The impact of uncertainty on the reliability of slope design and performance assessment is often significant. Conventional slope practice based on the factor of safety cannot explicitly address uncertainty, thus compromising the adequacy of projections. Probabilistic techniques are rational means to quantify and incorporate uncertainty into slope analysis and design. A spreadsheet approach for probabilistic slope stability analysis is developed. The methodology is based on Monte Carlo simulation using the familiar and readily available software, Microsoft® Excel 97 and @Risk. The analysis accounts for the spatial variability of the input variables, the statistical uncertainty due to limited data, and biases in the empirical factors and correlations used. The approach is simple and can be applied in practice with little effort beyond that needed in a conventional analysis. The methodology is illustrated by a probabilistic slope analysis of the dykes of the James Bay hydroelectric project. The results are compared with those obtained using the first-order second-moment method, and the practical insights gained through the analysis are highlighted. The deficiencies of a simpler probabilistic analysis are illustrated. Key words: probabilistic analysis, slope stability, Monte Carlo simulation, spatial variability.
Rock falls can cause delays, damage, injury, and death to highway users. In 1982, a rock fell on a vehicle in the Argillite Cut on British Columbia (B.C.) Highway 99 killing a woman and disabling her father. The father successfully sued the provincial Ministry of Transportation and Highways for damages. The Supreme Court of Canada found that the Ministry could readily foresee the risk that harm might befall users of the highway if it were not reasonably maintained and that maintenance could be found to extend to the prevention of injury from falling rock. A risk analysis methodology can assess the probability of loss of life due to rock fall. Rock fall impact-mark mapping supplemented by documented rock fall records was used to establish a rock fall frequency. The risk of rock fall on this highway in 1982 can be compared with accepted societal risks. For the Argillite Cut, the probabilities of death of a one time user and a daily commuter on the highway were 6 × 10 -8 and 3 × 10 -5 per year, respectively. The annual probability of a rock fall causing a death in the exposed population was 8 × 10 -2 in the Argillite Cut. This was higher than the level of risk now commonly accepted in some industries and large engineering projects.Résumé : Les chutes de roches peuvent causer des retards, dommages, blessures et pertes de vie aux usagers des routes. En 1982, une roche est tombée sur un véhicule dans l'Argillite Cut sur la route 99 en Colombie-Britannique, tuant une femme et invalidant son père. Le père a poursuivi avec succès pour dommages le ministère des transports et des routes de la province. La Cour suprême du Canada a trouvé que le ministère pouvait facilement prévoir que les usagers encourraient des risques si la route n'était pas raisonnablement bien entretenue, et que l'entretien devrait s'étendre à la prévention de blessures résultant de la chute d'une roche. Une méthodologie d'analyse de risques peut évaluer la probabilité de perte de vie résultant de la chute d'une roche. Une cartographie des points d'impacts de chutes de roches avec comme ajout les dossiers des chutes de roches documentées a été utilisée pour établir une fréquence des chutes de roches. Le risque de chute de roche sur cette route en 1982 peut être comparé aux risques acceptables par la société. Pour l'Argillite Cut, les probabilités de décès pour un seul passage d'un usager et pour un passage journalier d'un banlieusard sur cette route étaient de 6 × 10 -8 et 3 ×10 -5 par année. La probabilité annuelle qu'une chute de roche cause un décès dans la population exposée était de 8 × 10 -2 dans l'Argillite Cut. Ceci était plus élevé que le niveau de risque présentement accepté dans certaines industries et dans de grands projets d'ingénierie.
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