RIGOROUS AND QUASI-RIGOROUS LIMIT EQUILIBRIUM SOLUTIONS OF 3D SLOPE STABILITY AND APPLICATION TO ENGINEERING
ZHU Dayong1,QIAN Qihu2 (1. School of Civil Engineering,Hefei University of Technology,Hefei,Anhui 230009,China; 2. Engineering Institute of Engineering Corps,PLA University of Science and Technology,Nanjing,Jiangsu 210007,China)
The rigorous and quasi-rigorous limit equilibrium solutions to 3D slope stability,which satisfy six and five equilibrium conditions respectively,are derived. Firstly,the normal stress distribution over the 3D slip surface is initially assumed,which is modified by a function with five parameters involved for the rigorous solution,or by a function with four parameters involved for the quasi-rigorous solution. The rigorous equilibrium equations are reduced to a sixth-order algebraic equation with respect to the 3D factor of safety;and adjustments of slip direction and rotational coefficient are needed for positive values of normal stresses over the slip surface. The quasi-rigorous equilibrium equations are reduced to a quartic equation with respect to the 3D factor of safety,the maximum real root of which is the quasi-rigorous solution. Only adjustment of slip direction is needed for quasi-rigorous solution;and the computation process is much simpler than that of rigorous solution. The results of example studies show that the difference between the rigorous and quasi-rigorous solutions is negligible;and the latter is thus more applicable to the practical engineering. The presented method features simple principle and high precision,accommodates generalized shape of 3D slip surface,and can be readily implemented into computer. This method has been used in the stability analysis of the abutment slope on the left bank of Yinpan Hydropower Station on Wujiang River,assisting in the design of abutment and stabilization measures.