Determination of the 3D most dangerous sliding surface for open-pit mine slopes based on multiple cross-profiles
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摘要:
目前，普遍采用二维剖面进行边坡稳定性分析，该方法能高效且较为准确地评估边坡的稳定性。然而，二维剖面不能描述边坡最危险滑面的三维空间形态和三维滑体。为解决此问题，在二维剖面边坡稳定性分析的基础上，通过将多个剖面与三维边坡模型进行关联，使用样条函数拟合出边坡三维最危险滑面。首先，通过设置剖面线和二维剖面图中图元的剖面名称、水平坐标定位及高程定位，建立了二维剖面图与三维边坡空间的关联；其次，利用多剖面合力法分别自动生成了各剖面的最危险滑面线，使用坐标转换公式将每个二维剖面的最危险滑面线转换到三维边坡空间；最后，利用样条函数插值，成功生成了该边坡的三维最危险滑面。以内蒙古锡林浩特某露天矿西南帮边坡为例，建立了边坡三维工程地质模型，生成了5个边坡稳定性分析二维剖面，通过该方法成功生成了该边坡的三维最危险滑面及三维滑体并验证了其合理性。研究成果为预估潜在边坡滑体位置、规模和破坏程度提供了新的思路。
Abstract:At present, the two-dimensional (2D) profiles are widely used for slope stability analysis, which has proved to be efficient and relatively accurate.
Objective However, the two-dimensional profile cannot describe the 3D spatial morphology of the most dangerous sliding surface sliding mass.
Methods and Results To address the limitation, based on the stability analysis of the two-dimensional profile slope, the three-dimensional most dangerous sliding surface of the slope is fitted using the spline function by associating multiple profiles with the three-dimensional slope model. Firstly, the relationship between the two-dimensional profile and the three-dimensional slope space is established by setting the profile name, horizontal coordinate positioning and elevation positioning of the graphic elements in the profile line and the two-dimensional profile. Secondly, the most dangerous sliding surface lines of each profile are automatically generated by using the multi-profile resultant force method, and the most dangerous sliding surface lines of each two-dimensional profile are converted to three-dimensional slope space by using the coordinate transformation formula. Finally, the spline function interpolation is used to fit the most dangerous sliding surface lines in the three-dimensional space to construct the three-dimensional most dangerous sliding surface. Taking the southwest slope of an open-pit mine in Xilinhot, Inner Mongolia as an example, a three-dimensional engineering geological model of the slope is established, and five two-dimensional profiles for slope stability analysis are generated. Through this method, the three-dimensional most dangerous sliding surface and three-dimensional sliding mass are successfully generated and their rationality is verified.
Conclusion The research results provide new insights for predicting the location, scale, and damage degree of potential slope sliding masses.
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图 2 剖面空间转换关系图
m'-n'. 剖面线编号；l0，l1. 水平定位线；y0，y1，y2，y3，y4，y5. 高程定位线；h0，h1，h2，h3，h4，h5. 实际高程值；下同
Figure 2. Profile space conversion relationship diagram
图 5 自动生成多剖面最危险滑面线流程图
Figure 5. Automatically generate the flow chart of the most dangerous sliding surface line of multi-profile
图 6 二维转三维坐标示意图
P0(x0,y0)和P1(x1,y1)为剖面线P0-P1的端点坐标，在剖面图上分别与水平定位线l0和l1对应；ri(xi, yi)为滑面线第i个顶点的二维坐标；$r_{i}{'}(x_{i}{'} , y_{i}{'} , {\textit{z}}_{i}{'}) $滑面线第i个顶点的三维坐标；$a=|x_i-x_{0}| $，$b=|x_i-x_{1}| $；yc为相应剖面图上的任意一条高程定位线的y坐标值；zc为该高程定位线的实际高程值；下同
Figure 6. Two-dimensional to three-dimensional coordinate diagram
图 8 采场现状及剖面线设计（蓝色线为剖面线，红色线为设置的坡顶和坡底范围，下同）
Figure 8. Stope status and profile lines design
图 10 1-1'剖面图及最危险滑面线
Figure 10. 1-1' profile and the most dangerous sliding surface line
图 11 三维最危险滑面线(a)和滑面(b)
Figure 11. Most dangerous sliding surface line (a) and sliding surface (b) in three-dimensional space
图 14 剖面线设置及滑面线对比
Figure 14. Setting of cross profile line and comparison between sliding surface lines
图 15 剖面0-0'与边坡模型滑面线比较
Figure 15. Comparison of sliding surface line of Profile 0-0' with slope model
表 1 岩体物理力学指标
Table 1. Physical and mechanical indexes of rock mass
地 层 岩体容重γ/(kN·m−3) 内聚力C/kPa 内摩擦角/(°) 古近系+新近系 19.3 85 24 碳质泥岩 18.3 30 14.22 砂岩 20.8 21 25.5 煤 13.9 58 26.32 泥岩 20.1 26 21.85 砂质泥岩 20.3 25.38 17.49 
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表 2 三维滑面线数据集
Table 2. Three-dimensional sliding surface line data set
剖面名 起点坐标 中间点 终点坐标 1-1' ( 2332.570° ,3138.609° ,988.160°)...... ( 2531.391° ,3402.430° ,929.969°)2-2' ( 2520.152° ,3023.592° ,1000.597° )...... ( 2794.880° ,3227.500° ,912.907°)3-3' ( 2578.475° ,2820.756° ,1011.972° )...... ( 2956.343° ,2966.455° ,906.414°)4-4' ( 2566.577° ,2619.273° ,1016.332° )...... ( 3042.078° ,2703.763° ,900.805°)5-5' ( 2461.401° ,2374.803° ,1014.647° )...... ( 2929.546° ,2347.221° ,919.825°)6-6' ( 2390.92° ,3210.362° ,945.09°)...... ( 2603.905° ,2366.407° ,959.674°)7-7' ( 2477.535° ,3330.966° ,919.107°)...... ( 2802.998° ,2354.676° ,922.035°)
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表 3 边坡模型与剖面0-0'滑面线误差参照
Table 3. Errors reference for sliding surface line of slope model and Profile 0-0'
高程z/m z1 中间点 zi zi+1 中间点 zn 剖面0-0' 1015.35 ...... 935.25 926.29 ...... 917.76 边坡模型 1007.07 ...... 938.12 928.07 ...... 912.09 误差 8.28 ...... −2.87 −1.78 ...... −5.67 误差率/% 0.82 ...... 0.31 0.19 ...... 0.62
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