A multi-scale hierarchical FEM-DEM approach for hydro-chemo-mechanical modeling of granular media

Numerical study of phenomena in granular media is typically classified into two categories according to the scale of the domain: macro-scale modeling which relies primarily on continuum theories, such as the Finite Element Method (FEM), and micro-scale modeling, which is based on interparticle forces, commonly performed using the Discrete Element Method (DEM).

However, granular/porous media are inherently discontinuous due to their micro-structure, and traditional continuum-based approaches cannot accurately capture microstructure-induced anisotropy in these media. Particle-based approaches like DEM have therefore been widely used for the modeling of such discontinuous domains.

On the other hand, it is not computationally feasible to resolve the entire intricate microstructure of large domains using DEM. Thus, this work implements a multi-scale approach that combines the accuracy of DEM at the grain scale with the computational efficiency of FEM at the macro-scale.

The approach is called “Hierarchical FEM-DEM”, originally developed to study the mechanical response and strain localization (shear bands) in granular media [1]. It then has been extended to hydro-mechanical problems in saturated media [2]. In this framework DEM assemblies are treated as Representative Volume Elements (RVE) attached to Gauss (integration) points of a macroscopic FEM mesh. The DEM is used for the calculation of the homogenized effective stress corresponding to the interpolated strain field on each Gauss point, thereby eliminating the need for phenomenological constitutive assumptions for the solid skeleton, that are common in conventional nonlinear FEM analyses.

In this study we apply this method by implementing it in MATLAB to investigate the hydro-chemo-mechanics of granular media. The model is going to be used to study the effect of fluid flow and pore pressure on the solid skeleton deformation, and generation of shear bands, how micro-scale solute-related heterogeneities influence the macro-scale mechanical behavior, based on thin sections made from field sample collected by the authors.

We use periodic boundary conditions for DEM assemblies to satisfy the compatibility between the microscopic deformation and the macroscopic strain field imposed at the Gauss points, ensuring the condition for the satisfaction of Hill-Mandel micro-macro energy equivalence during homogenization. At the macroscopic level, the boundary conditions are prescribed to simulate the in-situ loading and hydraulic conditions, corresponding to the field sites from which the samples were extracted.

References

[1] Guo, N. and Zhao, J., 2014. A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media. International Journal for Numerical Methods in Engineering, 99(11), pp.789-818.

[2] Guo, N. and Zhao, J., 2016. Parallel hierarchical multiscale modelling of hydro-mechanical problems for saturated granular soils. Computer Methods in Applied Mechanics and Engineering, 305, pp.37-61.