【摘要】 借助Biot多孔介质波动理论,采用多极坐标和复变函数方法,对弧形沉积渠道在入射地震纵波作用下的动态响应问题进行了研究.首先利用复变函数求解半空间多孔介质和弧形沉积渠道中满足Helmholtz方程的复势函数在极坐标下的通解;然后在复平面极坐标下把半空间多孔介质和弧形沉积渠道中的应力、位移和孔压用各自的势函数通解表示出来,并构建两个半径不等的大圆弧分别表示半空间直边界和沉积渠道结构直边界,随后利用两个大圆弧边界条件、半空间多孔介质和沉积渠道结构的交界面的连续条件及透水条件列出一组方程组,并对其联立求解得出未知系数值,从而求出两种介质中的势函数的特解;最后用所求的势函数特解求解并讨论了半空间多孔介质与沉积渠道交界处动应力集中系数和孔压集中系数在不同的参数条件下的分布及规律.更多还原

【Abstract】 In terms of Biot’s dynamic theory,the methods of the multi-polar coordinate and the complex function are used to solve the problem of the dynamic response of circular-arc sedimentary channel under seismic P-wave.The equations of the steady-state Biot wave motion are decoupled to Helmholtz equations by introducing potential functions and the general solution is obtained.Utilizing the general solution of the potential functions,expressions for the displacements,stresses and pore pressures within the porous media and the sedimentary channel can be obtained for certain boundary conditions.Here,two circular-arc with large radius are used to simulate the straight boundary of the porous media half-space.With different parameter conditions,Numerical results are shown and some laws are given and discussed.更多还原