一般条件下主动土压力的变分求解

发布时间：2018-11-20 07:47

【摘要】：基于库仑土压力理论的假设,主动土压力是由墙后填土在极限平衡状态下出现的滑动体产生,从墙后滑动体整体静力平衡方程出发,推导出坡面起伏且有不均匀超载、倾斜墙背、黏性填土等一般情况下的主动土压力泛函极值的等周模型。在该基础上,引入拉格朗日乘子,将主动土压力问题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,得到了线性的滑面函数和沿滑面线性分布的法向应力函数。结合边界条件和横截条件,主动土压力泛函极值问题进一步转化为单个未知量的一维方程问题。通过算例,土压力计算结果与库仑土压力理论解完全一致,但土压力作用点在墙体的相对位置却并非总是作用在墙高的1/3处。通过算例进一步表明,坡面的起伏和坡面超载的不均匀性对主动土压力大小和作用点位置有显著的影响。
[Abstract]:Based on the assumption of Coulomb earth pressure theory, active earth pressure is generated by sliding body in ultimate equilibrium state of backfill soil. From the static equilibrium equation of sliding body behind wall, the slope surface undulation and uneven overloading are derived. The isoperimetric model of the active earth pressure functional extremum under the general conditions such as inclined wall back, clay fill, etc. On this basis, the Lagrangian multiplier is introduced to transform the active earth pressure problem into the functional extremum problem with two functional independent variables. According to the Euler equation which must be satisfied when the functional takes the extreme value, the linear sliding surface function and the normal stress function with linear distribution along the sliding surface are obtained. Combined with boundary conditions and transversal conditions, the active earth pressure functional extremum problem is further transformed into a one-dimensional equation problem with a single unknown quantity. The calculated results of earth pressure are in good agreement with the Coulomb earth pressure theory, but the relative position of the earth pressure acting on the wall is not always one third of the wall height. The numerical examples show that the fluctuation of slope surface and the inhomogeneity of overloading on slope have a significant influence on the active earth pressure and the position of active point.
【作者单位】：重庆大学土木工程学院;重庆大学山地城镇建设与新技术教育部重点实验室;
【基金】：国家“十二五”科技计划支撑课题(No.2012BAJ22B04)
【分类号】：TU432

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