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Abstract

The region-matching technique is implemented to derive a series solution to the SH-wave scattering problem of an embedded truncated circular cavity. An introduced auxiliary boundary partitions the whole analyzed region into two subregions, whose displacement fields are expressed as a superposition of appropriate wavefunctions. Taking advantage of the method of images, the zero-stress boundary condition on the horizontal ground surface is satisfied automatically. Suitable Graf’s addition formulas facilitate the enforcement of boundary conditions on the artificial interface and curved cavity surface for determining the expansion coefficients. Effects of several parameters on steady-state surface motions are discussed. Transient changes in underground motion are also included. Comparisons with published data for circular cases show good agreement. The present study not only gives a theoretical groundwork for practical unlined tunnels, but also can be applicable to the earthquake-resistant design methods of underground structures.

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