Ground response curve of deep circular tunnel in rock mass exhibiting Hoek–Brown strain-softening behaviour considering the dead weight loading

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Abstract
In definition of the ground response curve for a tunnel, convergences of side wall, roof and floor may be different, because of the weight of the failed or plastic rock mass. In this paper, an analytical-numerical solution of the ground response curve for a tunnel excavated in an elastoplastic strain-softening rock mass considering the gravitational loading. In the proposed method, Hoek–Brown yield criterion and Mohr-Coulomb plastic potential function are used for the ground medium. The gravity loading is considered as a radial body force being applied to the ground medium. Two flexible and inflexible lining theories are introduced for the analysis of concrete lining. The derived differential equations cannot be integrated analytically; thus, they are solved by invoking finite difference approximations. Several illustrative examples are given to demonstrate the performance of the proposed method and to examine the effects of the gravity loading. The results obtained by the proposed method show that the gravity loads may affect the tunnel convergence, especially when the plastic region is wide.

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