半解析半数值法层状地基上高承台桩基础沉降的计算

Settlement Calculation of Layered Foundation with Elevated Cap by Semi-Analytical and Semi-Numerical Method

用半解析半数值方法计算层状地基上高承台桩基础沉降的难点在于求解地基基本解(荷载和位移之间的关系)及实现其数值计算。地基基本解有2种分析模型:一种是求解土的基本解,然后将其代入基础的有限元控制方程,这种模型得到的地基柔度矩阵很大,数值计算存在困难;另一种是将土和桩视作地基,用基本解表示,它由轴对称有限元法按照桩帽模型和圆筒模型考虑群桩效应求得,然后将地基基本解代入墩台的有限元控制方程并求解,即可得到高承台桩基础的沉降,这种模型得到的地基柔度矩阵元素相当少,适合数值计算。基于轴对称有限元法的半解析半数值方法,无需繁琐的公式推导,极大地减少工作量,计算效率高。算例结果表明,该分析方法和三维有限元法在分析桩的沉降时结果符合很好。

When semi-analytical and semi-numerical （SASN） method is applied for analyzing settlement of pile foundation with elevated cap, it is of some difficulty to use analytical method to solve the fundamental solution （FS） of soil, which expresses the relation of load and displacement of soil There are two models for solving the FS of soil. In the first model, the FS of soil is submitted to the governing equation of finite element method （FEM） of foundation to get the settlement. It is hard to solve by semi-numerical method with a large flexibility matrix of soil. In the second model, there is a soil system, which includes soil and piles. The FS can be easily obtained by axisymmetric analysis with FEM based on the models of pile hel- met and cylinder respectively. Then the FS of soil system is submitted to the governing equation of FEM of abutment instead of foundation, which is very easy to solve for the flexibility matrix of soil system has few elements. Application of axisymmetric analysis with FEM for solving fundamental solution of soil system as well as the SASN can save research time, need no cumbersome formula and calculate with high efficiency. Numerical example indicates that the SASN has more advantage than 3D FEM, but the results of the two methods agree very well.