Calculation Method of Three-Dimensional Slope Safety Factor with Simultaneous Change of Height and Angle

The simultaneous variation of slope height and slope feet angle is a significant feature of three-dimensional slopes. Expanding the safety factor of two-dimensional slopes to three-dimensional is the most popular approach for calculating the safety factor of three-dimensional slopes. In this approach, however, the influence of three-dimensional effects is seldom considered. To correct this oversight, a novel calculation method for the safety factor of three-dimensional homogeneous cohesive soil slopes is proposed, involving 2 key parameters: the variation rates of slope height and slope feet angle. The stress state of the soil column on its bottom surface is simplified by the synthesis vectors of the tangent and normal vectors, which are determined by different shovel angles on each side of the soil column. By using a three-dimensional limit equilibrium method with a shear exertion coefficient, the safety factor of a cohesive soil pit slope at the site of a tunnel entrance, with synchronously-varied height and feet angle, in the North Hubei Water Transfer Engineering is calculated. The calculation results are then compared with those obtained by existing literature and numerical simulation method. This comparison reveals that the deviation is small, and the shape of sliding surface is basically the same as that of numerical simulation method, which reflects the strong rationality of the method in this paper. Furthermore, by analyzing the impact of 2 key parameters, it can be seen that the slope safety factor F_s may have same values under different k₁ and k₂ combinations. And meanwhile, the three-dimensional characteristics of slopes in different degrees may have opposite effects on F_s.