Multi-species simulation of porous sand and water mixtures

Abstract

Fig. 1. Dam breach. Water pours in from a reservoir and slowly erodes a dam. As water seeps into the sand, its cohesivity decreases. When it eventually breaks, the landslide creates interesting dynamics in the debris flow. We present a multi-species model for the simulation of gravity driven landslides and debris flows with porous sand and water interactions. We use continuum mixture theory to describe individual phases where each species individually obeys conservation of mass and momentum and they are coupled through a momentum exchange term. Water is modeled as a weakly compressible fluid and sand is modeled with an elastoplastic law whose cohesion varies with water saturation. We use a two-grid Material Point Method to discretize the governing equations. The momentum exchange term in the mixture theory is relatively stiff and we use semi-implicit time stepping to avoid associated small time steps. Our semi-implicit treatment is explicit in plasticity and preserves symmetry of force linearizations. We develop a novel regularization of the elastic part of the sand constitutive model that better mimics plasticity during the implicit solve to prevent numerical cohesion artifacts that would otherwise have occurred. Lastly, we develop

Stabilized material point methods for coupled large deformation and fluid flow in porous materials

“…At the same time, since the MPM explicitly uses and traces material particles-like in a Lagrangian method-it is naturally able to incorporate the history-dependent solid behavior. Because of these attractive features, the MPM has been gaining increasing popularity for the simulation of large deformation processes in a variety of materials including fluid-infiltrated porous media [24][25][26][27][28][29][30][31][32][33].…”

Multiscale modeling of large deformation in geomechanics

“…Further studies are needed to find more efficient solutions schemes, ie, adaptive multiscale homogenization, to mitigate the computational cost of the multiscale modeling. It is also desired to enrich the functionalities of current multiscale approach by considering grain morphology, particle breakage, or hydro‐mechanical coupling . Although all cases discussed in this paper have been based on 2D simulations, it is straightforward to further implement the code in 3D as the multiscale framework is proposed in generalized form and, both the adopted MPM solver ( NairnMPM ) and DEM solver ( YADE ) have built‐in 3D capabilities.…”

A Temporally Adaptive Material Point Method with Regional Time Stepping

“…St. Venant‐Kirchhoff Hyperelasticity . The St. Venant‐Kirchhoff hyperelasticity model combined with the logarithm Hencky strain measure has been mostly used for granular media [KGP*16, TGK*17] and elastoplastic flow [GTJS17] in graphics. Note that plasticity does not contribute to the pressure wave.…”

“…Nearly incompressible and weakly compressible equation‐of‐state (EOS) fluids have been widely used in SPH [BT07]. In MPM, it is also used for simulating liquid in porous media [TGK*17]. The pressure is…”