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以滑动体静力平衡的两个力平衡方程为基础,引入拉氏乘子,将土压力问题以变分学观点来描述,转化为确定含有两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的欧拉方程,得出了主动土压力和被动土压力在取极值时,墙后土体的破坏是沿平面滑动。然后,将土压力的泛函极值问题进一步转化为带有约束的函数极值问题。这种函数极值可利用M atlab6.1优化工具箱提供的fm incon函数进行求解。当土体的粘聚力等于0时,土压力计算结果与库仑土压力理论解完全一致;而当土体的粘聚力不等于0时,归纳给出了相应的土压力计算公式。
Based on the two force balance equations of static balance of sliding body, Lagrange multiplier is introduced to describe the problem of earth pressure from the viewpoint of variational theory, which is transformed into the problem of determining the functional extreme with two function arguments. According to the Euler equation which must be satisfied when the extreme value of functional is satisfied, the failure of the soil behind the wall slides along the plane when the active earth pressure and the passive earth pressure take the extreme value. Then, the extreme value of the functional of earth pressure is further transformed into the function extreme value problem with constraints. This function extremum can be solved using the fm incon function provided by the Matelab 6.1 Optimization Toolbox. When the cohesion of soil is equal to 0, the calculated result of earth pressure is completely consistent with the theoretical solution of Coulomb earth pressure. When the cohesion of soil is not equal to 0, the formula of earth pressure is deduced.