Shape Optimization Of The Support Section Of A Tunnel At Great Depths

Underground tunnells are in common use in hydropower, transportation, mining and military underground projects. The section shape of tunnel is closely related to the stability of the tunnel. And a rational setion shape can improve the stress state in the tunnel and fully develop the self-supporting ability of surrounding rock, which is of help for the maintenance of underground engineering. In the process of engineering construction, the in situ stress field and the boundary conditions of the surrounding rock medium are basically unchanged after the axis of tunnel is selected. When designing, the stress distribution of rock and the stability can be improved only to constantly adjust the geometry of cross-section the tunnel, which results in a section shape optimization problem.Shape optimization of a tunnel is an important research items, and there have been a few studies in the past. However, most previous discussions are under the premise of bare hole, that is, without considering the support, which will greatly reduce the practical significance of studying the shape optimization problem. Because when the in situ stress is relatively large, failure of the surrounding rock of a tunnel even with the best excavation section can’t be avoided. To protect stability of a tunnel from the failure of surrounding rock, support should be set, so that a radial supporting force can be provided on the surrounding rock. In this way, the stress field in the surrounding rock changes, and the tangential stress along the inner edge of tunnel can be reduced.For the certain size of tunnel and support, the optimal shape in the paper is studied under the optimization criterion that minimizing the largest tangential stress along the inner edge of support. When finding the optimal support shape, two contact conditions along the interface between the lining and surrounding rock mass, i.e., pure bond contact condition and pure slip contact condition, are discussed respectively. Using the conformal mapping method of plane elasticity complex function, the optimizing process is actually to solve a series of forward problems. Tangential stress along the inner edge of support is selected as the objective function and coefficients of the mapping function is taken as design variables. The minimum value of the objective function is calculated based on the mixed penalty function method and the optimal shape of support meeting the given constraints can be obtained. Stress state in tunnel support with optimal shape can be improved significantly and the stress concentration along the inner edge of support is minimized.