考虑力矩平衡的三维剩余推力法

Three-dimensional residual thrust method considering moment equilibrium

在考虑力矩平衡的二维剩余推力法的基础上,提出了一种三维极限平衡分析方法。在忽略条柱间作用力的水平剪切分量的基础上,建立铅直方向(Z轴)、滑动方向(X轴)、垂直滑动方向(Y轴)的力平衡以及绕Y轴的力矩平衡共4个方程,平衡方程中纳入地下水、地震、支护力作用。行界面上柱间力作用方向角(条间力剪切分量与水平分量的比值)为条柱底滑面在滑动方向上的倾角乘以统一的修正系数(可称为推力方向修正系数,以进行修正),列界面上柱间力作用方向角为条柱底滑面在Y方向上的倾角。通过迭代计算,当调整稳定系数以使所有列的X向剩余推力和为零、改变滑动方向(X轴方位)以使所有行的Y向剩余推力和为零、调整推力方向修正系数以使绕Y轴的总力矩为零,求得滑坡的稳定系数、最优滑动方向及推力方向修正系数。该法适用于任意形态滑坡,并可计算得到最优滑动方向。最后对该法进行了工程应用及讨论。

Based on the two-dimensional residual thrust method considering moment equilibrium, a new three-dimensional limit equilibrium method was proposed. With horizontal shear component of intercotumn forces ignored, four equilibrium equations were formed, i.e., force equilibriums along the vertical direction, the sliding （X axis） direction, Y axis direction, and moment equilibrium around Y axis. The equilibrium equations contained the actions of underground water, earthquake and supporting forces. The directional angle of the force acting on the lateral vertical faces of each column was the dip of the sliding face in X direction multiplied by correction coefficient, which was named as the correction coefficient of thrust direction. The directional angle of the force acting on the longitudinal faces was the dip of the sliding face in Y axis direction. By means of iteration, when the total residual thrust along X direction of all rows became zero by adjusting the factor of safety, the total residual thrust along Y direction became zero by changing the sliding direction, as well as the total moment around Y axis became zero by adjusting the correction coefficient of thrust direction, the factor of safety of landslide, the optimized sliding direction and the correction coefficient of thrust direction could be solved. The proposed method was suitable for any landslide shape, and the slide direction could be calculated rather than guessed. At last, the method was used in practical engineering and the results were discussed.