【摘要】 在极限平衡法的框架内,引入Lagrange乘子,将被动土压力问题以变分学观点来描述,转化为含有两个函数自变量的泛函极值问题,进而根据力系几何关系将其转化为带有约束的函数极值问题。极值问题的计算结果表明,挡墙背后土体在被动临界状态时存在着沿某平面滑动和绕对数螺旋柱面转动两种破坏形式。在平面滑动破坏的情况下,土压力的大小完全等同于Coulomb(1776)和Rankine(1857)理论的结果;对于土体转动破坏情况,土压力的大小与Sokolovskii(1956)和Chen(1975)的结果比较吻合。与已有测试数据的对比表明,两类理论计算结果构成的有序实数对可以作为被动土压力大小的一个区间估计,包含了各种墙体变位模式下刚性挡墙上作用的被动土压力。更多还原

【Abstract】 Using the limit equilibrium approach,the problem of passive earth pressure on rigid retaining wall is formulated in terms of variation calculus with Lagrange multipliers,and is transformed as the functional extreme-value problem of two variables.It is further transformed into the solution of extreme value of restrained functions incorporating the geometrical relations of the forces.Computation results show that there exist two kinds of failure modes-sliding along a plane surface(translation)and rotation along a log-spiral cylinder surface(rotation)when the soil behind retaining walls reaches critical passive state.In the translational failure mode,the passive earth pressure coincides with the theories of Coulomb(1776)and Rankine(1857);in rotational failure mode,the passive earth pressure agrees well with that of Chen(1975)and Sokolovskii(1956).Comparisons with measured data indicate that the ordered real number pair predicted by the two theoretical theories can be regarded as an interval estimation of passive pressure,which comprises the earth pressures on the rigid retaining wall with any wall movement.更多还原