## 3 Test Results and Analysis
### Deformation Characteristics of Bolts
#### 3.1.2 Bolt Tensile Deformation Characteristics  
The bolt selected for the test was a common type of mining bolt with a length of 1200 mm. A comparison was made between blots of different lengths, but all other parameters were kept the same for all tested bolts. Figure 5 shows the axial (a,c) and radial (b,d) deformation curves of different parts of bolts of different lengths. It was found that the axial and radial deformation patterns of separate parts of bolts of different lengths are consistent, and the average sectional shrinkage rates of bolts that are 1200 and 2500 mm long are 54.64% and 55.24%, respectively, indicating that the tensile deformation characteristics of bolts of the same parameters have very little relationship with the length of bolts.  
Figure 4: The axial load–displacement curve of each bolt.  
From Figure 5a,c, it can be seen that in the axial deformation rule of bolts at different locations, the deformation at both ends of bolts is less than the deformation at the center of bolts, but the difference is not significant, while the axial deformation of bolts near the fracture location is obviously much larger than other parts due to the effect of shrinkage. The radial deformation rule of bolts in different positions can be seen in Figure 5b,d. The bolt diameter variation rule is similar to the bolt transverse deformation rule. The deformation of the bolt diameter at both ends is smaller than the deformation of the bolt in the middle position, and the closer to the necking fracture position, the larger the deformation of the bolt diameter. The mg3 bolt diameter variation curves for different parts of the bolt differ from the mg1 and mg2 curves in that two distinct troughs appear in the mg3 curve (marked in Figure 5b) because the mg3 necking fracture location is closer to the center of the bolt.  
The image data during the bolt tensioning process was recorded by the bolt state monitoring device, and the necking fracture process of the bolt and the diameter change rule of the necking fracture location when different axial displacements were applied to the bolt were collated and analyzed. Figure 6 shows the diameter change curve of the bolt shrinkage part. Due to the different amounts of axial deformation during bolt stretching, the tensile deformation ratio \(S\) is introduced. \(S\) is the axial displacement normalized by the total extension, and \(S\) is calculated by the following formula:  
\[S=\frac{Axial\ displacement}{Total\ extension} \tag{1}\]  
As can be seen from Figure 6, the diameter change pattern is the same for different necking locations. The bolt undergoes uniform elastic-plastic deformation during the elastic phase, yielding phase, and strengthening phase, and the diameter change curve is slow. When the bolt reaches the necking fracture phase, its diameter changes drastically, the section at the necking decreases rapidly, and fractures are about to occur.  
Figure 5: Axial (**a,c**) and radial (**b,d**) deformation curves of different parts of bolts. Bolt length: (**a**) 1200 mm; (**b**) 1200 mm; (**c**) 2500 mm; (**d**) 2500 mm.