成层饱和介质平面波斜入射问题的一维化时域方法

地震波斜入射下自由场的输入是大型结构抗震分析中亟待解决的问题之一,尤其是成层饱和多孔介质自由场问题,由于问题的复杂性,目前研究甚少. 本文基于Biot提出的饱和多孔介质动力方程,建立了一种新的求解平面波斜入射下基岩上覆饱和多孔介质成层场地自由场分析的一维化时域计算方法. 该方法首先根据Snell定律将饱和多孔介质二维空间问题转化为一维时域问题,通过对深度方向的有限元离散,得到饱和多孔介质波动问题的一维化有限元方程,然后采用单相弹性介质精确人工边界条件模拟基岩半空间的波动辐射和输入特征,通过考虑基岩与饱和多孔介质间透水或不透水边界条件以及不同饱和多孔介质交界面边界条件,形成基岩上覆成层饱和介质系统的整体有限元方程,最后采用中心差分法与Newmark平均加速度近似格式相结合的方法对时间进行离散,得到节点的动力时程的显式表达. 典型场地的地震反应分析表明,本文方法的计算结果与传递矩阵法结合傅里叶变换的计算结果完全吻合,证明了其有效性. 

ONE-DIMENSIONAL TIME-DOMAIN METHOD FOR FREE FIELD IN LAYERED SATURATED POROELASTIC MEDIA BY PLANE WAVE OBLIQUE INCIDENCE

The input of free field under oblique incidence of seismic waves is one of the urgent problems to be solved in the seismic analysis of large structures. Because of the complexity of the problem, there are few studies on the free field of layered saturated poroelastic media at present. In this paper, a 1-D time-domain finite element method is proposed to simulate the plane wave motion in layered saturated poroelastic media overlaid on bedrock subjected to the oblique incidence plane wave. The method is on the basis of Biot dynamic theory for saturated poroelastic media. Firstly, the spatially 2-D problem is transformed into a 1-D time-domain problem along the vertical direction according to Snell’s law. 1-D finite element equations for poroelastic media are established by discretization principle and finite element. Then an exact artificial boundary condition for elastic media is used to model the wave absorption and input effects of the truncated bedrock half space. The global finite element equations for the system of layered saturated poroelastic media overlaid on bedrock are developed according to the drained or undrained boundary conditions between the poroelastic medium and the bedrock. By solving the 1D equations, the displacements of nodes in any vertical line can be obtained combining the method of central differences and Average acceleration of Newmark, and the wave motions in layered poroelastic medium system are finally determined based on the characteristic of traveling wave. The method is verified and by comparing with the frequency-domain transfer matrix method with fast Fourier transform in analyzing two engineering site.