Propagation characteristics of tunnel compression waves with multiple peaks in the waveform of the pressure gradient: Part 2: Theoretical and numerical analyses

<jats:p> 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. </jats:p>