April 2006
Research Report: UCPRC- RR- 2005- 06
Calibration of Incremental- Recursive
Flexible Damage Models in CalME
Using HVS Experiments
Authors:
Per Ullidtz, Dynatest Consulting Inc
John Harvey, UC Davis
Bor- Wen Tsai, UC Berkeley
Carl Monismith, UC Berkeley
This work was completed as part of Partnered Pavement
Research Program Strategic Plan Element 4.1:
“ Development of the First Version of a Mechanistic- Empirical Pavement Rehabilitation,
Reconstruction and New Pavement Design Procedure for Rigid and Flexible Pavements
( pre- Calibration of AASHTO 2002)”
PREPARED FOR:
California Department of Transportation
Division of Research and Innovation
Office of Roadway Research
PREPARED BY:
University of California
Pavement Research Center
Berkeley and Davis
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DOCUMENT RETRIEVAL PAGE Report No: UCPRC- RR- 2005- 06
Title: Calibration of Incremental- Recursive Flexible Damage Models in CalME Using HVS Experiments
Authors: Per Ullidtz, Dynatest Consulting Inc.; John Harvey, UC Davis; Bor- Wen Tsai, UC Berkeley; and Carl
Monismith, UC Berkeley
Prepared for:
California Department of
Transportation
Division of Research and Innovation
Office of Roadway Research
FHWA No.:
F/ CA/ RR/ 2006/ 49
Date:
Stage 5, May 2007
Contract number:
UCPRC- RR- 2005- 06
Client Reference No:
UCPRC- RR- 2005- 06
Status:
Final, Caltrans approved
Abstract: Caltrans is in the process of implementing Mechanistic- Empirical design procedures. All mechanistic-empirical
methods must be validated/ calibrated against the behavior of real pavements. This should be done before
implementing models in design methods to ensure that designs will be reasonable. The Heavy Vehicle Simulator
( HVS) provides a first step in this validation/ calibration process. The short test section can be carefully constructed
with well characterized materials and instrumented to measure the pavement response. The climatic conditions may
be controlled or monitored closely and all load applications are known exactly. The pavement may also be tested
until it fails. The HVS may be seen as “ large scale” laboratory equipment, between the “ small scale” laboratory
equipment ( triaxial tests, bending tests etc.) and the reality of real pavements, which have uncertainties regarding
materials, loads and climatic conditions. The two HVSs owned by Caltrans have been used on 27 flexible pavement
test sections, with varying combinations of asphalt and granular layers. Temperature control was used during the
tests. Most sections have been instrumented with Multi- depth Deflectometers ( MDDs) to compare the measured
pavement deflections ( at several depths) to the deflections predicted by mechanistic methods, during the full
duration of tests carried to “ failure” ( in terms of rutting or cracking). Results from mechanistic models have been
compared with the deflection measurements and performance as a first step prior to empirical calibrations with field
results. The complete time history of each test has been compared rather than just the beginning and end
measurements. This report presents the validation of the mechanistic models for asphalt fatigue and for permanent
deformation with the HVS test results.
Keywords: Mechanistic- empirical, full- scale- testing, calibration, response, performance, flexible pavement
.
Proposals for implementation: None
Related documents: Kannekanti, V., and Harvey, J. June 2005. Sensitivity Analysis of 2002 Design Guide Rigid
Pavement Distress Prediction Models. Draft report prepared for the California Department of Transportation. Pavement
Research Center, Institute of Transportation Studies, University of California Berkeley, University of California Davis.
UCPRC- RR- 2005- 01
Signatures:
P. Ullidtz
Principal Author
J. Harvey
Co- principal
Investigator
C. L. Monismith
Co- principal
Investigator
D. Spinner
Editor
M. Samadian
Caltrans Contract
Mgr.
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DISCLAIMER
The contents of this report reflect the views of the authors who are responsible for the facts and
accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of
the State of California or the Federal Highway Administration. This report does not constitute a standard,
specification, or regulation.
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EXECUTIVE SUMMARY
The first step in a mechanistic- empirical ( ME) pavement design or evaluation is to calculate pavement
response — in terms of stresses, strains, and/ or displacements — using a mathematical ( or mechanistic) model.
In the second step, the calculated response is used as a variable in empirical relationships to predict structural
damage ( decrease in moduli or cracking) and functional damage ( rutting and roughness) to the pavement.
Both of these steps must be reasonably correct. If the calculated response bears little resemblance to
the pavement’s actual response, there is no point in trying to use the calculation to predict future damage to the
pavement. In other words, only if the calculated response is reasonably correct does it make sense to try to
relate the damage to the pavement response.
This study’s purpose was to evaluate the overall trends of the damage models in the draft software
package called CalME against those of Heavy Vehicle Simulator ( HVS) tests for which data was available. The
report presents simulations of HVS tests using the set of distress models included in CalME. These models are
for the typical flexible pavement distresses observed in California: asphalt fatigue, asphalt rutting, unbound
layers rutting, and reflection cracking. An Incremental- Recursive approach ( see item 4 below) was used for the
simulations included in this report because this approach can accurately indicate pavement condition at
different points during a pavement’s life.
Approaches Included in CalME
CalME software provides the user with four approaches to evaluating or designing a flexible
pavement structure:
1. Caltrans’ current methods: the R- value method for new flexible structures and the deflection
reduction method used by Caltrans for overlay thickness design for existing flexible pavements.
2. “ Classical” Mechanistic- Empirical ( ME) Design, which is based largely on the Asphalt Institute
Method which uses very simple methods to characterize materials, climate, and traffic inputs.
3. An Incremental approach, which is a standard Miner’s Law approach that permits damage
calculation for the axle load spectrum and expected temperature regimes, but without updating of
the material’s properties through the life of the project. This is an approach similar to the one for
cracking of asphalt included in the NCHRP 1- 37A Pavement Design Guide, also referred to as the
Mechanistic- Empirical Design Guide ( MEPDG). This type of approach is calibrated against an
end failure state ( such as, 25 percent cracking of the wheelpath) and it assumes a linear
accumulation of damage to get to that state.
4. An Incremental- Recursive approach in which the materials properties of the pavement — in terms
of damage and aging — are updated as the pavement life simulation progresses.
The current Caltrans methods and the Classical method are very fast in terms of computational time,
and user input is highly simplified. In CalME both of these options perform a “ design” function, calculating
and presenting pavement structures that meet the design requirements for the design traffic, materials, and
climate.
For design practice the Classical and Caltrans methods should be used to produce a set of potential
pavement sections. The Incremental- Recursive method should then be run to check the lowest- cost alternative
designs in the set to be certain that they meet design requirements. Once the final design has been selected, its
Incremental- Recursive output provides a prediction of the pavement condition across its entire life. The
prediction of the pavement’s condition through its life from the Incremental- Recursive output can be used as
the first prediction for use in a pavement management system.
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Use of Heavy Vehicle Simulator Data to Evaluate Models
The Incremental- Recursive models included in CalME were used to predict performance for all
twenty- seven of the flexible pavement HVS tests performed so far as part of the Accelerated Pavement Testing
( APT) program operated for the California Department of Transportation ( Caltrans) by the University of
California Pavement Research Center ( UCPRC). The HVS test data in this report come from tests performed
between the years 1995 and 2004. The HVS response data and corresponding laboratory test data were
extracted from the UCPRC HVS database.
During HVS testing, pavement response - in terms of deflections at the surface and/ or at multiple
depths - may be measured. A Road Surface Deflectometer ( RSD) measures deflections at the surface and is
similar to the Benkelman Beam used to develop the current Caltrans overlay design method in the 1950s. A
Multi- depth Deflectometer ( MDD) measures deflections at multiple depths.
In order to accurately predict the gradual degradation of a pavement, the response model must predict
measured deflections with reasonable accuracy. Although a model might predict deflections correctly, this
ability does not guarantee that the model can also accurately predict the stresses and strains in all the pavement
layers. However, the opposite is true: if a model predicts deflections incorrectly it will also produce incorrect
stress and strain predictions. Therefore when attempting to calibrate ME models from HVS tests, the research
team’s first concern was to make sure that resilient deflections were predicted reasonably well for the duration
of the test and for all load levels. This prediction depended on the moduli of all the pavement layers and on the
changes to the moduli caused by fatigue damage, slip between asphalt layers, non- linear elastic characteristics
of unbound layers, and the effect of confinement on granular layers. Once reasonably good agreement was
achieved between the measured and the calculated deflections then the permanent deformation models could
be calibrated with confidence.
Differences in boundary conditions, strain levels, and loading times, all of which can produce varied
effects in materials, result in differing moduli values. In this study, methods used for determining moduli ( also
referred to as “ stiffness”) values included backcalculation from Falling Weight Deflectometer ( FWD) and
MDD data, and direct measurement — employing laboratory triaxial testing for unbound materials and flexural
frequency sweep testing for asphaltic materials. Stiffnesses for the study’s asphalt materials were taken
primarily from flexural frequency sweep data. Stiffnesses for the unbound layers came primarily from MDD
data backcalculation.
In practice the FWD is seen by the research team as the primary tool for stiffness measurement of all
layers already constructed because it is used in the field on the full pavement system; this is thought to be
appropriate because the boundary conditions are those of real pavement, and most Caltrans’ work will be
rehabilitation and reconstruction with at least some layers already in place. The research team saw the flexural
beam test as the primary means for measuring the stiffness and fatigue characteristics of asphalt overlay
materials for new layers. For new pavement construction, a combination of FWD testing on existing
pavements and triaxial testing can be used to develop a database of stiffnesses of unbound granular layers and
subgrades based on different characteristics, such as Unified Soil Classification System ( USCS) classification.
The purpose of this study was to evaluate the overall trends of the CalME damage models against
those of the HVS test results. This was accomplished by comparing deflections calculated using moduli
determined from initial measurements and CalME damage calculations with measured deflections under HVS
loading. The results presented in this report verify that, overall, the CalME damage trends for deflection and
permanent deformation under loading are correct.
During HVS testing, deflections often increase markedly, sometimes becoming more than twice as
high at the end of the test as they were at the beginning because of damage to the asphalt concrete caused by
the repeated wheel loads. However, the flexible pavement design model of the NCHRP 1- 37A Design Guide
does not consider any decrease in the asphalt modulus as a result of fatigue damage ( except for rehabilitation
designs). In fact, the NCHRP 1- 37A Design Guide includes a model for aging that predicts a continuous
increase in the stiffness of the asphalt concrete layers across the life of the pavement, which results in
increased stiffness and smaller predicted deflections as the pavement is subjected to trafficking. While the
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aging is potentially important, the effect of updating stiffness for aging and not updating it for fatigue damage
results in calculation of very unrealistic elastic responses in the pavement during its life. This makes it
impossible to use the model to simulate an HVS test and, inversely, to use HVS tests to calibrate the model,
except for pavements with extremely thick asphalt concrete layers where little fatigue should develop.
Results of HVS Test Simulation Using CalME
The series of HVS tests in this report are grouped here by goals, which are defined as follows:
• Goal 1, a comparison of new pavement structures with and without asphalt- treated permeable base
( ATPB) layer under dry conditions, moderate temperatures, 20° C ( HVS Sections 500RF, 501RF,
502CT, 503RF)
• Goal 3 Cracking, a comparison of reflection cracking performance of ARHM- GG ( the acronym
ARHM, asphalt rubber hot- mix gap- graded, refers to the material specification at the time of
construction in April 1997.) and dense- graded asphalt concrete ( DGAC) overlays placed on the
cracked Goal 1 sections, dry conditions, 20° C ( HVS Sections 514RF, 515RF, 517RF, 518RF)
• Goal 3 Rutting, a comparison of rutting performance of ARHM- GG and DGAC overlays of
previously untrafficked areas of Goal 1 pavements, dry conditions, 40° C or 50° C at 50- mm depth,
four different tire/ wheel types ( HVS Sections 504RF, 505RF, 506RF, 507RF, 508RF, 509RF, 510RF,
511RF, 512RF, 513RF)
• Goal 5, a comparison of new pavement structures with and without ATPB layer under wet conditions
( water introduced into base layers), moderate temperatures, 20° C ( HVS Sections 543RF, 544RF,
545RF)
• Goal 9, initial cracking of asphalt pavement with six replicate sections in preparation for later
overlay, new pavement, ambient rainfall, 20° C ( HVS Sections 567RF, 568RF, 569RF, 571RF,
572RF, 573RF)
CalME models that the simulations evaluated included:
• A stiffness model for asphalt concrete modulus as a function of reduced time based on the model
used in NCHRP 1- 37A Design Guide, with some adjustments based on field observations;
• An asphalt concrete fatigue model that predicts damage, in terms of decrease in modulus, as a
function of load repetitions, tensile strain, and stiffness, using parameters from flexural beam testing;
• An ability to model partial bonding between asphalt concrete layers;
• A model that adjusts the stiffness of unbound layers as a function of the combined bending resistance
( a function of their stiffness and thickness) of the layers above them;
• A model that adjusts the stiffness of unbound layers as a function of load level, with an increased load
level increasing the moduli for the granular layers and decreasing modulus for the subgrade ( clay);
• A permanent deformation model for asphalt concrete as a function of permanent shear strain near the
pavement surface beneath the edge of a tire, with permanent shear strain predicted by the calculated
elastic shear strain and elastic shear stress;
• A permanent deformation model for unbound layers as a function of the vertical strain at the top of
each layer; and
• A reflection cracking model based on tensile strain calculated using a regression equation developed
from a large number of Finite Element analyses and the same damage parameters developed for
asphalt concrete fatigue.
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Response Models
During most of the HVS tests, resilient deflections were measured using the RSD and the MDD. The
following figure summarizes the measured deflections with those calculated using CalME damage models for
all of the sections in terms of the ratio of the initial deflections before HVS loading to the final deflections at
the end of the loading.
Assumptions made regarding differences between moduli from different measurement methods, shift
factors, slip between layers, and non- linear elasticity of unbound layers to obtain reasonably good agreement
between measured resilient deflections and those calculated with CalME are discussed in the report.
The observed behavior of the aggregate base ( AB) and subbase layers under HVS loading contradicts
the commonly accepted wisdom for granular materials, which is based primarily on triaxial testing. The
observed behavior is discussed in the report and is modeled in CalME.
Using these assumptions, it was possible to model resilient deflections reasonably well for the full
history of all of HVS test sections using the layered elastic analysis program ( LEAP) response model.
Final/ initial deflection
0.00
1.00
2.00
3.00
4.00
5.00
0.00 1.00 2.00 3.00 4.00 5.00
Measured
Calculated
RSD
MDD
Equality
Figure ES- 1. Ratio of initial to final deflection.
Damage of Asphalt Materials
Controlled strain fatigue tests conducted on beams were used to derive model parameters for the
decrease in modulus for all the asphalt materials — except for the ATPB, where laboratory tests were not
available. Working under the assumptions used in the modeling and using a shift factor with these damage
models produced the correct changes in resilient deflections during all the HVS tests.
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For reflection cracking, a simple model was used to calculate the strains in an overlay caused by
existing cracking in the original top layer. Using this model and the laboratory fatigue model, reasonably
correct resilient deflections were also predicted.
Relating visual cracking to the calculated asphalt damage proved to be difficult, and no single
relationship could be derived. Goal 1 and Goal 5 showed differences between the drained and the undrained
sections; for Goal 3 Cracking, the increase in visual cracking was quicker than for Goal 1 and Goal 5; and for
Goal 9, visual cracking occurred at much less calculated damage than for the other experiments.
It is possible that the relationship between visual cracking and calculated damage depends on the
thickness of the asphalt layers, and that reflection cracks and cracks in new pavements develop differently. It is
also possible that the development of visual cracking depends on factors that the simulations did not consider.
No single relationship could be established between the relative increase in deflection and the amount
of surface cracking ( shown in the following figure), but it may be noted that visible cracking was not observed
until deflection had increased by 50 percent or more.
Cracking versus relative deflection
0
2
4
6
8
10
12
1 1.5 2 2.5 3 3.5 4 4.5
Deflection/ initial deflection
Cracking m/ m2
500RF
501RF
502CT
503RF
514RF
515RF
517RF
518RF
543RF
544RF
545RF
567RF
568RF
569RF
571RF
572RF
573RF
Figure ES- 2. Cracking versus increase in deflection.
Permanent Deformation of Asphalt
The following figure shows the measured and predicted final permanent deformation of the asphalt
layers from Goal 1, Goal 3, and Goal 5, where data were available. Permanent deformation was calculated for
the upper 100 mm of the asphalt layer( s).
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Permanent deformation in AC ( pro rated)
0
2
4
6
8
10
12
14
16
18
20
0 2 4 6 8 10 12 14 16 18 20
Measured, mm
Calculated, mm
Equality
20 º C at surface
45 or 50 º C at surface
Figure ES- 3. Measured and predicted final permanent deformation of asphalt.
In Figure ES- 3, the 20° C outlier point with a measured deformation greater than the calculated one is
Section 543RF, which was a wet, drained test where the ATPB stripped and collapsed. The two relatively low
values at high temperatures are from the test with a bias- ply dual tire and from the test with an aircraft tire. The
correlation coefficient between measured and calculated values is 0.82 and the standard error of estimate is 2.2
mm.
The parameters for predicting permanent shear strain were based on Repeated Simple Shear Tests at
Constant Height ( RSST- CH).
Permanent Deformation of Granular Layers
The permanent deformation of the granular layers for Goal 1, Goal 3, and Goal 5 are shown with
average measured values in Figure ES- 4. It should be noted that the permanent deformations are rather small
except for Section 543RF, the wet drained section, where the permanent deformation includes part of the
ATPB.
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Permanent deformation of granular layers
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14
Measured, mm
Calculated, mm
Goal 1
Goal 3
Goal 5
Equality
Figure ES- 4. Final permanent deformation of granular layers.
Permanent deformation was calculated both at the top of the AB and at the top of the aggregate
subbase ( ASB). The two materials are rather similar and might have been treated as a single layer.
Permanent Deformation of Subgrade
The final permanent deformation of the subgrade is even smaller than that of the granular layers, with
a maximum measured value of less than 2 mm. In addition, the data scatter is as large as that of the granular
layers, with an average coefficient of variation of 70 percent. This is far from ideal for the calibration of a
subgrade permanent deformation model. The mean measured and predicted final deformations are shown in
Figure ES- 5. The subgrade and granular results indicate that rutting of the unbound layers is probably not a
major concern for existing Caltrans pavements that need rehabilitation unless there is poor drainage or
significant amounts of water are entering cracks in the asphalt layers.
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Permanent deformation of subgrade
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Measured, mm
Calculated, mm
Figure ES- 5. Final permanent deformation of the subgrade.
Total Permanent Deformation at Pavement Surface
Figure ES- 6 shows the final calculated permanent deformation at the pavement surface versus the
measured final deformation averaged from profilometer measurements along the HVS test area.
Calculated final permanent deformations that underestimated the measured final permanent
deformations were worst for the Goal 5 sections in which water was dripped into the base layers, especially for
the drained section, 543RF in which the ATPB stripped.
The correlation coefficient between measured and calculated deformations is 0.61 and the standard
error of estimate is 2.6 mm.
Conclusions and Recommendations
The overall results from this study indicate that Incremental- Recursive models provide reasonable
results when predicting the response and performance of pavement under HVS loading. However, now that the
models have been shown to match the mechanics of the flexible pavements under HVS loading, additional
work remains to be done before these models can be used for pavement design and performance prediction.
There are significant differences between HVS testing and field results, and the approach used in this
study has limitations because of those differences. These include the effects of age and of seasonal variation
that have not been quantified in the simulations because HVS tests are of relatively short duration and are
performed, to varying degrees, in controlled environments. Field calibration is required to evaluate the
response difference between the field pavement and the Incremental- Recursive simulation that should be
attributed to aging and seasonal effects. It is likely that the effects of aging can be dealt with using shift factors.
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Permanent deformation at pavement surface
0.0
5.0
10.0
15.0
20.0
0.0 5.0 10.0 15.0 20.0
Measured, mm
Calculated, mm
Goal 1 Goal 3 45/ 55° C
Goal 3 20° C Goal 5
Goal 9 Equality
Figure ES- 6. Final permanent deformation at the pavement surface.
The effects of rest periods between loadings and of faster traffic have also not been included in the
calibration. It is expected that different shift factors will result because of rest periods and different trafficking
patterns.
Lastly, moduli from frequency sweep data, triaxial tests, FWD tests, and MDD deflections used in this
study are similar but they are not identical. The NCHRP 1- 37A Design Guide study proposes relying primarily
on triaxial testing to characterize the stiffness of flexible pavement layers and the permanent deformation
parameters of asphaltic materials.
Recommendations are made in this report for the most practical and economical methods for
characterizing materials based on the understanding that the majority of Caltrans’ work over the next several
decades will be rehabilitation and reconstruction, with some addition of lane capacity.
Recommendations are also made regarding the next steps to develop the CalME models. These
include:
1. Perform a sensitivity analysis using “ typical” values for properties and climate in the database
established to date, and compare the results from the Classical, Incremental, and Incremental-
Recursive methods included in CalME to evaluate reasonableness of sensitivity across the three
methods.
2. Simulate mainline highway case studies and test track data ( such as WesTrack and NCAT track)
using the recommended methods for characterizing flexible pavement materials in conjunction
with the Incremental- Recursive models in CalME, and compare the simulated and measured
results, as was done for the HVS results presented in this report. This step will provide validation
for the models
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3. Address the variability of the input parameters ( moduli, thicknesses, traffic loading, etc.) and
uncertainty on the damage models. Several approaches should be considered, including the
approach used in the NCHRP 1- 37A method.
4. Make final decisions regarding use of cemented layers in the flexible pavement structure, then
calibrate. It is generally recommended that “ semi- rigid” pavements, in which asphalt concrete is
placed directly on cement- treated base ( CTB) or lean concrete base ( LCB), not be used because of
the relatively quick reflection of shrinkage cracks. However, because Caltrans has used semi- rigid
pavements in the past and they remain in the current design method, it is therefore important to
have models for the response and performance of these layers. The models in the NCHRP 1- 37A
Report should be the starting point for such a validation- and- calibration exercise.
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TABLE OF CONTENTS
Executive Summary........................................................................................................................ .................... iv
Approaches Included in CalME ...................................................................................................................... iv
Use of Heavy Vehicle Simulator Data to Evaluate Models ............................................................................. v
Results of HVS Test Simulation Using CalME .............................................................................................. vi
Response Models......................................................................................................................... .............. vii
Damage of Asphalt Materials ..................................................................................................................... vii
Permanent Deformation of Asphalt ........................................................................................................... viii
Permanent Deformation of Granular Layers................................................................................................ ix
Permanent Deformation of Subgrade ........................................................................................................... x
Total Permanent Deformation at Pavement Surface.................................................................................... xi
Conclusions and Recommendations................................................................................................................ xi
List of Figures........................................................................................................................ .......................... xvii
List of Tables ............................................................................................................................... .................... xxv
1.0 Introduction................................................................................................................... ......................... 1
1.1 Models and Approaches Included in CalME .......................................................................................... 1
1.1.1 Validation Using Heavy Vehicle Simulator Data .......................................................................... 2
1.2 HVS tests.......................................................................................................................... ...................... 4
1.2.1 Goal 1 and Goal 3 Tests................................................................................................................. 4
1.2.2 Goal 5 Tests ............................................................................................................................... ... 6
1.2.3 Goal 9 Tests ............................................................................................................................... ... 7
1.3 Response and Damage Models ............................................................................................................... 8
1.3.1 Asphalt Modulus ............................................................................................................................ 8
1.3.2 Fatigue........................................................................................................................ ................. 21
1.4 Weak Bonding........................................................................................................................ .............. 24
1.5 Unbound Layers ............................................................................................................................... .... 25
1.5.1 Triaxial Tests.......................................................................................................................... ..... 25
1.5.2 Influence of Stiffness of Layers above an Unbound Layer.......................................................... 26
1.5.3 Influence of Load Level ............................................................................................................... 39
1.6 Permanent Deformation ........................................................................................................................ 40
1.6.1 Asphalt ............................................................................................................................... ......... 40
1.6.2 Unbound Materials...................................................................................................................... 47
1.7 Reflection Cracking .............................................................................................................................. 48
2.0 Goal 1 Cracking Test Simulations ........................................................................................................ 50
2.1 Goal 1 Resilient Deformations.............................................................................................................. 50
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2.1.1 Section 501RF Resilient Deflections ( Undrained)....................................................................... 50
2.1.2 Section 503RF Resilient Deflections ( Undrained)....................................................................... 56
2.1.3 Section 500RF Resilient Deflections ( Drained)........................................................................... 60
2.1.4 Section 502CT Resilient Deflections ( Drained)........................................................................... 65
2.2 Visual Cracking Versus Damage of the Top Asphalt Layer, Goal 1 .................................................... 69
2.3 Goal 1 Permanent Deformation............................................................................................................. 72
2.3.1 Section 501RF Permanent Deformations..................................................................................... 73
2.3.2 Section 503RF Permanent Deformations..................................................................................... 75
2.3.3 Section 500RF Permanent Deformations..................................................................................... 77
2.3.4 Section 502CT Permanent Deformations..................................................................................... 79
3.0 Goal 3 Reflection cracking tests............................................................................................................ 81
3.1 Resilient Deflections ............................................................................................................................. 81
3.1.1 Section 517RF DGAC on Section 501RF Resilient Deflections ................................................. 81
3.1.2 Section 518RF ARHM on Section 503RF Resilient Deflections................................................. 86
3.1.3 Section 514RF DGAC on Section 500RF Resilient Deflections ................................................. 91
3.1.4 Section 515RF ARHM on Section 502CT Resilient Deflections ................................................ 96
3.2 Visual Cracking Versus Damage of the Overlay, Goal 3, 20 º C.......................................................... 101
3.3 Permanent Deformation Goal 3, 20 º C................................................................................................. 104
3.3.1 Section 517RF 75- mm DGAC Permanent Deformations .......................................................... 105
3.3.2 Section 518RF 38- mm ARHM Permanent Deformation ........................................................... 107
3.3.3 Section 514RF 75- mm DGAC Permanent Deformations .......................................................... 109
3.3.4 Section 515RF 38- mm ARHM Permanent Deformations ......................................................... 112
4.0 Goal 3 Rutting experiments................................................................................................................. 114
4.1 Section 504RF No Overlay, Wide- Base Single Tire........................................................................... 115
4.2 Section 505RF DAGC Overlay, Bias- Ply Dual Tire........................................................................... 117
4.3 Section 506RF DGAC Overlay, Radial Dual Tire .............................................................................. 119
4.4 Section 507RF DGAC Overlay, Wide- Base Single Tire .................................................................... 121
4.5 Section 508RF ARHM Overlay, Wide- Base Single Tire.................................................................... 123
4.6 Section 509RF ARHM Overlay, Radial Dual Tire ............................................................................. 125
4.7 Section 510RF ARHM Overlay, Radial Dual Tire ............................................................................. 127
4.8 Section 511RF ARHM Overlay, Wide- Base Single Tire.................................................................... 129
4.9 Section 512RF DGAC Overlay, Wide- Base Single Tire .................................................................... 131
4.10 Section 513RF DGAC Overlay, Aircraft Tire..................................................................................... 133
5.0 Goal 5 Wet conditions..................................................................................................................... ... 135
5.1 Section 543RF ARHM Overlay, Drained ........................................................................................... 136
5.2 Section 544RF ARHM Overlay, Undrained ....................................................................................... 145
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5.3 Section 545RF DGAC Overlay, Undrained ........................................................................................ 153
5.4 Visual Cracking versus Damage of the Top Asphalt Layer, Goal 5 ................................................... 160
6.0 Goal 9 Modified Binder ( MB) road, initial tests ................................................................................. 162
6.1 Materials Characterization .................................................................................................................. 162
6.2 Section 567RF MB Road .................................................................................................................... 169
6.3 Section 568RF MB Road .................................................................................................................... 173
6.4 Section 573RF MB Road .................................................................................................................... 176
6.5 Section 571RF MB Road .................................................................................................................... 179
6.6 Section 572RF MB Road .................................................................................................................... 183
6.7 Section 569RF MB Road .................................................................................................................... 186
6.8 Visual Cracking Versus Damage of the Top Asphalt Layer, Goal 9 .................................................. 190
7.0 Summary and recommendations ......................................................................................................... 191
7.1 Shift Factors and Damage Equations Used in Simulations ................................................................. 191
7.2 Response Model.......................................................................................................................... ....... 192
7.3 Damage of Asphalt Materials.............................................................................................................. 197
7.4 Permanent Deformation of Asphalt..................................................................................................... 199
7.5 Permanent Deformation of Granular Layers ....................................................................................... 201
7.6 Permanent Deformation of Subgrade.................................................................................................. 203
7.7 Total Permanent Deformation at Pavement Surface ........................................................................... 205
7.8 Recommendations ............................................................................................................................... 207
8.0 References..................................................................................................................... ..................... 209
9.0 Appendix....................................................................................................................... ..................... 212
9.1 Glossary ............................................................................................................................... .............. 212
9.2 List of Units ............................................................................................................................... ........ 214
9.3 List of Parameters in Equations .......................................................................................................... 214
9.4 Parameter Values Used in Simulations ............................................................................................... 216
9.5 Section 569RF Simulated with a CTB Model from an HVS Nordic Experiment............................... 217
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xvii UCPRC- RR- 2005- 06
LIST OF FIGURES
Figure ES- 1. Ration of final to initial deflection .........................……………………………………………... vii
Figure ES- 2. Cracking versus increase in deflection ..........................……………………………………...… viii
Figure ES- 3. Measured and predicted final permanent deflection of asphalt ........................... .....…………...... ix
Figure ES- 4. Final permanent deformation of granular layers .............................……………………………… x
Figure ES- 5. Final permanent deformation of the subgrade .............................……………………………...… xi
Figure ES- 6. Final permanent deformation at the pavement surface............................……………………..… xii
Figure 1. Layout of 20° C test sections. Goal 3 rutting sections are distributed in the area between the 20° C test
sections. ............................................................................................................................... ....................... 4
Figure 2. Drip watering system for Goal 5 tests. ................................................................................................. 7
Figure 3. Layout of Goal 9 test sections. ............................................................................................................. 9
Figure 4. Example of modulus versus reduced time relationship. ..................................................................... 10
Figure 5. Modulus versus temperature for different viscosity versus temperature relationships....................... 12
Figure 6. Frequency sweep data for Goal 1 and Goal 3 materials compared to models. ................................... 13
Figure 7. Example of input parameters for the modulus- versus- reduced time relationship for the AC bottom
layer. 21
Figure 8. Example of damage versus number of load applications. .................................................................. 23
Figure 9. Example of Equation 6 damage parameters of AC bottom layer ( Goal 1)......................................... 24
Figure 10. Simple Drucker- Prager failure condition.......................................................................................... 28
Figure 11. EAC 10,000 MPa, no slip, 40 kN load. .............................................................................................. 29
Figure 12. EAC 10,000 MPa, slip, 40 kN............................................................................................................ 30
Figure 13. EAC 2,000 MPa, slip, 40 kN.............................................................................................................. 31
Figure 14. EAC 2,000 MPa, slip, 100 kN load. ................................................................................................... 33
Figure 15. Displacement field in particulate sample........................................................................................... 34
Figure 16. Displacement field in elastic solid ( FEM). ........................................................................................ 35
Figure 17. Modulus of Layer 2 as a function of the stiffness of the asphalt layers, for the undrained sections. 36
Figure 18. Modulus of Layer 2 as a function of the stiffness of the asphalt layers, for the drained sections. ... 37
Figure 19. Modulus of subgrade as a function of the stiffness of the pavement layers. .................................... 37
Figure 20. Results of RSST- CH tests. [ Note: FMFC indicates field- mixed field compacted specimen taken by
coring the pavement. AV5.5 indicates cores with approximately 5.5 percent air- voids. Each title in the
legend indicates the RSST- CH test temperature ( 40, 50, or 60 ° C) and average shear stress ( MPa).]...... 42
Figure 21. Normalized plastic strain versus number of load repetitions. ( Note: legend is the same as in Figure
20). 44
Figure 22. Average values for Figure 21 curves................................................................................................ 45
Figure 23. Best fitting Gamma function. ( Note: legend is the same as in Figure 20 and Figure 21. ................. 46
Stage 5 Distribution
xviii UCPRC- RR- 2005- 06
Figure 24. Input parameters for permanent deformation ( rutting) of subgrade in second column. ................... 48
Figure 25. Comparison of fitted vs. calculated strain for AC- on- AC overlay, 2D. ........................................... 49
Figure 26. Section 501RF pavement structure................................................................................................... 51
Figure 27. Section 501RF temperatures during testing...................................................................................... 52
Figure 28. Section 501RF 40 kN top modules deflection.................................................................................. 52
Figure 29. Section 501 RF 40 kN resilient compression of pavement layers. ................................................... 53
Figure 30. Section 501RF 40 kN deflection of subgrade................................................................................... 53
Figure 31. Section 501RF 100 kN deflection of top modules............................................................................ 54
Figure 32. Section 501RF 100 kN resilient compression of pavement layers. .................................................. 54
Figure 33. Section 501RF 100 kN deflection of subgrade................................................................................. 55
Figure 34. Section 501RF calculated moduli at 40 kN and actual temperature. ( Note: in this and all other
figures showing change in elastic moduli ( E) under loading the lines are plotted for the modulus of each
layer, i. e., E1 is the modulus of the first layer, E2 is the modulus of the second layer, etc.)..................... 55
Figure 35. Section 503RF pavement structure................................................................................................... 56
Figure 36. Section 503RF temperatures during testing...................................................................................... 56
Figure 37. Section 503RF 40 kN deflection of top modules.............................................................................. 57
Figure 38. Section 503RF 40 kN compression of pavement layers. .................................................................. 57
Figure 39. Section 503RF 40 kN deflection of subgrade................................................................................... 58
Figure 40. Section 503RF 100 kN deflection of top modules............................................................................ 58
Figure 41. Section 503RF 100 kN resilient compression of pavement layers. .................................................. 59
Figure 42. Section 503RF 100 kN deflection of subgrade................................................................................. 59
Figure 43. Section 503RF calculated layer moduli at 40 kN and actual temperature........................................ 60
Figure 44. Section 500RF pavement structure................................................................................................... 60
Figure 45. Section 500RF temperatures during testing...................................................................................... 61
Figure 46. Section 500RF 40 kN deflection of top modules.............................................................................. 61
Figure 47. Section 500RF 40 kN resilient compression of pavement layers. .................................................... 62
Figure 48. Section 500RF 40 kN deflection of subgrade................................................................................... 62
Figure 49. Section 500RF 100 kN deflection of top modules............................................................................ 63
Figure 50. Section 500RF 100 kN compression of pavement layers. ................................................................ 63
Figure 51. Section 500RF 100 kN deflection of subgrade................................................................................. 64
Figure 52. Section 500RF calculated moduli at 40 kN and actual temperature................................................. 64
Figure 53. Section 502CT pavement structure................................................................................................... 65
Figure 54. Section 502CT 40 kN deflection on top of AC. ............................................................................... 65
Figure 55. Section 502CT 40 kN compression of pavement layers................................................................... 66
Figure 56. Section 502CT 40 kN deflection of subgrade................................................................................... 66
Figure 57. Section 502CT 100 kN deflection at top of AC. .............................................................................. 67
Stage 5 Distribution
xix UCPRC- RR- 2005- 06
Figure 58. Section 502CT 100 kN resilient compression of pavement layers. .................................................. 67
Figure 59. Section 502CT 100 kN deflection of subgrade................................................................................. 68
Figure 60. Section 502CT calculated moduli at 40 kN and 20 º C. ..................................................................... 68
Figure 61. Cracking versus relative decrease in modulus of top AC layer for Goal 1....................................... 69
Figure 62. Goal 1, cracking versus increase in deflection. ................................................................................ 70
Figure 63. Permanent compression of AC layers. ............................................................................................. 73
Figure 64. Permanent compression of granular layers....................................................................................... 73
Figure 65. Permanent deformation of subgrade................................................................................................. 74
Figure 66. Permanent deformation at pavement surface.................................................................................... 74
Figure 67. Permanent compression of AC layers. ............................................................................................. 75
Figure 68. Permanent compression of granular layers....................................................................................... 75
Figure 69. Permanent deformation of subgrade................................................................................................. 76
Figure 70. Permanent deformation at pavement surface.................................................................................... 76
Figure 71. Permanent deformation of the AC layers. ........................................................................................ 77
Figure 72. Permanent compression of the granular layers................................................................................. 77
Figure 73. Permanent deformation of the subgrade. .......................................................................................... 78
Figure 74. Permanent deformation at pavement surface.................................................................................... 78
Figure 75. Permanent compression of the AC layers......................................................................................... 79
Figure 76. Permanent deformation of granular layers. ...................................................................................... 79
Figure 77. Permanent deformation of subgrade................................................................................................. 80
Figure 78. Permanent deformation at surface of pavement. .............................................................................. 80
Figure 79. Section 517RF pavement structure................................................................................................... 82
Figure 80. Section 517RF AC temperature during testing................................................................................. 82
Figure 81. Section 517RF 40 kN deflection of top modules.............................................................................. 83
Figure 82. Section 517RF 40 kN compression of pavement layers. .................................................................. 83
Figure 83. Section 517RF deflection of subgrade.............................................................................................. 84
Figure 84. Section 517RF 100 kN top modules deflection................................................................................ 84
Figure 85. Section 517RF 100 kN compression of pavement layers. ................................................................ 85
Figure 86. Section 517RF 100 kN deflection of subgrade................................................................................. 85
Figure 87. Section 517RF calculated moduli at 40 kN and actual temperature................................................. 86
Figure 88. Section 518RF pavement structure................................................................................................... 86
Figure 89. Section 518RF AC temperature during testing................................................................................. 87
Figure 90. Section 518RF 40 kN top modules deflection.................................................................................. 87
Figure 91. Section 518RF 40 kN resilient compression of pavement layers. .................................................... 88
Figure 92. Section 518RF 40 kN deflection of subgrade................................................................................... 88
Figure 93. Section 518RF 100 kN top modules deflection................................................................................ 89
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xx UCPRC- RR- 2005- 06
Figure 94. Section 518RF 100 kN compression of pavement layers. ................................................................ 89
Figure 95. Section 518RF 100 kN deflection of subgrade................................................................................. 90
Figure 96. Section 518RF calculated moduli at 40 kN and actual temperature................................................. 90
Figure 97. Section 514RF pavement structure................................................................................................... 91
Figure 98. Section 514RF AC temperature during testing................................................................................. 91
Figure 99. Section 514RF 40 kN top modules deflection.................................................................................. 92
Figure 100. Section 514RF 40 kN compression of pavement layers, MDD1 and MDD2................................. 92
Figure 101. Section 514RF 40 kN compression of pavement layers, MDD3 and MDD4................................. 93
Figure 102. Section 514RF 40 kN deflection of subgrade................................................................................. 93
Figure 103. Section 514RF 100 kN top modules deflection.............................................................................. 94
Figure 104. Section 514RF 100 kN compression of pavement layers, MDD1 and MDD2............................... 94
Figure 105. Section 514RF 100 kN compression of pavement layers, MDD3 and MDD4............................... 95
Figure 106. Section 514RF 100 kN deflection of subgrade............................................................................... 95
Figure 107. Section 514RF calculated moduli at 40 kN and actual temperature............................................... 96
Figure 108. Section 515RF pavement structure................................................................................................. 96
Figure 109. Section 515RF AC temperature during testing............................................................................... 97
Figure 110. Section 515RF 40 kN top modules deflection................................................................................ 97
Figure 111. Section 515RF 40 kN resilient compression of pavement layers. .................................................. 98
Figure 112. Section 515RF 40 kN deflection of subgrade.................................................................................. 98
Figure 113. Section 515RF 100 kN top modules deflection.............................................................................. 99
Figure 114. Section 515RF 100 kN compression of pavement layers. .............................................................. 99
Figure 115. Section 515RF 100 kN deflection of subgrade............................................................................. 100
Figure 116. Section 515RF calculated moduli at 40 kN and actual temperatures. .......................................... 100
Figure 117. Cracking in overlay versus relative decrease in modulus of overlay, Goal 3............................... 101
Figure 118. Goal 3, 20 º C, cracking versus increase in deflection.................................................................... 102
Figure 119. Section 517RF permanent deformation of AC layers................................................................... 105
Figure 120. Section 517RF permanent deformation of granular layers........................................................... 105
Figure 121. Section 517RF permanent deformation of subgrade. ................................................................... 106
Figure 122. Section 517RF permanent deformation at pavement surface. ...................................................... 106
Figure 123. Section 518RF permanent deformation of AC layers................................................................... 107
Figure 124. Section 518RF permanent deformation of granular layers........................................................... 107
Figure 125. Section 518RF permanent deformation of subgrade. ................................................................... 108
Figure 126. Section 518RF permanent deformation at pavement surface. ...................................................... 108
Figure 127. Section 514RF permanent deformation of AC layers................................................................... 109
Figure 128. Section 514RF permanent deformation of granular layers, MDD1 and MDD2........................... 109
Figure 129. Section 514RF permanent deformation of granular layers, MDD3 and MDD4........................... 110
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xxi UCPRC- RR- 2005- 06
Figure 130. Section 514RF permanent deformation of subgrade. ................................................................... 110
Figure 131. Section 514RF permanent deformation at pavement surface. ...................................................... 111
Figure 132. Section 515RF permanent deformation of AC layers................................................................... 112
Figure 133. Section 515RF permanent deformation of granular layers........................................................... 112
Figure 134. Section 515RF permanent deformation of subgrade. ................................................................... 113
Figure 135. Section 515RF permanent deformation of the pavement surface................................................. 113
Figure 136. Section 504RF pavement structure............................................................................................... 115
Figure 137. Section 504RF permanent deformation at pavement surface from profilometer.......................... 115
Figure 138. Section 504RF calculated permanent deformation of pavement layers........................................ 116
Figure 139. Section 505RF pavement structure............................................................................................... 117
Figure 140. Section 505RF temperatures during testing.................................................................................. 117
Figure 141. Section 505RF permanent deformation at pavement surface from profilometer.......................... 118
Figure 142. Section 505RF calculated permanent deformation of pavement layers........................................ 118
Figure 143. Section 506RF pavement structure............................................................................................... 119
Figure 144. Section 506RF temperatures during testing.................................................................................. 119
Figure 145. Section 506RF permanent deformation at pavement surface from profilometer.......................... 120
Figure 146. Section 506RF calculated permanent deformation of pavement layers........................................ 120
Figure 147. Section 507RF pavement structure............................................................................................... 121
Figure 148. Section 507RF temperatures during testing.................................................................................. 121
Figure 149. Section 507RF permanent deformation at pavement surface from profilometer.......................... 122
Figure 150. Section 507RF calculated permanent deformation of pavement layers........................................ 122
Figure 151. Section 508RF pavement structure............................................................................................... 123
Figure 152. Section 508RF temperatures during testing.................................................................................. 123
Figure 153. Section 508RF permanent deformation at pavement surface from profilometer.......................... 124
Figure 154. Section 508RF calculated permanent deformation of pavement layers........................................ 124
Figure 155. Section 509RF pavement structure............................................................................................... 125
Figure 156. Section 509RF temperatures during testing.................................................................................. 125
Figure 157. Section 509RF permanent deformation at pavement surface from profilometer.......................... 126
Figure 158. Section 509RF calculated permanent deformation of pavement layers........................................ 126
Figure 159. Section 510RF pavement structure............................................................................................... 127
Figure 160. Section 510RF temperatures during testing.................................................................................. 127
Figure 161. Section 510RF permanent deformation at pavement surface from profilometer.......................... 128
Figure 162. Section 510RF calculated permanent deformation of pavement layers........................................ 128
Figure 163. Section 511RF pavement structure............................................................................................... 129
Figure 164. Section 511RF temperatures during testing.................................................................................. 129
Figure 165. Section 511RF permanent deformation at the pavement surface. ................................................ 130
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xxii UCPRC- RR- 2005- 06
Figure 166. Section 511RF calculated permanent deformation of the pavement layers.................................. 130
Figure 167. Section 512RF pavement structure............................................................................................... 131
Figure 168. Section 512RF temperatures during testing.................................................................................. 131
Figure 169. Section 512RF permanent deformation at pavement surface from profilometer.......................... 132
Figure 170. Section 512RF calculated permanent deformation of the pavement layers.................................. 132
Figure 171. Section 513RF pavement structure............................................................................................... 133
Figure 172. Section 513RF permanent deformation at pavement surface from profilometer.......................... 134
Figure 173. Section 513RF calculated permanent deformation of pavement layers........................................ 134
Figure 174. Cores from trafficked area of Section 543RF after HVS loading show stripping and disintegration
of ATPB, as well as signs of moisture damage between the the three lifts of asphalt concrete ( Bejarano et
al. 2003). ............................................................................................................................... .................. 135
Figure 175. Section 543RF pavement structure............................................................................................... 136
Figure 176. Section 543RF temperatures during testing.................................................................................. 137
Figure 177. Section 543RF Road Surface Deflectometer, at 40 kN. ............................................................... 137
Figure 178. Section 543RF Road Surface Deflectometer, at 100 kN. ............................................................. 138
Figure 179. Section 543RF 40 kN top module. ............................................................................................... 138
Figure 180. Section 543RF 40 kN top of aggregate base. ............................................................................... 139
Figure 181. Section 543RF 40 kN top of aggregate subbase........................................................................... 139
Figure 182. Section 543RF 40 kN deflection of subgrade ( 850 mm depth). .................................................... 140
Figure 183. Section 543RF 100 kN top module. ............................................................................................. 140
Figure 184. Section 543RF 100 kN top of aggregate base. ............................................................................. 141
Figure 185. Section 543RF 100 kN top of aggregate subbase......................................................................... 141
Figure 186. Section 543RF 100 kN deflection of subgrade ( 850 mm depth). .................................................. 142
Figure 187. Section 543RF Permanent deformation of asphalt layers............................................................. 142
Figure 188. Section 543RF permanent deformation of granular layers plus top of subgrade.......................... 143
Figure 189. Section 543RF permanent deformation in subgrade ( 850 mm depth)........................................... 143
Figure 190. Section 543RF permanent deformation at pavement surface. ...................................................... 144
Figure 191. Section 543RF calculated layer moduli, at 40 kN and actual temperatures. ................................ 144
Figure 192. Section 544RF pavement structure............................................................................................... 145
Figure 193. Section 544RF temperatures during testing.................................................................................. 145
Figure 194. Section 544RF Road Surface Deflectometer, at 40 kN. ............................................................... 146
Figure 195. Section 544RF Road Surface Deflectometer, at 100 kN. ............................................................. 146
Figure 196. Section 544RF 40 kN top module. ............................................................................................... 147
Figure 197. Section 544RF 40 kN top of aggregate base. ............................................................................... 147
Figure 198. Section 544RF 40 kN top of aggregate subbase........................................................................... 148
Figure 199. Section 544RF 100 kN top module. ............................................................................................. 148
Stage 5 Distribution
xxiii UCPRC- RR- 2005- 06
Figure 200. Section 544RF 100 kN top of aggregate base. ............................................................................. 149
Figure 201. Section 544RF 100 kN top of aggregate subbase......................................................................... 149
Figure 202. Section 544RF Permanent deformation of asphalt layers............................................................. 150
Figure 203. Section 544RF permanent deformation of aggregate base. .......................................................... 150
Figure 204. Section 544RF permanent deformation on top of basecourse. ...................................................... 151
Figure 205. Section 544RF permanent deformation at pavement surface. ...................................................... 151
Figure 206. Section 544RF calculated moduli of pavement layers................................................................... 152
Figure 207. Section 545RF pavement structure............................................................................................... 153
Figure 208. Section 545RF temperatures during testing.................................................................................. 153
Figure 209. Section 545RF Road Surface Deflectometer, at 40 kN. ............................................................... 154
Figure 210. Section 545RF Road Surface Deflectometer, 100 kN. ................................................................. 154
Figure 211. Section 545RF 40 kN top module. ............................................................................................... 155
Figure 212. Section 545RF 40 kN top of aggregate base. ............................................................................... 155
Figure 213. Section 545RF 40 kN top of aggregate subbase........................................................................... 156
Figure 214. Section 545RF 100 kN top module. ............................................................................................. 156
Figure 215. Section 545RF 100 kN top of aggregate base. ............................................................................. 157
Figure 216. Section 545RF 100 kN top of aggregate subbase......................................................................... 157
Figure 217. Section 545RF permanent deformation of asphalt layers............................................................. 158
Figure 218. Section 545RF permanent deformation of aggregate base. .......................................................... 158
Figure 219. Section 545RF permanent deformation at pavement surface. ...................................................... 159
Figure 220. Section 545RF calculated moduli of pavement layers.................................................................. 159
Figure 221. Visual cracking versus relative decrease in modulus of layer 1, Goal 5 Wet conditions. ............. 160
Figure 222. Goal 5, cracking versus increase in deflection. ............................................................................ 161
Figure 223. MB road, AC modulus- versus- reduced time parameters from frequency sweep. ......................... 162
Figure 224. Moduli from FWD compared to frequency sweep tests, Goal 9 ( MB road). ................................ 163
Figure 225. MB road, damage parameters for AC in first column. .................................................................. 165
Figure 226. MB road, backcalculated modulus of AB versus time. ................................................................ 166
Figure 227. MB road, modulus of AB versus stiffness of AC......................................................................... 166
Figure 228. MB road, subgrade modulus versus stiffness of pavement layers. ................................................ 167
Figure 229. Section 567RF pavement structure................................................................................................ 169
Figure 230. Section 567RF load levels. ........................................................................................................... 169
Figure 231. Section 567RF temperatures during testing................................................................................... 170
Figure 232. Section 567RF Road Surface Deflectometer................................................................................. 170
Figure 233. Section 567RF MDDs at 90mm and 330 mm. ............................................................................. 171
Figure 234. Section 567RF permanent deformation of MDDs......................................................................... 171
Figure 235. Section 567RF permanent deformation at pavement surface from profilometer........................... 172
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xxiv UCPRC- RR- 2005- 06
Figure 236. Section 567RF calculated moduli at 40 kN and actual temperature.............................................. 172
Figure 237. Section 568RF pavement structure................................................................................................ 173
Figure 238. Section 568RF temperatures during testing................................................................................... 173
Figure 239. Section 568RF Road Surface Deflectometer................................................................................. 174
Figure 240. Section 568RF permanent deformation at pavement surface from profilometer........................... 174
Figure 241. Section 568RF calculated layer moduli at 40 kN and actual temperature..................................... 175
Figure 242. Section 573RF pavement structure................................................................................................ 176
Figure 243. Section 573RF temperatures during testing................................................................................... 176
Figure 244. Section 573RF Road Surface Deflectometer................................................................................. 177
Figure 245. Section 573RF permanent deformation at pavement surface from profilometer........................... 177
Figure 246. Section 573RF calculated layer moduli at 40 kN and actual temperature..................................... 178
Figure 247. Section 571RF pavement structure................................................................................................ 179
Figure 248. Section 571RF temperatures during testing................................................................................... 179
Figure 249. Section 571RF Road Surface Deflectometer................................................................................. 180
Figure 250. Section 571RF MDDs at 90 mm, 300 mm, and 525 mm. ............................................................. 180
Figure 251. Section 571RF permanent deformation of MDDs......................................................................... 181
Figure 252. Section 571RF permanent deformation at the pavement surface. ................................................. 181
Figure 253. Section 571RF calculated layer moduli at 40 kN and actual temperature..................................... 182
Figure 254. Section 572RF pavement structure................................................................................................ 183
Figure 255. Section 572RF temperatures during testing................................................................................... 183
Figure 256. Section 572RF Road Surface Deflectometer................................................................................. 184
Figure 257. Section 572RF permanent deformation at the pavement surface. ................................................. 184
Figure 258. Section 572RF calculated layer moduli at 40 kN and actual temperature..................................... 185
Figure 259. Section 569RF pavement structure................................................................................................ 186
Figure 260. Section 569RF temperatures during testing................................................................................... 186
Figure 261. Section 569RF Road Surface Deflectometer................................................................................. 187
Figure 262. Section 569RF MDDs at 90 mm, 300 mm, and 525 mm.............................................................. 187
Figure 263. Section 569RF permanent deformation of MDDs......................................................................... 188
Figure 264. Section 569RF permanent deformation at pavement surface from profilometer........................... 188
Figure 265. Section 569RF calculated layer moduli at 40 kN and actual temperature..................................... 189
Figure 266. Cracking versus relative decrease in modulus of AC layer for Goal 9 ( MB road)........................ 190
Figure 267. Goal 9 ( MB road), Cracking versus increase in deflection ( RSD) ................................................ 190
Figure 268. Ratio of final over initial deflection. ............................................................................................. 195
Figure 269. Cracking versus calculated decrease in modulus of top layer. ...................................................... 197
Figure 270. Cracking versus increase in deflection. ......................................................................................... 198
Figure 271. Measured and predicted final permanent deformation of asphalt................................................. 199
Stage 5 Distribution
xxv UCPRC- RR- 2005- 06
Figure 272. Final permanent deformation of granular layers. ......................................................................... 201
Figure 273. Final permanent deformation of the subgrade. .............................................................................. 203
Figure 274. Final permanent deformation at the pavement surface ( profile data). ........................................... 205
Figure 275. Modulus of AB layer backcalculated from FWD tests in center line. ........................................... 217
Figure 276. Pavement structure for Section 569RF.......................................................................................... 219
Figure 277. Damage parameters used for DGAC of Section 569RF................................................................ 219
Figure 278. Damage parameters used for CTB of Section 569RF.................................................................... 220
Figure 279. Section 569RF Road Surface Deflectometer................................................................................. 220
Figure 280. Section 569RF MDD resilient deflections..................................................................................... 221
Figure 281. Section 569RF permanent MDD deformations. ............................................................................ 221
Figure 282. Section 569RF average permanent deformation from pavement profile....................................... 222
LIST OF TABLES
Table 1. Summary List of HVS Tests ................................................................................................................... 3
Table 2. Design Thicknesses for Goal 1 Sections ................................................................................................. 5
Table 3. As- built Thicknesses for Goal 5 Sections ............................................................................................... 6
Table 4. As- built Thicknesses of Goal 9 Sections ................................................................................................ 8
Table 5 Influence of Slip Value in LEAP on Calculated Vertical Deflections and Horizontal Strains ............. 25
Table 6. Triaxial Tests on Subgrade.................................................................................................................... 26
Table 7. Triaxial Tests on Aggregate Base ( AB) ................................................................................................ 26
Table 8. Layer Thicknesses Used for FWD Backcalculation.............................................................................. 36
Table 9. Moduli Parameters from FWD ............................................................................................................. 38
Table 10. Moduli Parameters from Calibration to MDD Deflections................................................................. 38
Table 11. Initial Moduli Used in HVS Simulations ( MPa)................................................................................. 39
Table 12. Summary of Moduli ( MPa)................................................................................................................. 39
Table 13. Parameters Used in Equation 20......................................................................................................... 41
Table 14. AC on AC, 2D Structural Parameter Combinations ........................................................................... 49
Table 15. Initial Moduli MPa ( 1.8 km/ h, 40 kN, Actual Temperature) for Each Section................................... 71
Table 16. Final Moduli MPa ( 1.8 km/ h, 40 kN, Actual Temperature) for Each Section.................................... 71
Table 17. Percentage Decrease in Layer Moduli for Each Section..................................................................... 72
Table 18. Damage Parameter for Asphalt Layers at End of Test for Each Section ............................................ 72
Table 19. Initial Damage Parameters for “ Old” Asphalt Overlay Sections ........................................................ 81
Table 20. Layered Moduli at Start of Test, MPa .............................................................................................. 103
Table 21. Layer Moduli at End of Test, MPa ................................................................................................... 103
Table 22. Percentage Decrease in Moduli ........................................................................................................ 104
Table 23. Initial Permanent Deformations, Goal 3, in mm............................................................................... 104
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xxvi UCPRC- RR- 2005- 06
Table 24. Tire Types and Pressure, MPa .......................................................................................................... 114
Table 25. Estimated Temperatures for Section 513RF ..................................................................................... 133
Table 26. Parameters for FWD Moduli versus Reduced Time, Goal 9 ............................................................ 164
Table 27. MB Road, Stiffness Parameters for AB............................................................................................ 167
Table 28. Summary of Damage Equations and Shift Factors Used in All Simulations.................................... 192
Table 29. Measured and Calculated Road Surface Deflectometer Deflections ( RSD), in mm......................... 193
Table 30. Measured and Calculated Deflections of the Top Multi- depth Deflectometer ( MDD), in mm........ 194
Table 31. Final Permanent Deformation of Asphalt, in mm............................................................................. 200
Table 32. Final Permanent Deformation of Granular Layer, in mm................................................................. 202
Table 33. Parameters used for Granular Materials in Equation ( 29) ................................................................ 202
Table 34. Final Permanent Deformation of Subgrade, in mm.......................................................................... 204
Table 35. Parameters Used for Subgrade in Equation ( 29)............................................................................... 204
Table 36. Final Permanent Deformation at the Pavement Surface, in mm....................................................... 206
Stage 5 Distribution
1 UCPRC- RR- 2005- 06
1.0 INTRODUCTION
The first step in creating a Mechanistic- Empirical ( ME) pavement design or evaluation is to calculate
pavement response — in terms of stresses, strains, and/ or displacements — using a mathematical ( or
mechanistic) model. In the second step, the calculated response is used as a variable in empirical relationships
to predict structural damage ( decrease in moduli or cracking) and functional damage ( rutting and roughness) to
the pavement.
Both of these steps must be reasonably correct. If the calculated response bears little resemblance to
the pavement’s actual response, there is no point in trying to use the calculation to predict future damage to the
pavement with the empirical relationship. In other words, only if the calculated response is reasonably correct
does it make sense to try to relate the damage to the pavement response.
1.1 Models and Approaches Included in CalME
This report presents the modeling of several series of flexible pavement Heavy Vehicle Simulator
( HVS) tests using the set of distress models included in the draft software package, CalME. These models are
for the flexible pavement distresses typically observed in California: asphalt fatigue, asphalt rutting, unbound
layers rutting and reflection cracking.
CalME software provides the user with four approaches for evaluating or designing a flexible
pavement structure:
• Caltrans current methods, the R- value method for new flexible structures, and the deflection
reduction method for overlay thickness design for existing flexible structures.
• “ Classical” Mechanistic- Empirical ( ME) design, largely based on the Asphalt Institute method. This
method uses a standard Equivalent Single Axle Load ( ESAL) for the traffic load, one temperature to
characterize the entire range of temperatures the asphalt concrete ( AC) layer will experience, and the
Asphalt Institute fatigue and unbound layers rutting equations, with an adjustment for air- void
content and binder content in the asphalt concrete.
• An Incremental method, using the typical Miner’s Law approach, permitting damage calculation for
the axle- load spectrum and expected temperature regimes, but with no updating of materials
properties through the life of the project. This is similar to the approach included in the NCHRP 1-
37A Design Guide, also referred to as the Mechanistic- Empirical Pavement Design Guide ( MEPDG).
This type of approach is calibrated against an end failure state, such as 25 percent cracking of the
wheelpath, and it assumes a linear accumulation of damage to get to that state.
• An Incremental- Recursive method in which the materials properties for the pavement are updated in
terms of damage as the simulation of the pavement life progresses. The Incremental- Recursive
approach was used for the simulations included in this report, and is the only approach that can
provide an accurate indication of pavement condition at different points during the pavement’s life.
The research team proposes that pavement designers should begin their designs by applying either an
existing Caltrans method or the Classical method. In CalME both of these options perform a “ design” function,
calculating and presenting pavement structures that meet design requirements for a predetermined number of
traffic loads. Then, the lowest cost alternatives in the set of candidate pavement structures meeting the design
requirements with either of these methods should be checked by the designer with the more comprehensive
and precise Incremental- Recursive method to be certain that they meet the design requirements. Once a final
design has been selected, its Incremental- Recursive output can be used to provide a prediction of the
pavement’s condition across its entire life.
Some distresses and some materials are not considered in either the Caltrans or Classical methods, and
can only be evaluated using the Incremental- Miner’s Law approach or the Incremental- Recursive approach.
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1.1.1 Validation Using Heavy Vehicle Simulator Data
The Incremental- Recursive models included in CalME were used to predict the performance of all the
flexible pavement HVS tests performed to date as part of the Accelerated Pavement Testing ( APT) program
operated for the California Department of Transportation ( Caltrans) by the University of California Pavement
Research Center ( UCPRC).
The HVS test data presented in this report come from tests performed between 1995 and 2004. The
HVS response data and the corresponding laboratory test data were extracted from the UCPRC HVS database.
HVS tests measure pavement response in terms of deflections, either at the pavement surface, using a
Road Surface Deflectometer ( RSD), at multiple depths, using a Multi- depth Deflectometer ( MDD), or both.
The RSD is very similar to the Benkelman Beam used in the development of the Caltrans new flexible
pavement and overlay design methods in the 1950s. In predicting the gradual degradation of the pavement it is
important that the response model provides a reasonably accurate prediction of measured deflections. Although
a correct prediction of deflections by the response model is no guarantee that it can also correctly predict the
stresses and strains in all of the pavement layers, the opposite is true: if the model inaccurately predicts
deflections, it will also provide inaccurate predictions of stresses and strains.
Therefore, in trying to calibrate the ME models from HVS testing, the research team’s first concern
was to make sure that the model predicted resilient deflections reasonably well for the duration of the test and
for all load levels. This prediction depended on the moduli ( often referred to as “ stiffnesses” in this report and
in the literature) of all of the pavement layers and on the changes to these moduli caused by fatigue damage,
slip between asphalt layers, non- linear elastic characteristics of the unbound layers, and the effect of
confinement on granular layers. Once reasonable agreement was achieved between the measured resilient
deflections and the calculated ones, then models of permanent deformation could be calibrated with some
confidence.
There are different methods for determining moduli and there are often differences in the results from
each method ( which should be expected based on the literature.) The methods used in this study included
backcalculation of moduli for all layers from Falling Weight Deflectometer ( FWD) and MDD deflection data ,
and direct measurement of moduli in the laboratory using triaxial tests for unbound materials and flexural
frequency sweep tests for asphaltic materials. Differences in measured moduli across the different methods are
due to variations in boundary conditions, strain levels, and loading times between the different measurement
methods, the effects of which vary among materials. The FWD does not fit under the HVS, so there is no FWD
data during an HVS test, there is only FWD data from before the HVS was placed on the pavement and from
after the HVS was taken off the trafficked section. The simulations in this report primarily relied on stiffnesses
for the asphalt materials taken from flexural frequency sweep data, and stiffnesses for the unbound layers taken
from backcalculation of MDD deflection data.
In practice, the research team views backcalculation using deflections from the FWD as the primary
tool for obtaining the stiffnesses of layers in existing pavements, as opposed to laboratory testing of materials
samples taken from the already constructed pavement. FWD deflections and backcalculation take into
consideration the stiffness of the layers as they occur in the constructed pavement structure, including the
effects of boundary conditions, water and temperature conditions, previous traffic and environmental
conditioning, and interaction between layers acting as a system in the in- place pavement structure. This is
important because most of Caltrans future work will be rehabilitating and reconstructing pavements already in
service.
The research team sees the flexural beam test as the primary tool for measuring the stiffness and the
fatigue characteristics of asphalt overlay materials for new layers. For new pavement construction, the team
sees the use of databases of moduli for granular bases and subbases and for subgrades backcalculated from
FWD tests on existing pavements, with the materials referenced by characteristics such as the Unified Soil
Classification System ( USCS) classification and relative density. The databases should also include some
laboratory triaxial tests for these materials, for comparison with any new base, subbase, and subgrade materials
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for which there is no previous FWD testing, and for which laboratory triaxial testing must be used to measure
stiffness.
The purpose of this study was to compare the overall trends shown by the damage models in
simulations of the HVS tests against the actual trends measured in the same HVS tests. Asphalt concrete
stiffnesses from flexural frequency sweep data were used in the simulations of the HVS tests, and the
stiffnesses of the underlying moduli were adjusted from their initial values as the asphalt concrete stiffness
changed with damage so they would match the measured and calculated deflections. The results presented
herein show that, overall, the damage trends for deflection and permanent deformation under loading were
verified.
During HVS testing, deflections often increase markedly, with deflection sometimes rising more than
twice as high at the end of the test than they were at the beginning. The flexible pavement design model of the
NCHRP 1- 37A Design Guide ( NCHRP 2004) does not consider any decrease in the asphalt concrete modulus
as a result of fatigue damage ( except for rehabilitation designs). In fact, the NCHRP 1- 37A Design Guide
includes a model for aging that predicts a continuous increase in the stiffness of asphalt concrete layers across
the life of the pavement, resulting in smaller predicted deflections as the pavement is subjected to trafficking.
While aging is potentially important, the effect of updating stiffness for aging and not updating it for fatigue
damage results in the calculation of unrealistic elastic responses during the pavement life. This may be
acceptable for pavements with extremely thick asphalt concrete layers where little fatigue should occur, but it
is impossible to use the model to simulate an HVS test and, inversely, to use HVS tests to calibrate the model.
The HVS test series in this report were grouped by “ goals,” which are defined as follows:
Table 1. Summary List of HVS Tests
Goal General Conditions HVS Test Numbers Original Report
References
Goal 1:
Comparison of structures with and
without ATPB layer under dry
conditions, moderate temperatures
New pavement, dry conditions, 20° C 500RF, 501RF,
502CT, 503RF
14, 15, 16, 17, 18
Goal 3 Cracking:
Comparison of reflection cracking
performance of ARHM- GG and
DGAC overlays
Overlays of cracked Goal 1 sections,
dry conditions, 20° C
514RF, 515RF
517RF, 518RF
8, 11, 13
Goal 3 Rutting:
Comparison of rutting performance
of ARHM- GG and DGAC
overlays
Overlays of previously untrafficked
areas of Goal 1 pavements, dry
conditions, 40° C or 50° C at 50- mm
depth, four different tire/ wheel types
504RF, 505RF
506RF, 507RF
508RF, 509RF
510RF, 511RF
512RF, 513RF
7, 10
Goal 5:
Comparison of structures with and
without ATPB layer under wet
conditions, moderate temperatures
New pavement, wet conditions, 20° C 543RF, 544RF, 545RF 2, 3, 4, 5, 13
Goal 9:
Initial cracking of asphalt
pavement in preparation for later
overlay
New pavement, ambient rainfall,
20° C
567RF, 568RF,
569RF, 571RF,
572RF, 573RF
1
ATPB: Asphalt- treated permeable base.
ARHM- GG: Asphalt- rubber hot- mix gap- graded.
DGAC: Dense- graded asphalt concrete.
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The Goal 1, 3, and 5 tests were performed inside a metal shed built over native subgrade. The shed
provided protection from sun, wind, and rain; however, changes in subgrade water content and the depth to the
water table were recorded during HVS tests. Goal 9 tests were performed on a road with no cover other than
what the HVS and its temperature cabinet provided.
The remainder of this chapter presents the general descriptions of the HVS tests and the models used
to simulate them.
1.2 HVS tests
1.2.1 Goal 1 and Goal 3 Tests
Figure 1 shows the layout of the Goal 1 and Goal 3 cracking sections.
Figure 1. Layout of 20° C test sections. Goal 3 rutting sections are distributed in the area between the
20° C test sections.
All the sections in Goal 1 had two layers of asphalt concrete ( AC), an aggregate base ( AB), and an
aggregate subbase ( ASB). In the two drained sections, part of the AB layer thickness was replaced by an
asphalt- treated permeable base ( ATPB) at a ratio of 1.4: 1.1. A constant temperature of about 20 º C was
maintained during Goal 1. The design layer thicknesses are shown in Table 2.
518RF
517RF
515RF
514RF
503RF
501RF
502CT
500RF
Undrained Drained
ARHM- GG
DGAC
Goal1
Goal3
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Table 2. Design Thicknesses for Goal 1 Sections
Layer Undrained ( mm) Drained ( mm)
AC top lift 61 61
AC bottom lift 76 76
ATPB None 76
AB 274 182
ASB 229 229
The subgrade was clay, with varying plasticity across the pavements.
Goal 3 was an overlay study with an aphalt rubber hot- mix gap- graded ( ARHM- GG) ( the acronym
ARHM, asphalt rubber hot- mix gap- graded, refers to the material specification at the time of construction in
April 1997.) concrete and a dense- graded asphalt concrete ( DGAC). The four Goal 3 Cracking tests were
performed at the same temperature as Goal 1 ( 20 º C), with similar wheel types and loads. For these tests the
design thickness of the DGAC overlay ( 75 mm) was approximately twice as thick as that of the ARHM ( 40
mm), and the overlays were placed over the four previously cracked Goal 1 sections. The remainder of Goal 3
was done at higher temperatures, with the two overlays placed on previously untested areas of the Goal 1
pavement, and several overlay thicknesses, tire types, and wheel loads used in the testing. ( Table 1 provides
the reference numbers for the reports containing the details regarding thickness, tire types, and wheels loads.)
All the HVS tests at 20 º C started with a wheel load of 40 kN, which was increased stepwise to 100
kN. Most of the load applications were at 100 kN. Bias- ply tires on a dual wheel were used for the Goal 1
tests. The same radial tires on a dual wheel were used for the Goal 3 Cracking tests, and the Goal 5 and Goal 9
tests. Various tires and wheels were used for the Goal 3 Rutting tests, with the load for the entire duration of
all but one test fixed at 40 kN. [ De Beer and Fisher ( 1997) describe the details of the tire contact stresses
measured.] For all the tests except the Goal 3 Rutting tests, the wheel load was a dual wheel with a centerline
distance of 305 mm and an assumed tire pressure of 690 kPa for all load levels. It was assumed that the wheels
distributed the load over two circular areas; this assumption was reasonably correct for the low load level ( 40
kN) but not for the high load level ( 100 kN, where the actual load distribution was closer to two rectangles
with one side twice the length of the other).
All the 20° C sections were instrumented with MDDs. Each section in Goal 1 had two MDDs. Each
section had two additional MDDs installed for Goal 3 testing. All MDD anchor depths were assumed to be
3,000 mm. Not all MDD modules functioned for the duration of the tests.
The as- constructed layer thicknesses given in Harvey et al. ( 1999) were used for the analyses of the
Goal 1 and Goal 3 results presented in this report. As- built layer thicknesses given in Bejarano et al. ( 2003)
and Bejarano et al. ( 2005) were used to analyze the Goal 5 and Goal 9 results respectively. The remaining data
was imported from the UC Pavement Research Center database, taken from a subset database named PRC-HVS.
mdb.
Although actual wheel speeds varied, they were assumed to be 7.6 km/ h during HVS testing and 1.8
km/ h during deflection measurement on the MDDs. All tests other than the Goal 3 Rutting tests were
performed with bidirectional loading. The Goal 3 Rutting tests were performed with unidirectional loading.
The temperature of the test sections was controlled by a “ temperature control box.” The actual
temperatures of the asphalt layers were recorded and used in the simulations.
Poisson’s ratio was assumed to be 0.35 for all layers.
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1.2.2 Goal 5 Tests
The Goal 5 tests were performed on the overlay structures of Goal 3 in locations where the overlay
had not been placed on previously trafficked and cracked Goal 1 pavement. The designed structures were:
• Section 543RF drained with ATPB and 40- mm ARHM- GG wearing surface,
• Section 544RF undrained ( no ATPB) and 40- mm ARHM- GG wearing surface, and
• Section 545RF undrained ( no ATPB) and 75- mm DGAC wearing surface.
The structures’ as- built thicknesses are shown in Table 3.
Table 3. As- built Thicknesses for Goal 5 Sections
Layer Section 543RF ( mm) Section 544RF ( mm) Section 545RF ( mm)
Wearing course 36 51 90
AC ( two lifts combined) 140 149 143
ATPB 64 none none
AB 180 272 259
ASB 223 205– 310 206– 280
All of the test sections had a 2 percent transverse gradient and an approximate 0.5 percent longitudinal
gradient in all the layers above the subbase. Holes with a diameter of 38 mm were drilled through the asphalt
concrete layers on the uphill side of the three HVS test sections, and a drip watering system was installed to
continuously put water into the pavement. Holes were drilled into the top of the ATPB layer of Section 543RF
so that water entered into that layer. Sections 544RF and 545RF had holes drilled into the top of their
aggregate bases, and water entered those layers. The water flow was greater into Section 543RF because of the
initial high permeability of its ATPB layer. Considerably less water flowed into the other two sections because
of the relative impermeability of their AB layer. Figure 2 shows the drip watering system. Each pavement
section had water introduced into it for more than a month prior to HVS loading. This allowed the section to
reach an approximate steady- state moisture condition.
Goal 5 testing used the same dual- wheel, radial tire configuration as Goal 3 testing. Similar loading
patterns and the same temperature control provided a basis for comparing the results from Goal 3 and Goal 5
tests to the result of Goal 1 ( dry condition) testing. In addition, two MDDs were installed in each pavement
section, with depths similar to those used for Goal 1.
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7 UCPRC- RR- 2005- 06
Figure 2. Drip watering system for Goal 5 tests.
1.2.3 Goal 9 Tests
Six HVS tests were performed on what were designed to be identical pavement structures. The
primary purpose of the six tests was to provide fatigue- cracked sections for subsequent placement of different
kinds of overlay for HVS reflection cracking tests; these would be similar to the work performed in the Goal 3
cracking tests.
The pavements were built so that they aligned with an existing access road. When the existing
structure was removed, its subgrade was compacted to state standards. ( Figure 3 shows the layout of the six
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8 UCPRC- RR- 2005- 06
test sections.) The structures’ design thicknesses were: 410 mm of AB with 90 mm of dense- graded asphalt
concrete ( DGAC). ( Table 4 shows the as- built thicknesses.)
The dual- wheel and radial tire configuration used for the Goal 3 tests was used for Goal 9. Loads were
generally lower than those used during Goals 1, 3, and 5 to minimize rutting. Temperatures were maintained
close to 20° C, as on the other cracking tests.
Two MDDs were placed in each test section. However, most of the MDD modules below the surface
either never functioned or failed during the test.
Table 4. As- built Thicknesses of Goal 9 Sections
Layer 567RF 568RF 569RF 571RF 572RF 573RF
AC 78 80 81 82 78 76
AB 352 349 337 352 349 337
1.3 Response and Damage Models
Response and damage models are presented in this section, and they are discussed in terms of the
materials properties common to the Goal 1, 3, and 5 tests. The materials properties of the Goal 9 tests are
discussed with the description of the simulations for those tests later in this report.
1.3.1 Asphalt Modulus
Asphalt modulus was determined as a function of temperature and loading time, using the NCHRP 1-
37A Design Guide model ( NCHRP 2004):
( ) ( ( tr))
E
1 exp log
log
β γ
α
δ
+ +
= + ( 1)
where E is the modulus in MPa,
tr is reduced time in sec,
α, β, γ, and δ are constants, and
logarithms are to base 10.
Reduced time is found from:
aTg
ref
visc
visc
lt tr ⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛
= × ( 2)
where lt is the loading time ( in sec),
viscref is the binder viscosity at the reference temperature,
visc is the binder viscosity at the present temperature, and
aTg is a constant.
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9 UCPRC- RR- 2005- 06
Figure 3. Layout of Goal 9 test sections.
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10 UCPRC- RR- 2005- 06
100
1000
10000
100000
0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000 10000
Reduced time, sec
Modulus, MPa
α/ 2 tr
( ) min δ= log E
max
min
log E
E
⎛⎜ ⎞⎟
⎝ ⎠
α =
Figure 4. Example of modulus versus reduced time relationship.
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11 UCPRC- RR- 2005- 06
Equation 1 may also be written:
( ) ( )
max
min
' min '
/ 2 / 2
log
log log
1 1
E
E
E E
tr tr
tr tr
γ γ
α α
α
δ
⎛⎜ ⎞⎟
= + = + ⎝ ⎠
+⎛⎜ ⎞⎟ +⎛⎜ ⎞⎟
⎝ ⎠ ⎝ ⎠
( 3)
where ( ) ( ( )) / 2 ' ln 10 and tr exp ln 10 α
γ γ βγ
= = − ×
trα/ 2 is the reduced time corresponding to log( E) = δ + α/ 2, as indicated in Figure 4. Equation 1 is
normally used with frequency sweep data to characterize the master curve. The form of the master curve
equation shown in Equation 2 provides some insight, and can be used if Emax and Emin were known. Emax is
related to the limiting stiffness of asphalt binder at temperatures below the glass transition temperature. Emin
appears to depend on the boundary conditions under which it was measured, with different values coming from
backcalculation of in- situ pavements and beam fatigue tests.
From Equation 2 it can be seen that changing trα/ 2 will shift the curve left or right and changing γ’
will change the curvature.
The loading time is determined from the speed of the wheel ( input on the incremental design screen in
CalME) and from the depth at which the loading time is desired.
Loading time is a rather uncertain notion, as it will vary for different types of responses. For example,
the loading time for transverse strain will be much longer than it is for longitudinal strain because of the actual
shape of the contact area of the tire on the pavement, which is longer in the longitudinal direction than the
transverse direction. The reason for the longer loading time for transverse strain is that the transverse strain is
tangential to the load, whereas the longitudinal is radial and therefore has a sign change. The loading time is
calculated from ( 200 mm + 2×depth)/( wheel speed in mm/ sec). The reference loading time is 0.015 sec ( 15
msec, roughly corresponding to the loading time of a standard FWD, where loading time refers to a creep test),
and the reference temperature is 20 º C.
The NCHRP 1- 37A Design Guide makes use of an “ effective depth” based on the equivalent thickness
of the layers, which results in longer loading times. The guide, however, then converts loading time into
frequency, using f = 1/ lt, rather than f = 1/( 2πlt), more than compensating for the longer loading time ( unless
loading time is defined differently, i. e., it is not based on a creep test).
Viscosity is found from:
log( log( visc cPoise)) = A + VTS * log( tK ) ( 4)
where tK is the temperature ( in ° K), and
A and VTS are constants, and
cPoise indicates units of centipoise
For all of the asphalt materials in this report a value of A = 9.6307 [ 10.5254 with temperature in º R
( degrees Rankine)] and VTS = - 3.5047 were used. These values correspond ( according to the NCHRP 1- 37A
Design Guide) to an asphalt with a penetration grade of 40– 50.
If the minimum modulus, Emin, the maximum modulus, Emax, and the modulus at two different
temperatures are known, the viscosity versus temperature relationship ( Equation 4) will have very little
influence on the modulus versus temperature relationship. This can be seen in Figure 5, where the resulting
modulus versus temperature relationship is shown for asphalts with penetration grades from 40– 50 to 200– 300
and for a PG64- 22 grade asphalt.
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12 UCPRC- RR- 2005- 06
Influence of viscosity
0
2000
4000
6000
8000
10000
12000
14000
- 20 0 20 40 60
Temperature, C
Modulus, MPa
40- 50
60- 70
85- 100
120- 150
200- 300
PG64- 22
Figure 5. Modulus versus temperature for different viscosity versus temperature relationships.
The constants δ, β, γ, and aTg, and the modulus at the reference temperature ( 20 º C) were derived from
flexural frequency sweep tests. The constant a is calculated by the program. The frequency sweep tests were
available for the top and bottom asphalt layers of Goal 1 and for the overlays in Goal 3.
The fit between frequency sweep data and model data is shown in Figure 6. In fitting the model to the
frequency sweep data it was assumed that the minimum modulus ( 10δ) was 200 MPa ( δ = 2.3010). In the
frequency sweep test the measured modulus was considerably lower. However, based on FWD testing, it was
assumed that an asphalt layer’s modulus, even at very low frequencies and high temperatures, had a minimum
value greater than the one measured in the frequency sweep test on a flexural beam. This variance is
attributable to the differences in boundary conditions between a laboratory test, such as a flexural beam
frequency sweep and the same material when it is part of a layered pavement structure in the field.
Specifically, a flexural beam is suspended in space without confinement in a flexural frequency sweep test. In
contrast, the same asphalt concrete material, confined below and on its sides when it is part of a pavement
layer, has its modulus increased. ( In this confined condition, the aggregate in the asphalt concrete, which has
its own relatively unchangeable high modulus, also has a large compressive stress component applied to it.)
Figure 7 shows an example of the input parameters for the AC bottom layer. A modulus- versus-reduced
time relationship was assumed for the ATPB, based largely on laboratory triaxial testing. The ATPB
had a modulus of 1144 MPa at a temperature of 20 C and a loading time of 0.015 sec. A minimum modulus of
200 MPa was assumed.
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13 UCPRC- RR- 2005- 06
0
2000
4000
6000
8000
10000
12000
14000
16000
- 4 - 3 - 2 - 1 0 1 2
log reduced time
E MPa
28
28
28
28
19
19
19
19
15
15
15
15
AC top
0
2000
4000
6000
8000
10000
12000
14000
16000
- 4 - 3 - 2 - 1 0 1 2
log reduced time
E MPa
28
28
28
28
19
19
19
19
15
15
15
15
AC bottom
0
2000
4000
6000
8000
10000
12000
14000
16000
- 4 - 3 - 2 - 1 0 1 2
log reduced time
E MPa
25
25
10
25
10
25
25
10
25
10
25
10
10
DGAC
0
2000
4000
6000
8000
10000
12000
14000
16000
- 4 - 3 - 2 - 1 0 1 2
log reduced time
E MPa
25
25
25
25
25
25
10
10
10
ARHM
Figure 6. Frequency sweep data for Goal 1 and Goal 3 materials compared to models.
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21 UCPRC- RR- 2005- 06
Figure 7. Example of input parameters for the modulus- versus- reduced time relationship for the AC
bottom layer.
1.3.2 Fatigue
The modulus of damaged asphalt was calculated as:
( ) ( )
( ( tr))
E
1 exp log
log 1
β γ
α ω
δ
+ +
× −
= + ( 5)
where the damage, ω, was calculated from:
( t)
MPa
E MN A × × ⎟ ⎟⎠
⎞
⎜ ⎜⎝
⎛
× ⎟ ⎟⎠
⎞
⎜ ⎜⎝
⎛
= × × δ
με
με
ω
β γ
α exp
200 3000
( 6)
where E is the modulus of damaged material,
MN is the number of load repetitions in millions ( N/ 106),
με is the strain in μstrain,
t is the temperature in º C, and
α, β, γ, and δ are constants ( these constants are the same as the constants in Equations
1 through 5, and different in Equation 6).
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22 UCPRC- RR- 2005- 06
The initial ( intact) modulus, Ei, corresponds to a damage, ω, of 0, and the minimum modulus,
Emin= 10δ, to a damage of 1.
Equation 5 leads to:
( ) ( ( ) ) ( )
⎟⎠ ⎞
⎜⎝ ⎛
⎟⎠
⎞ ⎜⎝
⎛
=
⎟ ⎟⎠
⎞
⎜ ⎜⎝
⎛
=
− = − × −
min
min
log
log
,
log log 1 ,
E
E
E
E
or
E
E
E
E
E E or
i
i
i i
i
ω
δ δ ω
ω ( 7)
The NCHRP 1- 37A Design Guide calculates the modulus of damaged asphalt, for rehabilitation
purposes, using Equation ( 5), but at the same time the Guide defines ω as the relative decrease in modulus
( although this is mistakenly indicated as E/ Ei in the report for the Guide). This definition of ω included in the
NCHRP 1- 37A Design Guide is inconsistent with Equation 5, as shown in Equation ( 7)
The one- stage Weibull distribution, Equation ( 8), could be used instead of Equation 6:
SR = exp(− α × Nβ ) ( 8)
where SR is the stiffness reduction (= E/ Ei),
N is the number of load applications, and
α and β are constants, different from those used in previous equations.
Combining Equations ( 7) and ( 8) one gets:
( ) β
α β α
ω N
E
E
E
E
N
E
E
SR
E
E
E
E
i
i i i
i ×
⎟⎠ ⎞
⎜⎝ ⎛
=
⎟⎠ ⎞
⎜⎝ ⎛
− ×
=
⎟⎠ ⎞
⎜⎝ ⎛
=
⎟⎠ ⎞
⎜⎝ ⎛
⎟⎠
⎞ ⎜⎝
⎛
=
min
min ln min ln min ln
ln
ln
ln
( 9)
which has the same format as Equation 6. In the present version of CalME ( September 2006) it is
assumed that α and β can be written in the format:
( ( ) ( ))
A B t C ( w)
A B t C w D t w
ln
exp ln ln
= + × + ×
= + × + × + × ×
β β β β
α α α α α ( 10)
where t is the temperature in º C,
w is the internal energy density ( ½ ×ε2×E),
and αA, αB, αC, αD, βA, βB, and βC are constants fit from the beam fatigue data.
Fatigue parameters were determined for the AC top and AC bottom of Goal 1 and for the DGAC and
ARHM overlays of Goal 3, based on four- point bending beam tests at 10 Hz under controlled strain.
In determining the fatigue parameters it was assumed that for Equation 6 that β was equal to two times
γ. This reduces the number of parameters to be determined by one, and it ensures that the damage is a function
of the internal energy density ( ½ ×ε2×E).
The parameters were determined by minimizing the root- mean square ( RMS) difference between the
calculated relative modulus ( E/ Ei) and the experimental data for values of E/ Ei > 0.3, the stiffness ratio to
which most of the beam fatigue tests were carried out.
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23 UCPRC- RR- 2005- 06
An example of damage versus number of load applications is shown in Figure 8 which shows the
damage at a temperature of 20 º C for a constant strain of 400 μstrain. The four materials are surprisingly similar
with respect to damage.
Damage of asphalt
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 500000 1000000 1500000 2000000 2500000
Number of load applications
Damage
Goal1Top
Goal1Bottom
Goal3DGAC
Goal3ARHM
Figure 8. Example of damage versus number of load applications.
For ATPB a damage function ( Equation 6) was chosen based on the damage function for the bottom
lift of Goal 1, but with a value of A about fifty times as high.
Figure 9 shows an example of the damage parameters for Equation 6 for the AC bottom lift of Goal 1.
The parameters of interest here are the values of the first column ( under the heading “ Fatigue, dE/ Ei”). The
response type is the horizontal tensile strain at the bottom of the layer ( the minor principal strain) indicated by
the Response type “ e”. The parameters A, α, Reference strain ( Respref), β, Reference modulus ( Eref), γ, and δ
are given. The parameter Std A is a Standard Deviation factor on A that is used in the Monte Carlo
simulations, which are not used in this report. The number of in situ load applications is divided by the Shift
Factor given at the bottom of the column to allow for differences between laboratory testing and field
conditions. A Shift Factor of 3 was used for all materials, i. e., three HVS loads were assumed to give the same
damage as one laboratory load.
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24 UCPRC- RR- 2005- 06
Figure 9. Example of Equation 6 damage parameters of AC bottom layer ( Goal 1).
1.4 Weak Bonding
Weak bonding between the top and bottom asphalt lifts of Goals 1, 3, and 5 was found for certain
areas of the HVS test sections. It appeared that the top AC layer had moved horizontally with respect to the
bottom AC layer. During forensic studies a brown discoloration and scratch marks were observed on the
surfaces of the materials at the interface where slip had apparently occured. Cores showed no bonding at the
interface.
The layered elastic analyis program ( LEAP) option of CalME has a parameter that controls the degree
of bonding between two layers, referred to as “ slip” in LEAP if less than full bonding and “ stick” if full
bonding. Full bond corresponds to a high value ( 105 is used in CalME), and a value of 0 corresponds to full
slip ( i. e., there is no bond between the layers). The logarithm of this parameter is decreased linearly until the
final slip is reached, as a function of the number of loads in ESALs. The number of ESALs corresponding to
final slip is not known, but the shape of the deflection- versus- number of loads curve can serve as a guide.
The LEAP program treats the pavement structure as a continuum, which means that the two materials
above and below the slip interface will be in contact for all points of the interface. This is not a completely
realistic assumption, but with the present response models it cannot be changed. [ A three- dimensional Finite
Element Model ( FEM) would be required to change that assumption.]
It is likely that this incorrect modeling of the slip interface will have different effects on deflections,
on horizontal strains at the interface, and on the shear stress and strain at a depth of 50 mm. ( This depth is used
for calculating the permanent deformation of the AC layer. This is described later). For deflection and shear
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25 UCPRC- RR- 2005- 06
stress, it is likely that friction between the two layers immediately under the wheel will result in only a partial
slip occurring because of the high compressive normal force, whereas the maximum horizontal strains may
well correspond to a condition closer to full slip.
Table 5 Influence of Slip Value in LEAP on Calculated Vertical Deflections and Horizontal Strains
Slip Value 0- 10- 4 10- 3 10- 2 10- 1 1 10 102 103 104 105
d 0 mm* 0.526 0.526 0.525 0.517 0.473 0.396 0.370 0.367 0.367 0.367
d 625 mm* 0.276 0.276 0.276 0.272 0.253 0.228 0.220 0.220 0.219 0.219
Ex top* 230 230 229 222 182 83 14 0 - 2 - 2
Ex bottom* 232 232 232 232 226 196 168 162 161 161
* Note: d 0 mm is vertical deflection at surface, d 625 mm is vertical deflection at 625 mm depth, Ex top is
horizontal strain at the bottom of the top asphalt layer, Ex bottom is the horizontal strain at the bottom of
the bottom asphalt layer.
Table 5 shows an example, taken from Section 501RF, of the influence of the slip value on the
deflection at the surface ( d 0 mm) and the deflection of the subgrade ( d 625 mm), and the horizontal strain at
the bottom of the top AC layer ( Ex top, tensile as positive) and at the bottom of the bottom AC layer ( Ex
bottom).
A slip value of 0.0001 was chosen for the main simulations. This corresponds to full slip between the
layers. At the interface with full slip the shear stress will be zero. The shear stress used for calculating
permanent deformation in the asphalt is at a depth of 50 mm, which is only slightly above the interface. When
full slip develops, the shear stress at depth 50 mm will therefore decrease considerably. As was mentioned
above, this may not be realistic, so a second simulation was carried out with full bonding to determine the
permanent deformation of the asphalt. During this simulation the stiffness factors for the unbound layers and
the shift factor for asphalt fatigue were adjusted to assure that the pavement deflection history was still correct.
These simulations with no slip were only used for determining the permanent deformation of the asphalt.
1.5 Unbound Layers
1.5.1 Triaxial Tests
Table 6 shows the results of triaxial tests on the subgrade material ( Harvey et al. 1996). Two
specimens were tested, compacted at different density and moisture content ( MC) and either soaked or
saturated. The tests were done at a confining stress of 7 kPa, which is close to the static confining stress at the
top of the subgrade. The parameters C and n are defined by the equation:
n
d
MPa
C E ⎟ ⎟⎠ ⎞
⎜ ⎜⎝
⎛
= ×
0.1
σ ( 11)
where E is the modulus, and
σd is the deviator stress.
The column “ E( 30 kPa)” indicates the modulus, at a deviator stress of 30 kPa, which is a typical stress
at the top of the subgrade under a 40 kN dual wheel load.
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26 UCPRC- RR- 2005- 06
Table 6. Triaxial Tests on Subgrade
Density MC% Condition C n E( 30 kPa)
2.06 g/ cm3 22.4 Soaked 36.2 - 0.34 55 MPa
2.12 g/ cm3 15.8 Soaked 66.5 - 0.32 98 MPa
2.12 g/ cm3 15.8 Saturated 41.5 - 0.27 57 MPa
Triaxial tests were done on one AB specimen, with the results shown in Table 7. The sample was
compacted to a density of 2.47 g/ cm3 at a MC of 5.5 percent. The top of the specimen was exposed for ten days
to simulate the effects of exposure to air on the test section. The moisture content dropped from 5.5 percent to
2.9 percent during the ten days. After testing the specimen was saturated and tested again.
Table 7. Triaxial Tests on Aggregate Base ( AB)
Condition k1 k2 E( 50 kPa)
Exposed 481 0.16 430 MPa
Saturated 201 0.49 143 MPa
The constants k1 and k2 are defined by the equation
2
1 0.1
k
MPa
k E ⎟ ⎟⎠
⎞
⎜ ⎜⎝
⎛
= ×
θ
( 12)
where E is the modulus, and
θ is the bulk stress.
The column “ E( 50 kPa)” indicates the modulus at a bulk stress of 50 kPa. According to the theory of
elasticity, the bulk stress in the AB a