饱和土沉积谷场地对平面SV波的散射问题的解析解

SCATTERING OF PLANE SV WAVES BY CIRCULAR-ARC ALLUVIAL VALLEYS WITH SATURATED SOIL DEPOSITS

把波函数展开方法用于饱和多孔介质中波的传播的研究中 ,给出了不同土层界面条件 (透水条件和不透水条件 )下具有饱和土沉积层的圆弧形沉积河谷场地对平面SV波散射问题的解析解 .其中沉积谷软土场地用饱和多孔介质的Biot动力学理论模拟 ,半空间场地用单相介质弹性动力理论模拟 .对于入射角大于临界入射角时 ,产生的面波的波函数用有限Fourier级数展开 ,这种方法适用于较大的入射波频率范围 ,这是现存的数值方法所不能比拟的一大优点 .文中算例分析了入射波频率和入射角对地震地面运动的影响 .

On the basis of Biot dynamic theory for saturated porous media, an analytic solution of two-dimensional scattering and diffraction of plane SV waves by circular-arc alluvial valleys with saturated soil deposits is presented using the Fourier-Bessel series expansion technique with the deposits simulated by Biot dynamic theory for saturated porous media, and the half space assumed to be elastic single-phase media. For incidence beyond critical angle, the surface waves generated are expensed in terms of finite Fourier series. The method is applicable to the case of a wide range of frequencies, and thus it is preferable to the presently available numerical methods. The surface displacement amplitudes presented by numerical results show that the results depend on the angle of incidence, the dimensionless frequency of the incident SV wave.