Hydrological Flow Propagation Models for Complex Tunnel Networks Using the Manning Formula and Graph Theory

Predicting unsteady open-channel flow in complex network systems represents a fundamental challenge in hydrological modeling, with applications ranging from urban stormwater management to infrastructure risk assessment. This study addresses this challenge by developing flow propagation models for water spreading through underground tunnel networks, using mine tunnels as a representative case study. The research considers both single and dual water inrush points in rectangular cross-section tunnels under horizontal and sloped conditions. A graph theory representation of the tunnel network is established, incorporating the effects of flow velocity, wave velocity, and tunnel slope. Based on the Manning formula and continuity equation, propagation models for single and dual water inrush points are developed and solved using Python programming to determine water arrival times at each node and tunnel filling conditions. The methodological contribution lies in systematically integrating Manning-based hydraulic calculations with node-by-node graph traversal algorithms, while explicitly coupling wave velocity with steady flow velocity to estimate wave front arrival times. Results demonstrate that the model produces physically consistent predictions, with dual inrush points increasing the number of affected tunnel sections by 58.5% compared to single-source scenarios. The proposed framework provides a computationally efficient tool for water propagation analysis applicable to various network-based hydrological systems beyond the specific case study presented.