A high-speed train entering a tunnel generates a compression wave. When the compression wave reaches the exit portal of the tunnel, a micro-pressure wave radiates outward. The magnitude of the micro-pressure wave is approximately proportional to the pressure gradient of the compression wave arriving at the exit portal. As the micro-pressure wave can cause environmental problems, tunnel entrance hoods have been installed at many portals of long slab track tunnels on the Japanese high-speed railway, the Shinkansen to reduce the magnitude of the micro-pressure wave. In this study, field measurements were taken in a Shinkansen long slab track tunnel with a hood at its entrance. The compression wave distorts during its propagation through a long slab track tunnel. The dependence of the propagation characteristics on the initial compression waveform was clarified on the basis of field measurements on different trains and hood window configurations. It was shown that compression waves with a waveform of the pressure gradient that has shallow valleys tend to steepen more easily and that the optimum window pattern of the hood depends on the length of the tunnel. Furthermore, a mathematical model corresponding to the results of the field measurements was proposed to describe the distortion of the compression waves.

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A high-speed train entering a tunnel generates a compression wave that propagates through the tunnel toward its exit. When the compression wave reaches the tunnel exit, a pressure pulse causing environmental problems (the micro-pressure wave) is radiated from the exit portal. The magnitude of the micro-pressure wave is approximately proportional to the maximum pressure gradient of the compression wave arriving at the tunnel exit. In a long Shinkansen tunnel with concrete slab tracks the compression wavefront steepens due to the nonlinear effect during its propagation because the whole surfaces of the tunnel being smooth. Hence, it is necessary to investigate the distortion of the compression wave in a tunnel and clarify the characteristics of compression wave propagation for estimating and reducing the micro-pressure wave. In this paper, we introduce a new simple equation governing the distortion of the compression wave propagating through a Shinkansen tunnel with concrete slab-tracks and propose a new simple scheme for a numerical calculation. A space evolution type equation with one variable is derived from the three conservation equations (mass, momentum, and energy including the wall friction and heat transfer terms) of the 1D CFD by assuming small disturbances excited by the compression wave. The numerical calculation scheme based on the simple equation remarkably reduces the computing time because its CFL condition is relaxed. The calculation results by the present scheme agree well with those by a conventional scheme based on the 1D CFD and the accuracy of the simple equation is verified.

This paper is the second part of a two-part study on the propagation characteristics of compression waves generated by a train entering a long slab track tunnel with a tunnel entrance hood, which generates a tunnel compression wave with multiple peaks in the waveform of its pressure gradient. In Part 1, we described field measurements on the propagation characteristics of the compression waves generated by Shinkansen trains in a 9.7-km-long tunnel, and we compared the results with those of simulations. It was shown that initial waveforms whose pressure gradient waveforms have shallower valleys tend to steepen more easily, and a mathematical model of the distortion based on the field measurements using a quasi-laminar friction model was proposed. This follow-up report describes the theoretical and numerical analyses conducted on the basis of the mathematical model. Initial waveforms of the pressure gradient that have no valleys and are higher on their right-hand side grow up easily during propagation; this is due to the unsteady friction being small in the region where the magnitude of the second time derivative of the pressure is small. This results in a dependence of the propagation characteristics on the initial waveform of the compression wave.