陈建功, 胡日成, 许明. 考虑合力作用点位置的主动土压力计算[J]. 工程力学, 2016, 33(11): 132-139. DOI: 10.6052/j.issn.1000-4750.2015.03.0246
引用本文: 陈建功, 胡日成, 许明. 考虑合力作用点位置的主动土压力计算[J]. 工程力学, 2016, 33(11): 132-139. DOI: 10.6052/j.issn.1000-4750.2015.03.0246
CHEN Jian-gong, HU Ri-cheng, XU Ming. ACTIVE EARTH PRESSURE CALCULATION CONSIDERING FORCE POINT LOCATION[J]. Engineering Mechanics, 2016, 33(11): 132-139. DOI: 10.6052/j.issn.1000-4750.2015.03.0246
Citation: CHEN Jian-gong, HU Ri-cheng, XU Ming. ACTIVE EARTH PRESSURE CALCULATION CONSIDERING FORCE POINT LOCATION[J]. Engineering Mechanics, 2016, 33(11): 132-139. DOI: 10.6052/j.issn.1000-4750.2015.03.0246

考虑合力作用点位置的主动土压力计算

ACTIVE EARTH PRESSURE CALCULATION CONSIDERING FORCE POINT LOCATION

  • 摘要: 从滑动土体整体静力平衡方程出发,推导了坡面起伏,且有不均匀超载,墙背倾斜,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。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。通过算例表明,对于一般土体,在作用点位置系数下界限处,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,在作用点位置系数上界限处,主动土压力达到最大。在作用点位置系数上下界限处所对应的主动土压力构成的数值范围,包含了各种挡墙变位模式下的主动土压力。通过算例对比分析,采用库仑土压力理论进行的抗倾覆设计存在安全系数偏低的缺点,应该根据主动土压力和作用点位置的区间估计来指导设计。

     

    Abstract: Considering an inclined rough retaining wall under general conditions such as curvilinear fill, cohesive soil, and uneven surface load, a functional extreme-value isoperimetric model about active earth pressure is deduced based on the force equilibrium equations of sliding mass. Then the problem of active earth pressure is transcribed as a functional extreme-value problem of two undetermined functions by means of a Lagrange undetermined multiplier. According to Euler equations, logarithmic spiral sliding surface and normal stress function along the sliding surface are obtained. Combined with the boundary conditions and transversality conditions, the conditional functional extremum problem of active earth pressure changed equivalently into the problem of searching the minimum of unconstrained optimizations of a function with two unknown Lagrange multipliers. For general soil, the active earth pressure resultant force is minimal when the point of a resultant force is on the low limit of location and it increases nonlinearly as the point of the resultant force moved up, the slip face is changed from a plan to a logarithmic spiral face accordingly. The active earth pressure resultant force is maximal when the point of the resultant force is on the high limit of location. The minimal and the maximal active earth pressure can be regarded as an interval estimation of active pressure, which comprises the earth pressures on the rigid retaining wall with any wall movement. The result shows that the design method of anti-overturning stability of retaining wall based on Coulomb's earth pressure theory maybe lead to a lower safety factor. It is a feasible method to guide the design based on the interval estimation of the active earth pressure and its action point.

     

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