The indirect boundary element method (IBEM) is used to study the surface motion of an alluvial valley in layered half-space for incident plane P-waves based on Wolf’s theory. Firstly, the free field response can be solved by the direct stiffness method, and the scattering wave response is calculated by Green’s functions of distributed loads acting on inclined lines in a layered half-space. The method is verified by comparing its results with literature and numerical analyses are performed by taking the amplification of incident plane P-waves by an alluvial valley in one soil layer resting on bedrock as an example. The results show that there exist distinct differences between the wave amplification by an alluvial valley embedded in layered half-space and that in homogeneous half-space and there is interaction between the valley and the soil layer. The amplitudes are relatively large when incident frequencies are close to the soil layer’s resonant frequencies.
The indirect boundary element method(IBEM) was established to solve the problem of 3-D seismic responses of 2-D topographies,by calculating the free-field responses with the direct-stiffness method and simulating the scattering wave fields with the dynamic Green's functions of moving distributed loads.The proposed method yields accurate results,because the 3-D dynamic stiffness matrixes used are exact and the fictitious moving distributed loads can be acted directly on the interface between the alluvial valley and the layered half-space without singularity.The comparison with the published methods verifies the validity of the proposed method.And the numerical analyses are performed to give some beneficial conclusions.The study shows that 3-D scattering by an alluvial valley is essentially different from the 2-D case,and that the presence of soil layer affects not only the amplitude value of surface displacements but also the distribution of surface displacements.
