A two-phase Volume of Fluid approach to model rigid-perfectly plastic granular materials

TL;DR

This work presents a two-phase volume-of-fluid framework that integrates a rigid-perfectly plastic granular model with a Drucker-Prager yield criterion into a monolithic FV-VoF solver to simulate granular flows with large deformations. An Eulerian finite-strain measure is introduced to identify and quantify failure regions, and a regularized Bingham-like viscosity ensures numerical stability across varying strain rates. Validation against 2D dam-break experiments and comparison with elastoplastic SPH data demonstrate good agreement for both non-cohesive and cohesive materials, though higher yield stresses pose challenges that point to the need for elastoplastic extensions. The approach enables large-displacement, arbitrary-shape granular-fluid problems within a standard FV-VoF framework, offering a path toward practical geotechnical and coastal applications involving landslides and debris flows.

Abstract

Granular flow problems characterized by large deformations are widespread in various applications, including coastal and geotechnical engineering. The paper deals with the application of a rigid-perfectly plastic two-phase model extended by the Drucker-Prager yield criterion to simulate granular media with a finite volume flow solver (FV). The model refers to the combination of a Bingham fluid and an Eulerian strain measure to assess the failure region of granular dam slides. A monolithic volume-of-fluid (VoF) method is used to distinguish between the air and granular phases, both governed by the incompressible Navier-Stokes equations. The numerical framework enables modeling of large displacements and arbitrary shapes for large-scale applications. The displayed validation and verification focuses on the rigid-perfectly plastic material model for non-cohesive and cohesive materials with varying angles of repose. Results indicate a good agreement of the predicted soil surface and strain results with experimental and numerical data.

Figures (8)

• Figure 1: Initial configuration and boundary conditions of the 2D soil collapse case (all dimensions in meter).
• Figure 2: Comparison of the measured and predicted final surface and failure line for the validation case of Bui et al. Bui2008 ($t=20$ s; $\phi = 19.8^\circ$; $C=0$).
• Figure 3: Comparison of strain predictions for a final time ($t=20$ s) of the 2D validation case of Bui et al. Bui2008 ($\phi = 19.8^\circ$; $C=0$). Top: Norm of the deviatoric Euler-Almansi strain predicted by the current method. Bottom: Accumulated deviatoric strain from Bui2008.
• Figure 4: Comparison of the temporal evolution of the soil surfaces and failure lines predicted for the 2D soil collapse verification case at $\phi = 25^\circ$ angle of repose and $C=0$ with two different computational models.
• Figure 5: Comparison of the temporal evolution of the soil surfaces and failure lines predicted for the 2D soil collapse verification case at $\phi = 45^\circ$ angle of repose and $C=0$ with two different computational models.