Probabilistic assessment of rock slopes stability using the response surface approach – A case study

Abstract

This paper examines the stability condition of a jointed rock slope in the south western region of Saudi Arabia using deterministic and probabilistic approaches, under both dry and wet conditions. The study area is characterized by complex geology in rugged terrains. The stability analysis is carried out using the code FLAC3D to generate a 3-dimensional, ubiquitous joint model, to determine the influence of the dominant, unfavourable discontinuity orientation with respect to the slope face. The deterministic analysis is first implemented using the mean values of the selected random variables, namely the dip, dip direction and friction angle of the dominant discontinuity set, and the stability condition is assessed with a factor of safety based on the classical frictional joint constitutive model. A Box-Behnken design (BBD) approach is then adopted to create the surface response function as a second order polynomial for the factor of safety. To do so, fifteen FLAC3D models are generated in accordance with the BBD. Based on this, 10,000 simulations of different slope realizations are carried out using Monte-Carlo simulation technique, and the probability of unsatisfactory of performance of the rock slope is assessed. It is shown that the probabilistic approach provides more insight and confidence in the stability condition of the rock slope, both under dry and steady state heavy rainfall conditions. A discussion is presented on the significance of accepting lower safety factors when heavy rainfall conditions are encountered. Keywords: Rock slope stability, Box-Behnken design, Probabilistic analysis of slopes, Response surface