Persistent Homology Reveals Loop Hierarchy and Recirculation Risk in Underground Mine Ventilation Networks

Abstract

Underground mine ventilation sustains safe working conditions by supplying fresh air, diluting contaminants, and controlling heat and humidity throughout active workings. Because air moves through a connected system of shafts, drifts, and raises, the ventilation problem is inherently one of network flow-and in large mines, that network can grow complex enough that standard simulation tools, while numerically reliable, leave engineers with little guidance on which circuits matter most, which redundancy is structurally meaningful, and where recirculation risk is concentrated. We address this gap by developing a physics-guided topological workflow that layers three complementary analyses: a physical graph filtration on real airway adjacency, an adjacency-preserving flag complex companion, and resistance-geodesic Vietoris-Rips persistent homology. The physical graph filtration preserves all existing airway circuits, the flag complex applies a stricter structural test through clique completion, and the resistance-geodesic branch recasts the network as an operational metric space in which loop persistence is governed by cumulative airway resistance. Together, these three branches distinguish circuits that physically exist in the mine from those that remain topologically persistent once resistance is taken into account.
The framework was applied to Montana Tech's Underground Mine Education Center (UMEC) under two operating conditions—natural ventilation and main-fan-assisted flow with two auxiliary fans off—using field-calibrated Ventsim models as the network basis. Under natural ventilation, two persistent H1 loops emerged, with the southern circuit nearly an order of magnitude stronger than the upper loop; under fan assistance, the upper loop disappeared entirely, leaving only the southern circuit. The disappearance of the upper loop is physically coherent-the exhaust fan draws air outward through that branch, preventing it from sustaining a closed resistance-informed circuit. The southern loop's persistence across both operating states identifies it as the network's most structurally stable redundancy candidate and the strongest target for recirculation-focused engineering attention. These results demonstrate that persistent homology can complement conventional ventilation analysis by providing a grounded, resistance-informed method for ranking loop structures according to recirculation potential.