Probabilistic analysis of rock slope stability and random properties of discontinuity parameters, Interstate Highway 40, Western North Carolina, USA

Probabilistic analysis has been used as an effective tool to evaluate uncertainty so prevalent in variables governing rock slope stability. In this study a probabilistic analysis procedure and related algorithms were developed by extending the Monte Carlo simulation. The approach was used to analyze rock slope stability for Interstate Highway 40 (I-40), North Carolina, USA. This probabilistic approach consists of two parts: analysis of available geotechnical data to obtain random properties of discontinuity parameters; and probabilistic analysis of slope stability based on parameters with random properties. Random geometric and strength parameters for discontinuities were derived from field measurements and analysis using the statistical inference method or obtained from experience and engineering judgment of parameters. Specifically, this study shows that a certain amount of experience and engineering judgment can be utilized to determine random properties of discontinuity parameters. Probabilistic stability analysis is accomplished using statistical parameters and probability density functions for each discontinuity parameter. Then, the two requisite conditions, kinematic and kinetic instability for evaluating rock slope stability, are determined and evaluated separately, and subsequently the two probabilities are combined to provide an overall stability measure. Following the probabilistic analysis to account for variation in parameters, results of the probabilistic analyses were compared to those of a deterministic analysis, illustrating deficiencies in the latter procedure. Two geometries for the cut slopes on I-40 were evaluated, the original 75° slope and the 50° slope which has developed over the past 40 years of weathering.