Shape optimisation of the support section of a tunnel at great depths

Abstract The shape optimisation of a cavity is typically performed without considering the previous support, which may significantly reduce the practical significance of such analyses. Even when an excavation section is optimised, failure of the surrounding rock in a tunnel cannot be prevented in the presence of excessive in situ stress. Thus, a support should be established to protect the stability of a tunnel from the failure of the surrounding rock. This study examines the optimal shape of the support that satisfies the optimisation criterion, which minimises the largest tangential stress along the inner edge of the support, for a specific net tunnel size and support strength. The optimisation process is to solve a series of forward problems using the conformal mapping method for a plane elasticity complex function. The tangential stress along the inner edge of the support is selected as the objective function, and the coefficients of the mapping function are considered as the design variables. The minimum value of the objective function is calculated based on the mixed penalty function method and the optimal support shape that satisfies the given constraints can be obtained. The stress state of an optimally shaped tunnel support is significantly improved compared to non-optimal configurations, and the stress concentration along the inner edge of the support is minimised.