Continuum model of regularly jointed mediums

Abstract

A continuum description is presented for a rock mass containing one or more sets of regularly spaced parallel joints. It is assumed that the length scale of interest is large compared with joint spacing and that the relative displacement across joints is small compared with joint spacing. On the large scale of several joint spacings, the discrete relative tangential and normal displacements across joints of each set are viewed as continuous displacement fields defined so as to give the same net emplacement across a representative element of jointed rock. The resulting in-plane displacement gradients associated with these continuous fields contribute to the strains at points in the intact block material between joints, and so enter the constitutive laws for the block stresses. In turn, the relative motion across a joint depends on the tractions on the joint plane, and so joint motion and block deformation are interdependent. In particular a strain decomposition analogous to that of classical plasticity theory is obtained. Tentative models for the joint mechanics involving a Coulomb criterion and joint slip, both ideal slip and slip hardening, together with elastic block response, are described to illustrate the complete constitutive theory.