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

Xu Zhang, Haiquan Bi (), Honglin Wang, Yuanlong Zhou, Nanyang Yu, Jizhong Yang and Yao Jiang
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Xu Zhang: School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China
Haiquan Bi: School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China
Honglin Wang: School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China
Yuanlong Zhou: School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China
Nanyang Yu: School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China
Jizhong Yang: China Railway Eryuan Engineering Group Co., Ltd., Chengdu 610031, China
Yao Jiang: China Railway Eryuan Engineering Group Co., Ltd., Chengdu 610031, China

Mathematics, 2025, vol. 13, issue 15, 1-21

Abstract: 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.

Keywords: tunnel pressure wave; train wave signature; wave modeling; tunnel modeling; mathematical method validation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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