## 4 Discussion
### Evolution of Failure
#### 4.1.2 Fractures of BTC  
Figure 8 shows the load-displacement curves and the corresponding maps of \(U\) in BTC tests. The initiation and propagation of cracks in the discs could be determined by observing the development of the horizontal displacement resulting from the DIC. In the BTC-01 test, the distribution of \(U\) was approximately symmetrical along the vertical central line when BTC-01-a approached the peak force, as shown in Figure 8c. With a careful observation, the crack initiated from the upper loading point at the boundary and then propagated from the upper boundary to the centre of the disc as shown in Figure 8d. At the same time, another crack was also observed at the downside of the disc centre near the bottom steel plate at the time of BTC-01-b. Then, the crack propagated through the disc and the two fracture patterns extended oppositely, as shown in Figure 8e. According to Figure 5a, the final fracture profiles of the BTC-01 test also revealed the serious damage of the sample near the loading point. Consequently, it was determined that fractures did not initiate at the centre of the disc but at the boundary in the BTC-01 test. By contrast, it was found that the crack formed at the centre of the disc in the BTC-03 test as shown in Figure 8f-h. Based on the above, it can be concluded that the initiating location of cracks is uncertain without recording and analysing the fracture process in Brazilian tests with the central loads at the boundaries.  
Figure 7: Comparing the initial location of cracks on the surface of discs in BTC (BTC-03) and BTD (BTD-03) by examining the deformed images (**a**,**d**), images of the horizontal displacement U (**b**,**e**), and the horizontal tension strain \(\varepsilon_{x}\) (**c**,**f**) at the occurrence of the first crack.  
Interestingly, in the BTC-03 test, although the load had already passed its peak and started to decrease to zero quickly, the crack had not yet crossed through the central line at the time of BTC-03b. This proved that the propagating speed of the crack initiating at the centre of the disc was significantly lower than that of the crack at the boundary. Figure 9 shows the horizontal strains of \(\varepsilon_{x}\) at the centre of the disc and near the boundaries. In the BTC-01 test, the \(\varepsilon_{x}\) of \(P_{up}\) increased more than that of \(P_{0}\) and \(P_{down}\) as shown in Figure 9a, indicating that the concrete connecting to the upper steel plate was compressed and crushed first, which led to the crack initiating at the upper boundary. However, in the BTC-03 test, the \(\varepsilon_{x}\) of \(P_{0}\) increased sharply first, which meant the crack initiated at the centre of the disc as shown in Figure 9b. There was a clear gap of about 3 s between the history curves of \(P_{0}\) and \(P_{up}\) at the time of the crack forming, with a sharp increase in the strain (see Figure 9b). However, the cross-through time of the crack in the BTC-01 test was quite shorter than 0.2 s. These results demonstrated that the propagating speed of the crack at the centre of the disc was lower than that at the boundary of the disc in the BTC.  
Figure 8: The load–displacement curves of the BTC-01 (**a**) and BTC-03 (**b**) tests and the developing maps of \(U\) to determine the initiation and propagation of cracks in the BTC-01 (**c–e**) and BTC-03 (**f-h**) tests corresponding to the upper load–displacement curves.