Ground motions around a partially filled semi-circular alluvial valley with a lined tunnel under cylindrical SH waves

The interaction between surface irregularities and underground tunnels has notable effect on seismic waves, resulting in amplification or attenuation of ground motions. However, previous studies for scattering issue induced by the interaction between irregular topographies and understructures were only based on the assumption of plane shear horizontal (SH) waves. Actually, the significance of source effects on topographic amplification cannot be underestimated. Meanwhile, the thickness and material damping of local alluvium can exert momentous influence on ground motions. In this study, a series solution is proposed to tackle the scattering phenomenon caused by a partially filled semi-circular alluvial valley with a lined tunnel under cylindrical SH waves, and the impact of source distance on the ground motions of the irregular topography with a tunnel is revealed for the first time. Firstly, the wave-function expansion approach and classical mirror image method are developed to constructive wave-function expressions in different polar coordinate systems. Then, applying the appropriate Graf's addition formula, it becomes possible to unify the coordinate systems for different subregions. Furthermore, according to continuity conditions of stress and displacement, the region-matching technique is adopted to determine the unknown coefficients of the algebraic equations. Finally, to illustrate the interaction between a partially filled alluvial valley and a lined tunnel on ground motions, a comprehensive parametric analysis is performed in both the frequency and time domains. A significant finding is that ground motions of combined topography is affected by the source location, and the source distance cannot be disregarded unless the source distance surpasses 100-time valley width. This indicates the need to closely examine how the source location influences the amplification effect due to combined topography, particularly when the source is near the terrain.