Effects of double-layer lingings on seismic responses of undersea tunnels under incidence of plane P₁ waves

Seawater and seabed soil are regarded as the ideal fluid and saturated porous media respectively. Based on the ideal fluid wave theory and Biot's theory, considering the dynamic interaction of seawater-seabed-tunnel, using the wave function expansion method and Hankel function integral transformation method, the analytical solutions for the seismic response of a double-layer lining undersea tunnel under the incidence of plane P₁ waves are obtained. Compared with the previous "large arc hypothesis" method, the Hankel function integral transformation method can directly convert the scattered waves by the double-layer lining undersea tunnel from the cylindrical coordinate system to the rectangular coordinate system, which can better deal with the boundary conditions (surface for the seawater and seawater-seabed interface). On the basis of the analytical solutions, the influences of the stiffness ratio of the inner to outer linings as well as their thickness ratio on the displacement and stress responses of the double-layer lining undersea tunnel are analyzed, and some suggestions are put forward for its anti-shock design. The research results show that: (1) The seismic dynamic stress responses of the undersea double-layer lining tunnel is significantly smaller than those of the single-layer one under the same parameters. (2) The effects of the stiffness ratio and thickness ratio of the inner to outer linings on the displacement responses of tunnel are related to the different locations of the linings. (3) With the increase of the stiffness ratio and thickness ratio of the inner to outer linings, the stress responses of the outer linings of the tunnel all decrease. (4) Considering the influences of the stiffness ratio and thickness ratio of the inner to outer linings on the displacement and stress responses of the tunnel, it is suggested that the selection ranges of the stiffness ratio and thickness ratio of the inner to outer linings of the undersea double-layer lining tunnel should be no more than 3 and 2, respectively.