A mixed total Lagrangian-updated Lagrangian Smoothed Particle 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 landslides triggered by 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, represented by the internal stress, from contact forces interactions with other bodies, represented by the contact stress. Internal stress effects are calculated using total Lagrangian SPH interpolations, while contact stress effects are computed with updated Lagrangian. Discontinuities are simulated by employing a threshold on plastic deformation, in which highly plastic deformed particles detached from their original body are treated as a separate particulate material with neighboring interactions via contact stress. Numerical tests confirm the method’s capability in accurately modeling elastic collisions, friction forces and discontinuities from both tension and shear stresses, and the results are validated against experimental data. Finally, we show the applicability of the proposed method 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.