饱和砂层震动孔隙水压力二维扩散解析理论的研究

Study on the Two-dimensional Theory of Seismic Pore Pressure Generation-dissipation

本文将Terzaghi二维固结理论与震动孔隙水压力增长模式相耦合,提出了一类饱和砂层震动孔隙水压力的二维扩散解析理论。文中首先给出了计算饱和砂层中震动孔隙水压力生长与扩散的理论解,并讨论了几种不同起始孔压场分布情况下解的简化表达形式;其次,证明了该解析解是适定的。因为所采用的震动孔隙水压力增长模式是一个随时间和土的物理力学参量而变化的一般函数,其具体函数形式可根据实际条件来合理选定,这使得所给出的理论解带有普遍性。

This article presents a class of the analytical theory for calculating seismic pore-water pressure generation and dissipation in saturated sand layer with a horizontal ground on the basis of combining the two-dimensional formulation of Terzaghi's consolidation theory with a seismic pore-water pressure generation model. At first, two general analytical solutions are obtained by applying the Sturm-Liouville Systems and Duhamel Integral and several specific expressions of the solutions for different practical engineering boundary value problems induced by strong earthquake are discussed. It is then verified by means of maximum and minimum principles that these solutions are properly.