Steady State Response of Radial Heterogeneous Saturated Soil-circular Tunnel Lining Based on Theory of Porous Medium

Considering the influence of liquid phase of soil, construction and in-situ stress on the soil around the tunnel, the soil around the tunnel was regarded as heterogeneous saturated soil, and it was assumed that the solid shear modulus of solid phase changed along the radial direction. Using the multi circle model, the saturated soil around the tunnel was divided into the undisturbed saturated soil and disturbed saturated soil, and the disturbed saturated soil was divided into multiple thin concentric rings. The steady-state solutions of saturated soil in undisturbed area and each circle were solved, and the transfer matrix between radial displacement of solid phase and liquid-phase, radial stress of solid phase at the outer and inner boundaries of saturated soil in the disturbed region was obtained. Taking the circular tunnel lining as elastic medium, the radial displacement and radial stress of the circular tunnel lining were obtained by using the elastic dynamics theory. Considering the continuity condition and the boundary condition of the problem, the analytical solution of the steady-state response of radial heterogeneous saturated soil-circular tunnel lining was obtained. Numerical examples showed that there were obvious peaks and troughs in the curves of radial displacement and radial stress of saturated soil varying with frequency, and there was a certain mutation near when Rω/v=1.0. The ratio of shear modulus in the affected area and the variation law of shear modulus along the radial direction had a great influence on the steady-state response of heterogeneous saturated soil-circular tunnel lining system, and the influence of tunnel lining thickness had a certain relationship with frequency. The influence of heterogeneous characteristics and the liquid phase on the dynamic characteristics of saturated soil-circular tunnel lining system could not be ignored.