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.
A probabilistic slope analysis methodology based on Monte Carlo simulation using Microsoft Excel and @Risk software is applied to investigate the failure of the Shek Kip Mei cut in Hong Kong. The study demonstrates the techniques used in quantifying uncertainties in shear strength of granitic soils based on a large database of triaxial tests. Probabilistic back-analyses of the failure are applied to estimate the probability distribution of the pore water pressure. Using the back-calculated pore pressure, the inclination of the Shek Kip Mei slope is redesigned to a flatter inclination, and the probability of unsatisfactory performance and reliability index are estimated.
Probabilistic slope stability analysis offers an efficient framework for logical, systematic incorporation of uncertainty into slope design. The slow integration of probabilistic slope analyses into practice is attributed, among other factors, to the lack of published studies illustrating the implementation and benefits of such techniques. A spreadsheet-based, probabilistic slope analysis methodology is applied to evaluate the stability of a section of the Syncrude Tailings Dyke in Fort McMurray, Canada. The dyke is approximately 44 m high and is founded on presheared clayshale. The performance of the dyke is governed by uncertainties about material properties and pore-water pressures. Starting with field and laboratory data, this study demonstrates the techniques used in quantifying the various components of parameter uncertainty, conducting a probabilistic assessment, and estimating the probability of unsatisfactory performance. The probability of unsatisfactory performance of the dyke is estimated to be 1.6 × 103. Field monitoring data indicate that the dyke performance is adequate. The study thus provides a first link between probability figures and performance. The analysis also quantifies the relative contributions of the various sources of uncertainty to the overall uncertainty in the factor of safety.Key words: probabilistic analysis, slope stability, Monte Carlo simulation, spatial variability, tailings dyke, clayshale.
Conventional slope practice, based on the deterministic factor of safety, cannot address the uncertainty in the input parameters of slope analyses in any explicit way. It relies entirely on the subjective judgment of the designer, which varies substantially among geotechnical engineers. Probabilistic techniques are powerful tools that can be used to quantify and incorporate uncertainty into slope analysis and design. A probabilistic slope analysis methodology based on Monte Carlo simulation using Microsoft® Excel and @Risk software is applied to investigate the Lodalen slide that occurred in Norway in 1954. Starting with field and laboratory data, the study demonstrates the techniques used in quantifying the uncertainties in soil properties and pore-water pressure, conducting a probabilistic assessment, and estimating the probability of unsatisfactory performance. The probability of unsatisfactory performance of the Lodalen slope is estimated to be 0.70, indicating that failure was imminent. The inclination of the Lodalen slope is then flattened, hypothetically, to different angles and the relationships between the slope angle, the factor of safety, and the probability of unsatisfactory performance are investigated.Key words: probabilistic analysis, slope stability, Monte Carlo simulation, spatial variability, Lodalen slide.
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