34 Vol.34 o. 05 Chins Journal of Rock chanics and Enginring Dc.05 (. 70069. 43007) Przyna Cam-clay () TU 435 A 000695(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 04000505 (43734)(4309) Fund rojctsth ational atural Scinc Foundation of China(43734)th ational atural Scinc Foundation for Young Scintists of China(4309) (98)0 E-mailngfia@nwu.du.cn DOI0.37/j.cnki.jrm.04.4
34 543 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]
544 05 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. 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 ( = 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) 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 3 3 3 = s = ( σ δ ) σ g ( ) = 0 = g = (4) (5)
546 05 (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. 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 = 0.55 3 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 = 0.874 min = 0.577ϕ c = 3. 60% ζ = aml / = σ aml / = 0.3 f = Hz max = 00 000 3 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 ) ()
548 05 = c =.3α ε (40) 0 5 0 4 0 50 0 5 300 (40)α α αα = 0.00 3 = 3.54 0 0 0 0 0 3 0 4 0 5 (b) η = 0.75 Tabl Valus of ovrstrss function aramtrs /kpa η ζ aml α 00 0.500 0.300 0.00 3.5 00 0.750 0.300 0.00 3 3.54 00.000 0.300 0.00 5 3.55 00.350 0.300 0.00 4 3.57 0 0 0 0 0 3 0 4 0 5 (c) η =.00 (3) = 00 kpaη = 0.500.75.00.35 ζ aml = 0.3 4 = 00 kpa η η = 00 300 kpa η 0 0 0 0 0 3 0 4 0 5 (d) η =.35 4 Fig.4 Exrimntal rsults and fittd curvs of umulatd dviatoric strain of draind cyclic triaxial tsts ε - ( 5) 0 0 0 0 0 3 0 4 0 5 (a) η = 0.50 0 0 0 0 0 3 0 4 0 5 5 ( = 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)
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