层状场地中局部不均体对平面P波的散射

Scattering of P waves by a local nonhomogeneous body in a layered half-space

利用间接边界元方法,在频域内求解了层状场地中局部不均体对平面P波的散射。利用精确的土层动力刚度矩阵进行自由场反应分析,求得位移和应力响应。通过计算虚拟分布荷载的格林影响函数,求得相应位移和应力;根据边界条件确定虚拟分布荷载,最终得到问题的解答。研究了入射P波时,不均体宽度、埋深、厚度、入射角、入射频率度等参数对地表位移幅值的影响,并与相应自由场的结果进行了比较。不均体对P波散射有重要影响,在工程场地地震安全性评价中,应合理考虑局部不均体对场地设计地震动参数确定的影响。

The scattering of P waves by a local nonhomogeneous body of arbitrary shape in a layered half-space is modeled using the indirect boundary element method （IBEM） in the frequency domain. The free-field responses are calculated by using the exact dynamic-stiffness matrix of soil layers to determine the displacements and stresses at the interface of the local nonhomogeneous body; and fictitious distributed loads are then applied at the interface in the free field to calculate the Green＇s functions for displacements and stresses. The amplitudes of the fictitious distributed loads are determined from the boundary conditions; and the displacements arising from the waves in the free field and from the fictitious distributed loads are summed to obtain the solution. The effects of width and thickness of the local nonhomogeneous body, and the incident angle and frequency on the surface displacements for P waves are studied. These results are compared with that of one-dimensional model. The local nonhomogeneous body has important influence on the scattering of P waves. The influence of local nonhomogeneous body on determination of design earthquake ground motion parameters should be considered reasonably in evaluation of seismic safety for engineering site.