库仑土压力的变分法研究

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。

STUDY OF THE COULOMB EARTH PRESSURE BY VARIATIONAL METHOD

Based on two force equilibrium equations of a sliding mass,earth pressure is formulated in terms of calculus of variation,and is transcribed as the functional extreme-value of two undetermined function arguments by means of Lagrange’s multiplier.According to Euler equation that must be satisfied when a functional reaches its extreme,it was concluded that the failure of soil mass behind wall is in the mode of sliding on a plane surface when the active earth pressure and the passive earth pressure get the min/max solutions.The functional extreme-value of earth pressure is further transformed to determine the min/max solution of restrained functions.The fmincon function in the optimization toolbox of MATLAB 6.1 can be used to find the min/max solutions.When the soil cohesion equals 0,the calculated earth pressure is same as the theoretical solution of Coulomb.However,when soil cohesion doesn’t equal 0,the corresponding computation formula is also presented.