时间差分格式对路基Biot固结有限元分析的影响

Influence of time difference schemes on Biot’s consolidation FEA of roadbed foundation

应用虚功原理和线性差分法导出经过时空离散的Biot固结有限元方程,研究了路堤荷载作用下地基变形和孔压发展规律。采用有限元法,分析了基于常见的中心差分、Galerkin差分和全隐式差分等3种格式的结果及其相对偏差在空间和时间域的变化规律。结果表明:3 种格式的数值解答基本一致;中心差分和Galerkin差分计算的路基中心沉降在固结初期偏小,在后期则稍微偏大,而对侧向位移和超静孔压的规律则刚好相反;不同差分格式对超静孔压和坡脚附近的竖向变形影响较明显,尤其是中心差分格式的偏差较大等。可供地基设计和数值仿真时参考。

Based on virtual work principle and linear difference method, the finite element equations are formulated after time-spatial discretization. The distributions of deformation and excess pore pressure (EPP) for roadbed under embankment are studied using finite element method. The results and their relative errors for finite element analysis by Crank-Nicholson, Galerkin and fully-implicit time difference schemes (TDS) are compared respectively in time and spatial domain. The results show that basic reqularities of numerical solutions by three TDSs remain nearly same; the value of roadbed center settlement by Crank-Nicholson and Galerkin TDSs is underestimated at earlier consolidation process and slightly overestimated later, in reverse of lateral displacement and EPP; the EPP and vertical deformation near slope toe are affected mostly apparently by different TDS, especially for Crank-Nicholson TDS. The following conclusions could be drawn that the relative errors of results by different TDSs relate closely to consolation process, but the abstract errors keep so small that every TDS could satisfy the need of engineering analysis.