三维滑裂面形状对安全系数的影响

 基于滑面正应力修正模式的假定，根据边坡的平衡条件，导出含安全系数的平衡方程组，通过反复迭代求解安全系数。假设滑面是一簇幂函数绕 y 轴旋转得到的曲面，通过变化幂函数的幂次，得到不同形状的滑面。据此，讨论滑面形状对安全系数的影响，结果表明安全系数是幂次的单值函数且存在极小值。所以，可以通过优化幂函数中的幂次得到最小安全系数对应的最危险滑面，并分析最危险滑面所对应的幂次随滑体长度的变化规律。最后，讨论三维边坡端部效应。研究结果表明：该方法能够得到更小的安全系数，最危险滑面所对应的幂次随着滑体长度的增大先略微降低后逐渐增大。端部效应分析显示：当滑体长度大于坡高10倍时，端部效应可以忽略；端部效应随着内摩擦角的增大而有所增强，随着黏聚力的增大而减弱，与边坡倾角没有关系。

IMPACT OF 3D SLIP SURFACE'S SHAPE ON FACTOR OF SAFETY

Based on the assumption of the modification of normal stress over the slip surface,the solution to the factor of safety is derived by iteration,according to the equilibrium conditions of the slope. Regarding the slip surface as a curved surface yielded from a family of power function rotating on y-axis,slip surfaces of different shapes are obtained by changing the values of the power function's power. Accordingly,by discussing the impact of the slip surface's shape on the factor of safety,the results reveal that the factor of safety is the single-valued function of power and its minimum value exists as well. As a result,the critical slip surface is obtained by optimizing the value of power,and the change law of the relationship between the value of power and the length of the sliding mass is analyzed. At last,the end effect of 3D slope is also discussed. It is demonstrated that the presented method can derive smaller factor of safety;the value of power corresponding to the critical slip surface decreases slightly and then increases gradually with the increase of length of the sliding mass. The analysis reveals that the end effect can be neglected when the length of the sliding mass is bigger than the height of the slope by 10 times,and it is proportional to the internal friction angle,inversely proportional to the cohesive stress and does not has close relation with the change of the slope inclination.