横观各向同性地基上刚性矩形基础分析

Analysis of a rigid rectangular plate footing on transversely isotropic subgrade

对横观各向同性地基上刚性矩形板进行了求解。首先,利用表面受矩形均布荷载作用下的层状横观各向同性地基的位移解答,获得地基的柔度矩阵;然后,通过刚性矩形基础与层状横观各向同性地基的协调条件,建立刚性矩形基础与横观各向同性地基共同作用的方程,进而求得基础的地基反力。通过编制相应的程序,确定了合理的网格划分值;最后,进行算例分析,分析了地基横观各向同性性质、矩形刚性基础的长宽比以及地基分层性对地基反力的影响。分析表明:以上3种因素对地基反力有重要影响。

This paper presents a solution of a rigid rectangular plate on transversely isotropic foundation. Firstly, the flexibility matrix of the subgrade is achieved based on the displacement solution of transversely isotropic multilayered foundation soils subjected to uniform rectangularly-distributed loading. Secondly, the governing equation of the interaction between the rigid rectangular plate and the layered transversely isotropic foundation soils is developed by using the compatibility conditions of the plate and the foundation, and the governing equation is solved for the reactional force of the foundation. This procedure is then implemented into a computer code with a proper meshing scheme. Finally, a case study is performed, and the effects of the properties of transversely isotropic foundation soils, the length-to-width ratio of the rigid rectangular plate, the thickness of the foundation soil and soil stratification on subgrade reactions are analyzed. The results indicate that the three factors mentioned above have significant influence on the subgrade reaction.