Multi-phase SPH model for simulation of erosion and scouring by means of the shields and Drucker-Prager criteria.

A two-phase numerical model using Smoothed Particle Hydrodynamics (SPH) is developed to model the scouring of two-phase liquid-sediments flows with large deformation. The rheology of sediment scouring due to flows with slow kinematics and high shear forces presents a challenge in terms of spurious numerical fluctuations. This paper bridges the gap between the non-Newtonian and Newtonian flows by proposing a model that combines the yielding, shear and suspension layer mechanics which are needed to predict accurately the local erosion phenomena. A critical bed-mobility condition based on the Shields criterion is imposed to the particles located at the sediment surface. Thus, the onset of the erosion process is independent on the pressure field and eliminates the numerical problem of pressure dependant erosion at the interface. This is combined with the Drucker-Prager yield criterion to predict the onset of yielding of the sediment surface and a concentration suspension model. The multi-phase model has been implemented in the open-source DualSPHysics code accelerated with a graphics processing unit (GPU). The multi-phase model has been compared with 2-D reference numerical models and new experimental data for scour with convergent results. Numerical results for a dry-bed dam break over an erodible bed shows improved agreement with experimental scour and water surface profiles compared to well-known SPH multi-phase models.