旋转对称边坡三维安全系数显式解

Explicit solution to three-dimensional factor of safety of rotational symmetrical slope

为使三维边坡稳定性计算便于工程应用,采用滑面正应力修正方式,不需考虑条柱间作用力具体分布形式,推导出旋转对称边坡三维安全系数极限平衡显式解。根据简单的平衡条件,假设三维滑面正应力的初始分布,再乘以待定的修正系数;根据三维旋转对称滑体的垂直力平衡与对旋转轴力矩平衡的条件,推导出关于安全系数的2次代数方程;最终直接解出三维安全系数。算例表明,三维安全系数显式解结果与解析解完全一致,与复杂的条柱法计算结果比较接近,可以在边坡工程中推广应用。

The three-dimensional slope stability analyses are commonly too complex to be applied in practical engineering. By modifying the normal stresses over the slip surface without the consideration of the details of inter-column forces, the explicit limit equilibrium solution was derived to the three-dimensional factor of safety of the rotational symmetrical slope. The normal stresses were initially assumed based on the simple equilibrium condition and then multiplied by a modfication coeffcient to be determined. According to equilibrium conditions of vertical force and moment about the rotational axis, a quadratic equation in terms of the factor of safety was obtained, which directly yields the explicit solution to the three-dimensional factor of safety. Studies of examples demonstrate that the explicit solution to three-dimensional factor of safety of the slope is identical to the analytical solution and in approximately agreement with the results of methods of inter-colomns. Thus, the explicit solution to three-dimensional slope stability obtained in this paper can be applied in practical engineering.