Unified modelling of granular media with Smoothed Particle Hydrodynamics

Abstract

In this paper, we present a unified numerical framework for granular modelling. A constitutive model capable of describing both quasi-static and dynamic behaviours of granular material is developed. Two types of particle interactions controlling the mechanical responses, frictional contact and collision, are considered by a hypoplastic model and a Bagnold-type rheology relation, respectively. The model makes no use of concepts like yield stress or flow initiation criterion. A smooth transition between the solid-like and fluid-like behaviour is achieved. The Smoothed Particle Hydrodynamics method is employed as the unified numerical tool for both solid and fluid regimes. The numerical model is validated by simulating element tests under both quasi-static and flowing conditions. We further proceed to study three boundary value problems, i.e. collapse of a granular pile on a flat plane, and granular flows on an inclined plane and in a rotating drum.

A basic hypoplastic constitutive model for sand

“…Its simplicity and robustness make it an ideal basic model to build more sophisticated models, e.g., critical state model and high-order model [5,8,9,13,30,31]. The failure surface is derived from the constitutive equation and likes that of DruckerPrager.…”

Numerical integration and FE implementation of a hypoplastic constitutive model

“…It is through I e that the model captures the effects of density and confining pressure on the strain-stress behaviour. Several forms for I e can be found in the literature [7,15,21,41], but in the present work, a different formulation for the critical state function I e is proposed:…”

Study of the interaction between dry granular flows and rigid barriers with an SPH model

“…However, in the interaction problems between dry granular flows and structures, the soil elements should stay in a critical state where the dilatancy is zero and the ignorance of the dilatancy in this study should not introduce much error. Additionally, even though the constitutive model accounts for the compressibility, the majority of existing numerical models can not satisfactorily reproduce the desired compressible behaviour due to numerical errors . Therefore, in the present study, the dry granular mass is modelled as an incompressible material with the governing equations as follows: …”

“…Readers are referred to other works and He for the basis of SPH such as the smoothing kernels, the kernel approximation, and the particle approximation. Here, we focus on introducing the different part of our incompressible SPH scheme.…”

“…Therefore, the computation is less time‐consuming. Efforts have been made to implement soil mechanics models in the SPH method to study slope stability, large deformations of soils, and soil‐water interaction problems . McDougall and Hungr approximated the reduced shallow‐water equations for dry soils with SPH techniques and studied the run‐out of landslides in 3D space.…”