Numerical modeling of 2-D granular step collapse on erodible and nonerodible surface

The study of the collapse of a granular step is of great interest for understanding transient dense granular flow conditions and for modeling geophysical flows in granular materials. We present the results of a series of finite elements simulations considering variable column aspect ratios and properties for an elastoplastic material with a Mohr-Coulomb yield rule and nonassociate flow rule. The adopted approach does not suffer limitations of typical shallow water equation methods, being able to consider strong vertical motion components. Transition from initial instability to complete flow development is simulated for columns with different aspect ratios (a <= 20). Simulation results are compared to original tests and available well-documented experimental data, in terms of flow development, duration, profile geometry, velocity distribution, erosion and deposition, and evolution of the interface between static and moving material. Tests involving a thick erodible layer have been performed and numerical simulation results are compared also with a real case study. Numerical results support both those of qualitative and theoretical models and the proposed general scaling laws and clarify the dependence on frictional properties. Power laws describe the normalized runout versus aspect ratio (a > 4) relationship with constants of proportionality dependent on internal friction angle and exponents ranging between 0.68 and 0.77, in good agreement with experimental results. Total duration and evolution in three successive phases agree with observations. Time for the flow front to cease motion with respect to aspect ratio is best represented by the 3.68a(0.448) relationships for a 30 degrees internal friction angle material.