RESEARCH ARTICLE

Finite element modeling of environmental effects on rigidpavement deformation

Sunghwan KIM, Halil CEYLAN, Kasthurirangan GOPALAKRISHNAN*

Department of CCEE, Iowa State University, Ames, Iowa 50011, USA*Corresponding author. E-mail: rangan@iastate.edu

Higher Education Press and Springer-Verlag Berlin Heidelberg 2014

ABSTRACT In this study, nite element (FE)-based primary pavement response models are employed forinvestigating the early-age deformation characteristics of jointed plain concrete pavements (JPCP) under environmentaleffects. The FE-based ISLAB (two-and-one-half-dimensional) and EverFE (three-dimensional) software were used toconduct the response analysis. Sensitivity analyses of input parameters used in ISLAB and EverFE were conducted basedon eld and laboratory test data collected from instrumented pavements on highway US-34 near Burlington, Iowa. Basedon the combination of input parameters and equivalent temperatures established from preliminary studies, FE analyseswere performed and compared with the eld measurements. Comparisons between eld measured and computeddeformations showed that both FE programs could produce reasonably accurate estimates of actual slab deformations dueto environmental effects using the equivalent temperature difference concept.

KEYWORDS jointed plain concrete pavements (JPCP), curling and warping, sensitivity analyses, rigid pavement analysis anddesign, nite element analysis (FEA)

1 Introduction

Studies focusing on deformation characteristics of early-age JPCP subjected to pure environmental effects havedrawn signicant interest among concrete pavementresearchers [17]. It is believed that the early-agedeformation of portland cement concrete (PCC) slabscould result in the loss of pavement smoothness [2,8] andthe tensile stresses induced by these deformations couldresult in early-age cracking [9,10]. However, the complexnature of the curling and warping phenomenon arisingfrom interactions of multiple environmental factors hasresulted in difculties in predicting the jointed plainconcrete pavements (JPCP) deformation characteristicsunder environmental effects.The application of nite element (FE) modeling

techniques in recent times has signicantly improved ourunderstanding of concrete pavement behavior [1121].Especially, the new American Association of State High-way and Transportation Ofcials (AASHTO) pavementdesign guide and its associated software, Pavement-ME

(or DARWin-ME), employs FE-based mechanisticanalysis models to calculate concrete pavement responsesfor providing pavement analysis and performance predic-tions under various what-if scenarios. Thus, it isnecessary to evaluate the FE-based pavement responsemodels in relation to their prediction accuracies. But, onlyfewer studies are reported in the literature primarilyfocusing on concrete pavement responses to trafc loadingconditions [22].This study focuses on evaluation of two FE-based

primary response models, namely ISLAB 2000 [23] andEverFE 2.24 [24], for characterizing the deformation ofearly-age JPCP under environmental loading. Thesemodels were selected primarily because they possessome special advantages over other FE programs. TheISLAB 2000 2.5-D FE program was used as the mainstructural model for generating rigid pavement responsesin the new AASHTO pavement design procedure develo-ped under the NCHRP 1-37A project [25], and EverFE2.24 is the only 3D FE program specically designed formodeling and analyzing rigid pavements [26]. Bothmodels are used signicant by pavement design engineers.The main differences between these two programs includeArticle history: Received Jan. 31, 2014; Accepted Mar. 17, 2014

Front. Struct. Civ. Eng.DOI 10.1007/s11709-014-0254-x

nite element structures and analysis functions, foundationtypes that can be assumed, and number of layers abovefoundation.The numerical models used in both the FE programs for

computing slab deformation under environmental effectsare briey discussed in this paper. Sensitivity analyses ofinput parameters used in ISLAB 2000 and EverFE 2.24were carried out based on eld and laboratory test datacollected from instrumented pavements on highway US-34near Burlington, Iowa. Field-measured and the FE-computed slab deformations are also discussed andcompared in this paper. The primary objective of thisstudy is to evaluate the ability of FE programs formodeling the deformation of early age JPCP underenvironmental effects.

2 Existing rigid pavement FE programsused in modeling environmental effects

The temperature and moisture variations across the depthof rigid pavements result in pavement deformation referredto as curling and warping. Other factors contributing tocurling and warping include the permanent built-innegative or positive curling that occurs during the concretehardening, the permanent warping due to differentialshrinkage, and the weight of the slab contributing to thecreep of the slab [27,28]. Therefore, the deformationcaused by each of these factors must be taken intoconsideration. Although analytical [29] or numericalsolutions have been used in the past to predict the rigidpavement responses, such as stress, strain or deectionunder environmental effects without conducting laboratoryor eld experiments, these methods have their ownlimitations and have not been successfully used in fullycharacterizing the environmental effects.

2.1 ISLAB 2000

ISLAB 2000 is a 2.5-D FE program for the analysis of rigidpavements developed by Applied Research Associates(ARA), Inc. with support from the Michigan Departmentof Transportation and the Minnesota Department ofTransportation [23]. The ISLAB 2000 is the most recentversion of an evolving ILLI-SLAB program developed in1977 at the University of Illinois at Urbana-Champaign,and is the primary structural model for generatingpavement responses in the MEDPG software [25]. Duringthe improvement and extension of ILLI-SLAB over theyears, curling analysis was incorporated in 1989 byKorovesis [30].To calculate the deection due to temperature, a thin

plate element (Kirchhoff plate element) having threedeection components at each node (i.e., a verticaldeection in z-direction, a rotation (x) about the x-axis,and a rotation y about the y-axis) is used for a concrete

slab on Winkler foundation or dense liquid foundation.The equilibrium matrix equation of element assemblageshown in Eq. (1) is formulated using the principle of virtualwork and is used to calculate the stress, strain anddeection incorporating the element boundary condition[30]. Temperature effect is considered through the loadvector in Eq. (1). The stressstraintemperature relationshown in Eq. (2) is used to derive this load vector due totemperature.

P KU , (1)where, P = load vector = PB + PSPI + PC; PB = loadvector due to element body forces; PS = load vector due toelement surface forces; PI = load vector due to elementinitial stresses; PC = concentrated loads; K = structurestiffness matrix; and U = deection vector.

t tTE tE, (2)where, t = stress due to temperature; and t = strain due totemperature = tT.Since the load vector in Eq. (1) includes the selfweight

of the layer and the temperature distribution, the calculateddeformation shown in Fig. 1(a) is more realistic than ananalytical solution but still does not include the deectiondue to the moisture changes and the permanent curling andwarping.

2.2 EverFE 2.24

EverFE is a 3D FE analysis tool for simulating theresponse of JPCP to trafc loads and temperature effects.The original software, EverFE 1.02, was developed at theUniversity of Washington and has been continuouslyupgraded. The most recent version, EverFE 2.24, was usedin this study. EverFE 2.24 is in the public domain and caneasily be obtained [24].EverFE uses ve elements for simulating JPCP systems:

20-noded quadratic element having three deectioncomponents at each node are used for the slab, elasticbase, and sub-base layer; 8-noded planar quadraticelements model the dense liquid foundation below thebottom-most elastic layer; 16-noded quadratic interfaceelements implement both aggregate interlock joint andshear transfer at the slab-base interface; and 3-nodedembedded exural elements coupled with conventional 2-noded shear beams are used to model the dowel bars andtie bars [26]. The subgrade models available in EverFE aredense liquid foundations with and without supportingvertical tension [26]. Similar to ISLAB 2000, theequilibrium matrix equation of element assemblage isformulated and is used to compute the stresses, strains anddeections incorporating boundary condition of element.The formulation of structural stiffness, K, is required tosolve the equilibrium equation. However, 3D models ofrigid pavement systems need combinations of large

2 Front. Struct. Civ. Eng.

memory and computational requirements if using the directmatrix factorization for K. To circumvent this problem,EverFE employs multi-grid methods to solve the equili-brium equation, which are some of the most efcientiterative techniques available [31,32].Like ISLAB 2000, the temperature changes are

converted to equivalent element strains via the slabcoefcient, and these strains are numerically integratedover the elements to generate equivalent nodal forces [33].The computed deections from EverFE 2.24 can beprovided in the form of 3D deformed shapes, as shownin Fig. 1(b), or in terms of numerical values, depending onthe users choice. Like ISLAB 2000, EverFE 2.24 also haslimitations with respect to environmental effect analysis,i.e., it cannot directly calculate deections due to themoisture change and the permanent curling and warping.

3 Sensitivity of FE-based input parametersto slab deformations under environmentaleffects

The MEPDG developed under the NCHRP 1-37Aemploys FE-based models to compute pavement primaryresponses for predicting rigid pavement performance.Although ISLAB 2000 and EverFE 2.24 have limitationsin calculating slab deformations under environmentaleffects, it is important to evaluate these programs andcompare eld measurements and predicted responses as arst step in calibrating the models to improve the accuracyof prediction. To do this, it is desirable that the inputparameters used in the simulations be as close as possibleto the actual situation. However, it is not necessary tocollect all input parameters in the eld or from laboratorytesting and use them to model actual behavior. Sensitivityanalyses can be performed to identify the critical inputparameters that have the most effect on curling analysis.Based on the results of sensitivity analyses, realisticcombinations of input parameters can be established tomodel the actual eld behavior.A total of eight key inputs related to material properties

and climate were selected for sensitivity analyses usingboth ISLAB 2000 and EverFE 2.24. The concretepavement was modeled as a six-slab system (3 panels ineach lane) over a dense liquid foundation. Based on typicalrigid pavement geometry used for highway pavements inIowa (IDOT, Available at http://165.206.203.37/Oct_2005/RS/frames.htm (accessed May, 2006)), eachslab was modeled. The passing lane was 3.7 m in width,and the travel lane was 4.3 m in width. The transverse jointspacing and thickness of each slab were 6 and 267 mm.It is important to note that EverFE 2.24 employs either

tension or tensionless supporting dense liquid foundationbelow the bottom-most elastic layer [33]. The tensionlesssupporting foundation accounts for the subgrade withcompression. The tension supporting foundation accountsfor the subgrade with compression and tension. TheEverFE 2.24 assumes the tension supporting foundation bydefault while the ISLAB 2000 automatically assumestensionless supporting foundation when the curlinganalysis is performed to provide more realistic solutions.The dense liquid foundations used in sensitivity analysis ofthis study employed tensionless supporting foundation forISLAB 2000. In the case of EverFE 2.24, both tensionlessand tension supporting foundation were employed.When any one input parameter was varied over the

typical range of values, the values of the other inputparameters were held constant at standard values duringthe sensitivity analyses. Table 1 summarizes the inputparameters and ranges used in this study. These rangeshave been selected based on the information reported in theliterature [25] related to curling and warping studies.Analytical results were used to quantify the slab

deformation and shape for each combination of inputs.The total amount of deformation was quantied using therelative corner-to-center (Rc) deection in the deneddirection on surface of modeled concrete pavements. TheRc values could easily be calculated by subtracting theelevation of center in the dened direction from that ofcorner in the same direction. The centers of deneddirections could be varied, i.e., the centers in transverse,longitudinal and diagonal directions correspond to mid

Fig. 1 Deformed slab shape generated from ISLAB 2000 and EverFE2.24 due to temperature differences. (a) ISLAB 2000; (b) EverFE 2.24

Sunghwan KIM et al. FE modelling of environmental effects on rigid pavement deformation 3

transverse joint, mid longitudinal joint and slab center,respectively.The mid-line slabs in the traveling lane were selected in

this study. This is because the middle slabs among three-panels in each lane (i.e., 6slab assembly) were connectedto the other slabs through transverse joints, whichrepresents realistic slab condition in JPCP. The diagonaldirection Rc values for the modeled concrete pavement aresummarized in Tables 2 and 3.Based on the observation of absolute difference (ABD)

of Rc between two adjacent input values in one parameter,the calculated Rc are signicantly inuenced by severalinput parameters including the coefcient thermal expan-sion (CTE), temperature difference between top andbottom of slab, elastic modulus and modulus of subgardereaction. This nding is quite reasonable considering thoseparameters composing the equilibrium matrix equation ofelement assemblage of these two FE programs (see Eqs.(1) and (2)). Especially, small changes in CTE andtemperature difference between top and bottom of slabresulted in relatively large difference of Rc.The differences in deections calculated using the two

FE programs were also investigated. The deections ofEverFE 2.24 with tensionless foundation were nearlysimilar to those of ISLAB 2000 with tensionless founda-tion within about 7% of average difference. Wang et al.[22] reported that small differences could be found evenwhen the basic theory underlying the FE programs is thesame. They explained that small differences observedactually lie in the details of each program related toprogram coding issues such as nonlinearity, approxima-tion, treatment of elements at interfaces and discontinu-ities, rounding off of numbers, etc.However, the deections of EverFE 2.24 with tension

foundation were about 30% less than those of ISLAB 2000with tensionless foundation. The magnitude of differencesbetween the two programs increased as the estimateddeections increased in general. These results indicate thata good agreement of curling analysis between the twoprograms could be obtained with the same foundationmodel (tensionless foundation).

3.1 Test pavement description

A newly constructed JPCP section on well-graded granularbase on US-34 near Burlington, Iowa was selected for thisstudy. The transverse joint spacing was approximately 6 m.The passing lane was approximately 3.7 m in width, andthe travel lane was approximately 4.3 m in width. Tie-barsof 914 mm length and 12.7 mm diameter were insertedapproximately every 762 mm across the longitudinaljoints. Dowel bars of 457 mm length and 38 mm diameterwere inserted approximately every 305 mm across thetransverse joints. The powder type curing compounds weresprayed on slabs during early cure period, but no protectionagainst wind was employed in the test sections.Two test sections in the JPCP travel lane, one

corresponding to afternoon (June 7, 2005, 5:30 PM CST)construction conditions and the other representative of latemorning (June 8, 2005, 10:45 AM CST) construction,were selected for eld data collection.Thermochron I-Buttons were placed throughout the

depth of the pavement in each section during constructionto observe the temperature effect on the slab behaviorduring early age (7 day after construction). As illustrated inFig. 2, surface proling was conducted using a rollingproler (SurPRO 2000) over diagonal and transversedirections on four individual slabs in each test section atdifferent times (the morning and the afternoon) represent-ing negative/positive pavement temperature differenceconditions, especially, to study the slab deformationbehavior.A rolling proler can measure true unltered elevation

prole of the slab surface (ICC, available at http://www.internationalcybernetics.com/ rollprole.htm (accessedMay, 2006)). The raw elevation prole of surface wasltered using a procedure suggested by Sixbey et al. [34]and Vandenbossche [35] to obtain slab deformation patternscalled slab curvature prole. A series of laboratory testswere undertaken during the controlled eld evaluationperiods to provide material input parameter values for FEmodeling. A more detailed description of the test sectionsand test procedures is provided by Kim [36].

Table 1 Summary of input parameters

parameter standard value ranges of value

unit weight/(kg$m3) 2400 2240, 2400, 2560

Poissons ratio 0.2 0.1,0.2,0.3

coefcient of thermal expansion, CTE/( C1) 9.6 106 6.3 106, 9.6 106, 13.5 106, 17.1 106

elastic modulus/MPa 30483 13,790, 30,483, 41,370

load transfer efciency, LTE/ % 90 0.1, 50, 90

modulus of subgrade reaction, k/(kPa$mm1) 62.4 8.1, 35.3, 62.4, 89.6

FE Mesh size/(mm mm) 254 178 152 152, 254 178, 305 305temp difference between top and bottom of slab/C 1. 8.5C: positive temp. diff.

2. 6.6C: negative temp. diff. 13.3C to 13.3C with increments of 2.2C

4 Front. Struct. Civ. Eng.

3.2 Simulation methods

The FE simulations were conducted based on the actualgeometric proportions and the collected material proper-ties. Note that the actual geometric proportions in US-34near Burlington, Iowa are same as the ones used forsensitivity analyses in this study. The modulus of subgradereaction (k) was required in FE simulations. The results ofprevious sensitivity runs demonstrated that the slabdeformation increased by increasing the modulus of

subgrade reaction (k) from 8.1 kPa/mm to 35.3 kPa/mm,but after 35.3 kPa/mm, the slab deformation did notincrease much. The k-value, 35.3 kPa/mm, is a typicalminimum value for Iowa conditions and therefore, 62.4kPa/mm was assumed as the k-value for the FE simula-tions.The values of input parameters used in this simulation

are summarized in Table 4. A six-slab system (3 panels ineach lane), as shown in Fig. 3, was used and the middleslab in the travel lane was selected representative of eld

Table 2 Sensitivity of relative corner deections (Rc) to input parameters in ISLAB 2000 and EverFE 2.24 at positive temperature difference

condition

input parameter input value

Rc/M ABD of Rc in input valuesa)/M difference of Rc

b)/%

ISLABc) EverFEd) EverFEe) ISLABc) EverFEd) EverFEe)ISLABc) &EverFEd)

ISLABc) &EverFEe)

unit weight/(kg$m3)

2,240 1035 975 792 0 0 0 6.2 30.8

2,400 1007 954 792 28 21 0 5.6 27.2

2,560 983 933 792 25 20 0 5.3 24.1

Poissons ratio 0.1 954 898 758 0 0 0 6.3 25.9

0.2 1008 954 792 53 56 33 5.7 27.3

0.3 1066 1012 830 58 58 38 5.3 28.4

CTE/(106 C1)

6.3 564 518 518 0 0 0 8.9 8.9

9.63 1008 954 792 444 436 274 5.7 27.3

13.5 1599 1474 1110 591 520 318 8.5 44.0

17.1 2193 1975 1406 594 502 296 11.0 55.9

Elasticmodulus/MPa

13790 540 504 504 0 0 0 7.2 7.2

30483 1007 954 792 467 450 288 5.6 27.2

41370 1189 1128 921 182 175 129 5.4 29.1

LTE/% 0.1 1018 957 794 0 0 0 6.4 28.2

50 1012 952 791 6 4 4 6.2 27.9

90 1008 954 786 4 1 5 5.7 28.3

k/(kPa$mm1) 8.1 1660 1614 1614 0 0 0 2.8 2.8

35.3 1,149 1032 1032 510 583 583 11.4 11.4

62.4 1,007 954 792 142 78 240 5.6 27.2

89.6 932 856 653 75 98 138 8.9 42.6

mesh size/(mm mm)

152 152 1007 956 793 0 0 0 5.3 27.0254 178 1007 954 792 0 2 1 5.6 27.2305 305 1006 951 791 1 3 1 5.8 27.2

temp. diff./C 2.2 211 207 207 0 0 0 2.3 2.3

4.4 427 414 414 215 207 207 3.1 3.1

6.7 721 621 621 294 207 207 16.1 16.1

8.9 1072 1012 828 351 391 207 6.0 29.5

11.1 1455 1279 1035 383 267 207 13.7 40.5

13.3 1861 1699 1242 406 420 207 9.5 49.8

a) Absolute difference (ABD) of Rc between two adjacent input values in one parameterb) % Difference of Rc in FE programs =

Rc of ISLAB 2000 Rc of EverFE 2:24

Rc of EverFE 2:24

100

c) ISLAB 2000 with tensionless foundationd) EverFE2.24 with tensionless foundatione) EverFE2.24 with tension foundation

Sunghwan KIM et al. FE modelling of environmental effects on rigid pavement deformation 5

conditions. Since previous sensitivity runs indicated nosignicant differences in curling analysis results betweenISLAB 2000 and EverFE2.24 with same dense liquidfoundation (the tensionless supporting foundation), thetensionless supporting liquid foundation for ISLAB 2000and the tension supporting liquid foundation forEverFE2.24 were selected in comparing the measuredslab deformations.Even though the slab temperature prole with depth has

been recognized as a nonlinear distribution, the observed

temperature proles under which pavement prole datawere collected in this study showed a nearly lineartemperature distribution as illustrated in Fig. 4, so that atemperature difference between the top and bottom of slabwas used in this simulation.

3.3 Equivalent temperature difference

Even though ISLAB 2000 and EverFE 2.24 can model slabdeformations due to temperature changes, they cannot

Table 3 Sensitivity of relative corner deections (Rc) to input parameters in ISLAB 2000 and EverFE 2.24 at negative temperature difference

condition

input parameter input value

Rc/M ABD of Rc in input valuesa)/M difference of Rc

b)/%

ISLABc) EverFEd) EverFEe) ISLABc) EverFEd) EverFEe)ISLABc) &EverFEd)

ISLABc) &EverFEe)

unit weigh/(kg$m3)

2240 851 806 611 0 0 0 5.5 39.2

2400 828 790 611 23 17 0 4.8 35.4

2560 807 776 611 21 14 0 4.0 31.9

Poissons ratio 0.1 790 734 585 0 0 0 7.6 34.9

0.2 828 790 611 38 56 26 4.9 35.5

0.3 870 856 641 42 66 30 1.7 35.7

CTE/(106 C1)

6.3 466 400 400 0 0 0 16.4 16.4

9.63 828 790 611 363 390 211 4.9 35.5

13.5 1326 1213 857 498 423 246 9.3 54.7

17.1 1838 1629 1085 512 416 228 12.8 69.4

Elasticmodulus/MPa

13790 486 470 390 0 0 0 3.2 24.7

30483 828 790 611 342 319 222 4.8 35.4

41370 970 922 711 143 132 100 5.2 36.5

LTE/% 0.1 843 796 613 0 0 0 5.9 37.5

50 830 788 611 14 9 3 5.3 35.9

90 828 790 607 1 2 4 4.9 36.5

k/(kPa$mm1) 8.1 1276 1247 1247 0 0 0 2.4 2.4

35.3 923 797 797 353 450 450 15.9 15.9

62.4 828 790 611 95 7 185 4.9 35.5

89.6 778 721 504 50 69 107 7.9 54.3

mesh size/(mm mm)

152 152 829 791 612 1 0 0 4.7 35.4254 178 828 790 611 1 2 1 4.9 35.5305 305 825 788 611 3 2 1 4.7 35.0

temp. diff./C 2.2 212 208 208 0 0 0 2.0 2.0

4.4 488 415 415 276 207 207 17.7 17.7

6.7 847 807 621 359 392 206 5.0 36.5

8.9 1266 1091 829 419 284 208 16.1 52.7

11.1 1724 1536 1036 459 446 207 12.3 66.5

13.3 2208 1923 1243 484 387 207 14.8 77.7

a) Absolute difference (ABD) of Rc between two adjacent input values in one parameterb) % Difference of Rc in FE programs =

Rc of ISLAB 2000 Rc of EverFE 2:24

Rc of EverFE 2:24

100

c) ISLAB 2000 with tensionless foundationd) EverFE2.24 with tensionless foundatione) EverFE2.24 with tension foundation.

6 Front. Struct. Civ. Eng.

directly model the slab deformations due to moisturevariations and permanent curling and warping, which canbe signicant for concrete pavement behaviors. Therefore,if FE modeling was conducted using the actual materialinputs and the linear / nonlinear temperature distribution,the calculated deection could not estimate the actualdeection due to environmental effects [1]. However, it hasbeen believed that this limitation of these FE programscould be circumvented if the effects of other environmentaleffects could be converted to equivalent temperaturedifference [26,30].Since all of the environmental effects are highly

correlated with each other, it is quite difcult to quantify

each of these effects in terms of temperature differences.Therefore the concept of combining all of the active effectsinto an equivalent temperature difference has been usedby previous researchers [1,20,37,38]. Using this concept,the relation between actual measured temperature differ-ence and equivalent temperature difference associated withactual pavement behavior could be established. Anequivalent temperature difference was determined toproduce each FE calculated deformation that matchesmeasured deformation (measured along the slab diagonalfor a given measured temperature difference). Once theequivalent differences were determined for all of themeasured temperature differences, they were plotted todevelop the linear relations shown in Figs. 5 and 6.Based on linear regression equations from Figs. 5 and 6,

equivalent temperature differences calculated from mea-sured pavement prole data were used as inputs for bothFE programs. Note that the linear regression equationsfrom Figs. 5 and 6 are different because of differentfoundation models used.

4 Examination of FE models based on eldmeasurements

Comparisons between the eld-measured slab curvatureproles and the FE-computed slab curvature proles in

Fig. 2 Surface proling pattern

Table 4 Values of input parameters used in FE simulation

layer No. of lane slabs slab width/m slab length/m slab depth/mm

geometryproperties

concrete passing 3 3.7 6 267

travel 3 4.3 6 267

materialproperties

concrete property value

modulus of elasticity/MPa 22000

unit weight/(kg$m3) 2400

Poissons ratio 0.2

coefcient of thermal expansion/(C1) 11.2 106

dowel bar diameter/mm 38

length/mm 457

spacing/mm 305

modulus of elasticity/MPa 200000

Poissons ratio 0.3

tie bar diameter/mm 13

length/mm 914

spacing/mm 762

modulus of elasticity/MPa 200000

Poissons ratio 0.3

subgrade modulus of subgrade reaction/(kPa$mm1) 62.4

Sunghwan KIM et al. FE modelling of environmental effects on rigid pavement deformation 7

terms of Rc and the curvature of slab prole (k) wereundertaken to evaluate the accuracy of the FE-basedmodels. The curvature of slab prole (k) was calculated

using a methodology reported by Vandenbossche andSnyder [39]. The quantitative comparisons between themeasured proles and the FE-modeled proles for testsection 1 and test section 2 are presented in Figs. 7-10.From these gures, it is clearly noted that the measured

slab curvature proles at negative temperature differencesshow more pronounced upward curl than at positivetemperature differences, except for transverse directionmeasurements on test section 1. The behavior of transversedirection measurement on test section 1 is quite difcult toexplain. The deection due to temperature changes couldbe confounded by other environmental effects such asmoisture loss, especially at early ages under poor curingconditions of JPCP. However, it is believed that tempera-

Fig. 3 PCC slab system layout used in nite element simulation

Fig. 4 The example of the observed temperature proles under which pavement prole data were collected

Fig. 5 Equivalent temperature difference versus measured tem-perature difference for ISLAB 2000 with tensionless foundation

Fig. 6 Equivalent temperature difference versus measured tem-perature difference for EverFE2.24 with tension foundation

8 Front. Struct. Civ. Eng.

ture change could be a main dominating factor for slabdeformation due to environmental effects. At this time, theonly plausible explanation for this behavior is that built-inconstruction slope in the transverse direction could behigher than in the diagonal direction. The built-inconstruction slopes used to normalize the raw surfaceprole data were not measured, but estimated from the rawprole data. Therefore, they still inuenced the slabcurvature prole and the relative corner-to-edge deectionused in transverse slab edge curvature prole may be lessobvious than the relative corner-to-center deection.An Analysis of Variance (ANOVA) statistical test was

conducted to determine whether the measured slabcurvature properties (Rc and k) were statistically differentfrom the FE-based predictions. ANOVA results can beexpressed in terms of a pvalue, which represents theweight of evidence for rejecting the null hypothesis [40].The null hypothesis of sample equality cannot be rejectedif the pvalue is greater than the selected signicance level.

Table 5 presents the ANOVA results for Rc and k in termsof pvalue. For the signicance level () of 0.05, Table 5conrms that the FE-based predictions provide goodestimates of slab curvature properties in terms of Rc andk under different conditions except the positive tempera-ture transverse direction proles. Considering the trans-verse direction measurements on test section 1 as discussedpreviously, the inaccuracy of FE-predictions for thepositive temperature transverse proles is not unexpected.

5 Conclusions

This study evaluated two FE-based primary responsemodels, namely ISLAB 2000 and EverFE 2.24, used incharacterizing the deformation of early age JPCP underenvironmental effects. Both models are used signicantlyby pavement design engineers. However, fewer studieshave actually compared their prediction accuracies espe-

Fig. 7 Comparison of relative corner deection (Rc) between measured and FE-predicted slab curvature proles in test section 1. (a)Diagonal direction at negative temperature difference; (b) transverse direction at negative temperature difference; (c) diagonal direction atpositive temperature difference; (d) transverse direction at positive temperature difference

Sunghwan KIM et al. FE modelling of environmental effects on rigid pavement deformation 9

Fig. 8 Comparison of relative corner deection (Rc) between measured and FE-predicted slab curvature proles in test section 2. (a)Diagonal direction at negative temperature difference; (b) transverse direction at negative temperature difference; (c) diagonal direction atpositive temperature difference; (d) transverse direction at positive temperature difference

10 Front. Struct. Civ. Eng.

Fig. 9 Comparison of curvature (k) between measured and FE-predicted slab curvature proles in test section 1. (a) Diagonal direction atnegative temperature difference; (b) transverse direction at negative temperature difference; (c) diagonal direction at positive temperaturedifference; (d) transverse direction at positive temperature difference

Sunghwan KIM et al. FE modelling of environmental effects on rigid pavement deformation 11

cially under environmental load conditions. Using typicalrigid pavement geometry for Iowa highway pavements,sensitivity analyses were conducted using ISLAB 2000and EverFE 2.24 for identifying the input parameters thathave the most inuence on PCC slab deection due toenvironmental effects. The procedure and the results of theFE analyses based on established input parameter

combinations and equivalent temperature differenceswere presented. Comparisons between the eld-measuredand the FE-computed slab deformations due to environ-mental effects were performed. Based on the results of thisstudy, the following conclusions were drawn:1) A good agreement of curling analysis results between

ISLAB 2000 and EverFE 2.24 FE could be obtained when

Fig. 10 Comparison of curvature (k) between measured and FE-predicted slab curvature proles in test section 2. (a) Diagonal directionat negative temperature difference; (b) transverse direction at negative temperature difference; (c) diagonal direction at positivetemperature difference; (d) transverse direction at positive temperature difference

Table 5 ANOVA results for Rc and k of slab curvature proles

temperature differencecondition

response

direction

diagonal transverse

pvaluepredicted vs. actual:

different ?pvalue

predicted vs. actual:different ?

positive Rc 0.67 no 0.00 yes

k 0.99 no 0.00 yes

negative Rc 0.91 no 0.70 no

k 0.99 no 0.18 no

12 Front. Struct. Civ. Eng.

using same dense liquid foundation model (the tensionlesssupporting foundation).2) An equivalent temperature difference at a certain

temperature difference can simply be determined bymaking the FE calculated deformation match the measureddeformation.3) The results from this study showed that the computed

slab deformations from both FE programs using equivalenttemperature difference have reasonable agreement with theeld measured deformations.4) Temperature difference and CTE are the parameters to

which slab deformations are most sensitive based onISLAB 2000 and EverFE 2.24 FE analyses for typical rigidpavement geometry used in Iowa.

Acknowledgements The authors gratefully acknowledge the FederalHighway Administration (FHWA) for supporting this study. The contentsof this paper reect the views of the authors who are responsible for the factsand accuracy of the data presented within. The contents do not necessarilyreect the ofcial views and policies of the Federal Highway Administration.This paper does not constitute a standard, specication, or regulation.

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