The Novel Two-Phase High-Order Updated-Lagrangian Nonlocal General Particle Dynamics for Coupled Seepage Flow and Large Deformation Problems

Abstract

The previous updated Lagrangian nonlocal general particle dynamics (UL-NGPD) can only tackle the first-order nonlocal differential derivatives, so it can not solve the coupled seepage flow and large deformation problems. In this paper, the novel two-phase high-order UL-NGPD is first proposed to study the coupled seepage flow and large deformation problems. Governing equations are derived from the balance laws of fluid-solid interactions in unsaturated porous media, and the matric suction based elasto-plastic constitutive model is developed to consider the matric suction effects in unsaturated geomaterials. Moreover, the novel high-order spatially nonlocal operators are first proposed to obtain accurate second-order nonlocal differential derivatives. On this basis, the novel integral-differential formulations of two-phase high-order UL-NGPD are derived. The numerical implementations of boundary conditions and time integration for coupled seepage flow and large deformation problems are established. Then, the two-phase high-order UL-NGPD framework is implemented to solve coupled seepage flow and large deformation problems. Finally, the proposed method is employed to investigate the reservoir-induced Shuping landslide in Three Gorges Reservoir Region to demonstrate that two-phase high-order updated-Lagrangian nonlocal general particle dynamics is a promising method for handling coupled seepage flow and large deformation problems in geomaterials.

Keywords: Two-phase high-order updated-Lagrangian nonlocal general particle dynamics, Hydro-mechanical coupling, Large deformation, Seepage-induced landslide, Unsaturated porous media