# Flexural Wave Propagation and Defect States of Periodic Slab Track Structure in High-Speed Railway
## 2 Flexural Wave Analysis Model for Unit Slab Track Structure  
The CRTS III slab track structure has been extensively employed in China's high-speed railway systems. Due to the periodic characteristics of the track structure, the unit cell includes the rail, fastening system, slab, self-compacting concrete (SCC) layer, isolation layer, and baseplate within the range of a single slab, as illustrated in Figure 1. The track slabs include prefabricated components integrated with cast-in-place SCC to form a composite layer during on-site construction. After long-term service, since the SCC layer is a post-cast structure, typical defects can be found such as breakage, debonding between the SCC and the track slab, and inadequate SCC layer filling. These localized damages disrupt the periodicity of the ballastless track structure. Considering the multiple periodic characteristics of the track structure, taking the CRTS III slab track structure as the research object, the flexural wave propagation model for periodic slab track is established and the supercell method is developed for the propagation of elastic waves in periodic track structures with defects. In the supercell with length \(L_{\text{s}}\), the defective cell is centrally located, bordered by a certain number of non-defective cells on both sides, as shown in Figure 2.  
In the CRTS III slab track system, the rails are constructed from metal, while the slabs, SCC, and baseplates are fabricated from concrete. The fastening assembly in the slab track comprises clips, spikes, flat washers, insulating blocks, gauge blocks, rail pads, iron pads, elastic pads beneath the iron pads, and pre-embedded sleeves situated within the track slabs. Isolation layers are generally composed of geotextiles, with polyurethane or rubber materials employed in areas necessitating vibration mitigation. Consequently, the predominant source of structural elasticity is attributed to the fastening system and the isolation layer. In the model, the rail and composite slabs are denoted by beams, while the fastening system and isolation layer are represented by spring elements. The unit cell of the slab track structure is the length \(L\) of one slab, which includes periodically supported rail with a fastening spacing of \(d_{\text{r}}\), and uniformly distributed springs representing the isolation layer beneath the composite slab. The unit cell contains \(N_{\text{r}}\) fastenings and \(N_{\text{s}}\) isolation layer springs. This takes into account the local defects arising from damage to the SCC layer, where the length of the local defect is \(l_{D}\), simulated by the failure of springs. Due to the presence of multiple discrete support characteristics within the structure, solving the wave equations using the transfer matrix method (TMM) becomes challenging. Furthermore, the TMM is unsuitable for large-sized structures and high-frequency analysis, as it is prone to matrix ill-conditioning [36]. The Floquet transform method enables the  
Figure 1: CRTS III slab ballastless track structure and its unit cell: (**a**) Picture of the real object; (**b**) components within the unit cell; (**c**) cross section of the slab track and its typical dimensions. Figure 2: Supercell model of slab track with local defect. analysis of infinite periodic structures within a single cell and effectively mitigates matrix ill-conditioning problems.