非饱和土半空间中复合衬砌隧道对平面P波的散射规律研究

RESEARCH ON THE SCATTERING LAW OF DIFFRACTION OF PLANE P WAVES BY A COMPOSITE LINING TUNNEL IN AN UNSATURATED POROELASTIC HALF-SPACE

  • 摘要: 场地与弹性波相互作用会导致散射波的产生,散射波传播至场地边界时会出现次生散射波。入射波、反射波和散射波的叠加会显著增加场地地震响应的复杂程度,而利用波函数的Fourier-Bessel级数展开法可以更精确地得到满足边界条件的散射波势函数,建立不同条件下复合衬砌隧道对P波散射的解析解。该文基于非饱和多孔弹性介质理论,利用波函数的Fourier-Bessel级数展开法,研究了平面P波入射下非饱和半空间中复合衬砌隧道的散射问题。通过数值算例,分析了P波入射下饱和度、衬砌刚度、衬砌厚度等物理力学参数对非饱和土半空间复合衬砌隧道中地表位移幅值与动应力集中系数(DSCF)的影响规律。研究结果表明:饱和度与入射波频率对地表位移幅值与DSCF的变化影响显著,隧道左侧位移变化剧烈且峰值较高,隧道右侧位移更为平缓且峰值更低,这种变化在频率升高时更为显著。增加内层衬砌的刚度可降低外衬DSCF,但会显著放大自身的DSCF。增大内层衬砌的厚度可以在一定程度上降低衬砌的DSCF,但其减震效果有限,不宜过度增加内衬厚度。

     

    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.

     

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