A Biot formulation for geotechnical earthquake engineering applications
The mechanical behavior of saturated soil is mainly governed by the interaction between the soil skeleton and the pore fluid, and this interaction may lead to significant loss of strength known as liquefaction under seismic loadings. The main objective of this thesis is to develop and implement a cyclic constitutive model capable of modeling soil skeleton dilatancy during earthquake excitation. The constitutive model is based on the fuzzy-set plasticity theory and enhancement is made on the description of dilatancy behavior under cyclic loading. A robust Biot formulation, in which the governing equations of motion of the soil mixture are coupled with the global mass balance equations, is developed to describe the realistic behavior of saturated soil. The finite element discretization is established without neglecting the convective terms. An unconditionally stable implicit time integration scheme, Hilber-Hughes-Taylor a method is used and an iterative algorithm based on Newton-Raphson method is developed to solve the nonlinear time-discretized problem. A numerical study of sand liquefaction is performed and compared with the centrifuge experimental results to show the capabilities of the proposed formulation on pore water pressure generation and strength loss occurred in loose granular soil deposit under cyclic loading. The computed results show good agreement with the experimental data. The capability of the enhanced fuzzy-set model in simulating cyclic soil behaviors including liquefaction is validated. It is concluded that the developed Biot formulation and computational procedure are an effective means to assess liquefaction potential and liquefaction-related deformations.