ELASTOPLASTIC ACCUMULATION MODEL FOR PREDICTING SOIL PLASTIC ENVELOPE DUE TO HIGH-CYCLIC LOADING

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1 34 Vol.34 o. 05 Chins Journal of Rock chanics and Enginring Dc.05 ( ) Przyna Cam-clay () TU 435 A (05)5408 ELASTOPLASTIC ACCUULATIO ODEL FOR PREDICTIG SOIL PLASTIC EVELOPE DUE TO HIGH-CYCLIC LOADIG JIA Pngfi KOG Lingwi (. Stat Ky Laboratory of Continntal DynamicsDartmnt of Gologyorthwst UnivrsityXi anshaanxi 70069China. Stat Ky Laboratory of Gomchanics and Gotchnical EnginringInstitut of Rock and Soil chanics Chins Acadmy of ScincsWuhanHubi 43007China) AbstractAt rsntthr is no comrhnsiv thortical framwork that not only can dscrib rasonably th bhiour of normal cyclic dformation of soilbut is also suitabl for its calculation and rdiction at high-cyclic conditionsi..at larg numbrs of load cycls. In this aran lastolastic umulation modl was dvlod which incororats th charactristics of high-cyclic loading and allows a fr slction of th intgration st siz. This modl adots th thortical framwork of Przyna viscolasticity and uss an umulatd lastic strain incrmnt ovr a numbr of load cycls as a rsons nvlo. Basd on th gnral rincils of critical stat soil mchanicsth umulatd lastic volumtric strain was usd as th hardning aramtr to dscrib th siz of th lastic strain umulation using a owr law. A factor rrsnting th influnc of rag strss was introducd to dscrib th strain hardning rocss. In additionth rincils of th modifid Cam-clay modl at (43734)(4309) Fund rojctsth ational atural Scinc Foundation of China(43734)th ational atural Scinc Foundation for Young Scintists of China(4309) (98)0 ngfia@nwu.du.cn DOI0.37/j.cnki.jrm.04.4

2 th rag strss stat wr usd to dscrib th dirction of th lastic strain umulation. Th dvlod modl was calibratd with data from cyclic triaxial tsts. It was found that th modl can dscrib with a sufficint lvl of uracy th lastic strain umulation at low strss lvls. Howvrthr wr som discrancis btwn th modl rdictions and xrimntal rsults at high strss lvlsscially whn th rag strss lvl was clos to or highr than th critical stat valus. Ky wordssoil mchanicssandlastic nvlolastolasticumulation modlhigh-cyclic loading [] [-6] ( 50) [4] A. Suikr [7-8] Przyna [9-0] [] [] Suikr Ruhr-Bochum Bochum [43] Suikr [3] [4] Suikr Bochum Suikr Bochum Cam-Clay [5]

3 Cauchy σ ε ( = 3) ( ) ε ε = σ ii /3 () ε = ε () ii = 3 ss / (3) ji ε = ji /3 (4) s s = σ δ (5) = ε ε δ (6) δ Kronckr i = j δ = i j δ = 0. ε ε ε ( ) ε = ε + ε (7) (7) & ε = & ε + & ε (8) (8) wton (8) dε dε dε = + (9) d d d. d dε dσ Hook dε d ds = δ + (0) d K d G d K G [6] K n = Krf rf () K rf rf n (0) () (0) dε dε dε d dε = () K d dε = (3) 3G (0)(3) [7] [6].3 Przyna dε = φ( f ) m (4) d φ( f ) f m g φ( f ) acauly φ( f) ( f0) φ( f ) = (5) 0 ( f 0) Przyna [8-0] A. Suikr [7] η = / ( ) ()

34 545 [-3] T. Wichtmann [3] Cam-clay [3] = 00 kpa aml / = 0.3 aml D ε = D (6) ε ε ε Cam-Clay c ( η ) D = (7) η c c =.5 (σ σ aml ) D η Cam-Clay [3] Fig.

= 00 000) ( =0 000) ( = 000) ( = 00) ( = 0) Cam-Clay () (8) sh ( ε ) η Cam-Clay sh d dε η = (9) sh (9)( η / ) η d sh 0 η d sh 0 aml aml sh φ( f) = α + ( ε ) aml (0)

4 [-3] T. Wichtmann [3] Cam-clay [3] = 00 kpa aml / = 0.3 aml D ε = D (6) ε ε ε Cam-Clay c ( η ) D = (7) η c c =.5 (σ σ aml ) D η Cam-Clay [3] Fig. Comarison btwn xrimntal rsults and flow rul of modifid Cam-Clay(CC) modl at th dirction of strain umulation [3] () sh aml aml sh f = + ( ε ) aml (8) aml sh ( ε ) ε ( = ) ( =0 000) ( = 000) ( = 00) ( = 0) Cam-Clay () (8) sh ( ε ) η Cam-Clay sh d dε η = (9) sh (9)( η / ) η d sh 0 η d sh 0 aml aml sh φ( f) = α + ( ε ) aml (0) α (0)(4) aml dε aml sh = α + ε aml ( ) m () d (3) Cam-Clay ( ) g = ( ) 0 + = 0 () - () 0 ( ) 0 = + (3) () g g g m = = + σ σ σ = δ σ = s = ( σ δ ) σ g ( ) = 0 = g = (4) (5)

5 (5)(4) m s 3 ( ) 3 = δ + (6) (6)() aml dε aml sh α ε aml = + d 3 ( ) 3 δ + s (7).4 () () [+ ] d dε d = d K d (8) d (8) ε d = d ε (9) K ε ()(9) n ε d = ε rf K rf dε (30) n+ n+ rf = Krf Δε n+ rf rf Δ ε = ε ε (3) (30) (3) (3) n+ n [( ) ( ) rf ( rf ) ε ] + = + + Δ n n K (33) (33) K + K = (34) Δε Poisson ν G + G (3) 3 ν = K + ν (35) = + 3G Δε (36) () Δ ε =Δ ε ε (37) Δ ε =Δ ε ε (38) Δ ε =Δ ε ε (39) (7) sh Δ ε = α + ( ) Δ sh Δ ε = α + Δ = = + Δε sh sh sh sh sh η (38)(39)(33)(36) (40) (4) (4) n [( ) + n ( ) = + + rf ( rf ) ( Δε Δε )] n + n K (43) = + 3 G ( Δε Δε ) (44) (8)(44) wton-rahson 3 4 T a = { a a a a } (45) trial trial trial trial trial + trial trial [( ) ( ) rf ( rf ) ε ] n n n+ a = = + n+ K Δ atrial = trial = 3GtrialΔε (46) 3 atrial =Δ ε trial = 0 4 atrial =Δ ε trial = 0 (8)

34 547 trial sh ε trial ftrial = trial + ( ) (47) f trial 0 f trial 0 3 3.

0.55 mm max = 0.874 min = 0.577ϕ c = 3. 60% ζ = aml / = σ aml / = 0.

6 trial sh ε trial ftrial = trial + ( ) (47) f trial 0 f trial η σ c σ a = σ c + σ a /3 = σ a h σ aml aml = aml σ /3 aml = σ aml - aml / aml = 3 ζ aml aml aml aml σ ζ = = (48) 3. () K s G s () n Ks = Krf (5) rf rf a rf = a = 00 kpa K rf = 48 Pan = Ks/Pa /kpa Fig. Strss stat in a cyclic triaxial tst ε ε 3 ε = ε + ε (49) 3 ε = ε ε3 (50) 3 d 50 = 0.55 mm max = min = 0.577ϕ c = 3. 60% ζ = aml / = σ aml / = 0.3 f = Hz max = Fig.3 Exrimntal rsults and th fittd curv showing th rlationshi btwn scant bulk modulus and rag hydrostatic rssur Poisson Poisson 50 + ν ε = 50 = (5) 3 ν ε = 50 ν = 0.3 Poisson 3( ν ) Ks G s = (53) ( + ν ) ()

7 = c =.3α ε (40) (40)α α αα = = (b) η = 0.75 Tabl Valus of ovrstrss function aramtrs /kpa η ζ aml α (c) η =.00 (3) = 00 kpaη = ζ aml = = 00 kpa η η = kpa η (d) η =.35 4 Fig.4 Exrimntal rsults and fittd curvs of umulatd dviatoric strain of draind cyclic triaxial tsts ε - ( 5) (a) η = ( = 00 kpaη =.35ζ aml = 0.3) Fig.5 Comarison btwn cyclic triaxial tst rsult and fitting curv of ovrstrss function( = 00 kpa η =.35ζ aml = 0.3)

8 () Δε Δ () ε η / Cam-Clay (3) ( ) (Rfrncs) [] DAFALIAS Y FHERRA L R. Bounding surfac lasticity alication to isotroic cohsiv soils[j]. Journal of Enginring chanics986() [] GE Y. Cyclic constitutiv modling of granular matrials[ph. D. Thsis][D]. BouldrTh Univrsity of Colorado003. [3] ABDELKRI BOET GDE BUHA P. A comutational rocdur for rdicting th long trm rsidual sttlmnt of a latform inducd by ratd traffic loading[j]. Comutrs and Gotchnics003 30(6) [4] IEUIS A WICHTA T TRIATAFYLLIDIS T. A high-cycl umulation modl for sand[j]. Comutrs and Gotchnics 0053(4)4563. [5]. [J]. 0068(7)89895.(HUAG aosongli JinjunLI Xingzhao. Cumulativ dformation bhiour of soft clay in cyclic undraind tsts[j]. Chins Journal of Gotchnical Enginring0068(7)89895.(in Chins)) [6]. [J] ()5965.(ZHAG HongboIAO HaitaoSOG Xiuguang. Constitutiv modl of silty sands for cumulativ dformation undr long-trm traffic loading and numrical intgration[j]. Journal of Shandong UnivrsityEnginring Scinc0040()5965.(in Chins)) [7] SUIKER A. Th mchanical bhiour of ballastd railway tracks[ph. D. Thsis][D]. DlftDlft Univrsity of Tchnology00. [8] SUIKER ADE BORST R. A numrical modl for th cyclic dtrioration of railway tracks[j]. Intrnational Journal for umrical thods in Enginring00357(4) [9] PERZYA P. Fundamntal roblms in viscolasticity[j]. Advancs in Alid chanics [0] OLSZAK WPERZYA P. On thrmal ffcts in viscolasticity[j]. Zitschrift FÜR Angwandt athmatik Und Physik ZAP969 0(5) [] LEAITRE JCHABOCHE J. chanics of solid matrials[]. CambridgCambridg Univrsity Prss []. [ ][D]. 006.(ZHAG Hongbo. Long-trm cumulativ dformation of cohsionlss matrial inducd by ratd loading[ph. D. Thsis][D]. ShanghaiTongji Univrsity006.(in Chins)) [3] WICHTA T. Exlicit umulation modl for non-cohsiv soils undr cyclic loading[ph. D. Thsis][D]. BochumRuhr Univrsity Bochum005. [4] KARG CFRACOIS SHAEGEA Wt al. Elasto-lastic long-trm bhior of granular soilsodlling and xrimntal validation[j]. Soil Dynamics and Earthuak Enginring00 30(8) [5] ROSCOE K HBURLAD J B. On th gnralizd strss-strain bhiour of wt clay[c]// Procdings of Enginring Plasticity. w York[s.n.] [6] VEREER P A. Formulation and analysis of sand dformation roblms[ph. D. Thsis][D]. DlftthrlandsDlft Univrsity of Tchnology980. [7] BORJA R. Cam-clay lasticity Part II imlicit intgration of constitutiv uation basd on a nonlinar lastic strss rdictor[j]. Comutr thods in Alid chanics and Enginring99 88()540. [8] DESAI C SZHAG D. Viscolastic modl for gologic matrials with gnralizd flow rul[j]. Intrnational Journal for umrical and Analytical thods in Gomchanics987(6) [9] ROWE R KHICHBERGER S D. Th significanc of rat ffcts in modlling th Sackvill tst mbankmnt[j]. Canadian Gotchnical Journal99835(3) [0] KELL CSHARA JHUGHES Dt al. An imrovd lasticviscolastic soil modl[j]. Canadian Gotchnical Journal008 45(0) [] LUOG P. chanical ascts and thrmal ffcts of cohsionlss soils undr cyclic and transint loading[c]// Procdings of IUTA Confrnc on Dformation and Failur of Granular atrials. Dlft [s.n.] [] CHAG C SWHITA R V. Draind rmannt dformation of sand du to cyclic loading[j]. Journal of Gotchnical Enginring 9884(0) [3] WICHTA T IEUIS A TRIATAFYLLIDIS T. Exrimntal vidnc of a uniu flow rul of non-cohsiv soils undr high-cyclic loading[j]. Acta Gotchnica006()5973.

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