Uncertainty in Probabilistic Open Pit Slope Stability Analyses: Implications for Reliability-Based Designs

The presence of uncertainty is acknowledged in various fields of Engineering. Also, there are many sources of uncertainties. In geotechnical engineering, probabilistic slope stability analysis (PSSA) is a tool used to quantify parameter uncertainty. It achieves this by considering any strength parameter of a material as a random variable with a specific probability distribution. The outcomes of such analyses are evaluated through design acceptance criteria (DAC) that incorporate uncertainty in terms of design reliability – also known as Reliability-Based Design Acceptance Criteria (RBDAC) – having different ranges of DAC depending on the level of reliability, but also based on the potential consequence of the failure. Nevertheless, other forms of uncertainty are not usually accounted for in PSSA. Open pit slopes, akin to other mining earth structures, are subject to various types of uncertainties. This leads to the question of what emerges when these other sources of uncertainties are considered in PSSA and evaluated within the RBDAC. This work is performed to study specific sources of uncertainty within open pits slopes, especially those referred to as parameter uncertainty, geometrical uncertainty, and computational uncertainty. These sources of uncertainty are explored using PSSA and subsequently evaluated within the RBDAC matrix proposed by Macciotta et al. (2020). The research is divided into two parts. The first part of the work primarily focuses on parameter uncertainty in the rock mass strength. It is an in-depth exploration of rock strength variability in terms of the Hoek-Brown failure criterion and Mohr-Coulomb failure criterion, considering univariate and bivariate distributions using two rock mass strength parameters. The aim of this work is to demonstrate consistent results whether Hoek-Brown or Mohr-Coulomb are being used and to comprehend the underlying reasons for any disparities. The second part of the work stress tests the applicability of the RBDAC proposed by Macciotta et al. (2020) for open pit slopes, while also exploring the implications of introducing additional uncertainties (geometrical and computational) in addition to parameter uncertainty. This is performed through the integration of diverse scenarios, allowing for the creation of designs at different reliability levels and evaluations at different areas of the RBDAC matrix. Both works were conducted on a modified open pit slope, inspired by the geotechnical, geological, and hydrological characteristics of an implemented pit slope located in British Columbia, Canada. The outcomes of this research yield significant insights for forthcoming probabilistic open pit slope stability analyses. The results of the first work underline that there will be differences in the outcomes of the PSSA between considering the variability of the rock mass strength using Mohr-Coulomb and Hoek-Brown unless an inherent correlation between the Mohr-Coulomb strength parameters is considered and estimated from the equations provided by Rafiei and Martin (2019) and through Monte Carlo simulations. This inherent correlation tends to be negative, consistent with considerations taken in soils, but it shifts to positive values as the GSI decreases or the confining stress increases. The results of the second work showed that our case study can be optimized in terms of computational time by reducing the number of realizations from 10 000 to 1000 with minimal influences of statistical uncertainty. Nonetheless, it was found significant differences (attributed to computational simplifications) when PSSA is performed with fixed slip surfaces compared to the results using iteration-specific slip surface generation. It was observed that the former significantly overestimated the design stability. The work also demonstrated that the introduction of additional scenarios (meaning an increase in epistemic uncertainty), leads to higher coefficients of variation and thus an elevated probability of failure. These results can be the defining factor between designs deemed acceptable or not, as per the RBDAC criteria. Based on these outcomes, it is suggested that practitioners consider, depending on the necessity of the design, the integration of other sources of uncertainty in the assessment of open pit slopes, beyond the consideration of parameter uncertainty alone. This will ensure a more precise and consistent interpretation of the design, enabling well-informed decisions on open pit design. This also is facilitated in a practicable manner by utilizing the RBDAC matrix proposed by Macciotta et al. (2020), where uncertainty is evaluated in a transparent manner.

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