A Simple Closed-Form Solution for Analysis of Tunnels in Mohr–Coulomb Grounds Considering Gravity Loading

In tunnels, convergences of sidewalls, roof and floor may be different, because of weight of the failed or plastic rock mass. In this paper, a closed-form analytical solution for a deep tunnel excavated in an elastoplastic rock mass is proposed. Using the proposed solution, the effects of the weight of the plastic or failed region developed around the tunnel are investigated. In the proposed method, brittle–plastic or elastic–perfectly plastic behavior and Mohr–Coulomb yield criterion and plastic potential function are used for the ground medium. The gravitational loading is considered as a radial body force being applied to the ground medium. Illustrative examples are given to demonstrate the performance of the proposed method and to examine the effects of the gravity loads. The results obtained by the proposed method show that the gravity loading may affect the tunnel convergence, considerably.