PLAXIS LIQUEFACTION MODEL UBC3D-PLM - Knowledge Base

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Chapter 1Key Features of UBC3DThe UBC3D-PLM model has been developed by Tsegaye (2010) and implementedas a user-defined model in PLAXIS. It is closely based on theUBCSAND model introduced by Puebla et al. (1997), Beaty and Byrne(1998). The original UBCSAND is a 2-D model developed for prediction ofliquefaction in sandy soils. Its formulation is based on classical plasticitytheory with a hyperbolic strain hardening rule, based on the Duncan-Changapproach with modifications. The hardening rule relates the mobilized frictionangle to the plastic shear strain at a given stress. It contains a 2-DMohr-Coulomb yield surface and a corresponding non-associated plastic potentialfunction. The flow rule in the model is based on the stress-dilatancytheory developed by Rowe (1962), linearised and simplified according toenergy considerations.The main difference between the UBCSAND model and the UBC3Dmodel is the latter generalized 3-D formulation. The UBC3D model uses theMohr-Coulomb yield condition in a 3-D principal stress space. Moreover, amodified non-associated plastic potential function based on Drucker-Prager’scriterion is used, in order to maintain the assumption of stress-strain coaxialityin the deviatoric plane for a stress path beginning from the isotropicline (Tsegaye, 2010).2
Comparing with the previous version of UCB3D implemented in PLAXIS,in the latest version a correction is made in the equation of the plastic multiplierwhich governs the constitutive relationship between the stresses andstrains and higher accuracy is succeeded during monotonic loading. Finally,a soil densification rule is added in order to predict a more realistic evolutionof excess pore pressures during cyclic loading. This allows the increase ofthe volumetric strains with a decreasing rate during shearing. Moreover,the bulk modulus of water is depended on the degree of saturation which isspecified via PLAXIS input and therewith this user defined model can beused in the Advanced calculation mode of PLAXIS.The main characteristics of the model as implemented by (Tsegaye, 2010)and modified by the authors are presented in the following sections.1.1 Yield SurfacesThe UBC3D-PLM model uses the well known Mohr-Coulomb yield functiongeneralized in 3-D principal stress space. In order to understand how thealgorithm deals with the complexity of the 3-D representation of the yieldsurfaces, the full set of the Mohr-Coulomb yield functions are introduced(pressure is positive, tension is positive):f 1a = 1 2 (σ′ 2 − σ ′ 3) + 1 2 (σ′ 2 + σ ′ 3) sin φ ′ − c ′ cos φ ′ (1.1)f 1b = 1 2 (σ′ 3 − σ ′ 2) + 1 2 (σ′ 3 + σ ′ 2) sin φ ′ − c ′ cos φ ′ (1.2)f 2a = 1 2 (σ′ 3 − σ ′ 1) + 1 2 (σ′ 3 + σ ′ 1) sin φ ′ − c ′ cos φ ′ (1.3)f 2b = 1 2 (σ′ 1 − σ ′ 3) + 1 2 (σ′ 1 + σ ′ 3) sin φ ′ − c ′ cos φ ′ (1.4)3
Page 1: PLAXIS LIQUEFACTION MODELUBC3D-PLMA
Page 5 and 6: 3.6 Reproduced stress path in p ′
Page 7: AbstractIn this report the formulat
Page 11 and 12: Figure 1.2: Projection of the yield
Page 13 and 14: ( ) mepK = KBP e A (1.9)P ref( ) ne
Page 15 and 16: The plastic potential function is f
Page 17 and 18: the secondary loading in order to e
Page 19 and 20: loading surface is used again. A ne
Page 21 and 22: The drained bulk modulus of the soi
Page 23 and 24: modelling the inherent and induced
Page 25 and 26: Table 1.1: Input Parameters for the
Page 27 and 28: whereas the P P RMAX can reveal if
Page 29 and 30: Chapter 2Validation of the UBC3D in
Page 31 and 32: Pore Pressure, u (kPa)UBC3DEx.Pore.
Page 33 and 34: first cycle of post-liquefaction be
Page 35 and 36: Shear Stress , τ (kPa)1086420-2-4-
Page 37 and 38: 1.2Excess Pore Pressures\nitial Ver
Page 39 and 40: Chapter 3Validation of theUBC3D-PLM
Page 41 and 42: Figure 3.2: The finite element mesh
Page 43 and 44: checked but the results are not fur
Page 45 and 46: used again when the stress path exc
Page 47 and 48: EPP (kPa)EPP (kPa)EPP (kPa)Measurem
Page 49 and 50: Figure 3.8: Reproduced stress path
Page 51: S.S. Park and P.M. Byrne. Practical

PLAXIS LIQUEFACTION MODEL UBC3D-PLM - Knowledge Base

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