摘要
从基坑柔性支护结构后的滑动土楔体的整体静力平衡方程出发,推导了考虑作用点位置的主动土压力泛函极值等周模型。在此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。对于一般黏性土,依据泛函取极值时必须满足的欧拉方程,得到了对数螺旋线的滑裂面函数和沿滑裂面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以两个拉格朗日常数为未知量的函数优化问题。同时,讨论了滑裂面为平面和圆弧面两种特殊情况。通过算例表明,对于一般土体,在作用点位置系数下限处,主动土压力最小,滑裂面为平面;随着作用点位置的上移,主动土压力呈非线性增长,相应滑裂面为对数螺旋面。对于砂性土,位置系数上限值随内摩擦角的增大而增大,其相应的土压力值也随之增加。对于软黏土,滑裂面为圆弧面,随着作用点位置的上移,主动土压力呈非线性下降,滑裂面背离基坑方向移动。
Based on the force equilibrium equations of the sliding mass behind the flexible supporting structure, a functional extreme value isoperimetric model is developed for calculating the active earth pressure with considering the point of resultant force. The problem of concern is cast into a functional extreme-value problem of two undetermined functions by means of Lagrange undetermined multiplier. According to Euler equations, logarithmic spiral sliding surface and normal stress function along the sliding surface are obtained. With combining the boundary conditions and transversality conditions, the conditional functional extremum problem of active earth pressure is changed equivalently into the problem of searching the minimum of unconstrained optimizations of function with two unknown Lagrange multipliers. Two special cases in which the slip faces are plan and arc surface are discussed. For a general soil, the active earth pressure resultant force is minimal when the point of resultant force is on the low limit of location; it increases nonlinearly as the point of resultant force moves up, and the slip face is changed from plan to logarithmic spiral face accordingly. For a sandy soil, the upper limit of location factor increases and the active earth pressure increases as the internal friction angle increases. For a soft clay, the active earth pressure is maximum when the point of resultant force is on the lower limit of location; it decreases nonlinearly as the point of resultant force moves up, and the slip face is arc face and moves away from pit accordingly.
出处
《岩土力学》
EI
CAS
CSCD
北大核心
2016年第12期3365-3370,3379,共7页
Rock and Soil Mechanics
基金
国家"十二五"科技计划支撑课题(No.2012BAJ22B04)~~
关键词
柔性支护结构
主动土压力
变分方法
滑裂面
flexible retaining wall
active earth pressure
variational method
slip surface
