Two-dimensional elastoplastic analysis of a long, cylindrical cavity under non-hydrostatic loading

Abstract This paper describes a two-dimensional elastoplastic model of a long, cylindrical cavity in an infinite rock mass subject to non-hydrostatic far-field stress loading. The rock is assumed to behave as an elastoplastic dilatant material that is characterized by a cohesive frictional yield strength. The analysis is based on a solution of the elastoplastic interface that is applicable when the underground cavity becomes completely surrounded by a zone of failed rock, and for stress conditions for which the problem is statically determined. This latter restriction limits the range of deviation from a hydrostatic stress condition that can be analyzed with the model. The stress and displacement field induced by excavation unloading of the cavity is determined on the basis of a proportional load trajectory that involves a monotonic decrease of internal pressure in the cavity. For this particular load history, the elastoplastic boundary grows in a self-similar manner. This allows both displacement and stress field to be calculated in a unit plane, defined by dividing all physical lengths by the characteristic size of the plastic zone. This feature of the solution eliminates the need to solve continuously for the stress and displacement during the evolution of the plastic region. Explicit formulation of the stress field in the plane and of the displacement field in the elastic region is provided; determination of the displacement field in the elastic region is obtained numerically using the method of characteristics. Some important specific results are discussed; a single parameter, the “obliquity” ( m ), defined as the ratio between the stress deviator at infinity and the yield limit, is found to control the shape of the failed rock region and the uneven closure of the cavity. It is found also that the direction of maximum closure may become perpendicular to the maximum far-field compressive stress under some loading conditions.