Meshfree Methods for Geotechnical Disaster Simulation and Prediction

This thesis presents meshfree frameworks based on the semi-Lagrangian Reproducing Kernel (RK) approximation to effectively handle extreme geotechnical events within one mathematical framework. The semi-Lagrangian RK approximation combines advantages of the Eulerian and Lagrangian formulations, that is, state variables follow material points while the approximation function is updated in the current configuration to allow extreme deformation and material separation. The approximation is extended to the u-p (displacement-pressure) formulation based on Biot's theory for considering poromechanics of geomaterials. Drucker-Prager plasticity with a single-parameter damage model is also employed to properly represent the behavior of the solid phase of geomaterials. Additionally, variationally consistent stabilized nodal integration schemes and kernel contact algorithms are introduced in the u-p semi-Lagrangian RK framework to enhance accuracy and stability of solutions using the Galerkin formulation and to naturally model arbitrary contacts. Detailed studies of the temporal stability of the frameworks are performed using the von Neumann method to provide a guideline of time step selection when explicit time integration schemes are adopted. The robustness and effectiveness of the proposed u-p semi-Lagrangian RK formulation is verified with FEM solutions in several slope stability analyses. The run-out simulation capability of the presented method is also validated with experimental data and actual data from a landslide site. The proposed framework can be applied to study other geotechnical events under extreme conditions, which is demonstrated in simulating the penetration process of a projectile penetrating into the soil. Additionally, the strong form collocation method with the RK approximation is introduced to study the poromechanics of geomaterials, as an alternative approach. The governing equations are directly solved in the strong formulation with the point collocation method, in which the domain integration is not required in contrast to the Galerkin weak formulation. The effectiveness of the method is studied and demonstrated in hyperelasticity, elastodynamics, and poroelasticity problems.