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为求解挡土墙被动土压力破裂曲线和土压力分布,取墙后填土的水平微分单元为研究对象,根据水平方向和竖直方向的力平衡以及力矩平衡,推导出基本微分方程。再通过求解出土压力分布表达式,推导出总的土压力泛函,利用欧拉方程求解泛函极值,其极大值就是被动土压力,极值曲线即是土体的破裂曲线。最后,利用基本求解思路,提出了挡土墙光滑情况下的滑裂曲线及土压力分布形式。
In order to solve the passive earth pressure rupture curve and the earth pressure distribution of the retaining wall, taking the horizontal differential element of the backfill as the research object, the basic differential equation is deduced according to the balance of the horizontal and vertical forces and the moment balance. Then by solving the expression of the pressure distribution of the earth pressure, the total earth pressure functional is deduced. The Euler equation is used to solve the functional extreme value. The maximum value is the passive earth pressure, and the extreme value curve is the soil rupture curve. Finally, using the basic idea of solution, the slip curve and earth pressure distribution form with smooth retaining wall are put forward.