Analytical study of post-closure behaviour of a deep spherical cavity in a dilatant viscoplastic rock mass

The long-term stability of an underground deep cavity involves a lot of complex time-dependent mechanical processes. This paper presents an analytical approach for the post-closure behaviour of a deep spherical cavity inside a dilatant viscoplastic rock mass considering three stages: (1) excavation, (2) free convergence and (3) backfill contact and post-closure. The viscoplasticity is modelled by means of a linear Norton-Hoff's law, and the dilation is incorporated by assuming that the volumetric plastic strain rate is a simple function of the equivalent deviatoric plastic strain. The analytical model proposed in this paper completes a previous work of the authors by adding the consideration of the dilatant behaviour of the rock mass. After presenting the analytical developments, a few numerical examples are presented to illustrate the applicability of the model. In particular, a parametric study shows the influence of key parameters such as dilation parameter, backfill stiffness, viscosity and delay of contact between the rock mass and the internal backfill. This analytical model provides a useful benchmark for complex numerical simulations as well as a useful tool for quick preliminary studies.