中文摘要：

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。

英文摘要：

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.