A DEM model for soft and hard rocks: Role of grain interlocking on strength
Introduction
The ratio between the uniaxial compressive strength (UCS) and the tensile strength (TS) of brittle rocks, i.e. σc/σt, 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 σc/σt 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 σc/σt 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.
Section snippets
Model presentation
The role of grain interlocking on the macroscopic behavior of granular cohesive materials outlined in this paper was investigated using the YADE Open DEM platform (Kozicki and Donzé, 2008, Kozicki and Donzé, 2009, Šmilauer et al., 2010), which operates according to a classic DEM algorithm involving two steps. First, based on constitutive laws, interaction forces between Discrete Elements (DE, also referred to as “particles”) are computed. Second, Newton's second law is applied to determine, for
Influence of the degree of interlocking on the macroscopic behavior
The purpose of this paper being to investigate the role of grain interlocking on the macroscopic behavior of granular cohesive materials, models predictions were examined by performing uniaxial tension and compressive test simulations on a numerical assembly made up of 10,000 DE with a uniform particle size distribution such as (Fig. 4). A preliminary study showed that 10,000 DE provides the best compromise regarding both computational efficiency and representativeness in terms of
Comparison with real rocks
The choice is made here to reproduce the behavior of two distinct rock types, the Lac du Bonnet granite (after experiments carried out by Martin and Chandler, 1994, Martin, 1997) and the Fontainebleau sandstone (after experiments done by Sulem and Ouffroukh (2006)), representative of hard and soft brittle rocks respectively. According to the previous results, in regards of the respective effects of the model parameters on the material response, the calibration procedure was run as follow:
- 1.
Choice
Conclusion
The present work proposes a micromechanical investigation toward the effect of grain interlocking on the behavior of rock based on simulations using the Discrete Element Method. It is shown that the degree of interlocking in the model is a function of the density of bonds linking the discrete elements.
Based on this description, the brittleness of the medium appears to be strongly related to the degree of interlocking between their constitutive particles. By implicitly modifying the
Acknowledgments
The work described in this paper was performed as part of the LOP Project's research into how failures may develop and propagate through jointed rock masses. The LOP Project is an international research and technology transfer project on the stability of rock slopes in open pit mines, established with the objective of addressing a perceived industry wide need for improved knowledge of the mechanisms of rock slope failure in open pit mines. The project is funded by a consortia of international
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