流体饱和多孔介质动力问题的显式时域解法

An explicit integrator method for the dynamic problem of fluid-saturated porous medium in time domain

为了简化分析,Zienkiewicz等基于Biot理论,在忽略流体相对于土骨架运动的加速度条件下,建立了以土骨架位移u和孔隙流体压力p为基本变量的u-p格式饱和两相介质动力方程。针对该u-p方程,在空间上,采用伽辽金法有限元离散,并结合对角化形式的质量矩阵和流体压缩矩阵,忽略相邻结点间的惯性和流体压缩量间的耦合作用。在时域内,基于杜修力等提出的显式算法和Euler预估-校正法,建立了一种具有二阶精度的全显式时域积分法。采用一维饱和土模型,对比提出算法的数值解与Simon方法的解析解,发现两者吻合良好,验证了本文方法的正确性。并分析了饱和土二维动力问题,以及渗透系数和排水条件对饱和土动力响应的影响。

Zienkiewicz et al.（1980）established the dynamic solid-fluid coupled equations in u-pform for fluid-saturated porous media based on Biot＇s consolidation theory with the variables of displacement u and pore pressure p,by neglecting the acceleration of the pore fluid with respect to the solid skeleton.In this study,for the u-pequations,the Galerkin finite element method is used to discrete the computing space domain,combined with a diagonal mass matrix and the fluid compression matrix to ignoring the coupling between the inertia and fluid compression between adjacent nodes.In time domain,based on explicit algorithms derived by Du and Wang（2000）and the Euler predictor-corrector method,a completely explicit method with second-order accuracy is proposed.A one-dimensional model of saturated soil is used to compare the numerical solution by the proposed method and the analytical solution derived by Simon（1984）.The good agreement between the results obtained by the two methods indicates the accuracy of the proposed method.Finally,a two-dimensional model of saturated soil is analyzed.Two examples with different permeable coefficients or drained boundaries are analysed to reveal the effect on the dynamic responses of saturated porous medium.