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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。
Aiming at the shortcomings of traditional gradual increment method, such as calculating the efficiency and so on, which are based on the conventional method of determining the base area of the extended base, according to the principle of limit state design and the requirement of China National Standard “Basic Design Code for Building Foundation” A Concise New Method for Solving Basal Area Calculation. This method converts the checking formula of bearing capacity into a one-dimensional cubic inequality and a four-quadratic inequality, so that it can be solved theoretically by using Cardan’s formula method or Ferrari’s method respectively. For simplicity, it is also possible to quickly and accurately find the floor area floor solution that meets the checking requirements with mathematical software such as MAPLE. Through comparative analysis of examples, the superiority of this method is verified, which provides a new reference for the optimization design of foundation engineering.