Application of Cross model for granular flow and impact analysis using three-dimensional B-spline material point method

Abstract

Granular flow and impact, such as landslides and debris flows, are typical problems involving large deformations of non-Newtonian free surfaces, which are of great interest in geological engineering and also pose challenges for traditional mesh-based numerical methods. As an enhancement of the traditional Material Point Method (MPM), the B-Spline Material Point Method (BSMPM) can not only effectively reduce mesh-crossing and quadrature errors, but also facilitate the tracking and capturing of free surfaces and contact interfaces. In this paper, the non-Newtonian general Cross model, the rheological parameters of which are determined by the Bingham model and the Mohr-Coulomb yield criterion, is introduced into the three-dimensional BSMPM (3D BSMPM) for simulating granular flow and impact problems. Interparticle effects of granular materials are represented by artificial damping forces. Dynamic simulations are carried out on the collapse of sand column and glass beads, the flow of bentonite suspensions, and the impact between granular mass and elastic obstacles. The overall evolution of granular flow and impact behavior are presented and compared with existing experimental and/or original MPM results. It is found that the proposed method well reproduces the overall process of granular flow and impact behavior, including its various stages of formation, acceleration, deceleration, and deposition, as well as the impact pressure. The results show that the granular flow and impact behavior can be well represented by the proposed 3D BSMPM with the Cross rheological model, demonstrating the effectiveness of the proposed method in simulating complicated environmental fluid dynamics.