NonPAS: A Program for Nonlinear Analysis of Flexible Pavements

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1 International Journal of Integrate Engineering, Vol. 7 No. (05) pp. -8 NonPAS: A Program for Nonlinear Analysis of Flexible Pavements Ali eza Ghanizaeh,*, Arash Ziaie, Department of Civil Engineering, Sirjan University of Technology, 7837 Sirjan, Iran eceive...; accepte..., available online... Abstract: The primary step in esign of a pavement using echanistic-empirical (-E) metho is the analysis of pavement an calculation of the critical responses of pavement uner various loaings. This confirms the nee for eveloping pavement analysis software as an analytical base of the -E metho. To this en, NonPAS program has been evelope for linear an nonlinear analysis of flexible pavements. Develope program allows nonlinear analysis of flexible pavements using five nonlinear moels, incluing -θ, Uzan, Uzan-Witczak, EPDG 00 an Bilinear moels. Nonlinear Analysis of flexible pavements by utilizing these constitutive moels provies a more accurate moeling of granular material behavior. Develope program can be use to analyze a pavement system consists of maximum of 0 layers, which is subjecte to a maximum of six circular loas. NonPAS program allows for calculating the responses at 400 ifferent points of pavement. In orer to valiate the results of linear an nonlinear analysis, responses obtaine from NonPAS have been compare with responses obtaine using enlayer program. esults show very goo agreement between responses, which are obtaine using both linear an nonlinear analysis an approve that evelope program can be use with high reliability for the purposes of pavement analysis an esign. eywors: NonPAS; Pavement analysis; nonlinear constituent moels; layere theory. Introuction Up to now several computer programs have been evelope for flexible pavement analysis an esign. Each of these programs has been evelope accoring to requirements of their evelopers an o not warranty nees of other users. For this reason, each of the countries an organizations which aim to use -E pavement esign methos, evelop their own software base on specific local conitions an their empirical calibrate moels. The first step for implementation of an -E pavement esign metho is the analysis of pavement an computation of critical responses of pavement uner various loaings. Consequently, eveloping such a program is essential for using -E pavement esign methos, which is the next horizon of pavement esign in Iran an other eveloping countries. The simplest metho for the stuy of stress, strain an eflection in flexible pavements uner a circular loa is consiering the pavement system as a homogeneous half space an then analyzing it using the halfspace theory of Boussinesq in 885 []. Two general methos may be use for more realistic analysis of flexible pavement, incluing multi-layere theory metho an finite element metho (FE). Currently, most of the programs are employing multi-layere theory to analyze pavement structure an compute the critical responses. Some of these programs like CHEVON, DAA, ENLAYE, ELSY5 an BISA are so popular an have been serve for many years. During recent years, most flexible pavement analysis programs use FE metho for nonlinear analysis of *Corresponing author:ghanizaeh@sirjantech.ac.ir 05 UTH Publisher. All right reserve. penerbit.uthm.eu.my/ojs/inex.php/ijie pavement structure [-5]. A few multi-layere pavement analysis programs also have the ability to consier the nonlinear characteristics of granular materials such as enlayer an Everstress. These two programs are capable of moeling the nonlinear behavior of granular material using only -θ an Bilinear moels [6-7]. oeling of pavement using multi-layere theory is simpler than finite element metho. Analyses of pavement using layere theory by the computer system requires less time compare with the finite element metho. On the other han, for the amateur users, working with programs base on multi layer elastic theory is simpler than finite element metho [7]. In this research work, a comprehensive computer program was evelope for analyzing flexible pavements. The evelope program has the capability of moeling pavement materials using five ifferent nonlinear moels. Effect of utilizing ifferent nonlinear moels on critical responses of pavement is also explore.. Constitutive moels for unboun granular materials The response of a granular soil sample uner repeate loaing uring construction phase an initial trafficking tens to shake own to the elastic response. The amount of plastic eformations ecrease with the increase in loa repetitions until the response is essentially elastic. These observations have le researchers in the pavement community to simulate the behavior of granular materials as elastic or resilient materials [8].

2 Int. J. of Integrate Engineering Vol. 7 No. (05) pp. -8 The concept of a resilient moulus of a material was originally introuce by See et al. in 96 [9]. See et al. efine resilient moulus,, as the ratio of applie ynamic eviator stress,, to the resilient or recovere strain, r, uner a transient ynamic pulse loa given by r / r. epeate loa triaxial test is commonly employe to quantify the resilient moulus of granular materials an cohesive soils. The resilient response of granular materials an fine-graine soil is stress epenent (resilient moulus is not constant, but epens on the repeate stress state). Several oels have been evelope over the years that combine applie stresses an material characteristics to escribe the nonlinear behavior of granular materials uner traffic loaing. The -θ moel has been the most famous for characterizing the resilient response of the granular bases an subbase materials [0]. The resilient moulus ( ) is given as follows: r () θ = First invariant of stress tensor = σ + σ +σ 3 σ = ajor principal stress. σ = Intermeiate principal stress σ 3 = inor principal stress/confining pressure, = egression analysis constants obtaine from experimental ata. Uzan (985) observe that the -θ moel i not summarize measure ata well when shear stresses were significant, an propose a three parameter moel []. This moel is given as 3 () 3 = The eviator stress in a triaxial test configuration,, an 3 = material constants Witczak an Uzan (988) propose a moification to the Uzan moel by replacing the eviator stress term in Eq. () by an octaheral shear stress term []. This octaheral shear stress moel also consiers the ilation effect that takes place when a pavement element is subjecte to a large principal stress ratio / 3. This moel is calle Universal oel an is given as follows: 3 (3) oct oct =Octaheral shear stress,, an 3 = ultiple regression constants evaluate from resilient moulus test ata. In EPDG 00 Guie, resilient moulus is estimate using a generalize constitutive moel for Level analysis for the nonlinear stress-epenent moeling of both the unboun aggregates an finegraine soils [3]. The ifference in material behavior preicte by Universal an EPDG 00 were only foun in the regression variables an both of them give same values for resilient moulus [4]. The EPDG 00 Guie moel is as follows: k3 oct pa p a p a τ oct = Octaheral shear stress p a = Atmospheric pressure,, an 3 = multiple regression constants evaluate from resilient moulus test ata. Typically, fine-graine soil moulus ecreases in proportion to the increasing stress levels thus showing stress-softening type behavior. The constitutive relationships are primarily establishe between the resilient moulus an the eviator stress. For a fine graine subgrae layer, the bilinear moel has been the most commonly use resilient moulus moel [5]. This bilinear soil moel is given as follows: ( ) ( ) 3 4,, 3, an 4 =moel parameters obtaine from regression analyses of resilient moulus test Among the moels presente, the EPDG 00 Guie moel has been also use for moeling the nonlinear behavior of unboun AP base, asphalt treate base an cement treate base materials [6-9]. 3. NonPAS Program In this research work, a comprehensive computer program was evelope for analyzing flexible pavements. The evelope program has the capability of moeling pavement materials using five ifferent nonlinear moels. Effect of using ifferent nonlinear moels on critical pavement responses has been explore. In esign of NonPAS program, it has attempte to provie a userfrienly environment for pavement analysis purpose. Furthermore, it has trie to evelop the program base on moular programming because of the possibility of future evelopment plan an its conversion to -E esign software. Inputs for this program inclue: General settings, incluing the selection of the unit system (SI or Imperial), the maximum number of iterations for nonlinear analysis, an the maximum acceptable error for convergence of nonlinear analysis. Layer's specifications, incluing the number of layers, elastic moulus, Poisson's ratio, thickness, ensity, layer type (linear or nonlinear), nonlinear behavior of layer, coefficients of nonlinear moel an the epth of stress points for calculation of resilient moulus in each layer. Loaing Specifications, incluing the type of axle (single, tanem an triem), type of wheels (single or (4) (5)

3 Int. J. of Integrate Engineering Vol. 7 No. (05) pp. -8 ual), axles istance, wheels istance, contact pressure an contact raius. In cases of nonlinear analysis, nonlinear properties incluing coorinate of stress point, an the slope of stress istribution are efine. Evaluation points, incluing the number an coorinates of points in X-Y plan an also the number an epth of points to estimate the esire responses. esults of pavement analysis, incluing stresses, strains an eflections in three main irections, shear stresses, principle stresses an strains, maximum shear stress, octaheral shear stress, octaheral shear strain an maximum horizontal principle are compute in ifferent response points. These results can be save in a text file. The enlayer program computes the vertical stress at the center of the wheel as 39.0 Psi an NonPAS computes this response as Psi. The actual amount of this response (vertical stress uner the wheel loa) is equal to 00 Psi. This can be explaine by shortcoming of enlayer program in computation of accurate responses at the top of pavements as mentione by another research []. Fig. NonPAS User Interface. 4. Valiation of linear elastic analysis using enlayer Program The enlayer program is one of the most well-known program in fiel of pavement analysis an esign which is evelope by Yang H. Huang at the University of entucky. This program has the capability of linear, nonlinear an viscoelastic analysis of flexible pavements uner multiple loaing [7]. Previous researches showe that responses compute by this program are comparable with other pavement analysis program incluing both FE an layere analysis programs such as ILLIPave, ICHPave, ELSY 5, Bisar an etc [7]. For valiation of NonPAS program for linear elastic analysis of flexible pavements, a typical five layere pavement system was consiere an analyze uner the effect of ual wheel loa using both NonPAS an enlayer, an then results were compare. Specification of each layer of pavement section is represente in Fig. (). The wheel contact area was assume to be circular with raius of 4 inches an pressure of 00 psi. Distance between ual wheels was also assume as 3.5 in. esults for linear elastic analysis of pavement at the center of contact area using both NonPAS an enlayer have been presente in Fig. (3) to (7) As can be seen, compute responses using NonPAS show goo agreement with kenlayer responses. Just in case of surface responses (epth of zero), the compute responses using enlayer an NonPAS i not match completely. Fig. Pavement section for valiation of linear elastic responses. The accuracy of NonPAS program has been improve by a more accurate algorithm for numerical computation of the following Hankel inversion semi-infinite integration: * qa m. a J ) m H ( (6) 0 m H * is the response ue to the vertical loa of mj ( mr / H ) 0, m is the constant of integration, is the response ue to the vertical loa of q, a is the raius of contact loa, H is the istance from the surface to the upper bounary of the lowest layer, J 0 is a Bessel function of the first kin an of orer zero an J is a Bessel function of the first kin an of orer one. Fig. 3 Vertical stress vs. Depth. 3 3

4 Int. J. of Integrate Engineering Vol. 7 No. (05) pp. -8 Fig. 4 inor principle stress vs. Depth. Fig. 5 ajor principle stress vs. Depth. 5. Comparison of compute responses with enlayer results For valiation of results which are compute using NonPAS Program, a typical three layere pavement system was analyze using both NonPAS an enlayer, an then results were compare. Specification of each layer of pavement section is represente in Fig. (8). As can be seen, granular base an subgrae have been moele using -θ an bilinear nonlinear behavioral moel respectively. aterial constants for these two layers have been shown in Fig. (8). Contact area was assume to be circular with raius of 6 inches an pressure of 80 psi. For increasing accuracy of nonlinear analysis, base layer was ivie to six layers with the same thickness of inches for each sub layer. The stress point for computation of resilient moulus of subgrae soil has been assume one inch in epth from the surface of subgrae soil. Two values were assume for the slope of loa istribution (SLD) as 0 an 0.5. Since the performance of pavement is usually preicte using the critical responses of pavement, here, only these responses are compare to show the corresponence of results of enlayer an NonPAS. Critical responses were assume as surface vertical eflections, raial stresses an strains at the center of loaing at ifferent epths, an also vertical stresses an strains at the center of loaing at ifferent epths. Final resilient mouli compute by NonPAS an enlayer are given in Fig. (9) an (0). Nonlinear analysis results at the center of contact area, assuming SLD=0, have been emonstrate in Fig. () to (5). As can be seen, the compute results using both programs match very well. esilient moulus corresponence in various epths results in same responses. Fig. 6 inor principle strain vs. Depth. Fig. 8 Pavement section for valiation of nonlinear elastic responses. Fig. 7 ajor principle strain vs. Depth. 4

5 Int. J. of Integrate Engineering Vol. 7 No. (05) pp. -8 Fig. 9 esilient moulus vs. Depth (SLD=0.0). Fig. 0 esilient moulus vs. Depth (SLD=0.5). Fig. Vertical stress vs. epth (SLD=0.0). Fig. Vertical strain vs. epth (SLD=0.0). Fig. 3 aial strain vs. epth (SLD=0.0). Fig. 4 Vertical eflection vs. epth (SLD=0.0). 5 5

6 Int. J. of Integrate Engineering Vol. 7 No. (05) pp. -8 epths. In orer to analysis more accurately, the base layer was ivie into six sub-layers each of them ha two inches thick, an the stress point was assume at the center of each of these sub-layers. For computation of subgrae resilient moulus, stress point assume one inch in epth from the surface of subgrae soil. As can be seen, compute responses using NonPAS show goo agreement with enlayer responses. Table : Nonlinear coefficients for ifferent moels. oel Name 3 -θ Uzan EPDG Fig. 5 Surface eflection vs. raial istance (SLD=0.0). 6. Comparison of compute results using ifferent nonlinear moel In orer to compare the results of nonlinear analysis using ifferent nonlinear moels, pavement system shown in Fig. (6) was analyze using three ifferent nonlinear moels. Subgrae soil was moele using bilinear moel an accoring to the parameters shown in Fig. (6). Granular base was moele using three moels, incluing -θ, Uzan an EPDG. Constant coefficients for each of these moels have been obtaine using ynamic triaxial tests, which were conucte by Hopkins et al. (00) base on a sample of the crashe stone base material [0]. Calibration results for each of the moels are given in Table (). Hopkins et al use eviator stress instea of octaheral shear stress for calibration of EPDG oel. esilient mouli obtaine using any of the moels at ifferent epths have been shown in Fig. (7). As evience, the results of the -θ moel oes not show a goo agreement with two other moels an resilient moulus obtaine from Uzan an EPDG is less than the resilient moulus obtaine from the -θ moel. Consiering that the only possible alternative for moeling coarse graine material in enlayer program is -θ moel, the results of the analysis using enlayer have been given only for -θ moel. Critical responses of pavement incluing maximum horizontal tensile strain at the bottom of asphalt layer, maximum vertical compressive strain at the top of subgrae an also surface eflection at three ifferent istance from the center of one of wheels in irection of ual wheels are given in table (). Fig. 6 Assume configuration for pavement structure an loaing. Loaing was consiere to be a tanem Axel with ual wheels. Contact area an contact pressure of all wheels was assume to be constant an same as what shown in the Fig. (6). Stress points were consiere in the intermeiate position of the wheels an in ifferent Fig. 7 Compute resilient moulus at ifferent epths using ifferent moels. Uzan an EPDG moels are sensitive to both bulk an eviator stress an the -θ oel just epens on bulk stress an so the same results for these three moels can be observe almost at specific values of bulk an 6

7 Int. J. of Integrate Engineering Vol. 7 No. (05) pp. -8 eviator stress. Table () illustrates that the compute critical responses using these three moels o not match exactly. Due to higher precision of Uzan an EPDG, these two moels are recommene for nonlinear moeling of coarse aggregate materials. These two moels can represent the behavior of coarse aggregate uner ifferent stress state better than -θ moel. Unlike the enlayer program that only allows nonlinear moeling of coarse aggregate materials using -θ oel, NonPAS program has the capability of moeling these materials using other nonlinear moels an can provie enough accuracy to estimate pavement responses. Table Compute critical responses by means of ifferent nonlinear moels. aial Distance enlayer NonPAS (in) k-teta k-teta Uzan EPDG 00 aximum horizontal tensile strain at the bottom of asphalt (micro strain) 0 in in in Vertical strain at the top of subgrae (micro strain) 0 in in in Vertical Deflection (inch) 0 in in in Summary NonPAS program has been evelope for linear an nonlinear analysis of flexible pavements. It allows nonlinear moeling of coarse an fine aggregate materials in flexible pavements using five ifferent nonlinear moels, incluing k-θ, uzan, uzan-witczak, EPDG 00 an bilinear moel. Compute responses using NonPAS show goo agreement with enlayer responses. In case of vertical eflections, the compute responses using these two programs o not match completely. This may be explaine by shortcoming of enlayer program in computation of accurate responses at the surface of pavements as mentione by other researchers. NonPAS program can compute the responses at the surface of pavement more accurately than kenlayer, which is so important for preicting of top-own cracking, that is the result of tensile strain at the top of surface layer. It can be mentione that the NonPAS program can be use as a reliable program for linear an nonlinear analysis of flexible pavements, an its computational algorithm can be use in eveloping echanistic-empirical pavement esign software. eferences [] Boussinesq, J.: Applications es potentials a l'etue e l'equilibre et u mouvement es solies elastique. Gauthier-Villars, Paris, (885). [] im,., Tutumluer E., an won J., Nonlinear pavement founation moeling for threeimensional finite-element analysis of flexible pavements, International Journal of Geomechanics, volume 9, no. 5, (009), pp [3] ojarra, H., Three imensional nonlinear finite element analysis of airport pavements. North Carolina State University, Ph.D Dissertation, (0). [4] Sarneja, S.A., Ghanizaeh, A.., an Fakhri,., Evaluation of three constitutive moels to characterize granular base for pavement analysis using finite element metho. Journal of Applie Sciences esearch, volume 5, no. 7, (0), pp [5] aharaj, D. an Gill, S., The behavior of flexible pavement by nonlinear finite element metho. International Journal of Latest esearch in Science an Technology, volume 3, no., (04), pp [6] Sivaneswaran, N., Pierce, L., an ahoney, J. Everstress Version 5.0: Layere elastic analysis program. Olympia, Washington State Department of Transportation, (00). [7] Huang, Y. H., Pavement analysis an esign. n eition, Prentice Hall. Inc., New Jersey, (004). [8] Hjelmsta,., an Taciroglu, E., Analysis an implementation of resilient moulus moels for granular solis. Journal of Engineering echanics, volume 6, no. 8, (000), pp [9] See, H. B., Chan, C., an Lee, C., esilience characteristics of subgrae soils an their relation to fatigue failures in asphalt pavements. Proc., International Conference on the Structural Design of Asphalt Pavements. Supplement, (96), pp [0] Hicks,. G., an onismith, C. L., Factors influencing the resilient response of granular materials. Highway esearch ecor, volume 345, (97), pp.5-3. [] Uzan, J., Characterization of granular material. Transportation esearch ecor, volume 0, (985), pp [] Witczak,., an Uzan, J., The universal airport pavement esign system. eport I of V: Granular material characterization, University of arylan, USA, (988). [3] NCHP: Guie for mechanistic empirical esign of new an rehabilitate pavement structures, Final eport for Project -37A. Washington, DC: National Cooperative esearch Program, (004). [4] im,., Tutumluer, E., an won, J.: Nonlinear pavement founation moeling for threeimensional finite-element analysis of flexible pavements. International Journal of Geomechanics, volume 9, no. 5, (009), pp

8 Int. J. of Integrate Engineering Vol. 7 No. (05) pp. -8 [5] Thompson,.., an obnett, Q. L., esilient properties of subgrae soils. Transportation Engineering Journal, volume 05, no., (979), pp [6] He, W., Laboratory evaluation of unboun rap as a pavement base material..s. Thesis, University of Tennessee, noxville, (006). [7] Li, P., Characterization an implementation of stress epenent resilient moulus of asphalt treate base for flexible pavement esign, Ph.D Dissertation, University of Alaska, Fairbanks, (03). [8] Jitsangiam, P., & Nikraz, H., echanical behaviours of hyrate cement treate crushe rock base as a roa base material in Western Australia. International Journal of Pavement Engineering. volume 0, no., (009), pp [9] Puppala, A. J., Hoyos, L.., & Potturi, A.. esilient mouli response of moerately cementtreate reclaime asphalt pavement aggregates. Journal of aterials in Civil Engineering, volume 3, no. 7, (0), pp [0] Hopkins, Tommy C., Tony L. Beckham, Charlie Sun, an Bixian Ni., esilient moulus of entucky soils, esearch report TC-0-07/SP F, (00). [] Chen, D. H., Zaman,., Laguros, J., an Soltani, A., Assessment of computer programs for analysis of flexible pavement structure. Transportation esearch ecor, volume 48, (995), pp