Upload
bloomdido
View
80
Download
0
Embed Size (px)
DESCRIPTION
BACKCALCULATION OF PAVEMENT LAYERS MODULI USING 3D NONLINEAR EXPLICIT FEA
Citation preview
BACKCALCULATION OF PAVEMENT LAYERS MODULIUSING 3D NONLINEAR EXPLICIT
FINITE ELEMENT ANALYSIS
ByGergis W. William
Thesis Submitted to the College ofEngineering and Mineral Resources
at West Virginia Universityin Partial Fulfillment of the Requirements
for the Degree of
Master of Science in
Civil Engineering
Samir N. Shoukry, Ph.D., ChairDavid R. Martinelli, Ph.D.
W. J. Head, Ph. D.
Morgantown, West Virginia 1999
ii
ACKNOWLEDGMENTS
For his excellent support and advice in both my academic and research works, for many hours
spent improving, evaluating, correcting my work, and his friendship, I would like to express my
gratitude to Dr. Samir N. Shoukry whose assistance and guidance made this work feasible.
Appreciation is also extended to Dr. David Martinelli and Dr. W. J. Head for serving on the
examining Committee.
Thanks to Mr. George Hanna, West Virginia Division of Highways, who performed the field
tests using FWD. I would like also to thank Professor Per Ullidtz, Technical University of Denmark,
who provided some of his results for comparison with my results listed in Chapter 8, Table 8.2.
I would like thank to my parents for their love, support, and understanding and for being there
when times were rough. I would like also to thank my sister and my grand father for their love and
support Thanks are also extended to my friends for their encouragement and help.
The author gratefully acknowledges the financial support for this research from West Virginia
Division of Highways, and Mid Atlantic Universities Transportation Center.
iii
ABSTRACT
BACKCALCULATION OF PAVEMENT LAYERS MODULI USING3D NONLINEAR EXPLICIT FINITE ELEMENT ANALYSIS
by:
GERGIS W. WILLIAM
After reviewing the existing literature on FWD testing and backcalculation algorithms, a newbackcalculation approach based on Three Dimensional Finite Element Modeling (3D FEM) wasdeveloped. This approach accounts for the transient dynamic nature of FWD load, the threedimensional geometry of the pavement structure, and the friction and bonding characteristics ofpavement layers interfaces. The 3D FEM backcalculation approach was used to backcalculate thelayers moduli of flexible, rigid, and composite pavement sites located in West Virginia. The layersmoduli of each site were also evaluated using three widely used backcalculation algorithms:MODULUS, EVERCALC, and MODCOMP. Comparison of their results with those obtained using3D FEM revealed that the former should be multiplied by correction factors in order to match thelatter. Using 3D FEM backcalculation results as reference values, correction factors were developedfor each program and pavement type. The mechanistically evaluated correction factors were foundto be in close agreement with the experience-based factors recommended for flexible and rigidpavements in the American Association of State Highway and Transportation Officials (AASHTO)Pavement Design Guide.
The 3D FEM approach was also used to predict the apparent depth to bedrock. The decayof vertical stress and displacement in the subgrade layer were examined and used to predict theapparent depths to bedrock for four pavement sites located in Texas. The 3D FEM results werefound to be in good agreement with the measured values provided by Texas DOT.
A parametric study was conducted to evaluate the effect of the subgrade layer thickness(assumed in the finite element pavement structural model) on the stress and deformation obtained ontop of the subgrade layer and on the 3D FEM-generated deflection basin. It was found that asubgrade layer thickness of 6 ft. would produce satisfactory results.
The effect of concrete slab length on the deflection basin was examined for both doweled andundoweled concrete slabs. For doweled concrete pavements, slab length has no effect on thedeflection basin. For broken slabs or undoweled ones, the minimum slab length required to producean acceptable deflection basin was found to be 10 ft.
KEYWORDS:Falling Weight Deflectometer, Pavement Evaluation, Nondestructive testing, Backcalculation, FiniteElement Analysis of Pavements.
iv
TABLE OF CONTENTS
ACKNOWLEDGMENT ii
ABSTRACT iii
TABLE OF CONTENTS iv
LIST OF TABLES vi
LIST OF FIGURES vii
CHAPTER 1
INTRODUCTION 1
1.1 BACKGROUND 1
1.2 BACKCALCULATION PROBLEMS 4
1.3 OBJECTIVE OF THIS THESIS 5
1.3.1 Organization of this Thesis 6
CHAPTER 2
LITERATURE REVIEW 8
2.1 BACKCALCULATION PROGRAMS 8
2.2 PROGRAM SELECTION 9
2.3 DESCRIPTION OF SELECTED BACKCALCULATION PROGRAMS 10
2.3.1 Description of MODCOMP3 Program 11
2.3.2 Description of MODULUS5.0 Program 12
2.3.3 Description of EVERCALC4.0 Program 13
2.3.4 Description of ELMOD4 Program 15
CHAPTER 3
COMPARISON OF BACKCALCULATION RESULTS FOR SHRP TEST SECTIONS 20
CHAPTER 4
COMPARISON OF BACKCALCULATION RESULTS FOR SEVEN SELECTED SITES
IN WEST VIRGINIA 34
CHAPTER 5
FIELD TESTING 66
5.1 PAVEMENT SITES 66
5.2 MEASUREMENTS 67
v
5.3 DEFLECTION TESTING 69
5.4 EVALUATION OF BACKCALCULATED MODULI 70
5.5 CONCLUSIONS 70
CHAPTER 6
EVALUATION OF BACKCALCULATION ALGORITHMS THROUGH
FINITE ELEMENT MODELING OF FWD TEST 76
6.1 INTRODUCTION 76
6.2 REVIEW OF FINITE ELEMENT MODELING OF PAVEMENTS 76
6.3 GUIDELINES FOR 3D-FEM OF PAVEMENT STRUCTURES 78
6.4 FINITE ELEMENT MODELS OF EXPERIMENTAL TEST SITES 81
6.4.1 Flexible Pavement Model 81
6.4.2 Rigid Pavement Model 81
6.4.3 Composite Pavement Model 82
6.5 STRUCTURAL MATERIAL MODELING 83
6.6 LAYERS MODULI EVALUATION FROM FE MODEL RESULTS 84
6.7 VERIFICATION OF FINITE ELEMENT MODELS 85
6.7.1 Deflection basins 85
6.7.2 Displacement time-history 86
6.8 EVALUATION OF BACKCALCULATION PROGRAMS 87
CHAPTER 7
SOME FACTORS INFLUENCE BACKCALCULATIONS OF RIGID PAVEMENTS 103
7.1 INTRODUCTION 103
7.2 FINITE ELEMENT STRUCTURAL MODEL 103
7.2.1 Model Loading and Material Model 105
7.2.2 Model Verification 106
7.3 PERFORMANCE ASSESSMENT OF BACKCALCULATION PROGRAMS 107
7.4 EFFECT OF SLAB LENGTH AND DOWEL BARS 108
7.5 CONCLUSIONS 109
CHAPTER 8
EFFECT OF 3D FEM MODEL DEPTH ON BACKCALCULATIONS OF FLEXIBLE PAVEMENTS 117
8.1 INTRODUCTION 117
8.2 FINITE ELEMENT STRUCTURAL MODELS 121
vi
8.3 EVALUATION OF LAYERS’ MODULI 122
8.4 EVALUATION OF DEPTH TO BEDROCK 123
8.5 EFFECT OF 3D FE MODEL DEPTH ON 3D FEM RESULTS 125
8.5.1 Effect of Model Depth on Deflection Basin 126
8.5.2 Effect of Stress Wave Reflection from Model Bottom on Deflection Basin 126
8.5.3 Effect of Model Depth on the 3D FEM-Calculated Depth to Bedrock 126
8.5.4 Effect of Model Depth on Stresses Induced in Subgrade 127
8.6 EFFECT OF LOAD DURATION ON THE DEFLECTION BASIN 128
8.7 CONCLUSION 128
CHAPTER 9
CONCLUSIONS 144
REFERENCES 148
APPENDIX A PARAMETRIC INPUT FILE TO GENERATE FLEXIBLE PAVEMENT MODEL 158
VITA 166
vii
LIST OF TABLES
TABLE 2.1 Available Backcalculation Programs. 18
TABLE 2.2 Comparison of Selected Backcalculation Programs. 19
TABLE 3.1 Moduli Range and Poisson’s Ratio for Backcalculation Inputs. 23
TABLE 3.2 Backcalculated Layer Moduli (Ksi) for SHRP Sections. 24
TABLE 4.1 Assumptions Used in Different Backcalculation Algorithms. 38
TABLE 4.2a Backcalculated Layer Moduli (Ksi) for Flexible Pavement Sections. 40
TABLE 4.2b Backcalculated Layer Moduli (Ksi) for Composite Pavement Sections. 41
TABLE 4.2c Backcalculated Layer Moduli (Ksi) for Rigid Pavement Sections. 42
TABLE 4.3 Comparison of Pavement Moduli Backcalculated by Different Programs. 43
TABLE 4.4 Number of Backcalculated Out of Range Moduli. 45
TABLE 5.1 Deflection Data Collected from Field Tests. 72
TABLE 5.2 Backcalculated Layer Moduli (Ksi) for Tested Pavement Sections. 73
TABLE 6.1 Correction Factors for Backcalculated Subgrade Modulus. 90
TABLE 7.1 Properties of Pavement Materials. 105
TABLE 8.1 Layer Thicknesses and Temperature Measurements. 130
TABLE 8.2 Backcalculated Pavement Layers’ Moduli, Ksi. 131
TABLE 8.3 Comparison Between Measured and Calculated Depth to Bedrock. 132
TABLE 8.4 Effect of Assumed Model Depth on the Calculated Depth to Bedrock. 133
viii
LIST OF FIGURES
FIGURE 1.1 FWD setup and schematic presentation of stress bulb. 8
FIGURE 3.1 SHRP sections data used for backcalculations. 25
FIGURE 3.2 Comparison of backcalculated moduli for SHRP section A. 26
FIGURE 3.3 Comparison of backcalculated moduli for SHRP section B. 27
FIGURE 3.4 Comparison of backcalculated moduli for SHRP section C. 28
FIGURE 3.5 Comparison of backcalculated moduli for SHRP section D. 29
FIGURE 3.6 Comparison of backcalculated moduli for SHRP section E. 30
FIGURE 3.7 Comparison of backcalculated moduli for SHRP section F. 31
FIGURE 3.8 Comparison of backcalculated moduli for SHRP section G. 32
FIGURE 3.9 Comparison of backcalculated moduli for SHRP section H. 33
FIGURE 4.1 Backcalculated layer moduli (Ksi) for flexible pavement section US52_pre station 16.250. 46
FIGURE 4.2 Backcalculated layer moduli (Ksi) for composite pavement section US52_pre station 18.360. 47
FIGURE 4.3 Backcalculated layer moduli (Ksi) for composite pavement section US52_pre station 19.179. 48
FIGURE 4.4 Backcalculated layer moduli (Ksi) for composite pavement section US60_smi station 1.230. 49
FIGURE 4.5 Backcalculated layer moduli (Ksi) for composite pavement section US60_smi station 2.267. 50
FIGURE 4.6 Backcalculated layer moduli (Ksi) for composite pavement section US60_smi station 3.393. 51
FIGURE 4.7 Backcalculated layer moduli (Ksi) for composite pavement section WV2_frie station 4.296. 52
FIGURE 4.8 Backcalculated layer moduli (Ksi) for composite pavement section WV2_frie station 6.100. 53
FIGURE 4.9 Backcalculated layer moduli (Ksi) for composite pavement section WV2_frie station 7.333. 54
FIGURE 4.10 Backcalculated layer moduli (Ksi) for flexible pavement section WV3_whit station 40.806. 55
FIGURE 4.11 Backcalculated layer moduli (Ksi) for flexible pavement section WV3_whit station 41.013. 56
FIGURE 4.12 Backcalculated layer moduli (Ksi) for flexible pavement section WV3_whit station 41.221. 57
FIGURE 4.13 Backcalculated layer moduli (Ksi) for flexible pavement section WV71_blu station 0.009. 58
FIGURE 4.14 Backcalculated layer moduli (Ksi) for flexible pavement section WV71_blu station 1.259. 59
FIGURE 4.15 Backcalculated layer moduli (Ksi) for flexible pavement section WV71_blu station 2.740. 60
FIGURE 4.16 Backcalculated layer moduli (Ksi) for rigid pavement section US2_moun station 18.250. 61
FIGURE 4.17 Backcalculated layer moduli (Ksi) for rigid pavement section US2_moun station 19.028. 62
FIGURE 4.18 Backcalculated layer moduli (Ksi) for rigid pavement section US19_hic station 20.856. 63
FIGURE 4.19 Backcalculated layer moduli (Ksi) for rigid pavement section US19_hic station 21.563. 64
FIGURE 4.20 Backcalculated layer moduli (Ksi) for rigid pavement section US19_hic station 21.839. 65
FIGURE 5.1 Flexible pavement section. 74
FIGURE 5.2 Rigid pavement section. 74
FIGURE 5.3 Composite pavement section. 74
ix
FIGURE 5.4 Instrumentation layout. 75
FIGURE 6.1 Finite element mesh of the flexible pavement model. 91
FIGURE 6.2 Finite element mesh of the rigid pavement model. 92
FIGURE 6.3 Finite element mesh of the composite pavement model. 93
FIGURE 6.4 Impact loading curves used in different finite element models. 94
FIGURE 6.5 Load-Deflection relation for different types of pavements. 95
FIGURE 6.6 Fringes of vertical Stress at time of maximum FWD load. 96
FIGURE 6.7 Vertical stresses in different types of pavements due to FWD load. 97
FIGURE 6.8 Comparison between experimental and FE deflection basins for different pavements models.. 98
FIGURE 6.9 Fringes of vertical displacement at time of maximum FWD load. 99
FIGURE 6.10 Deflection-time histories for different pavement models. 100
FIGURE 6.11 Comparison between backcalculated deflection basins and measured basins. 101
FIGURE 6.12 Comparison of backcalculated layer moduli for the three types of pavements. 102
FIGURE 7.1 Finite element mesh for a rigid pavement. 110
FIGURE 7.2 Cross section in a doweled joint. 110
FIGURE 7.3 Impact load curve used in finite element model (Ref. (48)). 111
FIGURE 7.4 Model Verification. (Slab length=20 ft) 112
FIGURE 7.5 Comparison between the results of backcalculation programs. 113
FIGURE 7.6 Effect of slab length on deflection basin. 114
FIGURE 7.7 Change of maximum deflection with slab length for undoweled pavement. 115
FIGURE 7.8 Effect of slab length on the backcalculation results ( Using MODULUS). 116
FIGURE 8.1 Finite element model. 134
FIGURE 8.2 Measured FWD impact load curves used in finite element models. 135
FIGURE 8.3 Measured and FE-calculated deflection basins. 136
FIGURE 8.4 Subgrade vertical displacement versus depth. 137
FIGURE 8.5 Subgrade vertical displacement on a logarithmic scale versus depth. 138
FIGURE 8.6 Decay of vertical stress and displacement in subgrade. 139
FIGURE 8.7 Effect of the depth to bedrock on the deflection basin. 140
FIGURE 8.8 Effect of reflective subgrade bottom on deflection basin. 141
FIGURE 8.9 Subgrade vertical displacement for different model depths. 142
FIGURE 8.10 Effect of model depth on vertical stress distribution for site 3. 143
FIGURE 8.11 Effect of load duration on the deflection basin. 144
Numbers in parentheses refer to numbers of references.1
1
CHAPTER 1
INTRODUCTION
1.1 BACKGROUND
Backcalculation is an analytical procedure in which the deflection data collected during a
Falling Weight Deflectometer (FWD) test are used to predict the moduli of different pavement layers.
The backcalculation procedure involves theoretical calculations of the deflections produced under a
known applied load using an assumed set of layers’ moduli. The theoretical deflections are then
compared with those measured during the test. In case of differences between the theoretical and
measured deflections, the assumed pavement layers moduli are adjusted and the process is repeated
until the differences between the theoretical and measured values fall within acceptable limits.
Techniques like iteration, database searching, regression analysis, and artificial intelligence (neural
networks) have been used as backcalculation tools (1,2) .1
Most of the existing backcalculation algorithms use iterative analysis. In this case, the
solution for the theoretical deflections is initiated at the distant sensor locations assuming that surface
deflections at the distant sensor positions are due to strains or deflections in the subgrade layer only
and independent of the overlaying layers (3-5). As shown in Figure 1.1, the stress zone intersects
the interface between the subbase and subgrade layers at the radial distance r = a . This means thate
any surface deflection value obtained from the deflection basin at or beyond the distance r = a is duee
only to the deformation within the subgrade layer. Thus, in-situ modulus of the subgrade can be
evaluated from the known values of measured deflections at the outer geophone positions. From the
above discussion, a value is obviously very important. The AASHTO Guide for Design of Pavemente
Structures (1993), Section 5.4.5, Step4: Deflection Testing points out that the deflection used to
backcalculate the subgrade modulus must be measured far enough from the center of load application
r � 0.7ae
ae a2� D(3
Ep
MR
)
2
2
so that it provides a good estimate of the subgrade modulus. The guide suggests that minimum
distance may be determined from the following relationship:
the following formula is provided for the determination of a (5):e
where a = radius of a stress bulb at the subgrade-pavement interface, inches;e
a = FWD load plate radius, inches;
D = total thickness of pavement layers above the subgrade, inches;
E = effective modulus of all pavement layers above the subgrade, psi;P
M = subgrade resilient modulus, psi.R
The AASHTO guide gives a graph for the determination of the ratio E / M for a six inchP R
radius loading plate, known total thickness of pavement layers above the subgrade, known maximum
deflection under the center of the loading plate, and known load magnitude.
The following aspects should be considered for the evaluation of subgrade modulus from
FWD data:
1. Different types of pavement structures produce a different spread of stress zone (stress bulb).
Flexible pavements are characterized by localized stress distribution while rigid pavements
have a wider spread of stress zone. The stress zone in composite pavements falls between the
above two, depending on: the type of overlay, construction practice, and condition of the
second layer (old top layer). Calculation of a is useful in the determination of geophonee
location for the evaluation of subgrade moduli.
3
2. Accuracy of measurement progressively diminishes at distant geophone locations due to the
fact that the displacement magnitude is close to the resolution accuracy of the geophone.
Measurements below 2.5 mils (0.0025 inch) should be processed with care.
3. High load magnitude could be an additional source of error in the evaluation of linear resilient
subgrade modulus since it is likely to produce nonlinear deformations in the soil layer.
AASHTO Guide for Design of Pavement Structures (1993), Section 5.4.5, suggests the use
of a load magnitude of approximately 9,000 lb to avoid nonlinearity of the subgrade response.
Subgrade layers are the most complex layers in the pavement structure due to their physical
nature and construction practices. Undisturbed natural soil deposits frequently reveal an increase in
the value of elastic modulus with depth, due to higher consolidation of geologic material. Therefore,
if such a soil sample is divided into layers, the top layers will have lower moduli than the lower ones.
The backcalculation process is based on the assumption that surface deflection at a certain offset is
characteristic of the elastic modulus at a certain depth. However, deflections measured at distant
locations are very small and cannot be measured accurately based on geophone resolution. Higher
loads can produce deflections of large magnitudes, but unfortunately they will also cause stresses in
the soil that fall into the nonlinear zone. This again alters the accuracy of linear elastic modulus
evaluation for deeper layers. The only subgrade modulus that can be accurately predicted by FWD
test is the resilient modulus of the top of the subgrade layer positioned right under a base-subgrade
interface.
During the 1998 annual Transportation Research Board (TRB) Meeting of the Committee on
Backcalculation of Pavement Moduli, a specific question regarding accuracy of subgrade moduli
calculation was addressed to L. Irwin, the developer of the MODCOMP3 backcalculation program.
He suggested improving accuracy of subgrade modulus evaluation by dividing the soil layer into a
larger number of thin sublayers. Regarding the depth of top subgrade layer, he suggested calculating
the depth by subtracting the height of pavement structure above the subgrade from the depth of frost
penetration value, which is 30 to 36 inches for West Virginia.
4
Assumption of a thicker layer in backcalculations consistently produced higher subgrade
modulus value. This observation shows that a thicker layer assumption leads to overestimation of
subgrade moduli, which is an undesirable outcome.
In the backcalculation procedure, the modulus of the lowest subgrade layer is changed in the
iterative procedures until such value is found that will produce surface deflection at the distant
geophone that agrees with the measured one, within a certain tolerance. Once the modulus value for
the lowest layer is found, it is assumed to be the “true” value and is used as a constant in the
evaluation of moduli for the upper layers. The solution progresses from the distant geophone
locations to the center of load application and the layers moduli are evaluated from the bottom to
top layers. Knowledge of existing pavement layer thicknesses, Poisson’s ratios, and load magnitude
are necessary conditions for the backcalculation procedure. The pavement layers moduli derived in
the above process are further used for the stress and strain analysis of the pavement structure. The
moduli are usually averaged from the results of several load drops in order to lower the weight of the
random error that is introduced during every FWD drop.
The major assumption used in backcalculation algorithms is that the amount of surface
deflection at any point is dependent on the stress-strain state in subsequent layers. This assumption
is true for static loading, but may be violated if the load is dynamic, or if there is discontinuity
(separation) at one or more interfaces.
1.2 BACKCALCULATION PROBLEMS
Although FWD load is an impact load by nature (6-9), most of available backcalculation
programs are based on the static multilayer elastic theoty. The major limitation of the elastostatic
analysis of the FWD load is that it does not account for factors such as material inertia and damping
. As noted by Hoffman and Thompson (10), inertial effects in the pavement layers subjected to FWD
impact may be significant and therefore need to be considered in the theoretical analysis.
5
As pointed out by Chou et al. (11), none of the programs based on the static multilayered
elastic theory could guarantee accurate results for every test section. Chou et al. stated that two
independent agencies who used the same backcalculation software to determine moduli for the same
pavement section produced different results. Therefore, engineering judgement plays an important
role in the evaluation of the test results.
Irwin et al. (12) reported that most errors occur during the evaluation of the surface layer
modulus and Huang (4) stated that this is especially true in the case of thin asphalt layers. One
reason may be the difference between patterns of dynamic and static deformations of the surface
layer.
1.3 OBJECTIVES OF THIS THESIS
Most of the existing backcalculation algorithms are based on simplifying approximations which
include that:
1. the pavement structure has infinite extension perpendicular and along the traffic direction,
3. all pavement layers are fully bonded, and
4. the short duration loading impulse (25 millisecond) applied by the FWD may be approximated as
a static applied load.
The work presented in this thesis is directed towards developing a backcalculation technique in which
the actual pavement geometry, the full FWD loading pulse time-history, and the properties of the
interfaces between pavement layers are accounted for in the backcalculation of the pavement moduli
profile. The structural moduli profile obtained using such a backcalculation technique could be used
to evaluate the performance of existing backcalculation programs. It could also be used in situations
where existing backcalculation algorithms would produce unrealistic results such as in the case of
composite pavements. To achieve this objective, Three Dimensional Finite Element Modeling (3D
FEM) was used to simulate the pavement structure. The use of 3D FEM allows loading the model
6
with the exact FWD loading-time history measured from FWD load cell, as well as representation of
the properties of interfaces between different layers. Although elastic material models were assumed
for all pavement layers (based on the experimental measurement of FWD load-deflection relation),
the 3D FEM approach allows the use of any nonlinear material models including thermo-elastic and
thermoplastic material models.
1.3.1 Organization of this Thesis
The work presented in this Thesis starts in Chapter Two which contains a review of the research
studies which aimed at evaluating the performance of existing backcalculation algorithms. Two major
studies were reviewed in some detail: the Strategic Highway Research Program ( SHRP) study whose
results were first published in 1993 and the MnDOT study published in 1996. The outcome of this
review was the selection of four major backcalculation programs that were the most widely used by
the pavement community. In Chapters Three and Four, the results from the four programs were
compared to each other using SHRP-LTPP data and using data for seven different roads measured
in West Virginia. Chapter Five outlines the FWD testing procedures used for testing three pavement
sites in West Virginia. 3D FEM backcalculation procedures were presented in Chapter Six. The 3D
FEM-backcalculated layer moduli were compared with those obtained using the previously selected
conventional backcalculation algorithms and correction factors were obtained. Some factors which
influence the results of backcalculation of rigid pavements were examined in Chapter Seven. The
factors which influence the backcalculation of flexible pavements were examined in Chapter Eight.
Chapter Nine presents the conclusions drawn from this work along with some points for future
research.
7
FIGURE 1.1 FWD setup and schematic presentation of stress bulb.
8
CHAPTER 2
LITERATURE REVIEW
2.1 BACKCALCULATION PROGRAMS
In 1993, a comprehensive review of existing software for backcalculation procedures was
published as a result of Project SHRP-90-P-001B, sponsored by the Strategic Highway Research
Program (13). After considering a large number of different backcalculation programs, the study was
narrowed down to the following three: MODULUS, WESDEF, and MODCOMP3. The programs
were tested by a group of independent researchers and practicing engineers for different types of
pavement structures. Evaluation criteria that were considered are the repeatability of results obtained
by different users, reasonableness of results, deflection matching errors, ability to match assumed
moduli from simulated deflection basins, and versatility.
As a result of this evaluation, the MODULUS program was judged to be the best and was
therefore chosen for routine use on SHRP and LTPP data. Nonetheless, the MODULUS program
had one drawback that it required deflections to be measured at the specific sensor locations. This
means that some of the points in the deflection basin will be excluded from the matching procedure.
The results from WESDEF program were found to have the highest level of sensitivity to user input.
However, in the same report it was pointed out that this could have been due to the default depth to
bedrock that was not overridden by the users in cases of semi-infinite subgrade layers. The authors
concluded that the MODCOMP3 program tends to over predict subgrade modulus and under predict
base and subbase moduli.
Research was conducted recently by the Minnesota DOT to select a backcalculation software
for the Minnesota Road Research Project (14). The strategy of that study was to compare the
performance of the candidate programs for flexible pavement evaluation in terms of usability and
accuracy of backcalculation results. Four different programs were evaluated: EVERCALC3.3,
9
EVERCALC4.0. WESDEF, and MOCOMP3. All four programs were based on the multilayer linear
elasto-static forward calculation subroutines. As a result of this project, the EVERCALC4.0 program
was recommended for routine research of the Minnesota Road Research test sections.
2.2 PROGRAM SELECTION
Information about sixteen different backcalculation programs available on the market was
collected and is presented in summarized form in Table 2.1. The selection of programs to be
evaluated during the current project was based upon the following recommendations:
1. SHRP Report on Layer Moduli Backcalculation Procedure, 1993 (13).
2. Minnesota Road Research Project Report on Selection of Flexible Pavement
Backcalculation Software, 1996 (14).
As a result, four backcalculation programs were selected for evaluation:
� MODCOMP3 Developed at Cornell University
� MODULUS5.0 Developed by Texas Transportation Institute
� EVERCALC4.0 Used by Washington State DOT
� ELMOD4 Developed by Dynatest
Evaluation of the above programs using data from eight SHRP test sections and twenty-one
sections for seven different roads in West Virginia is presented in this report.
10
2.3 DESCRIPTION OF SELECTED BACKCALCULATION PROGRAMS
2.3.1 Description of MODCOMP3 Program
MODCOMP3 was initially developed by Irwin and Speck for the U.S. Army Cold Regions
Research and Engineering Laboratory. Later, MODCOMP3 was modified by Irwin and Szebenyi
(15) in 1991 at Cornell University.
The MODCOMP3 program uses CHEVRON computer code as a forward calculation
subroutine. This code is based on the multilayer linear elasto-static theory that is traditionally used
for flexible pavement analysis. Fitting the calculated results with the experimentally obtained ones
is implemented through an iterative analysis approach. The modulus of each layer is assumed to
affect the deflection measured at a certain distance from the load. The program first evaluates the
modulus of the deepest layer corresponding to the deflection reading at the farthest geophone
location specified and then it works upwards to calculate the moduli of near surface layers. The
drawback of the program is that the user is responsible for the accurate prediction of the exact
distance that would reveal the deflection characterizing the modulus of a particular layer.
The program can handle from two to fifteen layers, including the bottom layer that is treated
as a semi-infinite half space. Layers moduli can be treated both as known or unknown. No more than
five unknown layers are recommended for use in the analysis. Based on the readings at distant
geophone locations, the program has the ability to calculate the depth to bedrock. Up to ten
geophone locations can be included in backcalculation. The program can accept up to six different
loading cases in the analysis. Layers can be treated both as linear elastic or nonlinear elastic.
The backcalculation analysis is initiated by the set of initial seed moduli specified by the user.
Since no moduli range can be specified, therefore the algorithm has the potential of producing out
of range moduli.
11
The process of backcalculation terminates when one of the following conditions is met:
1. The deflection fit precision tolerance is satisfied.
2. The modulus convergence tolerance is satisfied.
3. The allowed number of iterations is exhausted.
At the end of each iteration, MODCOMP3 checks two tolerances before proceeding to the
next iteration. If either of the tolerances is satisfied, the calculations cease.
The deflection fit precision is a check on the match between the measured deflections and
the deflections that have been calculated at the same radii using the backcalculated moduli. Only the
sensors that are assigned to the layers are included in this check. This means that the whole deflection
basin may not be used in the backcalculation process. For example, if the pavement structure consists
of three layers and the FWD test setup has seven geophones, the user will need to choose three out
of seven geophone readings to backcalculate pavement moduli. In this case, initially, different
geophone selections will produce different sets of moduli; then, the deflection basin built using the
backcalculated moduli will fit the measured basin only at the selected points. So the program leaves
little opportunity to achieve a full match between measured and calculated basins. The accuracy of
the solution is highly dependant on the success in the selection of the “right” geophones for
backcalculation of pavement moduli.
The modulus convergence is a check on the rate of change of the backcalculated moduli
from one iteration to the next. A tolerance of 1.5 percent is typically assigned; but if a value close
to zero is used, this tolerance check is eliminated because it will not be satisfied before either the
deflection fit precision tolerance is achieved, or the allowed number of iterations is exhausted.
2.3.2 Description of MODULUS5.0 Program
MODULUS5.0 was developed by Texas Transportation Institute (16,17). This computer
12
code uses WESLEA program as a forward calculation subroutine. WESLEA is based on the
multilayer linear elasto-static theory that is traditionally used for the purposes of flexible pavement
analysis. The WESLEA subroutine is used to build a data base for the calculated deflection basins of
a given pavement system. A pattern search technique is then used to determine the set of layers
moduli that produce a deflection basin that fits the measured one.
The deflection data collected during the FWD test can be read directly from the DYNATEST
FWD field data diskette or manually typed by the user. Up to eight different load drops at each
station can be considered in the backcalculation analysis, and up to seven geophone locations can be
included in the backcalculation.
The maximum number of unknown layers is limited to four in order to minimize the errors and
produce acceptable results. The depth to the stiff layer can be automatically calculated in the
program. In addition, the user can specify different depth values.
MODULUS5.0 uses weighting factors assigned to each geophone deflection reading.
Different values of weighting factors can maximize or minimize the significance of a certain deflection
value in the backcalculation process. If the weighting factors are not specified by the user, the
program implements an automatic weighting factor determination algorithm. In this case, if a
nonlinear subgrade stiffening with depth is detected, the backcalculation program automatically drops
a maximum of one sensor reading by assigning to it a zero weighting factor.
The backcalculation program has two analysis options. In the first option called “Full
Analysis”, the program asks the user to specify the moduli range to be used in the backcalculation.
The user can specify moduli ranges for up to three layers except the subgrade, and provides a seed
modulus value for the subgrade layer. This feature prevents the program from producing out-of-
range moduli for all layers except the subgrade. Although the program allows the user to enter up
to seven different locations, the manual has a note stating that in MODULUS5.0 the sensors must
be placed at 0, 12, 24, and 36 in..
13
In the second option called “Material Types,” the user is asked to input only the material types
and layers thicknesses and the program automatically selects acceptable ranges of moduli and
Poisson’s Ratios. Both options produce similar outputs for the same types of pavement layer
materials. However, it is worth noting that this program was designed in Texas and oriented to the
pavement design practices used there. Thus, the material selection table is limited to those materials
that are frequently used in Texas and cannot cover all the wide range of pavement materials used in
road construction in the USA. As a result, it is more appropriate to use the first option of the
program in the current backcalculation evaluation process.
Both computed and measured deflection basins can be plotted on the screen. This feature provides
the user with a visual assessment of the accuracy of the program.
2.3.3 Description of EVERCALC4.0 Program
EVERCALC4.0 was developed by J. Mahoney at the University of Washington for
Washington DOT (18). The EVERCALC4.0 uses the WESLEA computer code developed by
Waterways Experimental Station, U.S. Army Corps of Engineers, as a forward calculation subroutine
and a modified augmented Gauss-Newton algorithm for solution optimization. The WESLEA
computer code is based on the multilayer linear elasto-static theory that is traditionally used for
purposes of flexible pavement analysis. The fit of the calculated deflection basin with the
experimentally measured one is implemented through the iterative analysis approach.
The program can handle up to seven sensor measurements and eight drops per section.
Flexible pavement sections containing up to five layers can be evaluated.
To initialize the backcalculation process, initial moduli, as well as moduli ranges, need to be
specified for all the layers. This feature prevents the program from producing out-of-range moduli
for all the layers. At the end of each iteration, the deflections calculated by WESLEA are compared
14
with the measured ones. The discrepancies between the calculated and measured deflections are
characterized by Root Mean Square (RMS) error. The iterations are terminated when one of the
following three conditions are satisfied: (1) RMS falls within the allowable tolerance, (2) the changes
in modulus between two successive iterations fall within the allowable tolerance, or (3) the number
of iterations has reached the maximum limit. When two or more deflection data sets for the same
location are analyzed, the final moduli from the first deflection data is used as a seed moduli for the
next one.
If the pavement section contains no more than three layers, the program can assign the seed
moduli internally. In this case, a set of regression equations is used to determine a set of seed moduli
from the relationships between the layers moduli, surface deflections, applied load, and layer
thickness.
A stiff layer that has a known modulus can be included in the analysis. In this case, the depth
to the stiff layer will be calculated by the program. Inclusion of the stiff layer in the analysis normally
results in a decrease of the subgrade modulus and an increase of the modulus of the layer above the
subgrade (subbase or base) layer.
The program is also able to normalize the modulus of the Asphalt Concrete (AC) layer to that
evaluated at the standard laboratory conditions (for a temperature of 77 F and 100-millisecondo
loading time).
A disadvantage of the EVERCALC4.0 program is that the output files are stored in binary
format, which complicates the communication of EVERCALC4.0 with any other software when
needed (such as an external data base of deflection basins, etc.).
The FWD “raw” deflection data file can be used for the direct input if DYNATEST FWD
model 8000 is used. In this case, the EVERCALC4.0 program will internally convert FWD data to
the EVERCALC4.0 deflection data file. Otherwise, deflection data should be entered manually and
15
saved in a deflection data format provided by EVERCALC4.0. The EVERCALC4.0 program
provides excellent visualization of the results in a variety of graphs and bar charts. The program can
handle English or Metric units.
2.3.4 Description of ELMOD4 Program
ELMOD4 was developed by Dynatest Consulting Inc. ELMOD is an acronym for Evaluation
of Layer Moduli and Overlay Design. The program accepts DYNATEST-FWD file format. If such
a file does not exist, no means for manual input of deflection data is provided by the program. The
ELMOD4 program is capable of calculating pavement layer moduli using one of these two options:
the Odemark-Boussinesq transformed section approach or the deflection basin fit backcalculation.
The first method can be used for one to four layers pavement systems. The second method can
handle up to five layers. In both methods, the dependancy of AC material on temperature conditions
is accounted for. In order to use this feature of the program, the 24-hour air temperature should be
entered in the Structural Data input screen.
Odemark’s layer transformed (structural) section approach is used in conjunction with
Boussinesq’s equations to calculate deflections. An iterative procedure is used to determine layers
moduli which results in the same deflections as measured by a FWD. This method provides the
apparent moduli for the as-measured deflections at each FWD test point, it also takes the nonlinearity
of the subgrade into consideration. This approach is very reliable for flexible three layered pavement
systems that include an unbound base layer plus the bound surface layer . Four layer flexible systems
may also be evaluated using the Odemark-Boussinesq mode provided that the ratio E /E is known.2 3
The program includes a procedure for the automatic calculation of this ratio for granular materials
from the thickness of layers number two and three. For the backcalculation input, a “layer” can
consist of several materials. To better simulate the theoretical conditions on which the backcalculation
approach is based, the program developers suggest combining an asphalt layer with an adjacent gravel
layer or another stabilized layer.
16
A total of five layers, including the subgrade, may be backcalculated if the “deflection basin
fit” backcalculation option is utilized; however, many layers are not recommended unless one or more
of them are assigned some fixed modulus. The deflection basin fit backcalculation method is done
either by using the normal Odemark transformed section factors (0.8 for multi-layered systems and
0.9 for two-layered systems) and adjusting the moduli accordingly, or by recalculating the factors by
a numerical integration forward calculation procedure using a modified version of WES5 and then
performing the deflection basin fit backcalculation using “calibrated” transformed section factors.
The developers of the program recommend the use of the first approach for backcalculation.
ELMOD4 can also provide a theoretical estimate of the equivalent depth to a rigid layer from
the measured deflections. If this option is not chosen, ELMOD4 considers an infinitely thick
nonlinear subgrade. In case of a stiff layer input, linear elastic behavior of the finite subgrade layer
is assumed. ELMOD4 calculates the equivalent depth of an apparently stiff layer and compares this
calculated depth with the user’s maximum depth input; if it is less than the input depth it uses the
calculated depth to perform the analysis. If the calculated depth is greater than the input depth, the
analysis reverts to the consideration of a semi-infinite (nonlinear) subgrade.
ELMOD4 backcalculates the elastic moduli of up to five layers provided that the following
conditions are met:
1. The structure should contain only ONE bound upper (stiff) layer, where E /E �5. If the1 subgrade
structure contains more than one bound layer, they should be combined into one analysis for
the purpose of structural evaluation.
2. The moduli should decrease with depth by approximately E /E >2. Where E is the modulusi i+1 i
of the ith layer counted from the surface.
3. The thickness of the upper (bound) layer (H1) should be larger than half the radius of the
loading plate (generally > 75 mm or 3 inches).
17
4. For three layered structures, the thickness of the upper layer should be less than the diameter
of the loading plate and the thickness of layer one should be less than that of layer two (H1<
H2).
5. When testing on/near a joint, a very wide crack, on gravel surfaces, the structure should be
treated as a two-layer system.
Another limitation of the ELMOD4 program is that Poisson’s Ratios are assumed to be 0.35
for all layers. This is suitable for asphaltic and unbound granular materials, but different from the
values for the cohesive soils (0.42-0.45) and concrete (0.15-0.18).
The main features of the above four reviewed programs are summarized in Table 2.2.
18
TABLE 2.1 Available Backcalculation Programs.
Name of the Name of Theoretical Backcalculation Sourcemain program subroutine for method for method
pavement analysis pavement analysis
BISDEF BISAR Multilayer elastic Iterative USACE-WES
CHEVDEF CHEVRON Multilayer elastic Iterative USACE-WES
CLEVERCALC CHEVRON Multilayer elastic Iterative Royal Institute ofTechnology,
Sweden
COMDEF BISAR Multilayer elastic Data Base M. Anderson
ELSDEF ELSYM5 Multilayer elastic Iterative Texas A&MUniversity,
USACE-WES
EMOD CHEVRON Multilayer elastic Iterative PCS/LAW
EVERCALC CHEVRON Multilayer elastic Iterative J. Mahoney
FPEDDI BASINPT Multilayer elastic Iterative W. Uddin
ILLIBACK ILLIBACK Plate on elastic Closed form University offoundation theory solution Illinois
ILLI-CALC ILLIPAVE Nonlinear elasto- Iterative University ofstatic finite Illinois
element modeling
ISSEM4 ELSYM5 Multilayer elastic Iterative R. Stubstud
MODCOMP CHEVRON Multilayer elastic Iterative L. Irwin, Szebenyi
MODULUS WESLEA Multilayer elastic Data Base TexasTransportation
Institute
PADAL PADAL Multilayer elastic Iterative S.F.Brown et al.
WESDEF WESLEA Multilayer elastic Iterative USACE-WES
MICHBACK CHEVRON Multilayer elastic Iterative Michigan StateUniversity
19
TABLE 2.2 Comparison of Selected Backcalculation Programs.
Name of the Forward Theoretical Back- Maximum Number of sensors Maximum Use of bedrock Temperature Developed Operatingmain program back- method for calculation number of used in analysis number of in corrections by Environment
calculation pavement method unknown different backcalculationsolution analysis layers load levels
MODCOMP3 CHEVRON Multilayer Iterative Five Internally or user Six Calculates depth No l. Irwin, DOSelastic Analysis specified number to bedrock upon Szebenyi,
of layer-sensor users request. Cornellassignments,up to Universityten sensors
MODULUS5.0 WESLEA Multilayer Data Base Four Program selects No limit Automatically No Texas DOSelastic Search optimum number calculates depth Trasportation
of sensors to use to bedrock and Institute in backcalculation, includes it in thecan be overridden analysis, can beby user through overridden byspecification of user.weighting factorsfor up to sevensensors
EVERCALC4.0 WESLEA Multilayer Iterative Five Up to seven sensors Eight Calculates depth Yes J. Mahoney, Windowselastic Analysis to bedrock only if University of
bedrock modulus Washingtonis known.
ELMOD4 ELMOD4, Odemark- Iterative Five As provided in raw as provided Calculates depth Yes Dynatest WindowsWES5 Boussinesq Analysis FWD data file in raw to bedrock and
FWD data includes it in thefile. analysis, can be
overridden byuser.
20
CHAPTER 3
COMPARISON OF BACKCALCULATION RESULTS
FOR SHRP TEST SECTIONS
To evaluate the performance of backcalculation programs, the deflections and loadings
measured for eight different SHRP sections were used with each of the four selected programs. The
data required for the backcalculation were obtained from the SHRP-P-651 report. The types of
materials and thicknesses for all eight sections are given in Figure 3.1. Six of the SHRP sections were
for flexible pavement structures and the other two were for composite pavements constructed by
overlaying original plain Portland Cement Concrete (PCC) pavement structures with asphaltic
concrete. The moduli ranges for the different sections were obtained from the literature. The values
were those commonly used to characterize a particular type of geologic material. When the
information on a particular material type was not available in the literature, the modulus range for this
material was interpolated from the published SHRP backcalculation results. The ranges of pavement
layers moduli and Poisson’s Ratios are presented in Table 3.1.
All of the selected programs, MODCOMP3, MODULUS5.0, EVERCALC4.0, and ELMOD4
produced sets of pavement moduli that were within an acceptable match with the published results
of backcalculation obtained from the SHRP project report, as listed in Table 3.2.
During different backcalculation runs, it was found that the inclusion or omission of a stiff
layer resulted in different values for subgrade modulus and affected, to some extent, the
backcalculated values of other layers. Inclusion of the stiff layer results in evaluation of a lower
subgrade modulus. This dependancy was observed mainly in MODCOMP3 and MODULUS5.0
programs.
It was noted that the results from MODCOMP3 program were very sensitive to the
assignment of the deflection sensor reading to a particular layer. Different layer-deflection
21
assignments may result in different results. Another disadvantage is that when the number of
deflection sensors exceed the number of pavement layers, some of the deflection sensor readings are
ignored in the backcalculation; and instead of the whole calculated deflection basin fit, only the
chosen deflection sensor readings are fitted with the calculated ones. This limited approach makes
the task of deflection basin fitting extremely difficult. A possible solution is to divide one or two
layers into sublayers so that the number of sensors and layers will be equal. This approach has two
drawbacks. First, it is difficult to decide which layers to subdivide so that the surface deflection will
accurately predict their deflections. Second, division of a layer into sublayers may result in the
calculation of two completely different moduli for the same layer.
The EVERCALC4.0 program terminates as soon as a moduli tolerance of one percent is
satisfied. However, frequently this solution does not satisfy the deflection basin tolerances and has
a high Root Mean Square value (RMS) error between measured and calculated deflections. All the
attempts to override the default, one percent moduli tolerance, have failed. The program does not
save this change upon its exit from the data input file. For most of the eight SHRP sections, subgrade
moduli backcalculated by EVERCALC4.0 program were around the upper bound of the moduli range
obtained from SHRP report. This might mean that EVERCALC4.0 has a tendency to overestimate
the subgrade modulus.
The ELMOD4 program produced good results for the flexible pavement sections with
unbound granular bases. However, backcalculations for the sections that include a stabilized or
concrete layer under the surface AC layer resulted in over prediction of the surface layer modulus and
under prediction of the base layer modulus. This could be due to the limitations of the ELMOD4
forward calculation algorithm that were discussed previously in Section 2.4.
The results of backcalculations for the eight SHRP sections are presented in Figures 3.2
through 3.9 for SHRP sections A through H. Each figure contains bar charts for comparison between
pavement layers moduli evaluated by the above four backcalculation programs and the maximum and
minimum values of moduli produced for the same layers during the SHRP project evaluation. All the
22
tested programs produced results that fall within the range obtained during SHRP project program
evaluation.
Out of the four tested programs, MODCOMP3 program proved to be the most user-sensitive
and required more engineering judgement. The approach of using seed moduli only, without
specifying the acceptable moduli range, can lead to the calculation of unexpectably high or low
moduli in different layers. The accuracy of the solution is highly dependent on the layer-deflection
assignments. Totally different sets of moduli can be backcalculated for different layer-deflection
assignments.
The ELMOD4 program failed to perform well on the sections that contained a stiff layer
under the AC surface. However, it produced good results for flexible pavement sections with
unbound granular bases.
Both MODULUS5.0 and EVERCALC4.0 are user-friendly and capable of producing
pavement moduli within an acceptable range. MODULUS5.0 program allows to internally assign
layer moduli based on the material types specified by the user. This feature can be advantageous if
the material type is known and supported by the program. The EVERCALC4.0 program is fitted
with a temperature correction option. This feature enables the user to adjust the backcalculated
modulus of the AC layer to the modulus value measured at the standard temperature testing
conditions.
23
TABLE 3.1 Moduli Range and Poisson’s Ratio for Backcalculation Inputs.
Material Type Moduli Range Poisson’s(Ksi) Ratio
Portland Cement Concrete 1000 - 10000 0.15
Asphalt Concrete (cold->hot) 200 - 2,500 0.25 - 0.35
Unstabilized Crushed Stone or Gravel Base Course (well drained) 10 - 160 0.35 - 0.40
Unstabilized Crushed Stone or Gravel Subbase (poorly drained) 10 - 100 0.40 - 0.42
Asphalt Treated Base 10 - 90 0.35
Sand Base 5 - 80 0.35
Sand Subbase 5 - 80 0.35
Cement-Stabilized Base and Subbase 500 - 2,500 0.25 - 0.35
Lime-Stabilized Base and Subbase 5 - 200 0.25 - 0.35
Subgrade Soil Cohesive Clay 3 - 4 0.42- 0.45
Subgrade Soil Fine-Grained Sands 25 - 30 0.42 - 0.45
Cement Stabilized Soil and Bedrock 100 - 1000 0.20
Lime Stabilized Soil 100 - 400 0.25
24
TABLE 3.2 Backcalculated Layer Moduli (ksi) for SHRP Sections.
Surface Layer Base Layer Subbase Layer Subgrade
SHRP Section AMODULUS 993 65.8 16.8 36.4
EVERCALC 918 70 14 39
MODCOMP3 1000 80.4 16.7 29.6
SHRP MAX 1320 92 92 40
SHRP MIN 720 10 10 13
SHRP Section B
MODULUS 1009 57.4 27.6
EVERCALC 813 87 23
MODCOMP3 547 175 24.2
SHRP MAX 1420 155 27
SHRP MIN 500 85 22
SHRP Section CMODULUS 566 500 36.5
EVERCALC 572 447 36
MODCOMP3 613 537 36.4
SHRP MAX 630 1020 37
SHRP MIN 450 400 26
SHRP Section DMODULUS 2526 678.7 20.1
EVERCALC 1933 967 20
MODCOMP3 2230 870 19.1
SHRP MAX 3050 2510 21
SHRP MIN 1400 430 12
SHRP Section EMODULUS 991 753.3 51.8 33.6
EVERCALC 1034 689 11 79
MODCOMP3 1090 696 157 63.3
SHRP MAX 2310 890 182 52
SHRP MIN 850 90 34 32
SHRP Section FMODULUS 1069 79.4 32.5
EVERCALC 1015 77 44
MODCOMP3 1180 50.3 41.3
SHRP MAX 1300 178 45
SHRP MIN 720 37 28
SHRP Section GMODULUS 1426 8311.8 19.5 21.6
EVERCALC 1248 7470 133 31
MODCOMP3 1050 7130 30 30.6
SHRP MAX 2440 11400 133 31
SHRP MIN 820 3900 19 18
SHRP Section HMODULUS 282 4272.3 26.1
EVERCALC 308 3789 25
MODCOMP3 239 6140 15.1
SHRP MAX 7761 6300 36
SHRP MIN 200 0 19
25
FIGURE 3.1 SHRP sections data used for backcalculations.
26
SHRP SECTION A
0
5
10
15
20
25
30
35
40
45
Subgrade
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION A
0
10
20
30
40
50
60
70
80
90
100
Subbase layer
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION A
0
10
20
30
40
50
60
70
80
90
100
Base layer
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION A
0
200
400
600
800
1000
1200
1400
Surface layer
Bac
kcal
cula
ted
mod
uli,
Ksi
FIGURE 3.2 Comparison of backcalculated moduli for SHRP section A.
27
SHRP SECTION B
0
200
400
600
800
1000
1200
1400
1600
Surface layer
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION B
0
5
10
15
20
25
30
Subgrade
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION B
0
20
40
60
80
100
120
140
160
180
200
Base layer
Bac
kcal
cula
ted
mod
uli,
Ksi
FIGURE 3.3 Comparison of backcalculated moduli for SHRP section B.
28
SHRP SECTION C
0
5
10
15
20
25
30
35
40
45
Subgrade
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION C
0
100
200
300
400
500
600
700
800
900
surface layer
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION C
0
200
400
600
800
1000
1200
Base layer
Bac
kcal
cula
ted
mod
uli,
Ksi
FIGURE 3.4 Comparison of backcalculated moduli for SHRP section C.
29
SHRP SECTION D
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Surface layer
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION D
0
500
1000
1500
2000
2500
3000
Base layer
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION D
0
5
10
15
20
25
Subgrade
Bac
kcal
cula
ted
mod
uli,
Ksi
FIGURE 3.5 Comparison of backcalculated moduli for SHRP section D.
30
FIGURE 3.6 Comparison of backcalculated moduli for SHRP section E.
SHRP SECTION E
0
10
20
30
40
50
60
70
80
90
Subgrade
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION E
0
20
40
60
80
100
120
140
160
180
200
Subbase layer
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION E
0
100
200
300
400
500
600
700
800
900
1000
Base layer
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION E
0
500
1000
1500
2000
2500
Surface layer
Bac
kcal
cula
ted
mod
uli,
Ksi
31
SHRP SECTION F
0
5
10
15
20
25
30
35
40
45
50
Subgrade
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION F
0
20
40
60
80
100
120
140
160
180
200
Base layer
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION F
0
200
400
600
800
1000
1200
1400
Surface layer
Bac
kcal
cula
ted
mod
uli,
Ksi
FIGURE 3.7 Comparison of backcalculated moduli for SHRP section F.
32
SHRP SECTION G
0
5
10
15
20
25
30
35
40
45
50
Subgrade
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION G
0
20
40
60
80
100
120
140
Subbase layer
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION G
0
2000
4000
6000
8000
10000
12000
Base layer
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION G
0
2000
4000
6000
8000
10000
12000
14000
Surface layer
Bac
kcal
cula
ted
mod
uli,
Ksi
FIGURE 3.8 Comparison of backcalculated moduli for SHRP section G.
33
SHRP SECTION H
0
5
10
15
20
25
30
35
40
Subgrade
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION H
0
2000
4000
6000
8000
10000
12000
14000
Surface layer
Bac
kcal
cula
ted
mod
uli,
Ksi
SHRP SECTION H
0
1000
2000
3000
4000
5000
6000
7000
Base layer
Bac
kcal
cula
ted
mod
uli,
Ksi
FIGURE 3.9 Comparison of backcalculated moduli for SHRP section H.
34
CHAPTER 4
COMPARISON OF BACKCALCULATION RESULTS
FOR SEVEN SELECTED SITES IN WEST VIRGINIA
FWD deflection data from seven different road sites in West Virginia were provided by
WVDOT for the backcalculation of layers moduli using three different backcalculation programs:
MODULUS5.0, EVERCALC4.0, and ELMOD4. The fourth program, MODCOMP3, was dropped
from the evaluation due to its high sensitivity to layer-deflection assignments, and its inability to
converge to a solution if a modulus of any layer, during the solution process, was found to be not
sensitive to a certain geophone deflection reading. Out of seven road sites, three were composite
pavements, two flexible, and two rigid. Pavement layer material types and layer thicknesses were
provided by WVDOT. Typical moduli ranges, as provided in Table 3.1, were used as seed moduli
values in the backcalculation programs.
In some cases, the backcalculation programs failed to produce a deflection basin that was
within the acceptable tolerance with the measured deflection basin. When this situation occurred, the
range of acceptable moduli was expanded in order to reach a convergence of the solution. The
assumptions used in backcalculations are provided in Table 4.1. When an infinite subgrade option
was used in the backcalculation analysis, most backcalculation programs over predicted the subgrade
moduli compared with the ones obtained through laboratory testing.
MODULUS5.0 and ELMOD4 programs calculate the depth to bedrock internally and use
this value in the backcalculation. Comparison of the backcalculated results obtained for different
pavement sections showed that when a section was assumed as infinitely thick, high values of the
subgrade moduli were frequently predicted. Inclusion of a finite depth to bedrock to the analysis led
to more realistic lower values for the subgrade moduli. EVERCALC4.0 calculates the depth to rigid
layer only if the subgrade modulus is provided. However, since the objective of backcalculation is
to obtain a subgrade modulus, the subgrade modulus is treated as an unknown. Therefore, it was not
35
possible to include the depth to bedrock in the analysis using EVERCALC4.0.
In practice, subgrades generally display an increase in the stiffness with depth due to
overburden pressure. However, laboratory tests are made for specimens of soil obtained immediately
after the base course. This resulted in a lower laboratory measured subgrade modulus. To account
for this, subgrade layers were divided into two layers and two different subgrade moduli were
evaluated for each section. In this case, the moduli of top subgrade layers were in closer agreement
with the laboratory measured moduli. This method did not work well with the ELMOD4 program
due to the limitation of the Transformed Section Method which is used as a forward calculation
algorithm. However, for the flexible pavement sections with granular bases, the ELMOD4 program
seems to produce reasonable subgrade moduli even with one layer subgrade system.
The following four step approach for evaluation of subgrade layer modulus was used in
backcalculation:
1. Run the program assuming that the subgrade layer is uniform and infinite and check the
subgrade modulus value. If the value is out of the expected moduli range for a given type of
subgrade material ( as given in Table 3.1) or the Root Mean Square (RMS) error for the
deflection basin fit is too high, proceed with the following steps.
2. Rerun the program using default depth to the subgrade layer calculated by the program and
check the moduli and RMS again.
3. If the resulting moduli in Step 2 are not acceptable, see if there will be any improvements by
increasing or deceasing the default depth value.
4. If subgrade modulus or RMS is not very sensitive to the changes in Step 3, subdivide the
subgrade layer into two sublayers with top subgrade sublayer height H not exceeding
36
H� (36" - Height of Pavement Structure above Subgrade)
Repeat the backcalculation process starting from Step 1.
The backcalculated moduli obtained for every pavement section using three different
backcalculation programs are given in Table 4.2. Table 4.3 shows which of the moduli were lower,
higher, or within the range of moduli acceptable for the section materials types. Table 4.4
summarizes the accuracy of the backcalculation results for different programs and pavement types.
From the section by section comparison of the performances of the three backcalculation
programs the following conclusions were drawn:
1. MODULUS5.0 performed well with all three types of pavement structures. This program
consistently produced subgrade moduli that were reasonably close to the laboratory evaluated
values and within the material range (below 25 psi), as shown in Figures 4.1 through 4.20.
During the backcalculation process, the first program run for each section was carried out
assuming an infinite subgrade layer. If the percent of error was greater than five, then the
finite depth to bedrock calculated during the first run was obtained and another run of the
program was carried out assuming bedrock at a finite depth. This procedure always resulted
in lowering the percentage of error.
2. ELMOD4 predictions were very poor for the composite pavement sections. Out of the three
different pavement types shown in Figures 4.1 through 4.20, the program worked best with
flexible pavements. For flexible pavements, all backcalculated moduli for the surface and base
layers were within the acceptable range of pavement moduli. In the case of composite
pavements, the program produced very high moduli for the surface and subgrade layers and
very low moduli for the base layer, as shown in Figures 4.2 through 4.9. It was concluded
that the program works only in cases where the layer moduli gradually decrease with depth.
The program performed a little better with the rigid sections; however, the ELMOD4
37
program over predicted subgrade moduli in three out of five rigid pavement cases.
3. EVERCALC4.0 worked fairly well with flexible and rigid pavements. However, in some
flexible and rigid cases, backcalculated moduli for the base layer were on the low margin of
acceptance. In three out of seven cases for the flexible pavement sections and in three out of
five cases for rigid pavements, the program backcalculated very low modulus values for the
base layers. For all composite pavement sections, high moduli values were predicted for the
subgrade. The resulting moduli for surface and base layers in the composite pavement
sections were either under predicted or over predicted compared to the acceptable range of
moduli, and no common trend was possible to track down.
38
TABLE 4.1 Assumptions Used in Different Backcalculation Algorithms.
BackcalculationProgram
Road/StationNumber
PavementType
Moduli Range , Ksi SubgradeDepth toBedrock (in.).
SurfaceLayer
Base Subgrade Second SubgradeModulus if it isSubdivided intoTwo Layers
MODULUS5.0 US52/16.250 flexible 300-3000 5-100 4-7 calculated internally 183.7
ELMOD4 US52/16.250 flexible n / a n / a n / a 0 max 300
EVERCALC4.0 US52/16.250 flexible 200-3000 5-100 2-6 2-60 infinity
MODULUS5.0 US52/18.360 composite 200-3000 1000-9000 4-10 calculated internally 227.2
ELMOD4 US52/18.360 composite n / a n / a n / a 0 max 300
EVERCALC4.0 US52/18.360 composite 200-2500 1000-10000 3-20 2-45 infinity
MODULUS5.0 US52/19.179 composite 200-3000 1000-9000 4-10 calculated internally 212.4
ELMOD4 US52/19.179 composite n / a n / a n / a 0 max 300
EVERCALC4.0 US52/19.179 composite 200-2500 1000-10000 3-30 2-40 infinity
MODULUS5.0 US60/1.230 composite 200-3000 1000-7000 4-6 calculated internally 300
ELMOD4 US60/1.230 composite n / a n / a n / a 0 max 300
EVERCALC4.0 US60/1.230 composite 120-3000 300-8000 2-20 4-35 infinity
MODULUS5.0 US60/2.267 composite 200-3000 1000-9000 4-10 calculated internally 134.5
ELMOD4 US60/2.267 composite n / a n / a n / a 0 max 300
EVERCALC4.0 US60/2.267 composite 120-3000 300-8000 2-20 4-35 infinity
MODULUS5.0 US60/3.393 composite 200-3000 1000-9000 4-10 calculated internally 96.0
ELMOD4 US60/3.393 composite n / a n / a n / a 0 max 300
EVERCALC4.0 US60/3.393 composite 120-3000 300-8000 2-60 4-35 infinity
MODULUS5.0 WV2/4.926 composite 200-3000 1000-9000 4-10 calculated internally 202.3
ELMOD4 WV2/4.926 composite n / a n / a n / a 0 max 300
EVERCALC4.0 WV2/4.926 composite 120-3000 100-7000 2-60 4.35 infinity
MODULUS5.0 WV2/6.100 composite 200-3000 1000-9000 4-10 calculated internally 300
ELMOD4 WV2/6.100 composite n / a n / a n / a 0 max 300
EVERCALC4.0 WV2/6.100 composite 120-3000 100-7000 2-60 4-35 infinity
MODULUS5.0 WV2/7.333 composite 200-3000 1000-9000 4-10 calculated internally 121.3
ELMOD4 WV2/7.333 composite n / a n / a n / a 0 max 300
EVERCALC4.0 WV2/7.333 composite 120-3000 100-7000 2-60 4-35 infinity
MODULUS5.0 WV3/40.806 flexible 200-3000 5-160 4-18 calculated internally 183.7
ELMOD4 WV3/40.806 flexible n / a n / a n / a 0 max 300
EVERCALC4.0 WV3/40.806 flexible 120-3000 -5-160 2-60 2-60 infinity
39
BackcalculationProgram
Road/StationNumber
PavementType
Moduli Range , Ksi SubgradeDepth toBedrock (in.)
SurfaceLayer
Base Subgrade Second SubgradeModulus if it issubdivided intoTwo Layers
MODULUS5.0 WV3/41.013 flexible 200-3000 5-160 4-18 calculated internally 108.9
ELMOD4 WV3/41.013 flexible n / a n / a n / a 0 max 300
EVERCALC4.0 WV3/41.013 flexible 120-3000 5-160 2-60 2-60 infinity
MODULUS5.0 WV3/41.221 flexible 200-3000 5-160 4-18 calculated internally 254.4
ELMOD4 WV3/41.221 flexible n / a n / a n / a 0 max 300
EVERCALC4.0 WV3/41.221 flexible 120-3000 5-160 2-60 2-60 infinity
MODULUS5.0 WV71/0.009 flexible 200-3000 5-160 4-18 calculated internally 61.65
ELMOD4 WV71/0.009 flexible n / a n / a n / a 0 max 300
EVERCALC4.0 WV71/0.009 flexible 120-3000 5-160 2-60 2-60 infinity
MODULUS5.0 WV71/1.259 flexible 200-3000 5-160 4-18 calculated internally 66.71
ELMOD4 WV71/1.259 flexible n / a n / a n / a 0 max 300
EVERCALC4.0 WV71/1.259 flexible 120-3000 5-160 2-60 2-60 infinity
MODULUS5.0 WV71/2.740 flexible 200-3000 5-160 4-18 calculated internally 49.10
ELMOD4 WV71/2.740 flexible n / a n / a n / a 0 max 300
EVERCALC4.0 WV71/2.740 flexible 120-3000 5-160 2-60 2-60 infinity
MODULUS5.0 WV2/18.250 rigid 1000-10000 10-160 4-18 calculated internally 182.7
ELMOD4 WV2/18.250 rigid n / a n / a n / a 0 max 300
EVERCALC4.0 WV2/18.250 rigid 1000-1000 10-160 2-60 3-38 infinity
MODULUS5.0 WV2/19.028 rigid 1000-10000 10-160 5-7 calculated internally 279.2
ELMOD4 WV2/19.028 rigid n / a n / a n / a 0 max 300
EVERCALC4.0 WV2/19.028 rigid 1000-1000 10-160 4-10 3-38 infinity
MODULUS5.0 US19/20.856 rigid 1000-10000 10-160 5-7 calculated internally 300
ELMOD4 US19/20.856 rigid n / a n / a n / a 0 max 300
EVERCALC4.0 US19/20.856 rigid 1000-1000 5-160 4-10 3-38 infinity
MODULUS5.0 US19/21.563 rigid 1000-10000 10-160 5-7 calculated internally 300
ELMOD4 US19/21.563 rigid n / a n / a n / a 0 max 300
EVERCALC4.0 US19/21.563 rigid 1000-1000 5-160 3-10 3-38 infinity
MODULUS5.0 US19/21.839 rigid 1000-10000 10-160 5-8 calculated internally 202.6
ELMOD4 US19/21.839 rigid n / a n / a n / a 0 max 300
EVERCALC4.0 US19/21.839 rigid 1000-1000 5-160 3-10 3-38 infinity
40
TABLE 4.2a Backcalculated Layer Moduli (Ksi) for Flexible Pavement Sections.
Site/Station Program Surface Layer Base Layer Top Subgrade
Layer
Subgrade
US52_pre
Station
16.250
MODULUS5.0 594.0 42.6 7.0 17.1
ELMOD4 537.0 27.0 14.8 14.8
EVERCALC4.0 510.0 61.0 7.0 20.0
WV3_whit
Station
40.806
MODULUS5.0 321.0 14.8 7.3 18.9
ELMOD4 315.0 12.7 19.5 19.5
EVERCALC4.0 291.0 7.0 12.0 26.0
WV3_whit
Station
41.013
MODULUS5.0 366.0 43.6 11.0 11.8
ELMOD4 360.0 32.3 10.1 10.1
EVERCALC4.0 418.0 5.0 3.0 24.0
WV3_whit
Station
41.221
MODULUS5.0 454.0 66.7 15.8 9.3
ELMOD4 540.0 61.7 9.8 9.8
EVERCALC4.0 520.0 18.0 16.0 12.0
WV71_blu
Station 0.009
MODULUS5.0 643.0 17.1 4.9 30.4
ELMOD4 487.0 59.6 11.2 11.2
EVERCALC4.0 751.0 5.0 4.0 35.0
WV71_blu
Station 1.259
MODULUS5.0 508.0 6.3 12.5 6.7
ELMOD4 498.0 8.1 8.0 8.0
EVERCALC4.0 425.0 5.0 3.0 27.0
WV_whit
Station 2.740
MODULUS5.0 274.0 9.7 4.9 6.2
ELMOD4 247.0 9.9 8.0 8.0
EVERCALC4.0 264 5.0 4.0 50
41
TABLE 4.2b Backcalculated Layer Moduli (Ksi) for Composite Pavement Sections.
Site/Statiom Program Surface Layer Concrete
Slab
Base Layer Subgrade
US52_pre
Station
18.360
MODULUS5.0 561.0 6122.9 8.0 36.1
ELMOD4 621.0 1214.0 49.8 49.8
EVERCALC4.0 516.0 7026.0 25.0 45.0
US52_pre
Station
19.179
MODULUS5.0 422.0 1638.7 8.8 34.9
ELMOD4 654.0 606.0 35.3 35.3
EVERCALC4.0 445.0 1023.0 17.0 36.0
US60_smi
Stastion
1.230
MODULUS5.0 274.0 6196.0 5.2 16.6
ELMOD4 973.0 611.0 23.5 23.5
EVERCALC4.0 273.0 3920.0 7.0 24.0
US60_smi
Sration 2.267
MODULUS5.0 747.0 2267.2 4.9 17.7
ELMOD4 4255.0 84.1 19.3 19.3
EVERCALC4.0 3000.0 384.0 14.0 30.0
WV2_frie
Station 4.926
MODULUS5.0 1620.0 1823.7 5.3 16.2
ELMOD4 8884.0 30.2 20.0 20.0
EVERCALC4.0 3000.0 550.0 5.0 35.0
WV2_frie
Station 4.926
MODULUS5.0 203.0 1326.7 7.7 19.8
ELMOD4 264.0 434.0 26.7 26.7
EVERCALC4.0 192.0 1323.0 4.0 29.0
WV2_frie
Station 6.100
MODULUS5.0 200.0 1910.1 11.0 18.6
ELMOD4 240.0 722.0 22.8 22.8
EVERCALC4.0 137.0 2473.0 22.0 22.0
WV2_frie
Station 7.333
MODULUS5.0 222.0 600.0 4.0 20.9
ELMOD4 305.0 136.0 31.9 31.9
EVERCALC4.0 301.0 121.0 11.0 35.0
42
TABLE 4.2c Backcalculated Layer Moduli (Ksi) for Rigid Pavement Sections.
Site/Station Program Surface Layer Base Layer Top Subgrade
Layer
Subgrade
US2_moun
Station
18.250
MODULUS5.0 5280.0 21.9 6.2 22.4
ELMOD4 4840.4 5.2 37.4 37.43
EVERCALC4.0 4308.0 17.0 4.0 38.0
US2_moun
Station
19.028
MODULUS5.0 6567.0 34.6 5.5 14.8
ELMOD4 6157.0 1.5 32.6 32.6
EVERCALC4.0 5679.0 10.0 4.0 23.0
US19_hic
Station
20.856
MODULUS5.0 8152.0 25.1 5.6 14.2
ELMOD4 6706.0 24.5 15.1 15.1
EVERCALC4.0 5948.0 5.0 3.0 18.0
US_hic
Station
21.653
MODULUS5.0 5094.0 20.1 6.4 7.0
ELMOD4 4117.0 16.0 10.6 10.6
EVERCALC4.0 3869.0 5.0 3.0 12.0
US_hic
Station
21.839
MODULUS5.0 7160.0 39.5 5.3 14.7
ELMOD4 4565.0 39.3 26.0 26.0
EVERCALC4.0 4716.0 5.0 3.0 34.0
43
TABLE 4.3 Comparison of Pavement Moduli Backcalculated by Different Programs.
Backcalculationprogram
Road/StationNumber
Pavement Type SurfaceLayer
Base Top Subgrade
MODULUS5.0 US52/16.250 flexible acceptable acceptable acceptable
ELMOD4 US52/16.250 flexible acceptable acceptable acceptable
EVERCALC4.0 US52/16.250 flexible acceptable acceptable acceptable
MODULUS5.0 US52/18.360 composite acceptable acceptable high
ELMOD4 US52/18.360 composite acceptable acceptable high
EVERCALC4.0 US52/18.360 composite acceptable acceptable high
MODULUS5.0 US52/19.179 composite acceptable acceptable high
ELMOD4 US52/19.179 composite acceptable low high
EVERCALC4.0 US52/19.179 composite acceptable acceptable high
MODULUS5.0 US60/1.230 composite acceptable acceptable acceptable
ELMOD4 US60/1.230 composite acceptable low high
EVERCALC4.0 US60/1.230 composite acceptable high high
MODULUS5.0 US60/2.267 composite acceptable high acceptable
ELMOD4 US60/2.267 composite very high very low high
EVERCALC4.0 US60/2.267 composite high very low high
MODULUS5.0 US60/3.393 composite acceptable acceptable acceptable
ELMOD4 US60/3.393 composite acceptable very low high
EVERCALC4.0 US60/3.393 composite acceptable low high
MODULUS5.0 WV2/4.926 composite acceptable acceptable acceptable
ELMOD4 WV2/4.926 composite acceptable low high
EVERCALC4.0 WV2/4.926 composite acceptable acceptable high
MODULUS5.0 WV2/6.100 composite acceptable acceptable acceptable
ELMOD4 WV2/6.100 composite acceptable low high
EVERCALC4.0 WV2/6.100 composite low acceptable high
MODULUS5.0 WV2/7.333 composite acceptable acceptable high
ELMOD4 WV2/7.333 composite acceptable low high
EVERCALC4.0 WV2/7.333 composite acceptable low high
MODULUS5.0 WV3/40.806 flexible acceptable acceptable high
ELMOD4 WV3/40.806 flexible acceptable acceptable high
EVERCALC4.0 WV3/40.806 flexible acceptable acceptable high
44
Backcalculation program Road/StationNumber
Pavement Type SurfaceLayer
Base Top Subgrade
MODULUS5.0 WV3/41.013 flexible acceptable acceptable acceptable
ELMOD4 WV3/41.013 flexible acceptable acceptable acceptable
EVERCALC4.0 WV3/41.013 flexible acceptable acceptable high
MODULUS5.0 WV3/41.221 flexible acceptable acceptable high
ELMOD4 WV3/41.221 flexible acceptable acceptable acceptable
EVERCALC4.0 WV3/41.221 flexible acceptable acceptable acceptable
MODULUS5.0 WV71/0.009 flexible acceptable acceptable high
ELMOD4 WV71/0.009 flexible acceptable acceptable acceptable
EVERCALC4.0 WV71/0.009 flexible acceptable low high
MODULUS5.0 WV71/1.259 flexible acceptable acceptable acceptable
ELMOD4 WV71/1.259 flexible acceptable acceptable acceptable
EVERCALC4.0 WV71/1.259 flexible acceptable low high
MODULUS5.0 WV71/2.740 flexible acceptable acceptable acceptable
ELMOD4 WV71/2.740 flexible acceptable acceptable acceptable
EVERCALC4.0 WV71/2.740 flexible acceptable low high
MODULUS5.0 WV2/18.250 rigid acceptable acceptable high
ELMOD4 WV2/18.250 rigid acceptable acceptable high
EVERCALC4.0 WV2/18.250 rigid acceptable acceptable high
MODULUS5.0 WV2/19.028 rigid acceptable acceptable acceptable
ELMOD4 WV2/19.028 rigid acceptable acceptable high
EVERCALC4.0 WV2/19.028 rigid acceptable low high
MODULUS5.0 WV19/20.856 rigid acceptable acceptable acceptable
ELMOD4 WV19/20.856 rigid acceptable acceptable acceptable
EVERCALC4.0 WV19/20.856 rigid acceptable low acceptable
MODULUS5.0 WV19/21.563 rigid acceptable acceptable acceptable
ELMOD4 US19/21.563 rigid acceptable acceptable acceptable
EVERCALC4.0 US19/21.563 rigid acceptable low acceptable
MODULUS5.0 US19/21.839 rigid acceptable acceptable high
ELMOD4 US19/21.839 rigid acceptable acceptable high
EVERCALC4.0 US19/21.839 rigid acceptable acceptable high
45
TABLE 4.4 Number of Backcalculated Out of Range Moduli.
Backcalculation
Program
Flexible Pavement
Sections
Composite Pavement
Sections
Rigid Pavement Sections
Surface
layer
Base Subgrade Surface
layer
Base Subgrade Surface
layer
Base Subgrade
MODULUS5.0 0 0 3/7 0 1/8 3/8 0 0 2/5
ELMOD4 0 0 1/7 2/9 7/8 8/8 0 0 3/5
EVERCALC4.0 0 3/7 5/7 3/9 4/8 8/8 0 3/5 3/5
46
460
480
500
520
540
560
580
600
620
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
10
20
30
40
50
60
70
Base Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
2
4
6
8
10
12
14
16
Top SubgradeM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
FIGURE 4.1 Backcalculated layer moduli (Ksi) for flexible pavement section US52_pre station 16.250.
47
0
100
200
300
400
500
600
700
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
1000
2000
3000
4000
5000
6000
7000
8000
PCC Slab
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
10
20
30
40
50
60
Base LayerM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4EVERCALC4.0
0
10
20
30
40
50
60
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
FIGURE 4.2 Backcalculated layer moduli (Ksi) for composite pavement section US52_pre station 18.360.
48
0
100
200
300
400
500
600
700
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
200
400
600
800
1000
1200
1400
1600
1800
PCC Slab
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
30
35
40
Base LayerM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4EVERCALC4.0
34.2
34.4
34.6
34.8
35
35.2
35.4
35.6
35.8
36
36.2
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
FIGURE 4.3 Backcalculated layer moduli (Ksi) for composite pavement section US52_pre station 19.179.
49
0
200
400
600
800
1000
1200
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
1000
2000
3000
4000
5000
6000
7000
PCC Slab
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
Base LayerM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
30
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
FIGURE 4.4 Backcalculated layer moduli (Ksi) for composite pavement section US60_smi station 1.230.
50
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
500
1000
1500
2000
2500
PCC Slab
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
Base LayerM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
30
35
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
FIGURE 4.5 Backcalculated layer moduli (Ksi) for composite pavement section US60_smi station 2.267.
51
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
200
400
600
800
1000
1200
1400
1600
1800
2000
PCC Slab
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
Base LayerM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
30
35
40
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
FIGURE 4.6 Backcalculated layer moduli (Ksi) for composite pavement section US60_smi station 3.393.
52
0
200
400
600
800
1000
1200
1400
PCC Slab
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
30
Base LayerM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
30
35
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
50
100
150
200
250
300
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
FIGURE 4.7 Backcalculated layer moduli (Ksi) for composite pavement section WV2_frie station 4.926.
53
0
50
100
150
200
250
300
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
500
1000
1500
2000
2500
3000
PCC Slab
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
Base LayerM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
FIGURE 4.8 Backcalculated layer moduli (Ksi) for composite pavement section WV2_frie station 6.100.
54
0
50
100
150
200
250
300
350
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
100
200
300
400
500
600
700
PCC Slab
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
30
35
40
Base LayerM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
30
35
40
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
FIGURE 4.9 Backcalculated layer moduli (Ksi) for composite pavement section WV2_frie station 7.333.
55
275
280
285
290
295
300
305
310
315
320
325
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
2
4
6
8
10
12
14
16
Base Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
Top SubgradeM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
30
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
FIGURE 4.10 Backcalculated layer moduli (Ksi) for flexible pavement section WV3_whit station 40.806.
56
330
340
350
360
370
380
390
400
410
420
430
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
30
35
40
45
50
Base Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
2
4
6
8
10
12
Top Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
30
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
FIGURE 4.11 Backcalculated layer moduli (Ksi) for flexible pavement section WV3_whit station 41.013.
57
400
420
440
460
480
500
520
540
560
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
10
20
30
40
50
60
70
80
Base Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
2
4
6
8
10
12
14
16
18
Top SubgradeM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4EVERCALC4.0
0
2
4
6
8
10
12
14
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
FIGURE 4.12 Backcalculated layer moduli (Ksi) for flexible pavement section WV3_whit station 41.221.
58
0
100
200
300
400
500
600
700
800
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
10
20
30
40
50
60
70
Base Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
2
4
6
8
10
12
Top SubgradeM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
30
35
40
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
FIGURE 4.13 Backcalculated layer moduli (Ksi) for flexible pavement section WV71_blu station 0.009.
59
380
400
420
440
460
480
500
520
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
1
2
3
4
5
6
7
8
9
Base Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
2
4
6
8
10
12
14
Top SubgradeM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
30
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
FIGURE 4.14 Backcalculated layer moduli (Ksi) for flexible pavement section WV71_blu station 1.259.
60
0
1000
2000
3000
4000
5000
6000
PCC Slab
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
Base Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4EVERCALC4.0
0
5
10
15
20
25
30
35
40
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
5
10
15
20
25
30
35
40
Top SubgradeM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4
EVERCALC4.0
FIGURE 4.15 Backcalculated layer moduli (Ksi) for flexible pavement section WV71_blu station 2.740.
61
0
1000
2000
3000
4000
5000
6000
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
5
10
15
20
25
Base Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
5
10
15
20
25
30
35
40
Top SubgradeM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
5
10
15
20
25
30
35
40
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
FIGURE 4.16 Backcalculated layer moduli (Ksi) for rigid pavement section US2_moun station 18.250.
62
5200
5400
5600
5800
6000
6200
6400
6600
6800
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
5
10
15
20
25
30
35
40
Base Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
5
10
15
20
25
30
35
Top SubgradeM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
5
10
15
20
25
30
35
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
FIGURE 4.17 Backcalculated layer moduli (Ksi) for rigid pavement section US2_moun station 19.028.
63
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
2
4
6
8
10
12
14
16
Top SubgradeM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
5
10
15
20
25
30
Base Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
2
4
6
8
10
12
14
16
18
20
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
FIGURE 4.18 Backcalcualted layer moduli (Ksi) for rigid pavement section US19_hic station 20.856.
64
0
1000
2000
3000
4000
5000
6000
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
5
10
15
20
25
Base Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
2
4
6
8
10
12
14
16
Top SubgradeM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
2
4
6
8
10
12
14
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
FIGURE 4.19 Backcalculated layer moduli (Ksi) for rigid pavement section US19_hic station 21.563.
65
0
1000
2000
3000
4000
5000
6000
7000
8000
Surface Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
5
10
15
20
25
30
35
40
45
Base Layer
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
5
10
15
20
25
30
Top SubgradeM
odul
us (
Ksi
)
MODULUS5.0 ELMOD4
EVERCALC4.0
0
5
10
15
20
25
30
35
40
Subgrade
Mod
ulus
(K
si)
MODULUS5.0 ELMOD4
EVERCALC4.0
FIGURE 4.20 Backcalculated layer moduli (Ksi) for rigid pavement section US19_hic station 21.839.
66
CHAPTER 5
FIELD TESTING
5.1 PAVEMENT SITES
Field tests were performed at three different sites located in Morgantown, West Virginia. The
selected sites were chosen to be representative of the three types of pavement structures: rigid,
flexible, and composite (rigid pavement overlaid by asphalt layer). In each tested site, the pavement
surface was checked so that it was free from visible signs of distress such as transverse or longitudinal
cracks.
1. Flexible Pavement Site
This site was the traffic lane of a divided four-lane road on Route 857, opposite Mountaineer
Mall. The lane width is 12 ft. and the asphalt concrete layer is 9 in. thick constructed over a 7 in. base
of crushed stone. The subgrade soil is a clay material. Figure 5.1 illustrates the different layers in this
section.
2. Rigid Pavement Site
This site was located on Route 857. The traffic lane of a divided four-lane jointed Portland
cement concrete pavement with untied shoulder. The spacing between the transverse joints in this
site varied between 20 and 45 ft. The lane is 12 ft. wide and the slab is 9 in. thick. The slabs are
supported by an 8 in. thick granular base of crushed stone. The subgrade soil in this site was silty clay.
Figure 5.2 provides a section of this site showing the different layers.
3. Composite Pavement Site
This site was located on Interstate I-68, station 2.644. The test was performed on the traffic
lane of the eastbound side. The pavement section consists of a 9.5 in. concrete slab overlaid by a 5
in. asphalt concrete layer. The concrete slab is supported by a 3 in. base of crushed stone. The
67
subgrade soil is clay material. Figure 5.3 illustrates the different layers of this pavement section.
Each site was fitted with a set of sensors to measure the temperature gradient and
displacements of the layers due to the application of FWD load. Two boreholes were drilled in each
site for the placement of these gauges. The two boreholes were placed at a distance of 6 ft from each
other as shown in Figure 5.4. Each borehole was drilled to a depth of 32 in. and core samples were
taken for laboratory testing by WVDOH. All boreholes were placed at a distance of 1 ft from the
shoulder edge of the traffic lane. During borehole sampling the correct thickness of each pavement
structure was identified and recorded. After placing the sensors in each borehole, it was filled with
fine sand and covered on top with a concrete mix. All lead cables of geophones and thermocouples
from each borehole were routed into a 0.75 in. deep groove sawn in the surface layer leading to the
end of the shoulder and then covered with concrete grouting. Each trench terminates with a small
hole to keep the ends of the cables accessible for measurements.
5.2 MEASUREMENTS
Temperature gradient through the depth of pavement structure was measured using
thermocouples. The thermocouples were placed such that one was at the interface between the base
and subgrade, and another at the interface between the surface layer and the base. For the composite
pavement site, an additional thermocouple was placed at the interface between the asphaltic layer and
the concrete. The connecting cables of each thermocouple were covered with Teflon. Additionally,
the cables were environmentally shielded using a 0.25 in. diameter polyethylene tube that extended
the full length of the cable. The connections of the tube with the thermocouple-sensing element were
sealed using a heat shrink water-proof tube. Each thermocouple was placed in position inside a 3 in.
diameter borehole that was drilled adjacent to the shoulder edge of the pavement site. Each
thermocouple had a sensitivity of 0.1(F. The temperature readings were acquired using a hand held
digital readout unit, type HH-21 produced by the OMEGA company. At the time of the Falling
Weight Deflectometer test, acquired temperature measurements were as follows:
68
Rigid Pavement Site
On top of the concrete slab T = 47.0 Foo
At the concrete-base interface T = 49.5 F1o
At the base-subgrade interface T = 51.5 F2o
Flexible Pavement Site
On top of the asphaltic layer T = 38.5 Foo
At the asphalt-base interface T = 41.0 F1o
At the base-subgrade interface T = 42.3 F2o
Composite Pavement Site
On the top the of asphaltic layer T = 38.3 Foo
At the asphalt-concrete interface T = 40.3 F1o
At the concrete-base interface T = 41.4 F2o
At the base-subgrade interface T = 41.6 F3o
None of the temperature measurements showed a significant temperature gradient, due to the
fact that the measurements were carried out during the months of March and April from 10:00 am
to 2:00 pm. The absence of a significant thermal gradient was considered advantageous from the
point of view of finite element modeling.
It was the intention in this study to measure the displacement of every pavement layer in order
to observe the possibility of separation between layers and to provide additional confirmation of the
accuracy of the finite element models. For this reason, a set of twelve geophones were acquired with
the following specifications:
Geophone type: PE-8-SM 6UB
Manufacturer: SENSOR, Netherlands.
Measuring direction: Vertical
69
Resistance: 375 Ohm
Resonant frequency: 4.5 Hz
Each geophone was placed in an environmentally isolated casing to protect the sensing
element from being damaged by underground water or humidity. During the installation of geophones
in each borehole, care was taken to ensure that they were vertically aligned inside each hole. The
displacement data measured from the geophones contained significantly high levels of noise, which
hindered any reliable readings. Considering the effort of arranging for traffic control and because of
the time span of the project, no attempts were made to replace the geophones with more sophisticated
sensors. Thus, additional geophone measurements were omitted on the basis that verification of the
FE models could be achieved through an additional comparison of the deflection-time histories with
those measured using FWD geophones.
5.3 DEFLECTION TESTING
The Falling Weight Deflectometer (FWD) test was performed using WVDOH equipment.
The equipment is manufactured by DYNATEST and operated by WVDOH Materials Division
personnel. The FWD was calibrated in accordance with SHRP procedures in May 1997. The
calibration results demonstrated that both the FWD load cell and sensors were in excellent condition,
and that their readings fell within the tolerance range set by the manufacturer. During each FWD test,
surface deflections were measured using nine geophone sensors located at distances of 0, 8, 12, 18,
24, 36, 48, 60, and 72 in. away from the center of the 11.8 in. diameter steel loading plate. The
sensors’ positions remained unchanged for all three pavement sites.
For every pavement site, the FWD deflection data were collected at three drop heights. At
each height two drops were made in accordance with ASTM-Standard D 4694 - 87, article 9.4.
Since the temperature measurements did not show appreciable thermal gradient, no temperature
corrections were considered necessary during the backcalculation of layers moduli. Table 5.1
70
contains a list of the load and deflection data measured using FWD for the three tested sites.
Additionally, the data were acquired in graphical format and the loading curves were digitized for use
with the finite element models, as will be discussed in the next chapter.
5.4 EVALUATION OF BACKCALCULATED MODULI
FWD deflection data obtained from testing the three sites were analyzed using three different
backcalculation programs: MODULUS5.0, EVERCALC4.0, and MODCOMP3. The information
required for the evaluation of layers moduli for each site includes the deflection data and the
pavement profile. The pavement profile consists of layer thicknesses and material types. The
material types were determined from visual examination of the layers material extracted during
borehole drilling. All backcalculation programs require the user to supply seed values for the moduli
of each layer. Those values were selected by referring to the ranges listed in Table 3.1. In some
circumstances, the backcalculation program failed to produce a deflection basin that fits the measured
one within the specified tolerance. In this case, the moduli ranges were expanded to reach a
convergence of the solution. As discussed in Chapter 4, the subgrade layers were divided into two
layers to take into account the change of the value of subgrade modulus with depth. Consequently,
two different subgrade moduli were evaluated for each section.
The results of backcalculated moduli obtained for each pavement section are given in Table
5.2. For every pavement site, an average modulus was estimated for each layer. This average was
obtained by taking the mean of the three moduli produced for the same layer by the three
backcalculation programs. Next, the average was used to estimate the Percent Deviation From
Average (PDFA) in modulus produced by each program (shown in Table 5.2 as percent error).
5.5 CONCLUSIONS
Based on the results listed in Table 5.2, the following conclusions were reached:
71
1. MODULUS5.0 program performed well with all types of pavement structures and resulted
in moduli values that seemed reasonable and close to the average.
2. EVERCALC4.0 program overestimated the values of subgrade moduli for the three types of
pavements compared to the other two programs. For the composite pavement structure, the
program overestimated the modulus of the asphalt layer.
3. MODCOMP3 program resulted in moduli values which seemed to be reasonable and within
the material range. However, the resulting modulus value of the concrete layer in the rigid
pavement section seemed to be high compared with those resulting from the other two
programs. This program requires more engineering judgement and experience from the user
in introducing the values of seed moduli for different layers to obtain reasonable results. The
high sensitivity of the program to the deflection reading assignments may cause the
termination of the program if the values of seed moduli are not compatible with the deflection
readings.
4. Comparison of the backcalculated moduli for the pavement layers reveals that for each
pavement type the results obtained using MODULUS5.0 were always close to the average
obtained from all three programs. The values of the layers moduli obtained for all pavement
structures using MODULUS5.0 seemed reasonable and the mean percent difference did not
exceed eleven percent.
5. None of the three programs tested in this study produced extremely unreasonable values.
This is reflected in the fact that the error relative to the average calculated modulus never
exceeded 100 percent for any layer.
6. It should be remembered that all three programs evaluated in this study are designed primarily
to handle flexible pavements. The capability of predicting layers moduli for rigid and
composite pavements is an added advantage.
72
TABLE 5.1 Deflection Data Collected from Field Tests.
Applied load Radial offset from center of loading plate (in.)
lbf psi 0.00 8.00 12.00 18.00 24.00 36.00 48.00 60.00 72.00
RIGID PAVEMENT SITE:
10124 92.6 3.46 3.23 3.04 2.74 2.43 1.90 1.40 0.98 0.69
10135 92.7 3.46 3.19 3.02 2.74 2.43 1.89 1.40 0.96 0.69
13110 119.9 4.63 4.30 4.05 3.66 3.25 2.52 1.87 1.35 0.98
13186 120.6 4.66 4.26 4.03 3.66 3.26 2.52 1.87 1.35 0.98
17877 163.5 6.37 5.89 5.56 5.04 4.47 3.47 2.59 1.89 1.38
17899 163.7 3.36 5.85 5.54 5.03 4.46 3.47 2.59 1.89 1.38
FLEXIBLE PAVEMENT SITE:
10037 91.8 10.11 8.82 7.97 6.78 5.70 3.88 2.45 1.49 1.02
10048 91.9 10.13 8.84 7.99 6.79 5.72 3.91 2.46 1.46 1.02
12793 117.0 13.33 11.73 10.63 9.10 7.67 5.21 3.40 2.15 1.29
12815 117.2 13.40 11.79 10.69 9.17 7.72 5.25 3.42 2.15 1.30
17853 164.2 18.23 16.07 14.60 12.58 10.62 7.41 4.81 2.97 1.96
17998 164.6 18.08 15.96 14.50 12.47 10.53 7.35 4.77 2.95 1.95
COMPOSITE PAVEMENT SITE:
9873 90.3 2.96 2.45 2.31 2.17 2.03 1.66 1.32 1.03 0.77
9873 90.3 2.97 2.46 2.31 2.19 2.03 1.68 1.32 1.03 0.79
12596 115.2 3.99 3.32 3.14 2.96 2.75 2.28 1.84 1.41 1.10
12617 115.4 4.00 3.35 3.15 2.97 2.76 2.29 1.83 1.41 1.09
17330 158.0 5.51 4.63 4.37 4.14 3.83 3.19 2.54 1.99 1.54
17384 159.0 5.50 4.62 4.36 4.13 3.82 3.19 2.55 1.98 1.54
73
Table 5.2 BACKCALCULATED LAYERS MODULI (Ksi).
PROGRAM Surface PDFA* Base PDFA Subgrade PDFA Subgrade PDFATop** Bottom
FLEXIBLE MODULUS 837 20.5% 34.9 -32.1% 10.7 18.9% 9.3 -50.0%
EVERCALC 338 -51.3% 100 94.4% 4.7 -48.1% 34.5 85.5%
MODCOMP 909 30.9% 19.4 -62.3% 11.6 28.8% 12 -35.5%
LAYERAVERAGE
694.6 51.4 9.00 18.6
RIGID
MODULUS 3278 -0.7% 162 11.2% 13.4 10.9% 14.5 -44.2%
EVERCALC 2997 -20.2% 52 -64.3% 20 65.6% 50 92.3%
MODCOMP 4540 20.9% 223 53.1% 2.8 -76.5% 13.5 -48.1%
LAYERAVERAGE
3755 145.7 12.1 26.0
COMPOSITE
MODULUS 805 -33.6% 5880 9.7% 156 39.3% 13.7 -33.0%
EVERCALC 2000 65.0% 5000 -6.7% 100 -10.7% 30 46.8%
MODCOMP 832 -31.4% 5200 -3.0% 80 -28.6% 17.6 -13.9%
LAYERAVERAGE
1212.3 5360 112 20.4
* PDFA= Percent Deviation from Average.** The subgrade was divided into two layers for the purpose of backcalculation.
74
75
FIGURE 5.4 Instrumentation layout.
76
CHAPTER 6
EVALUATION OF BACKCALCULATION ALGORITHMS
THROUGH FINITE ELEMENT MODELING OF FWD TEST
6.1 INTRODUCTION
In this chapter, a new approach for the evaluation of the performance of backcalculation
algorithms is developed using Finite Element (FE) analysis. Currently, the only means of assessing
the performance of a backcalculation algorithm is to compare the layers’ moduli results with
laboratory measurements of core samples. The wide discrepancies between the backcalculated and
measured moduli are often attributed to the difficulty in obtaining undisturbed soil samples. The end
result is that backcalculated moduli for the same pavement structure may differ widely, depending on
the backcalculation algorithm used and the assumptions made by the program operator. In this
Chapter, Three Dimensional Finite Element (3D-FE) approach is used to simulate the response of the
three sections, tested in Chapter 5, to FWD load. For each pavement structure, the deflection basin
obtained from the finite element model is compared with the one experimentally measured. The
elastic moduli used in the model are changed until a satisfactory agreement between the Finite
Element-Calculated and the experimental basins is reached. Next, the layers moduli are evaluated
from the FE-generated deflection basin using the three backcalculation programs MODULUS5.0,
EVERCALC4.0 and MODCOMP3, and the results are compared with the layers moduli used in the
finite element model. Correction factors for backcalculated moduli were developed and found to be
in close agreement with the values recommended by SHRP Pavement Design Guide.
6.2 REVIEW OF FINITE ELEMENT MODELING OF PAVEMENTS
A number of 2D finite element programs such as ILLI-PAVE and MICH-PAVE were
developed to analyze flexible pavements. In these programs, the 3D pavement structure is idealized
77
using 2D axially symmetric elements. To account for material nonlinearity, the unbounded nature of
granular soils, and “locked-in” lateral stresses produced by compaction, stress-dependant resilient
moduli were incorporated for granular and cohesive soils (4,19). In MICH-PAVE, a flexible boundary
was utilized at the bottom of the FE model to reduce computer memory and processing time (19).
Limitations of the axi-symmetric assumptions used in these programs include: inability to simulate
asymmetrical loading condition, assumption of full contact with the base layer, inability to simulate
cracks and rutting conditions, and the use of static loading. Other 2D finite element programs for rigid
pavements include ILLI-SLAB, JSLAB, KENSLABS, WESLIQUID, FEACONS III, KENSLABS,
and WESLAYER (20-25). In these programs the concrete slab was treated as a 2D medium-thick
plate. To accommodate the presence of the base layer, the slab and base are transformed into one
equivalent layer. Although the programs are specifically designed for rigid pavement analysis, the
actual behavior of concrete pavements is more complex than the 2D model idealization . The
capability of handling a moving load was introduced to ILLI-SLAB by Chatti et al. (26, 27); recently,
Roesler et al. (28) modified the program to allow for partial-depth crack analysis (ILSL97). The
major limitation of the 2D FE modeling approach is its inability to handle the geometrical features
near dowel bars without a significant degree of approximation. The need for developing a deep
understanding of pavement behavior motivated researchers to use the 3D FE approach.
None of the available 3D finite element codes is specifically designed for pavement analysis.
Ioannides et al. (29) studied stress-dependant foundation using the GEOSYS program which is
primarily designed for geotechnical problems. Starting the late 1980's, general purpose finite element
codes such as ABAQUS, DYNA3D, and NIKE3D were introduced in pavement engineering research
(30-38). Zagloul and White studied the dynamic response of flexible pavements to FWD loading and
moving loads using ABAQUS. The modeling results were found to be in close agreement with the
field measurements (39,41). Seaman et al. (34) examined the response of airport runways using
NIKE3D. This work was later extended by Kennedy et al. (35-38) who developed a user interface
to DYNA3D and NIKE3D specially designed for pavement structural analysis.
The earlier finite element codes developed for the purpose of modeling FWD test were based
78
on static interpretation of FWD load (41-43). Many studies were conducted to compare deflection
basins resulting from dynamic analysis and those from static analysis. Mamlouk and Davies
developed a multi-degree of freedom model based on the principle of elasto-dynamics; it accounted
for the three-dimensional response properties and the inertia effects. Transient loading was
represented by a series of steady-state harmonic loadings with different frequencies and magnitudes
(44, 45). Sebaaly modified the program to include the calculation of stresses and strains in pavements
caused by harmonic and impulsive loading (46). The results showed that the surface deflections
obtained using elasto-dynamic analysis of FWD tests were within 3 to 15 percent from field
measurements. Static representation of FWD load was found to produce surface deflections that
are up to 40 percent larger than field measurements (46, 47). Mallela et al. (48) developed a three-
dimensional response model for a rigid pavement structure subjected to FWD load. Linear elastic
materials were used to characterize all pavement layers. This assumption was based on the argument
that the stresses induced in each layer under standard 18 Kip equivalent single axle load are not likely
to produce stresses which exceed the elastic limits of each layer. The deflection basin resulting from
dynamic FEM showed a good agreement with the measured one while the deflection basin resulting
from the static FEM was 80 percent larger than that measured experimentally. Nazarian et al. (49)
conducted an investigation to assess the significance of layer stiffnesses, thicknesses, and the depth
to bedrock on the measured and backcalculated deflections. They found that the dynamic nature of
the FWD load significantly affects the deflections measured away from the load. The depth to
bedrock and load duration interacted to produce significantly different static and dynamic deflections.
Uddin et al. (50, 51) reported an increase of 22 percent in maximum deflections due to the presence
of multiple cracks. The role of pavement layers interfaces in transmitting FWD load was examined
by Shoukry et al. (52, 53) who reported stiffer FWD response due to the lack of adequate interface
representation.
6.3 GUIDELINES FOR 3D FEM OF PAVEMENT STRUCTURES
From the above review, it can be seen that 3D FE modeling of pavements has reached a
degree of maturity which permits its use in pavement structural evaluation problems. In building a
Fringe plots are colored visualization of the deformations and stresses in the finite element model. Each color1
represents a certain region of stress or the deformation. For example, see Figures 6.6 and 6.9.
79
finite element structural model, there are guidelines which help produce theoretical results close to
the experimentally measured ones. These guidelines can be summarized as follows:
1. Finite element model loading should have the same dynamic characteristics and time duration
as that applied in practice. This means that traffic and/or impact loads should be dynamically
applied in the model with the same duration or speed encountered in practice.
2. Structural interfaces between different parts should be represented in the model. Allowing
separation of the interfaces under inertia and/or thermal effects is a primary factor which
influences the deflections and stresses obtained from the model. Approximate values of
coefficients of friction at the interface help produce more realistic results.
3. For short time duration studies and transient analysis, it seems practical to assume that all
pavement layers behave elastically. The need for using nonlinear material models should be
assessed carefully by the engineer. In most cases, nonlinear material models require the use
of constants that may not be available and must be assumed. The benefits gained from using
nonlinear material models may be lost due to incorrect assumptions of material constants.
In most cases which do not involve repeated application of loads in the model, the use of
nonlinear material models for base and/or subgrade may not be necessary. On the other
hand, studies of rutting development in flexible pavements would certainly require the use of
inelastic material models.
4. The continuity of the stresses and deformation in the model should be checked using fringe
plots . The changes in fringe intensity from one element to another should be smooth and1
continuous. If this is not the case, the finite element mesh should be refined until smooth
patterns of fringes are obtained. This provides a confirmation of the adequacy of the FE mesh
80
but does not guarantee that the values are correct. The values of the stresses and deflection
throughout the model are primarily dependent on the material constants used and accuracy
in representing different geometrical features.
5. In Explicit Finite Element analysis, the model deformation should be displayed using a large
scale factor to ensure that zero energy modes did not develop anywhere in the model and that
none of the interfaces penetrate each other.
6. Finite element model results should be verified experimentally. One simple experimental
proof of the correct operation of pavement structural models can be obtained from comparing
deflection basins produced by FWD loading with those obtained from the model.
7. Finite element solutions are numerical solutions of sets of partial differential equations which
combine materials constitutive laws with the geometry of the structure. The equations are
based on the same fundamental stress-strain relations used in developing any closed form
solution. However, while closed form solutions are limited to geometrically simple structures,
finite element analysis can handle any geometry. Thus FE solutions are dependent to a great
extent on the accuracy of modeling the structural geometry. Thus, if the true structure
contains a crack, finite element modeling cannot produce deflection results that mimic the
experimentally measured ones unless the crack is accounted for in the model. Engineering
judgement should be exercised in deciding the level of structural details that should be
included in the model in order to produce reliable results.
8. Use should be made of computer visualization and animation capabilities to display model
results. The selection of a powerful post processor is a key factor in understanding the model
results and drawing conclusions.
81
6.4 FINITE ELEMENT MODELS OF EXPERIMENTAL TEST SITES
6.4.1 Flexible Pavement Model
Flexible pavements are continuous in the direction of traffic and jointless in the transverse
direction. Due to the softness of the asphaltic material, it is expected that the response of pavement
to the FWD load will be localized. For this reason, the pavement structure was modeled as a
multilayered system consisting of asphaltic concrete layer, base, and subgrade as shown in Figure 6.1.
The model width was chosen to be the full lane width of 12.0 ft. The flexible pavement section has
a shoulder made from the same material as the surface layer. This allows for the assumption of a
continuity of the propagation of in-plane stress waves generated by impact load. To simulate this
continuity, non-reflective boundaries were modeled along the pavement sides. The model length in
the traffic direction is 20.0 ft. The center of the loading plate was located at a distance 5.0 ft from
the lane edge adjacent to the shoulder. Due to the geometrical symmetry around a vertical plane
passing through the center of the loading plate perpendicular to traffic direction, only one half of the
pavement was meshed as shown in Figure 6.1. A tied interface between base and subgrade was
assumed while a sliding interface with a coefficient of friction of 0.9 was assumed between the
asphaltic layer and the base.
6.4.2 Rigid Pavement Model
The pavement structure was modeled as a multilayered system consisting of a Portland
Cement concrete slab, base, and subgrade as shown in Figure 6.2. The model width was chosen to
be the full lane width of 12.0 ft. The center of the loading plate was located at the center of the
concrete slab. Due to the geometrical symmetry around the transverse plane passing through the
center of the loading plate, only one half of the pavement was meshed as shown in Figure 6.2. The
influence of dowel bars on the deflection basin was assumed to be negligible due to two reasons: (1)
large distance of the transverse joint from the center of FWD load application, and (2) the relatively
82
small magnitude of FWD load. Therefore, dowel bars at the transverse joint were not included in the
model. Figure 6.2 also illustrates the boundary conditions used in the model. A sliding interface with
a coefficient of friction of 0.9 was assumed between the concrete layer and subgrade while a fully tied
interface was assumed between the subgrade and base.
6.4.3 Composite Pavement Model
The pavement structure was modeled as a multilayered linear elastic system consisting of a
Portland Cement concrete slab overlaid by an asphaltic concrete layer, a base, and a subgrade as
shown in Figure 6.3 . The model width is 12.0 ft and its length in the traffic direction was chosen to
be a full slab length of 27.0 ft. The center of the loading plate was located at the center of the model.
As a result of loading and geometrical symmetry around the transverse plane passing through the
center of the loading plate, only one half of the pavement was meshed as shown in Figure 6.3. A
tied interface was assumed between the asphalt and concrete layers. A sliding interface with a
coefficient of friction of 0.9 was assumed between the concrete and subgrade while the base/subgrade
interface was assumed to be fully tied.
In all models, bedrock was assumed to lie at a depth which will not introduce reflections
within the loading time duration under investigation (30 ms). This was achieved by applying
nonreflective boundaries which simulate the semi-infinite extent of the subgrade at the bottom of each
model. All models were meshed using 8-node brick element with 24 degrees of freedom per element.
The mesh sizes varied through each model to assure the accuracy of the results within the regions of
interest. Thus, a refined mesh was necessary in regions of high stress intensity such as concrete slabs.
A coarser mesh was used for the base and subgrade. A one in. thick and 12 in. diameter steel loading
plate (modulus of elasticity = 30,000 Ksi, unit weight = 0.2831 lb/in. ) was added to each pavement3
model for more accurate simulation of the FWD setup.
The impact loads used in this investigation were obtained from the measured FWD loads
83
applied during tests. The impact loading-time relations recorded by the FWD load cell were digitized
over one millisecond time intervals and the pressure-time history was calculated by dividing the load
by the area of the loading plate. Figure 6.4 illustrates the digitized pressure-time curves used for
modeling the three types of pavements.
6.5 STRUCTURAL MATERIAL MODELING
The surface deflections measured at various FWD sensor locations can be useful in
determining if the pavement structure displays a significant degree of nonlinearity due to the
application of the FWD load. FWD tests were carried out at three different loading levels, as listed
in Table 5.1. The deflections versus FWD load recorded at each sensor location are shown in Figure
6.5. The plots reveal that the deflections measured at all sensor locations are directly proportional
to the applied load. In the case of the flexible pavement, a negligible nonlinearity can be observed
for sensors located at 0 in. and 8 in. from the center of load application. For all other sensor
locations, the experimentally measured deflections fell close to a straight line obtained through least
squares fitting. This linearity indicates that the structural materials of all three pavements behaved
elastically under the loading levels applied in each case. Since in the present analysis FWD load will
be limited to 10,000 lb, it is safe to assume that all materials used in the three models can be
represented using linear elastic models. That is, each layer material is characterized by its modulus
of elasticity, density, and Poisson’s Ratio. This choice of material model has been further confirmed
from studying the amount of stresses induced in different layers due to the application of the FWD
load. Figure 6.6 illustrates by fringes the distribution of vertical stresses for different pavements.
Furthermore, the vertical stress along the vertical line passing through the center of the loading plate
was plotted versus depth in each pavement structure as shown in Figure 6.7. It can be noticed that
the stresses induced in base and subgrade layers are very small which validate the assumption of linear
elastic material models.
84
6.6 LAYERS MODULI EVALUATION FROM FE MODEL RESULTS
Since the purpose of this study is to evaluate the structural capacity of the three pavement
structures, the elastic moduli of the pavement materials are all unknown. An iterative procedure
similar to that commonly used in backcalculation algorithms was employed to determine those
moduli. Iterative procedure steps are as follows:
1. FWD test is conducted and the experimental deflection basin is obtained.
2. The experimental basin is used with any backcalculation program to evaluate a set of layers
moduli.
3. The layers moduli obtained from backcalculation are used in the finite element model and a
theoretical deflection basin is obtained.
4. The FE generated deflection basin is compared with the experimental basin. If the two basins
are in good match, the moduli used in the finite element program are taken to be the correct
moduli.
5. If the basins are different from each other, the layers moduli are adjusted and inserted in the
finite element program to produce a new deflection basin.
The above procedures are repeated until the condition in step number 4 is satisfied. This
method of determining layers moduli was considered to be superior to backcalculation for the
following reasons:
1. FE does not contain assumptions about pavement geometry as traditional backcalculation
algorithms do. The model accounts for the layers interfaces and the inertial properties of the
85
materials.
2. The load used in the finite element programs is the experimentally measured load-time history
applied by FWD. This permits comparing the experimental and theoretical deflection time
histories at all sensor locations. All existing backcalculation programs reach convergence
based only on the maximum deflection measured at each sensor location.
6.7 VERIFICATION OF FINITE ELEMENT MODELS
6.7.1 Deflection Basins
The initial seed moduli used in the FE models produced highly stiff responses in all cases.
Therefore the moduli of different layers were reduced. After several cycles of adjusting the values
of layer moduli used in each model, a satisfactory match between the FE-generated and the FWD-
measured basins was reached for every pavement structure. The final basins are plotted together with
those experimentally measured in Figure 6.8. In all cases, the FE deflection basins fell close to those
measured experimentally. Figure 6.8 (c) for the composite pavement shows deviation between the
experimental and theoretical basins near the center of FWD load application. This deviation may be
attributed to one or both of the following reasons:
1. Existence of unrepaired cracks in the concrete slab.
2. The center of FWD loading plate fell near a transverse joint in the overlaid slab.
Additionally, the asphalt material under the loading plate, being confined between the loading
plate and the underlying concrete, has suffered local excessive deformation that was recorded by the
FWD sensor located at zero offset. At the locations of other sensors, the surface of the asphalt layer
is free to follow the deformation of underlying layers. As indicated in Figure 6.8 (c) the FE model
successfully simulated this behavior, however lack of representation of a cracked concrete layer
resulted in the small deviation between the FE-generated and the FWD-measured deflections up to
86
24 in. offset from the center of load application.
Figure 6.9 illustrates the fringes of vertical deformation at the time of maximum FWD load
through two sections; one is perpendicular to the traffic direction and the other passes through the
FWD sensors line. The patterns of vertical displacement fringes illustrate the uniformity of
displacements through different layers.
6.7.2 Displacement-Time History
The FE-generated and experimentally measured deflection-time histories are compared in Figure 6.10
for three different sensor positions. The plots reveal that as the FWD load is applied, both the
theoretical and experimental deflections increase at almost the same rate. After peak deflections are
reached, the FWD measured deflection curves rebound much faster than the FE-generated
deflections. This behavior could be attributed to one of two reasons:
1. The top layer separates from the base. If this is the case, then the FWD sensors should have
recorded different values of positive deflections at different sensor positions. As seen from
Figure 6.10 (a), this cannot be true since the sensor located at 48 in. recorded almost the same
positive deflections as the sensor located at the center of load application. Furthermore,
Figure 6.10 (b) shows that the magnitude of rebound at the center of FWD load application
exceeds that recorded by the sensor located at 12 or 48 in. offsets, which excludes layer
separation as a reason.
2. Either all the sensors, or the FWD structure (which supports all sensors) rebounded following
the application of FWD load. It is unlikely that all sensors rebound as the FWD manufacturer
makes sure that the magnitude of spring loading is large enough to keep the sensors in
intimate contact with the pavement surface. The rebound of the whole FWD structure is
more plausible and is observed during the FWD test. When the sensor supporting-structure
87
rebounds, the spring loaded sensors are lifted slightly up and the deflection recovery portion
of each deflection-time history takes place at a faster rate than reality. This explains the
positive deflections shown in Figure 6.8.
According to the above discussion only the Downward Portion (DP) of the experimental
deflection-time history is suitable for comparison with 3D-FEM results. Of all sensors, the DP of the
deflection-time history recorded at the center of FWD load application is the least affected by possible
rigid body rebounding of the FWD structure. Figures 6.10 (a), (b), and (c) reveal that the FWD-
recorded deflection-time history at zero sensor position coincides with the FE-generated deflection-
time history. Additionally, the major features of the experimentally measured response are also seen
in the FEM response. These features are a time delay of displacements measured at different offsets,
and a time delay between maximum loading and maximum displacement response (recorded at the
center of FWD load application) of around three to five milliseconds in both the theoretical and
experimental data.
6.8 EVALUATION OF BACKCALCULATION PROGRAMS
Backcalculation programs terminate as soon as either the deflection basin fit precision
tolerance or the moduli convergence is satisfied. Although all the theoretical deflection basins from
different backcalculation programs match the FWD measured ones, this doesn’t mean that the layers
moduli profiles reached by these programs are correct. Backcalculation programs interpret the
measured deflection basin as being produced by an applied static load. The short load duration of
FWD load does not allow the structural materials to deflect fully in response to the maximum load
magnitude. This means that if the same FWD load is statically applied for a longer time duration, the
deflection basin measured would be larger. Previous studies(45-48) reported that experimentally
measured deflection basins produced by the application of static load (whose magnitude is equal to
FWD load) are up to 80 percent larger than those measured during FWD tests. Thus backcalculation
programs that are based on static interpretation of FWD load may overestimate the layers moduli.
88
The 3D-FEM approach accounts for both the inertia properties of the structural materials and the
dynamic nature of FWD load. When the backcalculated moduli were used as seed moduli in the FE
models they resulted in highly stiff basins. As the values of layers moduli were reduced, the FE
deflection basins converged to those experimentally measured. The measured, backcalculated, and
FE-generated deflection basins are compared in Figure 6.11. All deflection basins are very close to
each other. However, deviations were found between the backcalculated moduli using different
programs and those obtained using 3D-FEM as shown in Figure 6.12.
Using the FE-backcalculated subgrade modulus, a set of correction factors were computed
for the subgrade modulus value obtained from each program when used for different types of
pavements and the results are given in Table 6.1. The correction factor is computed by dividing the
FE-backcalculated subgrade modulus by the value obtained from the specific backcalculation
program. From the values listed in Table 6.1, the following remarks could be drawn:
1. MODULUS has the best consistency among the three programs. The correction factors
obtained for this program fell very close to the values recommended by the American
Association of State and Transportation Officials (AASHTO) Pavement Design Guide (5).
2. MODCOMP behaved similar to MODULUS with flexible pavements, however it
underestimated the value of the subgrade modulus of the rigid pavement.
3. EVERCALC produced a subgrade modulus for the flexible pavement that is very close to the
FE-backcalculated value. For rigid and composite pavements it under estimated the subgrade
modulus. The correction factors found for rigid pavements for this program fell within the
0.25 recommended for rigid pavements by AASHTO Pavement Design Guide (5).
4. The FE-backcalculated modulus for the three pavements tested in this study did not
significantly change. This may be due to the fact that the three pavement sections were
located in Morgantown, West Virginia within a circle of radius less than seven miles.
89
The AASHTO Pavement Design Guide recommends (based on experimental observations)
that a correction factor less than 0.33 is used with backcalculated subgrade modulus of flexible
pavements. For concrete pavements the recommended factor is less than 0.25. It can be seen from
table 6.1 that the mechanistic 3D-FEM approach in backcalculating layers moduli produced almost
the same result. That is, the FE-evaluated moduli don’t require correction and therefore can be used
as a reference for assessing the performance of backcalculation algorithms.
90
TABLE 6.1 Correction Factors for Backcalculated Subgrade Modulus.
PAVEMENT FE-Backcalculated MODCOMP MODULUS EVERCALC AVERAGE
TYPE Modulus (kPa)
Flexible 0.85*27.56 0.34 0.37 0.35
Rigid 26.18 1.34* 0.28 0.19 0.24
Composite 27.56 0.23 0.29 0.13 0.22* Value excluded for the calculation of average
91
Concrete
Base 8 in.
Subgrade
144 in.120 in.
FWD loading plate
Non-reflective bottom
Non-reflective boundariesfor all layers
Symmetry plane
9 in.
72 in.60 in.
Non-reflective endsof all layers
Non-reflective edgeof all layers
FIGURE 6.1 Finite element mesh of the flexible pavement model.
92
PCC slab9 in.
Base 8 in.
Subgrade72 in.
144 in.
162 in.
FWD loading plate
Non-reflectivebase & subgrade
Non-reflectiveends of layers
Non-reflective bottom
72 in.
Symmetry plane Reflective side of concrete slab
Non-reflective edgeends of layers
FIGURE 6.2 Finite element mesh of the rigid pavement model.
93
Asphalt 5 in.
PCC slab 9.5 in.Base 3 in.
Subgrade 72 in.
72 in.
162 in.
FWD loading plate
144 in.
Non-reflective base & subgrade
Reflective side ofconcrete slab
Non-reflective endsof all layers
Non-reflective bottom
FIGURE 6.3 Finite element mesh of the composite pavement model.
94
a. Flexible Pavement b. Rigid Pavement
c. Composite Pavement
FIGURE 6.4 Impact loading curves used in different finite element models.
95
a. Flexible Pavement b. Rigid Pavement
c. Composite Pavement
FIGURE 6.5 Load-Deflection relation for different types of pavements.
96
-6.000E+01>-5.500E+01>-5.000E+01>-4.500E+01>-4.000E+01>
-3.500E+01>-3.000E+01>
-2.500E+01>-2.000E+01>
-1.500E+01>
-1.000E+01>-5.000E+00>0.000E+00>
-7.000E+01>-6.417E+01>-5.833E+01>
-5.250E+01>-4.667E+01>
-4.083E+01>-3.500E+01>-2.917E+01>
-2.333E+01>
-1.750E+01>-1.167E+01>
-5.833E+00>0.00E+00>
a. Flexible Pavement b. Rigid Pavement
c. Composite Pavement
-1.500E+02>-1.375E+02>
-1.250E+02>
-1.000E+02>
-8.750E+01>-7.500E+01>
-6.250E+01>
-5.000E+01>
-3.750E+01>-2.500E+01>-1.250E+01>0.000E+00>
-1.125E+02>
Figure 6.6 Fringes of vertical stresses at time of maximum FWD load.
Asphalt LayerBase Layer
Subgrade
Vertical Stress, psi
0
20
60
40
80
10075604530150 90
ConcreteBase Layer
Subgrade
Vertical Stress, psi
AsphaltConcrete
Subgrade
Base Layer
Vertical Stress, psi
a. Flexible Pavement. b. Rigid Pavement
c. Composite Pavement.
0
20
60
40
80
100
0
20
60
40
80
10075604530150 90
75604530150 90
97
FIGURE 6.7 Vertical stresses in different types of pavement due to FWD load.
98
a. Flexible Pavement b. Rigid Pavement
c. Composite Pavement
FIGURE 6.8 Comparison between experimental and FE deflection basins for different pavements models.
99
FIGURE 6.9 Fringes of vertical displacement at time of maximum FWD load. (Display scale factor 2500)
100
FIGURE 6.10 Deflection-time histories for different pavement models.
101
a. Flexible Pavement b. Rigid Pavement
c. Composite Pavement
FIGURE 6.11 Comparison between backcalculated deflection basins and measured basins.
102
Surface layer (Ksi)
0
200
400
600
800
1000M
odul
us, K
si
Subgrade (Ksi)
0
2
4
6
8
10
12
14
Mod
ulus
, Ksi
Base layer (Ksi)
0
20
40
60
80
100
120
Mod
ulus
, Ksi
Subgrade (Ksi)
0
5
10
15
20
25
Mod
ulus
, Ksi
Base Layer (Ksi)
0
20
40
60
80
100
120
Mod
ulus
, Ksi
Surface Layer (Ksi)
0
1000
2000
3000
4000
5000
Mod
ulus
, Ksi
Subgrade (Ksi)
0
5
10
15
20
25
30
35
Mod
ulus
, Ksi
Base Layer (Ksi)
0
50
100
150
200
Mod
ulus
, Ksi
Surface Layer (Ksi)
0
500
1000
1500
2000
2500
Mod
ulus
, Ksi
PCC Layer (Ksi)
0
1000
2000
3000
4000
5000
6000
7000
Mod
ulus
, Ksi
a. Backcalculated layer moduli for flexible pavement
b. Backcalculated layer moduli for rigid pavement
c. Backcalculated layer moduli for composite pavement
FIGURE 6.12 Comparison of backcalculated layer moduli for the three types of pavements.
103
CHAPTER 7
SOME FACTORS INFLUENCE BACKCALCULATIONS
OF RIGID PAVEMENTS
7.1 INTRODUCTION
This chapter focuses on examining the behavior of rigid pavement layers during the Falling
Weight Deflectometer (FWD) test; factors affecting the design of a concrete slab, such as whether
the joints are doweled or undoweled and the spacing between transverse joints were considered.
Explicit finite element analysis was employed to investigate the response of pavement layers to the
action of FWD impulse load. The accuracy of the finite element models developed in this investigation
was verified by comparing the finite element-generated deflection basin with that experimentally
measured during an actual test. The results showed that the measured deflection basin can be
reproduced through finite element modeling of the pavement structure. The resulting deflection basins
from different models which simulate different pavement design features were processed using several
backcalculation programs. The results reveal the effect of different pavement design features on the
backcalculated moduli profile. It was found that ignoring the dynamic nature of the FWD load may
lead to crude results, especially during backcalculation procedures.
7.2 FINITE ELEMENT STRUCTURAL MODEL
A rigid pavement (SHRP section No. 285823) located in Mississippi was selected for this
study. The pavement structure was modeled as a multilayered linear elastic system consisting of a
Portland Cement Concrete (PCC) slab, base, and subgrade as shown in Figure 1. The model
dimensions were chosen to be the full lane width, that is 12 ft and extended in the longitudinal
direction from both sides to include two quarter parts of the adjacent slabs. The slab length was taken
to be 20 ft . To study the effect of the slab length on the performance of a rigid pavement under the
104
effect of FWD load, four other models were developed using slabs of lengths 16 ft, 15 ft , 12 ft, and
10 ft. The slab width was kept constant, 12 ft for all models. The center of the loading plate was
located at the center of the middle slab for all models. Due to the geometrical symmetry around the
longitudinal plane passing through the center of the loading plate, only one half of the pavement was
meshed. In absence of data about the depth to bedrock, it was assumed to be typical of what can be
found in West Virginia, i.e. from 5-15 ft under the bottom of the base layer. In this study, it was taken
as 6 ft measured from the bottom of the base layer. Additionally, nonreflective boundaries were
applied at the bottom of the subgrade to eliminate reflection of the stress wave from affecting the
surface displacements. To account for the effect of model size, nonreflective boundaries which
simulate a semi-infinite extension of layers were applied at all sides of base and subgrade as well as
the transverse ends of the two half slabs as shown in Figure 7.1. A sliding interface was assumed
between the concrete slab and the base layer, and a fully bonded interface was assumed between the
base layer and the subgrade. All layers were meshed using 8-node brick elements having 24 degrees
of freedom per element. The mesh sizes varied through the model to assure the accuracy of the results
within the regions of interest. Thus a refined mesh was necessary in regions of high stress intensity
such as concrete slabs especially at transverse joints. A coarser mesh was used for the base and
subgrade.
The steel dowel bars (modulus of elasticity=30, 000 psi, unit weight= 488.81 pcf) in the
transverse joints were modeled using brick elements. The main function of dowel bars is to transfer
the load across the joint while allowing the slabs to move longitudinally relative to each other in order
to relieve the tensile or thermal stresses due to slab contraction. Therefore the dowel bar may be
bonded to one concrete slab while its other end is free to slide in the adjacent slab. Consequently, one
end of the dowel bar was modeled with a tied interface with the concrete slab, while the other end
was modeled with a sliding interface with the adjacent concrete slab as illustrated is Figure 7.2.
105
7.2.1 Model Loading and Material Model
The FWD impact load was applied to the model through a 12 in. diameter steel loading plate.
The impact load used in this investigation was obtained from the experimental results of SHRP
section No. 285803 reported by J. Mallela, et al. (48). The impact pressure on the loading plate
surface was assumed to be uniformly distributed due to the semi-rigid behavior of the plate. The
pressure-time relation, Figure 7.3, was digitized over time increments of 0.25 milliseconds and the
values were used in the finite element program . The different load magnitudes employed in the FWD
tests are designed so that all pavement layers behave within their elastic limits. Thus the assumption
of linear elastic behavior of all layers is realized for this study. This assumption is further confirmed
by research studies (48,49) which indicate that the stresses induced in different pavement layers under
a maximum impact pressure of 92.8 psi (used in this study) are likely to be within the elastic range.
Therefore linear elastic materials models were used for all layers and the material parameters are
given in Table 1.
TABLE 7.1 Properties of Pavement Materials.
Material Property Values published in Ref. (48)
Concrete Slab, Modulus (Ksi) 4650thickness= 8 in. Poisson’s Ratio 0.18
Unit Weight (pcf) 149.8
Base Layer, Modulus (Ksi) 1700thickness= 6 in. Poisson’s Ratio 0.40
Unit Weight (pcf) 133.8
Subgrade, Modulus (Ksi) 11.87thickness =72 in. Poisson’s Ratio 0.30
Unit Weight (pcf) 129.85
106
7.2.2 Model Verification
Figure 7.4 (a) illustrates a comparison between the experimental deflection basin obtained
from SHRP data base for section No. 285803 and the corresponding deflection basin obtained from
the 3D-FEM model. Initially, the value of 11.87 ksi for the subgrade modulus, backcalculated by
Mallela (48), was used in the model. The FEM model produced a deflection basin which was on
average 16% less then the experimentally measured one. However, both the theoretical and
experimental basins showed a remarkable agreement in their slopes, this agreement indicated that the
FEM model is slightly stiffer than the actual pavement. The higher stiffness of the model may be
reduced by decreasing the layers moduli values used in the model. When the modulus of the subgrade
was reduced to 8.0 ksi, while keeping the moduli of the surface and base layers as listed in Table 7.1,
a remarkable agreement between the theoretical and experimental results was realized as illustrated
in Figure 7.4 (a). Since the original modulus value of 11.87 ksi was evaluated using backcalculation
(Mallela (48)), a 32% reduction in the modulus value will be within the expected error associated
with most backcalculation algorithms. In fact, it is not uncommon for the error in evaluating
subgrade modulus to exceed 100% (see Reference13). Even in well controlled laboratory testing of
subgrade modulus, errors more than 50% are expected.
The most important thing to consider is the ability of the model to simulate the relative
displacement of any point to another one on the structure. The success of this model is demonstrated
in the good agreement between the slopes of the deflection basins as we move away from the point
of load application. Only at a distance of 48 in. did the slopes of the experimental and theoretical
basins start to show some deviation. One reason for this divergence may be the approximate values
adopted for the moduli of the base and subgrade layers which were evaluated using backcalculation,
the value of subgrade modulus is the only one adjusted in this study. Another reason may be due to
unreported dowel bar looseness or loss of aggregate interlock. The third reason may be simply the
experimental error encountered in measuring very small displacements away from the center of the
loading plate. In order to illustrate the effect of dowel bars on the deflection basin, another FEM
model was constructed without dowels at the joints and its deflection basin was compared with the
107
experimentally measured one in Figure 7.4 (b).
7.3 PERFORMANCE ASSESSMENT OF BACKCALCULATION PROGRAMS
In this study, finite element modeling was used for the evaluation of conventional
backcalculation programs. Since a FWD measured deflection basin could be reproduced through
finite element modeling of the pavement structure, the FEM generated deflection basin can be used
to backcalculate the layers moduli. To evaluate the performance of different backcalculation
algorithms the following procedures were followed:
1.The rigid pavement structural model results were verified by comparing the FEM-generated
deflection basin with the FWD measured one as shown in Figure 7.4.
2. The theoretical deflection basin obtained from the finite element model was used together
with different backcalculation programs to evaluate the moduli of different layers, using
different backcalculation programs.
3. The backcalculated layers moduli were compared with the moduli used in the finite
element model as shown in Figure 7.5.
Figure 7.5 (a) illustrates the measured deflection basin together with those resulting from
using different backcalculation programs. It can be noticed that a remarkable agreement was achieved
between all the backcalculated basins and the measured one. However, the backcalculated layers’
moduli obtained from each program were found to be different from those used in the finite element
model as shown in Figure 7.5 (b). This is primarily due to the dynamic nature of the FWD which was
accounted for in FE analysis while the backcalculation programs are based on static analysis. Figure
7.5 (b) also indicates that all programs have produced top layer moduli close to that used in the FE
model. The values of the base modulus evaluated using conventional backcalculation programs are
108
significantly less than those used in the FE model. The subgrade layer modulus produced by all three
backcalculation programs was significantly larger than that used in the finite element model.
However, if we apply a correction factor of 0.28 (as recommended in Chapter 6 for MODULUS
program), in average, on the backcalculated subgrade modulus, the results become almost identical
to the modulus used in the finite element model. This further confirms the validity of the correction
factors reached in Chapter 6.
7.4 EFFECT OF SLAB LENGTH AND DOWEL BARS
The FE-generated deflection basins, for the models provided with dowel bars, are plotted for
different slab lengths in Figure 7.6 (a). The deflection basins are congruent indicating that, in the
presence of dowel bars, the slab length doesn’t affect the surface deflection values resulting from
FWD impact. This can be explained by the fact that the dowel bars transfer the load to the adjacent
slabs. Comparison of the deflection basins of the doweled models in Figure 7.6 (a) with those of
undoweled ones in Figure 7.6 (b) shows that dowel bars affect the value of the maximum deflection
measured at the center of FWD loading plate. Away from the center of load application, dowel bars
have the effect of introducing continuity of deformation at the transverse joint. Therefore no effect
of slab length on the measured deflection basin can be observed in Figure 7.6 (a) for doweled
pavement structures. In absence of dowel bars, Figure 7.6 (b), the slab length becomes an important
factor which affects the FWD deflection basin.
The plots in Figure 7.6 (b) for undoweled pavements indicate that as the slab length increases,
the surface deflection increases then begins to decrease at a slab length 15 ft. This is further illustrated
in Figure 7.7 which shows the change of the deflection under the center of FWD loading plate versus
slab length. Referring to Figure 7.6 (b), the difference between the deflections recorded at the
locations of the first and last sensors increases as the slab length increases. This causes
backcalculation programs to produce values of layers’ moduli which are slab length dependent for
undoweled pavement sections.
109
The deflection basins plotted in Figure 7.6-b were processed using MODULUS5.0 program
to study the effect of slab length on the backcalculated layers’ moduli. The resulting layers’ moduli
for each slab length together with the estimated depth to bedrock are plotted together with the value
used in FEM as shown in Figure 7.8. The plots show a significant change in the backcalculated
moduli values obtained for both the surface and the base layers from those used in FEM. However,
the values for subgrade modulus are found to be close to each other but still significantly larger than
that used in FEM. Therefore it seems that any change in the surface deflection affects the moduli of
the top layers more than they do the subgrade. This makes the use of a correction factor of 0.28 for
the subgrade modulus satisfactory for all slab lengths.
7.5 CONCLUSIONS
The 3D FEM approach used in this study provides a powerful tool for evaluating the
performance of existing backcalculation programs with rigid pavements under different situations
encountered in the field. Based on the presented results, the following conclusions can be drawn:
1. When testing an aged rigid pavement section in which cracks have developed, the FWD
testing engineer should check that the length of the tested slab part is not less than 10 ft to
assure that this part can produce a reliable deflection basin.
2. The correction factor of 0.28 reached in Chapter 6 is suitable for adjusting the backcalculated
subgrade modulus in all cases of doweled and undoweled joints. This value was found to be
in close agreement with the AASHTO experience-based correction factors.
110
60 in.
60 in.
8 in.
Subgrade72 in.
Loading Plate, 12 in. Diameter
144 in.Non-reflective sideof base & subgrade
Non-reflective bottom
Non-reflective sidesof concrete, base and
Reflective slab sides
240 in.
Concrete Slab,
Base, 6 in.
Nonreflective sides
Symmetry plane
Quarter slab
subgrade layers
Figure 7.1 Finite element mesh for a rigid pavement.
Figure 7.2 Cross section in a doweled joint.
0 0.01 0.02 0.03
30
60
90
0
Time, sec
111
Figure 7.3 Impact load curve used in finite element model (Ref. (48)).
112
Figure 7.4 Model verification. (Slab length=20 ft)
113
Figure 7.5 Comparison between the results of backcalculation programs.
Measured
FEM, E sub =8.00 ksi
MODULUS5.
EVERCALC4.0MODCOMP3
1.6
2.4
3.2
4.0
0 16 32 48 64
Distance from loading plate center, in.
Published, Ref. (48) FEM MODULUS
5EVERCALC MODCOMP 3
Subgrade
0
50
100
150
200
250
300 M
odu
lus,
MP
a
Base Layer
0
2000
4000
6000
8000
10000
12000
14000
Mod
ulus
, M
Pa
Concrete Slab
0 5000
10000 15000 20000 25000 30000 35000 40000 45000 50000
Mod
ulu
s, M
Pa
a. Deflection Basins.
b. Layers Moduli.
114
Figure 7.6 Effect of slab length on deflection basin.
0
1
2
3
4
5
10 12 14 16 18 20 22
115
FIGURE 7.7 Change of maximum deflection with slab length for undoweled pavement.
116
1.0 MPa=0.14504 ksi)
Figure 7.8 Effect of slab length on the backcalculation results ( Using MODULUS).
Base Layer
0 2000 4000 6000 8000
10000 12000 14000 16000
Mou
lus,
MP
a FE
Subgrade
0 20 40 60 80
100 120 140 160
Mod
ulus
, M
Pa
FE
Depth to Bedrock
0
2
4
6
8
10
De
pth
to b
edro
ck,
m.
Surface Layer
0
10000
20000
30000
40000
50000
60000
Mod
ulus
, M
Pa
FE
117
CHAPTER 8
EFFECT OF 3D FEM MODEL DEPTH ON BACKCALCULATIONS
OF FLEXIBLE PAVEMENTS
8.1 INTRODUCTION
Many researchers (Uddin et al.(54) , Yang et al. (55), Briggs et al. (56), Rhode et al. (57), and
Uzan (58)) reported that mechanistic analysis of pavement response to FWD impact load shows a
dependancy on the thickness of subgrade layer. Such a conclusion was reached under the assumption
that pavement response to a static load is equivalent to its response to a FWD impact load of the
same amplitude. Thus the elastic layer theory can be used to backcalculate the layers moduli.
However, Mamlouk (45), Seebaly (46), and Mallela (48) reported that the deflections produced under
impact loads may be from 40 to 80 percent less than those observed if the load was static. Under
the assumption of a statically applied load, each pavement layer, including the full subgrade depth,
has enough time to fully deflect, which is not the case if the applied load is a short duration impact.
On the other hand, the use of elastic layer theory and a static loading assumption required a
knowledge or estimate of the thickness of subgrade layer that can be used in backcalculation
programs in order to produce the same deflection measured from FWD test. The theoretical
dependancy of FWD surface deflections (predicted from the elastic layer theory) on the assumed
thickness of the subgrade layer is not supported in the literature by any known experimental
measurements where sites that have the same layers moduli profile but different depths to bedrock
are tested using FWD. Such measurements would be extremely difficult because of the variation of
subgrade conditions from one location to another. On the other hand, if FWD testing is to achieve
its objective, a means of nondestructive testing has to be developed to predict the appropriate depth
of subgrade layer that should be used in backcalculation algorithms.
Chang et al. (59) attempted to establish an analytical correlation between the results obtained
using Dynaflect (harmonic load) and those using FWD (impact load) to predict a depth to bedrock.
118
His results indicate that only the free vibration part of the FWD displacement-time history may be
correlated to the depth to bedrock; none of his results show that the FWD deflection basin is
influenced by the depth to the stiff layer. Bush (61) suggested using an arbitrary subgrade thickness
such as 20 ft in elastic layer-based backcalculations. Uddin (54) recommended that the actual
subgrade thickness should be used. Seng et al. (61) found that the depth to bedrock could be related
to the frequency of the free vibration portion of FWD sensors and the shear wave velocity in the
subgrade layer. For flexible pavements:
DB = T V / (6.33 -5.04 �) (1)d s1.08 1.13
and for rigid pavements:
DB = T V / (6.21 - 3.88 �) (2)d s1.11 1.14
Where:
T = the period of the free vibration portion of the FWD sensors, seconds.d
V = the shear wave velocity in the subgrade layer, ft/s.s
� = Poisson’s ratio of the subgrade material.
The major shortcoming in Seng’s approach is that the free vibration amplitudes from FWD
sensors are extremely small, which makes accurate measurement of the free vibration period difficult
if not impossible for many sites. If the layers’ interfaces are not fully bonded, the free vibration part
of surface displacements may not be related to the depth to bedrock.
Ullidtz (62) used Boussinesq’s equation to establish the concept of surface modulus and
compute the depth to bedrock. The surface modulus is defined (63) as the stiffness modulus of an
equivalent half space pertaining to a specific spacing from the load center that produces a deflection
identical to the deflection actually measured on the layered structure at the same spacing. The surface
modulus at a specific radius “r” from the center of FWD load application is given by:
E (r) = 2 (1-� ) P/(% r d ) (3)sm r2
119
where:
E (r) = Surface modulus at distance r from load center.sm
� = Poisson’s ratio.
P = Applied load.
d = Deflection at distance r.r
Ullidtz pointed out that if a stiff layer is found at a certain depth, it will have a consequence
that no surface deflection will occur beyond the offset at which the stress zone intercepts the stiff
layer. Thus the depth to bedrock can be obtained from the radial distance from the center of FWD
loading plate at which the surface deflection reduces to zero.
Rohde et al. (57) used Boussinesque’s analysis and the subsequent development by Ullidtz
to develop a set of regression expressions which accounted to the overall shape of the deflection basin
in the estimation of the apparent depth to bedrock. For flexible pavement sites having an AC layer
thickness greater than six inches and tested using 9000 lb FWD load, the apparent depth to bedrock
“B” is obtained from:
1/B= 0.0409 + 0.5669 r + 3.0137 r +0.0033 BDI - 0.0665 log (BCI) (4) o o2
where:
r = 1/r intercept by extrapolating the steepest part of the inverse radial distance (1/r) versuso
deflection curve, 1/ft.
BDI= Base Damage Index defined as the difference in surface deflection measured at radial
distances of 12 in. and 24 in., mils.
BCI= Base Curvature Index defined as the difference in surface deflection measured at radial
distances of 24 in. and 36 in., mils.
Other relations similar to Equation (4) were developed for different thicknesses of asphalt
layers and were subsequently implemented in MODULUS (16) backcalculation program.
120
Zaghloul et al. (41) examined the dependency of FWD deflection basin on the depth to
bedrock using 3D Finite Element Modeling (3D FEM). The FWD load was applied to the model as
an impact load of the same duration as measured from FWD load cell. The surface deflections were
computed and compared with those experimentally measured. He went on to change the depth of
the subgrade layer in the model from 95 in. to 140 in. while keeping the layers moduli and the applied
load the same. He reported that the variation of the depth to bedrock in the 3D FEM model had no
effect on the deflection basin, a conclusion that contradicts the findings in references 54-58.
Analysis of pavement structural response using 3D FEM analysis offers many advantages not
normally available using any other analytical approach. Perhaps one of the most important
advantages offered by 3D FEM is the ability to accurately simulate the nature and distribution of the
applied load. Other major advantages are:
1. accurate modeling of the pavement geometry including discontinuity at joints and modeling
of the surface layer with finite width bounded by shoulders,
2. the friction and separation at pavement layers’ interfaces are accounted for in the analysis,
and
3. any form of material behavior could be easily included in the model.
Realizing these advantages, Shoukry et al. (64) developed a new backcalculation algorithm
using 3D FEM. The method was shown to produce excellent results when tested on Flexible, Rigid,
and Composite pavement sites. The backcalculated moduli using 3D FEM were compared, for
several sites, with those obtained using three backcalculation programs: MODCOMP, MODULUS,
and EVERCALC. The 3D FEM results were considered to be more accurate than traditional
backcalculation algorithms. Correction factors were developed to adjust the values of layers moduli
evaluated using the MODULUS backcalculation program to the corresponding moduli values
obtained using 3D FEM. The mechanistically evaluated correction factors were found to be in close
agreement with the experience-based values recommended in the American Association of State
Highway Officials and Transportation (AASHTO) Pavement Design Guide.
1 The participants at this round-robin test were:1. F. Emanuel, University of Texas A& M. 6. J. Mahoney, University of Washington.2. D. Alexander, Waterways Experimental Station. 7. Y. R. Kim, North Carolina State University.3. G. M. Rowe and M. J Sharrock, England. 8. W. Uddin, University of Mississippi.4. L. Irwin, Cornell University. 9. S. Shoukry& G. William, West Virginia University.5. P. Ullidtz, Technical University of Denmark. 10. J. Uzzan, Technion, Israel.
121
The work presented in this chapter was initiated as a result of a round-robin test administered
by the Transportation Research Board (TRB) A2B05 subcommittee on Backcalculations of layers’
moduli. In this test, ten different research groups and individuals were requested to predict the1
depth to bedrock from the FWD measurements for two of four flexible pavement sites located in
Texas, USA. Texas DOT who provided the FWD data provided also the thicknesses of the surface
and subgrade layers of every site and the temperature of top, middle, and bottom of the asphalt layer
for every site. They also provided the measured depth to bedrock for sites No. 2 and 4. The author
participated in the test as it provided a good opportunity to evaluate the reliability of the 3D FEM
based backcalculation algorithm that was developed in Chapter 6 and to achieve the following
objectives:
1. Develop procedure for the evaluation of the apparent depth to bedrock from 3D FEM
pavement structural models which simulate FWD testing.
2. Investigate the effect of finite element model depth and the reflection from the model
bottom on the calculated deflection basin.
8.2 FINITE ELEMENT STRUCTURAL MODELS
The 3D FE models used for the backcalculation of the four Texas sites were identical to the
flexible pavement model that was used to calculate the flexible pavement site of West Virginia,
described in Chapter 6 and shown in Figure 8.1. The same input file that was used to generate the
flexible pavement model of chapter 6 was modified to be a parametric one. The advantage of using
a parametric input file is that it allows the user to change only layer thicknesses, applied load, and
122
material properties of different layers while the number of nodes, number of elements, model
boundaries, layers interface properties, conditions at model boundaries, and the subgrade layer depth
remained unchanged from those reported in Chapter 6. The parametric input file is listed in Appendix
A. In each model, the thicknesses of pavement layers were set to those of Texas sites listed in Table
8.1. The model was loaded using the measured FWD load provided by Texas DOT and shown in
Figure 8.2. In absence of any prior knowledge of the expected depth to bedrock , the thickness of
the subgrade layer in the model was left at 72 in.
8.3 EVALUATION OF LAYER MODULI
The iterative procedures described in Chapter 6 were used to backcalculate the moduli profile
of every site. The final FEM-computed deflection basins were plotted together with those
experimentally measured in Figure 8.3. For site 1, Figure 8.3 (a) shows a deviation between the
experimental and theoretical deflection basins at the position of the second FWD sensor. The reason
for this deviation is the presence of a large thermal gradient (16.6 C) in the asphalt layer, and theo
simplifying assumption (used in 3D FEM calculation) of an average elastic modulus for the asphalt
layer. Although the use of viscoelasto-plastic material model for the asphalt layer may improve the
convergence between the theoretical and experimental deflection basins shown in Figure 8.3 (a), this
would result in longer execution time. Thus for practical purposes, it was decided to use an average
elastic modulus for the asphalt layer and perform a temperature correction on the backcalculated
modulus similar to the practice used in elastic backcalculation programs.
Referring to the temperature measurements listed in Table 8.1, the backcalculated moduli
values of the asphalt layer should be adjusted to the standard temperature of 20 C (68 F). Theo o
following relation (65 ) used by the Japanese Highway agencies was used:
E = E * 10 (5)standard as -0.0184 (20-T )
123
where: E = Modulus at temperature 20 C (68(F).standardo
E = 3D FE-based backcalculated modulus at field temperature.as
T = The mean temperature of asphalt ( C).o
The 3D FEM-backcalculated layers’ moduli for each site are listed in Table 8.2 together with
three other sets of results that were independently computed by Ullidtz (66-68) who participated in
the TRB-A2B05 round robin test. Ullidtz used three different backcalculation algorithms:
1. A two dimensional (axially symmetric) finite element (2D FE) backcalculation program
with non-linear material models.
2. Waterways Experiment Station (WES) backcalculation program that is based on the elastic
layer theory.
3. A backcalculation program based on the Method of Equivalent Thickness (MET) with a
non-linear subgrade material model.
Examination of values listed in Table 8.2 reveal that the 3D FEM approach developed in this
Thesis independently produced layer moduli values that were close to the values provided by Ullidtz
for all sites. This indicates that the use of elastic material models in 3D FEM approach has no effect
on the backcalculated moduli specially for the subgrade layer. Examination of the subgrade layer
moduli backcalculated using different approaches reveals that the use of a nonlinear material model
for subgrade in the MET method resulted in subgrade moduli values which are close to those
obtained using the 3D FEM method and elastic material model. It should be remembered that the
correction factors computed in Chapter 6 are specific to MODULUS backcalculation program and
don’t apply to any of the three backcalculation algorithms used by Ullidtz.
8.4 EVALUATION OF DEPTH TO BEDROCK
Examination of the profile of displacement decay with depth at the location of the central
124
FWD sensor position shown in Figure 8.4 reveals that such a decay relation may be used to define
an apparent depth to bedrock. Thus, the same 3D finite element model used to backcalculate the
layers moduli can also be used to evaluate the depth to bedrock. The maximum vertical displacement
that propagates along the vertical line passing through the center of the FWD loading plate can be
obtained from the finite element model. From Figure 8.4, it seems plausible to assume that the
maximum vertical displacement measured at the center of the FWD loading plate decays exponentially
with depth. This assumption can be verified by plotting the natural logarithm of the deflection versus
depth as shown in Figure 8.5. The relation is a straight line over a significant portion of the curve.
Deviation from straight line relation is due to the effect of the fixed boundary at the model bottom.
The exponential decay of the maximum displacement in the subgrade layer with increasing subgrade
depth is assumed to be:
= e (6)z %%
��z
where: = Deflection at Depth zz
= FE calculated deflection at the top of subgrade.%%
Z = the depth of subgrade measured from top of subgrade to the point under consideration.
The displacement decay constant �� is determined in this analysis from the plots of Figure 8.5.
From Equation (6), the decay constant �� can be calculated as
��=1/Z . ln( / ) (7)z o
In order to minimize the error in calculation of the constant ��, it was calculated for all the
points which fall on the straight line portion of ln ( ) versus depth graph and the average value was
used to calculate the depth to bedrock.
The values of the decay constant �� obtained from Equation (7) for the four sites are listed
in Table 8.3. The apparent depth to bedrock is defined as the subgrade depth at which the vertical
125
displacement becomes very small. The definition of a small displacement can be related to the decay
of stress in subgrade layer. As it is common in the calculation of instantaneous settlement of a
foundation resting on a deep layer, the soil depth beneath the foundation should not be less than the
depth at which the maximum vertical stress decays to 10 percent of its value at the foundation level
(66). This depth can be identified by plotting the ratio between the vertical stress induced at any depth
in the subgrade to its value at the subgrade top as shown in Figure 8.6. The apparent depth to
bedrock can be predicted using the stress decay relation. However, the use of displacement decay
seems to be more convenient since the accuracy of calculating the displacement in FEM is higher than
that of stress calculation since the latter is dependent on the differentiation of nodal displacement with
respect to nodal position, so it is mesh dependant.
The plots in Figure 8.5 reveal that as the stress decayes to 10 percent of its value at the top
of subgrade, there is an 80 to 85 percent decay in subgrade displacement. Thus the deflection ratio
/ found at 10 percent decay of vertical stress is substituted in Equation (7) to calculate theo
apparent depth to bedrock, that is:
Apparent depth to bedrock =[ ln( / ) at 10% stress decay]/�� (8)o
The final values obtained after adjusting the computed depths to bedrock, so that their values are
measured from the top of the surface layer of each site, are listed in Table 8.3.
8.5 EFFECT OF 3D FE MODEL DEPTH ON 3D FEM RESULTS
Modeling of pavement structure in 3D-FEM requires adopting a pre-assumed depth of the
subgrade. The effect of this assumed depth on the model results should be examined. After evaluation
of pavement layers’ moduli and the depth to bedrock for each site using a model depth of 95 in.
(subgrade thickness= 72 in.), each 3D FE model was modified by changing the subgrade thickness
first to 40 in. and then to 144 inch. After each modification, the model for each site was loaded with
126
the corresponding FWD load and the deflection basin was obtained.
8.5.1 Effect of Model Depth on Deflection Basin
The 3D FEM-calculated deflection basins for different model depths are shown in Figure 8.7.
In each case, the subgrade depth was changed while keeping the layers’ moduli and the applied load
the same. As the depth to bedrock increases, the deflection values also slightly increase. However,
the amount of increase in deflection diminishes with the increase of the model depth. This means that
after a certain model depth, the deflection basin will remain the same and the subgrade below that
depth will not contribute to the surface deflection. This depth is the apparent depth to bedrock. The
differences observed between the deflection basins resulting from different model depths are very
small. Such differences are not expected to affect the accuracy of the backcalculated moduli. This
agrees with Zaghloul et al. (41) who found that the variation of depth to bedrock doesn’t affect the
peak surface deflections predicted by 3D-FEM.
8.5.2 Effect of Stress Wave Reflection from Model Bottom on Deflection Basin
To examine the effect of stress wave reflection from the model bottom on the 3D FEM-
generated deflection basin, reflective boundaries were applied to the bottom of the shallowest model
of each site (i.e. model with 40 inch subgrade layer thickness). Figure 8-8 illustrates that the wave
reflection causes a slight increase in the surface deflection measured at the center of the FWD loading
plate and decreases the deflections at sensor positions away from the center. The small deviations
observed in Figure 8-8 are not expected to have any significant effect on the backcalculated moduli.
8.5.3 Effect of Model Depth on the 3D FEM-Calculated Depth to Bedrock
The maximum vertical displacement in the subgrade at the position of the FWD loading plate
127
for each pavement site is plotted on a horizontal logarithmic scale versus depth in Figure 8.9. The
plots reveal that the change of the model depth slightly affects the maximum vertical displacement
observed on the top of subgrade ( ). The upper portions of the plots for model depths 95 in. ando
167 in. are almost congruent to each other. On the other hand, the vertical displacements of the
shallow models differ significantly from those obtained for the other two deeper models which
indicate that their results are influenced by the boundary conditions set on their subgrade bottoms.
The depth to bedrock was calculated for each model depth for every sites and the results are
listed in Table 8.5. The results indicate that the predicted values for the depth to bedrock resulted
from the models of depths 95 in. and 167 in. are very close to each other. The values obtained from
the shallow model are up to 25% less than those of the deeper models because of the effect of the
fixed boundary at the model bottom.
8.5.4 Effect of Model Depth on Stresses Induced in Subgrade
The above investigation of the effect of model depth is expanded to include the effect on the
stress level induced in the subgrade layer. For this reason, the vertical stress distribution is plotted for
the three different model depths as shown in Figure 8.10. The Figure shows the plots only for site 3
as an example and the other sites are similar. The plots show that at the upper one foot of the
subgrade, the vertical stresses obtained from different models are congruent to each other. For the
models of depths 95 in. and 167 in., the stress plots remain congruent up to depth of 2 ft from the
subgrade top, after which the boundary condition at the model bottom influence the stress profile in
the remaining subgrade depth.
From the above discussion, the use of subgrade layer thickness of 72 in. seems to be suitable
for use in finite element modeling of flexible pavements. A good degree of accuracy can be realized
since an increase in the model depth will not result in a significant change in the model results.
Limiting the subgrade thickness to 72 in. from the surface can significantly reduce the model size
128
which decreases the required computer memory and the computational time.
8.6 EFFECT OF LOAD DURATION ON THE DEFLECTION BASIN
To illustrate the influence of FWD loading time duration on the deflection basin, the flexible
pavement model used in site 3 was processed after modifying the load-time history so that the peak
of the load acts for a duration of 40 millisecond as shown in Figure 8.11 (a). The FEM-generated
deflection basin was plotted together with the one obtained using the shorter duration FWD load (as
measured) as shown in Figure 8.11 (b). The results in Figure 8.11 (b) illustrate that the surface
deflection under the center of the FWD loading plate increased by 150 percent. The increase in the
surface deflection decreases with the increase of radial distance from the center of load application.
The increase in the maximum deflection due to the increase of maximum load-time duration confirms
the findings of references (45-48) which reported that the deflection basins produced by an impact
load are 40 to 80 percent less than those produced by a static load of the same magnitude.
The most interesting point in Figure 8.11 (b) is that the two deflection basins intersect at an
offset of 48 in. from the center of the FWD load. This agrees with the experience-based choice of
this distance by some researchers (18,54) to calculate the subgrade modulus. The results indicate
that the deflection value at this sensor location is not affected by the assumption that FWD is acting
as a static load.
8.7 CONCLUSION
Based on the work presented in this chapter, a new mechanistic approach for evaluating the
apparent depth to bedrock has been suggested. This method can be applied for all types of pavements.
The method was verified by comparison with field measurements, as well as with the results of other
existing methods.
129
The effect of the pre-assumed FE model depth on the finite element results has been studied.
From this study, the following conclusions can be made:
1. The FE-generated deflection basin is insignificantly affected by the assumed model depth.
2. The FE-generated deflection basin is not sensitive to stress wave reflections at the bedrock.
3. The apparent depth to bedrock is the depth under which the subgrade will not deflect due
to the application of the FWD load. This indicates that the zone influenced by the FWD load
is in the load vicinity, which makes any prior knowledge about the depth to bedrock
unnecessary in backcalculation using 3D FEM.
4. For research purposes, modeling a flexible pavement structure with a subgrade thickness
of 6 ft seems to be suitable for producing satisfactory results for both displacements and
stresses at the top of the subgrade.
130
TABLE 8.1 Layer Thicknesses and Temperature Measurements.
Site 1 Site 2 Site 3 Site 4
Asphalt layer thickness, in.Base layer thickness, in.
8.00 8.00 7.25 7.2515 15 15 15
Temperature Measurements:½ in. from asphalt top ( C) 57.2 30.6 24.2 22.8o
Mid depth ( C) 50.5 28.7 24.3 21.1o
½ in. from asphalt bottom ( C) 40.6 27.5 24.4 19.4o
131
TABLE 8.2 Backcalculated Pavement Layers’ Moduli, Ksi.
A. Surface Layer
Method Computed by Site 1 Site 2 Site 3 Site 4
3D FEM This study 135 56 160 170
2D FE Ullidtz 160 140 790 669
WES Ullidtz 165 144 852 703
MET Ullidtz 154 123 669 560
B. Base Layer
Method Computed by Site 1 Site 2 Site 3 Site 4
3D FEM This study 450 90 120 47
2D FE Ullidtz 33.5 28.6 32.8 24.5
WES Ullidtz 31.5 27.8 23.8 19.5
MET Ullidtz 32.5 38.1 35 30.6
C. Subgrade
Method Computed by Site 1 Site 2 Site 3 Site 4
3D FEM This study 18 10 12 8.5
2D FE Ullidtz 36.8 10.5 18.2 11
WES Ullidtz 32.1 11.2 18.8 12.3
MET Ullidtz 20.0 8.5 11.9 8.5
132
TABLE 8.3 Comparison Between Measured and Calculated Depth to Bedrock.
Site 1 Site 2 Site 3 Site 4
Decay Constant (��), Model Depth= 95 in.
-0.03059682 -0.03478123 -0.03488303 -0.03333101
( / ) at 10% stress decayo 0.1903 0.1443 0.1446 0.1617
Calculated depth to bedrock, in. 76 78.65 77.69 76.91
Measured depth to bedrock, in.(By Texas DOT)
30.5 76 63 103
133
TABLE 8.4 Effect of Assumed Model Depth on the Calculated Depth to Bedrock.
Site 1 Site 2 Site 3 Site 4
Decay Constant (��)
Model depth= 63 in. -0.04471782 -0.046714987 -0.045303345 -0.034748846Model depth= 95 in. -0.03059682 -0.034781234 -0.034883027 -0.033331011Model depth= 167 in. -0.03007312 -0.034196126 -0.033572694 -0.032929402
Calculated Depth to Bedrock, in.
Model depth= 63 in. 60.10 64.44 64.94 74.68Model depth= 95 in. 77.22 78.65 77.69 76.91Model depth= 167 in. 78.17 79.61 79.85 77.58
134
- Sliding interface between the asphalt layer and the base (Coefficient of friction=0.90).- Fully tied interface between the base and the subgrade.
FIGURE 8.1 Finite element model.
135
0 0.020.01 0.03 0.060.050.04
120
100
80
60
40
20
0
-20
Time, sec.
0 0.020.01 0.03 0.060.050.04
120
100
80
60
40
20
0
-20
Time, sec.
0 0.020.01 0.03 0.060.050.040 0.020.01 0.03 0.060.050.04
120
100
80
60
40
20
0
-20
120
100
80
60
40
20
0
-20
140
Time, sec. Time, sec.
a. Site 1 b. Site 2
c. Site 3 d. Site 4
FIGURE 8.2 Measured FWD impact load curves used in finite element models.
-20
-15
-10
-5
0
0 20 40 60 80
Exp
FE
-25
-20
-15
-10
-5
0
0 20 40 60 80
Exp
FE
-12
-10
-8
-6
-4
-2
0
0 20 40 60 80
Exp
FE
-16
-14
-12
-10
-8
-6
-4
-2
0
0 20 40 60 80
Exp
FE
136
FIGURE 8.3 Measured and FE-calculated deflection basins.
137
FIGURE 8.4 Subgrade vertical displacement versus depth.
138
FIGURE 8.5 Subgrade vertical displacement on a logarithmic scale versus depth.
0 20 40 60 80 100 0 20 40 60 80 100
0 20 40 60 80 1000 20 40 60 80 100
40
80
120
160
Percentage of reductionPercentage of reduction
Percentage of reduction Percentage of reduction
a. Site 1 b. Site 2
c. Site 3 d. Site 4
Stress decay
Displacement decay
Stress decay
Displacement decay
Stress decay
Displacement decay
Stress decay
Displacement decay
40
80
120
160
40
80
120
160
40
80
120
160
139
FIGURE 8.6 Decay of vertical stress and displacement in subgrade.
-20
-15
-10
-5
0
0 20 40 60 80
Measured
Depth=63 in.
Depth= 95 in.
Depth=167 in.-25
-20
-15
-10
-5
0
0 20 40 60 80
Measured
Depth=63 in.
Depth= 95 in.
Depth=167 in.
-14
-12
-10
-8
-6
-4
-2
0
0 20 40 60 80
Measured
Depth=63 in.
Depth= 95 in.
Depth=167 in.
-16
-14
-12
-10
-8
-6
-4
-2
0
0 20 40 60 80
Measured
Depth=63 in.
Depth= 95 in.
Depth=167 in.
140
FIGURE 8.7 Effect of the depth to bedrock on the deflection basin.
-16
-14
-12
-10
-8
-6
-4
-2
0
0 20 40 60 80
Non-Reflective
Reflective
-14
-12
-10
-8
-6
-4
-2
0
0 20 40 60 80
Non-Reflective
Reflective
-20
-15
-10
-5
0
0 20 40 60 80
Non-Reflective
Reflective
-25
-20
-15
-10
-5
0
0 20 40 60 80
Non-Reflective
Reflective
141
FIGURE 8.8 Effect of reflective subgrade bottom on deflection basin.
142
Depth 63 in.
Depth 95 in.
Depth 167 in.
0.0001 0.001 0.01Vertical displacement, in.
20
40
60
80
100
120
140
0
Depth 63 in.
Depth 95 in.
Depth 167 in.
Vertical displacement, in.
20
40
60
80
100
120
140
0
Depth 63 in.
Depth 95 in.
Depth 167 in.
0.0001 0.001 0.01
Vertical displacement, in.
20
40
60
80
100
120
140
0
Depth 63 in.
Depth 95 in.
Depth 167 in.
0.0001 0.001 0.01
Vertical displacement, in.
20
40
60
80
100
120
140
0
0.0001 0.001 0.01
a. Site 1 b. Site 2
c. Site 3 d. Site 4
FIGURE 8.9 Subgrade vertical displacement for different model depths.
143
FIGURE 8.10 Effect of model depth on vertical stress distribution for site 3.
120
100
80
60
40
20
0
-200 0.01 0.030.02 0.050.04 0.070.06 0.08
Time, sec.
a. Impact load curves.
-30
-25
-20
-15
-10
-5
0
0 10 20 30 40 50 60 70 80
80 msec
40 msec
Distance, inch.
b. Deflection basins.
144
FIGURE 8.11 Effect of load duration on the deflection basin.
145
CHAPTER 9
CONCLUSIONS AND SUGGESTED RESEARCH
The importance of considering the dynamic nature of the FWD load in the deflection analysis
has been emphasized in this work. In this study, different pavement sections were evaluated with
different backcalculation programs that are currently in use. 3D Explicit Finite Element Analysis was
used to evaluate the moduli profile of different pavement structures and the resulting moduli were
compared with those obtained using three existing backcalculation programs: MODULUS5.0,
MODCOMP3, and EVERCALC4.0. The following conclusions can be made:
1. Comparison of the results obtained from the three backcalculation programs: MODULUS5.0,
EVERCALC4.0, and MODCOMP3 reveals that MODULUS5.0 has a consistent
performance for all types of pavement structures. EVERCALC4.0 and MODCOMP3
programs produce acceptable results; however, the moduli values may be overestimated
especially for the subgrade layer. The performance of the three programs decreases when
evaluating composite pavements.
2. The change of the seed moduli or the moduli range used as input for the backcalculation
programs may significantly alter the resulting moduli profile. In this case, the deflection fit
precision criterion used in backcalculation is not sufficient to judge the solution accuracy.
Thus the experience in analysis, with materials and with deflections, is essential to check that
the backcalculation process yields acceptable results.
3. A new mechanistic method for backcalculation of pavement layer moduli and estimating the
apparent depth to bedrock using 3D Explicit Finite Element approach was developed. The
method was used successfully to backcalculate pavement layer moduli for all types of
pavements: flexible, rigid, and composite. Backcalculation using 3D FEM offers the following
advantages:
146
a. The dynamic nature of the FWD load and the effects of inertia and material damping were
accounted for.
b. Layer interfaces and the 3D geometry of the pavement structure were taken into account.
4. The finite element approach enabled backcalculating the modulus of base layer in a composite
pavement structure which is extremely difficult, if not impossible, using traditional algorithms.
5. The method of evaluating the depth to bedrock is not specific for a particular type of
pavement. Therefore it may be used for rigid and composite pavements for which no method
is currently available.
6. The backcalculated modulus of subgrade using the threeconventional backcalculation
programs: MODULUS5.0, EVERCALC4.0, and MODCOMP3 requires multiplication by a
correction factor. Correction factors of 0.35, 0.24, and 0.22 were calculated using 3D FEM
for flexible, rigid, and composite pavement structures respectively.
7. The values of the correction factors obtained using 3D FEM are in good agreement with
those found by experience and recommended in the AASHTO Pavement Design Guide. This
suggests that 3D FEM backcalculation may be used as a reference for assessing the accuracy
of conventional backcalculation algorithms.
8. For doweled rigid pavements, the spacing between the transverse joints has no effect on the
deflection basin.
9. For undoweled rigid pavements, the slab length is an important factor which influences the
results of backcalculation programs.
10. For aged pavement sections in which transverse cracks developed, the FWD test should not
147
be carried out on a part of the slab that is less than 10 ft to assure that this part can produce
a reliable deflection basin provided that the slab width is 12 ft.
11. Provided that a subgrade layer thickness greater than 6 ft is used in modeling flexible
pavement structure using 3D FEM, any further increase in the subgrade layer thickness has
insignificant effect on the 3D FE-generated deflection basin.
12. Similarly, reflection of stress waves from the FE model bottom has little influence on the
FE-generated deflection basin provided that the subgrade layer thickness is greater than 4 ft.
13. When studying a flexible pavement structure using 3D FEM, limiting the subgrade thickness
to 6 ft was found to produce satisfactory results for both the stresses and displacements on
the top of subgrade layer.
14. Due to the dynamic nature of the FWD load, the pavement surface response depends on the
magnitude the FWD load pulse, shape, and duration. The assumption of static loading in
backcalculation programs may produce unrealistic results.
148
SUGGESTED FUTURE RESEARCH
The work presented in this study is one step towards a better understanding of the dynamic
response of pavement to FWD impact load. Future research studies should aim at:
1. Automation of the 3D FEM backcalculation procedures.
2. Utilization of the 3D FEM models developed for backcalculation in overlay design or in
pavement design.
3. Testing the reliability of the models developed in this thesis on a large number of pavement
sites under different environmental conditions.
149
REFERENCES
1. Meier, R.W., and G.J. Rix. “Backcalculation of Flexible Pavement Moduli Using Artificial
Neural Networks”. Transportation Research Record 1448, TRB, National Research Council,
Washington, D.C., 1994, pp. 75-82.
2. Meier, R.W., and G.J. Rix. “Backcalculation of Flexible Pavement Moduli from Dynamic
Deflection Basins Using Artificial Neural Networks”. Transportation Research Record 1482,
TRB, National Research Council, Washington, D.C., 1995, pp. 72-81.
3. R.W. May, and H.L. Von Quintus. “The Quest For a Standard Guide to NDT
Backcalculation”. Nondestructive Testing of Pavements and Backcalculation of Moduli
(Second Volume), ASTM STP 1198, Philadelphia, 1994, pp. 505-520.
4. Huang, Y.H. “Pavement Analysis and Design”. Prentice Hall, Englewood Cliffs, New
Jersey, 1993.
5. AASHTO Guide for Design of Pavement Structures, Chapter 3, “Guides for Field Data
Collection”. American Association of State Highway and Transportation Officials, 1993, pp.
32-37, 96-97.
6. SHRP. “SHRP’s Layer Moduli Backcalculation Procedure: Software Selection” . Contract
No. SHRP-90-P-001B, Prepared by PCS/Law Engineering for SHRP, 1991.
7. Stubstad, R.N., and B. Connor. “Use of the FWD to Predict Damage Potential to Alascan
Highways during Spring Thaw”. Transportation Research Record 930, TRB, National
Research Council, Washington, D.C., 1983, pp. 46-51.
8. Irwin, L.N. “Determination of Pavement Layer Moduli from Surface Deflection Data for
150
Pavement Performance Evaluation”. Proceedings, Fourth International Conference on
Structural Design of Asphalt Pavements, No. 1, Univ. Of Michigan, Aug. 1977.
9. McCullough, B.F., and A. Taute. “Use of Deflection Measurements for Determining
Pavement Material Properties”. Transportation Research Record 852, TRB, National
Research Council, Washington, D.C., 1982, pp. 8-14.
10. Seaman, L., J.W. Simons, D.A. Shockey, R.F. Carmichael, and B.F. McCullough. “Unified
Airport Pavement Design Procedure”. Unified Airport Pavement Design and Analysis
Concepts Workshops, Federal Aviation Administration, Washington, D.C., July 16-17, 1991,
pp. 447-537.
11. Chou, Y.J., J. Uzzan, and R.L. Lytton. “Backcalculation of Layer Moduli from
Nondestructive Pavement Deflection Data Using Expert System”. Nondestructive Testing
of Pavements and Backcalculation of Moduli, ASTM STP 1026, Philadelphia, 1994, pp. 341-
354.
12. Irwin, L.H., W.S. Yang, and R.N. Stubstad. “Deflection Reading Accuracy and Layer
Thickness Accuracy in Backcalculation of Pavement Layer Moduli”. Nondestructive Testing
of Pavements and Backcalculation of Moduli, ASTM STP 1026, Philadelphia, 1994, pp.229-
244.
13. SHRP-P-651. “Layer Moduli Backcalculation Procedure: Software Selection”. Contract No.
SHRP-90-P-001B, Prepared by PCS/Law Engineering for SHRP, Washington, D.C., 1993.
14. Deusen, D.V. “Selection of Flexible Backcalculation Software for the Minnesota Road
Research Project”. Report No. MN/PR-96/29, MnDOT, St. Paul, Minnesota, 1996.
15. Irwin, L. and T. Szebenyi. “User’s Guide to MODCOMP3, Version 3.2". CLRP Report
151
Number 91-4, Cornell University Local Roads Program, Ithaca, New York, March 1991.
16. Michalak, C.H. and T. Scullion. “MODULUS5.0: User’s Manual”. Report No. TX-
96/1987-1, Texas DOT, Austin, Texas, 1995.
17. Scullion, T., J. Uzan, and M. Paredes. “MODULUS: Microcomputer-Based Backcalculation
System”. Transportation Research Board, Record 1260, TRB, National Research Council,
Washington, D.C., 1990, pp. 180-191.
18. Lee, S.W., J.P. Mahoney, and N.C. Jackson. “Verification of a Backcalculation of
Pavement Moduli”. Transportation Research Board, Record 1196, TRB, National Research
Council, Washington, D.C., 1988, pp. 85-95.
19. Harichandran, R.S., M.S. Yen, and G.Y. Baladi. “MICH-PAVE: A Nonlinear Finite Element
Program for Analysis of Flexible Pavements”. Transportation Research Record 1286, TRB,
National Research Council, Washington, D.C., 1990, pp. 123-131.
20. Tabatabaie, A.M., and E.J. Barenberg. “Finite-Element Analysis of Jointed or Cracked
Concrete pavements”. Transportation Research Record 671, TRB, National Research
Council, Washington, D.C., 1978, pp. 11-19.
21. Hammons, M.I., and A.M. Ioannides. “Developments in Rigid Pavement Response
Modeling. US Army Corps of Engineers”. Technical Report Gl-96-15, August 1996.
22. Hammons, M.I. “Development of an Analysis System for Discontinuities in Rigid Airfield
Pavements”. US Army Corps of Engineers. Technical Report Gl-97-3, April 1997.
23. Ioannides, A.M. E.J. Barenberg, and M.R. Thompson. “Finite-Element Model With Stress-
Dependant Support”. Transportation Research Record 954, TRB, National Research
152
Council, Washington, D.C., 1984, pp. 10-16.
24. Tayabji, S.D., and B.E. Colley. “Analysis of Jointed Concrete Pavements”. Fedral Highway
Adminsteration, McClean, VA , Report No. FHWA/RD-86/041, February 1986.
25. Tayabji, S.D., and B.E. Colley. “Improved Rigid Pavement Joints”. Transportation
Research Record 630, TRB, National Research Council, Washington, D.C., 1983, pp. 69-78.
26. Chatti, K., J. Lysmer, and C.L. Monismith. “Dynamic Finite-Element Analysis of Jointed
Concrete pavements”. Transportation Research Record 1449, TRB, National Research
Council, Washington, D.C., 1994, pp. 79-90.
27. Chatti, K. “Dynamic Analysis of Jointed Concrete Pavements Subjected to Moving
Transient Loads”. Ph. D. Dissertation, University of California at Berkeley, 1992.
28. Roesler, J.R., and L. Khazanovich. “Finite Element Analysis of PCC Pavements with
Cracks”. Transportation Research Board, TRB, National Research Council, Washington,
D.C., 1997, Paper No. 970751.
29. Ioannides, A.M., and J.P. Donnelly. “Three-Dimensional Analysis of Slab on Stress-
Dependant Foundation”. Transportation Research Record 1196, TRB, National Research
Council, Washington, D.C., 1988, pp. 72-84.
30. Kuo C.M., K.T. Hall, and M.I. Darter. “Three-Dimensional Finite Element Model for
Analysis of Concrete Pavement Support”. Transportation Research Record 1505, TRB,
National Research Council, Washington, D.C., 1995, pp. 119-127.
31. Kuo, C.M. “Three-Dimensional Finite Element Analysis of Concrete Pavement”.
Department of Civil Engineering, University of Illinois, Ph. D. Thesis, 1994.
153
32. Zaghloul, S.M., and T.D. White. “Use of a Three-Dimensional, Dynamic Finite Element
Program for Analysis of Flexible Pavement”. Transportation Research Record 1388, TRB,
National Research Council, Washington, D.C., 1993, pp. 60-69.
33. Zaghloul, S.M., T.D. White, and T. Kuczek. “Use of Three-Dimensional, Dynamic
Nonlinear Analysis to Develop Load Equivalency Factors for Composite Pavements”.
Transportation Research Record 1449, TRB, National Research Council, Washington, D.C.,
1994, pp. 199-208.
34. Seaman, L., J.W. Simons, D.A. Shockey. “Unified Airport Pavement Design Procedure”.
Proceedings: Unified Airport Pavement Design and Analysis Concepts Workshops.
DOT/FAA/Rd-92/17, Volpe National Transportation Systems Center, July 1992, pp. 446-
537.
35. Kennedy, T.C., R.D. Everhart, T.P. Forte, and J.A. Hadden. “Development of a Governing
Primary Response Model (GPRM) For Airport Pavement Design and Analysis”. Final Report
to Volpe National Transportation Systems Center, Contract No. VA2043 DTRS-57-89-D-
00006, January, 1994.
36. Kennedy, T.C., and R.D. Everhart. “Dynamic Complaint Boundary”. Final Report to Turner
Fairbanks Highway Research Center, Contract No. DIFH 61-93-C-00055, May, 1995.
37. Kennedy, T.C., and R.D. Everhart. “Comparison of Predicted Pavement Structural Response
With Field Measurments Data”. Final Report to Turner Fairbanks Highway Research Center,
Mclean, VA 22101, Contract No. DTFH 61-93-C-00055, February 1996.
38. Kennedy, T.C., and R.D. Everhart. “Thermal Effects on Pavement Response”. Final Report
to Turner Fairbanks Highway Research Center, Mclean, VA 22101, Contract No. DTFH 61-
154
93-C-00055, March 1997.
39. Zaghloul, S.M., T.D. White, and T. Kuczek. “Evaluation of Heavy Load Damage Effect on
Concrete Pavements Using Three-Dimensional, Dynamic Nonlinear Analysis”.
Transportation Research Record 1449, TRB, National Research Council, Washington, D.C.,
1994, pp. 123-133.
40. Zaghloul, S.M., T.D. White, J.A. Ramirez, and NBR Prasad. “Computerized Overload
Permitting Procedure for Indiana”. Transportation Research Record 1448, TRB, National
Research Council, Washington, D.C., 1994, pp. 40-52.
41. Zaghloul, S.M, T.D. White, V.P. Drenvich, and B. Coree. “Dynamic Analysis of FWD
Loading and Pavement Response Using a Three-Dimensional Finite Element Program”.
Nondestructive Tesing of Pavements and Backcalculation of Moduli (Second Volume),
ASTM STP 1198, American Society of Testing and Materials, Philladelphia, 1994, pp. 105-
138.
42. Huang, Y. H., and S. T. Wang. “Finite-Element Analysis of Rigid Pavements with Partial
Subgrade Contact”. Highway Research Record No.485 , National Research Council,
Washington, D.C., 1974, pp. 39-54.
43. Huang, Y. H., and S. T. Wang. “Finite-Element Analysis of Concrete Slabs and Its
Implications for Rigid Pavement Design”. Highway Research Record No.466 , National
Research Council, Washington, D.C., 1974, pp. 39-54.
44. Davis, T.G., and M.S. Mamlouk. “Theoretical Response of Multilayer Pavement Systems to
Dynamic Nondestructive Testing”. Transportation Research Record No. 1022, TRB,
National Research Council, Washington, D.C., 1985, pp. 1-7.
155
45. Mamlouk, M.S., and T.G. Davis. “Elasto-Dynamic Analysis of Pavement Deflections”.
American Society of Civil Engineers, Journal of Transportation Engineerring,Vol. 110, No.
6, 1994, pp. 536-550.
46. Sebaaly, B.E. , M. S. Mamlouk, and T. G. Davis. “Dynamic Analysis of Falling Weight
Deflectometer Data”. In Transportation Research Record 1070, TRB, National Research
Council, Washington, D.C., 1986, pp. 63-68.
47. Sebaaly, B.E. “Dynamic Models for Pavement Analysis”. Department of Civil Engineering,
Arizona State University, Ph. D. Dissertation, 1987.
48. Mallela, J., and K. P. George. “Three-Dimensional Dynamic Response Model for Rigid
Pavements”. In Transportation Research Record 1448, TRB, National Research Council,
Washington, D.C., 1994, pp. 92-99.
49. Nazarian, S., and K. M. Boddapti. “Pavement-Falling Weight Deflectometer Interaction
Using Dynamic Finite-Element Analysis”. In Transportation Research Record 1482, TRB,
National Research Council, Washington, D.C., 1995, pp. 33-43.
50. Uddin, W., P. Noppakunwijai, and T. Chung. “Performance Evaluation of Jointed Concrete
Pavement Using Three-Dimensional Finite-Element Dynamic Analysis”. Transportation
Research Board, 76th Annual Meeting, Washington, D.C., 1997 , Paper No. 1414.
51. Uddin, W., D. Zhang, and F. Fernandez. “Finite Element Simulation of Pavement
Discontinuities and Dynamic Load Response”. Transportation Research Record 1448, TRB,
National Research Council, Washington, D.C., 1994, pp. 69-74.
52. Shoukry, S.N., D.R. Martinelli, and O. Selezneva. “Dynamic Response of Composite
Pavements Under Impact”. Transportation Research Record 1570, TRB, National Research
156
council, Washington, D.C., 1997, pp. 163-171.
53. Shoukry, S.N., D.R. Martinelli, and O.I. Selezneva. “Dynamic Considerations in Pavement
Layers Moduli Evaluation Using Falling Weight Deflectometer”. Proceedings of the
International Society for Optical Engineering, Nondestructive Evaluation of Bridges and
Highways, Vol. 2946, 4-5 December 1996, pp. 109-120.
54. Uddin, W., A. H. Meyer, and W. R. Hudson. “Rigid Bottom Considerations for
Nondestructive Evaluation of Pavements”. Transportation Research Record No. 1070, TRB,
National Research Council, Washington, D.C., pp. 21-29, 1986.
55. Yang, N. C. “Mechanistic Analysis of Nondestructive Pavement Deflection Data”. Cornel
University, Ithaca, New York, Ph. D. Dissertation, 1988.
56. Briggs, R. C., and S. “Nazzarian. Effects of Unknown Rigid Subgrade Layers on
Backcalculation of Pavement Moduli and Projections of Pavement Performance”.
Transportation Research Record No. 1227, TRB, National Research Council, Washington,
D.C., pp. 183-193, 1989.
57. Rohde, G.T., and R. E. “Smith. Determining Depth to Apparent Stiff Layer From FWD
Data”. Research Report 1159-1, Texas Transportation Institute, The Texas A&M University
System, College Station, Texas, 1991.
58. Uzan, J. “Advanced Backcalculation Techniques”. Nondestructive Testing of Pavements and
Backcalculation of Moduli (Second Volume), ASTM STP 1198, American Society for
Testing and Materials, Philadelphia, pp. 3-37, 1994.
59. Chang, D. W., Y. V. Kang, J. M. Rosset, and K. H. Stokoe II. “ Effect of Depth to Bedrock
on Deflection Basins Obtained with Dynaflect and FWD Tests”. Transportation Research
157
Record No. 1355, TRB, National Research Council, Washington, D.C., pp. 8-17, 1991.
60. Bush, A. J. “Nondestructive Testing for Light Aircraft Pavements; Phase II, Development of
the Nondestructive Evaluation Methodology”. Report FFA-RD-80-9-II, US Department of
Transportation, Washington, D.C., 1980.
61. Seng, C., K. H. Stokoe II, and J. M. Roesset. “Effect of Depth to Bedrock on the Accuracy
of Backcalculated Moduli obtained with Dynaflect and FWD Tests”. Research Report 1175-
5, Center for Transportation Research, The University of Texas at Austin, Texas, 1993.
62. Ullidtz, P., and R. N. Stubstad. “Analytical-Empirical Pavement Evaluation Using the Falling
Weight Deflectometer”. Transportation Research Record No. 1022, TRB, National Research
Council, Washington, D.C., pp. 36-43, 1985.
63. CROW. “Deflection Profile- Not a Pitfall Anymore” Record 17, CROW Information and
Technology Center for Transport and Infrastructures, The Netherlands, 1998.
64. Shoukry, S.N., and G. W. William. “Performance Evaluation of Backcalculation Algorithms
Through 3D Finite Element Modeling of Pavement Structures”. Paper No. 991277,
presented at the 78th Annual Transportation Research Board Meeting, Washington, D.C.,
January, 1999.
65. Private Communications. Email message from E. Beauving -CROW-NL to Dr. Smair
Shoukry, sent on March 31, 1999.
66. Naval Facilities Engineering Command. Soil Mechanics: Design Manual 7.01, September
1986.
66. Ullidtz, P. “Pavement Analysis, Development in Civil Engineering 19". Elsevier, 1987.
158
67. Ullidtz, P. “Modeling Flexible Pavement Response and Performance” Polytecknisk Forlag,
Denmark, 1998.
68. Private Communications. Email message from Professor Per Ullidtz to the author, sent on
March 24, 1999.
159
APPENDIX A
PARAMETRIC INPUT FILE TO GENERATE FLEXIBLE PAVEMENT MODEL
title FLEXIBLE PAVEMENT MODEL SUBJECTED TO FWD LOAD .
c Global Control Commands.dyna3d
lsdyopts hgen 2;endtim 0.040;glstat 0.001 matsum 0.001;d3plot dtcycl 0.001;qh 0.11;
parametersc Enter the surface Layer thickness (t1) with a negative sign, in.t1 -7.25c Enter the thickness of the Base Layer (t2) with a negative sign, in.t2 -15;
c Sliding Interface with friction Between the Surface Layer & Base.sid 1 fric 0.9 lsdsi 3;C Sliding Interface with Friction Between the Loading Plate & the Surface Layer..sid 2 fric 0.8 lsdsi 3;
plane 10.0 0.0 0.0 -1 0 0 0.001 symm;c Enter the Material Properties for Pavement Layers.dynamats 1 1 rho 2.240e-4 e 12e+4 pr 0.35;dynamats 2 1 rho 2.200e-4 e 120e+3 pr 0.30;dynamats 3 1 rho 1.950e-4 e 12.0e+3 pr 0.40;dynamats 4 1 rho 7.324e-4 e 29.0e+6 pr 0.30;
c Enter the measured Load Curve.lcd 10 0.0 2e-4 0.0 0.4e-3 0 0.6e-3 0
160
0.8e-3 0 1.0e-3 0 1.2e-3 0 1.4e-3 0 1.6e-3 0 1.8e-3 0 2.0e-3 1 2.2e-3 2 2.4e-3 4 2.6e-3 6 2.8e-3 10 3e-3 14 3.2e-3 19 3.4e-3 23 3.6e-3 30 3.8e-3 37 4e-3 47 4.2e-3 58 4.4e-3 72 4.6e-3 88 4.8e-3 107 5e-3 129 5.2e-3 152 5.4e-3 177 5.6e-3 203 5.8e-3 230 6e-3 257 6.2e-3 282 6.4e-3 306 6.6e-3 331 6.8e-3 354 7e-3 374 7.2e-3 392 7.4e-3 408 7.6e-3 422 7.8e-3 436 8e-3 449 8.2e-3 461 8.4e-3 473 8.6e-3 483 8.8e-3 493 9e-3 503 9.2e-3 514
161
9.4e-3 525 9.6e-3 536 9.8e-3 546 10e-3 558 10.2e-3 568 10.4e-3 579 10.6e-3 590 10.8e-3 600 11e-3 610 11.2e-3 620 11.4e-3 629 11.6e-3 638 11.8e-3 647 12e-3 656 12.2e-3 664 12.4e-3 673 12.6e-3 682 12.8e-3 691 13e-3 699 13.2e-3 708 13.4e-3 718 13.6e-3 726 13.8e-3 734 14e-3 742 14.2e-3 748 14.4e-3 753 14.6e-3 757 14.8e-3 759 15e-3 761 15.2e-3 760 15.4e-3 759 15.6e-3 755 15.8e-3 753 16e-3 746 16.2e-3 737 16.4e-3 729 16.6e-3 719 16.8e-3 708 17e-3 695 17.2e-3 682 17.4e-3 669 17.6e-3 657 17.8e-3 643
162
18e-3 630 18.2e-3 61518.4e-3 60318.6e-3 58918.8e-3 57519e-3 56119.2e-3 54819.4e-3 53419.6e-3 52019.8e-3 50520e-3 49120.2e-3 47820.4e-3 46520.6e-3 45120.8e-3 43921e-3 42621.2e-3 41321.4e-3 40221.6e-3 39021.8e-3 37822e-3 36822.2e-3 35622.4e-3 34422.6e-3 33322.8e-3 32223e-3 31023.2e-3 29823.4e-3 28523.6e-3 27323.8e-3 26124e-3 24924.2e-3 23724.4e-3 22624.6e-3 21324.8e-3 20125e-3 18925.2e-3 17925.4e-3 16725.6e-3 15725.8e-3 14626e-3 13726.2e-3 12826.4e-3 119
163
26.6e-3 11026.8e-3 10227e-3 9527.2e-3 8827.4e-3 8227.6e-3 7527.8e-3 6928e-3 6328.2e-3 5828.4e-3 5228.6e-3 4728.8e-3 4329e-3 3829.2e-3 3229.4e-3 2829.6e-3 2529.8e-3 2130e-3 1730.2e-3 1430.4e-3 1030.6e-3 730.8e-3 531e-3 231.2e-3 031.4e-3 031.6e-3 031.8e-3 032e-3 0;
c Define Asphalt-Concrete Layer.block1 3 31;1 16 19 22 37;1 4;
0.0 8.0 120.0;-72.0 -6 0 6 72.0;0.0 [%t1];
sii 1 2 ;2 4;1 1;2 s;
sii 1 3;1 5;2 2;1 s;
164
nr 1 1 1 3 1 2nr 1 1 1 1 5 2nr 3 1 1 3 5 2b 1 1 1 3 1 2 dy 1 rx 1;b 1 1 1 1 5 2 dx 1 ry 1;b 1 5 1 3 5 2 dy 1;b 3 1 1 3 5 2 dx 1 dy 1;
mate 1endpart
c Define Base Layer and subgrade .block1 41;1 25;1 5 15;
0.0 120;-72 72;[%t1] [%t1+%t2] [%t1+%t2-40];
mt 1 1 1 2 2 2 2mt 1 1 2 2 2 3 3
sii 1 2;1 2;1 1;1 m;
nr 1 1 1 1 2 3nr 2 1 1 2 2 3nr 1 2 1 2 2 3 nr 1 1 1 2 1 3c nr 1 1 3 2 2 3c Boundary Conditionsb 1 1 1 1 2 3 dx 1 dy 1 ry 1;b 2 1 1 2 2 3 dx 1 dy 1;b 1 2 1 2 2 3 dx 1 dy 1;b 1 1 1 2 1 3 dx 1 dy 1;b 1 1 3 2 2 3 dx 1 dy 1 dz 1 rx 1 ry 1 rz 1;
endpart
c Define Loading Plate (R=6 in).block
165
1 6 11 16 21;1 6 11 16 21;1 3;
-3. -3. 0. 3. 3.;-3. -3. 0. 3. 3.;0. 1.;
de 1 1 1 2 2 2de 4 1 1 5 2 2de 1 4 1 2 5 2de 4 4 1 5 5 2de 1 0 0 3 0 0
sf 2 1 1 4 1 2cy 0. 0. 0. 0. 0. 1. 6sf 1 2 1 1 4 2cy 0. 0. 0. 0. 0. 1. 6sf 2 5 1 4 5 2cy 0. 0. 0. 0. 0. 1. 6sf 5 2 1 5 4 2 cy 0. 0. 0. 0. 0. 1. 6
sii ; ; 1 1; 2 m;
c Ddfine applied pressure region.orpt - 0.0 0.0 -1000000 pr 1 1 2 5 5 2 1 0.145624;
mate 4endpart
merge stp 0.01
166
VITA
Gergis W. William was born in Alexandria, Egypt, on August 1, 1973. He received a Bachelor of
Science in Civil Engineering with honors from Alexandria University, Egypt. After his graduation
in June 1995, he joined the Consultative Bureau for Civil Constructions, Alexandria, as a structural
design engineer. During his employment, he took charge of several design projects which included
design of different types of hydraulic structures (Barrages, Syphons, Aqueducts, and pipelines),
bridges (over 20 bridges), roads (over 20 rural roads), three high-rise buildings, and Three steel
structures. In January 1998, he joined West Virginia University as a graduate research assistant in
the Department of Civil and Environmental Engineering, where he pursued a Master Degree in Civil
Engineering.
Publications:
1. Shoukry, S. N., G. W. William. “Performance Evaluation of Backcalculation Algorithms
Through 3D Finite Element Modeling of Pavement Structures”. Paper No. 991277, Accepted
for presentation and publication at the 78th Annual Transportation Research Board Meeting,
Washington, D.C., January, 1999.
2. Shoukry, S.N., and G. W. William. “Dynamic Backcalculation of Pavement Layer Moduli”.
Proceedings: ASNT Spring Conference and 8th Annual Research Symposium, American
Society of Nondestructive Testings, Florida, March 1999.
3. Shoukry, S.N., Gergis W. William, and D. R. Martinelli. “Assessment of the Performance of
Rigid Pavement Backcalculation Through Finite Element Modeling”. Proceedings of the
SPIE conference on Nondestructive Evaluation of Bridges and Highways III, California,
March, 1999, pp. 146-156.
4. Shoukry, S. N., and G. William. “3D FEM Analysis of Load Transfer Efficiency”.
Proceedings of the First National Symposium on 3D Finite Element Modeling for Pavement
Analysis & Design. Charleston, West Virginia, November, 1998, pp. 40-50.
5. Shoukry, S.N., D.R. Martinelli, G.W. William, and M. R. Fahmy. Applications of LS-DYNA
in Pavement Analysis and Design”. Proceedings: Fifth International LS-DYNA User’s
Conference, Detroit, Michigan, 1998.