A spring-like interface between saturated frozen soil and circular tunnel lining under the moving load in cold regions without considering frost heave

The vibration of underground or buried piping during construction and long-term operation causes secondary disasters, and becomes more complex when tubes are buried in cold regions. The interface between saturated frozen soil and lining is regarded as a thin spring-like layer whose thickness could be negligible. In this paper, the dynamic response of saturated frozen soil is studied in frequency domain by using the Helmholtz composition and Fourier transform to obtain analytical solutions of the radial and axial displacement, as well as expressions of the stiffness coefficient (K_r) and damping coefficient (C_r) of the spring-like interface. Numerical results indicate that K_r and C_r are related to physical properties of the lining and its surrounding soil, and the coefficients of the spring-like model could be changed by adjusting lining parameters to improve structure stability under the same load conditions. Also, the viscoelastic contact surface of the spring-like model is considered to have less effect on the surrounding soil than that when the lining has complete contact with the soil under load. The degree of soil freezing significantly affects the axial and radial displacement of the soil when the interface between lining and unsaturated frozen soil is taken into consideration.