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在很多计算地基极限荷载的近似方法中,大多数都是事先假定土体的滑动面,然后采用近似的应力分析去确定极限荷载。由于在分析过程中往往对于滑动面上局部的反力方向与位置采用了不合理的简化假定,因而影响了最后的计算结果。这样一来即使在个别简单的情况下,如象是不考虑自重或者是在理想粘性土的情况下,自所得的极限荷载公式中也不能得出与精确解相同的结果。本文按照极限平衡理论,首先推出确定滑动面上应力分布规律的两个基本微分方程(其中一个曾为Ja’kY在1936年推出过),然后根据基本方程来推导计算地基极限荷载的普遍公式。自这一公式中可以得到若干特殊情况下的精确解。为了叙述上的方便,以下的讨论分为三部份:(Ⅰ)基本方程的推导;(Ⅱ)基本方程的应用实例;(Ⅲ)利用基本方程推导地基极限荷载公式。
In many of the approximate methods for calculating the ultimate load of foundations, most of them assume the sliding surface of the soil beforehand and then approximate the stress analysis to determine the ultimate load. In the process of analysis, the simplifying assumptions about the direction and location of the local reaction force on the sliding surface are often used, which affects the final calculation results. As a result, the same result as the exact solution can not be obtained from the resulting ultimate load equation, even in the simplest case, as if it were weightless or in the case of ideal cohesive soil. In this paper, according to the theory of limit equilibrium, firstly, two basic differential equations (one was once published by Ja’kY in 1936) to determine the stress distribution on the sliding surface are derived. Then, the general formulas for calculating the ultimate load of foundation are deduced according to the basic equations. From this formula we can get some exact solutions in special cases. For the convenience of narration, the following discussion is divided into three parts: (I) Derivation of basic equations; (II) Application examples of basic equations; (III) Derivation of foundation load formula using basic equations.