Calculation method of slope stability coefficients based on spatial multi-profile slopes
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摘要:
在边坡稳定性分析中，通常需要对多个剖面的边坡稳定性进行单独计算。为了提高多剖面边坡稳定性系统计算的效率，提出了一种基于空间多剖面边坡稳定性系数计算的方法。首先，将二维剩余推力法扩展至空间剖面，形成空间剖面的剩余推力法；其次，通过在三维边坡工程地质模型上实现剖面图的自动生成和管理，进一步优化了计算流程；为了实现快速高效计算边坡稳定性系数，引入了基于多线程并行计算的方法，并结合空间剖面的剩余推力法，对空间多剖面边坡稳定性系数进行了更为准确和高效的计算。以内蒙古锡林浩特某露天矿为应用实例，建立了内排土场边坡三维边坡工程地质模型，在此基础上，自动生成了7个空间剖面图，采用多线程并行计算出7个剖面的稳定性系数，最后，通过可视化手段对计算结果进行了直观展示。采用多线程并行计算多剖面边坡稳定性系数能够充分利用计算资源，提高计算效率，同时，在实际工程应用中进一步证实了该方法的可行性和适用性。
Abstract:In conventional slope stability analysis, the slope stabilities for various cross-sections are calculated independently.
Objective To improve the calculation efficiency of slope stabilities for multiple profiles, this study prop oses a method based on spatial slope stability coefficient calculations.
Methods The two-dimensional residual thrust method is incorporated with spatial profiles, which forms a residual thrust method for spatial profiles.
Methods continued The calculation process of the residual thrust method for spatial profiles is optimized by the automatic generation and management of profiles within a three-dimensional engineering geological mode of a slope. In order to achieve rapid and efficient calculation of slope stability coefficients, a method based on multi-threaded parallel computation is introduced. Combining this approach with the residual thrust method for spatial profiles allows for more accurate and efficient computation of stability coefficients for multiple spatial profiles.
Results Using an open-pit mine in Xilinhot, Inner Mongolia, as a case study, we establish a three-dimensional slope engineering geological model for the internal dump site slope. On this basis, seven spatial profiles are automatically generated, and stability coefficients are calculated using multi-threaded parallel computation. Finally, the results are presented visually.
Conclusion The research findings indicate that adopting multi-threaded parallel computation for calculating slope stability coefficients for multiple profiles can fully utilize computing resources and significantly improve computational efficiency. Furthermore, application in engineering projects confirms the feasibility and applicability of the proposed method.
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图 1 第i个条块受力状态
Wi . 第i个条块的重量；Di . 第i个条块的剩余推力；Di-1. 第i-1个条块的剩余推力；Wp,i ，Wp,i-1. 作用于第i，i−1个条块的水平压力；αi. 第i个条块的底滑面与水平线的夹角；Ti . 第i个条块底面的剪切力；Ni . 第i个条块的法向力；（tx,i，ty,i），（tx,i-1，ty,i-1），（bx,i，by,i）和（bx,i-1，by,i-1）. 第i个条块的4个顶点坐标；oy. 高程方向；ox. 垂直于oy；（Wx,i，Wy,i），（Wx,i-1，Wy,i-1）. 第i个条块中间部分的坐标；下同
Figure 1. Force state of the i-th block
图 2 剖面受力情况示意图
S1，S2和S3. 剖面编号；ox'. 主滑方向；$ ox \bot oy $，$ ox' \bot oy' $；αx，$ {\alpha _y} $. $ xoy$和${x}'o{y}' $在x方向和y方向上的夹角；（tx,i, ty,i,tz,i），（tx,i-1,ty,i-1,tz,i-1），（bx,i,by,i,bz,i），（bx,i-1,by,i-1,bz,i-1）.空间中第i个条块的4个顶点坐标；（Wx,i, Wy,i,Wz,i）,（Wx,i-1,Wy,i-1,Wz,i-1）.空间中第i个条块中间部分的坐标；S'. 当前剖面对上一个剖面的作用力；S. 剖面集合；bi. 剖面第i个条块的宽度；β. 剩余推力与水平线的夹角；下同
Figure 2. Schematic diagram of the force situation in the profile
图 4 建立空间多剖面
P1, P2, P3, P4，P5. 剖面线编号；S1, S2, S3, S4，S5. 剖面编号；下同
Figure 4. Establishment of a spatial multi-profile
图 6 多线程并行计算边坡稳定性系数流程图（Fs. 边坡稳定系数，下同）
Figure 6. Flowchart for multi-threaded parallel calculation of slope stability coefficients
图 7 多剖面多线程并行计算流程图
Figure 7. Flowchart for multi-profile and multi-threaded parallel computation
图 8 露天矿三维边坡工程地质模型
Figure 8. Three-dimensional engineering geological model of the open-pit mine slope
图 9 边坡工程地质剖面（c. 黏聚力；φ内摩擦角；γ. 容重）
Figure 9. Engineering geological profile of the slope
图 11 多剖面稳定性系数计算结果图
Figure 11. Calculation results of stability coefficients for multiple profiles
表 1 边坡剖切线数据结构
Table 1. Data structure of slope profile lines
字段名 数据类型 说明 SectionName navrchar 剖面名称 SlopeCuttingtangent geometry 边坡剖切线 TimeProperty datatime 边坡剖切线存储的日期 
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表 2 岩层多边形图元数据结构
Table 2. Rock polygon map metadata structure
字段名 数据类型 说明 SectionName navrchar 剖面名 Rockpolygon geometry 岩层多边形 sectionElementPara navrchar 剖面图元属性参数 ColorProperty string 岩层多边形属性颜色
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表 3 岩石物理力学指标
Table 3. Rock physical and mechanical indexes
地层 黏聚力c/MPa 内摩擦角φ/(°) 容重γ/(kN·m−3) 排弃物料 0.0151 14.0 18.0 第四系 0 26.9 20.8 新近系、古近系 0.120 24.0 19.3 煤 0.100 30.0 12.2 泥岩 0.050 25.0 19.6
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