# Full-Scale Experimental Investigation of the Interaction between Trains and Tunnels
## 1 Introduction
### The Overpressure in Tunnel Phenomenon  
The effect of the interaction between the pressure field that surrounds a running train and the air in a tunnel is the generation of pressure waves that propagate along the tunnel at sonic speed. In particular, as can be seen in Figure 1, the entry and the exit of both train nose and train tail in the tunnel generate four pressure waves that move along the tunnel at sonic speed. Furthermore, the pressure inside the tunnel is also perturbed by the pressure field surrounding the train traveling at the same speed of the train. Anytime a traveling pressure wave reaches a discontinuity (i.e., the entrance and the exit of the tunnel, the train itself, another train in the tunnel, vent-hole, caves, etc. ), it is partially reflected, changing its travel direction and its compression/expansion characteristic, and partially radiated [27; 28; 29; 30]. As a result, a large number of pressure waves are generated that cross the tunnel headed in opposite directions, which then interact with each other, producing a complex pressure field. Depending on the tunnel wall roughness, the amplitude of a pressure wave may be reduced at faster or slower rate, while the wavefront may become steeper. If the amplitude and the gradient of the first pressure wave are above certain limits when it reaches the exit, it is partially radiated outside with an audible bang (\"Sonic Boom\") with consequent environmental annoyance [31; 32; 33], which gives rise to the need to reduce speed or modify the geometries by lengthening the nose of trains or the hoods of tunnels [34]. This issue is not the subject of the experimental tests and of this work, since it is not of concern in Italy, at least at the moment. Two of the major factors affecting the compression effect are the high blockage ratio and the low roughness of the track, while the Italian HS lines, as all the tunnels, are of double ballasted track type. In this work, the pressure variations generated by the entrance of a train in a tunnel, the so-called Train-Tunnel Pressure Signature, will be called the Train Wave Signature (TWS). As is shown in Figure 1, three pressure changes characterize this first part:  
* \(\Delta P_{N}\), the sudden and positive leap due to the entry of the train nose in the tunnel;
* \(\Delta P_{FR}\), another increase in pressure with much lower slope due to the friction effects caused by the entry of the train body into the tunnel;
* \(\Delta P_{T}\), the sudden and negative drop generated by the entry of the train tail in the tunnel. Once the train entered the tunnel, the pressure field around it generates another type of pressure variation, which moves in the tunnel with the train (Train Near-field Signature, TNS in Figure 2). The shape of this pressure variation is similar to the TWS, although it has an opposite sign, and the values of the \(\Delta\)P are a bit higher due to the blockage effect of the train. Finally, when the train leaves the tunnel, a second TWS, similar to the first one, is generated that starts to move at sonic speed into the tunnel headed in the direction opposite to the train one. Figure 1: Time-space representation of the pressure evolution within a 1640 m long tunnel crossed by a 200 m long train running at 250 km/h. Solid lines represent the head and tail of the train, the horizontal dotted line represents a sensor at 340 m from the entrance, the dashed lines represent the pressure waves generated by the train. Figure 2: Schematic representation of TWS (Train Wave Signature) and TNS (Train Near-field Signature) measured by the sensor of Figure 1.  
Since the pressure waves propagate along the tunnel at sonic speed and are reflected by the tunnel end, a train running in a tunnel meets the self-generated pressure waves several times during its passage and, furthermore, it could intersect the pressure waves or the pressure field produced by another train crossing the same tunnel.