Three-dimensional residual thrust method considering moment equilibrium

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 intercolumn 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.