基于力平衡的三维边坡安全系数显式解及工程应用

将基于滑面正应力分布的二维极限平衡显式解法推广到三维边坡稳定性分析,提出适合一般形状空间滑面的三维边坡稳定性简便计算方法.首先,假设三维滑面正应力的初始分布,然后对其修正,使滑体满足所有力的平衡条件,导出关于安全系数的2次代数方程,最终得到三维边坡安全系数显式解.该方法克服了目前条柱法存在的一些难以解决的困难,不需要考虑条柱间作用力具体分布,满足主要平衡条件,计算过程简单.算例表明,该显式解与楔体三维极限平衡解析解完全一致,与对称三维边坡严格极限平衡解答接近.该方法已用于某重力坝坝肩三维滑体初步稳定性分析,计算结果有助于坝肩边坡的加固设计.

Explicit solution to 3D safety factor of slope based on force equilibrium and its application to engineering

By extending the 2D explicit limit equilibrium solution based on normal stresses over the slip surface of the 3D slope, a simple and convenient method of 3D slope stability analysis is presented; it is applicable to general-shaped 3D slip surfaces. Firstly, the normal stress distribution over the 3D slip surface is initially assumed, it is then modified to satisfy all the three force equilibrium conditions. A quadratic equation is derived in terms of safety factor, it finally yields the explicit solution to the 3D safety factor. The proposed method has overcome some insurmountable difficulties encountered in the current methods of columns; and free of consideration of inter-column forces, satisfying the major equilibrium conditions and features; simple and practical computation process. Example studies show that the proposed explicit solution gives the 3D safety factor of a wedge identical to the analytical solution, agrees well with the rigorous limit equilibrium solutions of symmetrical slope. The method has been applied to the preliminary 3D stability analysis of a dam abutment; and the computation results offer a guidance for design of stabilization.