覆水饱和双相介质圆弧场地P波激励下散射问题的理论解

A theoretical solution for the scattering of incident plane P waves by a circular-arc site in saturated double-phase media with overlying water

采用波函数展开法对平面P波入射复杂水域地形的空间变异性地震动场进行研究,该水域地形具有覆水层、饱和双相介质、场地非平坦以及第二类分层(场地跨越分层界面)等属性。首先,依据地震波反射和透射特性推导直角坐标系下的自由波场分布;然后,根据场地属性并引入大圆弧法分析极坐标系下的含有待定系数的散射波场;进而,结合土-水分界面和饱和土层分界面边界条件,求解散射波场中的待定系数;最后,通过自由波场和散射波场得到覆水饱和双相介质圆弧场地波函数理论解。基于理论解,通过算例验证了理论推导的合理性及可靠性,分析了地表位移在不同入射条件下的差异性。结果表明,相对于均匀介质,饱和双相介质会显著影响地表位移分布。此外,入射波频率和角度对地震地面运动特性也有较大的影响。

Using the wave function expansion method,this paper mainly studies the earthquake motion field with spatial variability for an incident plane P wave into a complex terrain with overlying water.The site has comprehensive attributes such as a water-covered layer,the saturated double-phase media due to the overlying water,the non-flat site,and the second type of stratification(the site through geological layers).First,based on the reflection and transmission characteristics of seismic waves,the free wave field functions in a Cartesian coordinate system are derived.Then,considering the characteristics of the site and the large arc method,the scattering wave field functions with the undetermined coefficients in a polar coordinate system are determined.Furthermore,the undetermined coefficients are solved by the boundary conditions determined by the saturated soil interface and soil-water interface.Finally,a theoretical solution for the scattering by circular-arc site in saturated double-phase media under surface water is derived.The rationality and reliability of the theoretical solution is verified by a numerical calculation and the surface displacements at different conditions are analyzed.Numerical results show that:compared with the uniform medium,the saturated double-phase media significantly change the surface motion,and the incident wave frequency and angle have great influences on the ground vibration.