# Dynamic Response of a Heavy-Haul Railway Tunnel's Bottom Structures in Hard Rock
## 1 Introduction  
A heavy-haul railway has the remarkable advantages of large traffic volume, low cost and high efficiency; thus, countries all over the world are competing to increase the axle load of freight railways [1, 2]. However, the tunnel bottom structure is no longer capable of dealing with the long term impact of heavy-haul trains, as base diseases increase with the increase in axle load [3]. High traffic density, short maintenance intervals and limited working space are the distinguishing features of heavy-haul railway tunnels in China. After decades of operation, tunnel-base diseases are increasing over time in the Daqin heavy-haul railway (445 million tons in 2013 [2]), such as structure cracks, subsidence and soil pumping. Serious foundation subsidence and base rock voids have also been found in the Shuohuang [4] and Wari [5] heavy-haul railways, two other famous heavy-haul railways in China. Most base deterioration is appearing on the side of the full-load track [6], which aggravates the rail irregularity and threatens the safety of the train operations [7, 8]. Thus, the study of the dynamic response of the tunnel structure under the heavy-haul train load is essential, especially the heavy-haul railway tunnel with a heavy axle load, high train density and thin and vulnerable base structure [9]. In general, the thicknessand strength of the tunnel structure are dominated by the surrounding rock. The better the surrounding rock, the smaller the surrounding rock pressure, and the corresponding structural thickness of the tunnel will be designed thinner [10; 11]. Generally, scholars believe that the worse the surrounding rock conditions are, the higher the possibility of basement diseases in the tunnel [12]. However, according to the survey results after decades of operation, base diseases occur not only in soft rock areas [13], but also in hard rock [14]. Compared with the seismic response [15; 16; 17], the dynamic response of tunnel structures caused by trains is much smaller [18; 19; 20]. Although, due to the constraint of the surrounding rock, the seismic performance of the tunnel structure is better than that of the ground structure in seismic areas [21; 22; 23], the seismic response will still cause immediate and significant damage or deformation to the tunnel structure [24; 25]. In addition, the vibration of the tunnel structure caused by the train is often small and frequent; thus, the degradation of the tunnel bottom structure is gradual rather than immediate [19; 26]. Nevertheless, progressive degradation of the base is emerging in more and more heavy-haul railway tunnels as the axle load of the trains increases [27; 28; 29]. The field measurement of the Sanjiacun Tunnel in the Shuohuang railway system shows that, under the 21 t axle-load train, the vertical dynamic stress on the bottom surface is 61.6 kPa, and the maximum value of dynamic response is directly below the rail, on the side close to the center line of the tunnel [4]. Not only do the axle load and surrounding rock conditions have a significant impact on the dynamic response of the tunnel basement structure [30; 31], but the influence of the base support conditions also cannot be ignored. Through numerical simulations and tests, [PERSON] et al. [32] indicate that the cavity in the base rock performs multiple adverse effects on the mechanical performance of the substructure. [PERSON] [33] found that the loose base rock will cause the maximum principal stress of a tunnel's inverted arch to increase sharply. [PERSON] et al. [34] stated that the base void increased the tunnel bottom structure's dynamic response significantly. [PERSON] et al. [35] studied the dynamic response of crossing tunnels under a heavy-haul train load, and the results revealed that the vibration of the intersection is more significant than the vibration of the common section because of the presence of the lower tunnel (like a void). The research on the dynamic response of tunnels is mainly focused on tunnel bottom structures with poor surrounding rock [13; 31; 36].