Stability analysis of soil liquefaction using a finite element method based on particle discretization scheme

Mathematically, liquefaction corresponds to the unstable solutions of the governing equations of soil dynamics. Stability analysis of these solutions facilitates the understanding of the triggering and development of liquefaction. This paper presents a numerical approach for stability analysis of the solutions of the governing equations. The governing equations are linearized for small perturbations and discretized using a finite element method (FEM) based on the particle discretization scheme (PDS). By solving the discretized governing equations with the developed PDS–FEM code, unstable solutions are captured for perturbations in the form of a three-dimensional spherical wave. The present approach considers the dilatancy effect and the detaching effect. The numerical results show that the dilatancy effect triggers and the detaching effect spatially expands the unstable solutions. The existence and expansion of the unstable solutions provide a new perspective on the triggering and development of liquefaction.