Test data — hence this too is an empirical design procedure as opposed to a mechanistic-empirical approach.
3-4
(Eq. 3.2)
I
SM Fig ure 3 .2 .
Elustr ation of AASHTO Design Nomogr aph for Flexible P avements
3-5
A mechanistic-empirical approach to pavement design in corp orate s elements o f both approaches. The mechanist ic com ponent is the determination o f pavement structural responses such as stresses, strains, and deflections within the pavement layers through the use of mathematical models. The empirical portion relates these responses to the performance of the pavement str ucture. Fo r instance, it is possible to calculate the deflection at the surface of the pavement using so me of the tools dis cussed la ter. If these deflections are related to the life of the pavement, then an empirical relationship has been established between the mechanistic response of the pavement and its expected performance. There are currently no pure mechanistic approaches to pavement design. The basic advantages of a mechanistic-empirical pavement design procedure are: (a)
The ability to accommodate changi ng load types and quantify their impact on pavement performance.
(b)
The ability to utilize available materials in a more ef ficient manner.
(c)
The ability to accomm odate new materials.
(d)
Mo re reliable performance predictions.
(e)
A better evalua tion of the rol e of constructi on.
(f)
Use of material properties in the design process which relate better to actual pavement behavior and performance.
(g)
An improved defi nition of existing pavement l ayer properties.
(h)
The ability to accommodate env ironmental and aging effects on materials.
Currently, the primary means of mathematically modeling a pavement is through the use of layered elastic analysis. Although more complicated techniques are available (e.g., dynamic, visco-elastic models), we will restrict the dis cussion to basic linear elastic models subjected to static loading. Layered elastic analysis computer programs can 3-6
easily be run on personal computers and do not require data which may not be realist ically obtained. Finite el e ment approaches are likely to become more common as comp uting pow er increases. These approa ches can be used for both fle xible and rigid pavement s. Several other methods specific to rigid pavement analysis will be described in a separate section.
3.2 LAYERED ELASTIC SYSTEMS 3.2.1 Assum ptions and Input Requiremen ts The modulus of elasticity and Poisson's ratio of each layer define the material properties required for computing the stresses, strains, and deflections in a pavement structure using layered elastic or finite element models. Typical values for the moduli and Poisson's ratios of pavement materials were given in Sections 2.5 and 2.8 of these notes. In addition to the material properties of the layers, the thickness of each pavement layer must also be described. For computation purposes, the layers are assumed to ex tend infinitely in the horizontal direction, and the bottom layer (usually the subgrade) is assumed to extend infinitely down ward. Given the typical geom etry of pavements, these assumptions are considered to be fairly representa tive of actual conditions, except when analyzing jointed PCC pavements in the vicinity of the joints or edges, as well as edge loadings on asphalt pavements. It is assumed that material behavior is perfectly linearly elastic, hom ogen eous and isotropic. Hom ogen ous refers to pavement layers which are composed of the same ma terials throug hou t. Isotrop ic means that the material will possess the same properties along all axes (as opposed to wood which possesses differing material properties with respect to the direction of the grain). If non-linear or stress-sensitive behavior is modeled, iterative procedures are usual ly involved. As will be pointed out in Section 3.2. 3, most pavement materials do not exhibit these ideal ized characteristics. This can result in problems during the evaluation of deflection basins leading to unrealistic values o f moduli. 3-7
The loading conditions must be specified in terms of the magnitude of the load, the geometry of the load, and the number of loads to be applied to the str ucture. The magnitude of the load is simply the total force (P) applied to the pavement surfa ce. In pavement a nalysis, the load geometry is usually specified as being a circle of a given radius (r or a), or the radius computed knowing the con tact pressure o f the load (p) and the magnit ude o f the load (P). Althoug h most actual loads more closely represent an ellipse, the effect of the differences in geometry be come negligible at a very shallow depth in the pavement. Effects of multiple loads on a pavement surface can be approxim ated by summing the effects of individual loads. This is referred to as the Law of Superposition and is considered valid as long as the materials are not stressed beyond their elastic ranges (subject to plastic or perma nent deformation). To summarize, the following information must be avail able to compute the response of a pavement to loading: (a)
Material prop erties of each layer. (i) (ii)
Mod ulus of elasticity (E). Poiss on's ratio (fa).
(b)
Thickness o f each pavement layer.
(c)
Loadin g conditions. (i) Magn itude of load. (ii) Geom etry o f load. (iii) Num ber of loads.
Fig ure 3.3 shows how these inputs relate to a layered
elastic model of a pavement system. The outcome of a layered elastic analysis is the computa tion of stresses, strains, and deflections in the pavement.
3-8
Total Load Surface Base
Radius rora
♦
--------►
^1 > m
,
!
i
k
^2 » ^2
h2 \
Subgrade
E 3
, (J-3
Figure 3.3 - Layered Elastic Pavement Model
hi
r
ra
1
As will be mentioned in Section 3.2.5, the use of a layered elastic analysis computer program will allow one to calcu late the theoretical stresses, strains, and deflections any where in a pavemen t structure. How ever, there are only a few locations in which we are generally interested for the calculation of critical responses. These are .
Location
Response
Pavement Surface
Deflection
Bottom of AC or ATB
Horizontal Tensile Strain
Bottom o f PCC or CTB
Horizontal Tensile Stress
Top of PCC Slab (corner)
Horizontal Tensile Stress
Top o f Intermediat e Layer (Base or Subbase)
Vertical Compressive Strain
Top of Subgrade
Vertical Compressive Strain
The locations of these responses relative to a pavement structure and load are illustrated in Figure 3.4. The hori zontal tensile strain at the bottom of the asphalt concrete layer is considered indicative of potential cracking of the surfacing (fat igue failure). Fatigue o f PCC is related to tensile stress. Rutting failure in the subgrade can be pre dicted using the vertical compressive strain at the top of the subgrade. Deflections und er load at the pavement sur face are used in imposing load restrictions during spring thaw and overlay design (for example). In the next three sections, we will discuss the evolution of layered elastic analysis and try to get a qualitative under standi ng o f the proce ss. 3.2.2 One-layer system With Point Loading (Boussi nesq) The srcin of layered elastic theory is credited to VJ. Boussinesq [3.3] who published his classical work in 1885. He develope d solutions for computing stresses and deflections in a halfspace (soil) composed of homogene ous, isotropic, and l inearly elastic material. Boussinesq influence charts are still widely used in soil mechanics and found ation design. The governing diff erential equations for a point load on an elastic half space were postulated earlier by Kelvin. Boussine sq developed the closed form mathematical solution in 1885 for point load, while Love extended this work to a circular load in 1928.
3-10
1 . Pavement surface deflection 2. Horizontal tensile strain at bottom of bituminous layer 3. Vertical compressive strain at top of base 4 . Vertical compressive strain at lop of subgrade
Figure
3 .4
3-11
Pavement Response Locations Used in Evaluati ng Load Effects
In this approach, the stresses and deflections are calcu lated for a point load applied to the surface of a deep soil mass. Distance variables are expressed in terms of cylin drical coordinates, in which the distance from a point on the surface may be expressed as: R 2 = r 2 + z 2 = x2 + y2 + z 2
(Eq. 3.3)
as shown in Figur e 3.5. The vertical stress, o z, radial stres s, c r, and the verti cal deformation, u, can be calculated using the following for mulae for a point load: Vertical stress: -3Pz 2;zR 5
c?z
(Eq. 3.4)
Radial stress: „
_P(1+A0
Gr,z ~
2 jS J
-3r2z (l- 2 |i)R R 3 + R+z
(Eq. 3.5)
Vertical deformation below the surface: _
uz,r =
P0+/4 2 tE
gÜ - n) R
z2' R3
(Eq. 3.6)
Surface deflection at a distance, r, away from the load (i.e., Eq . 3.6 with z = 0 and R = r):
Uf
_
(Eq. 3.7)
o_V )p (*)(E)(r)
For all practical purposes, the equations for a point load can be used for a distributed load at points more than about two radii from the load. [~3.18] The deflection beneath the center of a rigid, circular load of radius, a, can be estimated by the equation:
0
_ (1 - U2)P (2)(E)(a)
(Eq. 3.8)
3-12
Figure 3.5 Cylindrical Coordinates in Onc-Laycr System
3-13
Example 1; A load of 40 kN (9,000 lb.) is placed on a 300 mm. (11.8 in.) diam eter plate. The plate is resting on a subgrade which has an elastic modulus of 51.7 MPa (7,500 psi) and a Poisson's ratio of 0.4. What is the deflecti on at the center o f the plate? P[i a E
== = =
0.40 N 40,000 150 mm 51.7 MPa
_ (1 - (0. 4) 2)40000 _ — ---------------------------z.l / mm (.Uo5 in.) 7 2(51.7)(150) V
uo Example 2:
Given the loading conditions above, what is the modulus of elasticity of the subgrade if the deflection at the center o f the plate is 0.72 mm (0.028 in)?
E (°2 )(u f 0e)(a)^ ( 1 ~2(0.72)(150) ( 0 4 ° )2) 40000 “ »» M P a (22,500 psi) Conclusions: As you can see from exampl es 1 and 2, pavement model ling is a simple process for one-layered pavement systems. Note from the examples that modulus and deflections are inversely, linearly related so that if the modulus increases by a factor of three the deflections will decrease by a fac tor of th ree. The Boussinesq equations were modified through mathe matical integration to approximate the effects of a circular distributed l oad on the pavement sur face. The equations for stress, strain, and displacement below and along the centerline of a circular load are as follows: Vertical Stress at depth z:
Oz — Go
1
XJT
--------------
[\ + {a! z f j
3-14
(Eq. 3.9)
Radial and Tangential Stress at depth z:
Or
— O? — O o
1
+ 2 /i
1
1+
a/
1+
(
( 1
V
/\2 M i
+K)
(Eq. 3.10)
J)
Vertical Strain at Depth z:
£z
—
(i+//)
Ob
(Eq. 3.11)
1+
(% )
2^2
Deflection at depth z: /
\
Where: CTo = stress on surface (M Pa), E = elastic modulus (MPa) a = plate radius (mm) z = dep th below pavement surface (mm) = Poisson 's ratio 3-15
3.2.3 Odemark's Method [3 .18] In 1949 Odemark developed an approximate solution to the calculation of stresses, strains and displacements in a layered syst em. Since then a number o f exact solutions to the same problem have been devised ( ELSYM 5, BISAR, ALIZ E III, CIRCLY, etc.). So why use time on an approximate solution? First, it should be recalled that the "exact" solutions are only close to "exact" in a mathematical sense related to the numerical integration procedures. The assumptions made with respect to equilibrium, compatibility and con stitutive equations (Hook's law) are not correct for pave ment structures. Load s are dynamic, materials are not continuous, some are even particulate (granular) and deformations are not only elastic, but also plastic, viscous and visco-elastic, and they are mostly non-linear and ani sotrop ic. In a physical sense, therefore, all solution s are approximate. There are two advantages to using Odemark's method: (a)
It is simple and very fast, it may be included in a spread sheet or used in a Pavement Management System, where millions of computations must be performed.
(b)
a non-linear elastic subgrade (or a subgrade where the modulus, or apparent modulus, varies with the distance from the load) may e asily be included. This may be extremely important for the interpretation of deflection data.
Odemark's method is based on the assumption that the response below a given layer, will depend on the stiffness o f that layer onl y. The stiffness of a l ayer is: E *I (1
where:
-
E is the modulus, I is the moment of interia, and is Poisson's ratio 3-16
(Eq . 3.13)
This assumption is used to change a layered system into a semi-infinite halfspace, for which Boussinesq's equations may be used. Consider a two-layer system as shown below: hi> ^1, |ij E 2> ^2
A layer with thickness hj, modulus E^ and Poisson's ratio Hi, rests on a material with modulus E 2 and Poisson's ratio (j-2 The stiffness of the upper layer is: I * Ei i-
where:
X2 *b * h,3*Ei
(Eq. 3.14)
m 2=
b is the width und er consideration
If the system is transformed to the following: he, E2, [x2
e 2 >^ 2 The stiffness will be:
I *E , Xa'b’ he’E;?
________________e
(Eq. 3.15)
i- n 22" For the new stiffness to be identical to the srcinal stiff ness: h„e = h. * 3
Hi ^ 1~ H22 E2 1 - H i 2
The new system is a semi-infinite halfspace where Boussi nesq's equation can be used. With a multi layer system the method is used successively. First layer one is changed to the elastic parameters of 3-17
(Eq. 3.16)
layer two and the equivalent thickness, hej, is calculated. Any materials below layer two are assumed to have the same elastic parameters as layer two. Then layer one and two are changed to the elastic parameter of layer three, etc. It has been found that the best agreement with the "exact" solutions normally is obtained when Poisson's ratio is assumed to be the same for all layers. The equation for the equivalent thickness may then be written as: n- 1
(Eq. 3.17) To get a better agreement with the exact solutions, the equivalent thickness is normally multiplied by a factor, f. For the fir st structural interface (e.g., between surfac ing and base) f is 0.9 for a two-layer system and 1.0 for a multi layer system. For all othe r interfaces f is 0.8. Example 1 A 300 mm (11.8 inch) diameter plate is loaded to 40 kN (9,000 lbs.) on an asphalt concrete pavement over a sub grade . The asphalt con crete is 15 cm ( 6 inches) thick and has a modulus of elasticity of 3450 MPa (500,000 psi); the subgrade modulus i s 69 MP a (10,000 psi ). What is the deflection at the center of the loaded area ? Wha t is the vertical stress at the top o f the subgrade? Use Poisson's ratio = 0.35. Hint: The total deflection of the pavement surface is the sum o f the sub grad e def lecti on an d the com pres sion o f the asp hal t layer. First, calculate the deflections at the surface and at a depth of 150 mm for an asphaltic half space. Com pute the compression of the asphalt layer by subtracting the deflection at the bottom of the layer from the deflection a t the surface. Convert the asphalt layer to an equivalent subgrade thickness using Odemark's method and calculate the subgrade deflect ion at this depth. The sum of the asphalt compression and the deflection of the subgrade at this point can then be summed to obtain the overall deflection. The stress at the top o f the subgrade can also be calculated at a depth equal to the equivalent asphalt thickness. 3-18
1)
Calculate the plate pressure, then the deflection at the surface o f the asphal t half-space using Equation 3.12 (No te that sinc e z=0, most terms drop out:
40,000 N ... .. .. .. load
_ 2(1-.352)(.56)(150) 3450 E ~ <¿.=.043 mm (.002 in.) (ELSYM5 gives .0017”) Note:
The above equation is an algebraic simplification o f Equ atio n 3.1 2 f o r the case where z = 0 (give it a try!).
2)
a
Calcu late deflection at 150 mm (Eq. 3.12): (1+.35)(.56)(150) 3450
(i -2( . 35)Ou(l
iso = -
d 150 =.
% < ,)• -'% 150
027 mm (.001 in.)
(ELSYM5 gives .0011”) 3)
Asphalt compression = do-dz = 0.043 mm 0.027 mm = 0.016 mm (.0006 in.)
4)
Calculate equivalent thickness of asphalt
h e = f *h
, *3
S T = .9 (1 5 0 ) ^ p
VEh 5)
Calculate deflection at he (l+.35)(.56)(150) 69
dh. = ■
d h .
0.547 mm (.022 in.)
(ELSYM5 gives .0218”) 3-19
= 497 mm (19.57 in.)
6)
Total Deflection = 0.016 mm + 0.547 mm = 0.563 mm (.022 in.)>/ (ELSYM5 nan as a 2-layer system give .0231”)
7)
Stress at top o f subgr ade:
—
-----------------
/
- \
(l + (l50 /497) ]
3/ 2
= 069 MPa = 69 KPa ( 10 p s i ) /
It can be seen that these equations are quite cumbersome to utilize on a calculator, but on a computer they execute quite fast and give reasonable results, as can be seen when the prob lem is repeated in the following section. 3.2.4
Tw o-layer system (Burmister) Burmister [3.4] extended the one-layer solutions to two and three layers. We will restric t the discussion in this section to subgrade. two layers, Inanalogous full-depth asphalt layer over his work,toBua rmister assumed that the layers have full frictional contact (no slip) at the inter face, and that there are no shear or normal forces on the surface outside of the loaded a rea. He also assumed that Poisson's ratio for each of the two layers is 0.5 in order to simplify the mathematics. The exact equations are rather long and complicated even with this simplification, but the important parameters in the solution are listed below: p — load distributed over a circular plate (contact pressure) a
— radius of the flexible plate
h — thickness of the surface layer E 1 — modulus of elasticity for the surface layer E 2 — modulus o f elasticity for the subgrade In the equations, the geometry of the load and surface layer are specified by the ratio a/h, and the moduli of the layers by E 2 /Ej. Graphs based on these ratios were de veloped to aid in determining the surface deflections and stresses in pavements. Figure 3.6 is a graph which can be used to find the displacement coefficient Iaz, for 3-20
calculating the deflection on the surface at the center of the loaded area using the following equation:
(Eq. 3.18) Fig ure 3. 7 can be used to find the ratio of the vertical
stress in the pavement structure to the applied stress. Please note that Figu re 3. 7 is only valid when the radius of the load is equal to the surface thickness. Other graphs would be needed for different values of a/h. Example 1 (again): A 300 mm (11.8 inch) diameter plate is loaded to 40 kN (9,000 lbs.) on an asphalt concrete pavement over a sub grade . The asphalt con cret e is 15 cm ( 6 inches) thick and has a modulus of elasticity of 3450 MPa (500,000 psi); the subgrade modulus i s 69 MP a (10,000 ps i). What is the deflection at the center o f the loaded area? What is the vertical stress at the top of the subgrade? E 2 _ 69 M P a E I " 3450 MP a
__
1_
50
Area o f Plate = na2 = 0.0 707 m2 (1 1 0 in.2) a h
150 150
p = P/A =
40 kN = 566 kPa (82 psi) .0707 m
------------
3-21
1.0
3 2 2
Ratio of the Radius of fhe Flexible Bearing Area to the Thickness of the Surface Layer (a/h)
Figure 3
.6
Graph fo r Determining Displacement Coeffecient for Two-Layer Syst em
)
)
.
)
/a ,z s r te e m a r a P fo se lu a V
Vertical Stress Influence Coefficient «
Figure
3 .7 Vertical Stress a s a Fun ctio n o f Depth in a Two-Layered System, for a = h
)
Deflec tion at cen ter of load: From Figure 3.6:
Ia z = 0. 29
Az = 1.5 (566)(15°) (0.29) = 0.54 mm (.02 in.) 6 9 ,0 0 0 V 7 V
'
Vertic al stres s at top o f su bgra de: From Fig ure 3 . 7: o z/p = 0.12 g z
= 0.12 (566) = 68 kPa
(9. 9 psi)
Cl ass Exer cise Use the inf orma tio n in Example
1 to calc ulate ce nter
deflection and subgrade stress for a 450 mm (18 in.) plate with an 80 kN (18,000 lb.) load on a 225 mm (9 in.) AC layer. Deflection = .769 mm (.030") Stress 3.2.5
= .062 MP a (8.9 psi)
Multi-l ayer system The m ajo rity o f pavement str uctures are m ore co m pli cated than the tw o-layer system disc ussed a bove. Usua lly a base layer with or without an underlying subbase layer are placed between the asphalt concrete and subgrade. These layers may be either unbound or stabilized granular materials which have distinctly different properties from the sur face and subgrade l aye rs. One can imag ine that the solutions for systems with three or more layers become increasingl y m ore comp lex. For a three-layer pavement, several charts and tables have been developed by Peattie, Jones and Fox [3.5] to deter mine th e str esses, strains, and deflec tions. Pea tt ie [3.6] developed graphical solutions for vertical stress in threelaye r sy stems. J ones [ 3.7] presented so lutions f or hori zont al stresses i n a tabular f orm . Both o f th ese so lutions wer e based u pon a P oisson's rat io o f 0.5 for all lay ers.
3.2.6
Elastic Layer Comput er Pr ogram s The logic al exten sio n o f th ese so lutions was t he develop ment o f compu ter prog ram s in order t o expedite analy sis and allow greater flexibility in accommodating material propert ies and multipl e loads. Even the most el ementar y o f th ese program s a llo w fo r material s with Poisson's r atios
3-24
other than 0.5. Some are capa ble o f ascertaining the eff ects o f multiple wheel confi gur at ions an d/o r n onlinear material behavior. Dur ing the 1980 s, as th ese mainframe computer programs were converted to run on microcom puters, a greater potential was developed to use elastic analysis tools in pavement design and rehabilitation deci sio n making. A list o f laye red elastic com pu ter p rogram s is given in Table 3.1. Examples o f these programs inc lude B IS A R , E L S Y M 5, and WESLEA. BISAR, developed by Shell Oil Co. in the early 1970's is generally considered the benchmark to which all other layered elastic modelling programs are comp ar ed. Its com plex mathematic al models yield the m ost rigorou s ana lysis of stresse s and strains w ithin the pavement structure. B IS A R has two important features: 1) It can solve for the infl uence o f both normal and t an gential loading on the pavement surface, and 2) it allows the user t o sp eci fy the degree o f fric tion between the pavement layers. B IS A R is a proprietary program avail able from Shell Oil Co.
E L S Y M 5 is similar to B IS A R , except it cannot model vari able friction at between the pavement layers. E L Seley Y Mf5rom wa s developed the University o f Calif ornia at Berk code developed by Chevron Research. E L S Y M 5 wa s recently modif ied by the FH WA t o incl ude a user fri endly interfac e. Modific at ions were also made to the prog ra m by Dr. Lynn e Irwin o f Cornell Univ ersity to corr ect p rob lems in the mathematical integration routines which pro duced irregular answers under certain conditions. E L S Y M 5 is avai labl e from the F H WA.
WESLEA, develo ped by the U.S. Army Corp s o f En gi neers, Vicksburg Mississippi, represents the latest attempt at improving the state-of-the-art pavement modelling pro grams. WESLEA executes much faster than similar pro grams allowing it to be used more efficiently on micro compu ters . WE SL E A is avail able from the U.S. Army Corps o f Engine ers. This is not an exhaustive li st o f layered elastic c ompu ter programs currently in existence, they are simply a list of the most widely used. Typical input required for using these computer programs include: (a)
Material propert ies o f each layer. (i) (ii)
Modu lus o f elastic ity . P oisson's rat io.
3-25
Table 3.1 - Layered Elastic Computer Programs Number Programs
of
Number
Continuity
of Loads
Conditions at
Probabilistic
Interface
Considerations
Layers
Program Source
Remarks
(max) Full W E SL E A
10
10
Continuity to
No
Frictionless 3 2 6
B 1SAR
10
10
Full Continuity to
U. S. Army CE
•
Short run ning times
Waterways
•
Considers ho rizontal a s well as vertical
• •
Comparat ively long runn ing times (on 286 comput ers) Considers ho rizontal as well as vertical loads
•
Nonlinear respo
Experiment No
Frictionless
Shell International Petroleum Co., Ltd London, England
Full
Chevron
CHEV
5
2
Continuity
No
ELSYM5
5
10
Full Continuity to
No
Frictionless
Researc h
Company
5
2
(PSAD)
Fu ll
•
Short run ning time for particular
California,
•
Lates t version dated 199 3 - integration
Berkeley Yes
Continuity
nse of granular materials
point. proce dures enhanced
bv Cornell University •
Runn ing time is long for degrees of reliabili ty other than
•
Interative
Cooperative Highway Researc h
acc ounted fo r in
DAM A program o f the Asphalt Institute which makes use of the CHE V prog ram.
University of
National PDMAP
loads.
Statio n
50% (deterministic mode)
Program (Project 1-
process used to arrive at moduli for untreated
granular materials.
10B) Full VE S YS
5
2
Con t in u it y
Ye s
FHWA-US DOT
•
Runn ing time is long in probabilistic
•
Program considers materials time dependent
Full CHEVIT
5
12
Con t in u it y
Ye s
5+
10 +
Full
No
•
Modif ication of CHE V prog ram.
Waterways
•
Includes provision f or stre ss sensitivi ty of granular lay ers.
•
Permits considera tion of horizo nta l and v ertical loads; in
Canterbury,
Continuity to
Australia (For
Frictionless
Australia Research Board
)
and
visco elastic).
U.S. Army C.E.
Experiment Station MINCAB Systems CIR CLY
(el astic and
mode.
both as time independent
)
particular permits considerat
ion of radially directed
horzontal forces. •
Can consider orthotr opic material behavior.
•
Permits considera tion of strain energy.
)
(b)
Thickness
(c)
Load ing c onditions ( 2 o f 3 listed below). (i) (ii) (iii)
o f each pavement layer.
Magnitu de o f load. Radiu s o f load. Cont a ct pressur e.
(d)
Nu mber o f loads.
(e)
Locat ion of load(s) on the sur fac e (x,y coordina tes).
(f)
Locat ion o f analys is poi nt s for output (x, y,z coordinates).
F or the pu rp oses o f illustratio n, th ree typic al pavement cross-sections have been selected as shown in Figure 3.8. The initial conditions we will examine are: (a)
Material propert ies o f each lay er. Elastic Mo du lus Layer
Poisson's
MP a
psi
Ratio
3450
500,00 0
0.35
Crushed Stone Base
172
25,0 00
0.40
Fine-grained Subgrade
52
7,500
0.45
Asphalt Concret
b)
e
Layer Thic knesses AC Th ick n ess
Ba se Th ick n ess
Section
mm
in
mm
in
A
50
2
150
6
B
125
5
200
8
C
230
9
150
6
3-27
2’ (50 mm) ACP
6’ (150 mm) Base
Fine-grained subgrade
Seciion A (Thin Thickness Section)
5’ (125 mm) ACP
8* (200 mm) Base
Fine-grained subgrade
Section B (Me dium Thickness Seciion)
9* (230 mm) ACP
6" (150 mm) Base
Fine-grained subgrade Se db n C (T hick Sed ion)
Fig ure 3.8 Ty pica l" Pave ment Sectio ns
3-28
(c)
Loadin g Conditions Magnitu de o f Tire Load = 40 lcN (9,000 lbs. ) Tire Press ure = 552 kPa (80 psi )
(d)
Number of Loads = 1
(e)
Loc at io n of Lo ad: x = 0 y = 0
(f)
Locat ion o f Analysi s Points ( all at x=0, y=0) (i)
Sur face De flection (all at z=0 )
(ii )
H orizo nt al Tensile Strain at Bot tom o f ACP Thin Pa vement:
(iii)
z = 50 mm (2 in)
Mediu m Pa vement:
z = 12 5 mm (5 in)
Thick Pavement:
z = 230 mm (9 in)
Vertic al Co mp ress ive Strai n at Top o f Subgrade Thi n Pavement: Medium Pavement:
z = 200 mm (8 in) z = 330 mm (13 in)
Th ick Pa vement:
z = 380 mm (15 in)
A layered elastic analysis was performed using the inputs as defined above, and the results are listed in Table 3.2 under the
heading
"Standard Pavement"
.
As would be
expected, the surface deflection, the horizontal strain at th e bott om o f the AC, and the v ertical c ompr essive strain at the top o f the su bgrade all pavement thickness.
decrease with increasing
A compa rison of deflec tion basins
for the th ree standar d sections is g iven in
Figure 3.9.
In order to demonstra te the sensitiv ity of the analy sis to load and material changes, several other cases were run and compared to the Standard Pavement with the results shown i n Ta ble 3.2 . These i ncl uded: ♦
L ow Ti re Load: Tire load dec reased fro m 40 lcN(9,000 lb.) at 552 kPa (80 psi) to 4 kN (900 lb.) at 207 kP a (30 psi) . This i s a c ompa rison o f the eff ects o f a tru ck load versus a passenger vehic le.
♦
High Ti re Pressure: Increase fro m 552 kPa (80 psi) to 965 kPa (140 psi). This demonstra tes the dif feren ce in pavement response from a standard truck tire pres sure to on e which is an ex trem e.
3-29
Table 3.2 - Sensitivit y Analysis o f Va rious Input Parameters
Pavement Response Parameter Surface Deflecti on Top of AC Section A - Thin
Section B - Med.
Section C - Thick
Standard Pavement
1.219 mm (0.048")
0.686 mm (0.027”)
0.457 mm (0.018”)
Low Tire Load
0.152 mm (0.006”)
0.076 mm (0. 003" )
0.051 mm (0. 002")
High Tire Pressure
1.321 mm (0.052”) 0.711 mm (0.02 8”)
0. 483 mm (0 .019 ”)
Stabilized Subgrade
0.914 mm (0.036”)
0.584 mm (0 .023")
0. 406 mm ( 0.01 6”)
Asphalt Treated Base
0.533 mm (0.021”)
0.356 mm (0.014”)
0.305 mm (0.012”)
1.346 mm (0.053”) 0.838 mm (0.033”)
0.610 mm (0.024”)
Moisture Sensitive
Pavement Response Parameter Horizontal Tensile Strain - Bottom of AC or ATB (x 10"®) Section A - Thin
Section B - Med.
Section C - Thick
Standard Pavement
467
279
145
Low Tire Load
121
44
18
High Tire Pressure
735
352
163
Stabilized Subgrade
368
246
128
Asphalt Treated Base
196
88
71
Moisture Sensitive
482
433
257
3-30
Ta ble 3. 2 (c on t'd ) - Sensiti vi ty A nalysi s of Various Inp Strain
Calculated 2.5mm
ut P ara meter s (Subgr ad e
(0.1") Bel ow interfac
e)
Pavement Response Parameter Vertical Com pressive Strain - Top of Subgrade (x Section A - Thin
Section B - Med.
Section C - Thick
Standard Pavement
-2,220
-747
-370
Low Tire Load
-280
-81
-40
High Tire Pressure
-2,520
-786
-384
Stabilized Subgrade
-957
-437
-253
Asphalt Treated Base
-512
-229
-177
-2,580
-1,030
-608
Moisture Sensitive
10-*)
Location of FWD Sensors
D0 (0mm or 0 ft.)
D,
d
(305mm or 1 ft.)
2
(610mm or 2 ft.)
d
3
(914mm or 3 ft.) 0.00
0
FWD Deflec0.01 tion (in.)
FWD Deflec tion 250 (nm)
500-
—
MEDIUIV
0.02
— 0.03
750THIN
0.05 Figure 3.9
3-31
♦
Stabiliz ed Subgra de: In crea se subgrade modulus from 52 MPa (7,500 psi) to 345 MPa (50,000 psi) i n the t op 150 mm (6 in) o f soil. This c as e sh ows the ef fect o f subgrade impro vement.
♦
Asphalt Treated Base: Increase base cour se modulus fro m 172 MPa (25,000 psi) to 3450 MP a (500,000 psi). This represen ts an increase i n the structura l capaci ty o f the paveme nt.
♦
Moi stu re S ensi tiv e: Decrease AC modulus fro m 3450 MP a (500,000 psi) to 138 0 MPa (200,00 0 psi ). This illustrates a we ak ening o f the AC laye r du e to strip ping in the mixture.
Comparisons between the "Standard Pavement" case and the m odif ied input just described are gi ven in Ta ble 3.3. As would be expected, there is a dramatic decrease (on the order o f 75 to 90 percent ) in all of the pavement r e sponse parameters when a passenger vehicle loading is compa red to that of a truck lo ad. These dec reases be come even more meaningful when they are discussed in th e cont ext o f pavement life later on in these notes
.
The increase in tire contact pressure from 552 to 965 kPa (80 to 140 psi) results primarily in an increase in the ten sile strain in the asphalt con cret e. This par amet er increased 11 percent for the thick pavement and 57 per cent in th e thin pave ment. It i s interesting to n ote that very little change in the surface deflection or compressive strain in the subgrade resulted from the higher tire pres sure. In general, the su rface laye r o f the pa vement is sen sitive to changes in tire pressure, particularly "thin" sur face courses. The lower layers are most sensitive to changes in load. The in corp orat ion o f a stabili zed subgrade
lay er a ffected
the vertical compressive strain in that layer most effec tively, although significant improvement in the surface deflection and tensile strain in the asphalt surface can be noted for the thin pavement. The u se o f an asphal t treat ed base greatly inf luenced the resp onse par ameters in al l three pavement sec tions.
3-32
Table 3.3 - Comparisons of Changes in Pavement Responses from Standard Pavement
Low Tire Load »P erc en t Chang e f ro m stan dar d P avem ent« Section
Surface Deflection
Tensile Strain in AC
Compr. Strain in Subgrade
A
-88
-74
■ 87
B
-89
-84
-89
C
-89
-88
-89
High Tire Pressure »P erc en t Cha nge f ro m st an da rd Pav em ent« Section
Surface Deflection
Tensile Strain in AC
Compr. Strain in Subgrade
A
+8
+57
+14
B
+4
+26
+5
C
+6
+12
+4
Stabilized Subgrade »P erc en t Chan ge f ro m sta nda rd Pav em ent« Section
Surface De flection
Tensile Strain i n AC
Compr. Strain in Subgrade
A
-25
-21
-57
B
-15
-12
-41
C
-11
-12
-32
3-33
Table 3.3 - Comparisons o f Change s in Pavement Responses fro m Standard Pavement
Asphalt Treated Base »P erc en t Chan ge f ro m stan dar d P avem ent« Section
Surface Deflection
Tensile Strain in AC
Compr. Strain in Subgrade
A
-56
-58
-77
B
-48
-68
-69
C
-33
-51
-52
Moisture Sensitive »P erc en t Cha nge f ro m st and ar d P avem ent« Section
Surface Deflection
Tensile Strain in AC
Compr. Strain in Subgrade
A
+10
+3
+16
B
+22
+55
+38
C
+33
+77
+64
The thick pavement, Section C, demonstrated the greatest increase i n pavement resp onses to the presen ce of a moistur e susc eptible asphal t mi xture. Section A was the least affec ted o f the three .
Furt her i llustrat ion of the
eff ects o f a weak er s ur fac e layer i s present ed for all thr ee sections in the FWD basins shown in
3-34
Figure 3. JO.
Location ol FWD Sensors
). n i(
) m it (
n o ti c e fl e D
n o ti c fle e D
D W F
D W F
). in (
) m ^ (
n o tie c lf e D
n
D W F
D W F
.) n (i
) m ji(
n o ti c e fl e D
n io t c le f e D
D W F
D W F
tio c e fl e D
F igu re 3 „'10 Diff er en ces i n Defl ectio n Basins fo r the "Sta nda rd" vs. "Moisru re Sen sitive" Pa vement Sec tio ns
3-35
3. 3 3.3.1
ANALYSIS O F RIGID P AV EME NTS Introduction Several theories have been developed over the past years to a na lyze ri gid pavements.
These can be divided into f
our
major groups: a.
Contin uously Sup ported Slab Mode ls
b.
Elast ic Layer Mode ls
c.
Finite Element Mode ls
d.
Coupled Models
A desc riptio n o f eac h of these m ode ls fol lows. 3.3.2
Cont inuously Supported Sl ab Models Equa tio ns for analy sis o f concret e slabs on gra de wer e first published by Westergaard in Denmark in 1923. Westergaard developed closed-form solutions to compute critical stresses and deflections under a single load for three loading cases. These loading cases were: (a) interior load (b)
edge l oad and
(c) corn er load.
Westergaa rd
defined interior loading as the case when the load is at a considerable distance from the edge, while edge loading was described as the case when t
he lo ad is a t the edge,
but
at a co nsider able distan ce from the co rner . Westergaar d develo ped these equatio ns by considering the concrete slab as a medium-thick plate supported by the subgrade. The plate was assumed to be
o f constant thick
ness and to be infinite in both horizontal directions. The subgra de was r epresent ed by a se t o f un iformly dis tributed springs, which is referred to as the Winkler foundation. The
stif fness o f these springs was referred to
as the
modulu s o f subgra de reaction ( k). In this model, the su b grade cannot transfer shear stresses. Therefore, the slab is discontinuous at the edges as the soil beyond the edge does not pr ovi de any support.
The slab was also assumed
to be fully supported with no discontinuities in the slab. The disadvan ta ges of this model are: (a)
Slabs which have cracks cannot be ana lyzed
3-36
(b)
Loa d tra nsfe r betw een slab s cann ot be cons idered
(c)
E ffect of voi ds or p arti al subg rade suppo rt cannot be considered
(d)
The assumptio n that the subg rade or s ubbase beyo nd the edge does not provide support is incorrect.
In spite of th ese l imi tat ions, Westerga ar d's equat ions are still widely used. Westergaard's srcinal equations have been modified many times by different authors partly to bring them to better agreement with elastic theory and to get a closer fit to the experimental data [3.181. Ioannides et al [3. 221 carried out a detailed analy sis of Wester gaard's solutions to determine their form, theoretical background, limitations, and applicability. They studied Westergaard's srcinal equations as well as his "new for mulas" from 1948 and compared the results to the ILLISLAB finite element program. Based on this comparison they developed new expressions for corn er l oading. They also developed slab size requirements for using Wester gaard's equations. The Westergaard's equations for inte rior loading and edge loading, as well as the new solution for come r loading which were al are given in Table 3.4. Table
3-4 Westergaard's
develo ped by Ioannides et Equat ions
Interior Loading
Maximum Bending Stress
{ 3P(1+ji)/27ih2} {ln(2Ub) + 0.5 -y} + [3P(1+n)]/64h2] (bit)2
Interior Loading
Maximum Deflection
(P/8k/2) {1+(1/2 t0 [tn(al2l) +y -5/4]
Edge Loading
Maximum Bending Stress
[3(1+n) P/7i(3+n)h2] {/n(Eh3/100ka4) + 1.84 - 4p/3 +[(1-n)/2] +1.18(1+2|a)(a//)}
Edge Loading
Maximum Deflection
Corner Loading
Maximum Bending Stress
(3P/h2) [1.0- (clI)072]
Corner Loading
Maximum Deflection
(PlkP)tl.20S
3-37
(all)2
{P(2+1.2^)1/2 }/{Eh3k}1/2{1-(0.76 +0.4|i) (all)}
- 0.69(c/0]
For the interior and edge loading cases, the load is applied th rough a ci rcular ar ea wi th a radius ' a'. F or the com er load ing case the lo ad is appli ed thr ough a square loaded area with a side length of'c' Maximum Bending Stress ( psi) Maximum Defl ection (in) P = total appli ed l oad ( lb.) E = slab You n g's modulus ( psi) H = slab P oisson's rat io h=
slab thickness (in)
k=
modulus o f subgrade reac tio n (psi /in)
a=
radius of circular l oad ( in)
c=
side length o f square l oad ( in)
f t = (Eh 3/[12(1 - n2)k]}
{I is the radius
o f re lativ e
stiffness). b=
[(1.6a 2 + h2) 1/’] - 0.675h if a < 1.724h
b = a if a > 1.724h y = Euler's constan t (=0.577215 6649 0).
i n = natural logarithm Whil e Westergaar d considered the s
ubgrade suppo rt as
a
set o f springs , H ogg a nd Hall ( 5.30 ') consider ed t he su b grade as a semi-infinite elastic solid to develop a mathe matical model for determining maximum stress and deflection in a concrete slab under a single load applied at the interior o f the slab. 3.3. 3
Elastic Layer Model
The elastic l ayered m odel for rigid pavements is si milar to th e elast ic layered model f or fl exible pavemen ts. In this model each layer is defined by its elastic modulus, Pois son's rat io and thic kness. A limitatio n o f using the
layered
elastic model is that only the interior loading case, where the load is at a considerable distance from the edge can be ana lyzed. E dge
and
corn er loadin g
cases
cannot
be
evaluated by models based on elastic layer theory. In additio n, elastic laye r th eory cannot b e used if cracks exist in the concret e slab
or if voids or loss of support exis
below the slab.
3-38
t
Computer programs which use layered elastic theory can be used to analyze rigid pavements. Some elastic layer programs such as microcomputer version of
E L S Y M5,
assume that the interfaces between the layers are rough, although it is possible to define a no friction condition.
B IS A R an d WESLEA
Some programs such as
have the
ability to model the interface between the layers as having full adhesion, complete slip or at any condition intermedi ate between these two extremes. It is incorrect, however, to assume that full friction exists between the interface of the concrete slab and the unbound aggregate base or the subgrade. An
elasti c layer program wh
ich can handle vari
able interface condition gives the user the ability to model any interface condition. Therefore, such a model will give a better r epresentation o
f the exis ting co nd itio ns in the
field, assuming that these conditions are known. 3.3.4
Finite Element Models Numerous finite-element models for analyzing rigid pave ments are available. These finite element programs are capa ble o f inco rpora ting some or all o f the foll owing fac tors into analysis: partial slab support, load transfer, dowel looseness,
aggregat e interloc k, voids and cracks.
ILLI-SLAB is a finite element program which has been widely used to analyze rigid pavements (3.23). This pro gram was developed in the late 1970s at the University of Illino is and models
a mediu m-th ick plate o n a Winkler
foundation. This program can evaluate the structural o f a co ncret e pavement with
joints , cra cks or
both. Io an nides et al (3.24) ex pan ded
response
ILL I-SLAB for a
variety of support
cond itio ns inc luding stress dependent
resilient subgrade and Boussinesq elastic half space. 3.3.5
Coupled Models These are structural models that have been obtained by coup ling tw o or m ore o f the fo llo win g models: (a)
finite element
(b)
mu ltiple- layers systems
(c)
ana lytical (clo se d-form )
3-39
A descript ion o f cou pled models that have been d is summarized by
Majidzadeh
evelo ped
(3.2 5). A n example o f a
coupled model is the stress analysis model (RISC) devel oped by Majidzadeh (3.25). which couples finite element plate theory with multi-layer elastic theory. This model cons ists o f a tw o layer rigi d slab resting on
a semi-i nfinite
three-layer elastic solid foundation.
3. 4 DES IGN PROCESS 3.4. 1
Flexib le Pavement s 3.4.1.1
Introduction The design process described in
Section 3.3
an d
Section 3.3.4 covers mechanisticempirical concepts applied to the technical per detailed under
form an ce o f the pav ement alte rnative .
It do es
not cover the complete decision process, where the choice o f a pavement rehabil itatio n a lternativ e may be controlled by factors other than technical considerations. 3.4.1.2
Fat igue and Dam age Conc epts The usef ul liv es o f highway and
airport pa ve
ments are finite, and like everything else, tend to "wea r out ". The rate a t which a pavement wears is a function o f its structure, t he mat erials f rom which it is constructed, traffic levels and charac teristics, and the environment in which it exists. Pavement wear due to traffic is referred to as "dam age". Dam age c an be def ined as an al tera tion o f the physic al propert ies o f the pa vement structur e due t o the applic ation o f wheel loads. Generally the a lteratio ns take t he fo rm o f de for mat ion or cracking of the pavement lay ers. Da m age increases exponentially with increasing wheel loads.
When the
dam age reaches a
speci fied
level, the pavement is considered to have failed. For example, a single wheel load application may permanent ly com pres s or defo rm the asphalt laye r by so me minute amo unt.
Over a period of time
as thousan ds o f wheel loads are applied, the
3-40
permanent
defo rm at ion
leading to measurable
becom es
rutting.
sig nif icant
When the rutting
reaches a pre-specified level (such as 12.5 mm (.5 in.) for example) the pavement is said to have fail ed.
The num ber o f wheel lo ad s required
to
reach failure is typically referred to as "number of wheel load applications to failure", or
Nf.
Th e
damage at any point in time, D, is defined as the rat io o f th e acc um ulat ed wheel load
applic ations
N (since the pavement was new) to the total number expected to cause failure (Nf)
or
D --S -.
N,
Figure 3.11 illustrates this con cept . At N = 0, or 0 wheel load applications, D = 0. At failure or N = Nf, D
=
"consumes"
1. Each wheel load application 1/Nf o f the pavement's life.
Up to this point, the discussion has concerned only one load level for the wheel in question. H ow are many le vel s o f wheel lo ads taken into acco un t? levels.
Consider the si mple case of tw o load As stat ed earlie r, higher
impart greater damage per application.
whee l load s
Figure
3.12 shows two curves for two load levels A and B. Cur ve A repre sents the heavi er wheel lo ad. Let n t repre sent a given number o wheel load
A followed
f applic at ions o f
by n2 applic ations o f
wh eel lo ad B followe d by n3 app licat ions o f wheel lo ad A.
The total dama ge, D, is given by: D = ADj + AD 2 + ADj nl
n2
n3
“ Nf* + Nf B + Nf A This is an il lustratio n o f Miner's La w wh ich states that
damage is linearly cumulative, or N D = — L where i represents various wheel 1 loads or standard wheel load applied during a particul ar seaso n. N ote that for this app roach to
be successful,
N fi must be known for any magni
tu de o f wheel lo ad. 3-41
Number of Load Applications, N
Figure 3. 11 - Dam age vs . Nu m ber of Wheel Load Applications
3-42
D = AD., + AD2 + AD3 Damage, D = 1.0
Wheel Load A
Num ber of Applica tions, N
Figure 3. 12 - P rocedure to Sum
ma rize Dam age due
to Mu ltipl e Wheel Loads
3-43
As shown in Figure 3.4 and mentioned in Section 3.2.1, pavement distress relationships for flexible pavements typically consider horizontal tensile strai n at the bott om o f the surfaci ng laye r for sur face cracking, and vertical compressive strain on top o f the subgrade for rutting . Current rutting problems are often associated with plastic defor mat ion o f the AC surfaci ng and is not addr essed in this app roach. This i s for c ra cking and rutting due to applied wheel loads, with any given load resulting i n a spe cific strain leve l. As with man y materials, the distress relationships relate to strains resulting from stress levels well below the ultimate material strength i.e. a fatigue approach. The typical form of these distress relationships is: Nfi =
A EtjBE c for cracking
N ri = A' Svj B' for rutting whe re
Nfj
= numb er of rep et iti ons of a given wheel load (i), causing strain level 8tj, which will result in pavement failure by fatigue cracking.
8ti
=
horizontal tensile strain at the bottom o f the sur faci ng layer caused by wheel load i
evi
=
vertical compressive strain on t op o f subgrade c aused by wheel load i
E
AB,C,A',B'
elastic mo dulus o f surfac ing
=
experimentally determined constants
N ri
=
number of repeti tio ns o f a given wheel load, causing a strain level 8vi, which will result in pavement failure by rutting
Failure in cracking would occur when the number o f actual wheel loads o f magnitude i that have passed over the pavement equals Nfj, and simi larl y for rut ting . The basis of the design pr ocess lies in the following assumptions:
3-44
(Eq. 3.19) (Eq. 3.20)
(i)
if a wheel l oad i passes over the pavement a certain amount
o f the permanent da
occ u rs so that
UA
mage
o f the cracking life o f
the pavement is "consu me d"; and
-*Vri
of
the rutting life is "consumed" (ii)
Miner 's hypoth esis applies, i.e., that da ma ge (D) is linearly cumulative, so that total damage caused by Nj actual repetitions of load level
(Eq. 3.21)
i is D y, =
and D r/ = — ■ for cracking and ru -Ar
ri
tting ,
(Eq. 3.22)
respectiv ely . Furth er, f or the spec tru m of loads i, total damage for all loads is
Df = ,
and
I i
D' = ?
Nj_ N fi
(Eq. 3.23)
(Eq. 3.24)
f - , ’
and fai lure occ u rs in cracking when D f = 1.0 or rutting when D r = 1.0. Whichever occurs first controls the design. The process is often extended to include seaso nal effects by su mming dam age caused by lo ad i dur ing season j , with N ij repre senting actual r epetitions o f load level i during sea son j, etc. It should be noted that the equations pre sented a bove c ha racterize rutting as a f tion o f the subgrade str ain. 3.4.1.3
un c
Distress Criteria The main empi ric al portions o f the design p rocess are the equations used to compute the number of loadin g cycles to failure. Thes e are der ived by observing the per forman ce o f paveme nts and re lating the type and extent of observed failure to an initial strain un der var ious lo ads . Curr ently,
3-45
t wo t ypes o f fai lure c riteria are widely re cog nized, one relating to fatigue cracking and the other t o rutting ini tiating in the subgrade. Other relationships have been developed but are not commonly used, although they are gaining popu lari ty. As an example, c ompr ess ive stress in un bound base cour se materi als has been used to predic t onset o f paveme nt roughness [3.18 ]. Sim ilarly , compr essive st resses on t op o f cement stabilized subbase layers have been related to crushing dam age un der wheel loads [3.1 9]. Fur ther developments should be expected, since it is not rea sonable to f ocus only on cracking o f the surfaci ng or ru tting of the su bgrade while essen tially ignoring other structural layers and modes o f distress . Many equations have been developed to estimate the n umber o f repetitio ns t o fai lure in the fatigue m ode for asphal t concrete. Some rel y on the horizo nt al t ensi le strai n at the bottom o f the asphalt lay er, e t , and rel y on the modulu s o f the asphal t mix , E, as wel l. One co m m only acc ept ed criterion was suggested by Finn et al. [3.81: log Nf = 15.947 - 3.2 91 log The above equation assumes that failure is def ined as fatigue c ra cking over 10 percent o f the wheel path area. Figure 3.13 shows the relation ship between tensile strain in the asphalt concrete and th e nu mber o f cyc les t o fai lure fo r t wo lev els o f asphal t co n cret e mo dulus. It should be kept i n mind that other relatio nships may be based on dif ferent def initio ns o f fail ure. F or PCC analyse s the distress indicator is typically horizontal tensile stress at the bottom o f the PCC lay er, and in most cases this is normalized by considering the ratio o f this stre ss to the modulus of rupture . Rutt ing can ini tiate i n any layer of the structure, making it more difficult to predict than fatigue cracking. Curr ent fail ure criteria pertain t o rut ting which can be attributed mostly to an over str essed subgrade. This is typically expres sed i n terms o f the vertic al compr essive strain , ev, at the top o f the su bgrade lay er:
(Eq. 3.26) [This equation is rearranged from Chevron, as referenced in 2.121
3-46
Failure in this case is defined as 12.7 mm (0.5 in) depressions in the wheel paths o f the pav ement. Figure 3.14 illustrates how the vertical compres sive strain relates to th e nu mber o f cycles t o fail ure.
Load Applications (N f )
Figur e 3.1 3 - Limiting H
ori zo nta l Strain C
riterio n fo r Asphalt Concret
Fatigue Cracking.
3-47
e
SUBGRADE RUTTING
COMPRESSIVE STRAIN (*10“6)
LOAD REPETITIONS IN)
Figure 3.14 - Limiting Subgrade Strain Criterion for Rutting
3-48
Th e num ber of c ycl es to fail ure for our
example
pavement sections are given in Table 3.5 for both fatigue and rutting . The lower num ber o f the two cri teria indic ates t he expected
m ode o f fail ure.
The "Standard Pavement" with the thin crosssection for example is expected to fail after about 1.000 c ycles in rutt ing.
Th e mediu m sectio n, B,
o f the same case would 130.000 load repe titio ns.
sh ow rutting af ter Section C o f the
"Standard Pavement" would be expected to fail after about 3.3 million cycles in either fatigue or rutting.
The "Low Ti re Loa d" res ults indic ate
that structural fai lure o f the pavement s is unlikel y for any o f the pavement sec tions.
Increased tire
pressure primarily affects the fatigue life of all three sections, although sections A and B will still fail in rut ting first.
Subgr ade sta bilizat ion ten ds
to reduce rutting while having less effect on cracki ng. Th e use o f an asphal t tr eated base dra matically benefits all three sections from a struc tural viewpo int. The we ak ening of the pave ment due t o the presen ce of a moi stur e sensitiv e asphalt mixture has its most severe effect on the rut ting failure.
The basic conclus ion that c an be
drawn from Table 3.5 is that structural failure for thin (Section A) pavements and weak ("Moisture Sensitive") pavements will be in rutting according to these criteria. Ta ble 3. 5. Fa il ur e Criteria A
pplied To Typic
al Pavements
Mil lions o f Cyc les t o Fa ilure Section
Cri te ri on
Sta ndard Pavement
Low Tire
High Tire
Stabilized
Asphalt
Moisture
Load
Pressure
Subgrade
Treated
Sensitive
Base A B C
F a t igu e
0.07
6.10
0.02
0.15
0.001
10.73
0.001
0.05
1.31 0.79
0.14
Rutting F a t igu e
0.39
170.37
0.18
0.59
17.41
0.20
1.65
32.39
0.03
0.001
3,3 31.86
0.11
3 .36
3,8 95 .7 6
2.38
5.07
4 2.7 0
1.10
3.24
88,71 4.00
3.09
20.82
110.08
0.35
Ru t t in g
0.13
Fatigue Ru t t in g
3-49
3.4.1.4
Typic al Appr oach Designing a pavement using a mechanistic-empirical approach is an iterative process which can include the several steps shown in
Figure 3.15.
These inc lude: (a)
Determini ng the appro priate number o f sea sons.
(b)
Analyzing tr affi c for the design per iod to determine the
total nu mber o f tr affic l oads
in each season (n). (c)
Comput at ion of strai ns at critic al points i n the pavement for each season under consid eration.
(d)
Calc ulating the num ber o f cyc les to fail ure (Nf) for each season.
(e)
Calc ulating the dama ge rat io (n/Nf) for each season.
(f)
Sum ming the dam age ra tios for all seasons (D).
(g)
Increasing
or redu cing lay er thicknesses
D is not close to 1. (h)
Deter minin g final cross -section desig n.
3-50
if
Fig ure 3 .1 5 flow Di ag ram of a McchanisticEmpirical Design Procedure
3-51
At the outset, one should establish the lengths of the seasons to be considered in the design proc ess.
This selection
should refl ect time per iods
during which the material properties do not chan ge sub stant iall y. F or insta nce, if an area has thr ee months o f freez ing weather, say from De cember through February, the assumption could be that th e base and su bgrade material s are frozen (high moduli) and that the asphalt concrete is very stiff
(high modulus).
Dur ing the spri ng,
Mar ch and April, the moduli o
f the underlyi ng
layers may be very low, and the asphalt concrete modulus wil l be an i ntermediate
value.
The as
phalt concrete modulus will be at its lowest dur ing the summer (May through August) and the base and subgrade will have intermediate moduli. In the fall (September through November), the lower layers will probably maintain intermediate stiffnesses, and the asphalt concrete will again have
an intermedi ate modulus.
This type of
analysis would have to be customized to your par ticular materials
and climat e.
An exam ple o f
this kind o f info rm at ion is shown as follows:
Season Season
Length
Winter
3m on t h s
Spring
2 months
Summer
4m on t h s
Fall
3 months
Relative Modulus o
f Elastici ty
AC
Ba se
Subgrade
high
high
high
low
lo w
inter low inter
inter
inter
inter
inter
The traffic analysis is normally accomplished by using the initial traffic volume, an assumed growth rate, and the design period to calculate the nu mber o f tra ffic l oads on t he pavement its life.
over
F or a highwa y pavemen t, this norma lly
results i n a number o f 80 kN (18,000 lb. ) equiva lent si ngle axle loads
(ES ALs ).
The 80
(18,000 lb.) ESAL is a standard pavement design axle load with the standard 40 kN wheel design 3-52
kN
load r epresenting
one side o f the axl e. H owever,
it should be noted that since any realistic, mixed traffic loading condition can be used in layered elastic analysis, one is not restricted solely to an ESAL configuration. F or the pu rposes o f illustratio n, w e wil l use the loading condition in the previous example for the "Stan dard Pavement
".
Recall that thi s was a 40
kN (9,000 lb.) wheel with 552 kPa (80 psi) con ta ct pressure.
I f nT represents the
o f this type o f load expected then t he seasonal distributio Wint er:
nw = (3/12) n j
Spring:
nsp = (2/12 )n T
Summer: Fall:
total number
over t he design lif e, n can be estim ated:
ns = (4/ 12) n j nf = (3/1 2) nT
In this example, we are assuming that the ex pected traffic loads will be distributed evenly thr oughout the y ear.
I f there are
obvi ous sea
sonal patterns in the traffic, spring load restric tions for instance, then an adjustment would have to be ma de in the calc ulat ion t o a ccount for this. A layered elastic analysis would need to be per formed for the assumed loading condition for each
season
being
considered.
The
loading
condition as it would appear in the layered elastic analysis is illustrated in
Figure 3.4.
The initial thicknesses could be selected as the minimum allowable thicknesses for given classes o f pavement.
The critic al strains in the pavement
structure are determined at the locations noted in
Figure 3.4.
These strains are calculated for each
seaso nal change in modulus values for the var
ious
layers. Next , the nu mber o f load cycles to fail ure (Nf) for fatigue cracking and rutting are computed usin g fail ur e criteria.
3-53
Th ese wi ll be subsequ ent ly
discusse d in detail . F or the f at igue c riter ion, the nu mber o f cyc les t o fail ure is a function o horizo nt al t ensil e strain at
f the
the bott om o f the
asphalt co ncr et e and the modulu
s o f the asphalt
concret e. F or rutting, i t is a function of the verti cal c ompr essive strain at the
top o f the su bgrade.
The n umber o f cyc les to fai lure i s co mp u ted for each season. The damage for each season is defined as the ratio of the nu
mber o f loads expected for
time period, n, t
o the nu mber o f cyc les t o fai lure,
Nf, for that co nd ition i n the pave ment.
that
The total
damage, D, over the design life is then computed by summing the damage in each season:
(Eq. 3.27)
D = VN fw + " sp^ fsp + "s^ fs + n f/Nff I f the total da mage is cl ose t o 1, it means that close to
100 perce nt o f the pavement
life has
been expended. I f D is greater than 1, then the pavement has been underdesigned, and the layer thicknesses should be
inc reased.
I f the dam age i s
mu ch le ss than one, t hen the opposit 3.4.1 .5
e is true.
Sensitivity o f design to fail ure criteria T o illustrat e the impact o f fail ure criteria on design,
Figures 3.16 through 3.18
were devel
oped using the material parameters and loading conditions in the previous example for the "Standard
Pavement".
bituminous sur
Vario us thic knesses
of
fac e were plo tt ed against the com
put ed num ber of repetitio ns t o fai lure f or 150 mm (6 in.), 250 mm (10 in.), and 350 mm (14 in.) th ick granu lar bases.
The co nt roll ing criterio n in
the design is the one requiring a greater thickness o f su rface material
for a given tr affi c level. Keep
in mind that these charts were developed holding the material properties constant; they are not to be used in actual design.
3-54
)
)
E i - 500,000 psl (3,4 50 MPa ) 2 m 25, 000 p s i (17 2 MPa ) 7, 500 p s l (5 2 MP a) E3 e
3 5 5
AC Thickness (mm)
AC Thickness (In.)
Fig ure 3 .1 6 Design C hart of Example Pavement (6 i Base)
n (150 mm )
E i - 500,000 psl (3.450 MPa) E2 - 25.000 ps l (172 MPa) E3 7,500 psl (52 MPa)
3 5 6
AC Thickness
AC Thickness (mm)
(In.)
Fig ure 3.1
7 Desi gn Chan Base)
of Ex ample Paveme
)
nt (10 i n (250 mm)
)
E i - 500,000 psi (3.450 MPa) E 2 - 25.000 psi (172 MPa) E3 7,500 ps i (52 MPa)
3 5 7
AC Thickn ess (in.)
AC Thickness (mm)
Figure
3 . 18Dcsig n Chart of Example Pave Base)
ment (14 i n (350 mm)
The pavement designs resulting from three traffic leve ls are given i n Ta ble 3.6. resulting
thic kness
o f
In thi s table, the
asphal t
concret e
was
rounded to the nearest 12.5 mm (0.5 in), and the assum ed minimum thic kness o f the bituminous layer was 50 mm (2 in.) . It is interest ing t o note that the rutting criterion controlled the design in all cases except those involving the thicker two pavement sections at 2,000,000 load repetitions. The
choic e o f whic h o f the t hree equiv ale nt
pavement
desig ns t o use at a ny of the tr aff ic l ev
els would depend on a life-cycle cost analysis. 3 .4.2
Rigid Pa vements 3.4. 2.1
Fat igue and Dam age Conc epts In a concrete pavement, a crack will result when the t ensil e stress at the bott
om o f the slab
exceeds the tensile streng
o f the concrete.
th
Such stress can develop due to traffic loading an d/o r enviro nment al conditions.
Fu rt hermore,
number o f labo rat ory tests have shown that crac king o f concret e beams
can
occur
repeat ed app licatio n o f stress, which are
a
the with
smal ler
than th e tensi le strength o f the concret e. This type o f cracking is ref erred t o as fatigue cracking. Fatigue tests on concrete beams show that the nu mber o f repeated before fractur
loads t he c oncret e can sustai n
e is a f un ctio n o f the stress ratio ,
wh ich is the a ppli ed stress divi ded by the m odulus o f rupture o f the co ncrete.
The m odulus of rup
tur e of the c oncret e is the maximum t that the concrete can sustain.
3-58
ensi le stress
Table 3.6 - Comparison of Example Designs
40 kN (9,000 lb) Wheel Loads
2X104
2X105
Base Thickness
AC Thickness
mm
in.
mm
150
6
100
4.0
Rutting
250 3 60
10 14
60
2.5
Rutting
50
2.0*
Rutting
150
6
150
6.0
Rutting
250
10 14 6 10 14
130
5.0
90 220
3.5 8.5 8.0
Rutting Rutting Rutting Fatigue
7.5
Fatigue
360 150
2X106
Controlling Criterion
250 360
in.
200 190
* Assumed Minimum Thickness Typically a concrete pavement is subjected to a variety o f loads. The tensile stress in the co
ncr ete
caused by each load can be computed. The most cri tic al pavement stress occur s when the wheels loads are applied at or near the pavement edge and midwa y between th e joints.
For each lo ad,
the ratio between the applied load and the modulus o f rupture (s tress ra tio ) can be com puted.
Relationships
have
been
developed
between the stress ratio and the allowable load repetitions. Therefore, for each load the fatigue dam age during
the desig n period can be com
puted from:
D i= ~
(E q . 3 . 2 8 )
3-59
where, Dj = Fat igue dama ge f or lo ad i nj = Actua l load repetitio ns o f load i during the design period
applie d
Nj = Allowable load repetitions for load i ob tained from a fatigue relationship (based on the stress rat io) Applying Miner's hypotheses, when, -ZDj =1 the pavement fails due to traffic load associated dam age. Generally, when the stress ratio caused by a load is less than 0.5 it is assumed that no fatigue damage results from that load. Many failures in rigid pavements occur due to factors that are unrelated to fatigue. Pavement failures may result from relatively few repetitions o f heavy axle l oads at slab co rn ers a nd edges which cause: ♦
pumpi ng;
♦
erosio n o f subg rade, subb ase an d sho ulder materials;
♦
voids un der and adjac ent to the slab ; and
♦
faulti ng o f joints.
Failure due to these other causes should also be cons idered in the design pr ocess. 3.4.2.2
Distress Crite ria The failure criteria most commonly used in rigid pavements is that relating to fatigue cracking. Models for fatigue have been developed based on analys is o f laborat ory f atigue
studies as well as
analy sis o f per forma nce o bservations. fatigue relatio nships are generally plo o f a stress ratio and
Concret e
tt ed in terms
load applic ations t o fail ure.
The stress ratio is the stress induced due to the applied lo ad divi ded by the m odulus o f rupture.
3-60
Th e fatigue equat
ion based on the relationship f
or
concrete that is used by the Portland Concrete Association is [3.28]: log N = 11.78- 1 2.11 (t7t/ M R )f or 0.5
(Eq. 3.29)
log N = inf ini ty fo r o^/Mr < 0 .5 where, M R = M odulus o f rupture , psi crt = Induced tensile stress, psi N = All owable repeti tio ns As with flexible pavements the load repetitions to failure fo r a given lo ad lev el can be obta ined from this equatio n. The m aximum stress that is i
ndu ced
in the slab, which corresponds to that for edge loading should be used in these equations. The Portland Cement Association has developed deflection based criteria to account for erosion of material beneath slab developed
from
corn ers.
pavement
This c riteria was
performance
and
faulting data from the AASHO road test. The erosion criteria is used together with the fatigue cri teria in the th ickness design pr
ocedu re o f the
Portland Cement Association. An alternative f at igue r elatio nship is [3.2 7]:
lo g N = -1. 713 6/? + 4.2 84
for/? >1.25
( Eq. 3.30 )
an d log N = 2 .8 127/?- 12214 where N
is the number o
to cra ck 50%
fo r /? < 1.25 f wheel lo ad coverages
of the sl abs , and R is the ratio of
flexural stres s to mean modulus concret e. highly
o f rupture o f the
This rel atio nship has been fo un d to be
representat ive o f pavement
performan ce
observed under actual tra ffic conditio ns.
3-61
3.4.2.3
Typic al Appr oaches The design process for a rigid pavement is an iterative process. Mechanistic design procedures for concrete pavements have generally been based on limiting the flexural stress induced in the slab, so that fatigue cracking can be a
voi ded. The
following is a brief description of a typical mechanistic-empirical procedure for designing concrete pavements. (a)
Determ ine the desig n period, predicted traffic and traffic distribution.
(b)
De cide on a slab size and slab th ickness.
(c)
F or each tr aff ic load determine
the critic al
tensile stress in the pavement. Generally, the critic al stress i s taken as that
due t o the
load placed at the edge midway between the joi nt s. (d)
F or each load determine
the stress ratio,
wh ich i s the app lied stress divided modulus of rupture o (e)
by the
f the co ncrete.
Us e a fatigue relatio nship to obtain the allowable lo ad repetitions fo r each stress ratio.
(f)
Comp u te the fat igue dam age for each load level by dividing the applied load by the allowable load.
(g)
Sum the fatigue dam age due to a ll loads.
(h)
I f the sum o f fatigue dama ge is more than 1, increase the slab thickness and repeat the procedur e. I f it is much less
than 1, redu ce
the th ickness o f the slab and repeat the procedure. The above procedure is intended to prevent fa tigue failure in the concrete slab. The Portland Cement Association thickness design criteria addresses subbase and subgrade erosion as well
3-62
as fatigue.
The P CA meth od bases i t's th ickness
design on t he most
cri tic al o f th ese tw o fai lure
criteria. In addition to th
e selec tion o f an appr opriate cri
teria for damage or fatigue, there are many other controversial points in the mechanistic design of PC C paveme nts. These points o f cont roversy incl ud e incl usion and calculation o f war ping and curling stresses; lo th e come r,
cation
o f the critic al stress at
edge, or tra nsverse
joint ; and the
incl usion o f erosion/lo ss of support. shoul d be aware
use t hese or similar models to per
3.5 EXISTING OVERL
The user
o f these we akn esses when they form desi gns.
AY AND MECH ANISTI C-
EMP IRICA L DESIGN PROCEDURES
3.5.1
Introduction Several pavement design methods will be briefly over viewed.
The pavement desi
gn pr ocedu res fo r all- new o r
reconstructed pavements includes the Asphalt Institute MS-1 and the Shell method for AC pavements, and the P CA proc edur e for PCC.
Th eW SD OT m echanistic -emp
irical overlay design procedure is also shown. All o f th e design pr ocedu res
which follow use layer
moduli in so me ma nner, with the except
ion o f the Asphalt
Institute deflection based overlay design procedure.
3.5. 2 N ew Desi gn Proc edures 3.5.2.1
Asphalt Institute M S -1 [3.9] The Asphalt Institute presents a mechanistic based design procedure for streets and highways. The follo win g steps ar e used in this appr oac h: (a)
Dete rm ine the initial inputs:
(i)
Compu te the expec ted number of ESALs for the design period.
3-63
(ii)
Deter min e the design resil ient modulus o f the subg rade. wher e the conservatism
This is
is built into
the desig n. One selects a resil ient modulus value which fal ls below a specifi ed p ercent ile of test results for that sectio n o f road. (iii)
Select combin at ions o f layer materials.
Th ese may include:
♦
Full- Depth Asphalt Conc rete
♦
AC over Emulsif ied Asphalt Base
♦
AC o ver Untreate d Aggregate Base
(b)
Find lay er thickness combina tions for the materials selected.
(c)
Acc oun t for sta ge const ru ctio n, if used. This is don e on the basis o f rema ining li fe in the pavement.
(d)
Per form an econom ic analy sis o f the vari ous pavement sections.
(e)
Deter min e th e final desig n.
An example design chart from MS-1 is shown in
Figure 3.19
which can be used to determine the
asphalt concrete thickness for a 150 mm (6 in.) untreated granular base course. 3.5.2.2
Shel l Pavemen t Design Manua l 13.15] This is probably the earliest procedure that relies primarily on elastic layer analysis, with the srci nal Shell Design Charts published in 1963 [3.15], These charts were based on linear elastic analy ses, as was the method outlined in 1977 [3.15], Th e pr ocedu re is a fai rly general versio n o f the mechanistic-empirical process employing Shell's
B IS A R elastic layer program, and allows effects such as temperature to be considered.
3-64
Untreated Aggregate Base, 6.0 in. Thickness
i s p , R M , s u l u d o M t n e lii s e R e d a r g b u S
Figure 3.19 - Exam
ple of an Aspha lt Institute Design Ch
ar t [af ter Ref. 3 .91
A three layer structure is used in the analyses, with t he tra diti onal distress indic at ors o f asp halt tensile strain and subgrade compressive strain being used as the primary desig n criteri a. H ow ever, secondary criteria include asphalt rutting considerations as well as stress levels in cemented bas e laye rs. P oisson's ratio is 0.35 for asphalt and unbound materials; and 0.25 for cemented bases. al ves appsuch roachas invol ves shown deve lop ment o f The desigtypic n cur th ose in Figure 3.20. The current versio n o f the She ll Design p roce dure is avail able i n Eu rope as a per sona l com puter program [3.2 0], The Shel l Design Ma n u a l is available for use on PC computers at this time, as is BISAR. The name and phone number of the Shell representative in Houston appears in Ap p en d i x E . 3.5.2. 3
P CA Design Pr ocedur e [3. 21] This procedure is based on theoretical stress analyses srcinallymodified developed by Westergaard, and subsequently by finite-element pro cedure s. P CC sl ab material is char acter ized in terms o f modulus o f rupture (MR, in MPa, or psi) and the support material represented by the modulus o f subgrade reactio n (k in MPa /m or psi/i n). Th e distress indic at or for f at igue crackin g is the stress ratio (SR ) o f horizo nt al t ensil e str ess to MR. Subgra de rutt ing is not an iss ue, b ut the second distress criterion relates to erosion of foundation and shoulder materials, which is con tr olled by limiti ng def lec tions. Compu ter pr o grams are available to perform analyses on trial sections. Alternatively, the tabulated values shown in Table 3.7 are used in conjunction with an assumed design and performance. Figure The 3.21 evaluate fatigue and MR erosion procedure is illustrated in Table 3.8 (the erosion tables and nomographs have not been included in this text).
3-66
to
DENSE BITUMEN MACADAM (80/100) WEIGHTED MAAT = 12 °C SUBGRADE MODULUS =5 * 107 N/m2 TOTAL ASPHALT THICKNESS, mm
TOTAL THICKNESS OF UNBOUND BASE LAYERS, mm
Fi gur e 3. 2 0 - T yp i ca l S he l l D esi gn C urve
3-67
Table 3.7. PCA Slab Stress [3 .211 Equivalent Stress - No Concrete Shoulder (Single Axle/Tandem Axle)
Slab Thickness, in.
k of subgrade-subbase, pci 50
100
150
200
4
825/679
726/585
671/542
634/516
4.5
699/586
616/500
571/460
540/435
5
602/516
531/436
493/399
467/376
432/349
5.5
526/461
464/38?
431/353
409/331
6
465/416
411/348
382/316
6.5
417/380
367/317
7
375/349
7.5 8 8.5
300
500
700
584/486
523/457
484/443
498/406
448/378
417/363 363/307
379/305
390/321 343/778
382/296
336/271
304/246
285/232
341/286
324/267
300/244
273/220
256/207
331/290
307/262
292/244
271/222
246/199
231/186
340/323
300/268
279/241
265/224
246/203
224/181
210/169
311/300
274/249
255/223
242/208
225/188
205/167
192/155
285/281
252/232
234/208
222/193
206/174
188/154
177/143
9
264/264
232/218
216/195
205/181
190/163
174/144
163/133
9.5
245/248
215/205
200/183
190/170
176/153
161/134
151/124
10
228/235
200/193
186/173
177/160
164/144
150/126
141/117
10.5
213/222
187/183
174/164
165/151
153/136
140/119
132/110
11
200/211
17S/174
163/155
154/143
144/129
131/113
123/104
11.5
188/201
165/165
153/148
145/136
135/122
123/107
116/98
12
177/192
155/158
144/141
137/130
127/116
116/"¿02
109/93
12.5
168/183
147/151
136/135
129/124
120/111
109/97
103/89
13
159/176
139/144
129/129
122/119
113/106
103/93
97/85
13.5 14
152/168 144/162
132/138 125/133
122/123 116/118
116/114 110/109
107/102 102/98
98/89 93/85
92/81 88/78
320/264
Equivalent Stress - Concrete Shoulder (Single Axle/Tandem Axle)
S!ab Thickness, in.
k of subgrade-subbase, pci 50
150
200
300
500
700
559/468
517/439
489/422
452/403
409/388
383/384
479/400
444/372
421/356
390/338
355/322
333/316
417/349
387/323
367/308
341/290
311/274
294/267
418/360
368/303
342/285
324/271
302/254
276/238
261/231
6
372/325
327/277
304/255
289/241
270/225
247/210
234/203
6.5
334/295
294/251
274/230
260/218
243/203
223/188
212/180
7
302/270
266/230
248/210
236/198
220/184
203/170
192/162
7.5
275/250
243/211
226/193
215/182
201/168
185/155
176/148
8
252/232
222/196
207/179
197/168
185/155
170/142
162/135
8.5
232/216
205/182
191/166
182/156
170/144
157/131
150/125
9
215/202
190/171
177/155
169/146
158/134
146/122
139/116
9.5
200/190
176/160
164/146
157/137
147/126
136/114
129/108
10
186/179
164/151
153/137
146/129
137/118
127/107
121/101
10.5
174/170
154/143
144/;30
137/121
128/111
119/101
113/95
11
164/161
144/135
135/123
129/115
120/105
112/95
106/90
11.5
154/153
136/128
127/117
121/109
113/100
105/90
100/85
12
145/146
128/122
120/111
114/104
107/95
99/86
95/81
12.5
137/139
121/117
113/106
108/99
101/91
94/82
90/77
13
130/133
115/112
107/101
102/95
96/86
89/78
85/73
13.5
124/127
109/107
102/97
97/91
91/83
85/74
81/70
14
118/122
104/103
97/93
93/87
87/79
81/71
77/67
4
640/534
4.5
547/461
5
475/404
5.5
100
3-68
10,00 0 ,00 0 —
6-
4
-
2-
I.OOQOOO—
e-
6
-
«-
100,000-
e-
6-
4-
10,000— 6t4-
2-
1000-
e6-
Fatigue anal on stre sk ratio facto
ysts—all r (with a
owable t oad repetitions base d nd witho ut concre te shoulder) .
Figur e 3. 21 - PC A F atigue N omograph
3-69
[3.211
S N O I T I T E P E R D A O L E L B A W O L L A
Tab le 3.8. PCA Design Example [3 .211 lA j j^D L/r
Pioject
I na i thi ckn ess _____________ ^ Subbase-subgraoe
k
_______ /■
? /?
-
/¿ L n CL. Jr7i,er-r-//z/ct fTSrct/. Ooweiefl |omtt
n
_____
jijS ~£L
Modui m ftf ru pti jf» MR Load safely factor.
*
pci
Concrete IhOutOer.
pst
Design pfnoO
S-2-
IS F
_______________
yes
yes ______ no
^O
^
years
V-./ n i/ r7J r-£Ce / c.cS Fatigue analysis Aite load kips
Enpeciet) repetitions
Multiplied by IS F
3
2
Allowable repetitions
fatigue. peicent
4
S
1 Fqmw alpnl »Iff
Anovvrftie repet.t.ons
Single Axles
3D ?£ 2& 2 V<7•? 2n /£ /U fT.
*6 n
7 7
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31 £ Z/ .7 PA.fi P i, OW s> P/ £ / *? ?
.
230,030 / O o n or>n ¿/n//m
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¿,7 O-
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3 6 *
3.5. 2.4
Othe r New Desi gn Me thod s Many other mechanistic-empirical or purely emp irical pavement design methods are currently in use in various locations, but it is beyond the scope of thi s course to disc uss them.
The NH I
Course on Pavement Analysis and Design Checks pr ovi des an in- depth d isc ussion o f some o f these meth ods.
It shoul d be noted, however, that f
number o f proc edur es the basis of desi
or a
gn is the
same in that a layered elastic analysis is per formed to determine critical stresses and strains. The differences between these procedures typi cally lies in the ch oice o f th e distress
criteria
which are based on typical material types and related per form an ce req uirements.
3-71
3.5.3
Overlay Design Pr ocedures 3.5.3.1
Asphalt Institute M S -17 [3. 12] The Asphalt Institute M
S -17 is used to d esc ribe
two separate flexible pavement AC overlay design pr ocedu res : one i s the ef fective thickness procedure and the other is a deflection-based pr ocess.
Bot h wil l be brief ly described.
Effective Thickness Procedure This procedur e is based on t he f undamental assumption that a pavement structure becom es "thinner" as i t ages and is sub je ct ed t o t raffic. Th us, ea ch pa vem en t la yer is conver ted to an equivale nt th ickness o f AC in such a way as to acco deteriora ting ef fects. overviews the n
un t for such
The f ollowing brief ly
ecessary steps to
use this
procedure. (a)
Subgr ade Ana lysi s Determ ine the su bgrade resi lient modulus
(M r ). A variety of ways to d
o thi s are su g
gested in M S -17. This input, along with an estim ate o f futur e tra ffic (E SALs ) is required to
determine the thic
kness for a
"new" pavement structure. (b)
Tr affic Analysis
Determine the design ESALs. (c)
Effec tive Thic kness o f Existing Pavement Structure (T e) Tw o m ethods for determining the eff thickness o f the existi ng pavement are desc ribed i n MS -17.
ective structure
In Met hod 1, the
existing pavement is converted to an equiv alent t hic kness using Present
Ser vic e
ability Index (PSI) and equivalency factors presen ted i n the manual. limited to pavements
3-72
This met hod i s
consisting o f as phal t
concr ete and emulsif ied asphalt bases.
If
other material types are present, Method 2 must be used.
In Met hod 2, some e stimate
o f the condition must be made.
and th ickness o f each laye r Then each lay er is con
verted to an equiv alent th ickness o f AC through the use of "equivalency factors" (conversion factors) as shown in Table 3.9. The u se o f th ese wi ll be il lustrated in an ex amp le at th e end o f this sectio n. (d)
Determine
Thic kness o f N ew Paveme nt
(Tn) Using t he design su bgrade resi lient m odulus and ES ALs, determine the "f ull- depth " AC thickness for a new pavement structure.
Figure 3.22
(e)
can be used t o d o thi s.
Determ ine AC Overlay Thickness (T0) The required overlay thickness is T0 = Tn - Te
(E q. 3.31 )
Deflection Procedure This procedure is based simply on the use of pavement surface deflections obtained with the Benkelman Beam.
The basic steps inc lude the
following. (a)
Establish the pavement sec tion to u v sur veyed.
(b)
Per form deflection survey. The pr ocedu re in M S -17 ip based on r e bound deflections measured with the Benkelman Beam; however, the deflections can be ob ta ined from other
devic es and
"converted" to an equivalent Penkelman Beam deflection.
3-73
Table 3.9. Asphalt Institute Conversion Factors [3 .121
CONVERSION FACTORS FOR CONVERTING THICKNESS OF EXISTING PAVEMENT COMPONENTS TO EFFECTIVE THICKNESS (Te)
(These conversion factors apply ONLY to pavement evaluat ion fo r overlay design. In no Classification of Materia l
1
a) b) c)
Description of Material Native subgra de in all cases Improved Subgrade** - predominantly granular mate rials - may contain some silt and clay but have P.l. of 10 or less Lime modified subgrad e constructe d from high plasticity soils P.l. greater than 10.
II
Granular Subbase or Base - Reasonably well-graded, hard aggregates with som e plastic fines and CBR n ot less than 20. Use upper part of range if P.l. is 6 or less; lower part of range if P.l. is more than 6.
III
Cement or lime-fly ash stabilized subbases and bases** constructed from low plasticity soils - P.l. of 10 or less.
IV
a) b)
c)
Emulsified or cutback aspha lt surfaces and bases that show ex tensive cracking, considerable raveling or aggregate degradation, appreciable deformation in the wheel paths, and lack of stability. Portland cement concrete pave ments, (including those under as phalt surfaces) that have been broken into small pieces 0.6 m (2 ft.) or less i n maximum dimension, prior to overl ay construction. Use upper part of range when subbase is present ; lower part of range when slab is on subgrade. Cement or lime-fly ash stabili zed bases** that have developed pat tern cracking , as shown by reflected surface cracks. Use upper pa rt of range when cracks are narrow and tight; lower part of range with wide cracks. Dumping or evidence of instability.
3-74
Conversion Factors*
0.0
0.1 -0.2
0.3-0.5
Table 3.9 (cont'd) - Asphalt Institute Conversion Factors [3.121
(These conversion factors apply ONLY to pavement evalu ation for overlay de sign. In no case are they applicable to srcinal thickness design.) _______________________________ Classification Description Conversion of Material___________________________of Material ___________________________________ Factors* _
V
a) b) c)
VI
a) b)
VII
Asphalt concrete surface and base that exhibit appreciable cracking and crack patterns. Emulsified or cutback asphalt surface and bases that exhibit some line cra cking, some ravel ing or aggregate degradation, and s light deformation in the wheel paths but remain stable. Appreciably cracked and faulte d port land cement concrete pave ment (including such un der asphalt surfaces) that cannot be effectivel y undersealed. Slab fragments, rangin g in size fr om approximately one to four square meters (yards), and have been well-seated on the subgrade by heavy pneumatic-tired rolling.
0.5-0. 7
Asph alt concret e surfaces and bases that exhi bit some fine cracking , have small intermittent cracking patterns and slight deformation in the wheel paths but remain stable. Emulsified or cutbac k asphalt surface and bases that are stable, generally uncracked, show no bleeding, and exhibit little deformation
0.7-0.9
c)
in theand wheel paths. Portl cement concrete pavements (includi ng suc h under asphalt surfaces) that are stable and undersealed, have some cracking but contain no pieces smaller than about one square meter (yard).
a)
Asph alt concrete , including asphalt concrete base, gener ally uncracked, and with little deformation in the wheel paths. Portland cemen t concret e pavement that is stable, undersealed and generally uncracked. Portland cement concre te ba se, under a sphalt surface , that is stable, non-pumping and exhibits little reflected surface cracking.
b) c)
3-75
0.9-1.0
______________
FULL-DEPTH ASPHALT CONCRETE
EouXttonl «.000-t Smgi^AiK Lead (LAU
Fi gu r e 3. 22 - D esi gn C ha r t f o r Fu l l - D ep t h A spha l t C on cr et e ( f rom Ref. [3. 12])
3-76
(c)
Calc ulat e Representa tive Rebou n d De flec tion (RRD). The RRD is calculated from the deflection data for the design section by use o
f the
following: RRD = (x + 2s) (f) (c) where
RRD
(Eq. 3.32)
= represe ntative rebo und deflection (in.),
x
= me an o f the indi vidual deflec tion measur ements (in.),
s
= standard devi at ion o f the deflec tion measur ements (in.),
f
= temperature
adj ustment
factor, and c
= critical per iod adjustment factor.
The use o f appr opriat e adj ustment factors ("f ' and "c") are very i
mpo rta nt in calculat
ing a realistic RR D. I f all deflection mea s urements were obtained under uniform pavement temperature conditions, then only one val ue o f "f 1is needed t o adjus t the d e flectio ns to a standard temperat C (70°F).
ure o f 21.1°
I f this i s no t th e case, then indi
vidual measurement
s must be adjusted.
In
any case, Figure 3.23 ( a) can be used to obtain the necessary "f1value (or values) and Figure 3.23 (b)
provides an estimate of
pavement temperatur adjustment factor
e. The c ritic al period
("c") i s a bi t m ore
difficult to esti mat e. This f a ctor is inten ded to adj ust t he deflec tions t o the m ost "crit ical" p eriod o f the year for
a spe cific
pavement sectio n. I f for example, the most cri tic al per iod h appens t o be the spring tha w per iod (i f this eve n occur s for a given pavement ), th en that is the set o which must be estimated.
3-77
f defl ectio ns
THICKNESS OF UNTREATED AGGREGATE BASE
0
»0
so.00
01 ill
}
10
»0 MILL IME TERS INCHES ?>
C ° , E R U T A R E P M E T
F # , E R U T A R E P M E T
T N E M E V A P
T N E M E V A P
N A E M
N A E M
TEMPERATURE ADJUSTMENT FACTOR (F)
Figure 3. 23 (a) - A verage Pavement Tem perature versus Benkelman Beam Deflection Adjustment Factors for Full-Depth and Three-Layered Asphalt Concrete Pavements [from Ref. 3.121
3-78
PAVEMENT SURFACE TEMPERATURE PLUS 5-DAY MEAN AIR TEMPERATURE. *>F 0
20
40
60
80
100
120
140
160
180
200
220
240
260
, H T P E D
F ° , H T P E D
T A
T A
E R U T A R E P M E T
E R U T A R E P M E T
PAVEMENT SURFACE TEMPERATURE PLUS 5-DAY MEAN AIR TEMPERATURE, °C
Figure 3.23 (b)
- Predict ed Pavement Te m perature [from Ref. 3 J2
3-79
Thus, the spring time is the preferred deflection testing time and "c" would equal 1.0. If the deflec tions were obtained in t he summer, then "c" would presumably be greater than 1.0 (say 1.5 or so). Unfo rtu nately, each unique pavement section has its own unique "c" value. (d)
Calculate overlay thickness. Use Fig ure 3. 24 along with the design ESALs and the RRD to determine the nec essary overlay thickness.
3.5.3.2
The Shell Method D.lOl An overlay design procedure was developed by Shell Research, in The Netherlands, based on re sults of FWD testi ng. The deflection measure ments are used along with a knowledge of past traffic and the environment to estimate the re maining life of the existing pavement structure. The remaining life in combination with future traffic requirements are used to determine the re quired thickness o f overlay. The failure crit erion in this procedu re is based on fatigue. A flow chart of the procedure is shown in Figu re 3.25 , and an example of the overlay design procedure is given in Fig ure 3.26. The interpretation of the FWD results in this case is not done by backcalcul ation. Instead, the sub grade modulus and effective thickness of the asphalt layer are determined by the maximum deflection, a deflection ratio between the deflec tion at 600 mm from the load to the maximum, assumed Poisson’s ratios, thickness of the granu lar base, and assumed ratiomix of stiffness. base to subgrade modulus, the asphalt
3-80
RRD, MM
0 50
1.00
1.50
2 00
2.50
3 00
3.50
4.0 0
4.50 EAL
10 , 000,000 S R E T E M I L IL
5,000,000
E T E R M C N , O S C S E N L T K A IC H H P T S A
2 , 000,000 1, 000,000
500.000
200.000 100,000
Y F A O L R E V O
50.000
20.000 10,000
5,000
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.140
0.160
0.180
RRD, INCHES
F i gu r e 3 . 24 - A sph al t C on cr et e O ver l ay Th i ckn ess R equi r ed to R ed uce P ave men t D ef l ect i ons f r om a Measur ed t o a D esi gn D ef l ect i on V al ue ( R eb ou nd T e st) [ F r om Re f . 3. 12]
3-81
Figure 3. 25F 1o w Chart of Shell O verlay Design Method [ a f t er R e f . 3 . 1 0 ]
3-82
RRO, M M
S R E T E M I L IL M , S S E N K IC H T
E T E R C N O C T L A H P S A
Y F A O L R E V O
RRD, INCHES
Figure 3.2 4 Asphalt Concre te Ove rla y Thickne ss Required to Reduce Pavement Deflections from a M ea s u r e d to a De si gn De fl ec ti on V a l u e (R eb ou nd Test) [From Ref. 3.12]
3-81
Verification
Selection of optimum overlay
Figure 3 .2 5F1ow Chart of SheU Overlay Design Method [after Ref. 3.10]
3-82
»a M
¿
o
*
*
“ -
3.5 .3.3
Washington State Departmen t o f Transp ortation
Another mechanistic-empirical overlay design procedure (EVERPAVE) was developed by the Washington State Department of Transportation that is based on the backcalculation of material prope rties and fat igue and rutting failures. In this approach, layer moduli can be calculated for each deflecti on test point. The asphalt concrete modulus is corrected for temperature according to data for typical Washington mixtures (Figure 3.27). Next, an iterative process is used to determine an appropriate overlay thickness for each deflection test point as shown in Figure 3 28 .
.
Both the unstabilized base course (subbase) and subgrade moduli can be non-linear with stress state, i.e., the base, subbase, and subgrade layer moduli can tak e the following for m: K2 E = K, (q)
(Eq. 3.33)
or K4
(Eq. 3.34)
E = K3 (sd) 4
with the exponents being either positive or nega tive. The failure criteria used in EVERPAVE are based on two basic criteria: rutting and AC fatigue cracking. The rutting criterion was adop ted from the Asphalt Institute [3.9. 3.1- 7]: Nf =
where
1.05 x 1(T
4.4843
Nf
allowabl e number o f 18,000 lb . (80 kN) single axles so that rutting at the pavement surface should not exceed 0.5 in. (12.7 mm), and
Ey
vertical compressive strain at the top of the subgrade layer.
3-84
(Eq. 3.35)
Temperature (°C)
l) s p ( s u l u d o M tr ie l i s o R
Temperature (eF)
Figure 3.27 - Genera! StilTness-Temperature Relationship for Class B (Dense Graded) Asphalt Concrete in Washington State [from Ref. 3.131
3-85
Read Input Data •Material properties •Seasonal variation •Traffic Assume overlay thickness
Calculate seasonal traffic volume
T
• Determine seasonal material properties •Analyze pavement Structu re fs^, e,,~) 'Calculate performance life (NL N.Ì__________
I
Determine Damage Ratio
Ï
Compute Sum of Damage RaUo (SDR)
Increase overlay thickness
^ SDR <
KZ.
Produce overlay
design
Figure 3. 28 - W SDOT Overlay Desi gn Flow Chart
3-86
The fatigue cracking failure criterion is based on Monismith's laboratory based model [3.14] and the subsequent work by Finn, et al. f3.8] and Mahoney, et al. [3.131.
(Eq. 3.36)
Fatigu e cracking: Nfieid = (Niab) (SF) wher e
Nfieid = number of load application s of con stant stress to cause fatigue cracking, Niab = relation ship from laboratory data [3.13,3.141, 14.82 - 3.291 log
=
SF
10
—!L
Uo
- 0.854 log
(E
(Eq. 3.37)
= can range from abou t 4 to 10, depends on AC thickness, ESAL level, climate.
The Nfieid applications is estimated to result in about 10 percent or less fatigue cracking in the wheel path area. The srcinal Finn, et al. [3.81 model based on the Monismith laboratory work [3.14] and the results of the AASHO Road Test is: log Nf = where
5.947 - 3.291 log { - ^ 1 - 0 .854 l og JO"6
Nf
= number of axle applicati ons to result in 10 percent or less fatigue cracking in the wheel path area,
et
= horizontal tensile strain at the bottom
Eac
of the AC layer, and = modulus o f the AC layer (psi).
The difference between the Finn equation above and the Monismith laboratory based relationship is about 13.4. Thus, the laboratory fat igue rela tionship was "shifted" by a factor of 13.4 to more realistically represent a field fatigue prediction for the accelerated loading conditions at the AASHO Roa d Test. WSD OT studies [3.13] have shown, as stated above, that realistic shift factors for inservice WSDOT pavements are less than 13.4 3-87
(Eq. 3.38)
(more like 4 to 10). Generally, the shift fac tor is increased for high traffic conditions on say 100 to 150 mm (4 to 6 in.) AC. The shift fact or is low er for flexible pavements with AC thicknesses of abo ut 175 to 200 mm (7 to 8 in.) or thicker. It is appropriate to note that Finn, et al. [3.8] only analyzed the 100, 125 and 150 mm (4, 5, and 6 in.) thick flexibleandpavement from Loop 4 (7AC sections) Loop 6 sections (10 sections) from the AASHO R oad Test data. 3.5.3.4
Other Overl ay Design Procedures There are a number of other overlay procedures in use today that are based on mechanisticempirical techniques. For many of these, the overlay design itself follows the "Typical ap proach" outlined in Section 3.4.1.4, with distress criteria chosen to represent conditions relevant to the particular appl ication. This overl ay design is performed evaluation the existingon.strucThe ture, often after by the use of ofbackcalculati WSDOT EVERPAVE procedure described in Section 3.5.3.3 is a good example of this approach.
3.6 EXAMPLE 3.6.1 Introduction The medium AC thickness section (B) shown in Figure 3.8 will be used to illustrat e the use o f some o f the various AC overlay design procedu res. Even thou gh this is only a hypothetical pavement, we will make the necessary as sumptions to make use of this "pavement section." We assume that Section B can have two levels of AC stiffness, Eac = 3450 MPa (500,000 psi), which assumes no cracking, and E a c ~ 1035 MPa (150,000 psi), which implies extensive fatigue cracking of the AC surfacing. The necessary material properties, layer thicknesses, and deflections (calculated using ELSYM5) are summarized in Table 3.10. Further, we will design AC overlays for three assumed ESA L levels: 1,000,000; 2,000 ,000; and 5,000,000. 3-88
3.6.2 Asphalt Institut e Effective Thic kness Proce dure
Subgrade
(a)
Mr
(b)
Mr
= 52 MPa (7500 psi), a given
Traffic analysis Use E S AL levels of : 1,000,000 2 , 000,000 5,000,000 Therefore, obtain three overlay thicknes ses.
(c)
Effective thickness of existing pavement structure
(Te) Use Table 3.9 for equivalency factors. L
AC @ 34 50 MPa Î500.000 psj)
AC @ 1035 MPa (150.00 0 psD
AC
(125 mm)*(1.0 )= 125 mm (5 in.)
(125 mm) *(0.5 )= 63 mm (2.5 in.)
Bas e
(200 mm)*(0.2)= 40 mm (1.6 in.)
(200 mm)*(0.2)= 40 mm (1.6 in.)
Total:
(d)
165 mm (6.6 in.)
103 mm (4.1 in.)
Determine thickness of new pavement (Tn). Use Figure 3.22 and appropriate M r and ESAL levels.
______MR __________ESAL Level ____________Tn
_______
52 MP a (7500 psi)
1,000,000 2,000,000 5,000,000
3-89
231 mm(9.1 in.) 262 mm(10.3 in.) 312 mm(12.3 in.)
Table 3.10 - Pavement Response Summary for the Medium Thickness Section (Section B)*
125 mm (5”) AC 200 mm (8”) Base
Fine grained subgrade Load
P = 40 kN (9,000 lb)
a = 150mm (5.9 in.)
Calculated Deflections, fim (in.)
AC Moduli, MPa (psi) 1,035 (150,000) 3,450 (500,000)
d
D 0896.4
d
8-
685.0
Di2” 569.2
D 24” 351.3
D36” 237.2
48„
173.0
(0.03529) (0.02697) (0.02241) (0.01383) (0.00934) (0.00681) 690.4
589.0
517.9
348.2
242.1
177.3
(0.02718) (0.02319) (0.02039) (0.01371) (0.00953) (0.00698)
* Pavement responses obtained from ELSYM5 program
3-90
(e)
Determin e AC overlay thickness (T0). ESAL Level
Ea c , MPa (psi) ___________T0 = Tn - Te
1.000. 000 2.000.0 00 5.00 0.00 0
3450 (500 ,000 ) 3450 (500,000) 3450 (500 ,00 0)
231 - 165 = 66 mm (2.6 in.) 262 - 165 = 97 mm (3.8 in.) 312 - 165 = 147 mm (5.8 in.)
1.000.0 00 2.0 00.000 5.00 0.00 0
1035 (150 ,000 ) 1035 (150 ,000 ) 1035 (150 ,000 )
231 - 103 - 128 mm (5 in.) 262 - 103 = 159 mm (6.3 in.) 312 - 103 = 209 mm (8.2 in.)
3.6.3 Asphalt Institute Deflection Proce dure (a)
Ea c = 1035 MPa (150,000 psi)
Assume that Do from Table 3.10 represents the mean deflection with a standard deviation about Vi as large as the mean. Therefore, x s
= 896.4 pm (0.3529 in.) = 448.2 |jm (0.01764 in.)
Further, assume the deflections were obtained for an average pavement temperature of 60°F and the criti cal period adjustment factor (c) = 1.2 5. The tem perature adjustment factor (f) is 1.1 from Figure 3.23.
RRD
= (0.03529 + 2(0.01764))*(1.1)*(1.25) = 2464.7 nm (0.09703 in.)
Overlay thickness = (from Figure 3.24 ) = = (b)
122 mm (4.8 in.) for 1,000,000 ESAL s 147 mm (5.8 in.) for 2,000,0 00 ESALs 190 mm (7.5 in.) for 5,000,00 0 ESALs
Ea c = 3450 MPa (500,000 psi)
All calculations and estimations will be the same as (a) except Do = 690.4|im (0.02718 in.). Thus, x s f c
= = = =
690.4 |am (0.027 18 in.) 345.2 urn (0.01359 in.) 1.1 1.25
3-91
Therefore, RRD = (0.02718 + 2(0.01359))*(1.1) (1. 25) = 1898.5 nm (0.07475 in.) Overlay thickness = 97 mm (3.8 in.) for 1,000,000 ESALs (from Fig ure 3.2 4 ) = 122 mm (4.8 in.) for 2,000,000 ESALs = 157 mm (6.2 in.) for 5,000,000 ESALs (c)
= 1035 MPa (150,000 psi) and E a c ~ 3450 MPa (500,000 psi) Revised Ea c
If the pavement deflections had been taken during the critical period and no temperature adjustment was needed (i.e., measurements obtained at 21.1°C (70°F)) and all measurements were the same (i.e., s = 0, which is highly unlikely), then the resulting overlays would be the following: Ea c
=
1035 MPa (150,000 psi) RRD = 896.4 |am (0.03529 in.)
Ea c
= 3450 MPa (500,000 psi)
Ea c
=
RRD - 690.4 nm (0 02718 in.) 1035 MPa (150,000 psi)
Overlay thickness (from Figu re 3.2 4) Ea c
= 10 mm (0.4 in.) for 1,000,000 ESALs 43 mm (1.7 in.) for 2,000,000 ESALs = 74 mm (2.9 in.) for 5,000,000 ESALs =
= 3450 MPa (500,000 psi)
Overlay thickness (from Figu re 3.2 4)
= 0 mm (0.0 in.) for 1,000,000 ESALs = 0 mm (0.0 in.) for 2,000,000 ESALs = 46 mm (1.8 in.) for 5,000,000 ESALs
3.6.4 WSDOT Mechanistic-Empirical (a)
The EVERPA VE program was used with the fol lowing inputs (assumed location for seasonal effects is Spokane, Washington)
Case 1 ♦
Existing pavement moduli ♦ Ea c ♦ EBs ♦ Es g
= 1035 MPa (150,000 psi) = 172 MPa (25,000 psi) = 52 MPa (7,500 psi) 3-92
♦
New AC modulus = 3450 MPa (500,000 psi)
♦
Fatigue shift factor = 10
♦
ESAL levels
1,000,000 2 , 000,000 5,000,000
Case 2 Same as Case 1 but existing EAC = 3450 MPa (500,000 psi) (i.e., no initial fatigue cracking) Case 3 Existing pavement moduli ♦ EAc = 1035 MPa (150,000 ♦ EBs = 8,000 (0)0-375 ♦ E s g = 52 MPa (7,500 psi)
psi)
New AC modulus = 2760 MPa (400,000 psi) Fatigue shift factor =10 ESAL levels
1,000,000 2 , 000,000 5,000,000
Case 4 Same as Case 3 but existingE a c = 3450 MPa (500,000 psi) (i.e., no initial fatigue cracking) (b) Results Case 1 (Original surfacingE a c = 1035 MPa (150,000 psi)) "cracked AC" ESAL Level
AC Overlay Thickness, inches (mm)
1.000.000 2.000.000 5.000.000
30 mm (1.2 in.) 51 mm (2.0 in.) 89 mm (3.5 in.) 3-93
Case 2 (Original surfacing E a c = 3450 MPa (500,000 psi)) "uncracked AC" ESAL Level
AC Overlay Thickness, inches (mm)
1.00 0.00 0
0 mm
2.000.000 5.000.000
13 mm 43 mm
(0 in.)
(0.5 in.) (1.7 in.)
Case 3 (Original surfacingE a c = 1035 MPa (150,000 psi)) "cracked AC" ESAL Level
AC Overlay Thickness, inches (mm)
1.000.000 2.000.000 5.000.000
56 mm (2.2 in.) 81 mm (3.2 in.) 127 mm (5.0 in.)
Case 4 (Original surfacing E a c = 3450 MPa (500,000 psi)) "uncracked AC" ESAL Level
AC Overlay Thickness, inches ('mm')
1.000.000 2.000.000 5.000.000
5 mm 30 mm 71 mm
(0.2 in.) (1.2 in.) (2.8 in.)
3.6.5 Summary Refer to Table 3.11 for a summary of the various overlay thicknesses for the cases used in this example. Given that the "pavement section" used was purely hypothetical and required numerous assumptions, one should not expect the various overlay design procedures to result in similar solutions; however, there is a modest amount of agree ment among the design procedures used.
3.7 USE OF ELASTIC ANALYSIS SOFTWARE 3.7.1 Introduction In order to make use of the backcalculation results, we will become acquainted with a layered elastic analysis computer program, ELSYM5. Originally developed at the 3-94
Table 3.11 - Summary of Overlay Thicknesses for Medium Thicknes s AC Design Procedures Al - Deflection
1035MPa
Al - Eff. Tk. @E AC= 3450 MPa
(150 ksi) “cracked”
(500 ksi) “ uncrac ked”
(150 ksi) “cracked”
Al - Eff. Tk.
ESAL Lev el
@Eac =
@
e ac
=
1035 MPa
Al - Deflection
@ eac = 3450 MPa (500 ksi) “uncracked”
1,000,000
127 mm (5.0")
64 mm (2.5” )
122 mm (4.8”)
97 mm (3.8”)
2,000,000
157 mm (6.2”)
94 mm (3.7”)
147 mm (5.8” )
122 mm (4.8” )
5,000,000
208 mm (8.2”)
145 mm (5.7”)
190 mm (7.5”)
157 mm (6.2” )
Design Procedures
ESAL Le vel
WSDOT EVERPAVE @ ea c = 1035MPa “cracked” EBS = 25,000 psi
WSDOT EVERPAVE @ ea c = 3450 MPa “uncracked” EBS = 25,000 psi
WSDOT EVERPAVE
WSDOT EVERPAVE
@ Eac =
@ E Ac = 3450 MPa
1035 MPa EBS = 8,000 (0)0.376
8,000 (0)° 575
E bs ■—
1,000,000
30 mm (1.2”)
0 mm (0”)
56 mm (2.2”)
5 mm (0.2” )
2,000,000
51 mm (2.0” )
13 mm (0.5” )
81 mm (3.2”)
30 mm (1.2” )
5,000,000
89 mm (3.5” )
43 mm (1.7”)
127 mm (5.0”)
71 mm (62.8”)
3-95
University of California, Berkeley for use on a main frame, this version of ELSYM5 was adapted for use on microcomputers by the Federal Highway Administration. It is menu driven and, for the most part, self-explanatory. Until recently an integration error in ELSYM5 (as well as the CHEV program series) generated errors which were significant under certain conditions. This has been cor rected at Cornell University and care should be taken that the c orrec t version is being used. A rectangular coordinate system (X,Y,Z) is used for in put and output data. The horizontal plane is described by X and Y with Z defining the vertical axis. In this program, Z is positive in the downward direction. The loading conditions are defined by any two of three pa rameters: load, contact pressure, or radius of the loaded area. The other value is computed by the program. Each pavement layer is described by its modulus of elas ticity, and thickness.TheThe layers are num bered Poisson's from the ratio, top downward. subgrade layer is given a thickness of 0 to indicate a semi-infinite depth. 3.7.2 Software Demonstration In this section, we will describe the use of ELSYM5 in a step-by-step example including locating the program in the computer, inputting the data, running the problem, and retrieving the data. The user must first locate the disk drive and, if necessary, the sub directory in which ELSYM5 resides. For instance, ELSYM5
if we the "C" drive and"elsym", thenis type: located in theare "A"c urrently drive in in a directory named C:>a: The computer will respond with an A prompt, and we must tell it to go to the "elsym" directory: A:>cd\elsym This puts us in the proper place for accessing the pro gram. The various screens used in ELSYM5 are shown in Fi gur es 3.2 9 through 3.38.
3-96
Next, we begin the process of entering the data by typing: A:ELSYM>£/5y/w5 The title block and main menu for the program should appear as shown in Fig ure 3.29. One can choose to receive some abbreviated instructions on the program by typing 1 for the selection. Creating a data file or modify ing an existing done bytotyping a 2program or 3, respec tively. Selectingfile4 can will be allow you run the with the current data file, and 5 will allow you to exit from the program. In our example we will create a new data file, so we select 2. Screen 1.2 (.Figure 3.30 ) appears, and we can now enter the data for our problem. The data for the example comes from Section A of the "Typical Pavements" described ear lier. Option 1 is selected and the title is entered. After the RUN TITLE has been selected, Screen 1.2 returns. Next the pavement layer data are entered by choosing number 2 on Screen 1.2. Then Screen 1.2.2 appears (Figure 3.31), and the user inputs the number of layers, layer thicknesses, Poisson's ratios, and moduli. Layer numbers are entered automatically by the program. To go from one data field to the next, simply press the ENTER key on the computer. The user can incorporate a rigid layer below the subgrade by giving the subgrade a finite thickness. If this is not desired, then give the subgrade a thickness of 0. The data from Section A in the example are shown in Figu re 3.31. Screen 1.2 will come back after the user completes entering the data and presses the F2 key. Then Option 3 is chosen in order to provide the load data. This is done on Screen 1.2.3 (Figure 3.32). In this case, we have entered the load and pressure according to the example. The program will calculate the radius of the loaded area. The number of load locations (up to 10) is selected, and the X,Y coordinates of the center of the loads are input. When this is complete, the user presses F2 and Screen 1.2 appears again. The last items to be specified are the locations of interest for the analysis. This is done by selecting Option 4 on Screen 1.2. Then Screen 1.2.4 comes up as shown in 3-97
The user first enters the number of horizon tal positions for evaluation. In our example, we are inter ested in various points under the centerline of the tire, so 1 is entered. We want to evaluate the deflection at the pavement surface, the horizontal tensile strain at the bot tom of the AC, and the vertical compressive strain at the top of the subgrade; so three Z locations are specified as shown in Figu re 3.33. In order to obtain the vertical strain at the top of the subgrade, a point just below the base/subgrade interface must be specified. In this case, it was 203 mm (8.01 in.). Again, the key F2 returns us to Screen 1.2.
Fig ure 3.33.
Next, the user can choose to store the data in a file by selecting Option 5 on Screen 1.2. If this is done, the pro gram will prompt you for a file name. After this has been accomplished, return to the Main Menu by typing 6 on Screen 1.2. After the data have been entered or modified, select Op tion 4 on the Main Menu to have the program run the problem. When this is done, a message will appear on the screen as shown in Figur e 3.34. The program will prompt you for a file name if you want to save the results of your run. Otherwise, it will tell you that it is performing the calculations. A results menu for the first Z location will appear as shown in Figu re 3.35. Notice that this menu is for layer 1 at the pavement surface. Since we are interested in the deflection at this point, we type a 3, and the displacements appear as shown in Fig ure 3.36. At this point, we look under the heading UZ to find the vertical displacement. Once this value has been noted, a 4 is typed to move on to the next analysis point, which is layer 1, at a depth of 50 mm (2 in.). Here, we want to know the horizontal tensile strain at the bottom of the AC. So, a 2 is typed on the results menu and the results appear as in Figu re 3.37. The horizontal strains are listed under the heading EXX or EYY (.467E-03 or 467 x 10"6 in./in.). For the next loca tion a 4 is typed and the next results menu for layer 3 at a depth of 203 mm (8.01 in.) is displayed. We are inter ested in the vertical strain at this point, so we type a 2 and Figu re 3.3 8 appears. This value is found under the head ing EZZ (-.224E-02 or -224 x 10*6 in./in.).
3-98
MAIN MENU -ELSYM5Interactive Input Processor Ver sio n 1.1, Rel eas ed 04/93 Developed by SRA Technolo gies,
Inc.
Updated by Cornell Local Roads Program Under Contract to Federal Highway Administration MA IN M EN U 1.
Instructions
2.
Create a New Data File
3.
Mod ify an Existi ng Data File
4.
Perfo rm analysis
5.
Exi t - Retu rn to DOS Selection :
Figure 3.29 - ELSYM5 Main Menu
DATA FILE MENU Create a New Data
File Menu
1. Enter/Modify Run Title 2. En ter/Modif y Elastic Layer Data 3. E nter/Mod ify Loa d Data 4. Ent er/Modify Evaluatio n Location Data 5. Write Data to an Output File 6. Ret urn to Mai n Menu Selection:
Figure 3.30 - Screen 1.2
3-99
Screen 1.2.2
ELASTIC LAYER DATA Humber of lay er s: 3 Laye r (top to Number bottom)
Thickness (inches)
Poisson's Ratio
Modulus of Elasticity
1
2. 00
.35
500000.00
2
6.00
.40
25000.00
3
.00
.45
75 00 .0 0
Not«:
En te r zero
thi ckne ss whe n b ot to m l aye r is semi -inf init«
FI: Modif y This Screen; F 2 : Return To Screen 1.2
Figure 3.31 - Elastic Layer Data Screen
Screen 1.2.3'
LOAD DATA Ente r two of the following,
the third is calculated.
Load:
80
9000
lbs pressure:
psi Load Radi us:. 00 in
Numb er of lo ad l oca tio ns:
1
Location
Coordinates
number =
X =
1
0
Fl: Modify This Screen; F2: Return To Screen 1.2
Figure 3.32 - Load Data Screen
3-100
Y = 0
Screen 1.2.3'
EVALUATION LOCATION DATA Results are evaluated for all combinations of X-Y coordinates and Depths of Z. Hum ber of X-Y po siti ons : 1 Hum ber of Z posi tion s : 3
Figure 3.33 - Evaluation Location Data Screen
ANA LYS IS MODE OF E LSYM5 Do you wi sh the Results Saved on a Fil e *** PERFORMING CALCULATIONS ***
Figure 3.34 - Analy sis Mode of ELSY M5
3-101
(Y/N)==> n
Descriptio n o f "Standard" S ections
Earlier we discussed the evaluation of multi-layer systems using layered elastic theory. Now each group will run one of the cases for each of the standard sections (A, B, and C) which were described in Figu re 3.8. The layer thick nesses in the sections were: __________Thickness,
Laver Section A AC 2 (50) Base 6( 150 ) Stab. Subg.* 6(1 50 ) *For Group No. 4
in. (mm)__________ Section B Section C 5 (125) 9 (230) 8 (200) 6(1 50) 6(1 50 ) 6(1 50)
.4 Classroom Exercise Find your assigned group number, and run the case below for Sections A, B, and C on ELSYM5. Evaluate the sur face deflection, horizontal strain at the bottom of the AC, and the vertical strain on top of the subgrade at the center of the load. your resul ts with those listedresults, from Table 3.2. Compare If you notice a discrepancy in the please notify one of the instructors. Also, calculate the number of repetitions to failure for AC fatigue (Equation 3.25) and subgrade rutting (Equation 3.26) that you would expect in each case. These calculations are the basis of the mechanistic-empirical design approach. Repetitions to failure, combined with traffic (repetitions per year) provides the design life in years. RESULTS MENU FOR ELSYM5 LA YE R
=
1
Z
=
.00
1.
- Str esse s
Norm al
&
She ar
&
Principal
2.
- Strains
Norm al
&
She ar
&
Principal
3.
- Dis pla cem ent s
4.
- Retu rn or Contin ue with Next Layer Selection ==>
Figure 3.35 - Resul ts Menu for ELSYM 5
Displacements XP
YP
.00
UX
.00
UY
.00E+00
UZ
.00E+00
.483E-01
RESULTS MENU FOR ELSYM5 L AY ER
= 1
Z
=
.00
1.
- Stre sses
Norma l
&
She ar
&
Principal
2.
- Strains
Norma l
&
Shea r
&
Principal
3.
- Dis plac eme nts
4.
- Return or Continue
with Nex t Layer
Selection ==>
Figure 3.36 - First Output Location Requested
Nor mal
XP .00
YP
EXX
.00
.00
YP
—
She ar Str ain s
EYY
.467E-03
Principa l XP
Str ain s
EXY
-.572E -03
Strains
PE 1
.00
EZZ
.467E-03
.467E-03
Shear
PE 2
PE 3
.467E-03
LA Y ER
.000E+00
.104E-02
PSE2 .000E+00
FOR ELSYM5
= 1
Z
=
2.00
1.
- Str esses
Normal
£ Sheair Principal
2.
- Strains
Norm alt Shear I Principal
3.
- Disp lac eme nts
4.
- Return or Continue with Next Layer Selection ==>
Figure 3.37 - Second Location Strains
3-103
EYZ .00 0E+0
Strai ns
PSE1
-.572E- 03
RESULTS MENU
EXZ
.000E+00
PSE3 .104E-0
Nor ma l
XP .00
XP .00
YP .00
Str ain s
EXX
Shear Strains
EYY
.970E-03
EZZ
.970E-03
Princi pal — Strains YP PE 1 PE 2 .00
.970E-03
EXY
-.224E -02
EXZ .OOOE+OO
Shear Strai ns PSE1 PSE2
PE 3
.970E-03
.OOOE+OO
-.224E -02
.321E-02
.000E+00
RESULTS MENU F OR ELSYM 5
LA Y ER 1.
= 3
Z
=
8 .0 1
- Stresses
Normali Shear L Principal
2.
- Strains
Normal £ Sheatr Principal
3.
- Dis plac emen ts
4.
- Ret urn or Continue wit h Next Layer Selection ==>
Figure 3.38 - Third Location Strains
3-104
EYZ .000E+0
PSE3 .321E-0
Group No.: 1 Number of Layers: 3 Material Properties: Laver Number
Poisson ’s Ratio
1 2 3
.35 .40 .45
Modulus of Elasticity, psi (MPa) 500,000 25,000 7,500
(3450) (172) (52)
Load Data: Number of Loads: 1 Load: 9,000 lb. (40 kN) Contact Pressure: 80 psi (552 kPa) Results: Table 3.2 Results
Your Results Vertical Defl. @ Surface, in. Section A
___________
0.048 in. (1.219 mm)
Section B
___________
0.027 in. (0.686 mm)
Section C
___________
0.018 in. (0.457 mm)
Horizontal Strain in AC, in/in x 10-6 Reps, to failure Section A
___________
_______
467
Section B
___________
_______
279
Section C
___________
_______
145
Vertical Strain on Subgrade, in/in x 10-6 Section A
___________
_______
Section B
___________
_______
Section C
____________ _________________
3-105
-
2,220
-747 -370
Group No .: 2 Number of Layers: 3 Material Properties: Laver Number
Po isso n’s Ratio
1 2 3
.35 .40 .45
Modulus o f Elasticity, psi (MPa')
500,000 (3450) 25,000 (172) 7,500 (52)
Load Data: Number of Loads: 1 Load: 900 lb. (4 kN) Contact Pressure: 30 psi (207 kPa) Results: Table 3 .2 Results
Your Results Vertical Defl. @ Surface, in. Section A
0.006 in. (0.152 mm)
Section B
0.003 in. (0.076 mm)
Section C
0.002 in. (0.051 mm)
Horizontal Strain in AC, in/in x 10-6
Reps, to failure
Section A
121
Section B
44
Section C
18
Vertical Strain on Subgrade, in/in x 10"6 Section A
-280
Section B
-81
Section C
-40 3-106
Group No.: 3 Number o f Layers : 3 Material Properties: Laver Number
Poisso n’s Ratio
1 2 3
Modulus of Elasticity, psi (MPa) 500,000 (3450) (172) 25,000 (52) 7,500
.35 .40 .45
Load Data: Number of Loads: 1 Load: 9,000 lb. (40 kN) Contact Pressure: 140 psi (965 kPa) Results: Table 3 .2 Results
Your Results Vertical Defl. @ Surface, in. Section A
0.052 in (1.321m m)
Section B
0.028 in. (0.711 mm)
Section C
0.019 in. (0.483 mm)
Horizontal Strain in AC, in/in x 10-6
Reps, to failure
Section A
735
Section B
352
Section C
163
Vertical Strain on Subgrade, in/in x 10-6 Section A
-2,520
Section B
-786
Section C
-384
3-107
Group No .: 4 Number o f Layers: 4 Material Properties:
Laver Number
Poisson’s Ratio
1 2 3 4
Modulus of Elasticity, psi (MPa)
.35 .40 .40 .45
500,000 25,000 50,000 7,500
(172) (345) (52)
Load Data: Number of Loads: 1 Load: 9,000 lb. (40 kN) Contact Pressure: 80 psi (552 kPa) Results: Your Results
Table 3.2 Results
Vertical Defl. @ Surface, in. Section A
___________
0.036 in. (0.914 mm)
Section B
___________
0.023 in. (0.584 mm) 0.016 in. (0.406 mm)
Section C Horizontal Strain in AC, in/in x 10-6
Reps, to failure
Section A
___________
_______
368
Section B
___________
_______
246
Section C
___________
_______
128
Vertical Strain on Subgrade, in/in x 10'6 Section A
___________________________
-957
Section B
___________________________
-437
Section C
-253 3-108
Group No .: 5 Number of Layers: 3 Material Properties: Layer Number
Pois son ’s Ratio
1 2 3
.35 .35 .45
Modulus o f Elasti city, psi (MPa')
500,000 (3450) 500,000 (3450) 7,500 (52)
Load Data: Number of Loads: 1 Load: 9,000 lb. (40 kN) Contact Pressure: 80 psi (552 kPa) Results: Your Results
Table 3.2 Results
Vertical Defl. @ Surface, in. Section A
0.021 in. (0.533 mm)
Section B
0.014 in. (0.356 mm)
Section C
0.012 in. (0.305 mm)
Horizontal Strain in AC, in/in x 10-6
Reps, to failure
Section A
196
Section B
91
Section C
71
Vertical Strain on Subgrade, in/in x 10*6 Section A
-514
Section B
-229
Section C
-177
3-109
Group No.: 6 Number o f Layers: 3 Material Properties: Laver Number
Po isso n’s Ratio
1 2 3
Modulus o f Elasticit y, psi (MPa')
.35 .40 .45
200,000 (1380) 25,000 (172) 7,500 (52)
Load Data: Number of Loads: 1 Load: 9,000 lb. (40 kN) Contact Pressure: 80 psi (552 kPa) Results: Your Results
Table 3.2 Results
Vertical Defl. @ Surface, in. Section A
0.053 in. (1.346 mm)
Section B
0.033 in. (0.838 mm)
Section C
0.024 in. (0.610 mm)
Horizontal Strain in AC, in/in x 10*6
Reps, to failure
Section A
482
Section B
433
Section C
257
Vertical Strain on Subgrade, in/in x 10-6 Section A
-2,580
Section B
-1,030
Section C
-608 3-110
SECTION 3.0 REFERENCES
Hveem, F.N. and Carmany, R.M., "The Factors Un derlying a Rational Design of Pavements," Proceedings. Highway Research Board, 1948. Yoder, E.J., Principles of Pavement Design. 1st Ed., John Wiley & Sons, Inc., New York, 1959. Boussinesq, V.J., "Application des Potentiels a l'etude de l'equilibre, et du mouvement des solides elastiques avec notes sur divers points de physique mathematique et d'analyse," Paris, 1885. (Gauthier-Villars) Burmister, D.M., "The Theory Systems of Stresses Dis placements in Layered andand Applica tions to the Design of Airport Runways," Proceedings. Highway Research Board, Vol. 23, 1943. Yoder, E.J. and Witczak, M.W., Principles of Pave ment Design. 2nd Ed., John Wiley & Sons, New York, 1975. Peattie, K.R., "Stress and Strain Factors for ThreeLayer Elastic Systems," Highway Research Board Bulletin 342. Highway Research Board, 1962. Jones, A., "Tables Highway of StressesResearch in Three-Layer Elastic Systems," Board Bulletin 342. Highway Research Board, 1962. Finn, F.N., et al., "The Use of Distress Prediction Subsystems for the Design of Pavement Structures," Proceedings. 4th International Conference on the Structural Design of Asphalt Pavements, University of Michigan, Ann Arbor, 1977. The Asphalt Institute, Thickness Design — Asphalt Pavements for Highways and Streets. Man ual Series No. 1 (MS-1), College Park, Maryland, September 1981. 3-111
3.10
Classen, A.I.M. and Ditsmarsch, R., "Pavement Evaluation and Overlay Design — The Shell Method," Proceedings. 4th International Conference on the Structural Design of As phalt Pavements, University of Michigan, Ann Arbor, 1977.
3.11
Highway Research Board, "The AASHO Road Test, Report 5, Pavement SpecialNa Re port 6IE, Highway Research," Research Board, tional Academy of Sciences, Washington, D.C., 1962.
3.12
The Asphalt Institute, Asphalt Overlays for Highway and Street Rehabilitation. Manual Series No. 17 (MS-17), The Asphalt Institute, College Park, Maryland, June 1983.
3.13
Mahoney, J.P., Lee, S.W., Jackson, N.C., and New comb, D.E., "Mechanistic Based Overlay Design Procedure for Washington State Flexible Pavements," Research Report WA RD 170.1, Washington State Department of
3.14
Transportation, Olympia, Washington, 1989. Monismith, C.L., and Epps, J.A., "Asphalt Mixture Behavior in Repeated Flexure," Institute of Transportation and Traffic Engineering, Uni versity o f California, Berkeley, 1969.
3.15
Claessen, A.I.M., Edwards, J.M., Sommer, P., and Uge, P., "Asphalt Pavement Design — The Shell Method," Proceedings. Fourth Interna tional Conference on the Structural Design of Asphalt Pavements, University of Michi gan, Ann Arbor, 1977.
3 .16
AASHTO, AASHTO Guide for Design of Pavement Structures. and American Association of State Highway Transportation Officials, Washington, D C., 1986.
3.17
Shook, J.F., Finn, F.N., Witczak, M.W., and Mon ismith, C.L., "Thickness Design of Asphalt Pavements — The Asphalt Institute Method," Proceedings. Fifth International Conference on the Structural Design of As phalt Pavements, The Delft University of Technology, The Netherlands, 1982.
3.18
Ullidtz, P., "Pavement Analysis", Developments in Civil Engineering, Elsevier, 1987.
3-112
de Beer, M., "Developments in the Failure Criteria of the South African Mechanistic Design Procedure for Asphalt Pavements", 7th In ternational Conference on Asphalt Pave ments, Nottingham, U.K., 1992. Valkering, C.P. and Stapel, F.D.R., "The Shell Pavement Design Method on a Personal Computer", 7th International Conference on Asphalt Pavements, Nottingham, U.K., 1992. Portland Cement Association, "Thickness Design for Concrete Highway and street Pavements", PCA, Skokie, IL Ioannides, A. M., Thompson, M. R., and Barenberg, E. J., "Westergaard Solutions Reconsid ered," Transportation Research Record 1043, Transportation Research Board, 1985, pp. 13-22. Foxworthy, P. T. and Darter, M. I., "Preliminary Concepts for FWD Testing and Evaluation of Rigid Airfield Pavements," Transportation Research Record 1070, Transportation Research Board, 1986, pp. 77-88. Ioannides, A. M., Thompson, M. R., and Barenberg, E. J., "Finite Element Analysis of Slabs on Grade Using a Variety of Support Models," Proceedings, 3rd International Conference on Con crete Pavement Design and Rehabili tation, Purdue University, West Lafayette, Indiana, 1985, pp. 309-324. Majidzadeh, K., lives, G.J., and Sklyut, H., "RISC A Mechanistic Method of Rigid Pavement Design," Proceedings, 3rd International Conference on Concrete Pavement Design and Rehabilitation, Purdue University, West Lafayette, Indiana, 1985, pp. 325-339.
3-113
Finn, F., "Factors Involved in the Design of Asphaltic Pavement Surfaces", NCHRP #39, Highway Research Board, 1967. "Calibrated Mechanistic Structural Analysis Proce dures of Pavements", Phase II, Volume 1, Final Report, NCHRP 1-26, University of Illinois—Urbana-Champaign; The Asphalt Institute; Construction Technical Laborato ries, December 1992. Majizadeh, K., "A Mechanistic Approach to Rigid Pavement Design", Chapter Two of "Concrete Pavements", edited by A.F. Stock, 1988.
3-114
SECTION 4.0 NONDESTRUCTIVE TESTING DEVICES
4.1 INTRODUCTION 4.1.1 Types of Dat a Collected The following data are generally collected for pavement evaluation and monitoring purposes. (a)
Roughness (ride)
(b)
Surface distress
(c)
Structural evaluation (surface deflection)
(d)
Skid resistance
Period of 1940s and 1950s During this period highway maintenance personnel relied heavily on visual inspections to establish type, extent, and severity of distress, and on experience or judgment to establish maintenance programs. Unfortunately, experi ence is difficult to transfer from one person to another, and individual decisions made from similar data are often inconsistent. Period of late 1950s and early 1960s During this period the increased use of roughness meters and deflection and skid test equipment permitted objective data to be collected and used both alone and with visual distress surveys to aid in making maintenance and rehabili tation decisions. Period of 1970s and early 1980s During this period highway personnel could no longer rely on the luxury of managing roadways solely on the basis of field personnel experience. Because of limited resources, 4-1
it was essential to develop rapid, objective means to establish: (a)
Projects in need of maintenance or rehabilitation.
(b)
Types of maintenance or rehabilitation techniques currently required.
(c)
Types and schedule of maintenance or rehabilitation to be undertaken in the future to minimize life-cycle costs (construction, maintenance, and user costs) or to maximize the net benefit.
Present At present, three specific applications for pavement con dition data can be identified. (a) Establish priorities Condition data such as ride, distress, skid and deflection are used to identify the projects most in need of maintenance and rehabilitation. Often only ride and/or distress data are used; at other times ride, distress, and deflection data are combined into a single rating. Skid resistance data are often used separately. Once identified, the projects in the worst condition (lowest rating) will be more closely evaluated to determine repair strategies. (b)
Establish maintenance and rehabilitation strategies Data from visual distress surveys are used to de velop an action plan on a year-to-year basis; i.e., which strategy (repairs, surface treatments, overlays, recycling, etc.) is most appropriate for a given pavement condition.
(c)
Predict pavement performance Data, such as ride, skid resistance, distress, or a combined rating, are projected into the future to assist in preparing long-range budgets or to estimate 4- 2
the condition o f the pavements in a network given a fixed budget. 4.1.2 Benefits
(a)
Allocation of maintenance and rehabilitation funds.
(b)
Determination of structural adequacy.
(c)
Indication of highway network pavement condition and performance (city, county, state).
(d)
Measure of "year-to-year" differences in pavement condition and performance.
(e)
Overview of current practices.
4.2 SURFACE DEFLECTION MEASUREMENTS (NDT FOR STRUCTURA L EVALUATION) 4.2.1 Deflection Measurement Uses Surface deflections are a primary indicator of pavement structural response to applied loads. As such they are typically used for: ♦
pavement evaluation
♦♦ ♦ ♦ ♦
overlay or rehabilitation design and overall) load restrictions (both seasonal overload permit procedures pavement management applications evaluation of anomalies (the most common being void detection in PCC pavements)
The following general points can be made about surface deflections: (a)
A tolerable level of deflection is a function of traffic (type and volume) and the pavement structural sec tion. 4-3
(b)
Overlaying a pavement will reduce its deflection. The thickness needed to reduce the deflection to a tolerable level can be established.
(c)
The deflections exhibited by a pavement varies throughout the year depending on the type of pave ment (rigid or flexible), effects of temperature and moisture changes (including frost and thaw effects). For a flexible pavement structure, the magnitude of surface deflections increases with an increase in the temperatu re of the bituminous surfacing mat erial (due to decreasing stiffness of bituminous binder with increasing temperature).
4.2.2 Categories o f Nondestructive Testing Equipment (a)
Static or slow moving load deflection devices
(b)
Steady state deflection (vibratory) devices
(c)
Impact load deflection devices (FWD) The usage o f static, steady state, and impact NDT equipment by the 50 state highway agencies (SHAs) in the U.S. is shown in Table 4.1. Table 4.1. SHA Deflection Equipment [after Ref. 4.41
Device Benkelman Beam
Number of SHAs Using Device for Various Time Periods mid-1990s 1990 mid-1980s (estimated) 18 3 4
Dynaflect Road Rater FWD
18
11
5
4 5
5 30
4- 4
11 31
4.2 .3
Typica l ND T Patterns
This will vary with intended application of the data and authority for whom data is being collected. For the most part, the current approach is to test primarily in wheel paths since the pavement response at these locations reflect the effect of damage that has been accumulated. In some cases, specific undamaged locations are tested for calibrating the damage equations using historical traffic data. Testing at the project level often involves deflection measurements in all traffic lanes, although it is usual to use higher test densities in the more heavily trafficked lanes (usually the outer lanes). Tests are usually uni formly spaced at 15m (50') to 60m (200') intervals, depending on project length and the expected uniformity of the section. Test locations are often staggered between lanes to provide improved statistical coverage. A mini mum of 7 to 8 test locations per uniform section is desir able for statistical purposes. Multiple load level applica tion at each location allows evaluation of non-linear material response. At the network level test spacing may be on the order of 150 m (500') to 450 m (1,500') in one lane only; but again some thought should be given to sec tion uniformity and statistical coverage. For research applications, test spacing may be as low as 1.5 m (5 ft.) and more load applications may be used. SHRP uses 50 ft. spacing on its LTPP section, and applies 23 loads of which 16 are recorded. For jointed PCC pavements, test spacing may be similar, but each location (slab) may also involve joint and comer testing. On highway pavements, if only one side of a transverse joint is tested the load should be located on the leave slab since this is the side where loss of support is likely to occur. Typical production test rates using an FWD or HWD is about 30 locations an hour, if 3 or 4 test loads are applied at each location. Research oriented testing approaches should be based on the research objec tives. Generally speaking, acquisition of deflection data using an FWD is relatively inexpensive and it is probably better to perform more than the minimum number of tests once the NDT equipment has been mobilized than to have to return for additional data.
4-5
4.3 STATIC OR SLOW MOVI NG DEFLECTI ON EQUIPMENT Static or plate slow bearing moving tests deflection equipmentBeam. includes as wellmeasuring as the Benkelman This equipment provides deflection measurement s at one point under a non-movi ng or slow-moving load. Plate bearing tests are too time consuming and labor intensive for use in modern NDT testing but are covered here for sake of completeness. 4.3.1 Benkelman Beam (a)
Most widely used device (developed at WASHO Road Test — 1952). However, its use has declined in recent years in technologically advanced areas.
(b)
Operates on a lever arm principle (refer to Figure 4.1).
(c)
Must be used with a loaded truck or aircraft. Truck weight normally used is 80 kN (18,000 lb.) on a single axle with dual tires inflated to 0.48 to 0.55 MPa (70 to 80 psi).
(d)
Measureme nts made by placing tip of beam between dual tires and measuring deflection as the vehicle (truck) is moved away. Measurements made with a dial gage.
(e)
Standard Test Methods (i)
Asphalt Institute procedure [4.3] requires placement o f tip o f beam between dual tires even with the centerlin e o f the rear axle prior to movement o f the vehicle.
(ii)
AASHTO T 256-77 (Pavement Deflection Measurements) requires that the tip of the beam be placed between the dual tires 1.4 m (4.5 ft) forward of the rear axle prior to movement of the vehicle. 4- 6
‘s u r ^ ., .s .
,Ch" B r ic c o
°"'p°"'nnorB
enk^ B ean
4- 7
(iii) ASTM D4695-8 7 (Standard Guide for General Pavement Deflection Measurements) recom mends that the standard load for Benkelman Beam 80 xkN572 ( 18,000 lb.) onx a singlemeasurements axle with dualbe279 mm (11.00 22.5 in.) 12-ply tires inflated to 0.48 MPa (70 psi). Pavement deflecti on to be measured with a dial gage or LVDT to within 0.025 mm (0.001 in.). (e)
WASHO measurement involved load moving to wards deflection beam.
(f)
Manufactured by: Soiltest Inc. Materials Testing Division 2205 Lee Street Evanston, Illinois 60202
4.3.2
Plate Bearing Test (a)
(b)
Standard test methods (i)
AASHTO T222-81 (Nonrepetitive Static Plate Load for Soils and Flexible Pavement Compo nents, for Use in Evaluation and Design of Airport and Highway Pavements)
(ii)
ASTM D 1196-77 (same title as AASHTO T222)
Uses (i)
To determine modulus of subgrade reaction (k value).
(ii)
Typical uses of static (or near static) pavement surface deflections.
(iii) Asphalt Institute: overlay design and/or determination of remaining life. (iv) California DO T: overlay design.
4-8
4.3.3 Automated Beams [4.3] Various approaches have been developed to automate Benkelman beam measurements, typically bythe mounting the deflection beams on the truck that provides axle load. These move slowly (2 to 4 km/hr or approx. 1 to 2 mph) and measure deflections at 3.5 to 6 m (approx. 10 to 20 ft.) spacing in one or both wheel paths. The most com mon o f these is the La Croix Deflectograph, manufactured in Switzerland. The British Transport and Road Research Laboratory (TRRL) uses the Pavement Deflection Data Logging (PDDL) machine which is a modified version of the La Croix. CalTrans used the California Traveling Deflectometer, but this was never commercially produced and is no longer in service. 4.3.4 Curvature Meters [4.3] This is a simple portable device consisting of a long bar supported at each end with a dial gauge in the middle. It is used to estimate the curvature of the pavement surface caused by an applied wheel load from a measure of the middle ordinate for a fixed chord length of 0.3 m (1 ft.). 4.3.5 Typical Applications (a)
Structural adequacy and overlays to reduce deflec tion levels [4 .3],
(b) (c)
Network level relative structural response. Deflection basin evaluation (some cases).
4.3.6 Advantages/Disadva ntages of Static or Slow Moving Load Deflection Equipment (a)
Advantages (i)
Widely used and hence numerous analysis pro cedures available to use with such data
(ii)
Simplicity (deflection beam, plate load)
4-9
(iii) Instrument cost low (about $1,000 for Benkelman Beam) (iv) High coverage (automated beams) (V)
Move with traffic (automated beams)
(vi) Realistic load levels possible Disadvantages (0
Slow, requires traffic control
(ii)
Labor intensive
(iii) Typically does not provide deflection basin (iv) Fixed reference necessary (V) Load duration may be unrealistic (vi) Measurement may depend on technique (rebound vs. WASHO) (vii) High cost (automated beams) (viii) Repeatability is poor in comparison to more modern methods.
4.4 DYNAMIC VIBRATORY LOAD (STEADY STATE DEFLECTIONS) 4.4.1 General (a)
Several types of steady state deflection equipment are available. Primarily these include: (i)
Dynaflect (electro-mechanical)
(ii)
Road Rater (electro-hydraulic)
(iii) WES Heavy Vibrator 4-10
(iv) FHWA Cox Van
(b)
Equipment induces a steady state (non changing) vibration erator. to the pavement with a dynamic force gen
(c)
Pavement deflections measured with velocity trans ducers.
4.4.2 Dynaflect (a)
(b)
Standard test methods (i)
AASHTO T256-77
(ii)
ASTM D4695-87
Manufactured by: Geolog Inc. 103 Industrial Boulevard Granbury, Texas
(c)
Mounted on a two wheel trailer.
(d)
Dynaflect is stationary when measurements are taken. Force generator (counter rotating weights) started and deflection sensors (velocity transducers) lowered to the pavement surface. Refer to Figur e 4.2 (plot o f typical force output) and Figu re 4.3 (location of Dynaflect loading wheels and five ve locity transducers). The peak-to-peak dynamic force is 4.4 kN (1,000 lb.) at a fixed frequency of 8 Hz. This load is applied through two 102 mm (4 inch) wide, 406 mm (16 inch) diameter rubbercoated steel wheels which are placed 508 mm (20 inches) apart.
4-11
T N E M E V A P N O D E T R E X E E C R O F
TIME
Figure 4.2. Typical Force Output of Steady State Dynamic Deflection Devices (4.2] 4-12
4 in.
4 in. 10 in.
12 in.
12 in.
12 in. 10 in.
4 in. Loading Wheel Contact Area
4 in. •
Geophone (Defl ection Sensor)
Figure 4.3 - Standard Location of Dynaflect Loading Wheels and Geophones [4.21
4-13
12 in.
(e)
Disadvantages (i)
Requires traffic control.
(ii)
Dynamic load significantly less than normal truck traffic.
(iii) Relatively large static preload (816 kg (1800 lb.)). (iv) Pavement resonance may affect measurements. (v) (f)
Relatively small load may not produce ade quate deflections on heavy pavements.
Advantages (i)
High reliability (low maintenance)
(ii)
Can be used to obtain a deflection basin.
4.4.3 Road Rater (a)
(b)
Standard test methods (i)
AASHTO T256-77 (for Model 400 only)
(ii)
ASTM D4695-87
Manufactured by: Foundation Mechanics, Inc. 421 East El Segundo Boulevard El Segundo, California 90245
(c)
Two production models available as of November 1991: (i)
Model 400 B-l
(ii)
Model 2000 A-1
4-14
(d)
Force generator con sists of a steel mass, hydraulic actuated vibrator. Driving frequencies range between 5 and 60 Hz. Load ranges for various models: (i) Model 400 B: 2.2 to 13.3 kN (500 to 3,000 lb.) (ii)
Model 2000: lb.)
2.2 to 22.2 kN (500 to 5,000
The loading footprints for the two models are shown in (due to differences, one must be CAREFUL in comparing data between the models).
Figu re 4. 4
(e)
Deflections are measured with four velocity trans
(f)
ducers. Disadvantages (i)
Requires traffic control
(ii)
Low load level relative to truck traffic (Models 400 B and 2000).
(iii) Relatively large static preload required [4.2] (iv) Pavement resonance may affect measurements. (g)
Advantage (i)
Can measure deflection basin.
(ii)
Widely used - performance history correlation data widely available
(iii) Reliable
4-15
ROAD RATER MODEL 400B 3.5 in .
12 in.
12 in.
•
12 in.
Geophone
12 in.
(De flection
Sensor)
ROAD RATER MODEL
2000
12 i n.
12 in .
12 in .
12 i n.
Loading Wheel Contact Area f
Geophone
(Deflec tion Sens or)
Figure 4.4 - Standard Location of Loading Plate( s) and Geophones for the Road Rater Model 400B and Model 2000 [4.21
4-16
4.4.4 WES Heavy Vibrator [4.2] This was developed by the Corps of Engineers for airfield pavement evaluation. A 71 kN (16 kip) preload is ap plied, with a peak-to-peak vibratory load of 130 kN (30 kip) possible at a frequency o f 15 Hz. It is a large unit mounted in a semi-trailer and is not commercially available. (a)
Advantages (i)
Load variable up to 30,000 lb. peak-to-peak.
(ii)
Load frequency variable from 5 to 100 Hz.
(iii) Can be used on heavy pavements. (b) Disadvantages (i)
Mounted in 36' trailer.
(i)
Not commercially available.
4.4.5 FHWA Cox Van (Thumper) [4.2] This is an experimental device developed for FHWA that can apply static, dynamic or intermittent pulse loading. The Thumper is a research oriented device designed to emulate the characteristics of other dev ices. Load magni tudes of up to 45 kN (10 kips) are possible at frequencies ranging from .1 to 110 Hz. Deflections are measured using 6 LVDTs spaced at 0, 300, 460, 600, 910, and 1200 mm (0, 12, 18, 24, 36, and 48 in.). (a)
Advantages (i)
Can emulate most deflection devices
(ii)
Can apply a variable load at multiple frequencies.
(iii) Multi-frequency loading.
4-17
(b) Disadvantages (i)
Not commercially available.
4.4.6 Typical Uses of Steady State Pavement Surface Deflections (a)
Correlation with static deflections (Benkelman Beam).
(b)
Estimation of layer elastic modulus values.
(c)
Overlay design and/or determination of remaining life.
4.5 IMPACT (IMPULSE) LOAD RESPON SE DEVICES 4.5.1 General (a)
All impact load NDT devices deliver a transient im pulse load to the pavement surface. The subsequent pavement response (deflection) is measured.
(b)
Standard test methods (i)
ASTM 4694-87: Standard Test Method for Deflections with a Falling Weight Type Impulse Load Device
(ii)
Related test method ASTM D4695-87: Standard Guide for Gen eral Pavement Deflection Measurement
(iii) Significant features of ASTM D4694 ♦
Falling Weight ("force-generating device") ♦
Force pulse will approximate a haversine or half-sine wave 4-18
♦
Peak force at least 11,000 lb. (50 kN)
♦
Force-pulse within rangeduration of 20 to should 60 ms. be Rise time in range of 10 to 30 ms. Loading plates Standard sizes are 12 in. (300 mm) and 18 in. (450 mm) Deflection sensors Can be seismometers, velocity trans ducers, or accelerometers. Used to measure thepavement. maximum vertical move ment of the Signal conditioning and recorder sys tem
♦
Load measurements Accurate to at least ± 2 percent or ± 160 N (± 36 lb.), whichever is greater.
♦
Deflection measurements Accurate to at least ± 2 percent or ± 2\xm (± 0.08 mils), whichever is greater. Recall that 0.00008 inch = 0.08 mils and 0.002 mm = 2\im. Precision and bias
♦
Precision guide When a device is operated by a single operator in repetitive tests at the same location, the test results are questionable if the difference in 4-19
the measured center deflection (Do) between two consecutive tests at the same drop height (or force level) is greater than 5 per cent. For example, if Do = 0.254 mm (10 mils) then the next load must result in a Do range less than 0.241 mm to 0.267 mm (9.5 to 10.5 mils). (c)
Measurements obtained very rapidly.
(d)
Impact load easily varied.
(e)
Pavement responses are measured with geophones or velocity transduce rs (Dynatest, Phonix, Foundation Mechanics)combination and seismometers or LVDT/acc elerometer (KUAB).
(f)
The primary impact deflection equipment currently marketed in the U.S. include: (i)
Dynatest Dynatest Consulting Ojai, California U.S.A.
(ii)
KUAB KUAB Konsult and Utveckling AB Box 10 79500 Rittvik, Sweden
KUAB America 1401 Regency Drive East Savoy, Illinois 61874 U.S.A.
(iii) Foundation Mechanics, Inc. (Jils) 421 East El Segundo Boulevard El Segundo, California 90245 (iv) Resource International (Phonix) 281 Enterprise Drive Westerville, OH 43081
4-20
4.5 .2 Dynatest Falli ng Weight Deflectom eter (FWD)
(a)
Two models are primarily available—Dynatest Model 8000 (FWD) and Model 8081 (HWD).
(b)
Most widely used FWD in U.S. (as of 1993)
(c)
FWD is trailer mounted.
(d)
By use of different drop weights and heights can vary the impulse load to the pavement structure from about 6.7 to 120 kN (1,500 to 27,000 lb.). The weights are dropped onto a rubber buffer sys tem resulting in a load pulse of 0.025 to 0.030 sec onds (refer to Figur e 4.5). The standard load plate has an 300 mm (11.8 in.) diameter. A heavy weight version (HWD) with lb.) a load range of about 20 to 240 kN (6,000 to 54,000 is available.
(e)
Typical location of the loading plate and seven ve locity transducers is shown in Figu re 4.6. Ideally, transducers should be located to ensure that the positions are reasonable relative to the pavement structure being tested. The WSDOT sensor spacings with the 300 mm (11.8 in.) load plate are: mm
inches
0 8 12 24 36 48
2030 305 610 914 1,219
4-21
(Tim e f rom A to B is
TIME Variable, Dependi
ng on Drop Height)
A - Time at which weights are released B - Time at which weight package make first contact load plate C - Peak load reached
Figure 4.5 - Typical Force Output of Falling Weight Deflectometer
4-22
12 in.
H ------------------►
Loading Wheel Contact Area #
Sensor
Figure 4.6 - Typ ical Location o f Load ing Plate and Deflections Sensors for Falling Weight Deflectometers
4-23
The Strategic Highway Research Program (SHRP) sensor spacings with the 300 mm (11.8 in.) load plate are: mm0
inches 0
203 305 457 610 914 1,524
8 12 18 24 36 60
Texas sensor spacings with the 300 mm (11.8 in.) plate are:
(f)
m m0
in c h e0s
305 610 914 1219 1524 1829
12 24 36 48 60 72
SHRP FWD's T4.10. 4.111: Dynatest Model 8000E (i)
Loading plate: 300 mm (11.8 in.)
(ii)
Loads (flexible pavements): Drops result in loads o f approximately 27 kN (6,000 lb.), 40 kN (9,000 lb.), 53 kN (12,000 lb.), and 71 kN (16,000 lb.).
(iii) Maximum deflections recorded at each sensor for all four drops. A complete time — load and time — deflection "history" is recorded for the last drop at each of the four load levels.
4-24
(iv) SHRP Regional LTPP contractors use two computer programs to che ck FWD data [from Ref 4.101: ♦
FWDSCAN: checks FWD data files for completeness and readability.
♦
FWDCHECK: checks for section uni formity based on subgrade and pavement strength.
4.5.3 KUAB Falling Weight Deflectometer [4.5. 4.6. 4.9] (a)
Model 50 Load range: 7 to 65 kN (1,500 to 15,000 lbs.)
(b)
Model 150 Load range: 14 to 150 kN (3,000 to 34,000 lbs.)
(c)
Total of five models are available (as of 1991). The heaviest load model has a range of 14 to 290 kN (3,000 to 66,000 lbs ).
(d)
KUAB models are completely enclosed for prote c tion during towing. The impulse force is the result of a unique two-mass system. The deflection sensors are called seismometers and use LVDTs along with a mass-spring reference system (standard KUAB FWD equipped with seven deflection sensors). Each sensor has micrometer making static field calibra tions possible. The seismometers have three ranges: low (0-50 mils), medium (0-100 mils), and high (0200 mils).
(e)
Worldwide distribution of the KUAB FWD began in 1976 and subsequently over 60 units have been sold (as of 1991) [after Ref. 4.9~|.
(f)
The basic weight of a KUAB FWD and associated trailer is about 1,800 kg (4,000 lb.). A load of about 4-25
320 kg (700 lb.) is applied to the pavement by the loading plate prior to testing [4.9], (g)
An srcinal of thequarter KUAB- FWD the seg mented loadfeature plate (four circle is segments). This provides a more uniform pressure distribution to the pavement surface [4.9],
(h)
Accuracy and precision of KUAB 50 (based on KUAB product literature mostly from Ref. 4.9) (i)
(ii)
Accuracy ♦
Deflection sensors: ± 2 ^m (0.08 mils), ± 2 percent
♦
Load cell: ± 20 kg (± 44 lb.), ± 2 percent
Precision ♦
Deflection sensors: ± 1 ^m (± 0.04 mils), ± 1 percent
♦
Load cell: ± 10 kg (± 22 lb.), ± 1 percent
(iii) Range ♦
Deflection sensors range 0-5 .0 8 mm (0 - 200 mils)
4.5.4 Foundation Mechanics Falling Weight Deflectorneter [4J2] (a)
Current model is the JILS-20-FWD.
(b)
As of November 1991, three of these models have been in service for two years.
(c)
Uses seven velocity transducers to measure the deflection basin (location of sensors is variable). Load is measured with a transducer. 4-26
(d)
Load range: Approximately 7 to 107 kN (1,500 to 24,000 lbs.)
(e)
JILS-FWD mounted (tandem trailer) and includesisatrailer 16 horsepower gasoline axle engine to provide all necessary hydraulic and electrical power for operation. The gross weight of the unit is about 1,300 kg (2,800 lbs.). The FWD unit can be en closed with an available cover.
4.5.5 PhonixFWD [45, 4T3] (a)
Current models are ML6, ML11 and ML25.
(b)
As of 1992, it is estimated that there are three Phonix FWD's in the USA.
(c)
Six geophon es are used for deflection measure ments, with variable locations. Load is measured with a load cell.
(d)
Load range is approximately 10 kN to 110 kN (2.2 24.7 kips) for the ML 11.
(e)
The Phonix units are trailer-mounted and independ ent trailer pow er source is optional.
4.5.6 SASW Approaches Spectral analysis of surface waves (SASW) approaches evaluate pavements from Rayleigh wave measurements involving low strain levels. Until very recently, both data acquisition and analysis was cumbersome and time con suming. Recent equipment and software development under the SHRP-IDEA program appears to have made significant advances in the application of SASW tech niques [4.14], A brie f description of the SASW proce dures has been included as Appendix E at the end of the participant workbook. SASW is of potential interest to the highway engineer for a number of reasons: 4-27
♦
It can provide information to determine the ap proximate thickness of individual pavement layers without coring.
♦
It can provide a starting point for estimating modu li, and modular ratios of the pavement layers during the backcalculation process.
♦
It can detect rigid layers and provide an estimate of depth.
♦
It can more accurately determine & quantify modular values of thin ACP layers on the surface, as compared to the FWD.
SASW is a natural complement to the FWD. It cannot replace the FWD however, as it cannot predict moduli of paving layers under traffic loads, as most materials behave in a non-linear fashion. 4.5.7 Typical Uses of Impulse Pavement Surface Deflection (a)
Estimation of layer elastic moduli
(b)
Overlay design and/or determination of remaining life
(c)
Net work level monitoring
(d) Correlation with static deflections 4.5.8 Advantages and Disadvantages of Impulse Load Equipment (a)
Advantages 0)
Gaining worldwide use
(ii)
Best simulates actual wheel loads
(iii) Can measure deflection basin (iv) Relatively fast data acquisition 4-28
(v)
(c)
Only a small preload is placed upon the pave ment surface
(vi) No fixed reference required Disadvantages (i)
High initial cost
(ii)
Traffic control required
(iii) Relatively complex system
4.6 COMPARISON S AND CORRELATIONS BETWEEN FWD AND OTHER DEVICES 4.6.1 Introduction Numerous comparisons between deflection devices have been made and published to date, using various approaches and evaluation criteria [References 4,2 and 4^5 are examples]. It does seem, however, that the calibration center approach adopted by SHRP will become essentially an absolute reference standard by which the impulse load equipment will be evaluated. Four SHRP regional cali bration centers have been established, operated by State DOT personnel at each location. Some of the published comparison data has been included in this section. Corre lations between FWD deflections and those measured by other devices have also been included. It should be em phasized that such correlations may be misleading and should be used with care. Generally speaking, a
correlation equation between different devices is techni cally valid only for the specific location for which it was developed a t the time o f dev elopm ent, due to the effects of temperature, moisture, load-level, time-of-loading, material non-linearity, etc. From a practical standpoint, however, there may be situations where there are no alternatives but to rely on correlation equations.
4-29
4.6.2
Compari sons Betwee n Devices
4.6.2.1
Comparisons Between KUAB 150 and Dynatest 8000 (KUAB Literature) a) Refer to Table 4.2 for a comparison of model specifications. b)
Refer to Figu re 4.7 for a comparison of the falling weight systems for the KUAB and Dynatest models.
Table 4.2 - Equipm ent S pecifications [afte r Ref. 4 .61 KUAB Load Range Load rise time Load uration Load generator Load plate
Deflection sensor s
Deflection sensor positions Number of sensors Deflection sensor range Deflection resol ution Relative accuracy Test sequence Test time sequence (4 loads) Computer
DYNATEST
P H Ö N IX
J IL S
7 - 1 5 0kN 7 - 1 2 5k N 10 -2 5 0kN 8 -1 0 7k N 28 ms Variable 12-15ms selectable 56ms 2 5 -3 0ms 2 5 - 3 0ms selectable T w o -m a sss ystem O n e - m a s s s y s te m O n e - m a s s s y s te m O ne-m ass system S e g m e n t e d or n o n s e g Rigid with rubberized pad Segmented with rubber Rigid with mented wi th rubberized or split plate, tilts 6" (300 pads (300 mm) rubberized pad pads (300 & 450 mm & 450 mm diameter) (300 & 400 mm diameter) diameter) Seismometer with static Geophones with or G eo ph o ne s G e o p ho n e s field calibration device without dynamic cali 0-1.8 m
bration 0-2.25 mdevice
7 ( all a vaila ble positions) 5 m m ( 2 0 0 m i ls )
nU tionpe
2 mm (80 m ils) or 2 .5 mm (100 mils) 1(im(0 .0 4m ils) Same 2nm±2% Same Unlimited, user selected < 64 drops 35 secs. 25secs.
HP 85B or IBM compatible, MS DOS
4-30
Same
0 - 2 .5m 9to6
0 - 2 .4m 7
2 mm (80 mils)
2 mm (80 mils)
1m icron 2 microns ±2% User selected 2 0sec.(perdrop)
1m icron 2 microns ± 2% User select ed 30 secs.
IB Mcom patib le
IBM compatible
Figure 4 .7
Sketches of D ynatest and KUAB Falling Mass Systems [from R ef. 4 .6 )
4-31
4.6 .2.2
Selected comparisons for seven NDT devices [after Ref. 4.5] The U.S. Army Corps of(WES) Engineers, Experiment Station in Waterways Vicksburg, Mississippi, evaluated the following NDT devices: □ □ □ □ □ □ □
KUAB Model 50 FWD Dynatest 8000 FWD Dynatest HWD (Heavy Weight Deflectometer) Phonix FWD Dynaflect Road Rater 2008 WES 16 kip vibrator
The basic equipment characteristics are shown in
Table 4.3
Selected results from this evaluation include: (i)
Measured deflections on a short-term repeatability experiment based on 25 tests (measurements) on AC and PCC surfaced pavements: Figure 4.8.
(ii) Comparison of output of a "standard" load cell and each device in terms of absolute sum of percent difference:Figure 4.9. (iii) Plots of typical load pulses for the FWD's evaluated: Figure 4.10.
4-32
Tab ic 4 .3
ND T Device Characteristics (WES Evaluati on) [from R ef .4« 5|
Number and Type of Deflection
Dynamic Force Rin gt. Ib P
Load Transmit ted
by
Senvon
Kuab FWD
3000 to >5 000
7 tei smom eten
Dynatest HWD
10 000 to 55 000
Scctior.jlucd circular plate 11 8 in ‘ dn Circular plate 118 or 17.7 ¡a. dia Two 16-in dia by
Device Name
Dynaflect
1000 peak to peak
Dynales t FW D Road Rater 2006
WES 16-Kip Pho nLx FW D
1500 to 27 000 500 to 7000 peak to peak 500 to 30 000 peak to peak 2300 to 23 000
• 1 Ibf - 4 448 N. * 1 in. » 2.54 cm.
4-33
2urethanein width coated steel wheels Circular plate II 8 or 17.7 in. dia Circular plate 18 in. dia Circular plate 18 in. dia Circular plate 118 in. dii
7 le ophon ei
Deflection Sensor Spacinj Fixed at 0.8.12.18. ' 24,36.48 in. Variable, 12 to 96
in. 5 jeophone»
Variable, 0 to 48
in.
7 jeophone«
Variable, 12 to 96
in. 4 je o p h o n e*
Variable, 24 to 48
5 jeophone«
Vanable. 12 to 60
6 jeophonet
Variable. 58 in
io. in. 8. 3 lo
SHORT TERM REPEATABILITY
n it o a i r a v f o t n e i c i f f e o c
ESI 00
E 2
Di
CZ Z 02
DEVICE E S 03 CZ 3 04
C~7ì DJ
I-----1 DO
SHORT TERM REPEATABILITY
x .
n io t a i r a v
ro t n e i ic f f e o c
DEVICE a
DO
E 2 DI
EZ3 02
E 3 03
E 2 04
EH2 0 5
I
I os
Figure 4 . 8 Coeff icien t of Variation of Deflections from Short-term Repeatability Experiment (WES) [fromRef. 4 .5 ]
4-34
LOAD RECORDING ACCURACY ABSOLUTE SUM
OF PERCEhf
T DIF FER ENCE
T N E C R E P
DEVICE k —i
sk
cv a 7 *
rm
iok
ijk
t\ / i
20/21«
r 7~i
»ok
Fig ure 4 . 9 Averag e Absolute Sura of Percent Differen ce from Load Measurement Accuracy Exp eriment (WES) [from Ref. 4 . 5 ]
4-35
KUAB F
DYK
W D
ATEST
HWD
7lMt. m*fc
DYN
ATES
T FW
TIKE.
D
P H ON IX
F WD
TIME, mse
c
Figure 4.10 - Typical FWD Load Pulse Plots (WES) [from Ref. 4.51
4-36
Measured loading times for the load cell (standard) experiment performed by WES:
Device
Loading Time
(ms) KUABFWD
79.8
Dynatest FWD
30.4
Dynatest HWD PhonixFWD
28.1 40.7
Loading times are important in explaining differ ences in backcalculated moduli, particularly for visco-elastic materials such as asphalt concrete. Shorter loading times result in higher backcalcu lated moduli for AC (as evidenced by the Asphalt Institute equation (Equation 2.4)). This would help explain observed differences in deflections obtained with the various FWD types available. 4.6 .2.3
More comparisons between deflection measuring equipment [after Ref. 4.7] (a)
Operating characteristics of nondestructive equipment (refer to Table 4.4)
(b) First costs and operating costs of nonde structive equipment (refer to Table 4.5) 4.6.3 Correlations between deflection measuring equipment 4.6.3.1
Introduction In general, correlations between deflection de vices should be used with caution. Too often, a correlation is developed for a specific set of conditions that may not exist at the time the cor relation equation is used. It appears that the best approach is to obtain pavement parameters (such as layer moduli) from the specific NDT device being used. However, that said, a few of many such correlations that have been developed fol low.
4-37
Table 4.4 - Operating Characteristics of N o n d e s t r u c t i v e E q u i p m e n t [4 . 7 ] . ( N o t e : Info rmat ion was Pub lish ed in 19 86 .)
Data Point« per Day Ajmey Average Range Benkelman Beam
Lant Miles of Pavement per Day Range Average
kaho fi 11not* Louisiana VIchlgan MIssourl He« Jersey Ne» York Ov lahoma Of fon South Carolina Te«as Summary
40 >0- ->40«0 40 10 >00 Ito • so s so 4 400 1 >0 - so 10 1 1(0 1)0 • >IS >0 ISO )>S - 17S % >00 ISO - >00 • 10 40-100 1 so 40- 10 10 us >0->00 Dyna fleet - Network Maniement System 41 Arkansas ISO - >so 17S SO kJiho to to - no Hebruka 10 1« to - 100 Oregon s South Dakota 41 400- SS- SS0 49 10 Utah 4S0 >S Summary 140 40 - SS0 .•0 Dynafleet * Project Management System Aritona 4S >s- ss IS Arkansas 41 17S ISO - >so California • >S2 47 - 420 Kansas >4 no to - ISO Nebraska 10 10 10 - 100 Nevada 4S0 IS South Dakota 41 49 40 - SS Te«as >10 4 170 - >S0 Utah 4S0 *0 >50 - SS0 Virginia >71 S7- »2 IS Summary >00 ss >S - SSO Road Rater Illinois Kentucky Louisiana Maryland Pennsylvania Summary
17S 400 >10 >00 no »0 Fa1Hnj-We!|hl Deflectometer Alaska ISO Arliona 3S Florida 410 Tennessee ISO Washington ISO Sum mary 110
ISO - >00 ISO - 300 ISO • >00
100 • >50 100 - >50
4-38
s 40 70 10 10 ss so 11 •. 75 SS IS »
Th i s
Utilization Data Points Equipment (Days per Year) per Lana Mila Average Range
>0S - 1« to
I.7S >0 1t I.7S I.7S -
>01 s 10 100 so ISI s S3 10 St SS
1.7S 40 10 10 1.7S 10
35- 10
) s I
>0ts-
to-100 40 -SS - 110 70 >0 - 110 10 - >0 35 - 10 1 ->0 10 - 30 to - 100
1
%
1
>-
7
I - IS S - 70
s 1 30 1 >6 » 11 • SS 10 9 IS 11 11
70 40 4S 1(0 7S 71
%
SO•40 10- >0 It- 40
10 s
100 100 ISO no 9S 110 no 30 100 170 no iso no 95 100 110 13 no
>1
40 - SS 3- S 70 - 110 1 - >0 1 * no
3 3
tS 10 40 10 10 30 no ISO IS 10 37
3 2(0 1
ISO >0 100 130 too to
1 - >0 T 11 J - IS >0 - SO 10 • 150 US - I7S 10- >0 1 • us
to - 140 100 - >00 to - 100 to - >00 IS - 40 to - 140 0 - 360 it • no 100 - >00 90 - 100 to - no 4S - 14 IS - >00 SS - 10S to - >00 33 - >00
Table 4.5. First Costs an d Operating Costs of Nondestructive Equipment [4.71 (Note: This information was Published in 1986) Operating Agmey
Aver ag e
Coilt ( t)
Operatlnf Personnel Required
Per Lane Mile of Pavement
Par Cala Point
Range
Avenge
Range
Purchase Price (S)
Brnk tlrr in Bet m ld*ho DlmoU Loulllina V itiourl He« York Oklihoma Oregon S o u t h Car o lin a T titi Summary
10.00 >1.00
10.00 I.SS 4.17 1.50 1.00 >.31
>.10 4.00 >.00 >.00
1.00
•
• > 1 T
IS.00
ISO.00 i.oo >.1S a . io >.00 •
i.eo 1.10
4.>o ».00
1 . 0 0• 1 . 0 0 1.00
-
1.00
Dynafleet * Network Mintjement Syilem Ark ia u i 1.14 1.30 >.50 kuho n.oo 10.00 - >0.00 Oregon 110.00 South Dakota 1.» •.00 - «.so Utah 1.» 1.1» - 1.1» Summary >.11 1 . 1 » - >0.00
1.00
11.10 10.00 100.00 IS.00
».SI
110.00
>.00 1.00 I I . I S - 11 . 30 •4.00 - >20.00
1
• • 9 1
IS.00 - ys.oo >.00
-
«
>70.00
> .I S- « . > 0
9 I
•0.00 - 130.00
•
.IS l.ts
1.00 1.1»
4.14
1.1» - ISO.00
>
M l 1 .1 0 11.13 - >47.00
9 9 >
-
>00 • 1,000
0.so 1.3»
s
9 >0,000 - >3,000
Dynafleel - Project Management Syitem Arizona Arkanm California Kinid Hevada So uthDakota Ten* Utah Virginia
>0.00 1.14 1.1» 1S .00 • .7 1 • IS 1.00 1.00
e.io l.ts •.10 -
Summary
».)•
•.71 - 11.00
>1.11
1 .» > .71 • .00
1.10
-
>.00
S3.11 11.00
43.0 0 -
(3.0 0
9 9
».II
1.10
-
1.00
»4.07
11.11
11.00
9
t.oo
t.oo
>s.oo
>.00 ».10
TS .00 11.00 »4.00
10.00 - 14.00 >1.00 - 111.00
9 9 9 9
1.1»
1.50 - ».»0 •.IS - ».s o 10.00 - 11.00 •.S I - 1. 17 •.00 1.50 i.40 l.)S 1.00
10.00 ».SI II.IS TS.00 » .» I.1S »0.00 1.1S 17.30
1
17.41 - >4.11 •.00 «.30 >0.00 11.00 1.13 - 1 . 13 10.00 -
13.00
1.1» - X7.00
9 9 9 9 I 9
>0,000 - >3,000
Road Rtter lo«a M irylind Pennsylvania Summary
4
11.11
-
>3,000 - >3,000
Falllng-Wetght Deflettometer Alt ska Arizona Tmnene« W» jhlng lon Summary
>.00 >.7S
>.S0 >.>4 -
• .4)
1.00 - >S.00
4-39
>7.SO
T.oo -
i i i .oo
9
90,000 - 111,000
4.6 .3.2 Benkelman Beam to Falling Weight Deflectometer (based on unpublished data collected by WSDOT Materials Laboratory in 1982-1983) BB
1.33269 + 0.93748 (FWD)
(Eq. 4.1)
0.86
Std Error
= 3.20 mils
Sample Size = 713 matched deflection points where
4.6 3.3
BB
= Benkelman Beam _3 deflection (in. x1 0 ),
FWD
= FWp deflection (in. x 1 0 ' ) corrected to a 9,000 lb. load applied on a 11.8 inch diameter plate
Benkelman Beam to Dynaflect (a)
Arizona [after Reference 4.2]
where
BB
= 22.5 (DMD)
BB
= Benkelman Beam _3„ deflection (in. x1 0 ),
DMD
= Dynaflect Maximum Deflection (in. x 10'3).
4-40
(Eq. 4.2)
(b)
Asphalt Institute [after Reference 4.2]
where
(c)
= 22.30 (D) - 2.73
BB
= Benkelman Beam «3 deflection (in. x1 0 ),
D
= Dynaflect center deflec tion (in. x 1 0 " ), same as DMD (Arizona).
(Eq. 4.3)
Louisiana [after Reference 4.2]
where
4.6 .3.4
BB
BB
= 20.63(D)
R2
= 0.72
BB
= Benkelman Beam . 3 deflection (in. x1 0 ),
D
= Dynaflect^deflection (in. x 1 0 ’ ), same as DMD (Arizona).
(Eq. 4.4)
Benkelman Beam to Road Rater [from Reference 4.8] (a)
Stabilized pavements: for Benkelman Beam load at 9,000 pounds on dual tires with 7080 psi inflated tires and Road Rater at 8,000 pound peak-to-peak load at 15 Hz on a 1 2 inch diameter plate
where
BB
= 2.57+ 1.27 RR
R2
= 0.66
BB
= Benkelman Beam . 3 deflection (in x1 0 ),
4-41
(Eq. 4.5)
RR
= Road Rater (Model 2008) deflection at 8,000 pounds and 15
Hz (in x 10°). (b) Asphalt Institute [4.3] Recommends that correlation between Benkelman Beam and Dynaflect be used to correlate Benkelman Beam to Road Rater Model 400 (with caution). (c)
Western Direct Federal Division, Federal Highway Administration, Vancouver, Washington
Correlation for Benkelman Beam to Road Rater Model 400
where
4.6 .3.5
BB
= 8.0+ 9.1026 (D0)
BB
= Benkelman Beam deflection (in. x1 0 "^)
Do
= Maximum deflection from Road Rater Model 400 (deflection location between load pads) at a load of 1,300 pounds at 25 Hz.
Falling Weight Deflectometer to Road Rater [from Reference 4.8] For Road Rater at 8,000 pound peak-to-peak load at 15 Hz on a 12 inch diameter plate and FWD at 8,000 pounds (+ 5%) on a 12 inch di ameter plate
4-42
(Eq. 4.6)
-3.40+1.21 RR 0.94 Std Er ror = 3.23 mils
where
n
95
Do
Maximum FWD de flection middle of loading plate at 8,000 lb. load on 1 2 in. diameterj)late (in x 1 0 " ).
RR
Road Rater (Model 2008) deflection at 8,000 pounds and 15 Hz (in x 10" ).
This equation is shown inFigure 4.11. 4. 6 .3. 6
Use o f Correlation Equations Generally, the use of correlation equations should be avoided when possible, and treated with a high degree of caution when it is necessary to use them. Because the correlation model si a func tion of pavement type, time of testing, material properties, and a whole host of other variables under which it was developed, it is impossible to estimate it's accuracy on any given project. Sev eral suggestions are offered here: 1. The decision to use correlation equations should be based on the sensitivity of the bottom line of the analysis to errors in the model. For example, if the objective is to design an overlay, then the sensitivity of the overlay thickness to errors in the correlation equation should be used as a basis to decide if it may be used safely. 4-43
(Eq. 4.7)
*l l m , n o l! c e lf * O r e ? * m o t c le f e D t h g i e W g n il i o F
Roo d RoKr
Figure
Dcflt clion,mi
l*
4.11. Falling Weig ht Deflectometer versus Ro ad Rat er D eflect ion s 1 4 .8 ]
4-44
2. Correlation equations are generally docu mented in the literature. Track down the source and determine the r^ , or correlation coefficient the itequation, and the condi tions under for which was derived (pavement type, season, type of equipment, etc.). Compare the conditions under which it was developed to those in which it will be used. 3. Cross check pavement or overlay designs with results using other procedures, (e.g. AASHTO) until confident that use of the correlation equation provides reasonable results. 4. Formulate plans to eliminate the need for correlation if you have to use them,equations. either yourGenerally, data collection or data analysis methods are outdated.
4.7 CALIBRATION OF LOAD CELL AND DEFLECTION SENSORS The periodic calibration of measuring devices (i.e., load cell & deflection sensors) on NDT equipment is essential in the acquisition of meaningful pavement deflection data. In spite of its importance, little has been written on the calibration procedures. recently, nomanufacturer calibration procedures existed exceptUntil for established procedures. SHRP has developed reference calibration procedures which will be published pending further verification and adjustment. SHRP's calibration process consists of three stages: 1) ref erence calibration of the load cell,2 ) reference calibration of the sensors, and 3) relative calibration of the sensors. Ref erence calibration requires the establishment of an inde pendent reference measurement system which can accu rately measure the load and deflections. Both test and ref erence systems are then set up to measure loads and 4-45
deflections under the same conditions. A specially designed load cell, which will be calibrated annually at the National Bureau of Standards will be used for the calibration of the FWD loadsensors. cell. A commercial LVDT will be used to cali brate the Relative calibration procedures can further improve the accuracy of the sensors. In this process, all of the sensors are stacked in a special frame and are subjected to, and thus measure, the same pavement deflection simultaneously. Several test are usually performed at the same test point. Adjustment factors are determined by dividing the overall mean of all the deflection readings obtained by the mean for each individual sensor. Relative calibration should be per formed on a clean, distress-free pavement. ASTM D testing 4694-87 4695-87 provide guidelines for deflection andand address the calibration issue. How ever, no specific calibration procedures are recommended. According to these procedures, calibration of the load cell and sensors should be carried out once per month during continuous operation, or before testing begins whenever the equipment is used on an intermittentbasis. Experience with the FWD that has been in service at Cornell University con tinuously since 1981 has shown that the calibration should be performed every 6 to 1 2 months. States are able to calibrate their FWDs at the SHRP Regional centers in Harrisburg, Pa., Reno, Nev., College Station, TX, St. Paul, Minn. Alternatively, es than can establish sitesand of their own especially if they own stat more one FWD. Regardless of the calibration site used (SHRP, or in-house site) all users must perform a full calibration of their FWDs at least once per year to be eligible to collect data for the LTPP program.
4-46
SECTION 4.0
REFERENCES Hicks, R.G. and Mahoney, J.P., "Collection and Use of Pavement Condition Data," NCHRP Synthesis No. 76, Transportation Research Board, Washington, D C., July 1981. Smith, R E. and Lytton, R.L., "Synthesis Study of Nondestructive Testing Devices for Use in Overlay Thickness Design of Flexible Pavements," Report No. FHWA/RD-83/097, Federal Highway Admini stration, U.S. Department of Transportation, Washington, D.C., April 1984. The Asphalt Institute, "Asphalt Overlays for High way and Street Rehabilitation," Manual Series No. 17, The Asphalt Institute, College Park, Maryland, June 1983. Federal Highway Administration, "Automated Pavement Distress Data Collection Equipment Seminar," Volume I, Appendix D, Seminar at Iowa State University, Ames, Iowa, June 12-15, 1990. Bentsen, R.A., Nazarian, S., and Harrison, J.A., "Reliability Testing of Seven Nondestructive Pave ment Testing Devices," Nondestructive Testing of Pavements and Backcalculation of Moduli, ASTM STP 1026, American Society for Testing and Mate rials, Philadelphia, Pennsylvania, 1989, pp. 41-58. Crovetti, J.A., Shahin, M.Y., Touma, B.E., "Comparison of Two Falling Weight Deflectometer Devices, Dynatest 8000 and KUAB 2M-FWD," Nondestructive Testing of Pavements and Backcal culation of Moduli, ASTM STP 1026, American Society for Testing and Materials, Philadelphia, Pennsylvania, 1989, pp. 59-69. Epps, J A. and Monismith, C.L., "Equipment for Obtaining Pavement Condition and Traffic Loading Data," NCHRP Synthesis No. 126, Transportation Research Board, Washington, D C., September 1986.
4-47
SECTION 5.0 DEFLECTION ANALYSIS TECHNIQUES
5.1 INTRODUCTION 5.1.1 General This section discusses techniques that are used for pave ment deflection analysis, and also introduces the concepts and basis of layer modulus backcalculation from measured deflection basins. A manual approach is illustrated using ELSYM5 in a trial and error mode, followed by a discus sion of typical automated approaches. Backcalculation techniques that are applicable to rigid pavements are also discussed. 5.1.2 Deflection Basin Parameters (including maximum deflections) When loads are placed on the surface of a pavement, such as a truck, aircraft, or passenger car wheel, the pavement will deflect downward to form a bowl shaped depression known as a deflection basin. The size, depth, and shape of the deflection basin is a function of several variables, including the thickness and stiffness of the pavement, the underlying materials, and the magnitude of the load. A PCC slab with a high elastic modulus will spread the wheel load over a large area resulting in a shallow deflectionbasin. Flexible pavements are much less stiff and tend not to spread the load as much resulting in a deeper basin. The difference in the deflec tion basins will be most noticeable within a 610 mm (24") radius with respect to the center of the load. In addition to stiffness, loading has a definite effect on the deflection basin. For example, as the load is increased, the pavement deflection will increase. However, many times this increase in deflection is not linear as many aggregates and subgrade materials are stress dependent. 5-1
The deflections are measured at various radial offsets, r, with respect to the center of the load plate. These deflec tion measurements define the basin. The load, P, plate radius, plate pressure, p,when mustanalyzed also be measured known. a, and These parameters, with the or deflection basin, enable us to estimate the stiffness profile of the pavement with respect to depth below the surface. Studies have shown that the outer deflection sensors respond primarily to the subgrade characteristics, while the inner sensors respond to the subgrade and upper pavement layers. The slope of the deflection basin at close proximity to the load is largely a function of the stiffness of the upper pavement layers. Over the years numerous techniques have been developed to analyze deflection data from various kinds of pavement deflection equipment. A by summary of the Deflection Basin Parameters was provided Horak at Sixth Interna tional Conference on Structural Design of Asphalt Pave ment [5.1] and is shown in Table 5.1. All of these parameters tend to focus on four major areas: (a)
Deflection below the center of the load which repre sents the total deflection of the pavement. This was obviously the first deflection parameter which was developed for use with the Benkelman Beam. It has been used for many years as the primary input for several overlay design procedures.
(b)
The slope or deflection differences close to the load such as Radius of Curvature (R), Shape Factor (Fj), and Surface Curvature Index (SCI). These parame ters tend to reflect the relative stiffness of the bound or upper regions of the pavement section.
5-2
Table 5,L Summ ary o f Deflection Basin
Parameters (modified from Ref. S.U
Maximum Deflection
Benkelman Beam, Lacroix deflectometer, FWD
^0 r
Radius of Curvature
Me asuring Devic e
Formula
Parameter
R=
2
/ 2D0(D0/Dr
Curvature Meter
- »
r = 127mm |” ((D0 + Dj + D 2 + D 3 ) / 5)100
Spreadability
~ L D j...
D°
Dynaflect
spaced at 305 mm
A = e[l + 2 (D,/
Area
J
d
0 ) + 2(D 2/D 0 ) + (D3 / d
0 )]
FWD
( sensor spacing = 305 mm ( 12M)) Fl = ( D 0 D 2 ) / D l
FWD
Shape Factors f
Surface Curvature Index
2 =(Dl D 3)/D l
Benkelman Beam Road Rater FWD
SCI = Dq Dr, where r = 305m/w, or
r = 500 mm
Base Curvature Index Base Damage Index Deflection Ratio Bending Index Slope of Deflection
BCI = D6 \0 ~ D 9\5
Road Rater Road Rater
BDI = D 305- D610
Qr = Df /
Dq ,
where D f s
/2
Bl = D / a, where a = Deflection basin
SD = tan
( dq
- Df ) / r
FWD Benkelman Beam Benkelman Beam
where r = 610 mm
D0 = center deflection (r=0), D p D2, D3 = first, second, third sensor from the load respectively D 305 = deflection at 305 mm, etc
5-3
(c)
The slope or deflection differences in the middle of the basin about 300 mm (11.8 in.) to 900 mm (35.4 in.) from the center of the load. These parameters tend reflect of thethe relative stiffness of the base or lowertoregions pavement section.
(d)
The deflections toward the end of the basin. Deflections in this region relate to the stiffness of the subgrade below the pavement surfacing.
Correlations developed between basin parameters and pavement structural condition have been used for pave ment evaluation application. The parameters presented in this section were developed to provide a relative stiffness index, or a means of obtain ing the resilient modulus values of the surfacing layers in lieu of the more rigorous backcalculation process. In gen eral the success of these indices to accurately relate to the resilient modulus of the surfacing layers has been limited. There is a clear consensus; however, that the deflections measured at the outer deflection sensors relate quite well to the resilient modulus of the subgrade, (E s g ), and this forms the basic premise for most backcalculation tech niques. 5.1.3 Regression Equations for PredictingModuli Several researchers have developed regression equations to predict layer moduli directly from deflections. Similar relationships can be derived fairly easily from theoretical considerations [5.9], Regression equations are typically developed to reduce the effort involved in backcalculation for production purposes. Sources of error in regression include (1 ) the analysis programs on which they are based, (2 ) the quantity of data used in development of the equa tion, and (3) the degree to which the model (usually linear elastic) simulates actual material behavior. Some of the regression approaches include:
5-4
(a)
WSDO T Equations
Newcomb developed regression equations to predict E s g as part of an overall effort to develop a mecha nistic empirical overlay design procedure for WSDOT [5.2]. For two layer cases, the subgrade modulus can be estimated from: E Sg
= -466 + 0.00762 (P/D3),
(Eq. 5.1)
Es g
= -198 + 0.00577 (P/D4),
(Eq. 5.2)
Es g
= -371 + 0.00671 2( P/(D 3 + D4)),
(Eq. 5.3)
[Note: Variables are defined after Eq. 5.9] and for three layer cases Es g
= -530 + 0.00877 (P/D3),
(Eq. 5.4)
Es g
= -H I +0.00577 (P/D 4),
(Eq. 5.5)
Es g
= -346 + 0.00676 (2 P/(D 3 + D4))
(Eq. 5.6)
Where P = applied load, lbs D3 = third sensor from the load D4 = fourth sensor from the load etc... The R2 ~ 99% for all equations and the sample sizes were 180 (two layer case) and 1,620 (three layer case). Figures 5.1 and 5.2are used to illustrate typical results from Equations 5.4 and 5.5. These equations were developed from generated data using ELSYM5 on the following input data:
5-5
Two Laver Cases
Load, P, kN (lb.)
Surface Thickness Surface Modulus, Subgrade Modulus, hAc, mm (in.) E a c , MPa (psi) E s g , MPa (psi) 50 (2 ) 150 (6 ) 300 (1 2 )
2 2
(5,000) 44 ( 1 0 ,0 0 0 ) 67 (15,000)
13,800 (2 , 0 0 0 ,0 0 0 )
345 (50,000)
3,450 (500,000)
207 (30,000)
690 ( 1 0 0 ,0 0 0 )
69 ( 1 0 ,0 0 0 )
450 (18)
35 (5,000) 17 (2,500)
Three Laver Cases
Load, P, kN (lb.) 2 2
(5,000) 44 ( 1 0 ,0 0 0 ) 67 (15,000)
Surface Base Thickness, Thickness, hAC,mm (in.) he, mm (in.) 50 (2 ) 150 (6 ) 300 (1 2 )
Surface Modulus, E a c ,MPa (psi)
Base Subgrade Modulus, Modulus, E s g, MPa (psi) E b ,MPa (psi)
100
13,800
690
345
(4) 250 (1 0 )
(2 ,0 0 0 ,0 0 0 ) 3,450 (500,000)
( 1 0 0 ,0 0 0 ) 345 (50,000)
(50,000) 207 (30,000)
450 (18)
690 ( 1 0 0 ,0 0 0 )
207 (30,000)
69 ( 1 0 ,0 0 0 )
69 ( 1 0 ,0 0 0 )
35 (5,000) 17 (2,500)
(assumed that load applied on a 300 mm (11.8 in.) diameter load plate)
WSDOT DEFLECTION vs SU3GRADE MODULUS EQUATIONS
I) S K (
) a P M (
S U L U D O M
S U L U D O M
DEFLECTION AT 3 FT. (MILS)
Figure 5.1 - Deflection vs. Subgrade Modulus for Equation 5.4 (Three Layer Case - Deflection Measured at 3')[after Newcomb 5.2]
WSDOT DEFLECTION vs SUBGRADE MODULUS EQUATIONS
Figure 5.2 - Deflection vs. Subgrade M
odulus for Equation 5.5 (Three-Layer Case - D
eflect ion Measured at 4 ') [af ter Newcomb 5JJ
From this generated data (no stiff layer), regression equations were also developed for estimating the surface modulus (AC) for a two layer case (for ex ample a "full-depth" pavement): log Ea c = -0.53740 - 0.95144 logioE s g 2
(Eq. 5.7)
___
-1.21181 VhAC+ 1.78046 logio (PAi/D02) where R2 = 0.83 For a three layer case, equations were developed for both E a c and E b as follows: If both E a c and E b unknown: log E a c = -4.13464 + 0.25726 (5.9/hAc)
(Eq. 5.8)
+ 0.92874 V5.9/hB - 0.69727^hAC^B 0.96687 logio Esg + 1.88298 logio (PAi/Do2) where R2 = 0.78. log Eb = 0.50634 + 0.03474 (5.9/hAc) + 0.12541 V5 -9/hB - 0.09416 VhAC/hB + 0.51386 log E s g + 0.25424 logio (PAi/Do2) where
R2 = 0.70.
The following variables were used in equations 5.1 through 5.9: P
=
applied load (lbs.) on a 300 mm ( 11.8 in.) plate,
hAC ~
surface course thickness (in.),
hfi
base course thickness (in.),
=
5-9
(Eq. 5.9)
Ea c
=
surface course modulus (psi),
Eb
=
base course modulus (psi),
Es g
=
subgrade modulus (psi),
Do
=
deflection under center of applied load (in.),
Do. 6 7 =
deflection at 8 in. (0.67 ft.) from center of applied load (in.),
Di
=
deflection at 1 ft. from center of applied load (in.),
D2
=
deflection at 2 ft. from center of applied load (in.),
D3
=
deflection at 3 ft. from center of applied load (in.),
D4
=
deflection at 4 ft. from center of applied load (in.), and
Ai
=
approximate area under deflection basin out to 3 ft.
2 [2 (Do + Do.6 7 ) + (Do.67 + Di) + 3(Di + D2) + 3(D2 + D3)] = (b)
4Do + 6Do,67+ 8 D 1 +
12
D2 + 6 D 3
AASHTO Equations Witczak presented a regression equation in Part III of the 1986 AASHTO Guide for Design ofPave ment Structures [5.3] to predict the subgrade modulus. That equation is similar to the theoretical surface moduli presented in the next section, and has the following form:
5-10
Ec„ -
(P )(sf) /
Es g -
where
P Sf
= =
M
) ( r )
(Eq. 5.10)
plate load (lb.), subgrade modulus prediction factor, 0.2686 for p = 0.50 0.2792 for p = 0.45 0.2892 for p = 0.40 0.2874 for p = 0.35 0.2969 for p = 0.30
Dr
=
pavement at surface deflection measured r distance, from(in.) the load, and
r
=
distance from the load to Dr (in.).
Using an Sf value of 0.2892 where the Poisson's ra tio is 0.40, the equation reduces to the following equations for deflections measured at 610 mm ( 2 ft.), 914 mm (3 ft.), and 1,219 mm (4 ft.). Sg =
0.01205(p /d 2)
(Eq. 5.11)
Es g =
0.00803(p /d 3)
(Eq. 5.12)
Sg =
0.00603(p /d 4)
(Eq. 5.13)
e
e
In the AASHTO Guide, detailed procedures are provided to insure that the deflections used to de termine Es g are outside the pressure bulb from the test load. To most accurately represent the subgrade stiffness; however, the deflections closest to the load without being directly effected by the pressure bulb should be used. Stiff underlying layers will havethe greatest effect on deflections furthermost from the test load. For example in cases where total pavement thicknesses are around 300 mm (11.8 in.), deflec tions taken around 600 mm (23.6 in.) should be used 5-11
to determine E s g - This ensures that the modulus obtained is not contaminated by the effects of the upper pavement layers (See page 111-86 of the AASHTO Guide for the Design of Pavement Structures). (c)
South African Equations The following relation between deflections taken at 2000 mm (78.7 in.) was published by Horak [5JJ: logio Es g = 9,727 - 0.989 logio d2000
where
Es g
= subgrade elastic modulus (Pa), and
d2000
= deflection at a distance of 2000 mm from the (point) of loading
(Eq. 5.14)
(nm).
5.1.4 Surface Moduli These are based on Boussinesq or Boussinesq-Love equa tions, and are defined by Ullidtz [5.9] as "The 'weighted mean modulus' of the half space calculated from the surface deflection". Surface moduli calculated from deflections measured at some distance from the applied load can be considered representative of the subgrade response. In a recent NCHRP study [5.8] which will be used to revise Part III of the Pavement Guideequation [5.3], itbeis used rec ommended that AASHTO the Boussinesq point-load to solve for subgrade modulus:
where
Mr
= P(1 - |i2 )/(7 t)(Dr)(r)
Mr
= backcalculated subgrade resil ient modulus (psi),
P
= applied load (lbs.),
5-12
(Eq. 5.15)
pavement surface deflection a distance r from the center of the load plate (inches), and r
= distance from center of load plate to Dr (inches).
Using a Poisson's ratio of 0.40, Equation 5.15 reduces to Mr
= 0.01114 (P/D2)
(Eq. 5.16)
Mr
=
0.00743
(P/D3)
(Eq. 5.17)
Mr
=
0.00557
(P/D4)
(Eq. 5.18)
for sensor spacings of 610 mm (2 ft.), 914 mm (3 ft ), and instead 1,219 mm for (4theft.).same If a sensor Poisson's spacings, ratio of the 0.45equations is used become: Mr
= 0.01058(P/D2)
(Eq. 5.19)
Mr
= 0.00705 (P/D3)
(Eq. 5.20)
Mr
= 0.00529
(P/D4)
(Eq. 5.21)
Darter et al. [5.8] recommends that the deflection used for subgrade modulus determination should be taken at a distance at least 0 .7 times r/ae where r is the radial dis tance to the deflection sensor and ae is the radial dimen sion of the applied stress bulb at the subgrade "surface." The ae dimension can be determined from the following: (Eq. 5.22)
ae where
ae
= radius of stress bulb at the subgrade-pavement interface, (in.) NDT load plate radius (in.),
D;
= thickness of pavement layers i (in.) 5-13
I.
)
n
= number o f pavement layers
Ep
= effective pavement modulus
Mr
(psi), and = backcalculated subgrade resil ient modulus.
The effective pavement modulus, Ep may be derived from the following equation:
1
1
do
1
= 1.5pa f
Mr .
1+
+
D
■+ I------
D (e 7
3 a VM
--
where d0 = deflection measured at the center ofthe load plate (and adjusted to a standard temperature of 6 8 °F), inches p = NDT load plate pressure, psi a=
NDT plate radius, in.
D = total thickness of pavement layers above the subgrade, inches Mr = subgrade resilient modulus, psi Ep = effective modulus of all pavement layers above the subgrade, psi 5-14
(Eq. 5.23)
5.1.5 Backcalculation
Backcalculation involves estimating pavement layer moduli from measured surface deflections, and, usually, known layer thicknesses. The moduli which are obtained can be used in fundamental engineering analyses of the pavement using mechanistic approaches. Knowledge of material type for each layer can also allow one to use the modulus as an indication of material condition. Both manual and automated backcalculation procedures are discussed in detail in subsequent sections. Most backcal culation procedures are based on the assumption that deflections measured at some relatively large distance from the load primarily reflect subgrade response. This allows use of the outer sensor deflections for estimating subgrade modulus as a starting point, and the solution for all layers is typically derived iteratively from there. 5.1.6 Combining Indices for Project Analysis In many cases, use of more than one analytical approach can provide complimentary and supporting information, as illustrated by the Washington State procedure described below. Over the years WSDOT has found that the use of selected indices and algorithms provide a fairly complete and nec essary picture of the relative conditions found throughout a project. This picture is very useful in performing back calculation and may at times be used by themselves on projects with large variations in surfacing layers. WSDOT is currently using deflections measured at the center of the test load combined with Area values and Esg computed fl-om deflections measured at 610 mm (24 in.) presented in a linear plot to provide a visual picture of the conditions found along the length of any project (as illustrated inFigure 5.3). The Area value tends to provide a fairly good indication of the relative stiffness of the pavement section, particu larly the bound layer, because it is largely insensitive to subgrade stiffness. Combining the Area value in a plot with E s g and Do provides a good picture of the relative 5-1.5
stiffness of both the surfacing and subgrade that interact to produce the measured deflections. A more direct method, which is fairly commonly used in practice, is to consider the variation of deflections, layer moduli (including subgrade) and performance indicator such as remaining life or overlay along the project in a lin ear plot similar toFigure 5.3. This has the advantage of identifying relative performance of each pavement layer rather than the combined response reflected by the AREA parameter. 5.1.6.1
Area Parameter The Area value represents the normalized area of a slice taken through any deflection basin be tween the center of the test load and 914 mm (3 ft.). By normalized, it is meant that the area of the slice is divided by the deflection measured at the center of the test load, DO. Thus the Area value is the length of one side of a rectangle where the other side of the rectangle is D0. The actual area of the rectangle is equal to the area of the slice of the deflection basin between 0 and 914 mm (3 ft.). The srcinal Area equation is: A =
6
(Do + 2Di +2 D2 + D3 )/Do
where Do = load, surface deflection at center of test Di = surface deflectionat 305 mm (1 ft.), and
D2 = surface deflection at610 mm ( 2 ft.), D 3 = surface deflection at914 mm (3 ft.).
5-16
(Eq. 5.24)
Non — De at rue
W S DOT
SR
5X
O
M P 0.
0-
~ 7.
60
EB
i ve
C a. se
Pa vcme n t . Te a t .i ng
# 1a t
NOTE: *Su msa r y va iu es are n or aal iz ec to a 9 , COO poun d loa d anc aa ju st eo pave ment thi ckn ess and te ip er a u rc . u.oaulu* :s determination on tr .* ae i le ct io n at the 4th sensor '2 feet fro* loaa I
fo r b a se d
Dat e “este o = C2/09 /84 Mile
' - = == D eile ct:o n:ss *>
:o : : íemmmm :
2.900 3.100 3.300 3.500 3.700 3.750 4.300 4.500 4.700 4.900 5. 100 5.300 5.500 5.700 5.900 6.100 6.300 6.510 6.700 6.900 7.100 7.300 7.500
30
40
■■■■■■■■■+
zsmmmm smm c QB xsam 59 1 r«H H c JHH
im
6f lB
2 SM
o
25
1: H H i 1 :B B li H B *C8H M
i la m 32BH M m 2 :h
20
H
*^
j
30
35
.............
. . . . .
i iflHH ■»
= sx * >
.. liwmm .......... :+ma ii warn ii mm \:m .......... it mm naaamammmm . 2'wmmmmwarn . .. *) C■ ■ ■ ■ ■ ■ ■ ¡ iwarn warn 2 ■ : : ammm *»C wm HHH 2 'HHflBHHH mam m H-H2 H H H H i
3CHH
7EMBÜ
: = Area = s:
50
20
40
£0
ID :=
20
25
T------30 35
<=Suograoe 0 20 2 zammmm i zaaaaa
izmm
- flHBBH
i:mm 22mmmmm 2 cwmmmmmm i ~mmm 2 :mtmmm 3 smaammmammi - waaam 2 1aaaamm 34M H H BH H I 2 zmmmmm 2 smmmmmm wm mmmmmmm 3iw 1 2wmm . ... ltmmmm lAwmm m
5-17
-------- -----30 40 50 -
0
Figure 5.3. Illustration of Basic NDT Param eters as Used by W'SDOT (SR 510 MP 2.9 to MP 7.5)
Moduiu**> 30 40 50
.0
20
-
The approximate metric equivalent of this equa tion is: A = 150(Do + 2 D 3 0 0 + 2D600 + D9oo)/Do where Do = deflection at center of test load, D 3 0 0 = deflection at 300 mm, D600 = deflection at 60 0 mm, and D 9 0 0 = deflection at 90 0 mm. Figure 5.4 shows the development of the normal
ized area for the Area value using the Trapezoidal Rule to estimate area under a curve. The basic Trapezoidal Rule is: K = h (y2y0 + y, + y2 + l/ 2y , )
where
(Eq. 5.25)
K= any planar area, yo - initial chord, yj, y2 = immediate chords, y3
= last chord, and
h = common distance between chords. Thus, to estimate the area of a deflection basin using Do, Di, D2 , and D3 , and h = 12 in., so that h/ 2 = 6 in., then: K = 6 (D0 + 2Di + 2D2 + D3)
(Eq. 5.26)
Further, normalize by dividing byD q :
(Eq. 5.27) 5-18
o*
12*
24"
36"
(Section B "Standard Pavement")
b*\j
o o
O C\J • o O
o o
oa
12
12
'
N O
6
‘
o■ C5
O
’
Estimated Area Using Trapezoidal Rule A
- 23.3
Equal Area Bounded by D o and Area Parameter
Figu re 5.4. Com puting an Area Parameter
5-19
Thus, since we normalized by Do, the Area Pa rameter's unit of measure is inches (or mm) since it is in fact in2/in i.e., basin area per unit of center deflection. The maximum value for Area is 915 mm (36”) and occurs when all four deflection measure ments are equal (not likely to actually occur) as follows: If, Do = Di = D2 = D3 Then, Area = 6(1 + 2 + 2 + 1) = 36.0 in. For all four deflection measurements to be equal (or nearly equal) would indicate an extremely stiff pavement system (like Portland cement concrete slabs or thick, full-depth asphalt concrete.) The minimum Area value should be no less than 280 mm (11.0 in.). This value can be calculated for a one-layer sys tem which is analogous to testing (or deflecting) the top of the subgrade (i.e., no pavement struc ture). Using appropriate equations, the ratios of
always results in 0.25, 0.125, and 0.083, respec tively. Putting these ratios in the Area equation results in Area = 6(1+ 11.0 in. 2(0.25) + 2(0.125) + 0.083) Further, this value of Area suggests that the elas tic moduli of any pavement system would all be equal (e.g., Ei = E 2 = E 3 ). This is highly unlikely for actual, in service pavement structures. Low area values suggest that the pavement structure is not much different from the underlying subgrade material (this is not always a bad thing if the sub grade is extremely stiff — which doesn't occur very often). Typical Area values were computed for pavement Sections A, B, and C (refer toFigure 5.5) and are shown in Table 5.2 (along with the calculated 5-20
Table 5.2. Estimates of Area from Pavement
_________ and ---------C . Sections r:--- rrr — Cases ,—-----A, ? B,----
_____
___
Pavement Surface Deflections, mm Pavement Cases Standard Pavement Section A (thin)
(inches)
Area mm (in.)
Do
D 305
D 61 0
1. 21 9 (0 .0 4 8 )
. 229 .356 (0.009) (0 .0 1 4 ) .356 .254 (0 .0 14 ) (0.010) .305 . 22 9 (0.01 2) (0.009)
4 34
( 1 7 .1 )
592
(23.3)
686
(27.0)
D 91 5
Section B (med.)
.686
Section C (thick)
(0 .0 2 7 ) .457 (0 .0 1 8 )
. 66 0 (0 . 0 2 6 ) .508 (0 . 0 2 0 ) .381 (0 . 0 1 5 )
.914 (0 .0 3 6 ) .5 8 4 (0.023) .406 (0.016)
.508 (0 . 0 2 0 ) .432 (0 . 0 1 7 ) .330 (0 .0 1 3 )
.330 . 22 9 (0.013 ) (0. 009 ) .303 . 22 9 ( 0 . 0 1 2 ) (0 . 0 0 9 ) . 22 9 .279 (0.01 1) (0.009)
470
(1 8 .5 )
597
( 2 3 .5 )
69 6
(27.4)
.533 (0.021) .356 (0 .0 1 4 ) . 305 (0.012)
.457 (0.018) .305 (0 .0 1 2 ) . 279 (0.011)
.3 3 0 . 25 4 (0.013) (0.010) . 22 9 .254 (0.010) (0.009) .229 .203 (0.009 ) (0.008)
67 6
(26.6)
729
(2 8 .7 )
762
( 3 0 .0 )
1.346 (0.053) .838 (0.033) .610 (0.024)
. 660 (0.026) . 559 (0.022) . 457 (0.018)
.356 . 22 9 (0.01 4) (0.009 ) .356 .229 (0.01 4) (0.009 ) .254 .330 (0.013) (0.010)
4 06
(1 6 .1 )
526
(20.7)
6 10
(2 4 .0 )
Stabilize Subgrade Section A (thin) Section B (med.) Section C (thick) Asphalt Treated Base Section A (thin) Section B (med.) Section C (thick) Moisture Sensitivity Section A (thin) Section B (med.) Section C (thick)
5-21
surface deflections (Do, Di, D2 , D 3 )). Table 5.3 provides a general guide in the use of Area values obtained from FWD pavement surface deflec tions. As mentioned previously the "typical" sec Figure 5.5 are used throughout tions shownforinillustrative these notes purposes. Typical Area values for different pavement structures and conditions are: Paveme nt
Area, mm (in.)
♦ PCCP
610-840 (24-33)
♦
530-760 (21-30)
Thick ACP
♦ Thin ACP
410-530(16 -21)
♦
BST flexible pavement (relatively thin structure) ♦ Weak BST
380-430 (15-17) 300-380 (12-15)
The following example in the use of the plot of Do, Area Parameter, and Esg, comes from State Route 510 just north of Olympia Washington (refer to Figures 5.3 and 5.6). MP 2.9 to MP 3.75 (Figure 5.3) The pavement through this area consists of various layers of bituminous surfacing (BST) totaling about 75 mm (3 in.) over about 300 mm (12 in.) of good quality gravel base.ranging This is from confirmed Area Parameters 300 toby400 mm (12 to 16 in.). Within this section the sub grade consists of a sandy gravel with a modulus value of 150 MPa (22,000 psi) at MP 2.9 transitioning to 35 MPa (5,000 psi) at MP 3.55 (wet sandy silt) and increasing to 100 MPa (15,000 psi) nearMP 3.7. It is clear that the large variation in D0 through this section is due primarily to variations in the subgrade stiffness.
5-22
Table 5.3 - Trends of
Dq
and Area Values
FWD Based Parameter Generalized Conclusions*
Area
M aximum s ur fac e Deflection (D0)
L ow
Low
Weak structure, strong subgrade
L ow
High
Weak structure, weak subgrade
High
Low
Strong structure, strong subgrade
High
High
Strong structure, weak subgrade
* Naturally, exceptions can occur
SECTION A (THIN)
SECTION B
mm
50 mm (2 ”)
mm
AC BASE SUBGRADE (FINE GRAINED)
Figure 5.5 5-23
SECTION C -----------
W SD O T
N on
SR5LO NOTE:
-D
estruct
i v e
EB
MF>10.0
C a.s
e
P avem
ent
T es
ti
n g
#2«.
values are normalized to a 9,000 pound load and adjusted f o r pavement tnicxness and temperature. Modulus determination is based Su mm ar y
at the 4th
on t he ae rlec tion Date Mi l e
10.117 10.123 10.129
feet froa load)
T es te d = 12/1 8/89
<=== =De : l e c t i o n = =s* > 0
10.003 10.009 10.015 10.021 10.027 10.033 10.039 10.045 10.051 10.057 10.063 10.069 10.071 10.077 10.081 10.087 10.093 10.099 1 0.105 10.111
sensor (2
10
:C
20
40
<=Subgrade
<=======Area==s==ss>
50
1C
15
20
25
30
35
25
30
35
0
Modulus=>
10
20
30
40
50
10
20
30
40
50
2 61 3 51 301 2 31 1C| 8]
ci CB
121 3 59 351 4 21 4 Cl 44|
361
141
^ A1
221 241 221 10 Figure 5.6
20 40
50
10
Illustration of Basic NDT Parameters as Used by WSDOT (SR 5 1 0 MP 10.003 to 10.129)
5-24
M P 4.3 t o M P 6.1 (Figure 5.3)
The pavement through this area consists of an older Portland Cement Concrete Pave ment (PCCP) which had been overlaid with about 2 in. (2 in.) AC ten to fifteen years ago. The Area Parameters of about 700 mm (28 in.) confirms the existence of the underlying PCCP except at MP 5.3 where the roadway was widened with ACP to build a center left turn lane, and the deflec tion tests were taken on the ACP widening. The subgrade consists predominantly of silty sandy gravel 110 to 260 MPa (16,000 to 38,000 psi) with isolated deposits of both silty sands and sandygravels. Through this area the low Do values are due largely to the PCCP.
MP 10.105 to MP 10.123 (Figure 5.6) The Do deflections drop to the 360 to 610 Hm (14 to 24 mil) range and the Area Pa rameters increase to between 380 to 510 mm (15 to 20 in.) indicating that the ACP is only fatigue cracked in spotty areas. The subgrade modulus values also increase to between 138 to 165 MPa (20,000 to 24,000 psi).
5-25
5.1.7 Joint Evaluation in Rigid Pavements
5.1.7.1
Introduction Deflection testing using a FWD can be used to determine the condition of the transverse joints in concrete pavements. When a load is applied near a joint, the loaded as well as the unloaded slabs deflect. This occurs because a portion of the load that is applied to the loaded slab is carried by the unloaded slab through load transfer. The magni tude of the tensile stress induced in the loaded slab depends on the amount of load transfer at the joint. If the joint is performing perfectly, both the loaded and unloaded slabs show equal deflec tion near the joint. A perfectly efficient system for transferring load from one side the joint to the other can reduce the free edgeofstress by nearly 50%. Reducing the edge stress reduces fatigue damage while reducing deflections minimizes pumping potential. Therefore, good load transfer at the joints is essential for satisfactory perform ance of rigid pavements. The following factors affect the load transfer at joints. a)
aggregate interlock
b) c)
subbase/subgrade support load transfer devices
d)
temperature
A brief description of how each of these factors affect the load transfer follows. a)
Aggregate Interlock Interlocking of aggregate particles of the fractured surface below the saw cut at a joint provides load transfer between the 5-26
slabs at the joint. The main factors affect ing load transfer at the fractured surface are, the width of crack opening and the texture of theiscrack face. Asarea the between joint opens, there less contact the two faces of the joint and the load transfer reduces. When the joint opens completely a minimum load transfer is available through the base course or subgrade. The texture of the cracked face de pends on size of coarse aggregate, maturity of concrete at time of fracture, and strength of concrete [5.20], Angular, rough surfaced aggregates (such as crushed stone) gener ally provide better interlock and load trans fer than do rounded and smooth surfaced aggregate (natural gravel) [5.20], The main factor which determines the texture of a crack face is the mode of fracture. Concrete can fracture around the aggregate or through the aggregate. When fracture oc curs around the aggregate, many pullouts of aggregate particles exist, resulting in a rough interface. Early fracture (when the aggregate-paste bond) is weak results in many pullouts. When the concrete strength increases pullouts diminishes and more ag gregate fractures occur [5.20], b)
Subbase Support Some load transfer is provided by the sub grade or the subbase below the pavement. The amount of load transfer will depend on the type of subbase. Stabilized or lean con crete subbases will provide more load trans fer than an unstabilized subbase. Studies on undoweled airport pavements by Foxwor thy [5.32] have shown that generally a mini mum of 25% load transfer is provided by the subgrade. 5-27
c)
Load Transfer Devices Pavements with adequate dowel bars at joints provide increased load transfer across the joint. Pavements with However, dowels generally show good load transfer. with load repetitions looseness of the dowels can occur and this can lead to reduced load transfer.
d)
5.1.7.2
Temperature
The temperature has a significant effect on load transfer. When a joint opens as the temperature decreases there is less contact between the two faces of the slabs at the joint. This can significantly affect the load transfer between slabs. The effect of tem perature on load transfer will be described in detail in a later section. Determination of Load Transfer Nondestructive deflection testing can be used to evaluate the load transfer at joints in rigid pave ments. The test is conducted by applying a load near the joint and measuring deflections near the joint on the loaded and the unloaded slabs. The test can be conducted by using the FWD, and one of the common load and sensor configurations for measuring load transfer of the approach slab is shown in Figure 5.7(a). For this approach the sensor configuration for testing the leave slab load transfer is shown inFigure 5.7(b). The load transfer at the joint based on deflection is computed from the following equation: d = (du/dj) * 1 0 0 where, d = joint efficiency(deflection) du = deflection of the unloaded slab dj = deflection of the loaded slab
5-28
(Eq. 5.28)
a) A-» 3
App roach Side 305 mm 305 mm ( 12 ”) (12”)
Traffic
Load Transfer = —^(100) Ai
Í3* q
b) Leave Side A3
&
Joi nt o r Cra ck s 0 * • Ö o>. Load Transfer
^ ( 10 0 ) A
305 mm
305 mm
1
^2
Figure 5.7 - Arrangem ent of Deflect ion Senso rs for Determining Load Transfer Effici ency at Approach and Leave Sides of a Joint or Crack
5-29
Another method of calculating load transfer efficiency is given by: d = 7 ------y—T (du + d|)
(Eq. 5.29)
where du and dj were previously defined [5.44]. The theoretical joint efficiency (deflection) may range from 0 percent (none) to 1 0 0 percent (full). These two conditions are illustrated in Figure 5.8. The joint condition can be generally classi fied based on the following deflection transfer ef ficiencies: Good 75 - 100 %, Fair 50 - 75% and Poor < 50%. If joint performance is poor, fault ing is likely. The load transfer efficiency that was described previously was based on deflections. A joint load transfer efficiency based on stress can be defined by the following expression: S = (Su/Si) * 1 0 0 where, S = load transfer efficiency (stress) Su = stress in the unloaded slab Sj = stress in the loaded slab This stress based load transfer efficiency indicates the stress carried by the unloaded slab in relation to the stress carried by the loaded slab. Studies have indicated that a one to one relationship be tween deflection efficiency and stress efficiency does not exist [5.3], A relationship that has been developed between these two parameters is shown in Figure 5.9 [5.3], As it is difficult to measure stresses in concrete slabs, the deflection based efficiency is commonly used to measure load transfer in concrete slabs.
5-30
(Eq. 5.30)
Load
0 mm
Load
•A*
.51 mm ( 0 .02 0 ”)
.51 mm ( 0 .02 0•'” )
•
A •
Ci. •
A
C*. •
A
• A •
A
A
t».
A A
•
•
•
t».
•
A •
.51 Good Loa d Tran sfer= :— = 1. 00 .51
Figure 5.8 - Illustration of Poor and Good Load Transfer
5-31
•
A
i
0
20
40
60
Deflection Eff.cierKy (DTE 6
l
80 * 100) -
100
%
Fig 5. 9 Relat ionsh ip Be tween Joint Effic iency For Flexural Stress and De flec tion Methods of
Me asur em ent (By I. Korbus and E. J. Barenberg: Fr om DO T/FA A/R D-7 914 . IV). "Longitudinal Joint Systems In Slip-Formed Rigid Pavements — Volume IV*'.
5-32
The same procedures that were used for testing the load transfer across joints can be used to determine load transfer across cracks. Generally the load transfer efficiency decreases as the num ber of load applications the pavement is subjected to increases [5.20], Foxworthy [5.32] carried out a study to determine the effect of different ap plied load levels on joint efficiency. He tested airport joints with an FWD at three load levels which ranged from 6,500 - 23,000 and found that load transfer was consistent for the three load levels. 5.1.7.3
Effect of Temperature on Joint Testing When the temperature decreases, the concrete contracts and the joint opens. This causes less contact to occur between the fractured faces at the joint, and as a result the load transfer between slabs decreases. As the temperature increases, the slabs expand and more contact occurs at the fractured faces of the two slabs. This causes the load transfer between slabs to increase. There fore, the amount of load transfer depends on the temperature at the time of testing. Edwards et al [5.27] have shown that on a summer day when the pavement temperature rises substantially, load transfer may increase on the same joint from 50% in the morning to 90% in the afternoon. Greer [5.28] report that limited tests on Memphis Inter national Airport indicated that the transverse joint efficiency went up from 16% (December 1987) to 84% (May 1988) when the weather warmed. Foxworthy [5.32] conducted a series of tests on undowelled airport pavements to study the varia tion of load transfer efficiencies with temperature. Figure 5.10 shows the variation of joint efficien cies with temperature for four slabs having the same thickness. The load transfer efficiency gen erally approached 1 0 0 % with increasing tempera ture while with decreasing temperature the effi ciency approach a minimum of 20-25%. Foxwor thy [5.32] found that generally all joints showed the S-shape relationship shown in Figure 5.10 with a horizontal shift between the curves. In some instances, good load transfer existed throughout the temperature range, presumably due to small joint openings while some slabs 5-33
showed a poor load transfer and showed a flat response throughout the temperature range.
Fig ure
5.10
5-34
Relationship betw een air temperature and joint load transfer.
[5.32]
Several researchers have developed methods to correct the load transfer to a reference tempera ture and to predict the load transfer at different times or temperatures. Shahin [5.231 presented a chart shown in Figure 5.11, which can be used to adjust the load transfer to a reference time. Obvi ously, this chart would only be valid for use under the conditions used to develop it. Foxwor thy and Darter [5.26] developed a relationship to predict the load transfer efficiency at any tem perature once the load transfer at one tempera ture is known. 5.1.7.4
Joint Test Considerations The following guidelines should be followed when conducting tests to determine load transfer across joints or cracks. (a)
Testing should be performed when the joints are open. The best time to perform the test is during the night or in the early morning hours. Testing should be avoided during midday to minimize the possibility of joint lockup. On cool overcast days, joint testing may be performed throughout the day.
(b)
A load approaching 40 kN (9,000 lbf) or more should be used for testing on highway pavements.
(c)
The joint test should be carried out along the outer wheelpath.
(d)
Generally in highway pavements the load transfer efficiency of approach and leave slabs are different. Usually the lower load transfer occurs in the leave slab. When con ducting joint testing it is recommended that both the approach and leave slabs be tested to determine their load transfers.
5-35
TIM E
Or
DAY
D ( R O T C A T N IO T C E R O C 1 . .T (L R C r S N A R T D A O L
Figure 5.11 - Example Chart for Correcting Load Transfer for a Referenced Time o f Loading of 2: 00 p.m.
5-36
5.1.7.5
Example As an illustration of Load Transfer Efficiency (LTE) results for WSDOT routes 1-5 andmeasurements, 1-90 will be illustrated. The FWD deflec tion data was srcinally obtained during 1986 and 1987. The 1-5 loca tion illustrates a PCC pav e ment with generally few joint problems and good load transfer. The 1-90 locat ion has badly faulted transverse joints and generally poor load transfer. (a)
1-5 — MP 176.35 Northb ound (Seattle) Deflect ions were measured across trans verse joints, with the load applied on both the approach and leave slabs, across the longitudinal joint, and across two longitudi nal cracks. The air tem peratu re during testing was approximately 15.6°C (60°F) and the testing was conducted between 11 p.m. and 4 a.m. The measure d deflections were used to calculate load transfer effi ciencies at each location using Equation 5.28. The load trans fer efficiencies are summarized in Table 5.4. The average load transfer efficiency is the average deter mined for four load levels (approximately 26.7, 40.0, 53.4, and 66.7 kN (6,000, 9,000, 12,000, and 15,000 lbs.)). The results shown in Table 5.4 show that the average load transfer efficiency for the approach side o f the transverse joints was 91.2 percent and for the leave side was 92.1 percent. These load transfer eff iciencies were high for the temperature at which the joints were tested, as well as for the pave ment age (22 years) and number of load applications (approximately 13,000,000 ESALs). The load transfer ef ficiencies at the site showed very little variation, as evi denced by the low standard deviations and coefficients o f variation.
5-37
Table 5. 4. Summary of Load Transfe r Effici encie s — 1-5
Row
Location
Mean (%)LTE
1 (outer lane)
TJ-A TJ-L
90.7 91.4
2 (outer lane)
TJ-A TJ-L
3 (outer lane)
Standard Deviation
COV (%)
Maximum LTE (%)
Minimum LTE (%)
11.4 8.6
12.6 9.4
100.0 98.8
52.8 63.5
92.8 91.2
5.8 4.1
6.2 4.5
100.0 97.0
81.2 84.2
TJ-A TJ-L
92.0 94.4
3.0 2.9
3.3 3.1
96.6 99.2
87.2 89.4
4 (inner lane)
TJ-A TJ- L
88.9 91.8
12.3 7.7
13.7 8.4
100.0 100.0
49.0 69.9
5 (inner lane)
TJ-A TJ-L
91.5 91.8
4.8 2.9
5.2 3.2
97.7 95.4
80.8 85.8
LJ-A LJ-L
63.3 69.3
28.6 19.2
45.2 27.7
97.7 91.5
21.5 39.0
LC-A LC-L
74.7 59.2
20.4 29.6
27.3 50.1
95.2 92.3
51.2 13.5
Note s: 1) TJ = transve rse joint LJ = longitudinal joint LC = longitudinal crack A = approach L = leave 2) Appro ach and leave on longitud inal joint s refer to direct ion o f FWD movement between Lanes 1 and 2.
5-38
The load transfer efficiencies acro ss the longitudinal joint and longitudinal cracks were much lower and more variable than those for t he transverse joints. The average load transfer efficiency for the longitudinal joint, when the load was applied on Lane 2, was 63 .3 percent fo r the load applied on Lane 1, was 69.3 percent . There was si g nificant variation between the maximum and minimum load transfer efficiencies meas ured (21.5 to 97.7 percent). The mean load trans fer effic iencies meas ured on either side of the longitudinal crack were 74.7 percent and 59.2 percent . One explanation for the difference in loa d tran s fers may be that the crack faces were not vertical. If this were the ca se, when loaded on one side, the loaded slab would have been supported by the unloaded slab, which would have resulted in a higher measured load transfer efficiency. Even tho ugh several longitudi nal joint and crack locations showed low load transfer efficiency, these joints and cracks w ere no t faulted. They experienc ed little, if any, stress reversal because wheel loads moved parallel to the cracks rather than across them. (b)
1-90 — MP 278.60 Westbound (Spokane) Deflections were measured across each transverse joint and crack, with the FWD load applied to both the approach and leave slabs. The air temp erature during t esting ranged from 12.8°C (55°F) for Row 3 to 22.2°C (72°F) for Ro w 5. Testing was conducted between 4 a.m. and 10 a.m. With the FWD data, load transfe r efficien cies for each joint and crack were 5-39
calculated using Equation 5.28. Table 5.5 summarizes the load transfer efficiencies measured at this site. The results in Table 5.5 show that the average transverse joint approach site load transfer effici ency was 59.7 percent, and that of the joint leave side was 74.0 percent. The averag e load trans fer effici ency for the transverse crack approach side was 72.8 percent, and that for the crack leave side was 76.6 percent. There was al so a large variation in the load transfer efficiencies in each row, as evidenced by the high coeffi cients of variation. These load transfer efficiencies were, on the average, much lower than those measured at the 1-5 site. The lowest load transfe r efficiencies measured in each row at the I90 test site were about 25 percent . Some researchers have suggested that a load transfer efficiency between 15 and 25 per cent will be measured across a joint even if the joint faces are not in contact because the subgrade provides some shear resis tance. As described above, the 1- 90 join t conditions, (i.e. badly faulted) are consistent with the poorer LTE than the 1-5 joints, where little or no faulting was observ ed, join t faulting is generally attributed to traffic load associated damage. Reasons for greater damage at the 1-90 site are probably due to differences in traffic loading (quantity and magnitude); differences in suppo rt cond itions and climatic differences.
5-40
Table 5. 5. Summary o f Load Transfer Efficie ncies — 1-90
Row
Location
Mean LTE (%)
1 (innerlane)
TJ-A TJ-L
73.3 84.3
TC-A TC-L 2 (inner lane)
3 (outer lane)
4 (outer lane)
5 (outer lane)
Notes:
Standard Deviation
COV (%)
Maximum LTE (%)
Minimum LTE (%)
15.2 5.6
20.7 6.6
90.6 91.2
46.1 72.1
87.5 94.5
1.3 0.8
1.5 0.9
TJ-A TJ-L
69.5 84.5
24.0 10.5
34.6 12.5
TC-A TC-L
89.9 93.7
0.7 1.5
0.8 1.6
TJ-A TJ-L
53.7 75.9
32.1 20.0
TC-A TC-L
70.5 72.2
TJ-A TJ-L
-
-
-
-
93.7 95.7
29.8 65.7
-
-
-
-
59.8 26.3
93.8 94.2
11.4 38.0
17.6 20.6
25.0 28.5
89.2 92.9
38.3 37.5
55.2 67.7
21.1 16.3
38.2 24.1
82.5 84.5
21.3 32.5
TC-A TC-L
56.0 62.2
22.1 16.4
39.6 26.4
84.0 89.1
21.4 41.0
TJ-A TJ-L
46.9 57.7
17.3 14.5
36.8 25.2
75.0 78.5
24.6 33.8
TC-A TC-L
60.2 60.6
16.7 17.1
27.7 28.2
79.3 84.5
28.8 36.9
TJ = transverse joint TC = transverse crack A = approach L = leave
5-41
5.1.8
Void Detection i n Rigid Pavements 5.1.8.1
Introduction Voids are generally created below slab corners as a result of pumping and erosion of sub base/subgrade material. Nondestructive deflection testing can be used to detect the presence of voids. These tests consist of measuring deflec tions at the slab corner. Corner testing should not be conducted during winter as water below the corner can freeze and the corner can show good support. The deflection of the slab corners is very much influenced by slab curling. Before methods to detect presence of the are described, the effect the of slab curling on voids deflection measurements will be described.
5.1.8.2
Effect of Slab Curling on Deflection When the temperature at the slab surface is greater than at the bottom of the slab, the central portion of the slab tends to lift off so that firmer contact with the subgrade is obtained at edges and corners. This condition usually occurs during the warm mid-day period due to thermal expan sion of the concrete. If the temperature at the surface of the slab the bottom, the pavement will is liftless offthan the that jointsat and edges. In this case firmer contact is obtained at the center of the slab and this condition usually occurs in the early morning hours. Curling and warp ing may also occur as a result of changes in moisture content of the slab. Figure 5.12 illustrates this effect. Deflection measurements at slab corners when the slab is not in contact with the surface do not relate to pavement deflections. Figure 5.13 show s a load-de flection relationship at different 5-42
VOID
NIGHTTIME CURLING
Figure 5.12 - Slab Curling Due to Temperature Differentials in Slab. [5.451
5-43
)» F » ( D A O L
DE FLE CTI ON
(mm .IO3 )
Figure 5.13. Typical Load Deflection Relations at Slab Corner
5-44
temperature differentials beneath the top and the bottom of the slab obtained by Larsen [5.29]. In this figure a positive tem perat ure differ ential cor responds to the case where the temperature at the top of the slab is greater than at the bottom, while a negative temperature differential occurs when the top of the slab is cooler than the bot tom. This figure shows that the load-deflection relationship is essentially linear when there is firm contact between the slab and the subbase and non-linear when there is a loss of contact be tween the corner and the subbase. When there is a negative temperature differential in the slab, greater deflections are obtained at the corner when compared to deflections obtained for a positive temperature differential for the same load. Therefore, corner testing should be avoided when the slab is curled concave side upward. When testing corners, the ambient t emperature as well as the range of temperatures during the sea son in which testing is performed should be con sidered so that testing can be avoided when the slabs are curled concave upwards. Generally, corner testing should be avoided during the early morning hours. Larsen [5.29] investigated the ef fect o f test tempe rature on corner deflectio ns and report that uniformity in test data was obtained when tests were conducted in the night. 5.1.8.3
Methods for Void Detection The following methods can be used to detect the presence of void s. a)
Co me r Deflection Profile
b)
Variable Load Corne r Deflection Analysis
c)
Void Size Estimation Proc edure
d)
Mechanistic Based Approach
5-45
A description o f each of these m ethods foll ows. a)
Corner Deflection Profile This is an approximate method for detect ing voids and is described in the AASHTO Guide [5.3], In this method corner deflec tions are measured under a constant load (preferably 9 kips). The deflections at the approach and leave corners are then plotted as shown in Figure 5.14. This figure shows that the leave corners show higher deflec tion than the approach corners. Usually approach corners have less voids than leave corners and show less deflection. The cor ners which exhibit the lowest deflections are expected to have full supportwhich value. isA maximum allowable deflection, somewhat higher than the full support value can then be selected and used as a criteria to determine corners whi ch have voids. For example, in the figure a reasonable maxi mum deflection would be ,508mm (0.020 in.). A single value o f maximum allowable deflection used in this method may not be appropria te if load transfer varies from joint to joint. Because of this factor as well as the influ ence o f test tem perature on the results, this method must be viewed as an
b)
approximate method. Variable Load Corne r Deflection Analysis This method is described in the AASHTO Guide [5.3], In this method the comer de flections are measured at three load levels (e.g., 27, 40, 53 kN (6, 9, 12 kips)) to es tablish a load-deflection relationship at each corner.
5-46
)
)
)
JRCP JOINT DEFLECTION PROFILE
) S N O R IC M ( . L F E D
) S L I M ( . L F E D R E N R O C
R E N R O C
D W F
D W F
JOINT NO. ALONG PROJECT
Figure 5.14 - Profile of Corner Deflection for JRCP (60 ft. Jt. Space)
Typically locations with no voids cross the axis very near the srcin (less than or equal to 50 microns (0.002 in.)) as shown i n Fig ure 5. 15 (for the ap proach slab). I f the line crosses the deflection axis at a distance greater than 50 microns (0.002 in.), a void can be suspected (see leave slab before grout in Figure 5.15). The response before and after subsealing is shown in Figure 5.15.
c)
Void Size Estimation Proc edure
d)
A method to estimat e the size o f voids be low a slab corner was developed in the NCHRP Project 1-21 [5.34], This method requires deflection testing at the slab center (including the deflection basin), corner de flection and transverse joint load transfer to estimate the size of vo ids. Mechanistic Based Approach Several methods which use mechanistic based approaches to determine the presence of voids at slab corners have been devel oped. Shahin [5.23] presented a mechanistic procedure to detect voids by compa ring measured corner deflections with theoreti cal corner deflections. The elastic modulus of the slab and the modulus o f subgrade reaction below the slab are needed for this analysis. These values can be determined by conducting a deflection test at the center of the the above ues slab (thisand willbackcalculating be described later). In thisval method, a finite element program was used to establish a relationship between load transfer, corner deflection and k-value of the support as shown in Figure 5.16. These relationships were established based on given load position, load magnitude, slab dimensions, slab arrangement and slab elas tic properties. The computed corner deflec tion appropriate to the slab support condi tions is determined from this figure and
5-48
20
0 1 x s lb d a o L D W F
Corner Deflection - ins
Figure
x
10'5
5.15 Join t load deflection where large void under leave corner was suspected (Ohio 1-77)
5-49
z
o
p
o tu -I u. UJ o
«
UÜ r n:
o c w
o
o o UJ ►3 CL
s o o
LOAD TRANSFER {% )
re 5.16. Relationship o fL oa d Transfe r vs. 6Cfor Various Dynamic Subgrade Modulus (k). 5-50
compared to the measured deflection. The difference between the measured and com puted corner deflections can be used to de tect possible voi ds. Ullidtz [5.9] describes a method to detect voids by comparing the k-value at the cor ner of the slab to the k-value at the center of the slab. In this method, the elastic modulus and the k-value at the center of the slab has to be determined first. This can be accomplished by conducting a deflection test at the center of the slab and backcalculating the concrete modulus and the k-value of the su pporting mediu m. Thereafter, as suming that the elastic modulus of the slab is constant throughout the slab, the k-value at the corner is calculated based on the measured corner deflection and the degree of load transfer. Generall y if the k-value at the corner is between 0.6 to 0.8 of the kvalue at the center of the slab, poor corner supp ort is indicated. 5.1.9 Class Exercise A - Deflection Basin Parameters Three typical pavement structures are shown in Figure which represent thin, medium, and thick pavement sections for illustrative purposes. Table 5.6 shows the
5.5
deflections froml oad a typical FWD using 40 kNresulting (9,000 lb.) at 0.55 MPadeflection (80 ps i).testThe deflections were developed using elastic modulus values of 3,445 M Pa (500,00 0 psi) for the AC , 172 MP a (25,000 psi) for the granular base and 52 MPa (7,500 psi) for the subgrade for Cases A, B, and C. The subgrade elast ic modulus was increased to 103 MPa (15,000 psi) for cases Al, Bl, and Cl. The following class exercise (see Table 5.7) is provided to help gain a "hands-on feel" for the relative values of the various deflection basin parameters we have been discuss ing. To com plete the class exerci se, determine the Area value, Shape factors Fi and F 2, Surface Curvature Index for r = 305 mm (12 in.) and r = 610 mm. (24 in) for the six Cases shown above from the various formulas covered 5-51
in this section. If time allows, also complete the calcula tion of subgrade moduli shown in Table 5.8. Solutions are shown in Tables 5.9 and 5.11.
Table 5.6. Pavement Surface Deflecti ons for Class Exercise — Sections A (Thin AC), B( Medium AC), and C (Thick AC)
Calculated Deflections, ^m(mils) (inches) Case
Do
A EgQ = 52 MPa
1226 (48.28)
D 305 mm (12 in .)
666
(0.0483)
(26.23)
^610 mm (24 in.)
353
(0.0262)
(13.91)
^915mm (36 in.)
226
(0.01391)
(8.91) (0.0089)
(E s g
= 7500 psi) A1 E$g = 103 (Esg = 15000 psi)
818
690
B1 ~ 1^3 MPa = 15000 psi)
465
c Es g = (E s g =
=103 MPa = 15000 psi)
(27.18)
(18.30)
518
(17.92)
310
(11.90) (0.0119)
5-52
(20.39)
(12.20)
385
(15.17)
348
(9.20) (0.0092)
110
(13.71)
182
(7.18)
242
(12.01)
118
(6.70) (0.0067)
(4.64) (0.0046)
238
(0.0120) 170
(9.53) (0.00953)
(0.0072) 305
(4.32) (0.0043)
(0.0137)
(0.0152) 234
(6.69) (0.0067)
(0.0122)
(0.0179) 302
170
(0.0204)
(0.0183) 455
(14.10) (0.0141)
(0.0272)
52 MPa 7500 psi)
Cl ESq (E s g
358
(0.0322)
B E s g ^ 52 MPa (E s g = 7500 psi) Es g (E s g
(32.20)
(9.36) (0.0094)
123
(4.86) (0.0049)
Table 5.7. Class Exercise Area (in.)
Case
Fi
f2
Deflection Parameters
SCI12 or in.
SCI24 or in.
SCI305
SCIôio
A A1
B B1 C Cl Necessary formulas:
6 Dq (Do + 2D 12 in. + 2Ü24 in. + D 36 in.) Dp - P24"
Fi
D
12"
Pl2" ~ D36"
F2
D
24"
SC Inin. =
Do - D 12 in.
SCI24 in. =
D o - D24 in.
1"
= 25.4 mm
5-53
Tabl e 5.8. Class Exercise — Subgrade Moduli Subgrade Modulus MP a (psi ) Case
@610 mm
@ 914 mm @ 914 mm
(24 in.) Eq. 5.10*
(36 in.) Eq. 5.10*
(36 in.) Eq. 5.4*
A Al B B1 C Cl
*Use Poisson's Ratio = 0.45 Necessary formulas: Equation 5.4:
E sg = -530 + 0.00877 (P/D 36 in.)
Equa tion 5.10: ESg = (P)(Sf)/(Dr)(r) where Sf = 0.2792 for jo. = 0.45 1 MP a
=
145 psi
5-54
Table 5.9 - Solutions — Class Exercise — Deflection Parameters SCIir Case
Area, m m (in. )
Fi
A
43 4 (17.08)
1.31
A1
397 (14.55)
B
588 (23.16)
B1
514
f
2
SCI 2 4 "
or30 5 , SCI
s coi r610,
microns (mils)
microns (mils)
1.25
560 (22.05)
873 (34.37)
1.81
1.46
460 (18.10)
648 (25.51)
0.66
0.79
172 (6.79)
342 (13.47)
0.91
1.05
282
155 6
1 1
1 0
( .
C
694 (27.33)
0.39
0.48
70 (2.75)
150 (5.91)
C1
622 (24.48)
0.57
0.65
69 (2.70)
132 (5.20)
5-55
)
(
1 2
(20.23)
.
)
Table 5.10. Soluti ons — Class Exercise — Subgrade Moduli
Case
Subgrade Modulus, MPa (psi) @ 610 mm @ 914 mm @914 mm (24 in.) (36 in.) (36 in.)
A
51.9 (7,527)
54.0 (7,834)
57.4 (8,329)
Al
107.9 (15,650)
111.4 (16,157)
122.3 (17,741)
B
52.7 (7,637)
50.5 (7,324)
53.4 (7,752)
B1
100.5 (14,582)
103.7 (15,043)
113.6 (16,481)
C
60.1 (8,718)
51.4 (7,457)
54.5 (7,903)
Cl
107.7 (15,627)
99.0 (14,362)
108.3 (15,711)
5.1.10Class Exercise B - Load Transfer Efficiency The deflections in Table 5.11 were obtained on a jointed concload rete transfer pavement i n the early morning hours.the Calculate the efficiency at each point using proce dure illustrated in Figure 5. 7, Arrangement of Deflection Sensors.
5-56
Table 5.11 - Class Exercise "B" - Load Transfer Efficiency (LTE)
Test Slab
Load Position
D1
D2
D3
1
A L
6.21 5.92
5.23 5.76
6.11 5.23
2
A L
5.13 4.67
4.72 4.60
4.99 4.48
3
A L
7.36 8.62
7.21 8.36
7.15 8.23
4
A L
5.40 6.13
2.54 3.77
3.60 3.43
5
A L
4.45 6.31
2.67 4.36
3.31 3.91
A = Approac h Side L = Leave Side
5-57
L TE(% )
Table 5.12 - Solutions - Class Exercise "B"
Test Slab
Load Position
D1
D2
D3
LTE (%)
1
A L
6.21 5.92
5.23 5.76
6.11 5.23
84 88
2
A L
5.13 4.67
4.72 4.60
4.99 4.48
92 96
3
A L
7.36 8.62
7.21 8.36
7.15 8.23
98 95
4
A L
5.40 6.13
2.54 3.77
3.60 3.43
47 56
4.45 6.31
2.67 4.36
3.31 3.91
61 62
A L A = Appro ach Side L = Leave Side 5
In summary, this illustrates that it is not always necessary to perform full elastic layered backcalculation for evalua tion purposes. Simple and effective proced ures and equations have been used for many years to provide rela tively quick pavement condition information from deflec tion measurements.
5.2 MANUAL BACKCALCULATION Manual backcalculation basically involves a trial and error approach using one of the elastic layered programs to match a set o f measu red deflections. An initial set of moduli are assumed and surface deflections are calculated using the program and compared with measured deflec tions. Moduli are adjusted based on the comparison, and the procedure is
5-58
repeated until an acceptable match between measured and calcu lated deflection basins is achieved. Laye r thickne sses are necessary to use the approach. Although the approach is cumbersome, it provides an excellent learning experience. Tw o examples are presented. The first is a very simple problem using a theoretical deflection basin developed with ELSY M5. The second in volves actual field measured FWD deflections from one of the SHRP sites. The first example uses deflections generated for the medium thickness, typical section defined in Section 3.2.6 and shown in Figure 3.8, i.e. 125 mm (5") AC on 200 mm (8") base on a fine-grained sub grade. Surface deflect ions for a standard 40 kN (9,000 lb.) wheel at 0.55 MPa (80 psi) contact pres sure are (for a constant 305 mm (12") between deflection sensors) in microns (mils): D0
Dj
D2
D3
D4
D5
D6
691 (27.2)
518 (20.4)
348 (13.7)
242 (9.53)
177 (6.98)
137 (5.40)
111 (4.38)
We know, of course, that the layer moduli used to generate these deflections are 3450 MP a (500 ksi) for the AC, 172 MPa (25 ksi) for the base and 52 MPa (7.5 ksi) for the sub grade. To illust rate the approach esti mate the following values as seed moduli: Ea
c
=
2069 MP a (300 ksi)
E base
=
172 MP a (25 ksi)
Es g
=
103 MPa (15 ksi)
Poisson's ratios are the same as chosen in Section 3.2.6, i.e. .35, .4 and .45 for AC, base and subgrade. Using these val ues in ELSYM5 gives the following deflections in microns (mils):
5-59
D0
Di
D2
D3
D4
D5
D6
CALCULATED 528 (20.8)
323 (12.7)
180 (7.09)
116 4.55)
84 (3.30)
66 (2.58)
54 (2.13)
691 (27.2)
518 (20.4)
348 (13.7)
TARGET 242 177 (9.53) (6.98)
137 (5.40)
111 (4.38)
-24
-38
-48
-52
-51
ERROR % -52 -53
Starting with Dg, it is clear that the subgrade modulus of 104 MP a (15 ksi) is too high since D6 is too low. One method for adjusting moduli multiply by the the calculated defl ection to istheto target deflect ion.ratioIn ofthis case 54/111 = 0.49 so that the adjusted subgrade modulus becomes .49 * 104 MPa = 51 MPa (7.35 ksi). [Note: This approach works well here because the assumption of elastic behavior is correct for the theoretical basin derived with ELSY M5. Also, most of the deflection at D6 can be attributed to the subgrade.] The next trial, using Ea c
=
2069 MPa (300 ksi)
E Ba s e
= =
172 MP a (25 ksi) 51 MP a (7.35 ksi)
Es g
provides the followin g:
5-60
D0
Dj
D2
D3
D4
D5
D6
CALCULATED 782 (30.8)
551 (21.7)
358 (14.1)
245 (9.63)
179 (7.04)
138 (5.45)
113 (4.44)
691 (27.2)
518 (20.4)
348 (13.7)
TARGET 242 177 (9.53) (6.98)
137 (5.40)
111 (4.38)
+13
+6
+3
+1
-2
ERROR % +1 +1
The match is fairly good, with the largest error at D0, sug gesting t hat the AC modulus i s too low. No te that the deflection ratio adjustment factor does not work well at DO since most of the deflection is generated in the subgrade (For example, for this trial, 625 microns (24.5 mils) of the total deflection of 782 microns (30.8 mils) comes from the subgrade, i.e . 80%). Various method s are used for this ad justment. We will simply guess for the third trial and use an AC modulus twice as large as previously used, i.e. 4138 MPa (600 ksi) to get the following deflections: Dq
D!
D2
671 (26.4)
516 (20.3)
691 (27.2) -3
D3
D4
D5
353 (13.9)
CALCULATED 248 182 (9.76) (7.17)
141 (5.54)
114 (4.49)
518 (20.4)
348 (13.7)
TARGET 242 177 (9.53) (6.98)
137 (5.40)
111 (4.38)
0
+1
+3
+3
ERROR % +2 +3
D6
The error is still large at D0, but now the AC modulus is too high. Since trial runs 2 and 3 are identical excep t for AC modulus, we can try interpolating for a new AC modulus to get the following
5-61
4138 -
(413 8 - 2069) * 7— — 67 I| (782-671)
= 4138 - 373 = 3765M Pa(54 6ksi). Using this with ELSYM5 gives: D0
D2
D3
D4
D5
D6
686 (27.0)
521 (20.5)
353 (13.9)
CALCULATED 247 182 (9.74) (7.15)
140 (5.53)
114 (4.48)
691 (27.2)
518 (20.4)
348 (13.7)
TARGET 242 177 (9.53) (6.98)
137 (5.40)
111 (4.38)
-1
+1
+1
+2
+3
ERROR % +2 +2
This looks quite good, but now D6 shows the largest error. Additional iteration would involve adjusting the subgrade 114 mod ulus to 5 1 x — = 52M Pa(7500ksi) to g et: Do
Dj
D2
678 (26.7)
513 (20.2)
691 (27.2) -2
D3
D4
D5
D6
348 (13.7)
CALCULATED 242 178 (9.54) (7.00)
137 (5.41)
111 (4.38)
518 (20.4)
348 (13.7)
TARGET 242 177 (9.53) (6.98)
137 (5.40)
111 (4.38)
-1
0
0
0
ERROR % 0
0
The largest error is approximately 2% at D0, which is usu ally considered accept able. We have converged fai rly quickly in this example to E Ac = 2069 MPa (300 ksi), Ebs = 172 MPa (25 ksi), and E Sg = 52 MPa (7.5 ksi), and would have arrived at the correct AC modulus of 3450 MPa (500 ksi) in one or two more iterations. 5-62
In the second example actual pavement thickness data and deflections from Figure 5.17 and Table 5.13 are used with the ELSYM5 computer program to estimate a "reasonable" set layer(simply moduli.describe This secti is from F). the SH P GPSof sites d asonSection TheRP/LTP selected load is 9,512 lb. Use a "standard" FWD load plate with 300 mm (11.8 in.) diameter. It is note d that this is a relatively straightforward appearing pavement section; however... 5.2.1 Initial Esti mat es First, based on what we know from the prior information covered in this course, estimate/guess the approximate layer moduli. (a)
Asphalt Con crete From Figure 3.25 (SECTION 3.0) and for an aver age temperature (mid-depth) o f about 15.6°C (60° F), estimate EaC ~ 6,900 MPa (1,000,000 psi).
(b)
Base Course Since the base is crushed limestone, start with a E b « 40,0 00 psi (276 MPa). This is jus t a marginally educated guess. Use o f the Shell criterion f rom SECTION 2.0 results in a base modulus o f about 965 MPa (140,000 psi) which seems high (however, later on, a modulus of 965 MPa (140,000 psi) will not seem so high).
(c)
Subgrade Using Newcomb's equation for estimating subgrade modulus with a deflection measured 914 mm (36 in.) from the center of the load plate (refer to Section 5.1.3):
5-63
Asphalt Concrete 194 mm (7.65”) Crushed Limestone Base 368 mm (14.47”)
Silty Sand Subgrade 4,467 mm (175.88”) or oo
Possible Shale Rock Layer @ 5 m (16.5’(198”))
re 5. 17 - SHRP P avem ent Sect ion F (GPS-6A: AC Overlay of AC P avem ent - Se ction Loc ated in Kentucky )
Table 5.13 - Test Temperatures and Surface Deflections for SHRP Section F.
Air Temperature:
12.8° C (55.0° F)
Pavement Temperatures: Surface: Depth = 25 mm (1”): Depth = 100 mm (4”): Depth = 173 mm (6.8”):
10° C (50.0° F) 16.7° C (62.0° F) 15.7° C (60.3° F) 16.3° C (61.4° F) Deflection @
Load No .
FW D Load kN
lb
0 mm (0”) u m mils
203mm i8”) um mils
305mm
457mm
( 1 2 ” ']
um
nils
um m ils
610mm {24” ) um mils
914mm {3 6 ” )
um mils
1524mm (6 0 ” )
um mils
1
29.06 6534 83.3 3.28 68.3 2.69 59.2 2.33 47.8 1.88 39.6 1.56 27.7
1.09
17.3 0.68
2
42.3
9512 128.8 5.07 109.7 4.32 93.2 3.67 75.9 2.99 61.0 2.40 42.9
1.69
25.7 1.01
3
56.32 12662 184.9 7.28 151.6 5.97 131.3 5.17 108.2 4.26 88.6 3.49 60.2
2.37
33.8 1.33
4
74.78 16812 246 .6 9.71 207.5 8.17 180.6 7.11 149.4 5.88 122.2 4.81 83.6
3.29
46.5 1.83
5-65
= -530 + 0.00877 ( P/D3) = -530 + 0.0087 7 (9,512 lb./0.00169 i n.) ^ 48,83 0 psi (without a stiff layer i.e. subgrade is semi-infinite) . This seems a bit high, so try something lower, say 172 MPa (25,000 psi). (d)
Stiff Laver Fo r now, assume there is no stiff layer.
5.2.2 Class Exercise The following set of ELSYM5 results illustrate a manual approach to analyzing deflections Table 5.13 (Pavement section shown the in Figure 5.10).in Based on these results, each group should analyze three additional struc tures and record results for Runs 12, 13 & 14 below. (Note: There are no correct answers—this is just to get a "quick" idea o f how y our changes affect the deflections.)
i § I
Layer
Run h
o. 1
Material Properties E, MPa (ksi)
Calculated Deflections, jam (mils) 0 mm (0 in.)
AC
6,900 (1,000)
0.35
Base
276 (40)
0.40
Subg.
172 (25)
0.45
203 mm 305 mm 457 mm (8 in ) (12 in.) (18 in.)
196.6 (7.74)
168.1 (6.62)
Mea sure d deflections (mils): 5.07 Comment
4.32
150.8 (5.94)
610 mm (24 in.)
127.0 (5.00)
3.67
106.9 (4.21)
2.99
Calculated deflections too high; D 36 in. and D60 in. indicate "stiffer" subgrade required.
5-66
915 mm 1525 mm (36 in.) (60 in.) 76.7 (3.02)
2.40
1.69
44.5 (1.75)
1.01
(b) Layer
AC
Material Properties E, MPa (ksi) 0.35 6,900 (1,000)
Base
276 (40)
0.40
Subg.
241 (35)
0.45
Run No. 2 Calculated Deflections, |am (mils) 0 mm (0 in.) 167.9 (6.61)
203 mm 305 mm 457 mm (8 in.) (12 in.) (18 in.) 100.6 139.7 122.7 (3.96) (5.50) (4.83)
Mea sured deflections (mils): 5.07 Com ment:
2.99
2.40
31.0 (1.22)
1.69
1.01
Calculated Deflections, |im (mils) 0 mm (0 in.)
6,900 (1,000)
0.35
Base
345 (50)
0.40
Subg.
276 (40)
0.45
150.4 (5.92)
203 mm 305 mm 457 mm (8 in.) (12 in.) (18 in.) 107.7 87.4 123.2 (4.85)
Mea sured deflections (mils): 5.07 Com ment:
56.1 (2.21)
82.3 (3.24)
Run No. 3
Material Properties E, MPa (ksi)
AC
3.67
915 mm 1525 mm (36 in.) (60 in.)
Calcula ted deflections still too high, increas e base stiffness; D 36 in. and D60 in. improved but also increase subgrade stiffness a bit. (c)
Layer
4.32
610 mm (24 in.)
4.32
(4.24)
(3.44)
3.67
2.99
610 mm (24 in.) 71.1
48.5
27.2
(2.80)
(1.91)
(1.07)
2.40
Calcula ted deflection s still too high, increas e base stiffness a bit more; D 36 in. improved, D60 in. much better thus leave subgrade modulus as is for now.
5-67
915 mm 1525 mm (36 in.) (60 in.)
1.69
1.01
(d) Layer
Run No. 4
Material Properties E, MPa (ksi)
0 mm (Oin.)
AC
6,900 (1,000)
0.35
144.0 (5.68)
Base
414 (60)
0.40
Subg.
276 (40)
0.45
Calculated Deflection s, 203 mm 305 mm 457 mm (8 in.) (12 in.) (18 in.) 117.9 103.1 84.1 (4.64) (4.06) (3.31)
Me asured deflections (mils): 5.07 Comm ent:
3.67
610 mm (24 in.)
2.99
915 mm 1525 mm (36 in.) (60 in.)
68.8 (2.71)
47.8 (1.88)
2.40
1.69
27.2 (1.07)
1.01
Calculate d deflectio ns still too high, try a stiff layer locate d at 198 in. (5.03 m) depth. Redu ce base and subgra de moduli since the stiff layer will reduce the deflections s omewhat. (e)
Layer
4.32
(mils)
Run No. 5
Material Properties
Calculated Deflections, jj.ni (mils) 0 mm (0 in.)
E, MPa
203 mm 305 mm 457 mm (8 in.) (12 in.) (18 in.)
610 mm (24 in.)
915 mm (36 in.)
1525 mm (60 in.)
83.3
55.6
25.7
(3.28)
(2.19)
(1.01)
(ksi)
AC
6,900 (1,000)
0.35
Base
345 (50)
0.40
Subg.
172 (25)
0.45
Stiff Layer
6,900 (1,000)
0.45
168.4 (6.63)
Meas ured deflections (mils): 5.07 Comment:
140.7 (5.54)
4.32
Try a stiffer base and subgrade.
5-68
124.0 (4.88)
3.67
102.1 (4.02)
2.99
2.40
1.69
1.01
(f) Layer
Run No. 6 Calculated Deflections, jam (mils)
Material Properties E, MPa (ksi)
AC
6,900 (1,000)
0.35
Base
414 (60)
0.40
Subg.
272 (40)
0.45
Stiff Layer
6,900 (1,000)
0.45
0 mm (0 in.) 132.1 (5.20)
Mea sured deflections (mils): 5.07
203 mm 305 mm 457 mm (12 in.) (18 in.) (8 .in.) 90.9 71.9 105.7 (4.16) (3.58) (2.83)
4.32
3.67
2.99
610 mm (24 in.) 56.6 (2.23)
915 mm 1525 mm (36 in.) (60 in.) 15.5 35.8 (1.41) (0.62)
2.40
1.69
1.01
Comment: D 36 in. and D60 in. too low. Incr ease base stiffness and decrease subgrade stiffness. (g )
Layer
AC
Run No. 7 Calculate d D eflections, |im (mils)
Material Properties E, MPa (ksi) 6,900 (1,000)
0 mm (0 in.)
0.35
Base
552 (80)
0.40
Subg.
172 (25)
0.45
Stiff Layer
6,900 (1,000)
0.45
150.1 (5.91)
Meas ured deflections (mils): 5.07 Comment:
203 mm 305 mm 457 mm (8 in.) (12 in.) (18 in.) 124.5 (4.90)
4.32
110.0 (4.33)
3.67
91.4 (3.60)
2.99
610 mm (24 in.) 75.9 (2.99)
2.40
Increase subgrade sti ffness a bit to see if Do in. through D60 in can be reduced.
5-69
915 mm 1525 mm (36 in.) (60 in.) 52.8 (2.08)
1.69
26.2 (1.03)
1.01
(h)
Layer
AC
Run No. 8
Material Properties E, MPa .. il-i6,900 (1,000)
Calculated Deflections, |im (mils)
0.35
Base
552 (80)
0.40
Subg.
207 (30)
0.45
Stiff
6,900
0.45
0 mm 203 mm 305 mm 457 mm (0 in ) (Sin) (12 in.) (18 in.) 138.7 113.0 99.1 81.0 (5.46) (3.90) (4.45) (3.19)
Layer (1,000) Me asured deflections (mils): 5.07 Comment:
2.99
2.40
45.0 (1.77)
1.69
21.6 (0.85)
1.01
Run No. 9
Material Properties
Calculated Deflections, fim (mils)
E, MPa (ksi)
M.
AC
10,350 (1,500)
0.35
Base
552 (80)
0.40
Subg.
172 (25)
0.45
Stiff Layer
6,900 (1,000)
0.45
0 mm (0 ,n )
133.4 (5.25)
Me asure d deflections (mils): 5.07 Comment:
3.67
66.3 (2.61)
915 mm 1525 mm (36 in.) (60 in.)
No w try to reduce Do in. and increase D60 in. (slightly) by increasing the AC and reducing the subgrade stiffnesses. (i)
Layer
4.32
610 mm (24 in.)
203 mm 305 mm 457 mm (8 in.) (12 in.) (18 in.) 114.3 103.1 87.6 (4.50) (4.06) (3.45)
4.32
3.67
2.99
610 mm (24 in.) 73.9 (2.91)
2.40
Do in. improved but D 12 in. through D 36 in. increased a bit too much. Try increasin g the base stiffness. 5-70
915 mm 1525 mm (36 in.) (60 in.) 52.6 (2.07)
1.69
26.7 (1.05)
1.01
(j) Layer
Run N o. 10 Calculated Deflect ions, ^m (mils)
Material Properties E, MPa (ksi)
(0 in.)
AC
10,350 (1,500)
0.35
126.2 (4.97)
Base
690 (100)
0.40
Subg.
172 (25)
0.45
Stiff Layer
6,900 (1,000)
0.45
0 mm
Mea sured deflections (mils): 5.07 Comment:
108.2 (4.26)
4.32
83.1 (3.27)
3.67
915 mm 1525 mm (36 in.) (60 in.)
70.9 (2.79)
2.99
51.1 (2.01)
2.40
1.69
26.7 (1.05)
1.01
Run No. II Calculat ed Deflections,
Material Properties 0 mm
E, MPa (ksi)
(0 in.)
AC
10,350 (1,500)
0.35
Base
690 (100)
0.40
Subg.
190 (27.5)
0.45
Stiff Layer
6,900 (1,000)
0.45
120.9 (4.76)
Mea sured deflections (mils): 5.07 Comment:
97.5 (3.84)
610 mm (24 in.)
Do in., D 12 in., Dl8 in., D24 in. and D 36 in. all improved but D 36 in. not close enough. Try a slightly higher subgra de modulus. (k)
Layer
203 mm 305 mm 457 mm (8 in.) (12 in.) (18 in.)
203 mm 305 mm 457 mm (18 in.) (8 in.) (12 in.) 102.9 (4.05)
4.32
92.2 (3.63)
78.2 (3.08)
3.67
2.99
Jim
(mils)
610 mm (24 in.) 66.0 (2.60)
2.40
It appears that Run No. 10 provided a slightly better match of the calculated and measured deflections.
5-71
915 mm 1525 mm (36 in.) (60 in.) 47.2 (1.86)
1.69
24.1 (0.95)
1.01
(1) Layer
Run No. 12
Material Properties E,MPa
Calculated Deflections, urn (mils) 0mm
203 mm 305 mm 457 mm
(0 in
AC
0.35
Base
0.40
Subg.
0.45
Stiff Layer
0.45
)
(8 in.)
(12 m.)
(18 in.)
610 mm (24 in.)
915 mm 1525 mm (36 in.) (60 in.)
(m) Run No. 13 Layer
Material Properties E, MPa (ksi)
Calculated Deflections, |im (mils) 0 mm (0 in ;
AC
0.35
Base
0.40
Subg.
0.45
Stiff Layer
0.45
5-72
203 mm 305 mm 457 mm (12 in.) (18 in.) {8 in )
610 mm (24 in.)
915 mm 1525 mm (36 in.) (60 in.)
(n)
Layer
Run No . 14
Material Properties
Calculated Deflections, |am (mils) 203 mm 305 mm 457 mm (8 in.) (12 in.) (18 in.)
0 mm (0 in.)
E, MPa (ksi) AC
0.35
Base
0.40
Subg.
0.45
Stiff Layer
0.45
5.2.3 Problem Summary After 11 ELSYM5 runs and about an hour or so of effort, Run No. 10 appears to match the measured deflecti on the best. Thus, wh at in the beginning appeared to be a rather straightforward pavement sect ion is not. The resulting moduli are a bit unusual and are: EAC
=
Eb
= 690 MPa (100,000 psi)
ESG
10,342 MPa (1,500,00 0 psi)
=
RB @ 198 in. =
172 MPa (25,000 psi) 6,895 MP a (1,0 00,0 00 psi)
It should be apparent that a better method for performing backcalculation is desirable. Automated backcalculation programs perform this exercise more efficiently.
5-73
610 mm (24 in.)
915 mm 1525 mm (36 in.) (60 in.)
5.3 AUTOMATED BACKCALCULATION 5.3.1 Introduction This portion of SECTION 5 will be used to illustrate some fundamental characteristics about backcalculation com puter progra ms. This will include: a)
Typical Approach es
b)
Measures o f Convergenc e
c)
Converg ence Techniques
d)
Layers
e)
Summary of Existing Backcalculation Programs
The information presented below is generall y applicabl e to flexible pavements and partially applicable to rigid pave ments. For instance, the techniques can be used on con tinuous PCC pavements and for slab center tests on jointed PCC. However, PCC and overlaid PCC structures may pose problems so special consideration for backcal culation of r igid pavements is addressed in Section 5.4. 5.3.2 Typical Flowchart A basic flowchart which represents the fundamental ele ments in most known backcalculation programs is shown as Figure 5.18. This flowchart was patterned after one shown by Lytto n i5.1 0~|. Briefly, these elemen ts include: (a)
Meas ured deflections Includes the measured pavement surface deflections and associated distances from the load.
(b)
Laver thicknesses and loads Includes all layer thicknesses and load levels for a specific test location.
5-74
Occasion Usual Path
Figure 5.18 - Comm on Elements of Backcalculati on Program s (mod ified af ter Ly tton 15.11)
5-75
al Pa th
(C)
Seed moduli and Poisson's Ratio The seed moduli are the initial moduli used in the computer program to calculate surface deflections. These moduli are usually esti mated from u ser expe rience or various equations (as illustrated in SEC TIO N 2.0). Typical values for Poisson's Rati o are given in Section 2.8, Page 2-47.
(d)
Deflec tion calculation Layered elastic computer programs such as WESLEA, CHEVRON, BISAR, or ELSYM5 are generally used to calculate a deflection basin.
(e)
Error check This element simply compares the measured and cal culated ba sins. There are various error measures which can be used to make such comparisons (more on this in a subsequent paragraph in this section).
(f)
Search for new moduli Various methods have been employed within the various backcalculation programs to converge on a set of layer moduli which produces an acceptable error between the measured and calculated deflec tion basins.
(g)
Controls on the range of moduli In some of the backcalculation programs, a range (minimum and maximum) of moduli are selected or calculated to prevent program convergence to un reasonable moduli levels (either too high or low).
5.3.3 Measu res of Deflection Basin Convergence In backcalculating layer moduli, the measure of how well the calculated deflection basin matches (or converges to) the measured deflection basin was previously described as the "error check". This is also referred to as the "goodn ess of fit" or "convergence error." As comp uter speed has increased allowing greater numbers of iterations 5-76
the accepted level of convergence error has decreased quite substantially. It should also be mentioned that some programs may report errors based only on those deflec tion sensors used i n the basin matching routine. Conv er gence errors are the primary measure of how well the backcalculation routine has matched measured values. In some cases one should not expect low errors. Fo r instance, a badly cracked pavement violates the funda mental assumption of continuity, so that one should ex pect a difference between theoretical and measured deflections. Three o f the more common ways to calculate such m easures include: (a)
Average of absolute relative differences (ABS)
(Eq. 5.31) where ABS
=
average of absolute relative differences between the calculated and measured deflection basin, expressed as a percentage,
dci
=
calculated pavem ent surface deflection at sensor i,
dmi
=
measured pavement surface de flection at sensor i, and
nd
=
number of deflection sensors used in the backcalculation process.
5-77
(b)
Ro ot Mean Square (RMS) 1
RMS (%) =
"
rd
1n d Zm
ci
-d mi V
(100)
(Eq. 5.32)
where
(c)
RMS =
Root mean square error,
dci
as defined in 5.3.3(a),
=
dmi
as defined in 5.3.3(a), and
nd
as defined in 5.3.3(a).
Sum of absolute values of the relative differences (ARS) d ■ -d
A
(100)
i= l
where ARS
=
sum of the absolute values of relative difference s betw een the calculated and measured deflec tion basin, expressed as a per centage, [Note: ARS = nd * ABS]
dci
as defined in 5.3.3(a), and
dmi
as defined in 5.3.3(a).
It has been suggested in the literature that an RMS (%) error must be less than 1% [5.41], However, this is not always achievable in practice due to the inability to accurately characterize pavement layer thickness variations throug hout the project. Often 5-78
(Eq. 5.33)
the practicing engineer must seek to minimize the error to the greatest extent possible, realizing he must accept errors signifi cantly greater. A 1-2% error per sensor is generally considered to be acceptable for RMS or ABS. ARS should be approximately 1.5 * no. of sensors used. (d)
Example 1 From Table 5.13, calculate the ABS, RMS, and ARS for Loa d 2 and Run No. 10. The following deflections apply: Deflections |am (mils) Measured
nd 1 (0mm, 0") (203mm, 8") 2 3 (305mm, 12") 4 (457mm, 18") 5 (610mm, 24") 6 (915mm, 36") 7 (1,525mm, 60") (i)
128.8 109.7 93.2 75.9 61.0 42.9 25.7
Calculated
(5.07) ( 4 .32 ) ( 3 .6 7 )
(2.99) (2.40) (1.69) d.oi)
126.2 (4.97) 108.2 (4.26) 97.5 (3.84) 83.1 (3.27) 70.9 (2.79) 51.1 (2.01) 26.7 (1.05)
ABS 4.97-5.07
ABS % = 7
5.07 3.84 - 3.67 3.67
+
2.79 - 2.40 2.40 1.05-1.01 1.01
=
5-79
+
4.26-4.32 4.32
+
3.27 - 2.99 2.99 2.01 - 1.69 1.69
( 100)
8.1% (a high error! )
(ii)
RMS ( 4.26 - 4.32'
I f f 4. 9 7 - 5.07V
RMS (%) =
5.07
4.32
3.84 - 3.67f + p .27 - 299V + 3.67 2.99 V + p . 01 - 1 .6 9V + 1.69 )
=
( 2.79
- 2.40V 2.40
1/ 2
f 1.05 V
-1.0lV A 101
( 100)
10.4% (also a high error!)
(iii) ARS ARS (%)
5.14 - 5.07 1.05 - 1.01 4- ••• + 5.07 1.01
= =
(e)
56.5%
(still a high error !)
Example 2 Comp are Run No. 4 to Run No. 10 for Load 2. Use an ABS convergence measure. We already know ABS = 8.0% and ARS = 55.9% for Run No. 10. Calculate ABS and ARS for Run No. 4. Deflections |im (mils) Measured
nd 1 (0mm, 0") 2 (203mm, 8") 3 (305mm, 12") 4 (457mm, 18") 5 (610mm, 24") 6 (915mm, 36") 7 (1,525mm, 60")
128.8 109.7 93.2 75.9 61.0 42.9 25.7
5-80
Calculated
(5.07) ( 4 .3 2 )
(3 67)
(2.99) (2 4 0 ) ( 1 69)
.(L0.il
..
144.0 117.9 103.1 84.1 68.8 47.8 27.2
(5.68)
(4.64) (4.06) (3.31) (2.71)
(1.88) (107)
( 100)
ABS (%)
=y
+
5.68 - 5.07 5.07 4.06-3.67 3.67
+
+
4.64-4.32 4.32
3.31 -2.99 2.99
+
2.71 -2.40 2.40
+
=
1.88 - 1.69 1.69 10 . 1% f
ARS (%)
=
1.07 - 1.01 \ ( 100) 1.01 /
5.68 - 5.07 -f 5.07 V
. .
+
70.9% (Thus, based on the ABS and ARS measures, Run No. 4 has higher convergence errors than Run No. 10; however, both convergence errors are substan tially higher than normally acceptable when using a backcalculation computer program (recall the "fits" were done manually).) (f)
Example 3 As a final example of convergence measures, com pare RMSs for Run No. 10 and Run No. 11. This will conclusively tell us whe ther Run No. 10 was actually "better" than Run No. 11.
5-81
1.07 - 1.01 1.01 ( 100)
Recall for Run No. 10: RMS = 10.6% For Run No. 11 (Load 2): Deflections mm (mils) Measured Calculated 128.8 (5.07) 120.9 (4.76) (4 32) 109.7 102.9 (4.05) (367) 93.2 92.2 (3.63) 75.9 (2.99) 78.2 (3.08) 61.0 (2,1) 66.0 (2.60) 42.9 (1 69) 47.2 (1.86) 25.7 24.1 (0.95) (.10,1)
nd
1 (0mm, 0") 2 (203mm, 8 ") 3 (305mm, 12") 4 (457mm, 18") 5 (610mm, 24") 6 (915mm, 36") 7 (1,525mm, 60")
.....
1 "
RMS (%)
4.76 - 5.07V
=
4.05 - 4.32
v
4.32
5.07 ^3.63 - 3.67V 3.67 /
f3.08 - 2.99x2 2.99
1.86 - 1.69 1.69
0.95 -1.01 1.01
vv
+
(
2> '
6.5%
Oops, Run No. 11 was "better" than Run No. 10 after all. This possibl y su ggests an other reason for using converg ence measures. Also calculat e ARS: ARS: ARS (%)
4.05-4.32 4.32 3.08 - 2.99
=
+
240 0.95 - 1.01 1.01 40.8%
5-82
+
/ .
2.60 - 2.40 2.40 V 1/2
(100)
5.3.4 Class Exercise — Convergence Error The exercise is based on SHRP Section F, as shown 7.
Figure 5.1
Exercise No. 1 Load = 42.3 kN (9512 lb.) r = 150 mm (5.91 in.) Estimated moduli e a c
Eb s Es g
= 7,094 MPa (1028.8 k si) = 480 MPa (69.7 ksi) = 305 MP a (44.3 ksi)
Deflections, um (mils') 0 in. 8 in. 128.8 109.7 Measured: (5.07) (4.32) 131.8 106.9 Calculated: (5.19) (4.21)
12 in. 93.2 (3.67) 93.0 (3.66)
18 in. 75.9 (2.99) 75.4 (2.97)
24 in. 36 in. 61.0 42.9 (2.40) (1.69) 42.9 61.7 (2.43) (1.69)
Calculate ARS = ? see Section 5.3.3(c) (Answer: ARS = 11.06%) RMS= ? see Section 5.3.3(b) (Answe r: RMS = 2.07%) Exercise No. 2 Same section as above, except a different backcalculation attempt Estimated moduli = 5,929 MPa (859.9 ksi) = 888 MPa (128.8 ksi) E s g = 193 MP a (27.9 ksi) Rigid Base = 6,895 MPa (1000 ksi)
Eac
EB s
@ 198 in. (5.0 m) depth 5-83
60 in. 25.7 (1.01) 24.6 (0.97)
Deflections, jim (mils)
Measured: Calculated:
0in. 128.8 (5.07)
8in. 109.7 (4.32)
12 in. 93.2 (3.67)
18 in. 24 in. 75.9 61.0 (2.99) (2.40)
36 in. 42.9 (1.69)
60 in. 25.7 (1.01)
130.8 (5.15)
104.9 (4.13)
91.9 (3.62)
76.4 (3.01)
45.7 (1.80)
23.9 (0.94)
64.0 (2.52)
Calculate ARS = ?
(Answer: ARS = 26.5%)
RMS = ?
(Answer: RMS = 4.5%)
5.3.5 Measure of Modulus Converge nce Some backcalculation computer programs (such as EVERCALC and MODCOMP) have another conver gence criterion which can terminate the backcalculation process. This criterion checks the moduli changes from one iteration to the next. If the change of each layer modulus is below some preselected limit, the deflection matching process is overridden and the backcalculation process is stopped. This modulus check takes the follow ing form: Modulus Tolerance >
where
Modulus Tolerance
Ej(k+1) -EjOO Ej(k)
( 100)
= difference layer moduli from oneinitera tion (k) to the next
(k+1),
EiOO
= a specific layer modulus for the i-th layer at the k-th iteration, and
Ei(k+1)
= a specific layer modulus for the i-th layer at the (k+ l)-th itera tion.
This criterion can be particularly helpful if due to model ing errors (such as incorrect layer thicknesses) or 5-84
(Eq. 5.34)
deflection measurement errors the normal deflection basin convergence criterion cannot be achieved. In this manner, the program will terminate before the maximum number o f allowable iterations is achieved. 5.3.6 Convergence Technique s The straightforward goal of the backcalculation process is to estimate a set of layer elastic modul i that bes t match the measured and calculated deflections. A number of com puter programs have been developed during the past dec ade for this purpose, some of which are discussed below. Most of the currently used programs use elastic pavement analysis for the iterative deflection basin matching process which assume that the layer thicknesses and Poisson's ra tios are known. As was briefly described in Section 5.3.2, the process is started with initial (seed) moduli which are used to calculate a first deflection basin. The measured and calculated deflections are then compared and if they are different more than a preselected convergence error allows (such as ABS or RMS), the process is repeated until an acceptable convergence is achieved. This subsec tion is an attempt to describe how this iterative process typically is structured in backcalculation computer programs. (a)
BISDEFAVESDEF Programs The convergence technique used in these two U.S. Army Waterways Experiment Station developed backcalculation program s will be bri efly descri bed [5.12. 5.131. Basically, the iterative process in volves development of a set of equations which define the slope and intercept for each deflection and unknown layer modulus as follows: log (deflectionj) = Aji + Sji (log Ei) where
A = interce pt, S = slope, j
= 1,2,..., ND (where ND = number of deflections), and
i = 1,2, ..., NL (where NL = number of layers with unknown moduli)
5-85
(Eq. 5.35)
This is further illustrated by use of Figure 5.19 which shows how the deflection-modulus relation ship is developed from layered elastic analysis (srcinally done with the BISAR program, but more recently at using thewhich layered elasticWESLEA). system recently de veloped WES, is called
LOG MODULUS
Figure 5.19. Basic Process f or Matching deflection Basin s [from Ref. 5. 431
5-86
(b)
MOD ULUS Program The MODULUS program is quite unique in it's ap proach backcalculation in that program it first performs series oftoforward layered-elastic runs to a construct a database o f deflections based on u ser supplied moduli ranges. It then utilizes a patte rn search procedure to match each observed deflection basin in the field data file to a calculated deflection basin. If the measured deflection basi n falls between two calculated basins, the program utilizes an inter polation procedure to arrive at a final calculated deflection b asin. This negates the need t o iterate through a series of forward layered-elastic computer runs. MO DUL US seeks to m inimize the error be tween the calculated and measured deflection basins using the following equation:
(Eq. 5.36) where = squared error w™ = measu red d eflection at senso r i w ct
= computed deflection at sensor i
s
= number of sensors
w ei
= user supplied weighting factor for sensor i
The user supplied weighting factor can be used to lessen or completely omit consideration of any sen sor in the backcalculation process. This can be useful in many instances, for example when the sub grade is behaving in a non-linear fashion, the weighting of outer sensors can be set to cause MODULUS to fit the inner sensors only.
5-87
Although a rigorous discussion o f the pattern searc h procedure is beyond the scope of this course, it is necessary to discuss the "convexity test" and the meaning the MO results ofUS thisoutpu test because it doesearlier, appea r onofthe DUL t. As stated MOD ULU S generates a database of cal culated de flection basins for use in matching the observed, or measured basi ns. The error t erm, shown previousl y, represents the error between the measured and cal culated deflection basins. MODULUS searches for the combination of layer stiffne sses which minimizes the error term. The pattern search procedure will always converge in MODULUS, i.e. it will always find an answer. The question becomes: is it the best a nswer? Not 5.20 shows what may happen in the always.o Figure course f backca lculation. (MODUL US prefers to work in terms of modular ratios with respect to the subgrade. On one axis, the ratio of layer 1 with re spect to the subgrade is plotted. On the other axi s, the modular ratio of layer 2 with respect to the sub grade is shown). As can be seen from the pl ot, the error term reaches a minimum at point A and B. When MODULUS converges to an answer, it searches the surrounding area to see if it is indeed at the lowest point. If the area near t he solution is not convex, such as around point A or B, the program will indicate that the convexity test has f ailed. This means that the results obtained are suspect.
Convexity errors will occur for two reasons: 1) the operator has confined the ranges for the seed moduli too tightly or 2) the deflection basin is irregular and does not conform to layered-elastic theory (measuring across pavement cracks will result in irregular basins).
5-88
5.3.7
Summary of Backcalc ulation Programs (a)
Backcalculation Program s Shown in Table 5.14 is a summary of the most commonl y used backcal culation computer programs used or developed mostly in the U.S. (as o f No vem ber 1990). This summary was prepared by SHRP/PCS/Law for use by the SHRP LTPP Expert Task Group for Deflection Testing and Backcalcu lation. The summary identifies 13 separate computer programs along with some of their basic features. There are a number of other programs described in the literature, and the field keeps growing.
(b)
Typical Progra m Results The "typical" pavement in sections used in SEC TION 3.0 are shown, for convenience, as Fig ure 5.21. The ELSYM5 program was used to gen erate a "manufactured" deflection basin for each of the three sections. The four backcalculation pro grams (BOUSDEF, EVERCALC, MODULUS and MODCOMP) used in this course were then run with the known layer thicknesses and the "manufactured" deflection basins to illustrate typic al pro gram results. The assumed layer thicknesses, moduli, and Poisson's ratios are shown in Table 5.15. Further, the "manufactured" deflection basins obtained with ELSYM5 are shown. The results fromMODULUS the ELSYM5, BOUSDEF, EVERCALC, and MODCOMP programs are shown in Table 5.16. User's guides, program demonstration and application are included in SECTION 6 and the appendices.
5-90
Table 5.14 - Partial List of Layer Moduli Backcalculation Programs [Rada et al] Forward Calculation Method
Forward Calculation Subroutine
Backcalculation Method
NonLinear Analysis
Rigid Layer Analysis
flayer Interface Analysis
Maximum Number of Layers
Seed Moduli
Range of Acceptable Modulus
Ability to Fix Modulus
Convergence Routine
Error Conver gence Function
USACE-WES
Muhi-Layer Elastic Theory
BISAR (Proprietary)
Iterative
No
Yes
Variable
Required
Required
Yet
Sum of Squares of Absolute Error
Yes
BOUSDEI
ZHOU, etal. OREGON STATE UNIV.
Method of Equiv.
MET
Iterative
Yes
Yes
Fixed (Rough)
Cannot Exceed No. of Deflec., Works Best For 3 Unknown* 5, Works Best for 3 Unknowns
Required
Required
Yes
Sum of Percent Errors
Yes
CHEVDEF
USACE-WES
MuKi-Layer Elastic Theory
CHEVRON
Iterative
No
Yes
Fixed (Rough)
Required
Required
Yes
Sumof Squares of Absolute Error
Yes
ELMOD/ ELCON
P. ULL1DTZ DYNATEST
Method of Equiv. Thickness
MET
Iterative
Yes (Subgrade
Yes
Fixed (Rough)
Cannot Exceed No. of Deflec., Works Best For 3 Unknowns Up to 4, Exclusive of Rigid Layer
None
No
Yes
Relative Error on 3 Sensors
No
ELSDEF
TEXAS AAM UNIV., USACE-WES
Multi-Layer Elastic Theory
ELSYM5
Iterative
No
Yes
Fixed (Rough)
Required
Required
Yes
Sum of Squares of Absolute Error
Ye«
EMOD
PCS/LAW
MuHi-Layer Elastic Theory
CHEVRON
Iterative
Yes (Subgrade
No
Fixed (Rough)
Cannot Exceed No. of Deflec., Works Best For 3 Unknowns 3
Required
Required
Yes
Sum of Relative Squared Error
No
EVERCALC
J. MAHONEY, etal.
CHEVRON
Iterative
Yes
Yes
Fixed (Rough)
3 Exclusive of Rigid Layer
Required
Required
Yes
Sumof Absolute Error
No
FPEDDI
W. UDDIN
Muhi-Layer Elastic Theory Muhi-Layer Elastic Theory
BASINPT
Iterative
Yes
Yes (Variable)
Fixed (Rough)
Unknown
Program Gener ated
Unknown
Unknown
Unknown
No
ISSEM4
P. ULUDTZ, R. STUBSTAD
Muhi-Layer Elastic Theory
ELSYM5
Iterative
No
Fixed (Rough)
4
Required
Required
Yes
Relative Deflec. Error
No
MODCOMP 3
L. IRWIN, SZEBENYI
Muhi-Layer Elastic Theory
CHEVRON
Iterative
Yes (Finite Cylinder Concept) Yes
Yes
Fixed (Rough)
2 to 15 layers, Max 5 Unknown Layers
Required
Required
Yes
Relative Deflec. Error at Sensors
No
Program Name
Developed
BISDEF
By
Thickness
„
Only)
Table 5.14 (cont'd.) - Partial List of Layer Moduli Backcalculation Programs [Rada et al]
Program Name
Developed
Fortran! Calculation Method
Forward Calculation Subroutine
Back calculation Method
NonLinear Analyib
Rigid Layer Analysis
Layer Interface Analysis
Maximum Number of Layers
Seed Moduli
By
Range of Acceptable Modulus
Ability to Fix Modulus
MODULI'S
TEXAS TRANS. INSTITUTE
Mufti-Layer Elastic Theory
WESLEA
DataBase
Yes?
Yes (Variable)
Fixed?
Up to 4 Unknown plus Stiff Layer
Required
Required
Yes
Sumof Relative Squared Error
PADAL
S.F. BROWN, et al.
Multi-Layer Elastic THeofy
UNKNOWN
Iterative
Yes (Sub grade
Unknown
Fixed?
Unknown
Required
Unknown
Unknown
Sum of Relative Squared Error
Unknown
WESDEF
USACE-WES
WESLEA
Iterative
No
Yes
Variable
Upto5Layers
Required
Required
Yes
MICHIGAN STATE
CHEVRON
Iterative
No
Yes
Fixed
Required
Optional
Yes
Sumof Squares of Absolute Error Sum of Relative Squared Error
Yes
MICHBAK
Mu hi-Layer Elastic Theory Multi-Layer Elastic Theory
Convergence Routine
Error Conver gence Function Yes
Only)
5 9 2
Up to 4 Unknown plus Stiff Layer
Yes
2' (50 mm) ACP 6* (150 mm) Base
Fine-grained subgrad e
Section A (Thin Thickness Section)
5* (125 mm) ACP
6* (200 mm) Base
Fine-graîned subgrade
Section B (Medium Thickness Section)
9* (230 mm) ACP
6‘ (150 mm) Base
Fine-grained su bgrade Section C (Thick Section)
F ig u r e
5.21
5-93
’Typical" Pavement Sec tions
Table 5.15 "Typica l" Sections — Roadway Sectio ns and Backcalculation Results
Typical Pavement Sections Thickness, mm (in.) Layer
Thin (A)
Medium (B)
Thick (C)
Poisson's Ratio
Modulus, MPa (psi)
AC
51 (2.0)
127 (5.0)
229 (9.0)
0.35
3467 (500,000)
Base
152 (6.0)
203 (8.0)
152 (6.0)
0.40
172 (25,000)
_
_
0.45
--
52 (7,500)
Subgrade
Deflection Measurements Tire Load = 40kN (9000 lbs.) Tire Radius = 150 mm (5.9") Offset
Deflection, nm (mils)
Sensor No.
mm
(in.)
1
0
(0)
1 2 2 6 .3
(4 8 . 2 8 )
690.4
(27.18)
455.2
(17.92)
2
203
(8)
8 6 9 .4
(3 4 . 2 3 )
589.0
(23.19)
412.0
(16.22)
3
305
(12 )
6 6 6 .2
(2 6 . 2 3 )
5 1 7 .9
(20.39)
385.3
(15.17)
4
457
(18 )
4 7 1 .4
(18.56)
423.9
(16.69)
343.9
(13.54)
5
61 0
(24)
3 5 3 .3
(1 3 .9 1 )
348.2
(13.71)
305.0
(12.01)
6
914
(36)
2 2 6 .3
(8 .9 1 )
242.1
(9.53)
237.7
(9.36)
7
1219
(48 )
164.6
(6 .4 8 )
17 7. 3
(6 .9 8 )
185.9
(7.32)
8
1524
(60)
129.8
(5 .1 1 )
1 3 7 .2
( 5 .4 0 )
147.3
(5.80)
Thin
5-94
Medium
Thick
Table 5.16 "Typical" Sections — Roadway Sections and Backcalculati on Resul ts (Continued)
Backcalculation Results Layer Modulus, MPa(psi) Program
B a se
AC
Subgrade
ARS
RMS
(%)
(%)
BOUSDEF Thin Medium Thick
5516 3228 3490
(800,000) (4 6 8 ,1 0 0 ) (5 0 6 ,2 0 0 )
109 205 396
(1 5 ,8 0 0 ) (2 9 ,8 0 0 ) (5 7 ,5 0 0 )
50 50 48
(7 ,3 0 0 ) (7 ,2 0 0 ) (6 ,9 0 0 )
6.3 7 .9 2 .6
3295 3403 3390
(4 7 7 ,9 0 0 ) (493,500) (49 1,600 )
179 174 185
( 2 6 ,0 0 0 ) (2 5 ,3 0 0 ) ( 2 6 ,8 0 0 )
51 52 52
(7 ,4 0 0 ) (7,500) (7 ,5 0 0 )
5 .7 1. 0 1. 6
3517 3261 3618
(5 1 0 ,1 0 0 ) (473,000) ( 5 2 4 ,7 0 0 )
172 184 153
(25,000) ( 2 6 ,7 0 0 ) (2 2 ,2 0 0 )
52 52 52
(7,500) (7 , 5 0 0 ) (7 , 5 0 0 )
0.3 1.3 2 .2
3520 3 57 0 4130
(510,400) (5 1 7 ,6 5 0 ) (598,850)
174 1 70 54.3
( 2 5 ,2 3 0 ) ( 2 4 ,6 5 0 ) (7 ,9 0 0 )
5 1 .8 5 1 .8 5 3 .4
(7 ,5 0 0 ) (7 ,5 0 0 ) (7 ,7 0 0 )
0 .7 1.1 2 .8
EVERCALC Thin M e d iu m Thick
0 .9 0 .2 0 .2
MODULUS Thin Medium Thick MODCOMP Thin M ed iu m T h ic k
5.3.8. Verification of Backcalculation Results There have been and, undoubtedly, will be a number of attempts to verify that backcalculated layer moduli are "reasonable." To date, these attempts can be illustrated as those which examine measured, in-situ strains which are compared to calculated strains based on layered elastic analysis and backcalculated moduli and the other in which laboratory and backcalculated moduli are compared. (a)
Comparison Based on Strain Lenngren [5.14] in a recently completed study for RST Sweden which used backcalculated layer moduli (from a modified version of the EVERCALC program) to estimate tensile strains at the bottom of 5-95
0.1 0.2 0 .6
two thicknesses of AC (80 mm (3.1 in.) and 150 mm (5.9 in.)) pavement. For these actual pavement structures (located in Finland), actual, in-situ tensile strains were measured simultaneously along the de flection basins from an FWD. The instrumented pavement sections were developed by the Road and Traffic Laboratory (VTT) in Fin land. The strain gages were attached to the 150 mm (6 in.) cores which were, in turn, replaced into the AC surfacing. The deflections were induced in the two test pavements by use of a KUAB 50 FWD equipped with seven sensors (at 0 mm (0 in.), 200 mm (7.9 in.), 300 mm (11.8 in.), 450 mm. (17.7 in.), 600 mm (23.6 in.), 900 mm (35.4 in.), and 1,200 mm (47.2 in.)). The load plate had a diameter of 300 mm (11.8 in.). The applied load levels were ap proximately 12.5 kN (2,810 lb.), 25 kN (5,620 lb.), and 50 kN (11,240 lb.). The two pavement sections had either 80 mm (3.1 in.) or 150 mm (5.9 in.) AC surface course overlying a gravel and sand base (ranged from 550 to 620 mm (22 to 24 in.)), which, in turn, overlaid a "dry granular" subgrade (again, according to Lenngren [5.14]'). The computed results are shown in Tables 5.17 and 5.18. One can see that the backcalculated moduli were generally within ± 5 percent o f the measured values. (b)
Comparison of Laboratory and Backcalculated Moduli An attempt was made to compare resilient moduli from laboratory tasks (ASTM D4123 for AC cores and a simplified version of AASHTO T274 for un stabilized triaxial tests (base and subgrade)) to backcalculated moduli for five pavement sites in Wash ington state [5.15], The partial results of these com parisons are shown in Table 5.19. In reviewing these comparisons, the following apply: ♦
The backcalculated moduli were not adjusted for temperature or load rate effects. No stiff lay ers were used in the subgrade.
5-96
♦
The laboratory measured AC moduli were ad justed to a temperature estimated at the mid dle of the AC layer at the time of FWD testing.
♦
The laboratory moduli were all obtained at a load duration of 100 ms (about three to four times longer than the FWD load pulse).
♦
The laboratory tests on the unstabilized materials were done on remolded specimens.
Note that neither the backcalculated or laboratory moduli can be taken as the "truth." Why can such differences occur? There are numer ous reasons, the following are but a few: ♦
Remolding effects in laboratory compacted specimens (can include inability to reproduce field soil structure, density and/or moisture content).
♦
Load (stress) differences between FWD testing and laboratory tests.
♦
Nonrepre sentative field sample obtained for laboratory testing (e.g., sampling a subbase or improved fill material when attempting to sample the "true" subgrade soils.)
♦
Non homogeneity of in-situ pavement materials. Backcalculation results represent the "mean" valve of a large volume of soil. Within this vol ume, the stresses differ significantly as may the soil properties.
♦
Other sources of error which will be discussed later in SECTION 5.0.
5-97
Table 5.17 - Backcalculated and Measured Tensile Strains - 80mm (3.1") AC Section (after Lenngren [5.141)
Tensile Strain Bottom of AC (x 10-6) Time of Day (a.m. or p.m.) Backcalculated* Measured % Difference a .m .
119
123
-3
a .m .
119
122
-2
a .m .
74
64.9
+14
a .m . p.m .
60 2 84
6 4 .7 292
-8 -3
p.m.
2 84
2 83
~0
p.m*
167
159
+5
p.m.
167
158
+6
p .m .
87
8 4 .8
+2
p .m .
81
84.2
-4
*BackcaIculation process used sensors @ D0, D300, D600, D900 and D1200
5-98
Table 5.18 - Backcalculated and M easured Tensile Strains 150mm (5.9") AC section (after Lenngren [5.141)
Tensile Strain Bottom of AC (x 10*6) Time of Day (a.m. or p.m.) Backcalculated* % Difference M e a s u re d a.m. a.m. a.m.
66
6 9 .5
-6
71
69
+3
68
6 8 .7
-1
a.m. a.m.
38 127
34.7 130
+9 -2
a.m.
119
130
-8
p.m.
178
185
-4
p.m.
182
183
-1
p.m.
104
95.9
+8
p.m.
51
48.0
+6
p.m.
56
4 8 .5
+14
*Backcalculation process used sensors @ D0, D300, D600, D900 and D1200
5-99
Table 5.19 - Com parison of Backcalculat ed and Laboratory Modu li for Fi ve Test Sites in Washington State [from Ref. 5.15 along with updated Laboratory Results]
Moduli, MPa (ksi)
Location Section 1 Section 4 Section 5 Section 11 Section 15
AC
Base
Subg.
Convergence Error (RMS)
5 250 *
(7 6 1 )
159*
(2 3 )
1 8 6 * (2 7 )
1.2%*
27 9 0**
(4 0 5 )
1 86 **
(2 7 )
1 3 1 * * (1 9 )
n/a**
4730*
(6 8 5 )
331*
(4 8 )
1 8 6* (2 7 )
1.7%*
1570**
(2 2 8 )
2 2 1 **
(3 2 )
1 7 9* * (2 6 )
n/a**
57 7 0*
(8 3 6 )
2 7 6*
(4 0 )
2 4 8 * (3 6 )
2.3%*
33 6 0**
(4 8 7 )
1 86 **
(2 7 )
1 4 5 * * (2 1 )
n/a**
42 60 *
(6 1 7 )
18 6 *
(2 7 )
1 8 6* (2 7 )
1.4%*
35 2 0**
(5 1 0 )
2 2 1 **
(3 2 )
1 9 3 * * (2 8 )
n/a**
7 3 70 *
(1 0 6 9 )
269*
(39)
131* (19)
1.0%*
1 9 3**
(2 8 )
69** (10)
n/a**
10900** (1 5 8 0 )
Note s: *Backcalculation Method; Backcalc EVERCALC program. •‘ Laborat ory Metho d.
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ulated moduli obtained from the
5.4 BACKCALCULATION O F RIGID PAVEMENTS
5.4.1 Introduction In rigid pavement evaluation, the factors that are of inter est are the elastic modulus of Portland cement concrete (PCC) and the modulus of subgrade reaction (k-value) of the supporting medium. The elastic modulus of PCC and the k-value of the support can be backcalculated using the deflections obtained from a deflection test conducted on the interior of a rigid pavement. The elastic modulus of PCC can be used to evaluate the structural condition of the PCC slab, while the k-value of the supporting medium can be used to evaluate the supporting medium. The elas tic modulus of the PCC and the k-value of the supporting medium are required inputs for most overlay design meth ods. When conducting deflection testing on rigid pavements with the FWD, a load of 9,000 lb. or more should be applied to obtain the deflection basin. The effect of tem perature on the deflection basin measured at the slab inte rior has been found to be small [5.20], The maximum effect of temperature on deflections measured at the inte rior of the slab occurs during the warm mid-day period, when the slab is curled concave downward. If the effect of temperature on deflection is found to be significant, test ing during this period should be avoided. For backcalculation, pavements are generally treated as two-layer systemsrigid because the base or subbase will have little influence on the shape of the deflection basin when compared to the influence of the PCC and subgrade. An estimate of the modulus o f subgrade reaction (k-value) below the rigid pavement can be determined by computing the volume of the deflection basin as shown in Figure 5.2 2 [5.35], The k-value obtained in this manner is only an estimate.
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Sensor Offset, Inches 20
40
60
80
100
120
140
" i
160
180
200 220
A7
This point determined as the extension of a straight line through the outermost two deflection readings (maximum of 200 in. used in basin)
Volumetric k (PCI) =
t
Force (lbs.) £ Area n (Sq. in .) x ( Distanc e to Cent roid ) x 2 x n=1
Deflection, Mils
Figure 5.22
5-102
n
The backcalculation of composite pavements, which are concrete pavements overlaid by asphalt concrete creates some special problems. The backcalculation of these pavements are explained separately in Section 5.4.3. 5.4.2 Backcalculation Methods for Rigid Pavements Several methods are available to backcalculate the elastic modulus of PCC and the k-value of the supporting me dium for rigid pavements. These methods can be classified as: a)
Closed Form Solutions
b)
Elastic Layer Theory
c) d)
Method of Equivalent Thickness Database Approach
e)
Finite Element Methods
In all these methods the deflections are measured at the center of the slab. A description of each of these methods follows. a)
Closed Form Solution Hall and Mohseni [5.36] describe a closed-form solution for determining the elastic modulus of the PCC slab, the modulus of subgrade reaction and the elastic modulus o f the subgrade from the data from a deflection test. This method is applicable to a two layer system. In order to use this method deflections have to be obtained at distances of 0, 305, 610 and 915 mm (0, 12, 24 and 36 in.) from the load. This procedure uses the maximum deflection and the 'AREA' parameter which is computed from the de flection basin. The method uses relationships which were developed by Ioannides [5.35. 5.36], (Note: These are regression equations developed in U.S. units. To convert modulus values in psi to MPa divide by 145.) 5-103
The following steps must be used in this procedure: STEP 1: Determine the AREA parameter from the deflection basin using the following equation: AREA (in) = 6 ( 1 + 2 (Di/Do) + 2 (D2/D0) + (D3/D0)) where, Dq, D j, D 2 , D 3 are deflections at 0, 12, 24 and 36 inches from the load. STEP 2: Determine the dense liquid radius of rela tive stiffness (10 and the elastic solid radius of rela tive stiffness (le) using the following equations. lk = {In [(36-AREA)/1812.279]/(-2.559)}1/0-228
(Eq. 5.37)
le = {ln(36-AREA)/4521.676)/(-3.645)}1/0187
(Eq. 5.38)
These equations are valid for 1^ and le values be tween 15 and 80. STEP 3: Using the value of AREA calculated from the measured deflection basin and 1^ calculated from the previous step the k-value can be obtained from the Westergaard equation for center deflection which is: k = (P/8d0 l2k) * {1 +(l/27t)[ln(a/21k) + y-1.25] (a/lk)2} where, P = applied load (lbs.) d0 = maximum deflection at the center of the load (in) a = load radius (in) y = Euler's constant, 0.57721566490 STEP 4: Calculate the elastic modulus of the sub grade by using Losberg's deflection equation f5.39].
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(Eq. 5.39)
(Eq. 5.40)
Es = [2 P(l-n 2s)/d0le] [0.19245 + 0.0272(a/le)2 + 0.0199(a/le)2 ln(a/le)] STEP 5: The elastic modulus of the concrete can be computed from either o f the following equations: [l2
-
where, lk
1 < (l-V
Pc c ) k ]
■L-' pcc
(Eq. 5.41)
= dense liquid radius of relative stiffness , in. (from Eq. 5.37)
Epcc = PCC elastic modulus, psi Dpcc = PCC thickness, in (ipCC = PCC Poisson's ratio ( assume a value) k = k value ,psi/in (calculated from Eq. 5.39)
61e 0 le
“
(Eq. 5.42)
D 3p cc (l- H s2)
where, le = elastic solid radius of relative stiffness, in. (from Eq. 5.38) Hs = subgrade Poisson's ratio (assume a value) Es = subgrade resilient modulus, psi
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b)
Elastic Laver Theory
The approach used to backcalculate layer moduli of rigid pavements is essentially the same as that used for backcalculating flexible pavements. Backcalculation programs include a program for computing de flections as a subroutine. When backcalculating rigid pavements this subroutine should preferably be capable of handling variable interface conditions. Some programs cannot handle variable interface conditions and assume that full friction is present at all interfaces. At the interface between the PCC slab and the subbase full friction is usually not present. Friction can vary widely, ranging from 0 or near 0 for a PCC slab on subgrade to high friction for a PCC slab on cement treated base or for a bonded concrete overlay on PCC. Therefore, it is preferable to use programs that give the flexibility of choosing the interface condition. Once the layer moduli have been obtained from backcaiculation, the k-value below the slab can then be obtained by any of the following procedures. (i)
Using Correlations A method o f obtaining the modulus o f the subgrade reaction from the elastic moduli of the subgrade and subbase, and subbase thickness is described in the Navy Manual for Nondestructive Evaluation [5.35].from Thethe k-value of the subgrade is obtained elastic modulus o f the subgrade using the following equations; k= 10x
X = (Log 10E - 1.415)/l .284 where, k = modulus of subgrade reaction, psi/in E = subgrade modulus, psi
5-106
(Eq. 5.43)
If an untreated granular base or subbase is present above the subgrade, the effective k is determined using Figur e 5.23 . (ii)
Westergaard Equations Use the Westergaard equation for center deflection with the backcalculated PCC modulus and obtain k.
c)
Method of Equivalent Thickness The approach is similar to that used for flexible pavements. ELCON [5.33] is a program that is similar to ELMOD, which can be used to analyze deflection measurements two anddetermines three layerthe rigid pavements. Once theonprogram modulus o f concrete using the method o f equivalent thickness, it calculates the k-value of the support from the backcalculated subgrade modulus at slab centers. Edge and corner calculations use the Westergaard equations.
d)
Database Approach The drawback of programs using the database ap proach is that they can only be applied to the pave ment system configurations for which they were developed. DBCONPAS (Database for Concrete Pavement Systems) developed by Tia et al [5.25] uses a database of analytical results generated by FEACONS (Finite Element Analysis of Concrete Slabs) program. MODULUS is another database program that can be used for backcalculating rigid pavements.
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. N I U /C S IB . E S A B B U S R O E S A B F O E C A F R U S T A k E IV T C E F F E
THICKNESS OF BASE OR SUBBASE, IN.
Figure 5.23
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e)
Finite Element Programs
A method to backcalculate rigid pavement moduli using results from a finite element program is de scribed by Foxworthy and Darter [5.26], In this method deflections generated by the finite element ILLI-SLAB program is used to backcalculate the elastic modulus o f PCC and the k-value o f the sup porting medium. In order to use this method, de flections have to be obtained by the FWD with the seven sensors being placed at 12 in. intervals from each other. In this method, the deflection basin is characterized by the parameter 'AREA' which is obtained by the following equation. Area (in) = 6 * (1 + 2Di/Do + 2D 9/D 0 + 2D 3/D 0 + 2D4 /D 0 +2D 5/D 0 + d 6/d 0) In this equation Dq is the deflection obtained below the load while Dj, D 2 , D 3 , D4 , D 5 and D5 are de flections at 12, 24, 36, 48, 60 and 72 inches from the load. The program ILLI-SLAB is used to generate deflection basins for a range of PCC moduli and support k values. These results in terms of Dq and AREA are plotted as shown in Figu re 5.24 . This figure is used to obtain the elastic modulus of PCC and the k-value of the supporting medium by using Dq and AREA from the measured deflection basin. This graphical procedure is time consuming as the plot shown in the figure has to be generated for each slab thickness. In addition errors can arise during interpolation. An iterative computer program to carry out this procedure was developed later. 5.4.3 Backcalculation of Composite Pavements In this section, composite pavements refer only to asphalt overlays on rigid pavements. Most distresses in composite pavements occur due to deterioration of the concrete slab below the asphalt. PCC distresses that are most responsi ble for distresses in the asphalt overlay are slab cracking, punchouts, joint deterioration, deterioration resulti ng from poor PCC durability (D cracking and reactive aggregate distress), and deterioration of PCC and asphalt patches [5.241. Deflection testing can be used to evaluate the
5-109
condition of the PCC slab that is not visible and to obtain the k-value below the pavement.
)i n i( " a e r A " n i s a B n io t c e fl e D
Monimum Deflection, DO (mils)
Figure 5.24. A Typical ILLI-SLAB Grid f or the Backcalculation of E and k.
5-110
Generally it is difficult to achieve a solution when using orograms based on multi-layer elastic theory to backcalculate moduli of composite pavements, where the two upper layers are stiff when compared to underlying material. In general, iterative elastic layer backcalculation programs do not perform well in analyzing composite pavements [5.24], Their tendency is to under predict the modulus of the asphalt surface often going to the lower limits of the asphalt modulus range allowed by the user, and overpre dicting the modulus o f the PCC [5.241. Methods for backcalculating the moduli of composite pavements have been presented by Anderson [5.241 and Hall and Mohseni [136] Anderson [5.24] developed a program called COMDEF to backcalculate moduli of a three layer pavement which consists of an asphalt layer, concrete layer and a uniform subgrade. COMDEF can only backcalculate moduli based on deflections measured by the FWD, with seven sensors spaced 12 inches apart. The program cannot accommo date fewer sensors or different spacings. The program uses pre-calculated solutions stored in database files to backcalculate moduli. These deflection basins have been calculated using elastic layer theory. Interpolation tech niques are used with the database of precalculated solu tions to obtain deflections for cases not covered in the database. COMDEF includes 33 database files, with each standard database file containing deflections correspond ing to a fixed asphalt thickness. The deflections in one database file has been generated for the following matrix. PCC thickness (in) 4, 6, 9, 14, 20, 30 Asphalt Modulus (ksi) 33, 82, 205, 512, 1,280, 3,200 PCC Modulus (ksi) 82, 205, 512, 1,280, 3,200, 8,000, 20,000 Subgrade Modulus (ksi) 2, 6, 18, 54, 162
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COMDEF uses multiple application of two techniques to backcalculate. These two methods are: (a) stepwise direct optimization and (b) a iterative relaxation technique which uses matrices. allows the user to en force gradient to reasonable limitsAnonoption the asphalt modulus based on the temperature. A typical output o f the program is shown in Figu re 5. 25 [5.24], Hall and Mohseni Ì5.361 presented a method to backcal culate moduli of composite pavements. This procedure utilizes closed-form solutions for backcalculation of bare PCC pavements, with adjustments made to measured de flections to account for the influence of the asphalt con crete layer.
5.5 CRITICAL SENSITIVITY ISSUES IN BACKCALCULATION Lytton [5.10] discusses the need for experience both in analysis and with materials and deflections to ensure that the backcalculation process yields the most acceptable set of moduli for a given deflection basin. Many "well behaved" data sets will pose no problem, but in many cases the data is likely to be irregular in some way, making backcalculation difficult. Irregularities may result from a number of reasons, including pavement distress, variations in layer thicknesses, presence of bedrock o r other stiff layer, or moisture. Effects of these irregularities can be compensated for by recognizing prob able causes and adjusting during backcalculation. The ob jective in applying these adjustments to the pavement model is to yield more representative or reasonable values for layer moduli, not simply to fit the deflection basin more closely. It should be pointed out that, as backcalculation techniques mature many of these critical issues are being addressed by software modification. The intent of this section is to dis cuss some of the reasons that may cause backcalculation problems, and procedures that may provide better solutions.
5-112
206
NONUESTnuCTIVE
TESTING OF PAVEMENTS
PAVEMENT FACILITY OR FEATURE 10: EXAMPLE DATA 1 KDT LOADINGS PER TEST LOCATION STATION TRACK DATE TEHP LOAD 01 02 03 1.0
I
87042)
70.0 25025.
20.9
0«
DS
06
07
18.1 16.2 14.1 12. 0 10.0
8. 2
PAVEMEN T FACILITY OR FEATURE ID: EXAMPLE DATA SOLUTION FOR PROBLEM
1 OF
I FOR FILE ex»mpTe.out
STATION NUMBER • 1.00 TRACK NUMBER I DATE OF TEST 870421 SURFACE TEMPERATURE - 70.0 DECREES F THICKNESS OF AC - 6.00 INCHES THICKNESS OF PCC - 7.00 INCHES DYNAMIC LOAO• 25025. POUNDS MODULUS OF AC MODULUS OF PCC MODULUS OF SUBGRADE SENSOR NUMBER 1 2 3 4 S 6 7
55520B. PSI 50907B8. PSI 7975. PSI
DISTANCE ACTUAL PREDICTED FROM LOAD DEFLECTION DEFLECTION (NILS) (MILS) (INCHES) 20.90 20.90 0. 18.10 IB .10 12. 16.23 16.20 24. 14.09 14.10 36 . 11.97 12.00 48 . 9.99 10.00 60 . 8.22 8.20 72.
IN DEFLECTION SUM OFABSOLUTE VALUE OF ERRORS TOTAL PERCENTAGE ERROR IN DEFLECTION BASIN -
F ig u r e
0 .8 8 X
5 . 2 5 Example of CO MD EF Input Fi le and CO MD EF Outp ut Fil e.
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The primary rule is to always inspect the backcalculated moduli and apply a little engineering knowledge to the problem, if there is one. It should also always be kept in mind that if a layer stiffness is such that it has relatively little effect on the surface deflections, then backcalculation can provide little or no information about that layer. This will be discussed further in Section 5.5.5. 5.5.1 Input Data These include seed moduli, moduli limits and layer thick nesses as well as program controls such as number of it erations allowed and convergence criteria. Due to the non-uniqueness of the solution it is possible to obtain dif ferent layer modulus estimates for a given deflection basin by using different seed moduli, or limit for instance. Someestimate programs, as EVERCALC, have routines that will seedsuch moduli based on deflection basin char acteristics, which should provide a fairly reliable starting point. The basic approach is to choose seed moduli and moduli limits consistent with the materials and conditions in the pavement section at the time of test. Limits on moduli and convergence criteria should be set fairly wide initially, for a low number of iterations, to provide an ini tial indication of how reasonable the seed moduli are for a given basin. Note that if limits are not wide enough, and the iteration procedure fixes one of the lower layers at a value lower or higher than it appears to be in the deflection data, the compensating layer effect discussed below will result. Layer thickness effects are discussed in a subsequent sec tion. 5.5.2 Compensating Layer and Non-Linearity Effects This is an effect that essentially results from incorrect modeling of the pavement material response and the se quential nature of the backcalculation iterative procedure, as well as the geometry o f a deflection basin test. A typi cal result may show, as an example, subgrade modulus that is significantly higher than expected for the material
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type, while the base layer modulus is far too low and the surfacing modulus is too high. This probably occurs most commonly for a significantly stress softening subgrade, where the subgrade stress level for the outer sensors in a FWD test is very much lower than the subgrade stress level directly beneath the load plate. The apparent sub grade modulus for the outer sensor location is therefore higher than the apparent subgrade modulus directly beneath the load plate. If the subgrade is modeled as a linear elastic material, then, since most backcalculation routines first calculate subgrade modulus from the outer sensors, the higher modulus value is calculated and assumed to be constant throughout. At the next iteration, when the base modulus is being calculated, the too high subgrade modulus is compensated for by calculating a modulus that is too low for the base, in order to match the deflections measured in this region. In other words, alter nating layers exhibit a high or low compensating effect. Ideally, correctly modeling non-linear material response will remove this type of error, and this is becoming more and more common (e.g., MODCOMP3, EVERCALC, BOUSDEF can all use non-linear material models). If an elastic subgrade is used, then the inclusion of a stiff layer, (see 5.5.3) or the use of a layered subgrade, can help alleviate the problem. This is at least partially the reason why some backcalculation routines include a stiff layer by default at some depth (usually 20 ft ). 5.5.3 Subgrade "St iff1Layers 5.5.3.1
General For the purposes of a general definition, a "stiff1 layer is one below which there is little or no ap parent contribution to the measured surface deflections. "Stiff1 layers can be real or "apparent" and are possibly the most common problem encountered during the evaluation of deflection basins. For the purposes of backcalculation, a stiff layer can be considered as any layer below the sub5-115
grade appearing to have a stiffness which is 10 times the modulus of the subgrade. A stiff layer may be comprised of bedrock underlying the sub grade. Stress sensitive subgrade materials, whose modulus increases as deviator stress decreases may form an "apparent" stiff layer, a phenomenon also referred to as "non-linearity". Granular ma terials tend to increase in modulus as the confin ing stresses increase as well. These materials will exhibit an increase in stiffness with depth. Stiff layer effects, whether real or apparent, mani fest themselves in the outer deflection measure ments. Typically, they result in an attenuation of the deflections at the outer radii leading to unrealistically high and subsequently inaccurate moduli values for the subgrade. This error will invariably result in inaccurate base and surface moduli values. For the case where an actual rigid layer exists, a variety computer backcalculation programs such as MODULUS, BISDEF, and WESDEF have a rigid layer subroutine built in. If non-linearity is not severe, the stiff layer rou tine can handle this as well. Bedrock information can be obtained from geologic maps, or by per forming cone penetrometer tests or drilling on the shoulder o f the road. One solution to the "apparent" stiff layer prob lem, if a layered-elastic backcalculation program is used, is to divide the subgrade into two or more layers, allowing the backcalculation pro gram to assign modular ratios which achieve the best fit. Typically, for the case of the "apparent" stiff layer, these effects can be overcome by dividing the subgrade into two layers, the top of which is 300 mm (12”) or more, depending on the reasonableness of the resulting layer moduli. This results in longer computer run times, addi tional operator input, and the need to combine upper layers if the total number of layers exceeds four, if MODULUS is being used. 5-116
An alternative solution would be to utilize a backcalculation program such as MODCOMP3, which addresses non-linearity and can analyze morethis thanintroduces 4 layers. additional It should complexity be noted however, that to the procedure resulting in slower computer run times and additional input variables. It should be noted that high water tables can give the appearance of a stiff layer beneath the sub grade. Water is an incompressible fluid. When an impulse load is applied to a saturated soil, and the water has nowhere to go, it will build up pressure sufficient to resist the pressure exerted by the load. This pressure is known as pore water pressure, is equal and opposite in direction to the load, and can build up instantaneously. Thus, the saturated subgrade material is not deformed under the influence of a dynamic sur face load and the backcalculated subgrade modulus is unrealistically high leading to prob lems identical to the stiff layer case. Overcoming this problem can be handled the same way as the stiff layer case, however, an additional problem is present in this case. The stiff layer effect due to pore water pressure occurs only under dynamic loading. A slow-moving, heavy vehicle may impart vertical stresses in the subgrade of sufficient duration for the pore water pressure to dissipate, leaving only the soil skeleton to carry the load. The load could exceed the load carry ing capacity of the soil skeleton resulting in a deep foundation failure and depression of the pavement surface. Water tables tend to fluctuate throughout the year and from year to year in many parts of the country, a fact which further complicates the issue. It should be noted that the inclusion of a stiff layer, or subdivision of the subgrade into multiple layers is not a "cure-all" for backcalculation
5-117
problems. These approaches should be used only after all other options have been exhausted. 5.5.3.2
An Example It is often necessary to have a "deep," stiff layer within the subgrade in order to achieve reason able backcalculation results. This may be due to a rock layer or some other kind of "stiff1condi tion. This can be illustrated using one of the SHRP/LTPP GPS sites (and associated deflection data). Figu re 5.2 6 shows the two cases backcalculated — one with a stiff layer at a depth of 6.1 m (240 in.) (shown as Case 1) and the other which assumes a uniform subgrade'with a semiinfinite depth (Case 2). The mid-depth AC tem perature at the time of load testing wasand about 21°C (70°F) and the specific level associated deflections used in this illustration were: Load = 75.9 kN (17,054 lb.) Deflections: 0 mm (0 in.)
—382.2 (im (15.05 mils)
203 mm (8 in.) —301.5 nm (11.87 mils) 305 mm (12
n.)—
457 mm (18
n .) —201.2
|jm (7.92 mils)
610 mm (24
n .) — 161.5
fim (6.36 mils)
914 mm (36
n .) — 105.2
(im (4.14 mils)
257.0 |im (10.12 mils)
1,524 mm (60 in.)—52.3 |im (2.06 mils)
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Asphalt Concrete 126 mm (4.95 in.)
Asphalt Concret e 126 mm (4.95 in.)
Crushed Limestone Base 340 mm (13.40 in.)
Crushed Limestone Base 340 mm (13.40 in.)
Soil/Aggregate Subbase 305 mm (12 in.)
Soil/Aggregate Subbase 305 mm (12 in.)
Sand Subgrade 5.6 m (222 in.)
Sand Subgrade oo
Case 1
Case 2
Figure 5.26 - SHRP Pavement Section A (GPS-1: Asphalt Concrete Pavement with Granular Base - Section located in Florida)
5-119
The backcalculated results ar e:
Case 1: Layer
Modulus. MPa (psi)
♦
AC
10,474
♦
Base
♦
Combined Subbase/ Subgrade
♦
StifFLayer
396 177 6,895
(1,519,000) (57,400) (25,700) (1,000,000)
whereas the stiff layer modulus was preselected (or fixed) at 6,895 MPa (1,000,000 psi). Case 2: Laver
Modulus. MPa (psi)
♦
AC
13,900
♦
Base
♦
Combined Subbase/ Subgrade
216 239
(2,016,000) (31,400) (34,700)
Thus, one can see that the combined sub base/subgrade stiffness is actually a bit higher than the base in Case 2. Normally, this is an un reasonable result and suggests that the use of a stiff layer (such as Case 1) provides a more "reasonable" set o f layer moduli. 5.5.3.3
Load and Geostatic Stresses The need for stiff layers within the subgrade do main can certainly be due to rock layers or ex tremely stiff soils such as some glacial tills. However, there may be other conditions, not so immediately apparent, which warrant the use of a
5-120
stiff layer within the subgrade. First, we should look at some typical stresses in the subgrade due to an applied load and geostatic conditions. SHRP/LTPP Section F (recall Fig ure 5.1 7) was modeled with ELSYM5. Vertical and horizontal stresses were estimated under a 40 kN (9,000 lb.) load with a 0.69 MPa (100 psi) contact pressure. Two moduli conditions for Section F were used. The associated moduli and stresses follow:
Case A (a) Laver
Case Material Properties Modulus. MPa (psi)
Poisson's Ratio
6,895 (1,000,000)
0.35
Base (14.47 in.)
345 (50,000)
0.40
Subgrade (oo)
276 (40,000)
0.45
AC (7.65 in.)
5-121
(b)
Results
Load Stresses* kPa (psi) Depth, mm (in.) 1,525 (60)
oz -6.2 (-0.9)
3,050 (120)
-2.1
4,575 (180)
0
ox or ov -0.7 (-0.1)
7.6
(1.1)
5.5
(-0.3)
~0
2.1
( 0.3)
2.1 (0.3)
-1.4
(-0.2)
~0
1.4
( 0.2)
1.4 (0.2)
5,030 (198)
-1.4
(-0.2)
~0
1.4
(0.2)
6,100 (240)
-0.7
(-0.1)
~o
0.7
( 0.1)
0.7 (0.1)
7,625 (300)
-0.7
0.7
( 0.1)
0.7 (0.1)
~0
(-0.1)
12,200 (480)
~0
~0
24,400 (960) 25,375 (999)
~0 ~0
~0
~0 ~0
~0
~0
Case B
Layer AC (7.65 in.)
Case Material Properties Modulus. MPa (psi) 6,895
Poisson's Ratio
(1,000,000)
0.35
Base (14.47 in.)
621
(90,000)
0.40
Subgrade (175.88 in.)
207
(30,000)
0.45
Stiff Layer @ 198 in. Depth
6,895 (1,000,00)
5-122
(0.2)
~0
* Due to 40 kN (9,000 lb.) only. Stresses: (-) compression, (+) tension.
(a)
1.4
(0.8)
0.45
~0
~0
(b)
Results
Load Stresses* kPa (psi) GX Or Gy 0
Depth, mm (in.)
<7d
1,525 (60)
-5.5
(-0.8)
-0.7 (-0.1)
6.9
(1.0)
0.7
(0.1)
3,050 (120)
-2.8
(-0.4)
-0.7 (-0.1)
4.1
(0.6)
2.1
(03)
4,575 (180)
-2.1
(-03)
-1.4 (-0.2)
4.8
(0.7)
0.7
(0.1)
5,030 (198)
-2.1
(-0.3)
-1.4 (-0.2)
4.8
(0.7)
0.7
(0.1)
6,100 (240)
-1.4
(-0.2)
~0
1.4
(0.2)
1.4
(0.2)
7,625 (300)
-0.7
(-0.1)
~0
0.7
0.7
(0.1)
. (o.i)
12,200 (480)
~0
~0
~0
~0
24,400 (960) 25,375 (999)
~0 ~0
~0 ~0
~0 ~0
~0 ~0
Geostatic stresses are caused by the weight of the soil. Vertical geostatic stress, a v, can be straight forwardly calculated as follows [after Lambe and Whitman (5.2)]: av = (z) (y) where a v
= vertical stress,
z
= depth, and
y
= total unit weight of the soil
If we let g =10 0 lb./ft3 and a v units of psi, then ov where z
= 0.694 (z) = depth (ft)
Horizontal geostatic stress, .ïh, is related to the vertical geostatic stress by a factor called the co efficient of lateral stress, which is designated Kq :
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(Eq. 5.44)
K0 ~ 0.5 for normally consolidated sedimentary soils but can approach 3 for heavily preloaded soils (over consolidated). When K0 < 1, ctv = oi and ah = 03 . When K0> 1, Oh = oi and ov =03 . If we assume the subgrade soils have a density (y) = 100 lb./ft3, then using the prior, preselected depths: Geostatic Stresses, MPa (psi) Ko = 0.5 oh
Oil
Kn = 3
Depth, mm (in.)
°V
(K = 0.5)
(K = 3)
1,525 ( 60)
.02 (3.5)
.01 (1.8)
.07 (10.5)
3,050 (120)
.05 (6.9)
.02 (3.4)
0.14 (20.7)
.09 (13.7)
.02 (3.5) 0.24 (34.5) 0.09 (13.8)
4,575 (180)
.07(10.4)
.04 (5.2)
0.22 (31.2) 0.14 (20.8)
.04 (5.2) 0.36 (52.0) 0.14 (20.8)
5,030 (198)
.08(11.5)
.04 (5.8)
0.24 (34.5) 0.16 (23.1)
.04 (5.7) 0.4
6,100 (240) 0.1 (13.9)
.05 (7.0)
0.29 (41.7) 0.19 (27.9)
.05 (6.9) 0.48 (69.5) 0.19 (27.8)
7,625 (300)
0.12(17.4)
.06 (8.7)
0.36 (52.2) 0.24 (34.8)
.06 (8.7)
12,200 (480)
0.19(27.8)
0.1 (13.9)
0.58 (83.4) 0.38 (55.6) 0.1 (13.9) 0.96(139.0) 0.38 (55.6)
24,400 (960) 0.38(55.5) 25,375 (999) 0.40(57.8)
0.19(27.8) 0.2 (28.9)
1.15 (166.5) 0.77(111.1) 0.19(27.7) 1.2 (173.4) 0.80(115.6) 0.2 (28.9)
0 .05
(7.1)
.01 (1.7) 0.12 (17.5)
From the above, it can be easily seen that the geostatic stresses dominate the stresses within the deeper portions of the subgrade (with or without a stiff layer in the system). If the modulus of a subgrade layer was stress sensitive, the magni tude of the stresses shown could greatly affect the backcalculation results and hence the need for a multi-layer subgrade; however, the geostatic stresses are static and it is not clear how impor tant these stresses are. 5-124
0
0-d
0.6
Od .05
(7.0)
(57.5) 0.16 (23.0) (87.0) 0.24 (34.8)
1.91 (277.5) 0.77(111.0) 1.99 (289.0) 0.8 (115.6)
5.5.3.4
Depth to Stiff Layer
Recent literature (as of 1991) provides at least two approaches for estimating the depth to stiff layer [Rohde and Scullion [5.16], Hossain and Zaniewski [5.17]]. The approach used by Rohde and Scullion [5.16] will be summarized below. There are two reasons for this selection: (a) ini tial verification of the validity of the approach is documented, and (b) the approach is used in MODULUS 4.0 — a backcalculation program widely used in the U.S. (and used in SECTION 6 ). (a)
Basic Assumptions and Description A fundamental assumption is that the meas ured pavement surface deflection is a result of deformation o f the various material s in the applied stress zone: therefore, the measured surface deflection at any distance from the load plate is the direct result of the deflection below a specific depth in the pavement structure (which is determined by the stress zone). This is to say that only that portion of the pavement structure which is stressed contributes to the meas ured surface deflections. Further, no sur face deflection will occur beyond the offset (measuredtofrom the load ofplate) which cor responds the intercept the applied stress zone and the stiff layer (the stiff layer modulus being 100 times larger than the subgrade modulus). Thus, the method for estimating the depth to stiff layer assumes that the depth at which zero deflection oc curs (presumably due to a stiff layer) is re lated to the offset at which a zero surface deflection occurs. This is illustrated in Fi gure 5.27 where the surface deflection Dc is zero.
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Figure
5.27
Illustration of Zer o Deflection Due to a Stif f Lay er
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An estimate o f the depth at which zero deflection occurs can be obtained from a plot of measured surface deflections and the inverse o f the corresponding offsets This is illustrated inFigu re 5. 28 and is based on theoretical consideration of Boussinesq equations, as srcinally devel oped by Ullidtz.. The middle portion of the plot is linear with either end curved due to nonlinearities associated with the upper lay ers and the subgrade. The zero surface deflection is estimated by extending the lin ear portion of the D vs. ~ plot to D = 0, with the ~ intercept being designated as r0. Due to various pavement section-specific factors, the depth to stiff layer estimated from r0 may not be reliable. In an attempt to improve this, additional factors were considered and regression equations were developed based on BISAR computer pro gram generated data for the followin g fac tors and associated values: Load = P = 40 kN (9,000 lbs..) (only load level considered) Moduli ratios:
= 10, 30, 100
c Sg
— 0.3,
^ESg = 100 Sg
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1.0, 3.0, 10.0
Figure
5 . 2 8 Plo t of In verse of De flec tion Offset vs . Measured Deflection
5-128
Thickness levels: Ti = 25, 75, 125, 250 mm (1, 3, 5, and 10 in.) T 2 = 150, 250, 375 mm (6 , 10, and 15 in.) B = 1.5, 3.0, 4.5, 6.0, 7.5, 9.0, 15.0 m (5,10, 15, 20, 25, 30, and 50 ft.) where
Ej = elastic modulus of layer i, Ti = thickness of layer i, B = depth of the rigid (stiff) layer measured from the pavement surface (ft).
The resulting regression equations follow in (b). (b) Regression Equations Four separate equations were developed for various AC layer thicknesses. The depend ent variable is ^ and the independen t vari ables are r0 (and powers of r0) and various deflection basin shape factors such as SCI, BCI, and BDI (discussed earlier in SECTION 5.0). (i)
AC less than 50 mm (2 in.) thick
(Eq. 5.45) 0.0362 - 0.3242 (r0) + 10.2717 (r02) 23.6609 (r03) - 0.0037 (BCI) R2 = 0.98
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(ii)
AC 50 to 100 mm (2 to 4 in.) thick
(Eq. 5.46)
g
= 0.0065 +0.1 652 (r0) + 5.4290 (r02)- 11.0026 (r03) - 0.0004 (BDI) R 2 = 0.98
(iii) AC 100 to 150 mm (4 to6 in.) thick
(Eq. 5.47) ^
=
0.0413 + 0.9929 (r0) -
0.0012 (SCI)+ 0.0063 (BDI) - 0.0778 (BCI) R 2 = 0.94 (iv) AC greater than 150 mm (6 in.) thick
(Eq. 5.48) ^
=
0.0409 +0.566 9 (r0) +
3.0137 (r02) + 0.0033 (BDI) - 0.0665 log (BCI) R 2 = 0.97 where
= ~ intercept (extrapolation of the steepest section of the D vs. ~ plot) i n units of ^ ,
SCI = Do - D305 mm (Do '^1 2 in )> Surface Curvature Index, BDI = (D 305 - D 610 mm) (D12 Base Damage Index, 5-130
(Eq. 5.49)
- D 24 in ), (Eq. 5.50)
BCI = D6io - D914 mm (D 24 in. - D36 in ) Base Curvature Index,
(Eq. 5.51)
Di = surface deflections (mils) normalized to a 40 kN (9,000 lb.) load at an offset i in feet. (c)
Example Use the deflection data from SHRP Section F (Figure 5.17 ) to estimate B (depth to stiff layer). The drillers log suggests a stiff layer might be encountered at a depth of 5.0 m (198 in.). (i)
First, calculate normalized deflections (40 kN (9,000 lb.) basis).__________ Deflections, mm (mils)
Load Level, kN (lb.)
Dg
D0
D 12
D 18
°24
D 36
D 60
42.3 (9,512)
128 .8 (5. 07) 109 .7 ( 4.3 2)
93 .2 (3 .67 ) 75 .9 (2 .99 )
61 .0 ( 2. 40 )
42. 9 (1 .6 9)
25 .7 (1 .01)
40
(9 ,00 0)
120 .9 (4 .76 ) 102 .6 (4 .04 )
87 .4 (3 .4 4) 71 .1 (2 .8 0)
57.4 (2.26) 40.4 (1.59)
24.1 (0.95)
29
(6,534)
83 .3 (3 .28 ) 68 .3 (2 .69 ) 59 .2 (2 .33 ) 47 .8 (1 .88 )
39. 6 (1. 56) 27. 7 (1. 09)
17.3 (0.68)
(ii)
Second, estimate r0. Plot Dr vs. ~ (refer to Figu re 5.27):
Dr mm (mils) 4.76 4.04 3.44 2.80 2.26 1.59 0.95
r, mm (in.) 0 203 305 457 610 915 1,525
0" 8" 12" 18" 24" 36" 60"
1 1 r’ m
0
----
----
4.93 3.28 2.19 1.64 1.09 0.66
(1.50) (1.00) (0.67) (0.50) (0.33) (0.20)
where all Dr normalized to 40 kN (9,000 lb.) 5-131
PLOT OF DEFLECTION vs 1/R
) S N O R C I M (
) S L I M ( N IO T C E L F E D
N O I T C E L F E D
1/R (INVERSE OF DEFL. OFFSET 1/FT)
Figure 5.29 - Plot of Inverse of Deflection Offset vs. Measured Deflection for SHRP Section F
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(in) Third, use regression equation in (b)(iv) (for AC = 7.65 in. (194 mm)) to calculate B: ^ = 0.0409 +0.56 69 (r0) + 3.0137 (r02) + 0.0033 (BDI) - 0.0665 log (BCI) where r0 = ~ intercept (refer to Figur e 5.2 7)
= 0 (used steepest part of deflection basin which is for sensors at 24 and 36 inches) BDI = D 12 in. ■ D24 in. = 3.44 2.26= 1.18 mils BCI = D 24 in. * D36 in. = 2.26 1.59 = 0.67 mils £>
= 0.0409 + 0.5669 (0) + 3.0137 (02) + 0.0033 (1.18) - 0.0665 log (0.67) = 0.0564
B = 0~0564~ 17'^ ^eet (213 inches or 5.4 m) This value agrees fairly well with "expected" stiff layer conditions at 5.0 m (16.5 f t) as indicated by the drillers log even though the ~ value equaled zero.
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5.5.3.5
Example of Depth to Stiff Layer Estimates — Road Z-675 (Sweden) (a)
Overview This road located in south central Sweden is used to illustrate calculated and measured depths to stiff layers (the stiff layer appar ently being rock for the specific road).
(b)
Measurement of Measured Depth The depth to stiff layer was measured using borings (steel drill) and a mechanical ham mer. The hammer was used to drive the drill to "refusal." Thus, the measured depths could be to bedrock, a large stone, or hard till (glacially deposited material). Further, the measured depths were obtained independently of the FWD deflection data (time difference of several years).
(c)
Deflection Measurements A KUAB 50 FWD was used to obtain the deflection basins. All basins were obtained within ± 16 ft (5 m) of a specific borehole. The deflection sensor locations were set at 0, 200, 300, 450, 600, 900, and 1200 mm (0, 23.6,35.4, and 47.2 in.) from7.9, the11.8, center17.7, of the load plate.
(d)
Calculations The equations described in Section 5.5.3.3 were used to calculate the depth to stiff layer. Since the process requires a 40 kN (9,000 lb.) load and 305 mm (1 ft.) deflec tion sensor spacings, the measured deflec tions were adjusted linearly according to the ratio of the actual load to a 40 kN (9,000 lb.) load.
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(e)
Results
The results o f this comparison are shown in Given all the uncertainties concerning the measured depths, the agreement is quite good.
Figur e 5.30.
5.5.4 Pavement Layer Thickness Effects Due to limitations in the backcalculat ion software, and the limited time available to perform backcalculation activities in a production environment, pavement layer thicknesses are assumed to be constant over the pavement section un der test. This is never the case. Pavement layer thickness variations result from poor construction quality control during initial construction, periodic overlays over existing rough pavements, and spot level-ups over short distances. In Texas, spot level ups pose the greatest problem be cause they are performed by in-house maintenance per sonnel and no detailed records are kept to indicate the thickness or extent o f the level-up. On Texas SHRP sections, it has been found that asphalt concrete thicknesses may vary up to 2 in. within 500 ft. Pavement layer thickness variations will produce varia tions in the deflections from point to point which are in distinguishable from layer moduli variations. The net result is that this variation manifests itself in the backcalculated moduli for the various layers. A detailed research study found that if the pavement layer thickne ss variations are considered during the backcalculation process, the variation in layer modulus for the various layers was reduced significantly. In addition, more realistic moduli values were found for the various layers. Several methods exist to quantify pavement layer thick ness variations within a project. All are either expensive or time consuming. Examples discussed here include cone penetrometers, coring and drilling, and Ground Penetrat ing Radar.
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ROAD Z-675,SWEDEN - STIFF LAYER COMPARISONS 3 T
T
10 9
2.5 -
8
OJ On
7 ) (m H T P E D
6 5
1.5
4 3 2
0.5
1
0 3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 POINT NUMBER
FIELD
□ EQUATIONS
Figure 5.30 - Plot of Measured and Calculated Depths to Stiff Layer
) T (F H T P E D
The cheapest, slowest, and most painful is the Dynamic Cone Penetrometer. This device consists of a metal rod with a sharp metal cone at the bottom which penetrates the pavement layers in small increments as a weight is repeatedly lifted by hand and dropped. The speed of penetration of the cone is inversely proportional to the layer stiffness. By recording the depth of penetration, and noting the depth at which the penetration rate changes, the operator can approximate the thickness of each layer. Infiltration of fine material from the subgrade into the base can result in difficulty distinguishing the base/subgrade interface, as the change in rate of penetration is more gradual. Small vehicle mounted cone penetrometers exist, but are expensive to operate. They are faster than the hand op erated cone penetrometer but are still quite a bit slower than the FWD. These devices also provide an approxi mation o f layer thicknesses. The most common method of verifying layer thicknesses is by coring. This is the most accurate method available for measuring asphalt thickness, but is time consuming and expensive. It is a destructive process and requires backfilling the hole with quick setting concrete or coldmix asphalt patching material. If the base material does not contrast visually with the subbase or subgrade, it can be difficult to get an accurate measurement of base thick ness. Usually, a 100mm (4") core is required to obtain adequate visibility for measurement purposes. Granular base materials tend to fall apart when extracted from the hole. Large stones in the base can also roll around under the core barrel during the drilling process and disturb the surrounding material, making measurements even more difficult. Cone penetrometer testing and coring require extensive traffic control and closure of the lane in which the work is being performed. Neither can keep pace with the FWD. Finally, the quickest method of obtaining pavement layer thicknesses is with Ground Penetrating Radar (GPR). 5-137
GPR testing can be performed at highway speeds, so no lane closures or traffic control is required. Many miles of pavement can be surveyed during the day and GPR is much faster than the FWD. GPR can measure asph alt con cre te thick ness quite accurately and reliably. Reli ability is improved if limited coring is used for calibration purposes. Limitations of GPR are as follows: a)
If two adjacent pavement layers are constructed of similar materials, the interface between the two will not show up in the data and the thickness of the up per layer cannot be determined (example: Portland cement concrete slab and cement stabilized base)
b)
GPR is not accurate on reinforced Portland cement pavement due to signal attenuation by reinforcing steel. For non-reinforced PCC the accuracy improves if the underlying base or subbase is com posed of materials having a dielectric constant dif ferent than that of the slab.
c)
The presence of moisture adversely affects GPR per formance, so the pavement layers must be relatively dry
d)
Infiltration of fine material from the subgrade to the base may result in an indefinite base/subgrade inter face which may render GPR useless for base thick ness determination
e)
Software which analyses GPR data and reports layer thicknesses is still under development and available from limited sources
f)
GPR equipment costs several hundred thousand dollars and still requires interpretation by an experi enced technician.
Before employing any of the above methods in an NDT investigation, one should first determine if accurate layer thicknesses are critical to the analysis. If the objective of the analysis is to determine remaining life of a pavement based on a cracking or rutting model which utilizes
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