## 3 Results and Discussion
### Determination of the Frost-Heave Crack Propagation Law
#### 3.1.2 Crack Frost-Heave Propagation Process AE and DIC Comparison  
The purpose of this section is to compare the AE and DIC results under the same test conditions for more convincingly verify the correctness of using the crack tip surface strain to study the frost-heave crack propagation process. Due to space limitations, this subsection presents, in detail, only the AE and DIC results of test specimens with ID A1. According to the five stages of the crack cracking process in Section 3.1.1, the AE location and DIC results at different stages of the cracking process is illustrated in Figures 7 and 8.  
As can be seen from the Figure 7a, after the first stage of the frost-heaving process, the AE localization event on the surface of the specimen is very small and scattered. The acoustic emission events generated at this stage are mainly caused by the original defects and micro-cracks in the specimen during the temperature equilibrium process. It can be observed in Figure 8a that the surface strain field of the specimen that no obvious crack propagation appears on the surface of the specimen.  
After the second stage, AE localization events (Figure 7b) begin to concentrate in the initial crack region. As can be seen in Figure 8b, micro-cracks gradually form at the tip of the initial crack, which indicates that initial cracks begin to affect the surface strain field of the specimen, and a small number of micro-cracks are generated at this stage.  
The temperature decreases, the specimen undergoes a third stage, which is the stage of ice plug formation at the initial crack opening. The surface AE localization event of the specimen (Figure 7c) is densely distributed along the initial crack direction. The surface strains field of the specimen (Figure 8c) suddenly shows obvious crack propagation, and the crack propagates along the direction of the initial crack. This indicates that the frost-heave force in the crack suddenly increases due to the formation of ice plug at the opening of the initial crack, which causes the crack to propagate.  
After the fourth stage, the surface AE localization event of the specimen (Figure 7d) continues to extend slightly along the direction of crack propagation. The surface strain field results of the specimen (Figure 8d) show that the main crack propagation direction is slightly offset. The reason for the analysis is that there are a large number of randomly distributed coarse particles in the concrete structure. The crack encounters coarse aggregate blocking during the propagation process. The crack propagation direction circulates along the surface of the coarse aggregate.  
When the fifth stage is reached, the surface AE localization event of the specimen (Figure 7e) does not change significantly. The surface strain field of the specimen (Figure 8e) shows that the crack no longer propagates. It indicates that the water-ice phase transition is completed in the crack.  
Comparing Figures 7 and 8, it can be seen that the crack propagation path measured by DIC is basically consistent with the location even distribution of the AE on the surface of the specimen. This also verifies the accuracy of the DIC measurement of crack propagation in concrete cracks.  
Figure 7: Testing results of AE events location during crack frost-heave propagation. (**a**) Less and scattered, stage 1; (**b**) concentrated the tip of initial crack, stage 2; (**c**) densely distributed along the initial crack direction, stage 3; (**d**) the distribution extends slightly, stage 4; (**e**) unchanged distribution, stage 5.