Abstract In this study, the dynamic interaction between a surficial alluvial valley and an underground tunnel embedded in it under plane shear horizontal (SH) waves is investigated. Within the framework of classical elastodynamics, an analytical solution to the wave propagation and scattering around a circular lined tunnel embedded in a semi–circular alluvial valley in an elastic half space is proposed. Using the wavefunction expansion and the mirror image methods, the wave fields with unknown coefficients in three regions (i.e., the tunnel lining, alluvial valley, and rutted half space) are constructed separately in different polar coordinates to satisfy the traction–free boundary conditions along the horizontal ground surface as well as the inner surface of the tunnel lining. Using a series of transformations of the Graf’s addition formula, the coefficients of the wave fields are obtained by matching the three regions to satisfy the stress and displacement continuity conditions at the interfaces. Both the surface displacement amplitude of the alluvial valley and the dynamic stress concentration factor of the tunnel are calculated to determine the dynamic interaction effects between the surficial valley and underground tunnel. A mutual enhancement of the dynamic responses in the alluvial valley and embedded tunnel is found owing to the wave reflection, scattering, interference, and amplification.

中文翻译：

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嵌入在弹性半空间半圆形冲积谷中的圆形衬砌隧道对 SH 波散射的解析解

摘要 在这项研究中，研究了在平面剪切水平 (SH) 波下地表冲积谷和嵌入其中的地下隧道之间的动力相互作用。在经典弹性动力学的框架内，提出了围绕嵌入在弹性半空间中的半圆形冲积谷中的圆形衬砌隧道的波传播和散射的解析解。利用波函数展开法和镜像法，在不同极坐标下分别构建隧道衬砌、冲积谷和车辙半空间三个区域的系数未知的波场，以满足沿线的无牵引边界条件。水平地面以及隧道衬砌的内表面。使用 Graf 加法公式的一系列变换，通过对三个区域进行匹配，满足界面应力和位移连续性条件，得到波场系数。计算冲积谷地表位移幅值和隧道动态应力集中系数，确定地表河谷与地下隧道的动力相互作用效应。由于波的反射、散射、干涉和放大，冲积谷和埋藏隧道中的动态响应相互增强。计算冲积谷地表位移幅值和隧道动态应力集中系数，确定地表河谷与地下隧道的动力相互作用效应。由于波的反射、散射、干涉和放大，冲积谷和埋藏隧道中的动态响应相互增强。计算冲积谷地表位移幅值和隧道动态应力集中系数，确定地表河谷与地下隧道的动力相互作用效应。由于波的反射、散射、干涉和放大，冲积谷和埋藏隧道中的动态响应相互增强。