PLAXIS LIQUEFACTION MODEL UBC3D-PLM - Knowledge Base

f 3a = 1 2 (σ′ 1 − σ ′ 2) + 1 2 (σ′ 1 + σ ′ 2) sin φ ′ − c ′ cos φ ′ (1.5)f 3b = 1 2 (σ′ 2 − σ 1) ′ + 1 2 (σ′ 2 + σ 1) ′ sin φ ′ − c ′ cos φ ′ (1.6)The six combinations of the principal stresses in the equations define sixplanes in 3-D principal stress space. These planes defines the Mohr-Coulombyield surface as presented in Figure 1.1. The projection of the yield surfacein the π -plane is presented in Figure 1.2.Figure 1.1: The intersection of the six planes and finally the yield surfacein 3-D principal stress space. After Tsegaye (2010).The first step that has to be done by the model is to compute the principalstresses of the stress tensor. This is done after solving the eigenvalueproblem. The eigenvalues give the principal stresses and the eigenvectorswill be their directions. As far as isotropic behaviour is concerned the directionsof the principal stresses are fixed (rotation of the principal stressesis not included in UBC3D-PLM) so the material response is not dependenton the orientation. After the determination of the three principal stresses4