Comparison of numerical and experimental responses of ... · Comparison of numerical and experimental responses of pavement systems using various resilient modulus models Mehran Mazari,

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The Japanese Geotechnical Society

Soils and Foundations

Soils and Foundations 2014;54(1):36–44

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www.sciencedirect.comjournal homepage: www.elsevier.com/locate/sandf

Comparison of numerical and experimental responses of pavementsystems using various resilient modulus models

Mehran Mazari, Eric Navarro, Imad Abdallah, Soheil Nazariann

Center for Transportation Infrastructure Systems, The University of Texas at El Paso, El Paso, TX, USA

Received 1 September 2012; received in revised form 23 May 2013; accepted 15 June 2013Available online 18 January 2014

Abstract

The accuracy of the structural design of flexible pavements based on mechanistic approaches is directly related to the appropriateness of thestructural response algorithm and the material resilient modulus models selected. Mechanistic response algorithms can be based on layered theoryor finite element algorithms. The geomaterials can be modeled as linear or nonlinear. To evaluate the appropriateness of the numerical models andthe available resilient modulus models for estimating the response of pavements, several small-scale pavements were constructed and tested underdifferent loads, loading areas and moisture conditions. A nonlinear numerical structural model was then utilized with different resilient modulusmodels to match the experimental responses. With some modifications, a three-parameter nonlinear model provided the same patterns as theexperimentally measured values as long as the weight of the material was considered. In all cases, a transfer function was necessary toaccommodate the differences in stiffness properties due to the differences between the field and the laboratory compaction methods.& 2014 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.

Keywords: Resilient modulus models; Pavement response; Unbound materials; Light weight deflectometer; Plate load test; IGC: D00; D09; E02

1. Introduction

The development and implementation of mechanistic pave-ment design approaches, such as the Mechanistic-EmpiricalPavement Design Guide (MEPDG) in the United States, havebeen vigorously pursued over the last 20 years. In a mechanisticapproach, the relationship between the structural response (stress,strain or deflection) and the physical parameters is described

4 The Japanese Geotechnical Society. Production and hosting by0.1016/j.sandf.2013.12.004

ce to: 500 West University Avenue, Engineering Building,l Paso, TX 79968-0516, USA. Tel.: þ1 915 747 6911;8037.sses: [email protected] (M. Mazari),.utep.edu (E. Navarro), [email protected] (I. Abdallah),u (S. Nazarian).der responsibility of The Japanese Geotechnical Society.

through a numerical model. Brown (1996) discussed a spectrumof analytical and numerical models that can be used for thispurpose. The models are incorporated in several well-knowncomputer programs with different levels of sophistication.Multi-layer linear systems are the most common algorithms

used. In these models, the basic assumptions include that eachlayer is homogeneous, isotropic and linearly elastic, and that thematerial is massless. Multi-layer nonlinear systems, which are themost comprehensive approaches for studying pavement responses,can only be implemented through advanced numerical analyses,such as finite element methods. Multi-layer equivalent-linearmodels are a compromise between the multi-layer and the finiteelement options. These models utilize the multi-layer linear elasticlayered theory combined with an iterative process to consider thenonlinear behavior of the pavement materials in an approximatefashion (Ke et al., 2000). Since the lateral variation in moduluswithin a layer cannot be considered in a linear-elastic layeredsolution, a set of stress points at different radial distances areconsidered to compensate for this disadvantage to some extent.

Elsevier B.V. All rights reserved.

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Table 1Index properties and classification of geomaterials.

Material USCSclassification

Gradation % Atterberglimits

Moisture densitya

Gravel Sand Fines LL PI OMCb,%

MDDc,kg/m3

Granularbase

GW 60 30 4 13 9 5.7 2356

Fine-grainedsoils

CL 8 28 64 27 14 10.0 1996CH 0 3 97 86 53 25.9 1533ML 0 42 59 NPc NP 9.4 1995SC 0 55 45 23 12 11.4 1945

Commonsubgrade

SM 0 73 27 NPd NP 15.2 1794

aFrom modified Proctor test (AASHTO T180) for granular base and standardProctor test (AASHTO T99) for fine-grained soils.

bOMC¼Optimum Moisture Content.cMDD¼Maximum Dry Density.dNP¼Non-Plastic.

M. Mazari et al. / Soils and Foundations 54 (2014) 36–44 37

The material-related input parameters for the pavementresponse models are primarily the stiffness parameters andPoisson0s ratio for each pavement layer. The resilient modulusmodel for a linear elastic material is rather simple, since thestiffness parameter is a modulus that is independent of the stateof stress applied to the pavement. Bounded materials (e.g., hotmix asphalt and stabilized layers) generally display a linear or anearly linear stress–strain relationship. Unbound geomaterialscan exhibit nonlinear and anisotropic behaviors. A material isconsidered nonlinear if its modulus depends on the state ofstress. The nonlinear behavior of granular materials may beexplained by hyperbolic constitutive relationships (Maheshwariand Khatri, 2012). Granular materials generally exhibit stress-hardening behavior as their stiffness increases with an increasein stress. Fine-grained soils, which generally display a decreasein modulus with an increase in stress, are defined as stress-softening.

Resilient modulus (MR) tests are commonly used tomeasure the stiffness parameters of materials. In general, thesetests measure the stiffness of a cylindrical specimen subjectedto numerous repeated axial stresses and confining pressures.Cyclic load triaxial tests have also been employed in geotech-nical and railway studies by many researchers, such asFortunato et al. (2010), Trinh et al. (2012), Inam et al.(2012), Dash et al. (2010) and Youngji et al. (2010). Themost commonly applied resilient modulus models are the so-called universal models that relate the modulus to thedeviatoric stress, confining pressure or a combination of them(Puppala, 2007). Andrei et al. (2004) recommended thefollowing equation to determine the resilient modulus:

MR¼ k1Paθ�3k6Pa

� �k2 τoctPa

þk7

� �k3ð1Þ

where MR¼ resilient modulus, Pa¼atmospheric pressure,θ¼bulk stress, τoct¼octahedral shear stress and k1 throughk7 are regression constants. Parameter k6 is intended to accountfor pore pressure or cohesion; it is a measure of the material0sability to resist tension. Even though Eq. (1) is fundamentallyappealing, Eq. (2) (a.k.a., the k1�k3 model) is more widelyused.

MR¼ k1Paθ

Pa

� �k2 τoctPa

þ1

� �k3ð2Þ

The procedure for conducting MR tests has been undercontinuous modification. The American Association of StateHighways and Transportation Officials (AASHTO) alone haveadopted several test protocols over the last 20 years (e.g.,T292-91, T294-92, TP46-94 and T307-03). The so-calledNCHRP 1-28A (Witczak, 2004) protocol is also gainingpopularity. These approaches differ in specimen size, thecompaction method, loading time, stress sequence, and typeand location of the displacement transducers (i.e., inside oroutside the confining chamber and mounted on the specimenor platen-to-platen measurements). As such, they may yielddifferent k1�k3 values. For example, Gupta et al. (2007)indicated that the resilient moduli from internal displacement

measurements are up to three times greater than those madeoutside the confining cell.The main objective of this paper is to demonstrate the

implication of various MR test methods and resilient modulusmodels on the accuracy and the reliability of the prediction ofthe response parameters (e.g., displacements) of pavementlayers. The secondary objective is to discuss the need fortransfer functions between the measured and the estimatedresponses of geomaterials prepared to the same densities andmoisture contents as the MR laboratory specimens. To thatend, several model pavements were constructed and testedunder different loads, loading areas and moisture conditionswith different sources of geomaterials. Nonlinear numericalstructural models were then utilized with different resilientmodulus models to match the experimental responses. Theresults of that investigation are presented in this paper.

2. Laboratory testing

Laboratory resilient modulus tests are used to determine theimpact of load-related parameters that affect the behavior ofpavement layers. Such tests consist of applying cyclic axial loadsat different confining pressures to a cylindrical specimen. Theresilient modulus is then defined as the ratio of the applieddeviatoric stress and the resulting axial resilient (recoverable)strain (Andrei et al., 2004). The focus of this study is a granularbase and four fine-grained soils with the index parameters shownin Table 1. Table 1 also contains information related to an SMsoil that was used as common subgrade in all the small-scalespecimens prepared in this study. MR tests for all geomaterialswere carried out as per AASHTO T307 (but with internal loadand displacement sensors) and additionally as per NCHRP 1-28A(for granular base materials only).Two compaction methods were used to prepare the specimens:

constant energy and constant density. The constant energymethod (a.k.a., the Proctor method) has been the traditionalmeans of estimating the moisture–density curve for at least the

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Table 3Laboratory MR results on fine-grained soil specimens prepared with constantenergy method following AASHTO T307 protocol.

Geomaterial Target moisturecontent

Nonlinear parameters RepresentativeMR, MPaa

k1 k2 k3

CL 0.8 OMC% 1307 0.43 �0.16 167

M. Mazari et al. / Soils and Foundations 54 (2014) 36–4438

last 80 years and is well-known to pavement and geotechnicalengineering communities. In that method, soil samples at differentmoisture contents are subjected to the same compaction energy(e.g., 25 blows of a 2.495 kg rammer as per AASHTO T99)resulting in specimens with variable densities. The state of thepractice in earthwork consists of compacting a layer to apredetermined density, independent of the energy (in this case,the number of passes of the compactor), and the moisture content.In the constant density method of compaction (unlike the Proctormethod), the number of blows (i.e., the compaction energy) ischanged by a trial and error process to achieve a desired densityindependent of the moisture content (Pacheco and Nazarian,2011). This method has not yet been standardized and is deemedto be more representative of the field compaction process.

The results of the MR tests on specimens prepared withconstant energy from the granular base material at threemoisture contents (optimum moisture content, OMC, 2% dryof OMC and 1% wet of OMC) are shown in Table 2. Thespecimens prepared at OMCþ2% were too wet to test. Thestiffness parameters k1�k3 from the AASHTO T307 andNCHRP 1-28A protocols are different, despite the fact thatthe instrumentation was the same. These changes are due to thedifferences in the loading sequences used in the two protocols.In AASHTO T307, the deviatoric stress is increased at eachconfining pressure, whereas in NCHRP 1-28A protocol, theconfining pressure is varied for a given deviatoric stress. Theresults from the external instrumentation, as advocated byAASHTO T307 would have been significantly less than thosereported in Table 2 for the internal instrumentation, asdiscussed by Gupta et al. (2007) and others.

The MR tests on the fine-grained soil specimens prepared withboth the constant energy and the constant density compactionmethods were carried out following the AASHTO T307 protocol.These tests were conducted on specimens prepared at threedifferent moisture contents (OMC, 120% OMC and 80% OMC)to investigate the effects of moisture variations on the modulus.All constant density specimens were compacted to the corre-sponding MDD of the material. The MR results for the specimensprepared with the constant energy method are listed in Table 3for fine-grained soils. The representative laboratory modulifrom similar specimens prepared with the constant energy andthe constant density methods are compared in Fig. 1. Moduli

Table 2Laboratory MR results on granular base specimens prepared with the modifiedproctor constant energy method (AASHTO T180).

Protocol Target moisturecontent

Nonlinear parameters RepresentativeMRa, MPa

k1 k2 k3

AASHTO T307 OMC�2% 2031 0.44 �0.14 270OMC 538 0.71 �0.10 89OMCþ1% 674 0.49 �0.10 94

NCHRP 1-28A OMC�2% 1365 0.50 �0.30 181OMC 694 0.60 �0.40 92OMCþ1% 658 0.70 �1.80 53

aFrom Eq. (2) based on presumptive τoct and θ of 52 kPa and 214 kPa.

from these two compaction methods are correlated reasonablywell with a standard error of estimate of about 14 MPa. Theoutliers typically correspond to the specimens that were eithermuch wetter or much drier than their corresponding OMCs formaterials whose variations in dry density with moisture contentare more pronounced.Witczak et al. (2000) recommended the following model, as

part of MEPDG, in order to consider the changes in moduluswith the moisture content:

logMR

MRopt¼ aþ b�a

1þexpðlnð�b=aÞþkmðS�SoptÞÞð3Þ

where MR¼modulus at a degree of saturation S (decimal),MRopt¼modulus at the maximum dry density and optimummoisture content, Sopt¼ degree of saturation (in decimal) at themaximum dry density and optimum moisture content,a¼minimum of log (MR/MRopt), b¼maximum of log (MR/MRopt) and β and km¼ regression parameters. The MEPDGrecommended two separate sets of β and km for coarse grainedand fine-grained geomaterials, as reflected in Fig. 2. Eventhough the trends proposed by Eq. (3) are reasonable, the valuesare somewhat different from the model. This indicates that itmay be prudent to perform lab MR tests at several moisturecontents, if time and budget of the project permit.

3. Small-scale test

Fig. 3(a) shows a schematic of the general setup of thelaboratory small-scale study. The soil profile for each specimenconsists of 150 mm of one of the geomaterials described inTable 1 (except for the SM subgrade) and 400 mm of the SMsubgrade. A layer of pea gravel, 75 mm in thickness, wasplaced at the bottom of the specimen. The pea gravel layer,

OMC 1507 0.29 0.00 1821.2 OMC% 1350 0.29 �0.05 162

CH 0.8 OMC% 828 0.54 �0.22 112OMC 940 0.29 �0.42 1051.2 OMC% 606 0.26 �1.37 56

ML 0.8 OMC% 788 0.77 �1.61 95OMC 620 1.04 �1.91 831.2 OMC% 539 1.00 �1.40 78

SC 0.8 OMC% 2158 0.15 �0.50 218OMC 1408 0.34 �2.09 1191.2 OMC% 210 1.68 �4.12 28

SM (commonsubgrade)

0.8 OMC% 637 0.51 �1.05 49OMC 540 0.99 �2.37 301.2 OMC% 360 1.12 �2.32 20

aFrom Eq. (2) based on presumptive τoct and θ of 86 kPa and 21 kPa.

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0

50

100

150

200

250

0 50 100 150 200 250

Mod

ulus

at C

onst

ant D

ensi

ty ,

MPa

Modulus at Constant Energy, MPa

GWCLCHMLSC

Line of Equality

Fig. 1. Comparison of moduli from specimens prepared at constant energy andconstant density.

0

1

2

3

4

-40 -30 -20 -10 0 10 20

MR/M

Rop

t

S-Sopt, %

Fig. 2. Variations in modulus with degree of saturation for soil specimensprepared with constant energy method.

M. Mazari et al. / Soils and Foundations 54 (2014) 36–44 39

which was placed primarily to facilitate the saturation of thesubgrade under capillary conditions, was a uniformly-gradedmaterial with particle sizes between 4.75 and 9.5 mm. Thatlayer was deemed too thin and too deep to impact the results;as such, it was not characterized (Amiri et al., 2009).

The specimens were prepared in a 0.9-m-diameter PVC pipethat was placed on a hard floor (1-m-thick concrete) tominimize the movement of the bottom of the specimen. Thesize of the specimens was determined through finite elementmodeling by Amiri et al. (2009) to ensure that the interactionbetween the horizontal and vertical boundaries and the modelpavement would be minimal. A diameter of 0.9 m was deemedadequate since the stresses and strains at the boundaries weretypically less than 3% of the stresses applied to the specimen.Also, a geophone was used to monitor the movement of thefloor to ensure that the specimen would not move excessively.

A concrete mixer was applied to prepare the subgrade and thegeomaterial layer to the desired moisture contents. A specificamount of dry geomaterial, necessary to achieve the desireddensity for a 50-mm lift, was mixed with a precise amount ofwater to ensure the exact moisture content. The moist materialwas then transferred into the PVC container and compacted to thedesired density with a hand compactor.

Moisture sensors were embedded within the geomaterials atpredetermined depths during the construction of the specimen(see Fig. 3(a)). Nine geophones were embedded within thespecimen to measure the displacements at different depths.Three sets of resistivity probes were placed to monitor theprogression of the waterfront within the specimen during thesaturation process.

The specimens were subjected to cyclic plate load tests(PLTs) utilizing a servo hydraulic system (Fig. 3(b)). Thenominal contact stresses for the PLT were 210–620 kPa. Inaddition, a lightweight deflectometer (LWD) with a platediameter of 200 mm and a nominal contact stress of 210 kPawas employed to load the specimens (Fig. 3(c)).

4. Analysis of the results

A response algorithm using an equivalent multi-layersystem, as discussed by Ke et al. (2000), was utilized tosimulate the small-scale specimens with the laboratory derivedMR parameters k1�k3 of the layers as input. Ke et al. (2000)demonstrated that this numerical model can provide results thatare very comparable to those of a rigorous FE model. Thecircular load of the LWD or PLT with a uniform stressdistribution was applied to the top of the model. The inputparameters to the model were the number and thickness of thelayers, Poisson0s ratio, the unit weight and the nonlinearregression parameters of k1�k3 obtained from laboratoryresilient modulus tests. The stresses, strains and displacementsat the surface and at the middle depths of the layers were thencalculated by the algorithm. Such results are considered as thenumerical responses of the pavement system.The average experimental deflections at different depths due

to the LWD load, from a specimen with the granular base andthe common subgrade placed at OMC, are compared with thecorresponding numerical results in Fig. 4. The numericalresults when the lab stiffness parameters k1�k3 from theAASHTO T307 and NCHRP 1-28A protocols were used forthe base are similar, despite the differences in estimated k1�k3parameters. These similarities can be fortuitous since, despitedifferences in k1�k3 parameters between the two test proto-cols, their representative resilient moduli are similar. Asreflected in Table 2, for specimens tested at other moisturecontents and based on our experience, the stiffness parametersfrom the two protocols are different.The deflections from the numerical analyses in Fig. 4 are

greater than the measured ones within the geomaterial layerand lesser within the subgrade. This pattern can be attributed tothe nature of Eq. (2) (the MEPDG model) where the modulustends toward zero as the bulk stress approaches zero (i.e., asone moves deeper and further away from the loaded area). Thefact that the numerical and the experimental results cross oneanother was deemed as an impediment to developing arigorous, yet simple, transfer function between them. Toovercome this limitation, the following model (the modifiedMEPDG model) proposed by Ooi et al. (2004) was tried:

MR¼ k01Paθ

Paþ1

� �k02 τoctPa

þ1

� �k03ð4Þ

In this equation, MR tends toward a minimum equal to k01Pa

and not zero. Although Eq. (1) is fundamentally moreappropriate, it was felt that the uncertainty in estimating theadditional parameters from the raw MR data may be balancedby the simplicity of Eq. (4).

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Fig. 3. (a) Schematic of small-scale specimen, (b) plate load test, and (c) light weight deflectometer.

M. Mazari et al. / Soils and Foundations 54 (2014) 36–4440

The variation in displacements with depth, from a nonlinearanalysis using stiffness parameters k01–k03 fitted to Eq. (4), isalso shown in Fig. 4(a). The numerical deflections in this caseare consistently greater than the measured ones, but are not asclose to the experimental data as the previous case whenEq. (2) was used. Based on the statistical analysis alone, onemay conclude that the numerical model from Eq. (2) (with aslope of about 0.8) represents the experimental results betterthan the results from Eq. (4) (with a slope of 0.56). However,as will be discussed later, it is much easier to explain thedifferences between the experimental and the numerical resultsfrom Eq. (4) than from Eq. (2).

The differences between the experimental and the numericalresults are partially due to the differences in the laboratory andthe field moduli of the materials even though they wereprepared at similar densities and moisture contents. Seismicmethods can be used to describe such differences because thelab and the field seismic moduli are theoretically related

without any need for adjustment of the testing boundaryconditions (Nazarian et al., 2005).The seismic modulus is the low-strain initial tangent modulus

of a material obtained based on the principles of wave propaga-tion (Nazarian et al., 2005). The laboratory seismic moduli weremeasured with a Free–Free Resonant Column (FFRC) device(Williams and Nazarian, 2007) on the same specimens as thoseused in the lab MR tests. The FFRC modulus is estimated byapplying an impulse load to a cylindrical specimen whichpropagates seismic energy over a large range of frequencies.Depending on the dimensions and the stiffness of the specimen,some frequencies will be resonated. Combining the dimensions ofthe specimen with the resonant frequencies, the seismic modulusof the specimen can be estimated. The field seismic moduli forthe compacted layers in the small-scale specimens were obtainedusing a portable Seismic Property Analyzer (PSPA, Nazarianet al., 2005). Fig. 5 shows a schematic of both FFRC and PSPAtest methods.

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400

500

600

10.50

Dep

th, m

m

Deflection, mm

ExperimentalMEPDG Model (Eq. 2) with NCHRP 1-28A ProtocolMEPDG Model (Eq. 2) with AASHTO T307 ProtocolModified MEPDG Model (Eq. 4) with AASHTO T307

0

Numerical Deflection, mm

Modified MEPDG (T307)y = 0.56x

MEPDG (T307)y = 0.79x

MEPDG (1-28A)y = 0.80x

0.5

1

1.5Expe

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efle

ctio

n, m

m

Modified MEPDG Model (Eq. 4) with AASHTO T307 ProtocolMEPDG Model (Eq. 2) with AASHTO T307 ProtocolMEPDG Model (Eq. 2) with NCHRP 1-28A Protocol Line of Equality

1.5

10.50 1.5

Fig. 4. Comparison of experimental and numerical geophone deflections fromLWD tests on GW base materials placed at OMC, (a) geophone deflectionswith depth, (b) comparison of geophone deflections.

M. Mazari et al. / Soils and Foundations 54 (2014) 36–44 41

The lab seismic moduli of the same specimens used in thelab MR tests for the case shown in Fig. 4 were 90 MPa and49 MPa for the geomaterial and the subgrade layers, respec-tively. The field seismic moduli for the compacted layers in thesmall-scale specimen were 292 MPa (about 3 times greaterthan lab modulus) and 102 MPa (about 2 times greater than labmodulus) for the geomaterial and the subgrade layers,respectively.

As reflected in Fig. 4(b), the slope between the measuredand the numerical deflections is about 0.56 (i.e., the numericaldeflections are about twice the measured ones), which isconsistent with the differences in the seismic lab and thesmall-scale moduli observed. This case study points to theimportance of considering the differences between the lab andthe field measured moduli in order to develop a rigoroustransfer function.

The variations in deflections at the four contact stresses withdepth from the Plate Load Tests (PLTs), conducted shortlyafter the LWD tests, are presented in Fig. 6. The data presentedcorrespond to a 200 mm-diameter plate that is identical to thediameter of the LWD plate. The measured deflections increaseas the contact stress increases for all depths. However, theincreases in deflections are not linearly proportional to theincrease in contact stress, pointing to the nonlinear behavior ofthe materials (especially for the deflections within the geoma-terial layer).

As reflected in Fig. 6(b), the measured and the calculateddeflections from the nonlinear analyses with the model of Eq.(4) are globally correlated well with a slope of 0.64. This slopeis greater than the slope of 0.56 obtained from the LWD test inFig. 4(b). The differences in the two slopes may be attributedto the dynamic nature of the LWD tests as compared with thelow frequency (2 Hz) cyclic load applied in the PLT tests. A

comparison of the numerical results from Eq. (2) and theexperimental results is also included in Fig. 6(b). A consistenttrend is not observed even though these numerical results arestatistically closer to the experimental results.To analyze the impact of the plate diameter on the response

of the specimens, the plate load tests were repeated with plates100 mm and 300 mm in diameter. The measured and thenumerical deflections from the three plates at a constant stressstate of 210 kPa are correlated well with a slope of 0.55, asshown in Fig. 7(a). This would not have been the case with thelayered elastic analyses.The next step was to study the impact of the compaction

moisture content on the outcomes of the analyses. A small-scale specimen was prepared for which the geomaterial layerwas placed at 2% dry of OMC. As reflected in Fig. 8(a), theexperimental deflections are 0.37 of the numerical ones, whichindicates that the differences among the lab and the field areeven more significant when the geomaterial layer is placed dryof optimum. In that case, the seismic lab modulus was about26% of the corresponding modulus measured on top of thesmall-scale specimen. A careful examination of the data fromindividual plates demonstrates that the difference between themeasured and the estimated deflections differs more signifi-cantly as the plate diameter increases. The geomaterial layerexperiences more nonlinear behavior as the stresses increasewith changes in the diameter of the plate.Similar to our laboratory experiment, it was not possible to

test the small-scale specimen placed at OMCþ2%, because itwas too soft to maintain the stresses from the LWD or the PLTtests without significant rutting. As such, the specimen wasallowed to dry back to OMC before it was tested. In this case,the lab-derived stiffness parameters for the GW granular baseat the OMC were used to model the geomaterial layer.The measured deflections when the specimen was dried

back to OMC and the numerical deflections using the stiffnessparameters from the lab MR tests at OMC are compared inFig. 7(b). The measured deflections are about 0.3 times thenumerical ones, indicating that the geomaterial layer issignificantly stiffer than when it was placed and tested atOMC-2% (Fig. 8(a) with a slope of 0.37) or when it wasplaced and tested at OMC (Fig. 7(a) with a slope of 0.55). Thispattern demonstrates that the moisture content at the time oftesting, relative to the moisture content at compaction, mayimpact the laboratory and the field stiffness, as shown inPacheco and Nazarian (2011). Such a pattern can be morerigorously explained considering that the soil suction of amaterial compacted and tested at a given moisture content issignificantly different than the soil suction of a material placedat a higher moisture content and allowed to dry to a givenmoisture content. The patterns reported in Figs. 7 and 8(b) aresimilar to those reported by Khoury and Zaman (2004) andTinjum et al. (1997).Finally, the relationship between the measured and the

numerical deflections for the specimen placed and tested atOMC-2%, but with a subgrade layer saturated under capillaryconditions, is shown in Fig. 8(b). The slope of 0.29 of the bestfit line is less than 0.37 obtained in Fig. 8(a) for the same

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Fig. 5. (a) Free–free resonant column (FFRC) test, and (b) portable seismic property analyzer (PSPA) test.

y = 0.64x

0

0.5

10

Numerical Deflection, mm

0

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200

300

400

500

600

0.0

Dep

th, m

m

Deflection, mm

Exp. 210 kPa Exp. 340 kPa Exp. 480 kPa Exp. 620 kPa Num. 210 kPa Num. 340 kPa Num. 480 kPa Num. 620 kPa

1

1.5Expe

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efle

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n, m

m

210 kPa-with Modified MEPDG Model (Eq. 4) 340 kPa-with Modified MEPDG Model (Eq. 4)480 kPa-with Modified MEPDG Model (Eq. 4) 620 kPa-with Modified MEPDG Model (Eq. 4)210 kPa-with MEPDG Model (Eq. 2) 340 kPa-with MEPDG Model (Eq. 2)480 kPa-with MEPDG Model (Eq. 2) 620 kPa-with MEPDG Model (Eq. 2)

Line of Equality

0.5 1.0 1.5

0.5 1.5

Fig. 6. Comparison of experimental and numerical deflections from plate loadtests with a 200 mm loading plate at different stress states for GW granularbase materials placed at OMC, (a) geophone deflections with depth, (b)comparison of geophone deflections.

y = 0.55x

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1.5

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efle

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m

Numerical Deflection, mm

100 mm Plate200 mm Plate300 mm Plate Line of Equality

y = 0.30x

0

0.5

Numerical Deflection, mm

1

1.5Expe

rimen

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efle

ctio

n, m

m

Line of Equality

100 mm Plate200 mm Plate300 mm Plate

0.5 1.5

10 0.5 1.5

Fig. 7. Comparison of experimental and numerical deflections from plate loadtests at 210 kPa applied stress with different loading plate diameters for GWgranular base, (a) materials placed at OMC, and (b) materials placed atOMCþ2% and dried back to OMC.

M. Mazari et al. / Soils and Foundations 54 (2014) 36–4442

specimen, but with the subgrade placed and tested at theoptimum. This indicates that the laboratory parameters areunderestimating the field moduli.

An interesting pattern emerges when the numerical and theexperimental results from Fig. 8(a) and (b) are compared. Onaverage, the deflections from the specimen with the subgradesaturated condition are 1.16 times the deflections from thesame specimen, but when the subgrade was placed at OMC.

The numerical results, however, differ by 1.55 times. Aplausible explanation for this discrepancy can be the differ-ences in the generation of pore pressure during the lab MRtesting and the testing with the small-scale specimens. SinceMR tests are undrained cyclic tests, the pore pressuresgenerated in the lab close to saturation (in this case, 1.2OMC for the common subgrade) may cause lower thananticipated stiffness parameters. When these values are usedin the numerical models, the deflections within the body of thematerial are overpredicted, as discussed above.

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M. Mazari et al. / Soils and Foundations 54 (2014) 36–44 43

To further investigate the trends between the laboratorymeasurements and the numerical responses, additional small-scale specimens were prepared with the four fine-grained soilslisted in Table 1 at 0.8, 1 and 1.2 of their correspondingOMCs. The results from plate load tests with different platediameters (100, 200 and 300 mm) at various stress levels of210, 340, 480 and 620 kPa, when materials are placed atOMC, are depicted in Fig. 9. Observing the slopes from thisfigure, the numerical responses overestimate the measuredones by a factor of 0.25–0.36.

y = 0.31x

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4

0 1 2 3 4

Expe

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efle

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n, m

m

Numerical Deflection, mm

Line of Equality

y = 0.26x

0

1

2

3

4

0 1 2 3 4

Expe

rimen

tal D

efle

ctio

n, m

m

Numerical Deflection, mm

Line of Equality

Fig. 9. Comparison of experimental and numerical deflections from plate load testOMC and then tested after 24 h.

y = 0.37x

0

0.5

1

1.5

Expe

rimen

tal D

efle

ctio

n, m

m

Numerical Deflection, mm

100 mm Plate200 mm Plate300 mm Plate Line of Equality

y = 0.29x

0

0.5

Numerical Deflection, mm

1

1.5

Expe

rimen

tal D

efle

ctio

n, m

m

10 0.5 1.5

100 mm Plate200 mm Plate300 mm Plate Line of Equality

10 0.5 1.5

Fig. 8. Comparison of experimental and numerical deflections from plate loadtests at 210 kPa applied stress with different loading plate diameters for GWgranular base, (a) placed at OMC-2%, and (b) placed at OMC-2% and thentested after saturation of subgrade.

The slopes of the lines similar to Fig. 9 are summarized inFig. 10 for all materials and moisture conditions. In general,the average differences between the numerical and the experi-mental results (ignoring the case of the saturated subgradeconditions) vary between 0.33 and 0.55. To some extent thismay explain the findings of Von Quintus and Killingsworth(1998) that, on average, the lab derived moduli are 0.35–0.52of those measured in the field. The greatest mismatch betweenthe numerical and the experimental results is for the case whenthe subgrade was saturated. As indicated above, this may be atleast partially explained by the buildup pore pressure duringlaboratory MR tests.

5. Conclusions

The accuracy of a nonlinear response algorithm, as afunction of the laboratory derived stiffness parameters asinput, was evaluated in this paper under different loadingand moisture conditions. Based on the results presented, thefollowing conclusions are drawn:

y = 0.36x

0

1

2

3

4

0 1 2 3 4

Expe

rimen

tal D

efle

ctio

n, m

m

Numerical Deflection, mm

Line of Equality

y = 0.25x

0

1

2

3

4

0 1 2 3 4

Expe

rimen

tal D

efle

ctio

n, m

m

Numerical Deflection, mm

Line of Equality

s at all stress levels and all loading plate diameters for geomaterials placed at

Fig. 10. Summary of differences between numerical and experimental resultsfor geomaterials tested (the results from CH materials placed at 1.2 OMC werenot obtainable due to excessive cracking while drying).

Page 9

M. Mazari et al. / Soils and Foundations 54 (2014) 36–4444

�

The results from laboratory MR tests, following differentprotocols, yielded different stiffness parameters for thesame general resilient modulus model.

�

The resilient modulus model, proposed by the MEPDG,may not be as appropriate for the nonlinear modeling ofpavement responses, since the modulus tends toward zero inareas away from the load. Even though on average thenumerical results from the Ooi et al. (2004) model differmore from the experimental results than the traditionalMEPDG model, the Ooi model seems to explain theresponses of the materials more consistently. For the mostpart, the differences between the numerical results from theOoi model and the experimental results could be explainedby differences in the measured lab and field moduli at thesame moisture content and density.

�

Comparing the deflections measured and simulated under alight weight deflectometer (LWD) and plate load tests(PLTs) at different moisture conditions and loads, it seemsthat the current nonlinear response models simulate thepatterns of field measurements reasonably well.

�

A transfer function is needed to account for the differencesin the field and the lab stiffness of the different layers due todifferences in the compaction methods and loading bound-ary conditions. This transfer function seems to be a functionof the moisture content at the time of compaction as well asthe moisture content at the time of evaluation.

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