斜入射下水下地基场地地震输入的一维化时域方法

地震波斜入射下水下地基场地地震动输入问题，是涉及水层、饱和多孔介质和基岩三种不同性质介质耦合的复杂问题，目前理论成果还很匮乏。该文在现有的成层饱和多孔介质平面波斜入射的一维化时域方法的基础上，建立了水下地基场地的一维化时域计算方法。该计算方法依据Snell定理，将地震波斜入射下水层波动的空间二维问题转化为简单的一维问题，通过考虑水层与饱和多孔介质层交界面、不同饱和多孔介质交界面以及基岩与饱和多孔介质层交界面的边界条件，将已有的成层饱和土的一维化有限元方程与水层的一维化有限元方程组装，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，形成了水下地基场地的整体有限元方程，借助于中心差分法和Newmark法相结合的时步积分法，推导了地震波斜入射下水下地基场地各节点动力响应时程的显式表达式。通过与傅里叶变换得到的理论解和现有的文献进行了对比，初步验证了该文时域算法的有效性和精度，为地震波斜入射下水下地基场地地震动输入提供了一种新型高效的研究方法。

1D TIME-DOMAIN METHOD FOR 2D WAVE MOTION IN UNDERWATER SITE WITH OBLIQUELY INCIDENT PLANE WAVE

The problem of ground motion input of underwater foundation site under oblique incidence of seismic wave is a complex problem involving the coupling of water layer, saturated porous media and bedrock. At present, the theoretical results are still very scarce. Thusly, the 1-D time-domain method for underwater site is successfully established by the base of a 1-D time-domain method of porous media. Firstly, according to Snell law, the displacement of adjacent nodes in the horizontal direction can be replaced by that of the node in adjacent time, and 2-D equations can be transformed equivalently into 1-D equations, solved to compute the displacement of nodes along the vertical direction in time-domain method due to plane wave oblique incidence. Secondly, an exact artificial boundary condition of single-phase elastic media is introduced to represent the wave absorption and input characteristics of truncated bedrock, and the global finite element equations of the underwater site are assembled with the 1-D time-domain finite element equations of the porous media and water layer. Finally, with the aid of the central difference method and Newmark constant average acceleration method, the explicitnumerical solutions of displacement and acceleration are obtained. The reliability and rationality of the time-domain method are verified by comparing with the theoretical solutions obtained by Fourier transform and the existing literatures, which give convincing evidence for 1-D time domain finite element method of underwater site. It provides a new and efficient input method of seismic wave to deal with the dynamic response of underwater site.