Surface Motion of a 3-D Alluvial Valley in Layered Half-Space for Incident Plane Waves

Abstract eng:
This paper presents a solution for surface motion of a 3-D alluvial valley in layered half-space for incident plane waves in frequency domain by indirect boundary element method (IBEM), based on the exact dynamic stiffness matrices and the dynamic Green’s functions for uniformly distributed loads acting on an inclined plane in 3-D layered half-space by the authors. The free-field response is carried out to give the displacements and stresses on the curved plane which forms the boundary of the alluvial valley. The fictitious uniformly distributed loads are applied on the same curved plane to calculate the Green’s functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions, and the displacements due to the free field and due to the fictitious loads are summed up to obtain the whole motion. The accuracy of the solution is verified by comparison with related solutions. The numerical calculations are performed for a hemispherical alluvial valley in one single layer over half-space for incident waves, and it is shown that, there exist distinct differences between the surface motion of a alluvial valley in layered half-space and that in homogeneous half-space; the dynamic characteristics of the soil layer significantly affect both the amplitudes and frequency spectrum of the surface motion.

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