# A Quantitative Detection Method for Surface Cracks on Slab Track Based on Infrared Thermography
## 4 Case Study  
### Model Test  
To verify the effectiveness of the proposed algorithm, we conducted a laboratory test, in which a slab-track model was used. Considering that the actual size of the slab track (6.45 m long, 2.95 m wide along the concrete base, and 0.53 m high) was large, a scaled model of the track slab which could reflect the real temperature field of the slab under different conditions was used. (1) Size of the scaled model  
To determine the size of the scaled model, we used finite element (FE) simulation, though which the temperature field of the track slab was simulated. The relevant environmental parameters, boundary conditions, and model verification are given in [5]. A crack with a width of 0.2 mm and a depth of 20 mm was added to the slab surface, as shown in Figure 10.  
Figure 9: Slab-track structure and design cracking joint (DCJ). For the length of the track model, the track slab was a longitudinal concrete structure, and the size of the track slab in the length direction was much larger than that in the height and width direction. Furthermore previous studies [25,26] also ignored the heat transfer in the longitudinal direction when studying the temperature field of slab-track structures and simplified it into a two-dimensional heat-transfer structure. In this regard, to determine the length of the track model, in this study, we performed a large number of trial calculations. Based on the results of the trial calculations and [27], the length of the track model was set to 1.272 m.  
After the determination of the model length, the influence of the height and width on the temperature field of the track slab was further analyzed. In this study, the 1:3, 1:4, and 1:5 scale models (in both height and width direction) were chosen in the temperature calculation, and the other input parameters lowered ran from [5]. The temperature values in the crack and non-crack areas on the track-slab surface at different times are shown in Figure 11.  
Figure 11: Temperature in crack and non-crack areas on the surface of track slab: (**a**) in non-crack areas with different width scales; (**b**) in crack areas with different width scales; (**c**) in non-crack areas with different height scales; (**d**) in crack areas with different height scales. Figure 10: Diagram of structural model of slab track with surface crack. It can be seen from Figure 11 that when the reduction ratio of the scaled model in the width direction or height direction was larger (i.e., 1:3 scale), the temperature in the crack and non-crack areas on the slab surface had smaller errors with the full-scale model; the error caused by the height reduction is greater than that caused by the width direction. Therefore, the scale in the width direction was set to 1:3, i.e., 0.85 m; the height of the model was set to 0.53 m, the same size as the full-scale model. Table 2 lists the calculation results for the temperature with the scale model and the full-scale model, as well as the error of the scale model (compared with that of the full-scale model). It was found that the maximum error of the temperature in the scale model in the non-crack areas was 2.12%, and the average error was 1.41%; the maximum error in the scale model in the crack areas was 2.26%, and the average error was 1.46%. Therefore, it can be concluded that the scale model can effectively show the surface-temperature field of an actual slab track, and it can be used to validate the thermal imaging detection of surface cracks. In this test, the scale model of the track slab was produced according to the parameters specified by the China High-Speed Railway. The materials of the track slab, bearing layer, and CA mortar layer and their corresponding coordination are listed in Table 3. Figure 12 shows the scale model after curing.