Application of Stope Wall Convergence to the Design of Sub-Vertical Narrow Vein Orebodies at Depth

Abstract

Narrow vein orebodies, typically less than 3 m in width and hosting high-grade critical metals, present unique geomechanical challenges as mining operations extend to greater depths. Current industry practice relies predominantly on empirical tools, particularly the Mathews Stability Graph and the Equivalent Linear Overbreak/Slough (ELOS) Graph to design open stopes in such settings. However, these methods were originally developed from databases representing wide massive orebodies at depth, and their application to sub-vertical narrow vein geometries introduces systematic errors that can lead to underestimated instability, unplanned dilution, and stope failure. This thesis investigates the hypothesis that stope wall convergence is the dominant failure mechanism in deep sub-vertical narrow vein stopes, and that existing empirical frameworks are fundamentally inadequate as primary design tools for such conditions. The study further posits that a convergence-based design methodology is necessary to address this critical gap. A global database of 59 narrow vein mines was compiled from NI 43-101 Technical Reports and industry studies to characterize typical stope geometries and geomechanical parameters. Finite Element Method numerical modeling was conducted using RS2 and RS3 software (RocScience). Sensitivity analysis examined the effects of K-ratio and stope width on wall displacement, span ratio analysis assessed geometric compatibility with the Mathews Stability Graph, and comparative modeling of squat versus tall stopes evaluated ELOS values and horizontal displacement under equivalent hydraulic radius conditions. Wall convergence increased with rising K-ratio and decreased with increasing stope width, becoming negligible beyond approximately 4 m width, supporting a narrow vein classification threshold of 4 m. Stope span ratio analysis showed that the most of narrow vein stope operate at long-to-short span ratios exceeding 4:1, placing them outside the geometric assumptions of the Mathews Stability Graph database. Comparative modeling revealed that squat stopes exhibit ELOS values greater than tall stopes under the same material properties and stress conditions, alongside approximately 45% higher maximum horizontal displacement in tall stope, challenging the assumption of geometric equivalence in hydraulic radius-based methods, and confirming the dominance of wall convergence concept in narrow vein mines. Stability Graph methods do not adequately represent stability in deep narrow vein stopes and systematically underestimate instability when applied beyond their original scope. Wall convergence is confirmed as the primary failure mechanism. A convergence-based conceptual design chart, relating stability number to stope width and wall closure, was proposed as a more physically representative design framework. Numerical modeling should be incorporated into all narrow vein stope design processes to capture stress distribution, tensile failure zones, and wall convergence behavior. Future work should prioritize expanding the field dataset, developing calibrated site-specific convergence design charts, and exploring hybrid methodologies that combine numerical modeling with empirical approaches to enhance predictive reliability and practical applicability.