## 3 Experimental Results  
### The Slow-Wave Propagation Pattern at the Compaction Stage  
The rock samples' DIC data were studied at the first (compaction) stage at three loading rates (0.1, 0.5, and 1 mm/min). The variations of the strain component \(\varepsilon_{xx}\) on the sample surface at the initial stage of loading were analyzed. Here, the 3D diagrams and vertical views of the rock samples under the loading rate of 0.1 mm/min at the two time moments are presented and described in detail. Only the vertical views of the experimental results under the two loading rates (0.5 and 1 mm/min) are presented due to limited space. According to the relevant research by [PERSON], we also do the error analysis [40]. From our quantitative error analysis (Figure 2), we can see that the error decreases gradually with the increase of subset size. Moreover, when the subset size of this test is 48, the strain error is less than the test measured value. In addition, we also select the boundary for quantitative error analysis. The strain error increases slightly, but it is also less than the test strain. In this way, we can show that these test characteristics are not caused by errors. Figure 3 shows the strains at two time moments at the compaction stage under the loading rate of 0.1 mm/min (8 s, 16 s) and the 0 mm of the sample, to which the load was applied. The first column shows the 3D diagrams of the strain, from which the strain of the sample could be intuitively observed at a specific time moment for the sample under loading. The second column shows the vertical view of the diagram corresponding to the first column, from which the maximum strain and strain fluctuations along the length of the sample can be obtained. It can be seen from the 3D diagram in Figure 3a that the irregular strain fluctuations occurred throughout the entire stage. The fluctuations were more significant on the left side and gradually attenuated towards the right side. From the vertical view, it could also be observed that after applying load, strains with more significant fluctuations first appeared on the left side at the initial stage. By contrast, the fluctuations were milder on the right side, and the fluctuations were not synchronized on the left and right sides. At the distance 60-70 mm from the left side end, there was an isolated peak of compressive strain. Such a fluctuation pattern, which occurred in the form of a single moving peak, resembled a solitary wave or surge wave [41], i.e., a gravity wave, which is generally caused by the inertial force and gravity. Figure 2: Strain error analysis. According to Figure 3a, the strain values over the entire sample surface fluctuated consistently in the 3D diagram. Except for the leftmost side, there was no significant difference in the strain values within this region. As shown by the vertical view, the strain values fluctuated in a wave-like pattern. However, after the peak at the distance 65 mm from the left side end, the fluctuations were less significant than those on the right side. Although the strain values increased, the fluctuations were obscure and less regular. The strain values were slightly higher at the two ends. In Figure 3b, several large strain peaks occurred and showed a dispersed distribution. Their spatial distribution was non-uniform and disordered. Compared with Figure 3a, there are several complete wave fluctuations between 65 mm-100 mm, and the fluctuations are clear and obvious. According to the vertical views in Figure 3a,b, as loading continued, the fluctuations became more pronounced, and the degree of waviness increased. The peak values gradually increased and occurred more frequently. Moreover, the waviness became increasingly apparent. It is noteworthy that as the loading rate increased, the fluctuations on the left half side became more intensive. The peaks were also greater and denser. At the loading rate of 1 mm/min, the sample surface was subjected to a greater pressure than at other loading rates.