Abstract:
The interaction between the site and elastic waves induces the generation of scattered waves, which propagate to the site boundary and trigger secondary scattered waves. The superposition of incident, of reflected, and of scattered waves significantly amplifies the complexity of seismic responses at the site. By employing the Fourier-Bessel series expansion method for wave functions, the scattered wave potential functions satisfying boundary conditions can be more accurately derived. This approach enables the establishment of analytical solutions for P-wave scattering by composite lining tunnels under varying conditions, thereby providing a rigorous theoretical framework for characterizing wave propagation and structural interactions in complex geological environments. Based on the theory of unsaturated porous elastic medium, the diffraction of composite lining tunnel in unsaturated half-space under plane P-wave incidence is studied by using the Fourier-Bessel series expansion method of wave functions. Through numerical examples, analyzed is the influence of physical and mechanical parameters such as saturation, lining stiffness and lining thickness on the surface displacement amplitude and dynamic stress concentration factor (DSCF) in unsaturated soil half-space composite lining tunnel under P-wave incidence. The results show that the saturation and incident wave frequency have a significant effect on the change of surface displacement amplitude and of DSCF. The displacement change on the left side of the tunnel is drastic and has a higher peak value, while the displacement on the right side of the tunnel is gentler and has a lower peak value. This change becomes more significant when the frequency increases. Increasing the stiffness of the inner lining can reduce the DSCF of the outer lining, but it will significantly enlarge its own DSCF. Increasing the thickness of the inner lining can reduce the DSCF of the lining to a certain extent, but its damping effect is limited, and it is not appropriate to increase the thickness of the inner lining excessively.