Stability Analyses of Shallow Rectangular Tunnels in Anisotropic and Nonhomogeneous Soils Using a Kinematic Approach

Abstract

Conducting soil stability assessments around tunnels has always been a concern. However, most existing studies have regarded soil as an isotropic and homogeneous material. To overcome this limitation, within the framework of upper bound theory, this paper proposes a novel rotational–translational failure mechanism where the velocity discontinuity surfaces are derived numerically. This theoretical mechanism includes two cases according to the positions of the velocity discontinuity surfaces. An analytical solution for pore water pressure is obtained using the conformal mapping method, which involves solving the two-dimensional (2D) Laplace equation and considering the soil and shotcrete permeability. Then, upper bound expressions for the limit supporting pressure are derived by computing work equations with and without pore water pressure. Comparisons with previous work and numerical results illustrate that the presented approach offers improvements and could be applicable for stability analyses of shallow rectangular tunnels in anisotropic and nonhomogeneous soils. Finally, this paper discusses the effects of the anisotropy and nonhomogeneity of soil properties on the normalized limit supporting pressure and the collapsing domains of rectangular tunnels with different geometric shapes. In addition, the impact of pore water pressure on the changed water levels is assessed. The results demonstrate that for rectangular tunnels that are excavated in water-bearing zones, the width-to-height ratio plays a significant role in the stability of the surrounding soils.