# Flexural Wave Propagation and Defect States of Periodic Slab Track Structure in High-Speed Railway
## 1 Introduction
Slab cracking and interlayer separation under temperature loads are predominant damages in longitudinally connected ballastless track structures. In contrast, unit slab ballastless track structures mainly exhibit local damage to the mortar layer and contact loss between layers. Temperature deformation during the construction of ballastless tracks [PERSON] et al. (2016) and factors such as train loads, temperature fluctuations, water ingress, and foundation deformation during the operational period are important causes of damage to ballastless tracks [PERSON] et al. (2016); [PERSON] et al. (2016). In response to typical interlayer defect issues in ballastless track structures, [PERSON] et al. (2016) conducted experimental investigations to analyze the variation of interlayer separation between track slabs and CA mortar under different temperature effects in CRTS I slab track structures. [PERSON] et al. [PERSON] et al. (2016) obtained interface failure characteristics between the track slab and self-compacting concrete by performing static and fatigue splitting tensile tests, indicating that most interface failures were mortar failures and mortar-aggregate bond failures. [PERSON] et al. [PERSON] et al. (2016) explored the influence of interlayer separation in CRTS II slab ballastless track structures on the dynamic response of the vehicle-track system dynamics. The results indicated that interlayer separation has a minor impact on the stability of train operation but a pronounced effect on the response of the ballastless track structure. [PERSON] et al. [PERSON] et al. (2016); [PERSON] et al. (2016) studied the development characteristics of CA mortar damage under train loads and its impact on service performance, combining dynamic modeling and reliability methods, the limit values for different levels of separation between track slab and CA mortar were proposed. [PERSON] et al. [31] investigated the performance of CRTS III slab ballastless track structures under fatigue loads based on a full-scale experiment, discussing the dynamic response of the structure under different interlayer separations using finite element simulation. [PERSON] et al. [32] established a vehicle-track dynamic analysis model using Simpack to study the separation between track slabs and mortar layers in CRTS II type slab ballastless track, the influence of different separation lengths and heights on the dynamic response was discussed, and maintenance and repair control limit values were proposed. [PERSON] [33] analyzed the structural response characteristics of slab ballastless tracks after contact loss between layers using the finite element method and proposed a defect identification method by integrating the structural response during train passage and impact hammer tests. Interlayer defects within ballastless track structures can additionally result in mud pumping and dynamic geometric irregularities [34]. Subsequently, as the defect continues to deteriorate, the stability of train operation is diminished. Unit slab ballastless track structures have been widely implemented in high-speed railways due to their favorable environmental adaptability and construction convenience [21]. There are multiple features consisting of periodically distributed fastenings and periodic prefabricated slabs, which possess more special wave motion properties. On the other hand, the presence of local defects disrupts the periodicity of the track structure, modifying the propagation of elastic waves and generating elastic wave defect states. Investigating the propagation characteristics of elastic waves in defective unit slab ballastless track structures will provide a theoretical foundation for the vibration and damage mitigation of track structures. Prior investigations concerning the wave behaviors and defect states of track structures tend to have oversimplified analytical models. For example, Reference [35] employs a model of a beam with discrete supports to examine defect states resulting from fastening and sleeper damage.