Strain softening around cavities in rock-like materials

Abstract

Recent experimental work casts doubt upon the adequacy of classical and related mathematical models for explaining the stress and fracture within rocklike bodies near cavities. For example, the models predict tangential stresses which are too small very near the cavity walls and zones of fracture which extend too far from the cavities. Here we analyse first a spherical cavity then a circular bore in an infinite rock body with isotropic stress at infinity, using a model introduced recently. The new model is based upon a stochastic network of breakable bonds, in which broken bonds contribute to microscopic fracture surfaces. The new model stresses appear to be more in line with data and the zones of softened rock have smaller extent than those of the classical models. Dilatancy arises naturally in the new model. Softening criteria and ground-response curves are obtained, along with a fairly complete discription of the stress and strain components within the material. A family of surfaces governing potential fractures within the softened zones are described. In the spherical case, simple exact results, of practical relevance, are obtained in the limit of infinite isotropic stress.