Shallow circular tunnels subjected to Love waves under drained loading conditions

Abstract

Shallow tunnels are often subjected to seismic surface waves such as Love waves, which may be observed in softer soil layers overlying a stiffer/rock layer. These waves propagate horizontally with the particle motion in the plane perpendicular to the direction of propagation. A novel analytical solution for a shallow circular unsupported opening subjected to Love waves is proposed. The solution is achieved assuming that the ground is homogenous, isotropic, and elastic, the Love wave propagates along the direction of the tunnel axis and that no excess pore pressures are induced. That is, drained loading conditions apply. Complex variable theory and conformal mapping are employed to derive the solution, resulting in a system of linear equations to find the coefficients of the complex analytic functions. Verification of the solution is done by comparing its predictions with results from the Finite Element Method (FEM) software, Plaxis 3D. A parametric analysis with a select number of numerical experiments is completed to investigate the effects of opening size, depth and support on the performance of the tunnels. The results show that as the opening size is increased, the forces increase on the liner. Similarly, the increase in depth also significantly increases the forces on the liner and that leads to a decrease of the stress in the soil. A special analysis has been done to determine whether the relative stiffness between the support and the ground determines the response of the structure, as has been the case in many other problems. The results show that the relative stiffness is not a key parameter to estimate the response of shallow tunnels to Love waves. The research shows that shallow underground utilities and structures may be sensitive to Love waves, given the magnitude of displacements and stresses that they may induce to the structure, and thus utilities and other shallow structures should be designed to withstand the demand imposed by these waves.