A mixed total Lagrangian-updated Lagrangian Smoothed Particles Hydrodynamics method for geomechanics simulations with discontinuities

This study presents a novel approach for simulating geotechnical problems including the initiation and post-failure behavior of discontinuities. The developed method is constituted by a mixed total Lagrangian--updated Lagrangian Smoothed Particle Hydrodynamics (SPH) method, which the main characteristic is to distinguish between internal forces within a body and contact forces from interactions with other bodies as internal stress and collision stress, respectively. Internal stress effects are calculated using total Lagrangian SPH interpolations, while collision stress effects are computed with updated Lagrangian. Fractures are simulated by employing plastic deformation as a damage measure, with fully damaged particles detached from their original body and treated as a separate particulate material, interacting via collision stress. Numerical tests confirm the method's capability in accurately modeling elastic collisions, friction forces and tension and shear fractures, validated against experimental data. Finally, we show the applicability of the proposed by simulating a real-scale landslide scenario, the Selborne experiment. This final numerical test demonstrates the capability of the method to simulate a landslide detached from the main soil mass as observed in the experiment.