# Characteristics of Acoustic Emission Caused by Intermittent Fatigue of Rock Salt
## 4 Results and Discussion
### Influence of Time Intervals  
AE counts produced by each unique circle is summed and the data for the different fatigue intervals are shown in Figure 11. It is important to note that the first and the last circles of each process are not included because of their different mechanisms. The discrepancies between the accumulated AE counts produced by \(\alpha\) and \(\beta\) circles are quantitatively shown in Figure 11. The sum of the AE counts in \(\alpha\) circles is always larger than that in \(\beta\) circles during the stationary phase of fatigue, which means that the AE phenomenon in the \(\alpha\) circles is more active. Using dislocation theory, the dynamic proliferative mechanism proposed by [PERSON] and [PERSON] [29] can explain the effect of residual stress on grains. The dislocations move very fast during the unloading of an external force and have a lot of kinetic energy, which could manifest as residual stress in the rock salt. This situation can be described by elastic energy W\({}_{ela}\) inside a volume V, as shown in Equation (1). The elastic energy component drives the internal structural shape restoration of rock salt during the time intervals without the applied force:  
\[\text{W}_{ela}=\text{W}_{ela}(\sigma)=\sum_{i,j}\iiint_{V}\sigma_{i,j}\text{d} e_{i,j} \tag{1}\]  
The adverse movement of the initial dislocations is conducted under the effect of residual strain. A reverse dislocation is generated when the dislocation arrives at a crystalline surface, which is known as reflection of the dislocation on the crystalline surface. Ideally, this reflection would proceed until W\({}_{ela}\) is consumed to zero, the dislocations are propagated constantly, large slippages occur on an atomic plane, and the number of microscopic fractures increases constantly during the time intervals. This kind of propagation comes from new cores and growth [30]. It is necessary to note that the AE images during the time intervals are quiet because of the small scale of variation, even though the change occurs in the intervals of the non-stressed phase. The dislocations move back and forth as a result of external stresses along both the original and palingenetic paths. These dislocations move to consume less energy along the original path: most of the energy is used to generate new fractures and is consumed by frictional loss between the lattices. This explains why the total number of AE counts in the \(\alpha\) circles is greater than that in the \(\beta\) circles (as shown in Figure 11). Figure 11: _Cont._  
In order to discuss the influence of the fatigue intervals in more detail, we define:  
\[\text{N}_{i}(\text{X})=\text{N}_{2i+1}+\text{N}_{2i}\left(i=1,2,3,\,\dots\,\right) \tag{2}\]  
where N\({}_{2i+1}\) is the total number of AE counts produced by the odd-numbered circles (\(\beta\) circles), N\({}_{2i}\) is the total number of AE counts produced by the even-numbered circles (\(\alpha\) circles), \(i\) is the ordinal, and X is the fatigue interval (in seconds). Figure 12 shows the effect of the fatigue interval on the computed values of N\({}_{i}(\text{X})\). The number of AE counts can represent the energy change of the structural transformation inside rock because this phenomenon is closely related to the microscopic damage to the rock [31]. N\({}_{i}(\text{X})\), the difference between the total counts produced by one \(\beta\) circle and the adjacent \(\beta\) circle, can therefore reflect the variation of energy inside the rock salt during the non-stressed phase. Figure 12 shows that the longer the interval, the higher the value of N\({}_{i}(\text{X})\). Once the interval extends beyond the threshold (900 s), however, the longer time interval leads to more work required for the residual strain and greater energy release, so the internal structure of the rock salt adjusts more easily. As greater amounts of elastic energy shown in Equation (1) are consumed, more palingenetic glide planes are generated, and the internal structure of rock salt becomes more petroclastic.