Dynamic response of a lined tunnel in cold regions considering anisotropic frost heave

The dynamic response of harmonic load acting on the soil-lining system in cold regions considering anisotropic frost heave is studied in frequency domain. The lining is in close contact with the frozen soil and there exists relative movement between the frozen soil and unfrozen soil due to differences in composition and properties. An analytical solution of the vibration induced by the harmonic load in frozen soil is obtained considering the anisotropic frost heave in soil. Based on the continuity and boundary conditions between the unfrozen soil, frozen soil, and lining, the coefficients to be determined are obtained and the analytical solutions for the displacements and stresses in the different media of the tunnel system in cold regions are also obtained. The analysis of specific parameters of the model shows that the change in the parameters of the tunnel system (lining, frozen soil, and unfrozen soil) affects the amplitude of the circumferential stress, the amplitude of the radial displacement in the soil in different states and their peak frequencies in cold regions; anisotropic frost heave affects the stresses in the frozen soil; the amplitude of the radial displacements in the tunnel system in the cold regions decays with increasing distance from the center of the tunnel, and the amplitude of radial displacement in unfrozen soil decreases considerably compared to that of frozen soil.