# An Improved Cohesive Zone Model for Interface Mixed-Mode Fractures of Railway Slab Tracks
## 5 Application  
Interface damage, which even happens in the construction phase, has become a major problem for China Railway Track System (CRTS-II) slab track. To reveal the behavior of the slab track under the difference of temperatures, the effect of daily changing temperature on the curling behavior and interface stress of slab track in the construction stage was researched by the authors [2]. As a follow-up study, the interface damage of slab track under daily changing temperature is analyzed by implementing the improved cohesive zone model in this section.  
The CRTS-II slab track consists of precast slab, CA mortar, and concrete base, as shown in Figure 19. All of these components are modeled according to actual size. The dimensions, material properties, mesh, FE element type, and boundary conditions of each component are all the same as in [2]; those items are not covered again here.  
Interface cracks usually occur between the track slab and CA mortar, as shown in Figure 1. The interlaminar cracking is modelled based on the constitutive model proposed in this paper, by using the commercial software ABAQUS with a user-defined interaction (UINTER) subroutine. The validated interface parameters [42] are \(\phi_{n}=2.6\) N/m, \(\phi_{t}=4\) N/m, \(\sigma_{max}=0.015\) MPa, \(\tau_{max}=0.015\) MPa, \(\alpha=2\), \(\beta=2\), \(\lambda_{n}=0.1\) and \(\lambda_{t}=0.1\). Due to symmetry of the geometry and loading conditions, only a quarter of the slab track is established. The 3-D finite element model of CRTS-II slab track is built as presented in Figure 20.  
Based on the proposed model, the interface damage is simulated under gravity load and measured temperature. The measured temperature was input into the model as temperature load using user-defined subroutines named UTEMP [2]. In the analysis, the summer temperature (Figure 9 in [2]) is taken as an example. As the initial stress field has an influence on the stress history and stress level, the time of 14:30 with the maximum temperature difference is selected as the starting time.  
Figure 21 shows the interface crack opening (COPEN) distribution of the slab track system as a result of temperature change. It is found that the damage at four corners is the most obvious. Such damage mode is exactly the same as that observed in high-speed railway lines.  
The normal and the two shear stresses of the interface at the slab corner are shown in Figure 22. It can be observed that the interface damage is mainly caused by the presence of normal and lateral shear stresses. It is worth noting that the stresses change smoothly for the model proposed in the paper and PPR model, while piece-wise continuously for the cohesive zone model in ABAQUS. Moreover, the problem of self-repair for the PPR model is found in Figure 22b,c. The cause was mentioned before.  
Figure 23 shows the interface normal stresses (CPRESS) between the slab and CA mortar layer when interface cracking happens. It is found that the stress distribution for the model proposed in the paper and PPR model is almost the same, and continuously changes with location. However, that for the cohesive zone model in ABAQUS is rugged and unreasonable. For example, the tensile and compressive stresses occur simultaneously around slab corner. This may be due to the stress oscillation [33].  
Figure 19: CRTS-II slab track system components before longitudinal connection.  
Figure 20: The finite element model of CRTS-II slab track before longitudinal connection (1/4 model).  
Figure 19: CRTS-II slab track system components before longitudinal connection.  
Figure 22: Interface stresses of slab corner varying with time: (**a**) normal stress, (**b**) longitudinal shear stress, and (**c**) lateral shear stress.