Analytical Approach to the Coupled Effects of Slope Angle and Seepage on Shallow Lined Tunnel Response

Abstract

The existing analytical models of shallow lined tunnels pay little attention to the coupled effects of slope angle and seepage, leading to an overestimation of tunnel stability. In order to overcome such a problem, based on the methods of coordinate transformation, complex function and conformal mapping, we attempt to provide an analytical approach to estimate the effective stress and deformation in shallow lined tunnels considering the corresponding influence factors in this study. First, the stress function is extended to the Laurent series in the complex plane, followed by Laplace transform and inverse transform methods on stress function, and the analytical solutions for stress and displacement fields around the tunnel are achieved during different stages. Then, Mein–Larson formula and G–A formula are used to obtain the pore water pressure and effective stress of surrounding rock and lining, considering the effects of rainfall and groundwater. The analytical solution provided in this study can be reduced without considering the lining support and slope angle effects. Furthermore, the rationality and effectiveness of the proposed solution are achieved by a comparison of numerical results. Finally, a comprehensive parametric investigation based on the proposed solution is performed, including buried depth, slope angle and rainfall intensity. The results show that the small change of stress and deformation of the ground surface is observed as the buried depth becomes more than 30[Formula: see text]m. If the slope angle varies within a range from 0 to 30[Formula: see text], the influence of slope angle change on the stress and deformation of surrounding rock can be generally neglected. When the rainfall intensity is greater than a certain threshold or rainfall time is shorter than a value, these two parameters are in a limited effect on the seepage change.