Optimizing train entry timing to mitigate pressure waves in high-speed double-track tunnels: A train wave signature-based study

The construction of the railway network is advancing steadily, with a substantial increase in the number of railway tunnels. Among these tunnels, the proportion of double-track tunnels has risen significantly. Along with this trend, the pressure wave superposition effect caused by train crossings in double-track tunnels has become a critical issue, posing threats to the structural integrity of tunnels and passenger comfort. To address this issue, a double-track train wave signature (TWS) model is proposed, based on the principle of characteristic wave superposition. The first part of the paper introduces the principle of the single-track TWS method, outlines the construction of the double-track TWS method, and briefly describes the three-dimensional (3D) numerical model used. The proposed double-track TWS method is then validated through both field measurements and 3D numerical simulations. This is followed by an analysis of the propagation and evolution of wave systems within the tunnel during train crossings. Finally, the paper presents a systematic investigation of tunnel wall pressure amplitude variations resulting from different train entry timings. Key findings indicate that the TWS method achieves sufficient accuracy in simulating tunnel wall pressure for both single- and double-track configurations, with peak-to-peak errors within 10%, except at points near tunnel portals. For double-track crossings at constant speed, the maximum and minimum pressures, as well as peak-to-peak values on tunnel walls, exhibit periodic-like fluctuations with crossing positions. This phenomenon becomes more prominent in shorter tunnels. Moreover, adjusting the entry time difference between trains may even reduce peak-to-peak pressure values on tunnel walls by 50%, offering a theoretical foundation for optimizing train scheduling and tunnel design.