Abstract
Local inclusion topography has significant influence on seismic wave propagation, and the propagation characteristics of seismic waves in poroelastic soils are obviously different from those in single-phase media. Based on Biot’s theory, the scattering of plane P1 wave by inclusion in a three-dimensional poroelastic half-space is studied by using the indirect boundary element method (IBEM). The scattering field is constructed by introducing a virtual wave near the interface between inclusion and half-space and the surface of half-space, and the virtual wave density is obtained by establishing boundary integral equation based on the boundary conditions. The effects of the depth, geometric characteristics, boundary permeability, porosity, incident frequency, and incident angle of the inclusion on elastic wave scattering are systematically analyzed. The results show that due to the soil skeleton-pore water coupling effect, when the porosity is n = 0.3, the surface displacement amplitude of dry soil is larger than that of poroelastic soil. When the porosity is n = 0.36, the surface displacement amplitude of poroelastic soil is larger than that of dry soil. The surface displacement amplitude of poroelastic-drained condition is slightly larger than that of undrained condition. With the increase of inclusion depth, the scattering of elastic wave by inclusion decreases gradually. When P1 wave is incident, the surface displacement amplitude at the depth of H = 0.5 can be increased up to three times as much as that at the depth of H = 1.5. As the inclusion becomes narrower and flatter, the scattering of elastic waves by inclusion decreases gradually. When the ratio between height and length is S = 2/5, the surface displacement magnitude can reach up to 9.5.
Highlights
Local inclusion topography has significant influence on seismic wave propagation, and the propagation characteristics of seismic waves in poroelastic soils are obviously different from those in single-phase media
Based on Biot’s theory, the scattering of plane P1 wave by inclusion in a three-dimensional poroelastic half-space is studied by using the indirect boundary element method (IBEM). e scattering field is constructed by introducing a virtual wave near the interface between inclusion and half-space and the surface of half-space, and the virtual wave density is obtained by establishing boundary integral equation based on the boundary conditions. e effects of the depth, geometric characteristics, boundary permeability, porosity, incident frequency, and incident angle of the inclusion on elastic wave scattering are systematically analyzed. e results show that due to the soil skeletonpore water coupling effect, when the porosity is n 0.3, the surface displacement amplitude of dry soil is larger than that of poroelastic soil
Because of the scattering of incident wave by inclusion, the vertical acceleration will be generated, and there are more short period components of the vertical acceleration, and the nonlinear amplification effect of inclusion on ground motion is generally smaller than that of linear amplification, the Mathematical Problems in Engineering layered site is significantly different from its equivalent uniform site. He and Liang [7] studied the influence of the randomness of inclusion section shape on the extreme value of surface dynamic response in two dimensions; the results showed that the influence increased with the increase of velocity difference between inclusion medium and halfspace medium and increased with the decrease of inclusion burial depth
Summary
E stress caused by free wave field is σfij (i, j x, y), soil skeleton displacement is ufi , the relative displacement of the fluid is wfi , and the pore water pressure is pf(i x, y). When the poroelastic half-space free surface and the inclusion interface are both drained conditions, the boundary conditions of the problem are stress of free surface is zero, pore water pressure is zero. Stress, fluid relative displacement, and pore water pressure are continuous at the interface between half-space and inclusion. T(Es) + t(Ef) t(Ls), p(Es) + p(Ef) p(Ls), x ∈ S2, when the poroelastic half-space free surface and the inclusion interface are both undrained conditions, the boundary conditions of the problem are zero stress on the free surface and zero relative displacement of the fluid. From the above-mentioned drained and undrained boundary conditions, matrix equations can be constructed, respectively, virtual wave source density can be obtained, scattering wave field can be constructed, and total wave field can be obtained by superposition with free field
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