Non-associative Fractional-Order Bounding-Surface Model for Granular Soils Considering State Dependence
Tóm tắt
The constitutive behaviour of granular soil is usually non-associative and depends on the soil density and pressure. To simulate such dependence of the non-associative stress–strain response on material state, two distinct yielding and plastic potential surfaces were usually suggested in the traditional elastoplastic models, which, however, made the model to become complex. To solve this problem, a simple fractional-order plasticity model without using any plastic potential functions was proposed before. However, the model did not consider the dependence of deformation on the density and pressure of soil, which could make the model incompatible with the critical-state soil mechanics. In contrast to the previous study, a state-dependent non-associative bounding-surface model within the framework of critical-state soil mechanics is proposed in this study. The plastic flow direction is obtained using a state-dependent fractional-order differentiation of the bounding surface. To demonstrate the capability of the model, drained and undrained triaxial test results of different granular soils under a variety of initial states are simulated, from which good agreement between the model predictions and the test results is observed.
Tài liệu tham khảo
Li G, Liu Y, Dano C, Hicher P (2014) Grading-dependent behavior of granular materials: from discrete to continuous modeling. J Eng Mech 141(6):04014172. doi:10.1061/(ASCE)EM.1943-7889.0000866
Cho G, Dodds J, Santamarina J (2006) Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. J Geotech Geoenviron Eng 132(5):591–602. doi:10.1061/(ASCE)1090-0241(2006)132:5(591)
Farhang R, Jean-Noël R, Ali D (2017) Modeling granular materials: century-long research across scales. J Eng Mech. doi:10.1061/(ASCE)EM.1943-7889.0001196
Egner W, Egner H (2016) Thermo-mechanical coupling in constitutive modeling of dissipative materials. Int J Solids Struct 91:78–88. doi:10.1016/j.ijsolstr.2016.04.024
Einav I (2007) Breakage mechanics—Part II: modelling granular materials. J Mech Phys Solids 55(6):1298–1320
Xiao Y, Sun Y, Yin F, Liu H, Xiang J (2016) Constitutive modeling for transparent granular soils. Int J Geomech. doi:10.1061/(ASCE)GM.1943-5622.0000857
Yao Y, Hu J, Zhou A, Luo T, Wang N (2015) Unified strength criterion for soils, gravels, rocks, and concretes. Acta Geotech 10(6):749–759. doi:10.1007/s11440-015-0404-x
Yao Y, Wang N (2014) Transformed stress method for generalizing soil constitutive models. J Eng Mech 140(3):614–629. doi:10.1061/(ASCE)EM.1943-7889.0000685
Liu HB, Zou DG (2013) Associated generalized plasticity framework for modeling gravelly soils considering particle breakage. J Eng Mech 139(5):606–615. doi:10.1061/(ASCE)EM.1943-7889.0000513
Pastor M, Zienkiewicz OC, Chan AHC (1990) Generalized plasticity and the modelling of soil behaviour. Int J Numer Anal Meth Geomech 14(3):151–190. doi:10.1002/nag.1610140302
Khalili N, Habte MA, Valliappan S (2005) A bounding surface plasticity model for cyclic loading of granular soils. Int J Numer Meth Eng 63(14):1939–1960
Kan ME, Taiebat HA (2015) Application of advanced bounding surface plasticity model in static and seismic analyses of Zipingpu Dam. Can Geotech J 53(3):455–471. doi:10.1139/cgj-2015-0120
Sun Y, Indraratna B, Carter JP, Marchant T, Nimbalkar S (2017) Application of fractional calculus in modelling ballast deformation under cyclic loading. Comput Geotech 82:16–30. doi:10.1016/j.compgeo.2016.09.010
Sun Y, Shen Y (2017) Constitutive model of granular soils using fractional order plastic flow rule. Int J Geomech 17(8):04017025. doi:10.1061/(ASCE)GM.1943-5622.0000904
Yang J, Li X (2004) State-dependent strength of sands from the perspective of unified modeling. J Geotech Geoenviron Eng 130(2):186–198. doi:10.1061/(ASCE)1090-0241(2004)130:2(186)
Been K, Jefferies MG (1985) A state parameter for sands. Géotechnique 22(6):99–112. doi:10.1016/0148-9062(85)90263-3
Sumelka W, Nowak M (2017) On a general numerical scheme for the fractional plastic flow rule. Mech Mater. doi:10.1016/j.mechmat.2017.02.005
Podlubny I (1998) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, vol 198. Academic press, San Diego
Sumelka W, Nowak M (2015) Non-normality and induced plastic anisotropy under fractional plastic flow rule: a numerical study. Int J Numer Anal Meth Geomech 40(5):651–675. doi:10.1002/nag.2421
Sun Y, Xiao Y (2017) Fractional order plasticity model for granular soils subjected to monotonic triaxial compression. Int J Solids Struct 118–119:224–234. doi:10.1016/j.ijsolstr.2017.03.005
Li X, Dafalias Y (2000) Dilatancy for cohesionless soils. Géotechnique 50(4):449–460
Xiao Y, Liu H, Chen Y, Jiang J (2014) Bounding surface plasticity model incorporating the state pressure index for rockfill materials. J Eng Mech 140(11):04014087. doi:10.1061/(ASCE)EM.1943-7889.0000802
Bardet J (1986) Bounding surface plasticity model for sands. J Eng Mech 112(11):1198–1217
Xiao Y, Liu H, Chen Y, Jiang J (2014) Bounding surface model for rockfill materials dependent on density and pressure under triaxial stress conditions. J Eng Mech 140(4):04014002. doi:10.1061/(ASCE)EM.1943-7889.0000702
Roscoe KH, Burland JB (1968) On the generalised stress-strain behaviour of ‘wet’ clay. Engineering Plasticity. Cambridge University, Cambridge
Salim W, Indraratna B (2004) A new elastoplastic constitutive model for coarse granular aggregates incorporating particle breakage. Can Geotech J 41(4):657–671
Lee KL, Seed HB (1967) Drained strength characteristics of sands. J Soil Mech Found Div 93(6):117–141
Verdugo R, Ishihara K (1996) The steady state of sandy soils. Soils Found 36(2):81–91
Liu HB, Zou DG, Liu JM (2014) Constitutive modeling of dense gravelly soils subjected to cyclic loading. Int J Numer Anal Meth Geomech 38(14):1503–1518. doi:10.1002/nag.2269