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<p>The paper investigates the reduction of the uncertainty of the factor of safety (FOS) in the probabilistic analysis of the stability of the mine waste heap. A mine spoil in the Bełchatów lignite mine (central Poland) is chosen as a case study. To mitigate the strong variability of heap material, the heap constituents are segmented using the Gaussian mixture model (GMM) technique. This segmentation utilizes key parameters from the cone penetration test with pore pressure measurement (CPTu) data: normalized cone resistance <i>Q</i><sub><i>t</i></sub> and friction ratio <i>F</i><sub><i>r</i></sub>. Three segmentation approaches are explored: one based solely on <i>Q</i><sub><i>t</i></sub> values, another on <i>Q</i><sub><i>t</i></sub> and <i>F</i><sub><i>r</i></sub> treated independently, and a third that considers their cross-correlation. For each method, the optimal number of clusters is determined, and the spatial distribution of the segmented constituents is mapped using the kriging technique. Subsequently, a numerical model of the heap’s slope is developed to conduct probabilistic stability analysis. The results indicate that the use of segmented constituents significantly reduces the FOS standard deviation compared to modelling the heap as a single, highly variable layer. Specifically, while the reference model (without segmented constituent) yielded a mean FOS of 3.31 with a standard deviation of 1.66, applying the GMM segmentation approach increased the mean FOS by approximately 30% to 4.30 and reduced the standard deviation by over 40% to 0.96. This substantial improvement allows for a more reasonable and reliable heap slope design. The third variant utilizing the full GMM approach is particularly efficient. It leads to a clear decrease in uncertainty by segmenting a relatively small number of well-defined components.</p>

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On reduction of uncertainty in mine waste heap stability analysis: GMM-driven CPTu data segmentation approach

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月25日

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  • Irena Bagińska,
  • Marek Kawa,
  • Jakub Rainer,
  • Hubert Szabowicz

摘要

The paper investigates the reduction of the uncertainty of the factor of safety (FOS) in the probabilistic analysis of the stability of the mine waste heap. A mine spoil in the Bełchatów lignite mine (central Poland) is chosen as a case study. To mitigate the strong variability of heap material, the heap constituents are segmented using the Gaussian mixture model (GMM) technique. This segmentation utilizes key parameters from the cone penetration test with pore pressure measurement (CPTu) data: normalized cone resistance Qt and friction ratio Fr. Three segmentation approaches are explored: one based solely on Qt values, another on Qt and Fr treated independently, and a third that considers their cross-correlation. For each method, the optimal number of clusters is determined, and the spatial distribution of the segmented constituents is mapped using the kriging technique. Subsequently, a numerical model of the heap’s slope is developed to conduct probabilistic stability analysis. The results indicate that the use of segmented constituents significantly reduces the FOS standard deviation compared to modelling the heap as a single, highly variable layer. Specifically, while the reference model (without segmented constituent) yielded a mean FOS of 3.31 with a standard deviation of 1.66, applying the GMM segmentation approach increased the mean FOS by approximately 30% to 4.30 and reduced the standard deviation by over 40% to 0.96. This substantial improvement allows for a more reasonable and reliable heap slope design. The third variant utilizing the full GMM approach is particularly efficient. It leads to a clear decrease in uncertainty by segmenting a relatively small number of well-defined components.