A DEM model for soft and hard rocks: Role of grain interlocking on strength

Abstract

The Discrete Element Method (DEM) is increasingly used to simulate the behavior of rock. Despite their intrinsic capability to model fracture initiation and propagation starting from simple interaction laws, classical DEM formulations using spherical discrete elements suffer from an intrinsic limitation to properly simulate brittle rock behavior characterized by high values of UCS/TS ratio associated with non-linear failure envelopes, as observed for hard rock like granite. The present paper shows that the increase of the interaction range between the spherical discrete elements, which increases locally the density of interaction forces (or interparticle bonds), can overcome this limitation. It is argued that this solution represents a way to implicitly take into account the degree of interlocking associated to the microstructural complexity of rock. It is thus shown that increasing the degree of interlocking between the discrete elements which represent the rock medium, in addition to enhancing the UCS/TS ratio, results in a non-linear failure envelop characteristic of low porous rocks. This approach improves significantly the potential and predictive capabilities of the DEM for rock modeling purpose. A special emphasis is put on the model ability to capture the fundamental characteristics of brittle rocks in terms of fracture initiation and propagation. The model can reproduce an essential component of brittle rock failure, that is, cohesion weakening and frictional strengthening as a function of rock damage or plastic strain. Based on model predictions, it is finally discussed that frictional strengthening may be at the origin of the brittle ductile transition occurring at high confining pressures.

Introduction

The ratio between the uniaxial compressive strength (UCS) and the tensile strength (TS) of brittle rocks, i.e. σ_c/σ_t, constitutes one of their most fundamental characteristics (Altindag and Guney, 2010). Although the compressive strength is the most widely used parameter to characterize rock in the engineering practice (Brady and Brown, 2004), it is now well assumed that brittle failure in rock is mainly governed by tensile rupture mechanisms. A comprehensive model for rock should therefore be able to properly match both its specific compressive and tensile strengths.

The Discrete Element Method (DEM) using spherical discrete elements, which has brought interesting insights to the characterization of failure mechanisms in cohesive frictional materials, is now often used for rock modeling purpose. Due to their discontinuous nature, discrete models can deal with the initiation and propagation of microcracks inside heterogeneous media and constitute therefore a powerful tool to study how the microstructure affects the macroscopic properties of geomaterials. However, it seems that there is an intrinsic limitation in the basic formulation of these models: whatever the predefined values of the micromechanical parameters, they are unable to reach high σ_c/σ_t values representative of brittle rocks (Potyondy and Cundall, 2004, Schöpfer et al., 2009), restricting therefore their predictive capabilities to weak or poorly cemented rocks. One consequence is, for example, that calibrating those classical DEM to the compressive strength of a brittle rock results in an over prediction of its tensile strength, which can then be problematic when simulating problems where the stress path may be either tension or compression.

In low-porosity hard rocks like granite or basalt, grain interlocking contributes to high values of the σ_c/σ_t ratio as well as to high internal friction angle. Hence, to overcome the limitation of classical discrete models, it might be necessary to use an additional texture property like irregular shaped discrete elements as proposed by Potyondy and Cundall (2004) or Cho et al. (2007) to improve grain interlocking in order to simulate representative macroscopic behaviors. Indeed, the mechanical behavior of rocks is controlled by their microstructure and results from a combination of mechanisms occurring at the grain scale (Tapponier and Brace, 1976). Thus, a model capable of accurately replicating the microstructure of rock should then permit to properly simulate its macroscopic behavior as it has been demonstrated in 2D by Lan et al. (2010) or Kazerani and Zhao (2010) using polygonal particles. However, although in accordance with the true microstructure of rock, the treatment of non-spherical particles in 3D codes still highly penalizes calculation efficiency, and therefore limits their application to small scale problems.

As an alternative solution, it is possible to implicitly enhance the microstructure of a granular packing by increasing the density of bonds between the constitutive particles. DEM formulations using this feature have already been proposed by Donzé et al. (1997), Fakhimi (2004) or Shiu et al. (2008) for example, but no precise analyses were performed at that time concerning the potential contribution of the method on the macroscopic response of the simulated medium.

The objective of the present paper is to present a 3D DEM formulation capable of properly simulating brittle rock behavior, starting from microstructural considerations. The basic idea is to keep a simple formulation for the DEM in order to ensure high calculation efficiency (i.e. spherical particles and linear elastic contact laws), and then to show how, by simply controlling the degree of interlocking between the constitutive elements, the macroscopic response of the simulated medium can be adjusted to the targeted behavior.

After a brief description of the model features, a sensitivity analysis will be provided in order to emphasize the effects of grain interlocking on the material response. It will then be shown that the proposed approach, besides its predictive capabilities at the macroscopic scale, provides also good agreement in the description of brittle failure processes of rock in terms of crack initiation and propagation.