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为进一步揭示含直边界衬砌隧道对SH波散射的影响,根据弹性波动理论,结合“分区契合”思想,建立了弹性半空间中半圆隧道对波场散射问题的波动方程。利用傅里叶级数展开的方法,引入辅助函数和波函数展开技术,通过对连续性条件和边界条件的分析,求得半空间中含直边界衬砌隧道对SH波散射的封闭解析解。计算结果表明:入射波特性、半圆隧道衬砌材料特性、隧道埋置深度对地表位移幅值影响显著;对于软性和硬性衬砌隧道而言,当频率逐渐增大时,地表位移幅值也随之增大,地表位移幅值空间振荡更为剧烈;随着入射角度增大,地表位移幅值整体上呈减小趋势;随着隧道埋深d/a由2增加到5时,隧道上方地表位移幅值降幅显著。
In order to further reveal the influence of liner with liner with straight boundary on scattering of SH wave, according to the theory of elastic wave and the idea of “partition fit”, the wave equation of the semispherical tunnel in elastic semi-circular tunnel is established. By using the method of Fourier series expansion, auxiliary functions and wave function expansion techniques are introduced. By analyzing the continuity conditions and boundary conditions, the closed analytic solution of SH wave scattering in a straight boundary lining tunnel in half-space is obtained. The results show that the characteristics of incident wave, the characteristics of semi-circle tunnel lining and the depth of tunnel have a significant effect on the amplitude of surface displacement. For soft and rigid lining tunnels, the amplitude of surface displacement also increases with the increase of frequency As the incident angle increases, the amplitude of surface displacement decreases as a whole. As the tunnel depth d / a increases from 2 to 5, the surface above the tunnel Displacement amplitude decreased significantly.