## 3 Test Results and Discussion  
### Strength Characteristics  
#### 3.1.1 Effect of Applied Static Pre-Stress under the Same Dynamic Loading Rate  
Figure 6 shows the effect of applied static pre-stress on the superimposed uniaxial compressive strength (SUCS) and the elastic modulus of rock specimens, as detailed in Table 3. At the same dynamic loading rate, the specimens exhibit distinct mechanical  
Figure 4: Sketches of correlation match: (**a**) reference image; (**b**) deformed image.  
Figure 5: Recovering the third dimension by two cameras.  
Figure 3: Specimens with speckles.  
behaviors with different static pre-stresses, as shown in Figure 6a. When the dynamic loading rate is \(2\times 10^{-4}\) s\({}^{-1}\), no correlation is observed between the SUCS and the static pre-stress, and the SUCS remains around 80 MPa, slightly higher than the static compressive strength of 77.1 MPa. When the dynamic loading rate is increased to \(2\times 10^{-3}\) s\({}^{-1}\), the SUCS and static pre-stress begin to show a clear linear relationship, which can be expressed as:  
\[S_{1}=-49.34R+112.4595 \tag{2}\]  
where \(S_{1}\) is the SUCS when the dynamic loading rate is \(2\times 10^{-3}\) s\({}^{-1}\), and \(R\) is the ratio of static pre-stress to the UCS. The SUCS decreases from 92.53 to 77.62 MPa when the static pre-stress increases from 40% of the UCS to 70% of the UCS. For dynamic loading rates of \(1\times 10^{-2}\) s\({}^{-1}\) and \(2\times 10^{-2}\) s\({}^{-1}\), a similar relationship between the SUCS and applied static pre-stress can be written as:  
\[S_{2}=-83.37R+134.7045 \tag{3}\]  
\[S_{3}=-83.37R+134.7045 \tag{4}\]  
where \(S_{2}\) and \(S_{3}\) are the SUCS when the dynamic loading rates are \(1\times 10^{-2}\) and \(2\times 10^{-2}\) s\({}^{-1}\), respectively, and \(R\) is the ratio of static pre-stress to the UCS. The higher the dynamic loading rate, the larger the difference in SUCS under different static pre-stresses. As shown in Figure 6, the SUCS is decreased from 103.25 to 77 MPa at a dynamic loading rate of \(1\times 10^{-2}\) s\({}^{-1}\) and decreases from 107.82 to 81.90 MPa for the dynamic loading rate of \(2\times 10^{-2}\) s\({}^{-1}\). These results may be explained as follows. When the dynamic loading rate is below \(10^{-3}\) s\({}^{-1}\), the SUCS exhibits a weak rate dependence, similar to the pure static loading condition, so the SUCS remains nearly stable as the static pre-stress changes. The magnitude of the SUCS change increases under different static pre-stresses as the dynamic loading rate increases, as evidenced by the steeper fitting line in Figure 6. In addition, the lower the static pre-stress, the greater the contribution of the dynamic loading rate, and the larger the SUCS.  
At the same dynamic loading rate, the elastic modulus reaches the peak when the static pre-stress is 50% of the UCS. When static pre-stress is increased from 40% of the UCS to 50% of the UCS, the specimens are more compressed and some of the pre-existing cracks and micro-pores in the specimens are further closed, leading to the increment in elastic modulus. However, when the static stress is increased from 50% of the UCS to 70% of the UCS, the effect of static pre-stress on the elastic modulus becomes negligible. In addition, the higher the static pre-stress, the weaker the effect of the dynamic loading strain rate on the elastic modulus. Therefore, the elastic modulus increases first and then decreases with increasing static pre-stress.  
Figure 6: The (**a**) strength and the (**b**) elastic modulus influenced by the static pre-stress.