A Mathematical Method for Predicting Tunnel Pressure Waves Based on Train Wave Signature and Graph Theory

Previous research has demonstrated that the Train Wave Signature (TWS) method enables rapid calculation of pressure waves in straight tunnels. However, its application to subway tunnels with complex structural features remains insufficiently explored. This study proposes a generalized mathematical method integrating TWS with graph theory for the simulation of pressure wave generation, propagation, and reflection in complex tunnel systems. A computational program is implemented using this method for efficient simulation. The proposed method achieves high-accuracy prediction of pressure waves in tunnels with complex geometries compared with field measurements conducted in a high-speed subway tunnel with two shafts. We discuss the impact of iteration time intervals on the results and clarify the minimum time interval required for the calculation. Moreover, the sin-type definition of TWSs enhances the precision of pressure gradient prediction, and omitting low-amplitude pressure and reflected waves from the train can improve computational efficiency without compromising accuracy. This study advances the application of TWSs in tunnels with complex structures and provides a practical solution for aerodynamic analysis in high-speed subway tunnels, balancing accuracy with computational efficiency.