确定扩展基础基底尺寸的一种解析解法  

An analytical solution for calculating base-plane size of spread footings

作　　者：丁洲祥[1,2] 崔超[1] 曾巧玲[1] 

机构地区：[1]北京交通大学土建学院,北京100044 [2]中国矿业大学深部岩土力学与地下工程国家重点实验室,江苏徐州221008

出　　处：《岩土工程学报》2013年第10期1889-1894,共6页Chinese Journal of Geotechnical Engineering

基　　金：国家自然科学基金项目(41172221;51278028);深部岩土力学与地下工程国家重点实验室资助项目(SKLGDUE08007X)

摘　　要：针对传统的确定扩展基础基底面积的逐次渐进试算法在计算效率等方面的不足,根据极限状态设计原则和中国国家标准《建筑地基基础设计规范》要求,分别提出中心荷载和偏心荷载条件下扩展基础基底面积计算的一种简洁的解析求解新方法。该法将承载力验算公式转换为一元三次不等式和一元四次不等式,从而理论上可分别采用Cardan公式法或Ferrari法进行求解。简便起见,也可借助MAPLE等数学软件,快速和精确地得到满足验算要求的基底面积下限解答。通过算例对比分析,验证了该法的优越性,为基础工程优化设计提供新的参考。With regard to the disadvantages of the conventional iteration method for determining base-plane size of spread footings, a novel analytical method is proposed for design of base-plane size under centric and eccentric loads respectively, according to the concepts of the limit state and the specifications of Chinese National Code of Foundation Design for Buildings. In this method, the check formulae for bearing capacity of spread footings are transformed into cubic and/or quartic inequalities with one unknown quantity, which can be solved easily with Cardan＇s or Ferrari＇s methodology. For the sake of convenience, the advanced mathematical software such as MAPLE can be used to provide accurate value of base-plane size with a lower limit. Finally, the validity of the proposed method is verified through a case study, which proves the new method can provide good reference for engineering practice.

关 键 词：扩展基础 解析解 中心荷载 偏心荷载 基底面积 

分 类 号：TU47[建筑科学—结构工程]