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UBC Theses and Dissertations

Probabilistic assessment of rock slope stability using response surfaces determined from finite element models of geometric realizations Shamekhi, Seyedeh Elham


A new methodology for probabilistic rock slope stability assessment was developed. This methodology enables the analyst to estimate the probability of failure by incorporating the variability of the geometric parameters such as joint orientation and trace length in the stability analysis. This improves the reliability of any future design, remedial action or risk assessment. Although incorporating the variability of material strength parameters into numerical models is common in geotechnical engineering, similar analysis is very challenging when geometric parameters such as dip, dip direction, and trace length are considered non-deterministically. The challenge is related to mesh generation required for each numerical model as the geometric parameters change, resulting in high computational effort. For practical stability assessment, a representative yet computationally efficient number of realizations or numerical models is required. Therefore, commonly used sampling techniques such as the Monte-Carlo method that generate a large number of slope realizations cannot be used. The new methodology uses the Point Estimate Method to substitute each probabilistic variable by its two point estimates. As the number of probabilistic input parameters increase, the number of point estimates, and accordingly the number of realizations to be modeled, increase exponentially. To compensate for this problem, the methodology uses a ‘design of experiment’ framework to minimize the number of representative realizations needed. While Phase² finite element software is used in this thesis, the methodology is flexible and can be used to increase the efficiency of other numerical tools that require re-meshing to accommodate changes in geometric parameters. The developed methodology was evaluated for two different slope configurations. Analysis of variance was implemented to identify the significant parameters affecting the factor of safety. To estimate the probability of failure, central composite design was used to generate more realizations of the significant parameters and to fit response surfaces to the factor of safety values. A method is presented to select the most accurate response surface to estimate the probability of failure. This response surface can be used to predict the stability behaviour of any arbitrary geometric realization of the slope without the need for further numerical modelling. The sensitivity of the methodology to the selection of the initial point estimates was investigated and was shown to be unbiased.

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Attribution-NonCommercial-NoDerivs 2.5 Canada