广义Biot固结方程隐-隐式解法的推广及应用

The extension and application of implicit-implicit staggered solution procedure for generalized Biot's consolidation equation

无条件稳定的隐－隐式交叉迭代法是求解ｕ－ｐ形式的广义 Ｂｉｏｔ理论有限元列式的一种高效数值方法，在此基础上提出了能够考虑孔隙流体加速度的新解法，扩展了隐一隐式解法的适用范围．将广义Ｂｉｏｔ理论两种ｕ－ｐ形式的有限元列式作了统一表达，进而采用逐步积分法求解时域内的动力迭代方程。静力Ｂｉｏｔ理论描述的边值问题可视为其特例。通过波浪作用下弹性海床的动力反应分析，验证了所发展的数值解法的有效性。计算结果表明，土骨架和孔隙流体的加速度对海床动力反应的影响很小。

Based on unconditionally stable implicit-implicit staggered solution procedure. which is ef- ficient in numerically solving the finite element equation of u-p form generalized Biot's theory. a new algorithm is proposed. The new procedure could take the acceleration of pore fluid into consideration, which extends the application range of the implicit-implicit solution procedure. The numerical schemes for two FEM types of u - p form are described in an uniform expression, and the staggered equations can be numerically solved by step-by-step integration scheme in time do- main. The governing equations for boundary problems which are based on Biot's theory could be regarded as a special case. A case study for dynamic response of seabed subjected to wave loading is performed and the efficiency of the new procedure is verified. The numerical results show that the accelerations of soil skeleton and porous fluid have little effect on the seabed dynamic response.