A generalized interpolation material point method for modelling coupled seepage-erosion-deformation process within unsaturated soils

In this paper, a computational framework based on the material point method (MPM) is developed to study the coupled seepage-erosion-deformation process within unsaturated soils. Based on the mixture theory, the unsaturated erodible soil is conceptualized as a three-phase multi-species porous medium, which is represented as a set of Lagrangian material points in a three-phase multi-species single point MPM framework. Governing equations as well as constitutive models for describing the coupled seepage-erosion-deformation behaviour within unsaturated erodible soils are presented: the solid skeleton is modelled as an elasto-plastic material; the pore water is treated as a weakly compressible fluid; while the fine particles in the solid matrix can be eroded and transferred into liquidised fine particles, and transported with the flowing liquid. This governing system is discretised with the generalized interpolation material point (GIMP) method and solved explicitly. The proposed coupled seepage-erosion-deformation GIMP is validated via three numerical examples and then employed for simulating the rainfall-induced slope failure process involving internal erosion. Thanks to the capability of the MPM in capturing large deformations, the evolution of the coupled seepage-erosion-deformation behaviour during the whole slope failure process can be obtained. This suggests that the proposed coupled GIMP framework is a promising approach for future studies of internal erosion problems in unsaturated soils involving complex multi-couplings of seepage flow, phase change and large deformations, which are difficult to be modelled by traditional mesh-based methods.