Nonlinear Effects in Falling Weight Deflectometer Tests

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1 TRANSPORTATION RESEARCH RECORD 1355 Nonliner Effects in Flling Weight Deflectometer Tests DERWEN CHANG, JosE M. RoESSET, AND KENNETH H. STOKOE II The flling weight deflectometer (FWD) hs been used in the evlution of mteril properties of pvement systems for mny yers. The lod mplitude nd frequency content re intended to provide deformtion levels similr to those induced by truck wheel lods. Interprettion of the in situ mesured dt is normlly bsed on n elstic solution nd therefore does not tke into ccount the possible existence of loclied nonlinerities. The objective of this work ws to develop some understnding of the potentil for nonliner behvior in the FWD test. Anlyticl studies were conducted using both liner itertive solution nd nonliner solution with the generlied cp model to reproduce the nonliner soil behvior. Three pvement sections in Texs were considered using the finite discrete model. By vrying the level of lods FWD deflection bsins, induced strins, nd inelstic mteril properties were obtined. The results of this study indicte tht mteril nonlinerities re loclied nd re importnt for FWD tests on flexible pvements where the subgrde is reltively soft or the pvement is thin. In these cses, nonliner effects increse pek displcements by t lest 50 percent under 20,000 lod but re negligible for receivers t 3 ft or more from the source. In generl, FWD test with lod of 2,000 or less would not result in ny pprent nonliner effects t ny pvement site. For FWD tests on rigid pvements or flexible pvements with reltively stiff subgrde, nonlinerities re lso less pronounced. Nondestructive testing techniques hve been used by highwy engineers for yers to evlute in the field the structurl cpcity nd integrity of existing pvements. Among number of vilble testing methods, the flling weight deflectometer (FWD) is commonly considered to provide estimtes of mteril properties for levels of lod similr to those exerted by truck wheels s discussed by Uddin et l. (1). In this method, hydruliclly lifted weight is dropped on top of disc mounted on the surfce of the pvement nd outwrd by propgting wve motions re recorded by set of velocity trnsducers plced on the surfce (Figure 1). The pek displcements of these receivers form deflection bsin tht is then used to bckfigure the mteril profile on the bsis of elstic multilyer theory. In generl, the pek of the FWD lod rnges from 1,500 to 24,000 with frequencies between 0 nd 60 H. An illustrtion of the idelied FWD loding function used for the present study is shown in Figure 2. A number of reserch studies hve been conducted recently to understnd the effect of vrious fctors on the FWD mesurements such s the presence of much stiffer bedrock t finite depth. Roesset nd Sho (2), Dvies nd Mmlouk (3), D.W. Chng, Deprtment of Civil Engineering, Tmkng University, 180 ChungAn Street, ChungHo City, Tipei Hsien, Republic of Chin. J. M. Roesset nd K. H. Stkoe II, Deprtment of Civil Engineering, University of Texs t Austin, Austin, Tex nd Chng et l. in nother pper in this Record hve concentrted on the importnce of dynmic effects. Kng et l. ( 4) investigted the effect of the finite width of the pvement. Dynmic wve phenomen were found to be importnt in some cses in which the effects ought to be tken into ccount to ensure pproprite bckclcultions. Another concern in nlying the mesured dt is the possible nonliner behvior of the pving mterils induced by lrge lod levels. Such effects were reported by Nrin nd Stkoe (5), who performed set of FWD mesurements on secondry rod. Although the occurrence of nonliner behvior hs been considered n dvntge in better simulting the levels of strin nd stress cused by the truck wheels, it is necessry to ccount for the mgnitude nd sptil distribution of these nonlinerities under different lods for proper interprettion of the dt. The purpose of this work is to estimte the degree of nonlinerity tht cn be expected in different types of pvements s function of the lod mgnitude, nd to estimte ssocited errors in bckfiguring the mteril moduli. The work is limited to nlyticl predictions intended to provide n expected order to mgnitude. Experimentl work is needed to vlidte these predictions. NONLINEAR CHARACTERISTICS OF THE PAVING MATERIALS The most often used mterils for the pvement surfce lyer re portlnd cement concrete nd sphlt concrete. The loddependent behvior of these mterils is not of interest here becuse they re considerbly stiffer thn the bse nd subgrde mterils (soils). Nevertheless, it is necessry to point out tht loding rte would ffect the dynmic modulus of the sphlt mixtures, prticulrly for high tempertures. For the bse, the focus of interest in the present study is on untreted grnulr mterils. Deformtionl chrcteristics of grnulr mterils depend on the strin level nd the stte of stress. Such reltions re commonly expressed in highwy engineering in terms of the resilient modulus nd 1D recoverble strin. Alterntively, they cn be represented s the vrition of sher modulus nd dmping with sher strin s normlly done in erthquke engineering. Mny fctors hve been found to ffect the sher modulus (G) nd dmping rtio of soils. Hrdin nd Drnevich ( 6) rnked severl fctors in order of their importnce including stte of stress, void rtio nd strin mplitude. For given mteril with known void rtio nd stte of stress, the nonliner behvior is normlly represented by plotting the modulus nd dmping versus sher strin. As generl rule of thumb, mteril response

2 2 j Flling Weight Deflectometerj Loding Plted do. 11.e" T _,, '"" h.l E,=l ~~Mss j j! I j. ~~ ' J,~. L _. P(t) wxwy l 0 R 2 "._ Oeflecled Surfce of Pvement Bsed on Peo~ Deflection Mesured 01 ech GophOne Loction FWD fi\ O~t Scle:~ FIGURE 1 Lyout of the in situ instrumenttion nd geometric configurtion of the lod nd sttions of FWD test (1). TRANSPORTATION RESEARCH RECORD 1355 is considered to be liner elstic for strin levels less thn percent, nonliner elstic (reversible loddisplcement reltions) for sher strins between percent nd 0.01 percent, nd inelstic for strins lrger thn 0.01 percent. A comprehensive review of the reserch on shering chrcteristics of soils cn be found in work by Ni (7). The nonliner mteril chrcteristics used in this study re bsed on lbortory dt on clyey nd sndy soils. Both rely on smples representing common mterils collected t pvement sites in Texs. A typicl plot of the vrition of the sher modulus nd dmping with sher strin mplitude is shown in Figure 3. To simplify the mteril profiles t different sites, the curves for sndy soils re considered s representtive of grnulr bses, nd the dt of clys re used to model the subgrde. Owing to the Jck of more complete lbortory dt on sphlt concrete, strin mplitude nd rte dependence of its sher modulus nd dmping re neglected. ANALYTICAL MODEL AND APPROACHES Determintion of the displcements, strins, nd stresses creted in lyered medium by dynmic lods hs been subject of considerble interest nd reserch for the lst 20 yers in reltion to the design of mchine foundtions nd the seismic nlyses of buildings nd foundtions. A number of procedures hve been developed to solve the liner problem by modeling the ground with discrete model nd n bsorbing boundry to reproduce the frfield or by pplying nlyticl solutions with Fourier series expnsion in two or three dimensions. For the nonliner problem, model tht hs core ) 1.2,, :I 0.8 ~ 0.6 i FWD 0 8 ~ " <II Sndy Soils Clyey Soils 0 ~ 0~_,. ~,o,_,.~~,o._, 1~0.,._.,,0 b) 10 8,, 6 :I = c l 4 I Time, sec FWD ' E s 0 08 Shering Strin, % Sndy Soils Clyey Solle Frequncy, h FIGURE 2 Simplified loding history of FWD test nd corresponding lod spectr Shering Strin (%) FIGURE 3 Nonliner sher deformtionl chrcteristics of subgrde soils. 10

3 Chng et l. 3 region discretied with finite elements nd n pproprite set of boundry conditions t finite distnce is more ttrctive. Nonliner nlyses relted to foundtion engineering hve been conducted by Lysmer et l. (8) nd Roesset nd Scletti (9) ssuming liner hysteretic soil properties, ccounting pproximtely for the nonliner soil behvior using the soclled liner itertive or equivlent liner pproch. In this work, dynmic nlyses were conducted using two pproches: the pproximte nonliner pproch nd true nonliner nlysis. The first pproch, the liner itertive procedure, is conducted in the frequency domin, using prescribed nonliner curves of modulus nd dmping versus strin to select in ech cycle properties consistent with the levels of strin computed in the previous one; the time histories of the solutions re then obtined using fst Fourier trnsform. Corrections of the mteril properties re bsed on n equivlent mesure of sher strin defined s the shering strin intensity r = [f = (21 2 ) 112 where 1 2 is the second invrint of the sher strin tensor]. A lterl bsorbing boundry is plced t n pproprite distnce from the source to reproduce the energy dissiption in the fr field s suggested by Kusel et l. (JO). Using the second pproch, true nonliner nlysis, the solution is obtined in the time domin integrting the equtions of motion of the system. A generlied cp model proposed by Sndler et l. (11) is used to reproduce the nonliner mteril behvior (Figure 4). The equtions used in the model for filure envelope, hrdening cp nd the nonliner moduli suggested by Chen nd Bldi (12) re discussed in detil by Chng (13). Becuse the dt necessry to fit the prmeters of the plsticity model were not vilble, no ttempt ws mde to reproduce exctly the ctul behvior of specific site. The objective of the study ws, insted, to get n ide of the degree of nonlinerity tht could be expected using two different models with consistent vlues. The discrete models used for both types of nlyses re shown in Figure 5. The detils of the formultion, compu) modined DruckerPrger rilure envelope 00 subgrde ' E rigid rock Approximte Nonllner Anlysis E r. ~ Ro llh111ll+litt llhllfl11iit+ 1+1f++++FE region Energy ::.;.bsorbing.,., boundry Ht+HHi111,f+i H1111fll+ittt /. '/ '// '//. /////////////// rigid rock Nonliner Anlysis ~f mmm~83~e~1.}h}}~}}h}}h}ti!9t+th ~ ~~~~~ ~.J. _. ~.! HH11+ll1t+1 t~ ~ ~ n ll1rn region ~:t ~1 f I I t I I: I I I I l l I I I I I ~ 1 : r~ p c '. ' ' p ~ t~ ~ ~b c : : : : b I f I I ~ "). t v,.~~.:. ~:'.;. :.;.~.~~ ~ m9 FIGURE 5 Simplified pvement systems nd discrete models for nlyses. ttionl schemes, model behvior, nd simultion s well s mteril correltions for the nonliner nlyses cn be found in work by Chng (13). b) 112 J2 Tc von Mises DruckerPrget yield envcjopo filure envelope,,,, " L \.,~:::: comer... ; ;"~. <:_ UUMi11on portion Filure _,.,.,.. of the envelope L!:!:I elstic R j region XL FIGURE 4 Configurtion of the cp model in the 11J2 spce. II CASE STUDIES Site Description To investigte the possible existence of nonlinerities nd their loclition t vrious typicl pvement sites, three pvement sections were selected s mteril profiles for nlysis. They correspond to frmtomrket rod FM 195 in Pris, Texs; Route 1 in Austin, Texs; nd Interstte 10 in El Pso, Texs. Rod FM 195 ws selected to represent typicl flexible pvement on reltively soft subgrde. Route 1 represents flexible pvement where the subgrde is reltively stiff. Interstte highwy 10 represents typicl rigid pvement. The

4 ~ 4 TRANSPORTATION RESEARCH RECORD 1355 elstic mteril properties nd lyer thicknesses of ech profile s reported to the uthors from mesurements re presented in Tble 1. Rigid rock ws plced t depth of 20 ft in ll cses to reduce the sie of the finite element mesh nd to sve computtionl time. Clerly the depth to bedrock influences the dynmic mplifiction nd therefore the strins. The mteril prmeters in the nonliner gp model were selected to yield vrition of modulus nd dmping curves similr to those used in the pproximte pproch. The vlues were reported by Chng (13). To generlie the initil stte, hydrosttic stress of 10 psi ws pi:essigned to the soils in order to plce the initil cp. Approximte Nonliner Anlyses Deflection Bsin The results of the deflection bsin normlied with respect to the lod (deflections per pound) for 1, 1,000, 2,000, 5,000, 10,000 nd 20,000 lods nd the corresponding deflection rtios with respect to the 1 lod re plotted in Figures 6 nd 7 for the pproximte nonliner nlysis. Importnt nonlinerities on the pek displcements re found t the first two receivers (which re within 2 ft from the source) in site FM 195 for lods over 5,000. These effects would cuse n increse of pproximtely 56 percent in the pek displcements t site FM 195 with 20,000 lod. For Route 1 nd 110, nonliner effects were found to be insignificnt for ll lod levels. Vrition of Nonliner Mteril Moduli nd Dmping Vritions of the mteril sher moduli (in the normlied form) nd the dmping using the 20,000 lod t site FM TABLE I FM 195 Lyer Mteril Properties nd Thickness of Prolile t Sites Thickness (ft) ACP Bse 0.50 Sub grde Route 1 Lyer Thickness (ft) ACP Bse 0.50 Subgrde" Lyer Thickness (ft) CRC AC 0.5 Bse Sub grde Vs (fps) u Vs (fps) u Vs (fps) u E (ksi) E (ksi) E (ksi) y (pct) y (pct) y (pct) ,0 c. c. :ii :ii ]! ]! 0.1 'E 1 e c s 5000 D D I I Rd l I Distnce, It 0.0 c. :ii ]! 0.1 e D FIGURE 6 Dynmic deflection bsins t vrious sites from pproximte nonliner nlysis..2 \,8 ; : D.2 1,6 ; : , D 1,0 0, FM 195 0, i 1.8 : , D Route FIGURE 7 Rtio of deflection bsin t vrious sites from pproximte nonliner nlysis. 195 re presented in Tbles 2 nd 3. Note tht the sher modulus of the bse lyer cn be reduced to bout 14 percent of its originl vlue. The sher modulus in the upper portion of the subgrde lyer decreses to 45 percent of its initil vlue. The ssocited mximum mteril dmping t the site is 11 percent in the bse lyer nd 9 percent in the upper subgrde lyer. The loclied nture of these nonlinerities re clerly illustrted nd n ssumption of lterl homogeneity, s is implicitly done in norml bckclcultion procedures, is not pproprite.

5 Chng et l. 5 TABLE 2 Vrition or G/Gmx for FM 195 with 20,000 FWD Lod Depth, ft TABLE 3 Vrition or Mteril Dmping for FM 195 with 20,000 FWD Lod Depth, ft ' Nonliner Anlyses Deflection Bsin. The normlied deflection bsins nd their rtios re plotted in Figures 8 nd 9 for the nonliner nlyses. In the cse of FM 195, the nonliner effects of 20,000 lod cuse n increse of bout 140 percent in the pek displcement t the first receiver. For Route 1, the sme lod results in n increse of the displcement of bout 50 percent, much more signifi. 0.0 ]l ]l 1 'E e i5 Ci ~ O.B 0.0. ]l 0.1 'E i & FIGURE 8 Dynmic deflection bsins t vrious sites from nonliner nlysis. cnt thn the increse predicted by the previous solution. In generl, the nonlinerities for reltively lrge lods(> 10,000 ) re importnt within 3 ft from the source t these two sites. The displcements recorded t the frther receivers become smller with increse in the lod. For site 110, nonliner effects were gin found. The true nonliner displcement ws bout 50 percent lrger thn the pproximte one (from 1.6 to 2.4 times the liner displcement t FM 195). This ws expected nd hs been reported in the pst. 2, i i 5000 : : Ci i "'.. FM 195 Route 1 D s i : , Ci "' 0.8 FIGURE 9 Rtio of dynmic deflection bsins t vrious sites from nonliner nlysis.

6 6 TRANSPORTATION RESEARCH RECORD 1355 Vrition of Liner nd Nonliner Strin Field o.m Route 1 wl 1 FWD Lod Sher S1rln The vrition of the sher strins underneth the pvements using 1 nd 20,000 lods t ll sites is plotted in Figures The mximum strin is lwys found in the bse lyer. The levels of the strin distribution cn be used to correlte the vrition of the mteril properties tht induce the inelstic phenomen. CONCLUSIONS Dynmic nondestructive tests for evluting the structurl cpcity of pvements hve become populr tool for highwy engineers in selecting rehbilittion nd reconstruction strtegies. A considerble mount of reserch hs been conducted in recent yers to improve the understnding of the fctors ffecting these tests from both the nlyticl nd experimentl points of view. Although some problems still hve not yet been fully resolved specilly in the interprettion of the mesured dt, distinct nonliner phenomenon (lod dependence) hs often been noticed in FWD mesurements on light pvements. In this study investigtions bsed on forwrd nlyses modeling the nonliner phenomen were conducted to predict the response of the pvements. A study ws first conducted using n pproximte nonliner solution. Two sets of experimentl nonliner curves were used to model the D Ei 3.1E8 2.6Ei.c = 1.3:13 2.1Ei 1.6Ei c! Ei $.063 o Rdil Distnce, fl Route 1 wl s FWD Lod 6.DE 9 E 9 Sher Str ln 1.4E3 1.2E3 E3.c =! E4 6.1E4 c! E4 il ' Rdil Dlst11nc, fl FIGURE 11 Vrition of sher strin t Route 1 using 116 nd 20,000Ib FWD lods. 2.1E4 1.DE5 0,157 FM 195 wl 1 FWD Lod Sher Slrln wl 1 FWD Lod Sher Strin = 0.! E 7 1.Cl83 E 7 8.1Ei.c lf.1ei 1 4.1Ei Ei E E9 6.1E E9 ;: 83.c 4.1E 9 21 ue:j U33 3.1E9 2.1E9 1.11;.g E 10 & Rdil Distnce, fl o u 55 Rdil Distnce, fl D.167 FM 195 wl s FWD lod Sher Slrln WI s Lod Sher Slrln E3 7.1E E3 S.1E3.c = c! 4.1E3 3.1E3 2.ll3il 2.1E3 U D FIGURE 10 Vrition of sher strin t FM 195 using 116 nd 20,000 FWD lods. 1.1E3 E E4 1.5E E4 = E4.c 9.0E5 ~.! 7.0E5 :S E5 3.0E E Rdil Dltnce, fl FIGURE 12 Vritions of sher strin t 110 using 116 nd 20,000 FWD lods.

7 Chng et l 7 sher deformtionl chrcteristics of the bse nd the subgrde mterils. To simulte more relisticlly nonliner response, nlyses were lso conducted integrting the equtions of motion in time with the generlied cp model to reproduce mteril behvior. A set of nlyses ws conducted for three pvement sites using both methods. Solutions in terms of surfce displcements, strin distribution nd the modulus nd dmping spred were presented. The results of these studies indicte tht nonliner effects on the mesured deflections re directly relted to () the mgnitude of the lod, (b) the type of pvement, (c) the stiffness of the subgrde, nd (d) the thickness of the pvement surfce. If the test is performed on flexible pvement, thin surfce, reltively soft subgrde, nd with lrge vlue of the lod, lrge nonlinerities will tke plce ner the source. Results lso indicte tht for the FWD mesurements t frmtomrket rods such s FM 195 where the nonlinerities re importnt, the mximum difference in pek displcements due to the nonliner effects of 20,000 lod cn be t lest 50 percent. The nonliner effects will be smller for receivers t distnces beyond 3 ft from the source. The nonliner effects obtined from the nonliner nlyses re greter thn those from the pproximte nlyses. To resolve this problem more crefully, complete informtion of the mteril behvior under proper loding (using proper testing) must be obtined to clibrte the prmeters used for the nonliner mteril model. The possible effects of mteril nonlinerities on FWD mesurements were studied nlyticlly in this work. Correltion of these results with field mesurements is necessry. The pproximte nonliner nlysis provides better qulittive understnding of the mteril vritions under the rod. It lso requires less dt on the bse nd subgrde properties. It my underestimte strins, however, by bout 50 percent. The true nonliner nlysis would provide more ccurte results if the nonliner constitutive equtions were relistic nd their prmeters were known for the mteril in question. To fit these prmeters would require considerble mount of smple collection nd lbortory testing. This type of nlysis is thus more suited for reserch purposes thn for ctul use in prctice on regulr bsis. Both methods reveled the potentil for nonlinerities using lrge FWD lods prticulrly for flexible pvements nd soft subgrdes. The question tht must still be resolved is the mening of the bckfigured moduli when the properties chnge in the horiontl direction s will hppen when there is nonliner behvior. Both methods reveled the potentil for nonlinerities using lrge FWD lods. At rbitrry sites, the degree of the nonliner effects is indeed relted to the ctul thickness of the soil strtum nd should be studied independently. ACKNOWLEDGMENTS This work ws supported by the Texs Stte Deprtment of Highwys nd Public Trnsporttion under contrct 31888/ The uthors wish to express their pprecition for this support. REFERENCES 1. W. Uddin, A. H. Meyer, W. R. Hudson, nd K. H. Stokoe II. A Stnicturl Evlution Methodology for Pvements Bsed on the Dynmic Deflection. Center for Trnsporttion Reserch, University of Texs, J.M. Roesset nd K. Sho. Dynmic Interprettion of Dynflect nd Flling Weight Deflectometer Tests. In Trnsporttion Reserch Record 1022, TRB, Ntionl Reserch Council, Wshington, D.C., 1985, pp T. G. Dvie nd M. S. Mmlouk. Theoreticl Re ponse of Multilyer Pvement Systems to Dynmic Nondestructive Testing. In Tr1111sporwtio11 Reserch Record 1022, TRB, Ntionl Reserch Council, Wshington, D.C., 1985, pp V. K. Kng, J. M. Roesset, nd K. H. Stkoe II. Effect of the Finite Width of Pvements on Deflection Bsins Obtined with Dynflect nd FWD Tests. Trnsporttion Reserch Bord, 1990, pp S. Nrin nd K. H. Stkoe II. Effect of Sesonl Prediction on the Moduli of FrmToMrket Rods. Technicl Memorndum, Study No Center of Trnsporttion Reserch, University of Texs t Austin, Aug B. 0. Hrdin nd V. P. Drnevich. She.r Modulus nd Dmping in Soils: Me urement nd Prmeter Effec1s. Journl of the Soil Mechnics nd Foundtions Division, ASCE, Vol. 98, No. SM6, 1972, pp S.H. Ni. Dynmic Response of Snd Under Tme Trixil Stress Stte From Resonnt/Column Torsionl Sher Tests. Ph.D. disserttion. University of Texs t Austin, Aug J. Lysmer, T. Udk, C.F. Tsi, nd H.B. Seed. FLUSHA Computer Progrm for Approximte 3D Anlysis of Soi/ Structure Interction Problems. R eport EERC University of Cliforni, Berkeley, Nov M. Roesset nd H. Scletti. Nonliner Effects in Dynmic Soil tructurc lnte rc1ion. In Proc., Third lmemc1io11 Co11fere11ce on Numericl Methods in Geom echnics, Achen, April 1979, pp. L,457 1, E. Kimscl, J. M. Roessec. nd G. Ws. Dynmic Anlysis of Footing on Lyered Medi. Journl of 1/e 11gi11eeri11g Mechnics Division, ASCE, Vol. 101, No. EM5, Oct. 1975, pp I. S. Sndler, F. L. DiMggio, nd G. Y. Bldi. Generlied Cp Model for Geologicl Mterils. Journl of the Geotechnicl Engineering Division, ASCE, Vol. 102, No. GT7, 1976, pp W. F. Chen nd G. Y. 13ldi. Soil Pi ticitytlieory nd lmp/e111e1111io11. Developments in Geotechnicl Engineering Series 38, Elsevier Science Publishing Co., New York, N. Y., D. W. Chng. Nonliner Effects on Dynmic Response of Pvements Using the NonDestructive Testing Technique. Ph.D. Disserttion. University of Texs t Austin, My Publiction of this pper sponsored by Committee on Strength nd Deformtion Chrcteristics of Pvement Sections.

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