Simulation of post-liquefaction deformation of sand

Recent laboratory tests demonstrated that shear deformation develops continuously, following initial liquefaction, in sands that are subjected to cyclic loading. The effective stress paths after liquefaction repeat similar dilative and contractive behaviors in each cycle, but the corresponding shear strain amplitude increases continuously. The present study proposes a strain history dependence of soil modulus and uses an intrinsic variable to capture the reduction in the plastic shear modulus. Thus, the development of post-liquefaction deformation can be simulated within the framework of a bounding surface plasticity model (Wang et al., 1990). The basic differential equations of the model can be integrated to obtain the stress-strain relationships for post-liquefaction response in two phases. The integrated relationships demonstrate the development of cyclic shear strain in response to the declining modulus, although the effective stress paths in each cycle essentially repeat. Model simulations show reasonable agreement with recent laboratory test results in the deformations developed throughout the sequence of loading cycles.