## 3 Crack Evolution and Failure Characteristics of Rock Bridge Specim at Sudden Change Loading Rate  
Analysis of the Corresponding Relationship between Crack Propagation and Stress-Strain Curve under Uniform Loading  
The crack development and propagation of rock-like specimens are reflected in the stress-strain curves. The development and generation of cracks will cause the fluctuation and change of curves [13]. Specimens #1 (\(\alpha=30^{\circ}\), \(\beta=60^{\circ}\)) and specimen #2 (\(\alpha=30^{\circ}\), \(\beta=90^{\circ}\)) were loaded at different rates, and then the relationship between crack propagation and stress-strain curves was analyzed under uniform loading. The axial stress-strain relationship under uniaxial compression at different loading rates of specimen (\(\alpha=30^{\circ}\), \(\beta=90^{\circ}\)) is shown in Figure 3. The four rates are 0.5 mm/min, 1 min/min, 3 mm/min, and 5 mm/min, respectively. Table 1 lists the peak strength \(q_{c}\) and maximum strain \(\epsilon_{c}\) (that is, the strain corresponding to the peak axial stress) of the specimen at the corresponding loading rate. Figure 3: The stress-strain relationship of rock–like under different loading rates. Figure 2: Loading rate change diagram. It can be seen from the table that, with the increase in loading rate, the peak strength and elastic modulus increase and the maximum strain decreases [4]. The test results indicate that the stress-strain curve changes with the loading rate. The rock specimen goes through the stages of pore fracture compaction, elastic deformation, stable micro elastic fracture development, unstable fracture development, and post-fracture [14]. The general behavior of crack evolution of specimens under uniform loading is as follows: the stress-strain curve of specimens varies with the loading rate. When the loading rate increases, the elastic modulus increases, the peak strength also increases, and the peak strain decreases. During loading, as shown in Figure 4, the remote cracks usually appear first, and then the partial cracks of the rock bridge begin to develop. With the increase of loading rate, the crack propagation at the precast crack tip changes gradually from tensile crack to shear crack. The higher the loading rate, the less the macroscopic cracks of the specimen. At low rate, the internal defects of the specimen have enough time to develop and expand. For example, when loading at low rate, the rock bridge crack is a primary crack, and when loading at high rate, the rock bridge crack is a double crack. This is because microcracks in the rock bridge region fully develop at low rate; then, two precast cracks continuously develop in the stress concentration area and connect through the microcracks, resulting in a primary crack. When loading at high rate, there is not enough microcrack initiation in the rock bridge area, and the cracks of both sides develop relatively independently, leading to double cracks in the rock bridge area. The ultimate failure modes of specimens under different loading rates include shear failure, tensile failure, and tensile-shear mixed failure. As can be seen from Figure 5, tensile failure mode is the main choice of low-rate loading specimens. The change of loading speed will lead to the change of failure mode. For example, the specimens with a loading rate of 3 min/min are tensile-shear mixed \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Loading Rate** & **Peak Strength** & **Peak Strain** & **Elastic Modulus/GPa** \\ _v/(mm/min)_ & _q\({}_{c}\)_/mpa_ & _e\({}_{c}\)_/10\({}^{-3}\)_ & **Elastic Modulus/GPa** \\ \hline
0.5 & 9.70 & 11.37 & 1.20 \\
1 & 9.96 & 10.70 & 1.41 \\
3 & 10.81 & 10.39 & 1.42 \\
5 & 11.11 & 10.30 & 1.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Peak Strength, Strain, and Elastic Modulus of Specimens under Uniaxial Condition. Figure 4: Crack development diagram of crack specimen under uniform loading. failures; when loading rate is 5 mm/min, the ultimate failure mode of the specimens is mainly shear failure.