Two-dimensional soil and topographic amplification effects of a partially filled circular-arc alluvial valley under plane SH waves

Site amplification consists of two-dimensional (2D) soil layer amplification effects and topographic amplification effects. The objective of this study is to investigate the relative contribution of soil amplification and topographic amplification. To that end, the wavefunction series solution for the scattering of plane SH waves by a partially filled circular-arc alluvial valley is proposed. The wavefunction series solution is obtained by a novel method of over-determined system of equations in the framework of the wavefunction expansion technique with the aid of a region-matching strategy. The convergence tests are conducted to reveal the necessity of the proposed over-determined system of equations method. The validity of the proposed solution is verified by comparison with previous results. By adjusting the material parameters of the two sub-regions in the analytical model, both of the surface motions of the alluvial valley and the empty canyon are calculated. The site amplification patterns of the alluvial valley are compared with the topographic amplification patterns of the empty canyon with the same geometry, the results show that the soil amplification effects are usually larger than the topographic amplification effects within the alluvial valley, while the topographic effects dominate the amplification pattern of ground motions outside the alluvial valley. Afterwards, a parametric study in terms of the maximum surface motion is carried out to determine the relative importance of soil and topographic contributions in a more comprehensive manner and to further characterize the 2D soil layer amplification effects. It is evident that the maximum soil layer amplification generally far outweighs the maximum topographic amplification. The 2D soil amplification increases with the impedance contrast between the soil layer and the underlying bedrock but is not a simple linear superposition of 1D soil amplification and 2D topographic amplification.