Investigation of the Effect of Confinement on Intact Wombeyan Marble Using Continuum Grain-Based Model (CGBM)
Authors: Satheesh P. V. , Shirole D. , Sinha S. 
Published: August 2024

ABSTRACT:
The progressive failure of brittle rock under compression involves micro-crack initiation, accumulation, and propagation. With advances in numerical modeling, it is now possible to examine complex micro-mechanical processes (e.g., strain heterogeneity, force chains, micro-level damage processes) evolving in the rocks that are difficult to investigate under conventional laboratory settings. While several studies have investigated the micromechanical aspects of brittle rock damage processes under unconfined and confined conditions in discontinuum, understanding them in a continuum media remains limited. Accordingly, this study utilizes the CGBM (representing rock volume as aggregates of polygonal blocks separated by joint elements) technique to simulate the brittle rock failure process of intact Wombeyan marble under varying confinement levels, building upon previous work by Li and Bahrani (2021) in RS2. Specifically, micro-parameters of the intact Wombeyan marble were modified to capture the experimentally informed stress-strain behaviour, and the evolution of damage-induced non-linearity in such curves. The numerical results demonstrate CGBM's ability to capture critical characteristics of brittle rocks, including non-linear strength envelope and change in the failure modes with increasing confinement. Additional investigation on the influence of joint normal stiffness and tensile strength parameters on the simulated micromechanics was completed through strain-field heterogeneity and volumetric strain analysis. A complete understanding of the parametric influences is necessary for accurately predicting rock mechanical response and failure mechanisms, and for improving the capabilities of such models.

1. INTRODUCTION
The heterogeneous nature of the intact rock at the grain-scale governs its emergent macroscopic behavior (Hazzard and Young, 2000; Mahabadi et al., 2012; Potyondy et al., 1996). Grain size, grain boundaries, grain shape, mineral constituents, and micro-flaws present in the rock microstructure introduce stress heterogeneity in rock, which primarily drives rock damage and deformation processes (Fabjan et al., 2015; Lan et al., 2010; Potyondy, 2010; Shirole et al., 2020; Sinha and Walton, 2020; Wang and Cai, 2019). However, investigations that can illuminate such complex processes (i.e., heterogeneity, damage, inelasticity, etc.) evolving at the grain-scales, in general, are difficult to conduct via conventional laboratory-based experimental measures (Shirole et al., 2019, 2020, 2019b). To this end, numerical models that allow the explicit representation of rock microstructure as an assembly of discrete particles or blocks (Discrete Element Methods (DEMs)) have been found to be advantageous (Ghazvinian et al., 2014; Hamediazad and Bahrani, 2022; Peng et al., 2018). The Bonded Particle Model (BPM) and Grain-Based Model (GBM) are two primary DEM techniques utilized for analyzing the rock damage process. In BPM, the internal microstructure of rock is represented as an assemblage of circular and sphere-shaped grains via the discontinuum numerical tool Particle Flow Code (PFC2D and PFC3D) (Potyondy, 2002; Potyondy and Cundall, 2004; Potyondy et al., 1996). However, BPM suffers inherent limitations, such as its tendency to produce high intrinsic porosity in simulated rocks due to the spherical/circular shape of the particles (Gao et al., 2016). Therefore, it becomes challenging to model low-porosity rocks using BPM. On the other hand, GBM represents the internal grain structure of rocks as an assembly of polygons (Lan et al., 2010) or Trigons (Gao et al., 2016). A key issue with the use of Trigons (triangular grains) is its predisposition towards shear fracturing due to the availability of linear failure pathways (Ghazvinian et al., 2014; Sinha & Walton, 2020). GBM with polygonal grains provides a more realistic representation of the geometric features of rocks, as polygons can closely mimic irregular grain shapes found in natural rock formations. Additionally, GBM addresses particle interlocking issues more effectively compared to BPM. By utilizing Voronoi tessellation, GBM accounts for the irregular and non-uniform arrangement of grains within rocks, thereby capturing the complexities of rock microstructures more accurately (Ghazvinian et al., 2014; Sinha and Walton, 2018; Sinha and Walton, 2020).