ABSTRACT

An analysis of the scattering of steady-state SH waves by a shallow buried unlined elliptical tunnel is presented. For the horizontal boundary, a mirror method in elliptic coordinates is proposed, which is implemented using the Mathieu function addition theorem. Taking into account the stress-free condition of the tunnel, an infinite equation system was created and solved after truncating it. The orientation of the tunnel is arbitrary, and typical calculations are performed for tunnels arranged horizontally and vertically in the long axis. The effects of depth, the ellipse’s axis ratio, and wavenumber on the dynamic stresses around the tunnel are investigated.

中文翻译：

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SH波作用下浅水无衬砌椭圆隧道的动力应力分析

摘要

介绍了浅埋无衬里椭圆隧道对稳态SH波散射的分析。对于水平边界，提出了椭圆坐标中的镜像方法，该方法利用Mathieu函数加法定理实现。考虑隧道无应力条件，截断后建立并求解无限方程组。隧道的方位是任意的，典型的计算是针对长轴水平和垂直布置的隧道进行的。研究了深度、椭圆轴比和波数对隧道周围动应力的影响。