It has been suggested by several authors that relative stiffnesses could play a significant role in the phenomena of unstable slips along geological discontinuities, such as rock joints and faults. After reviewing some features of the shear behavior of rock joints, the authors present a set of constitutive equations that describes the complete stress-displacement surface. The proposed model, called CSDS, is compared with test results obtained from direct shear tests under constant normal stress and constant normal stiffness conditions. It is shown that the CSDS model can be used to estimate the post-peak stiffness of rock joints needed to establish whether slip is stable or unstable.
Unstable slips along existing discontinuities can represent a major hazard for underground openings. Such violent shear displacements may lead to large seismic events, which can in turn produce rockbursts around mine openings. It has been proposed (e.g. Dieterich 1972, Salmon 1974, Rice 1983) and sometimes demonstrated experimentally (e.g. Dieterich 1978) that the distinction between unstable and stable slip on rock joints can be explained by comparing-the loading system reaction curve with the post-peak behavior of the shearing surface. As shown in Figure 1, when the stiffness of the loading system (k?s) is smaller (in absolute values) than the post-peak stiffness of the rock joint (k'p), there is an excess of energy that leads to a violent failure due to a sudden slip along the surface. Otherwise, failure is gradual.
Thus, in problems involving the possibility of unstable slips, it is very useful to have a model that can describe as closely as possible the behavior of joints in the post-peak region. Some existing constitutive models are able to generate post-peak curves, but very few of them can follow adequately the non-linear behavior under strain softening conditions. In this paper, after briefly reviewing the behavior of joints under constant normal stress, the authors describe a new non-linear constitutive model that can follow closely their mechanical behavior in the pre-peak as well as in the post-peak region, for Figure 1. Influence of the relative stiffnesses of the loading system and of the post-peak behavior of a discontinuity in a direct shear test under constant normal stress. a) Violent failure. b) Gradual failure (after Salmon 1974). either constant normal stress or constant normal stiffness conditions.