Semi-implicit material point method for simulating infiltration-induced failure of unsaturated soil structures

This study presents a semi-implicit MPM to adequately characterize the mechanical behavior of unsaturated soil based on Biot's mixture theory. To represent the dependency of the degree of saturation on the suction, we employ the VG model along with a soil-water characteristic curve, which determines a functional form of permeability called the Mualem model. Hencky's hyperelastic model and the Drucker-Prager model assuming nonassociativity are adopted for elastic and plastic deformations, respectively. The novelty of this study is the incorporation of the fractional-step method into the MPM framework so that the pore water pressure is obtained by implicitly solving the pressure Poisson's equation, which reduces numerical instability and improves computational efficiency. Also, because the drag force between solid and liquid phases is evaluated using the intermediate velocity of pore water relative to the intermediate velocity of solid skeleton, the time increment can be chosen without considering the magnitude of water permeability. In addition, to suppress "odd-even" oscillation, we employ a sub-grid method in which two grids with different spatial resolutions are used for the velocities and pore water pressure. Furthermore, considering the advantages and disadvantages of two different interpolation schemes for pore water pressure, we suggest switching the schemes depending on the model conditions. Several numerical examples are presented to demonstrate the performance of the proposed method. Specifically, unidirectional consolidation and leak flow analyses are performed for verification purposes, followed by validation analysis of a model experiment of infiltration-induced landslides.