Joint compliances as a basis for rock mass properties and the design of supports

Abstract

The compliance of a continuous rock joint is related to a geometrical model involving serration angles and scoring angles. For a set of parallel joints, the compliances of member joints, relating relative movements to stress, can be used to generate the compliance of the joint set, relating strain to stress in local co-ordinates. Transformation of this compliance to global co-ordinates is based on standard techniques. With global co-ordinates as a reference the total compliance of a jointed rock mass is shown to be the sum of the compliances of the rock material and those of each of the joint sets. In a analogous way it is shown that the total stiffness of a reinforced jointed rock mass, containing sets of fully grouted bars or cables, is given by the sum of the stiffness of the jointed rock mass and each of the sets of reinforcement. The compliance and stiffness matrices, so derived, can be used in boundary value problems to predict the stresses and deformations produced by loading/excavation processes. However, in the general case, the components of these matrices will not be symmetric and will be path-dependent, thereby reflecting the nature of rock joint compliances. This will require a flexible computing technique with care in its application to ensure physical validity. In addition, restrictions need to be imposed, such as, quasi-static loading, monotonic stress change, limited deformations and well-behaved joint compliances. Several examples of jointed rock masses are shown and their compliances examined, particularly the case of orthogonal joint sets. One significant finding is that, for cases where the assumption of elastic behaviour is valid, it is possible for am orthohombic elastic material to represent both dilating and non-dilating jointed rock masses. The design of the reinforcement is based on balancing the softening effect of joint sets with the stiffening effect of reinforcement sets, with a general approach developed and several examples given. The difficulty of providing reinforcement in proportion to the theoretical requirement is highlighted.