Stability Assessment of Rock Slopes: Towards an Inverse-Reliability-Based Methodology

It is paramount that the stability of rock slopes be correctly accounted for under diverse operating and environmental conditions. Owing to different sources of uncertainty entailed in such stability problems, conventional deterministic approach through the calculation of a factor of safety (FOS) cannot reflect quantified uncertainties explicitly and sufficiently. Thus it is highly desirable to invoke the reliability approach to consider uncertainties in a systematic manner. Nowadays, the current design standards have an increasing tendency to ensure rock slope stability by pre-defining a target reliability index (or target probability of failure), viz., the reliability level of a rock slope is pre-set as a target to be satisfied. In such a situation and considering the fact that the FOS used as an indicator of slope performance still has a very wide acceptance, we focus on proposing an inverse-reliability-based methodology which aims at developing a two-fold indicator strategy, i.e., using the FOS and reliability together to deal with slope stability problems. The basic idea behind it is to utilize a so-called inverse first-order reliability method (IFORM) to directly calibrate the FOS provided the target reliability index has been given. In this way, the calibration scheme relating the FOS can be rationally done by not only incorporating uncertainties, but also satisfying a desired level of the prescribed reliability. Based on this, to make the IFORM computationally feasible and also reduce its computational cost, we introduce the response surface method (RSM) to generate a surrogate for the FOS-based limit state function (LSF), considering the lengthy and complicated form of the FOS in some recognized methods (e.g., within the framework of limit equilibrium). Distinguished from the existing RSMs that potential inadequacies may arise, we present an RSM based on a hybrid approach combining support vector machine (SVM; used as a regression technique) and uniform design (UD; pertaining to experimental design). Using a representative example of rock slope stability problem, we demonstrate the feasibility and validity of the developed methodology, during which the associated sensitivity study and further discussion are also performed. By dint of such a methodology, we can establish a link between the conventional deterministic approach and the reliability approach, where a logical and realistic framework is provided, for cases achieving the specified reliability, to assist in selecting the FOS which remains adequate for rock slope stability even in the face of uncertainty.