Coulomb土压力理论的两种解法

采用极限平衡变分法和Culmann分析方法，对土压力问题进行了研究。在极限平衡变分法中，以滑动体静力平衡的2个力的平衡方程为基础，引入Lagrange乘子，将以变分学观点来描述的主动土压力和被动土压力问题，转化为确定含有2个函数自变量的泛函极值问题。依据泛函取极值时，必须满足Euler方程，得出了主动土压力和被动土压力取极值时墙后土体沿平面滑动破坏的结论。在Culmann分析方法中，沿用了Coulomb土压力理论关于平面滑动破坏的假定，而在推导土压力计算公式的过程中，仅利用了滑动体沿某一特定方向的一个力的平衡方程。与目前通行的Coulomb土压力公式的证明过程相比，Culmann分析方法更为简洁。

Two methods to get the Coulomb earth pressure theory

The problem of earth pressure is studied by using the limit equilibrium variational method and the Culmann analysis method. In the limit equilibrium variational method, the problem of active earth pressure and passive earth pressure is formulated in terms of calculus of variation based on the two force equilibrium equations of the sliding mass, and is transcribed as the functional extreme-value problem of two undetermined function arguments by means of Lagrange multiplier. According to Euler equations that must be satisfied when a functional attains its extremal, the conclusion that the failure of soil mass behind wall is in the mode of sliding on a plane surface is drawn when the active earth pressure and the passive earth pressure get the minimax solutions. In the Culmann analysis method, the assumption that the soil failure is in the mode of sliding along a plane is adopted; however only one force equilibrium equation along some special direction is utilized to derive the computation formula of earth pressure. Compared with the popular proof process of the Coulomb earth pressure theory, the Culmann analysis method is more simple.