Closed-Form Solution to the Poromechanics of Deep Arbitrary-Shaped Openings Subjected to Rock Mass Alteration

The aim of this paper is to propose a closed-form solution to the poromechanics problem of stress and pore pressure distribution around noncircular openings at great depth subjected to hydrostatic water pressure and far-field geostresses. The problem is solved by superposing the effects of fluid and solid skeleton obtained over simple circular geometries and generalizing the obtained expression to various geometries of mined ore bodies using complex variable functions and conformal mapping techniques. The principal stresses obtained analytically over the opening boundary and within the domain are compared with the results of finite-element analysis to verify the proposed approach. The comparison conducted for a representative noncircular opening indicates good agreement between the analytical and numerical methods. Hence, a parametric study is used to investigate in detail the stress variation under different opening dimensions, heterogeneous initial total stress conditions, and far-field pore pressure values. The proposed solution could be instrumental in the design of underground openings and deep mass alterations (that include local anthropogenic damage zones). It could also be used to provide reinforcement solutions where stresses can reach the mechanical stability thresholds.