Simulation of Brittle Failure Around Canada’s Mine-By Experiment Tunnel Using 2D Continuum-Based Voronoi Tessellated Models

Abstract

The failure process of brittle rocks under compression involves the initiation, accumulation and propagation of tensile fractures before peak stress is reached. This process is influenced by the internal microstructure and the presence of heterogeneities in rock, creating localized concentrations of tensile stresses. A realistic simulation of this process requires an explicit representation of rock heterogeneities. The Voronoi tessellation technique is commonly used in numerical methods to simulate heterogeneities in brittle rocks. In this approach, the model domain is divided into several randomly generated polygonal Voronoi blocks separated by numerical ‘joint’ elements. This modelling approach is referred to as a Voronoi Tessellated Model (VTM). Discontinuum-based VTMs provide a better representation of the brittle rock failure process compared to conventional continuum methods. However, their higher computational costs may limit their practical applicability. In this study, a continuum-based VTM was developed using a two-dimensional finite element program to simulate the failure of Lac du Bonnet granite under laboratory and field loading conditions. For this purpose, the VTM with inelastic blocks and block boundaries was first calibrated to the intact (undamaged) rock strength obtained from laboratory tests and then to the rock mass strength estimated based on a tri-linear, brittle failure criterion. The calibrated VTMs were then used to simulate the brittle failure around a circular test tunnel at Canada’s Underground Research Laboratory (URL). As expected, the model calibrated to the intact rock strength did not capture the observed failure; however, the VTM calibrated to the tri-linear criterion did successfully replicate the observed V-shaped notch failure and damage zone around the test tunnel.

Highlights

• A heterogeneous continuum model was developed to simulate the brittle failure around a test tunnel at Canada’s Underground Research Laboratory.

• The heterogeneous continuum model calibrated to the laboratory peak strength of Lac du Bonnet granite did not adequately capture the observed V-shaped notch failure.

• The heterogeneous continuum model calibrated to the tri-linear failure criterion successfully simulated the observed V-shaped notch failure and the excavation damaged zone.

• The back analysis of the V-shaped notch failure using the calibrated model resulted in a spalling limit (σ₁/σ₃) of 11.2 for the granite.