中文摘要：

分别推导出满足所有6个平衡条件三维边坡严格极限平衡解答和满足5个平衡条件的三维边坡准严格极限平衡解答.假定空间滑面上正应力初始分布,对于严格解,用含5个参数的修正函数对其修正;对于准严格解,则采用含4个参数的修正函数.严格平衡方程组最终化为关于三维安全系数的六次代数方程,通过调节滑动方向和转动系数使修正后滑面正应力为正,从而得到有意义的严格极限平衡解答;而准严格平衡方程组最终化为关于三维安全系数的四次代数方程,其最大解析实根为准严格极限平衡解答,且只需调节滑动方向,计算过程更为方便实用.算例计算结果表明,三维边坡准严格解答与严格解答十分接近,对工程问题可直接采用准严格解答.该方法计算原理简单,易于编程实施,计算结果精度高,且适合任意形状空间滑面.应用该方法对重庆乌江银盘水电站左岸坝肩边坡及坝基岩体进行三维稳定性分析,克服了二维稳定性分析的局限性,计算结果更为合理可靠,为坝基与坝肩加固设计提供理论依据.

英文摘要：

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.