半球形饱和土沉积谷场地对入射平面Rayleigh波的三维散射问题的解析解

Three-dimensional scattering and diffraction of plane Rayleigh-waves bya hemispherical alluvial valley with saturated soil deposit

用Biot饱和多孔介质动力学理论模拟半球形两相饱和土沉积谷,用单相介质弹性动力学理论模拟周围半空间场地.利用Fourier-Bessel级数展开法,在频域内给出了半空间中半球形饱和土沉积谷场地在平面Rayleigh波入射下三维散射问题的解析解.利用这一解析解计算分析了入射波频率、场地特征(包括孔隙比)对地表位移幅值的影响,并与已有的三维半球形沉积谷场地在单相介质中的散射问题进行了对比分析.

The three-dimensional scattering and diffraction of plane Rayleigh-waves by a saturated hemispherical alluvial valley is studied in this paper. In order to consider the real site conditions for the problem, the hemispherical alluvial valley is assumed to be saturated porous media, which is more reasonable than to assume it as an elastic single-phase media; and the half space is assumed to be an elastic single-phase media. We use Fourier-Bessel series expansion technique to formulate the analytic solutions. The results of surface displacement amplitudes of the solutions are presented. The effects of incident wave frequency and the feature of the surface displacement amplitudes are discussed. The results are compared with those of the saturated hemispherical alluvial valley being assumed to be an elastic one-phase media.