Application of Fuzzy Sets to Geological Strength Index (GSI) System Used in Rock Slope

The stability assessment of slopes is difficult because characterization of rock masses and determination of their strength involve many uncertainties due to their complex nature. The fuzzy set theory is one of the tools to handle such uncertainties. And the difficulty can be overcome by using the Hoek-Brown empirical failure criterion in conjunction with the Geological Strength Index Classification System and fuzzy sets to express the uncertain parameters. For the stability assessment of slopes, a methodology has been presented in the study to process the fuzzy uncertainties in a slope reliability analysis. Simplified Bishop's method and interval theory were used to calculate the safety factor intervals with α-level intervals. The slope failure possibility was obtained by non-probabilistic fuzzy reliability analysis method and the possibility theory. In addition, a numerical example of slope instabilities in heavily jointed rock masses was analyzed and the result was evaluated to demonstrate and to check the performance of this approach. Its failure possibility is zero, which matches well with the result 0.12% of Monte Carlo method.