## 1 Introduction  
Since the emergence of heavy-haul railway transportation in the middle of the 20 th century, it has been widely valued by railways around the world, and has developed rapidly due to its large capacity, high efficiency, and low cost [1, 2, 3]. Traditional ballasted track structures have gradually been unable to meet the functional needs of heavy-haul railways in special sections, such as long tunnel segments, as Chinese standards for heavy-haul railway transit efficiency have improved. Therefore, the research and application of a new-type of ballastless track structure for heavy-haul railways has gradually become a major development direction of Chinese railways [4, 5]. Simultaneously, as Chinese railway construction progresses, mainline railway will be capable of carrying trains traveling at speeds higher than 200 km/h, and more and more long tunnels are advised to apply ballastless tracks [6]. Ballasted tracks are commonly used in the subgrade section of heavy-haul railways, but the tunnel section is affected by the limitation of section clearance and the inconvenience of maintenance [7,8]. The transportation of coal and other materials frequently requires passing through long tunnels, the \"Guiding Opinions on Optimization of Railway Engineering Design Measures\" [9] proposed that for the tunnels exceeding 1 km, the section of the tunnel group should adopt the ballastless track structure, in order to ensure the clearance and ventilation in the tunnel, as well as the long-term stability of the track structure. In this context, low vibration track (LVT) has gradually gained attention in the selection of ballastless tracks in heavy-haul railway tunnels due to its excellent damping performance [10,11], as shown in Figure 1. Since LVT has a double-layer damping structure, consisting of under-rail rubber pads and under-block rubber pads, compared with other types of track structures, it can greatly reduce the impact of heavy-haul trains. Therefore, the LVT is to be applied in the Xikang railway, Qinling railway tunnel, Yiwan railway, Xiangyu railway and other long railway tunnels in China [12]. LVT was first tested in the Swiss National Railway Tunnel in 1966 and since then, Denmark, Britain, France, Portugal, and other countries have successively laid this kind of track. There are also many kinds of LVT in Chinese subway tunnels and long tunnels, such as the Qinling Tunnel, Wushaoling Tunnel, and Yindongpo Tunnel. LVT has good elasticity, but the supporting blocks are independent of each other, which may cause a bad dynamic between the wheel and rail and risk rail displacement under heavy loads if the  
Figure 1: Heavy-haul train and LVT scene in the tunnel. (**a**) Design diagram of LVT section in tunnel and (**b**) LVT construction scene in the tunnel. train is larger [13]. If the track stiffness is too low, it may cause the track dynamic geometric deviation to exceed the limit under high-speed running conditions, which will affect the safety and comfort of running [14; 15]. Therefore, LVT is limited to railways operating at speeds below 200 km/h, and in China it is limited to railways operating at a speed of 120 km/h. In order to conduct research on the application of LVT in heavy-haul railways, it is necessary to consider the basic parameters of the under-rail and under block that affect the dynamic characteristics of the vehicle-track vibration system. The changes in the stiffness of the fasteners, the stiffness of the track bed, and the sleeper spacing directly affect the vibration of the system, and different parameters have different effects on the vibration of the system [16]. Therefore, the analysis of the basic parameters under the track is of great significance to improve the running performance of the train. Among them, parameter analysis varies the value of a parameter under the assumption that other parameters remain unchanged to obtain different responses, so that the parameters can be reasonably selected by analyzing the relationship curve between the response and the parameter [17].