Effects of a semi-circular valley on dynamic response of shallow tunnel with imperfect interface under Rayleigh wave incidence

In this paper, the two-dimensional scattering and diffraction of Rayleigh waves in an elastic semi-infinite space with a semi-circular valley is studied. The spring model is introduced to describe the imperfect interfacial relationship between the surrounding rock and the lining. By combining the wave function expansion with the method of images, the states of interfaces are systematically discussed through different parameters, including the relative position and the radius of the valley, the tunnel burial depth, and the dimensionless interface coefficients. The results show that the peak values of dynamic stress in lining gradually shift to the spandrel as the increase of dimensionless frequency, while high frequency will produce a greater stress concentration in the surrounding rock at the top of the arch, and the dynamic responses are negatively correlated with the incident frequency in the both lining and surrounding rock. The interface defects tend to weaken the DSCF in the lining but intensify that on the contact surface of surrounding rock, and the effects of transverse springs are greater than that of normal springs. In addition, the larger distance between the valley and the tunnel is beneficial to tunnel structure stability and reduce the valley surface displacement.