u‐p semi‐Lagrangian reproducing kernel formulation for landslide modeling

This paper presents a u-p (displacement-pressure) semi-Lagrangian Reproducing Kernel (RK) formulation to effectively analyze landslide processes. The semi-Lagrangian RK approximation is constructed based on Lagrangian discretization points with fixed kernel supports in the current configuration. As a result, it tracks state variables at discretization points while allowing extreme deformation and material separation that is beyond the capability of Lagrangian formulations. The u-p formulation following Biot theory is incorporated into the formulation to describe poromechanics of saturated geomaterials. In addition, a stabilized nodal integration method to ensure stability of the domain integration, and kernel contact algorithms to model contact between bodies, are introduced in the u-p semi-Lagrangian RK formulation. The proposed method is verified with several numerical examples and validated with an experimental result and the field data of an actual landslide.