# Upper Bound Limit Analysis of Uplift Failure in Pressurized Sealed Rock Tunnels

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Abstract

We investigate the problem of uplift failure of the rock mass above shallow, sealed, pressurized gas storage tunnels by means of the upper bound theorem of the limit analysis assuming a continuum rock mass model obeying the Mohr Coulomb failure criterion with tension cut off. The geometry of the failure surface is determined using calculus of variations. The effect of the strength parameters and the overburden on safety against uplift are studied using the derived solution. It is shown that uplift pressure increases significantly with the uniaxial compressive strength of the rock and with the overburden. Tensile strength has a significant effect only in rock masses with relatively high uniaxial compressive strength.

1 Introduction

Underground sealed rock tunnels can be used to store natural gas at relatively high pressures, e.g. up to 30 MPa in tunnels for compressed air energy storage (CAES). The internal gas pressure is borne by the rock, while the tightness of the system is guaranteed by a sealing lining. In relatively shallow reservoirs, uplift failure of the overlaying rock mass up to the surface is the most serious hazard scenario.

The problem of uplift in high-pressure sealed rock tunnels has received relatively little attention. Kim et al. (2012) suggested a limit equilibrium model assuming vertical slip surfaces and normal stress on these surfaces equal to the initial horizontal stress. This assumption is very uncertain in view of the tensile stress field expected around the expanding cavity. Brandshaug et al. (2001) investigated uplift failure for a specific case by means of a small strain numerical analysis of a continuum, elastic- perfectly plastic, no-tension medium obeying the Mohr Coulomb failure criterion. They adopted the strength reduction method for assessing the safety factor against uplift. Perazzelli et al. (2014) performed small and large strains numerical analyses assuming the same rock model as Brandshaug et al. (2001) and taking uplift pressure equal to the pressure of the last equilibrated solution. For weak rock masses, the deformations at failure are very large and necessitate a geometrically non-linear formulation in order to obtain the ultimate uplift pressure; the small strain approach may (depending on the stiffness of the rock mass) overestimate the ultimate pressure (Perazzelli et al. 2014). Tunsakul et al. (2014) developed a numerical method based on the element-free Galerkin (EFG) method with a cohesive crack model to simulate fracture propagation patterns in a continuum medium around a pressurised tunnel.

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ISRM-EUROCK-2015-143

October, 2015

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