土水势方程对Biot固结FEM的影响研究

Study on influence of soil-water potential equation on Biot's consolidation FEM.

常用的Biot(1941)固结理论中对Darcy定律的使用是不严格的,Biot(1962)引入土水势方程进行修正,但这种改进很少引起工程界的注意.探讨了Biot固结常用形式和改进形式在控制方程和有限元方程方面的主要差别,推导了改进形式基于不同场变量的两种增量有限元方程.改进形式的有限元方程系数矩阵具有非对称性.当土水势增量方程中忽略重力势变化的影响时,改进形式的控制方程和有限元方程即退化为相应的常用形式.通过工程算例分析,结果表明:常用形式的计算结果高估了地基沉降和总土水势,低估了侧向位移.使用改进形式有助于提高分析精度.

Darcy's law in general, is hot properly used in traditional Biot's(1941) consolidation (TBC) theory. Soil-water potential equation was introduced to perfect TBC by Biot(1962), while this development drew little attention in engineering circles. The main differences between governing equations and the corresponding FEM equations are discussed within the scope of modified Biot's consolidation (MBC) and TBC theories. Two kinds of incremental FEM equations based on different field variables are formulated for MBC theory, with the consolidation coefficient matrix asymmetric. Ignored the influence of gravity potential's change on incremental SWP equation ignored, the governing and FEM equations of MBC theory can be simplified to be the corresponding forms of TBC theory. Through numerical analysis of an illustrative project, the results show that foundation settlement and total soil-water potential are overestimated by TBC theory, but lateral displacement is underestimated, etc. The presented MBC theory conducts to higher accuracy in numerical analysis.