The strength of a regularly jointed rock mass is directional. This character depends on the orientation of the joints with respect to the loading directions and the nature and anisotropy of the applied state of stress. Analytical solutions are proposed in this paper to compare the strength of a regularly jointed rock mass under biaxial loading with its strength under axisymmetric loading. The intact rock strength is described by a Hoek and Brown criterion. The joints have no tensile strength and a shear strength described by a Coulomb criterion. The two loading conditions were selected in order to show the influence of the intermediate stress and the orientation of the joints on the strength of a regularly jointed rock mass.
The response of a jointed rock mass to three dimensional loading depends largely on the joint orientation and the anisotropy of the applied state of stress. Compared to intact rock, jointed rock is directional in its response to loading or unloading with reduced shear strength along the joint planes and vanishing or small tensile strength in a direction normal to the joint planes. Analytical models that describe the shear strength of an isotropic rock cut by a joint set have been proposed by Jaeger (1960) and Bray (1967). Mohr-Coulomb criteria with different values of cohesion and friction are associated with the intact rock and the joints. The models assume that the jointed rock response depends only on the largest and smallest applied principal stresses sl, s3 without any contribution of the intermediate stress s2. However, it is common practice in rock mechanics to use these models to predict the strength of a regularly jointed rock mass under more complex multiaxial or biaxial states of stress regardless of the orientation of the joint set with respect to the applied principal stresses. Laboratory triaxial and multiaxial tests have been conducted by several authors to study the influence of the intermediate stress on the strength of intact rock and rock joints. Based on the results of these tests it is commonly assumed, from a practical point of view, that intact rock strength depends only on the major and minor applied principal stresses (Hoek and Brown, 1980). Conversely, the results of tests conducted on samples built up from blocks of model material (Brown, 1970; Ladanyi and Archambault, 1972; Einstein and Hirschfeld, 1973; Reik and Zacas, 1978) have shown that the strength of jointed rock depends on the nature of the applied state of stress, the intermediate principal stress and the orientation of the joints with respect to the stresses. The models of Jaeger (1960) and Bray (1967) fail to fully take into account the influence of the intermediate stress and the orientation of the joints on the strength of a regularly jointed rock mass. It is likely that these two parameters vary from point to point in a rock mass upon loading or unloading. The purpose of this paper is to compare the strength of a regularly jointed rock mass under biaxial loading with its strength under axisymmetric loading.