半无限大弹性地基等效刚度公式及其应用

FORMULATION OF EQUIVALENT STIFFNESS FOR SEMI-INFINITE ELASTIC SUBGRADE AND ITS APPLICATION

根据Mindlin关于一集中力作用在半空间弹性体中的位移公式,采用能量等效原理推导出半无限大弹性地基考虑基础埋深时基坑底部的法向等效刚度和切向等效刚度公式、基坑坑壁的法向等效刚度和切向等效刚度公式。同理根据Boussinesq关于半空间体在边界上受法向集中力的位移公式和Cerruti关于半空间体在边界上受切向集中力的位移公式,推导出不考虑基础埋深时地基的法向等效刚度和切向等效刚度公式,以及运用这些公式计算出半无限大弹性地基取不同地基土时的等效刚度。最后举例说明了这些等效刚度公式在分析高层和超高层建筑的上部结构、基础、地基的共同工作时的应用。

Equivalent stiffness equations in the normal and tangential direction at the bottom and walls of a semi-infinite elastic ditch were formulated by employing the principle of energy equivalence and Mindlin＇s displacement equations in a semi-infinite elastic body subject to a concentrated force acting in the interior of the semi-infinite elastic body. Similar equivalent stiffness equations were formulated by Boussinesq＇s and Cerriti＇s displacement equations due to a concentrated force acting on the surface of a semi-infinite elastic body. Equivalent stiffnesses pertinent to a wide range of soil have been determined by these equivalent stiffness equations. Finally, some applications in analyzing the interactions between the superstructure and the foundation and the subgrade of tall and super tall buildings were illustrated by examples.