The aim of this work is to establish the response surface modeling (RSM) approach as a practical means to carry out probabilistic analysis of rock slopes with computationally intensive, large-scale numerical models that have proven reliable for assessing stability in complex, large open pit operations but which require considerable running time to estimate sufficient factor of safety (FoS) intervals. When compared to other well-established techniques such as Rosenblueth's Point Estimate Method (PEM), RSM
facilitates the inclusion of a greater number of random variables,
enables the sensitivity of individual variables to be readily ascertained,
better translates such sensitivity into response skewness and
allows for input variables to be characterized by explicit distributions based on sample histograms.
This research centers on evaluating the three-variable probability of failure (PoF) response for two slope geometries through both RSM and PEM in order to establish the applicability of response surface modeling to real-world analysis scenarios. FoS estimations were undertaken in a 3DEC  model of similar complexity to those currently employed in assessing stability for mine plans. The results show that the RSM approach renders comparable results to PEM and that, provided proper estimation points are used, differences can be attributed to a better representation of the output distribution. Further modeling is also done to demonstrate PoF estimations with five random variables, a task which could not be reasonably contemplated by applying the point estimate method. The impact of analysis decisions such as estimation points and input variable probability density functions (PDFs) is further illustrated by means of a simple 2-variable model which allows for PoF to be attained through closed form solution or estimated through Monte Carlo simulation.
The probability of failure (PoF), defined as the likelihood that the demanding forces will exceed resisting forces and the slope will be unstable, is perhaps the most common probabilistic slope stability criterion.