PLAXIS LIQUEFACTION MODEL UBC3D-PLM - Knowledge Base

More documents

Recommendations

Info

where k p Gis the plastic shear modulus number; np is the plastic shearmodulus exponent; φ mob is the mobilized friction angle, which is defined bythe stress ratio; φ peak is the peak friction angle; and R f is the failure ration f /n ult , ranging from 0.5 to 1.0, where n f is the stress ratio at failure andn ult is the asymptotic stress ratio from the best fit hyperbola.The hardening rule as reformulated by Tsegaye (2010) in UBC3D-PLMmodel is given as:Figure 1.4: The original UBCSAND’s Hardening Rule.Byrne (1998)From Beaty andd sin φ mob = 1.5K p G( ) (pnpp A1 − sin φ ) 2mobR f dλ (1.14)p A p m sinφ peakwhere dλ is the plastic strain increment multiplier.1.3 Plastic Potential FunctionThe plastic potential function specifies the direction of the plastic strain.A non-associated flow rule based on the Drucker-Prager plastic potentialfunction is used in the UBC3D-PLM (Tsegaye, 2010).8
The plastic potential function is formulated as:g = q − a ( p ′ + c cot φ p)(1.15)a =√3 sin ψmobcos θ +sin θ sin ψ√3(1.16)where θ is taken 30 ◦ to fit the Drucker-Prager surface in the compressionpoint.1.4 Flow RuleIn the UBC3D-PLM model the flow rule of the original UBCSAND modelis used, which is derived from energy considerations by Puebla et al. (1997).The flow rule used in UBCSAND is based on three observations: 1. thereis a unique stress ratio, defined by the constant volume friction angle φ cv ,for which plastic shear strains do not cause plastic volumetric strains; 2.stress ratios which lie below sin φ cv exhibit contractive behaviour, whilestress ratios above sin φ cv lead to a dilative response; and, 3. the amount ofcontraction or dilation depends on the difference between the current stressratio and the stress ratio at sin φ cv .The relationship is given as follows:dɛ p v = sin ψ m dγ p (1.17)sin ψ m = sin φ m − sin φ cv (1.18)where, dɛ p v is the plastic volumetric strain increment and φ cv is the constantvolume friction angle. A graphical representation of the flow rule isgive in Figure 1.5.9
Page 1: PLAXIS LIQUEFACTION MODELUBC3D-PLMA
Page 5 and 6: 3.6 Reproduced stress path in p ′
Page 7 and 8: AbstractIn this report the formulat
Page 9 and 10: Comparing with the previous version
Page 11 and 12: Figure 1.2: Projection of the yield
Page 13: ( ) mepK = KBP e A (1.9)P ref( ) ne
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

Create successful ePaper yourself

Delete template?

Save as template?