Analytical solution for deep circular tunnels covered by an isolation coating layer subjected to far-field shear stresses

Abstract

Tunnels built in areas subject to earthquake activity must withstand seismic loadings. Covering tunnel liners with a coating layer will be a possible way to mitigate seismic damage to tunnels. In this paper, an analytical solution is developed for the seismic response of deep circular tunnels covered by an isolation layer. Since the cross-section dimension of tunnels is normally much smaller than the wavelength of ground peak velocities, the inertial forces can be neglected, and the structure can be designed using the pseudo-static approach, where the seismic-induced loads or deformations can be approximated by far-field shear stresses. The ground and the isolation layer are assumed to be elastic, homogeneous, and isotropic in plane strain conditions, and the tunnel lining is represented as an elastic shell. Both the full-slip and no-slip conditions are considered for the contact between the tunnel and the isolation layer, while the interface between the isolation layer and the ground is assumed to be continuous. The relative stiffness method, proposed by Einstein and Schwartz (1979), is employed to obtain the closed-form solutions for tunnel distortion and internal forces, including axial force, bending moment, and shear force. The proposed solution is verified by providing comparisons between its results and those from the known results in literature and the Finite Element program. Parametric analyses are presented where the seismic mitigation effects of the isolation layer with different properties such as thickness, elastic modulus, and Poisson’s ratio. Results show that the elastic modulus and thickness of the isolation layer, as well as the tunnel-isolation layer interface conditions (i.e., full-slip and no-slip), have significant influences on the seismic mitigation effect, except for the Poisson’s ratio of the isolation layer. The proposed solution can be used as an effective tool for the design optimization of tunnel structures with an isolation layer.