Development of Coupled FEM and Fuzzy Rules–Based Procedures for Mitigation of Uncertainty in Forecasting Stability of Underground Pillars

Stability of underground working depends on geomechanical properties of rocks as well as geometrical and operational parameters of excavation. In this study, a fuzzy rule-based method, minimizing the subjectivity in rock engineering system (RES) is proposed to address the uncertainty in determining stability of underground pillars. A total of 243 elastoplastic 3D numerical models are analyzed by varying attributes of five input (leading) variables: (1) rock mass strength, (2) depth (in situ stress), (3) height of excavation (stope), (4) sequence of excavation with or without filling, and (5) crown pillar thickness. Interaction matrix between the leading input variables are evaluated using fuzzy “IF–THEN” rules considering the results of finite-element models (FEMs) and the “cause–effect” plot of the variables are also determined. Average equivalent plastic strain (EPS) over two consecutive pillars is the target output variable indicating the stability of the excavated zone (stope)–pillar system. Results of FEMs are plotted in the existing stope stability number graph and show that $\overline{\mathrm{ESP}}\approx 0.06-0.07$ denotes the boundary between “stable” and “transition” zone and $\overline{\mathrm{ESP}}\approx 0.09-0.1$ represents the boundary between “transition” and “caved” zone. A rib pillar stability index (RPSI) is formulated based on the vulnerability of a pillar for the evaluation of $\overline{\mathrm{EPS}}$ indicating the “stable” or “unstable” condition. Results show that plastic strain decreases exponentially with increasing RPSI having R² of 0.824. The proposed concept is applied to determine the stability of stopes of a hard rock mine by estimating RPSI and $\overline{\mathrm{EPS}}$ and finds that they are placed in “stable” zone for the given geomining conditions.