# Mechanical Properties of Metasandstone under Uniaxial Graded Cyclic Loading and Unloading
## 3 Test Results and Analysis
### Wave Velocity Characteristics Analysis  
The initial longitudinal wave data of rock samples B01-B06 are shown in Table 4. In order to show the trend of wave velocity at each point of the rock samples more intuitively, the initial wave velocity of rock samples was regarded as the wave velocity after unloading at level 0, and the relationship between the wave velocity and unloading level of rock samples is plotted. The variation in wave velocity at each point of the sample in the graded cyclic unloading test is shown in Figure 16.  
In Figure 17, the wave velocities of B01, B02, B04, and B06 increase slightly after the first level unloading, because the first level unloading has a certain compression effect on the rock, and the overall density of the rock increases. The wave velocity of B03 and B05 decreases slightly, which is caused by the development of internal cracks of these samples with low strength. The development and expansion of cracks during unloading have a greater impact on the decline in wave velocity than compression and density. After the second level unloading, the wave velocities of B01, B02, B04, and B06 remain basically unchanged, but the wave velocities of individual points increase or decrease, because the rock is heterogeneous, and there is certain variability in the structure and density changes of various points in the rock. After the third level unloading, the wave velocities of B01, B02, B04, and B06 decrease at almost all points, and the relative decrease in wave velocities of B04 and B06 is more obvious. It shows that the unloading of this level has caused damage to the interior of the two rock samples, and the internal cracks are obviously developed and damaged. After the 4 th stage unloading, the wave velocities of B01 and B02 decrease significantly, indicating that further crack development and expansion continued to occur in the samples, and these samples were finally destroyed in the loading stage of the 5 th level cycle. In terms of axial wave velocity, the axial wave velocity of the six samples after loading and unloading at all levels decreases, because the initiation and development of radial cracks \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Rock Samples** & **Point 0** & **Point 1** & **Point 2** & **Point 3** & **Point 4** \\ \hline B01 & 5642 & 5128 & 5137 & 5205 & 5299 \\ B02 & 5564 & 5215 & 5138 & 5194 & 5164 \\ B03 & 5456 & 5142 & 4987 & 5070 & 5051 \\ B04 & 5513 & 5108 & 4972 & 5051 & 5100 \\ B05 & 5410 & 5112 & 5163 & 5008 & 4950 \\ B06 & 5525 & 5092 & 5154 & 5123 & 5017 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Initial wave velocity at each point of rock sample (m-s\({}^{-1}\)). enhances the reflection of ultrasonic waves in the axial direction, thus reducing the axial wave velocity of the samples. It can be concluded that the development of radial cracks in rock samples is driven by any level of unloading and loading. Figure 17: Uniaxial loading and unloading levels of rock samples and changes of point wave velocity. (**a**) Wave velocity change of rock sample B01; (**b**) Wave velocity change of rock sample B02; (**c**) Wave velocity change of rock sample B03; (**d**) Wave velocity change of rock sample B04; (**e**) Wave velocity change of rock sample B05. (**f**) Wave velocity change of rock sample B06. From the relationship between the unloading level and the rate of decline of the wave velocity of the rock sample, it can be determined that there is a stress threshold. Below this threshold value, the wave velocity of rock samples will not decrease with the increase in stress; however, beyond this threshold value, with the increase in stress, there will be a qualitative change in the degree of rock damage, and the wave velocity of rock samples will drop rapidly. The phenomenon of a rapid decrease in wave velocity can be used in engineering to predict the damage instability of rock masses.