A 3D Continuum-Based Voronoi Tessellated Model (VTM) for Hard Rocks

In conventional continuum numerical models, rock is typically simulated as a homogeneous material. However, these models fail to capture pre-peak tensile damage in hard rocks under compressive loading. The Discrete Fracture Network (DFN) is widely used to generate various types of rock heterogeneities at different scales. Among these, the Voronoi structure has been successfully implemented in discontinuum models to replicate the failure process of hard rocks. More recently this method has been effectively applied in 2D continuum models; however, its suitability for simulating hard rock failure in 3D continuum models has not been investigated. This paper aims to address this research gap by presenting the development of the first 3D Voronoi Tessellated Model (VTM) using the finite element program, RS3. The central objective of this study was to replicate the failure process of hard brittle rocks under unconfined compression. For this purpose, the micro-properties of a previously calibrated VTM constructed using the 2D finite element program RS2 were utilized in the RS3-VTM. The results indicate that the stress-strain curve and the peak strength of the RS3-VTM are comparable to those of the RS2-VTM. Furthermore, the simulation results demonstrate that the RS3-VTM captures the anticipated failure mode of hard rocks in laboratory unconfined compression tests. 1. INTRODUCTION Experimental and numerical studies have indicated that, at low confinement, the failure process of brittle rocks involves the generation of localized tensile stresses due to grain-scale heterogeneities. These induced tensile stresses can lead to the initiation and propagation of tensile cracks before reaching peak stress, even when the rock medium is under an overall compressive stress field. To realistically simulate this process using numerical modeling, an explicit representation of the grain-like structure of rocks is required. Discrete Fracture Network (DFN) models are commonly used to generate various types of geological structures at different scales. Among them, the Voronoi structure has been extensively employed to replicate grain-scale heterogeneities (i.e., grains and grain boundaries) in brittle rocks.