Analytical elastic stress solution and plastic zone estimation for a pressure-relief circular tunnel using complex variable methods

Abstract

It is likely that a great number of excavation-induced failures, including rock burst, are activated in a highly anisotropic in situ stress field. Pressure-relief technologies are employed popularly as effective approaches of treating the induced failures, but there is a lack of study on their mechanisms in terms of the relief effect and distribution of the plastic zone. This paper proposes a pressure-relief method of grooving relief slots in the roof and floor of a circular opening considering the non-uniform stress distribution around a circular opening under anisotropic far-field stress. A conformal mapping method and complex variable theory are adopted to obtain a closed-form solution for released openings, stress ratios of the unreleased to released openings are used to describe the release effect, and effects of the lateral pressure coefficient and slot depth are discussed. Additionally, a negative exponential relation between the maximum stress ratio and the rock depth is found. On the basis of the elastic solution, this paper presents an approach of finding the distribution of the plastic zone around a non-circular opening for an anisotropic in situ stress state using the Mohr–Coulomb criterion, and investigates the release effect on the plastic zone for different lateral pressure coefficients and slot depths.