Dynamic response of composite linings of shallowly buried tunnels in saturated soils subjected to incidence of plane Rayleigh waves

Based on the Biot wave theory and the Fourier-Bessel series expansion method, a mechanical model for scattering of composite linings of shallowly buried tunnels in saturated soils subjected to incidence of plane Rayleigh waves is established. The analytical solutions of dynamic stress concentration coefficient, pore pressure concentration coefficient and displacement of saturated soils of the composite linings in frequency domain are solved. Through the parameterization analysis, the influences of the stiffness ratio, thickness ratio and tunnel depth on the dynamic response of the composite linings subjected to Rayleigh waves in different frequencies are studied. The results show that the incident frequency has a significant effect on the dynamic stress concentration coefficient and pore pressure concentration coefficient of the composite linings. Increasing the stiffness ratio and thickness ratio of inner linings to outer linings can significantly reduce the dynamic stress concentration factor and pore pressure concentration factor of the outer linings, and the maximum decrease can be more than 90%, but can significantly amplify the dynamic stress concentration factor of the inner linings, and the impact of shock absorption of the outer linings is limited when the amplitude exceeds a certain value. It is suggested that the stiffness ratio of inner linings to outer linings should be 2~4, and the thickness ratio should be 1~2. With the increase of the buried depth, the dynamic stress concentration coefficient of the inner linings decreases gradually, and the influences of Rayleigh waves on the dynamic response of shallowly buried tunnels are more significant. The results may provide theoretical support for the anti-shock design of underwater tunnels.