Fuzzy set approaches to classification of rock masses

Rock mass classification is analogous to multi-feature pattern recognition problem. The objective is to assign a rock mass to one of the pre-defined classes using a given set of criteria. This process involves a number of subjective uncertainties stemming from: (a) qualitative (linguistic) criteria; (b) sharp class boundaries; (c) fixed rating (or weight) scales; and (d) variable input reliability. Fuzzy set theory enables a soft approach to account for these uncertainties by allowing the expert to participate in this process in several ways. Hence, this study was designed to investigate the earlier fuzzy rock mass classification attempts and to devise improved methodologies to utilize the theory more accurately and efficiently. As in the earlier studies, the Rock Mass Rating (RMR) system was adopted as a reference conventional classification system because of its simple linear aggregation.

The proposed classification approach is based on the concept of partial fuzzy sets representing the variable importance or recognition power of each criterion in the universal domain of rock mass quality. The method enables one to evaluate rock mass quality using any set of criteria, and it is easy to implement. To reduce uncertainties due to project- and lithology-dependent variations, partial membership functions were formulated considering shallow (<200 m) tunneling in granitic rock masses. This facilitated a detailed expression of the variations in the classification power of each criterion along the corresponding universal domains. The binary relationship tables generated using these functions were processed not to derive a single class but rather to plot criterion contribution trends (stacked area graphs) and belief surface contours, which proved to be very satisfactory in difficult decision situations. Four input scenarios were selected to demonstrate the efficiency of the proposed approach in different situations and with reference to the earlier approaches.