u–p格式饱和两相介质动力问题的显–隐式交替算法

针对以土骨架位移u和孔隙流体压力p为基本未知量的饱和两相介质动力方程,提出基于中心差分法和精细时程积分法相结合的时域显–隐交替算法,分析饱和两相介质动力反应。该算法对孔压方程非齐次项的计算分别采用Gauss积分,梯形积分和Lagrange二次插值函数近似位移的方法近似模拟;同时提出一种基于精细积分方法的三次样条插值函数法,进而回避了对孔压方程耦合速度项积分时涉及的矩阵求逆运算问题。计算结果与Zienkiewicz显–隐式结果对比,两者结果基本一致,证明了方法的有效性。

Explicit-implicit staggered algorithm of u-p formulation for dynamic problems of fluid-saturated porous media

In order to describe the dynamic response of fluid-saturated porous media with the formulation of soil displacement u and pore pressure p, an explicit-implicit staggered algorithm is proposed based on the central difference method and precise time-integration method. The Gauss integration, trapezoid integration and the second-order Lagrange interpolation polynomial are utilized to simulate the soil displacement in the inhomogeneous term of the pore pressure formulation, respectively. Furthermore, an acubic spline interpolation method is developed based on the precise time-integration method, and it can avoid the computation of the inverse matrixes involved coupling velocity term. Finally, some cases are adopted to verify the proposed method. The computational results obtained by the proposed method have a good agreement with those by the Zienkiewicz's explicit-implicit method, indicating the effectiveness of the proposed approach.