## 3 Results and Discussion  
### Determination of the Frost-Heave Crack Propagation Law  
#### 3.1.1 Frost-Heave Crack Propagation Process  
The evolution process of the generalized strain curve and accumulated AE hits curve is shown in Figure 6. The time between micro-crack initiation and unstable propagation is very short, and no detailed analysis is made in this section; however, it will be discussed in Section 3.1.2 by analyzing the key parameters of micro-crack initiation strain and unstable propagation strain. According to the change in slope of the two curves, the process of frost-heave crack propagation was divided into five stages, as shown in Figure 6. As can be seen from the figure, in the first stage of the freezing process, the generalized strain at the crack tips of the concrete specimens increases slightly and the accumulated AE hits is small. At this stage, the damage to the concrete is mainly caused by micro-cracks which form at the crack tip, which is the reason for the lower acoustic emissions.  
When the cooling process reaches the second stage (see Figure 6), the slope of the accumulated AE hits curve increases; this occurs before the abrupt change in the slope of the generalized strain curve. At this stage, a small amount of water in the crack underwent a water-ice phase transition, and a small amount of energy release was detected. As a result, the slope of the accumulated AE hits curve increases gradually. However, at this stage, the mass of iced water does not form an ice plug at the crack opening, and the frost-heave force is not sufficient to cause crack propagation. Thus, the slope of the generalized strain curve does not change significantly.  
As the temperature continues to decrease, the generalized strain at the crack tip and the number of accumulated AE hits increase abruptly when the third stage (Figure 6) is reached. These phenomena indicate that the water-ice phase transition which occurs in the cracks and the formation of the ice plug at the crack opening result in an abrupt increase of frost-heave water pressure at the crack tip. The catastrophe point of the generalized strain curve represents unstable crack propagation. The accumulated energy is released in the form of acoustic emissions and, accordingly, the accumulated AE hits curve shows an abrupt increase in slope. Therefore, cracks propagate under the frost-heave force during this stage.  
When the cooling process reaches the fourth stage (Figure 6), the slope of the generalized strain curve decreases, and the count of accumulated AE hits increases slowly. This stage occurs after the  
Figure 6: Schematic diagram of the process of frost-heave crack propagation for specimen A1.  
abrupt changes of generalized strain at the crack tip. Due to the propagation of cracks in the third stage, the frost-heave force in the cracks is released. The unreleased frost-heave force in the cracks is insufficient to cause the main cracks to continue to propagate significantly.  
When the cooling reaches the fifth stage (Figure 6), the generalized strain at the crack tip tends to be stable, and the number of accumulated AE hits remains almost unchanged, which indicates that the water-ice phase transition has been completed and the final equilibrium state has been reached.  
The evolution law of generalized strain is in good agreement with the micro-damage of the crack tip, which verifies the correctness of using surface strain at the crack tip to study the frost-heave propagation process of cracks.