Evaluating geomechanical uncertainty and slope reliability analysis in openpit mine planning and optimization

Openpit mining requires careful planning to ensure both safety and profitability. One key challenge is determining how steep the openpit slopes can be without risking collapse. This is difficult because the strength of the underground rock varies and is not fully known. In this study, we examined a gold deposit in Alaska to find the best slope angles that balance safety and profit, considering geomechanical uncertainty. We used data on rock quality, called rock quality designation (RQD), to estimate how strong the rocks are, focusing on properties like cohesion and internal friction. By running thousands of simulations that account for the uncertainty in these properties, we evaluated the likelihood of slope failure at different angles. We found that slopes up to 48° are very safe, with no expected failures and a projected profit of $2.684 billion. Steeper slopes, like 56°, could increase profits to $2.935 billion but come with a 23 percent chance of failure. This shows a trade-off: steeper slopes may yield more profit but also carry higher risks. Therefore, mine planners must decide how much risk they are willing to accept for potential financial gains. Introduction In openpit mining, understanding the geomechanical properties of rock masses is essential for safeguarding both safety and economic efficiency. Neglecting these properties can lead to slope failures, resulting in equipment damage, production delays and financial losses. A key challenge is determining the optimal slope angle: steeper slopes reduce waste removal and increase profitability but also raise the risk of instability. Slope stability is commonly assessed using the factor of safety (FoS), which compares resisting forces to driving forces along potential failure surfaces. Traditional methods for calculating FoS include limit equilibrium, finite element and discrete element analyses. However, these approaches often assume homogeneous rock conditions, overlooking the natural variability in rock properties. This variability introduces geomechanical uncertainty, complicating the design of stable slopes. To address this, engineers use exploration data — such as geological surveys and drilling — to estimate rock properties, though data limitations persist. Typically, deterministic models average these properties across geomechanical domains, potentially masking local weaknesses. Recent studies have incorporated stochastic modeling and reliability-based analyses to better account for uncertainty in slope stability assessments. Despite these advancements, integrating geomechanical uncertainty into pit optimization remains limited. This research aims to bridge that gap by incorporating slope reliability into openpit design, balancing safety and profitability. Materials and methods This study focuses on an openpit gold deposit in Alaska, utilizing data from 145 core drill holes totaling 42,932 m. The geological setting comprises nine rock types, with four primary ones — Cambrian (CAM), Upper Sediments (UPS), Main Volcanics (MVC) and Lower Sediments (LOS) — being economically significant. Due to limited geomechanical data, RQDs from 27 drill holes served as the primary input for assessing rock strength parameters. The methodology encompasses four main steps: (1) Geological modeling and grade estimation: A 3D geological model was developed using 1-m composites and ordinary kriging for gold grade estimation, based on a 15 m × 15 m × 10 m block model. (2) RQD modeling and slope stability analysis: Histograms and probability density functions (PDFs) were generated for RQD values of each rock type. These were converted into unit weight, cohesion and friction angle using established correlations [1]. The Bishop simplified method, implemented via Rocscience Slide2, was employed for slope stability analysis. (3) Slope reliability analysis: Markov chain Monte Carlo (MCMC) simulations were conducted to account for geomechanical variability, producing distributions of FoS and corresponding probabilities of failure. (4) Openpit optimization: Various slope angles were analyzed to determine ultimate pit limits using the maximum flow-minimum cut algorithm, balancing economic returns with slope reliability. Fig. 1 RQD histograms and the fitted PDFs for all four rock types. Results The deposit comprises four primary rock types (CAM, UPS, MVC and LOS), typically arranged vertically from top to bottom in the sequence CAM → UPS → MVC → LOS, with occasional variations due to faulting. Gold grades across the deposit are generally low, averaging 0.012 g/t, with sporadic higher-grade zones exhibiting high nugget effects. Among the rock types, MVC displays the highest average gold grade at 0.020 g/t, aligning with its igneous origin. Statistical analyses reveal a positively skewed gold grade distribution with high coefficients of variation, indicating significant variability and necessitating robust estimation methods. The RQD values vary notably among rock types, with MVC exhibiting the highest mean RQD of 36.95, suggesting higher rock quality, while LOS has the lowest at 15.63, indicating poor rock quality (Table 1). All rock types show left-skewed RQD distributions with long right tails (Fig. 1). Exponential distributions best fit the RQD data, as confirmed by log-likelihood evaluations, and were utilized for subsequent Monte Carlo simulations in slope stability assessments using the limit equilibrium method. The number of random samples was determined by observing the convergence of the mean FoS value (Fig. 2).Slope stability and the associated cash flow analysis of the optimized pit were evaluated using both deterministic and stochastic approaches across nine slope angles ranging from 37° to 56° (Table 2). For slope angles between 37° and 48°, the mean FoS from the stochastic model remains high (9.1 to 9.8), with a 0 percent probability of failure and 100 percent slope reliability. This indicates that these slopes are stable under both deterministic and stochastic analyses. As a result, the economic value of the pit increases from $2.234 billion at 37° to $2.684 billion at 48°, reflecting the benefits of steeper, stable slopes that allow for greater pit optimization and resource extraction. However, beyond 49°, the mean FoS drops significantly, and the probability of failure increases. For instance, at 49°, the probability of failure rises to 12 percent, with a corresponding slope reliability of 88 percent, and an economic value of $2.721 billion. As the slope angle increases to 56°, the failure probability reaches 23 percent and reliability falls to 77 percent, though the economic value of the pit continues to rise, reaching $2.935 billion. This trend underscores the importance of accounting for geomechanical uncertainties in slope design. More information is available in the full paper. Fig. 2 Convergence plot of mean factor of safety (FoS) from stochastic slope stability analysis with number of Monte Carlo samples for slope angle of 49°. Conclusions, limitations and future research This study integrates geomechanical uncertainty into openpit mine planning by employing stochastic slope stability analysis. Key findings indicate that while deterministic models suggest high slope stability across various angles, stochastic analyses reveal increasing failure probabilities with steeper slopes. Notably, at 49°, the failure probability rises to 12 percent, with marginal economic gains beyond 48°, where a 100 percent reliability and $2.684 billion value are observed. Therefore, a 48° slope angle is recommended for conservative designs, balancing stability and economic return. Limitations include the model’s simplifications, such as the exclusion of rock fractures, freeze-thaw effects, and consideration of only a single failure mechanism. Future research should incorporate advanced numerical methods, multiple failure modes and site-specific analyses to enhance reliability and applicability of the findings. Selected reference Kring K, Chatterjee S (2020). Uncertainty quantification of structural and geotechnical parameter by geostatistical simulations applied to a stability analysis case study with limited exploration data. Int J Rock Mech Min Sci 125:104157

Evaluating geomechanical uncertainty and slope reliability analysis in openpit mine planning and optimization

Authored by: Evan Ricchio-Hitchcock and Snehamoy Chatterjee

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