The mechanical response of rock masses to loading and excavation, especially in low stress environments, is significantly affected by discontinuities. This paper examines the practical modelling of rock mass problems with explicit representation of discontinuities using special joint elements in the Finite Element Method. The paper discusses why it is possible to use this approach for routine, practical engineering analysis today. Through a few examples, it also presents the merits of the approach such as the ability to capture a range of mechanisms and scale effects due to discontinuities.
1. INTRODUCTION
The idea of using the continuum-based finite element method (FEM) to model blocky rock mass behaviour has been around since the 1960s. The first joint or interface element for simulating the behaviour of discontinuities was proposed then [1]. Over the years however, discontinuum-based numerical approaches such as the Discrete Element Method (DEM) and Discontinuous Deformation Analysis (DDA) surpassed the FEM as the tools of choice for modelling blocky rock masses. This paper briefly discusses the effects discontinuities (the terms discontinuities and joints will be used interchangeable throughout the paper) have on rock mass response to excavation and mechanical loading. It will argue that the Shear Strength Reduction (SSR) method, combined with modern computing advances, has made it possible to apply the FEM to the practical and routine engineering of structures in discontinuous rock masses as originally envisaged. Through a few examples, the paper will show how the FEM captures a spectrum of discontinuous rock mass behaviours ranging from individual block movements to continuum-like mechanisms, and combined modes. One of the examples looks at step-path (en-echelon) failure (that combines slip along joints with shearing through intact rock) determined by the FEM. The paper will outline two unique advantages of the FEM compared to pure discontinuum approaches.
2. RESPONSE OF DISCONTINUOUS ROCK MASSES TO EXCAVATION AND MECHANICAL LOADING
The influence of discontinuities on the mechanical response of rock masses to loadings and excavation has long been recognized [1, 2, 3, 4]. In some situations (especially in low stress environments such as are encountered in slopes and near surface excavations) discontinuities exert greater influence on behaviour than do intact rock properties. Discontinuities can cause the distribution of stresses and displacements induced in a rock mass to differ significantly from those predicted by classical elastic or elasto-plastic theories for homogeneous continua. The strength, deformation modulus, and stress-strain responses to loading of rock masses can be all affected by discontinuities in non-linear and anisotropic fashion. As well, discontinuities can make it very difficult to predict the strength and deformation characteristics of rock masses. The deformations of discontinuities contribute greatly to the behaviour of discontinuous rock masses under excavation. Discontinuities generally exhibit brittle (strain softening) behaviour; they typically have residual strength that is much lower than peak strength [2]. This leads to the development of progressive failure mechanisms. When the strength of a segment of a joint is reached, the material in this stressed zone yields and deforms considerably, while the strength drops to the lower, residual value.
