两相饱和介质层与单相介质层应力-位移函数的传递与退化  

Degeneration and Transfer of the Displacement-Stress Functions From Poroelastic Layered Media to Elastic Layered Media

作　　者：丁伯阳[1] 陈樟龙[1] 徐庭[1] 

机构地区：[1]浙江工业大学,杭州310014

出　　处：《应用数学和力学》2014年第2期162-180,共19页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11172268)~~

摘　　要：根据Biot孔隙弹性介质动力控制方程,利用快、慢纵波的解耦,求得满足两相饱和介质位移-应力传播的一阶微分方程组.该方程组及传递函数能退化到单相介质的位移-应力传播微分方程组.利用界面应力-位移连续条件,分析了位移-应力从两相饱和介质向单相介质传播,构建了界面过渡传递矩阵.使原有的6×6阶应力-位移传递矩阵过渡为4×6阶矩阵,能与单相介质的4×4阶应力-位移传递矩阵结合.最后,采用经典的波传播模型对比验算了结果,它们一致吻合.Based on Biot＇ s dynamic governing equations, through decoupling of the fast and slow dilational waves, the fLrst-order differential simultaneous equations for the displacement- stress propagation were obtained, which satisfy the kinetics of wave propagation in the multi- layer poroelastic saturated media. Both the simultaneous equations and the transfer funtions could be degenerated to those for the multilayer single-phase media. With the displacement- stress continuity conditions at the interface between the poroelastic and single-phase media, the interfacial transitional transfer matrix was established by analysis of the propagation of displace- ment-stress from the poroelastic medium to the single-phase medium. The 4x6 transfer matrix was derived from the 6x5 transitional transfer matrix of the multilayer poroelastic medium and could be combined with the 4x4 transfer matrix of the single-phase medium. Finally, the degen- erated results from presented method were compared with those from the previous classical wave-propagation models to get good consistency between them. The presented method has merits of simpler calculation and clearer physical sense compared with the classical ones.

关 键 词：两相饱和介质 单相介质 多层介质 应力位移函数 过渡传递矩阵 退化 

分 类 号：TU435[建筑科学—岩土工程] O39[建筑科学—土工工程]