# Study of the Load-Bearing Characteristics of Bolts under Asymmetric Freezing Conditions
## 3 Results and Analyses  
### Analysis of the Results of the Indoor Pulling Test of the Bolt  
#### 3.1.1 Influence of the Anchor Size on the Ultimate Pull-Out Force  
To further study the influence of the anchorage size on the bearing characteristics of uplift resistance, anchors with diameters of 30, 35 and 40 mm were selected as the comparison conditions, and soils with moisture contents of 10, 12 and 14% were combined for indoor pulling tests. The results are shown in Figure 7.  
For force-displacement data, a variety of functions were tried to fit, and the exponential function was found to be more appropriate. The curves of load-bearing capacity of the bolt vs. axial displacement of the bolt for different anchor sizes are shown in Figure 7. According to the analysis:  
1. The pull-out force of the anchor rod increased with increasing axial displacement, and the pull-out damage process could be divided into three stages: \"fast growth\", \"slow growth\" and \"constant growth\". Phase 1: The pull-out resistance increased rapidly with increasing pull-out displacement between 0 and 1 mm. Taking the water content of 10% as an example, the pull-out resistance of the 30 mm diameter anchor rod increased by 0.4 kN during this stage, while for bolts with 35 and 40 mm diameters, the pull-out force increased by 0.43 kN and 0.52 kN, respectively, accounting for 84% of the respective ultimate pull-out resistance, and the force-displacement curve  
Figure 7: Load-bearing capacity-displacement curves for bolts of different diameters. maintained a linear increase. Phase 2: The pull-out force increased slowly with increasing displacement from 1 to 3 mm, and the growth rate decreased continuously. The pull-out force basically reached the ultimate pull-out value at this stage. Phase 3: the pull-out force remained constant with increasing pull-out displacement from 3 to 10 mm, and the anchor pull-out force reached its limit and stabilized. The anchor formed a sliding state at the anchor-soil interface, and the pull-out force was provided entirely by the frictional force at the shear interface, at which time the anchor system could be considered to have failed. However, since the anchor rod was not completely pulled out, the anchor force maintained the peak state for a long time without decay. 2. The ultimate pull-out resistance of the anchor was influenced by the diameter of the anchor. The ultimate pull-out values of anchors with diameters of 30, 35 and 40 mm at 10% moisture content were 0.49, 0.54 and 0.64 kN, respectively. The pull-out resistance increased with increasing diameter, and the pull-out resistances of 35 and 40 mm diameters were 1.102 and 1.306 times that of anchors with 30 mm diameter, respectively. The ultimate pull-out resistances of anchors with diameters of 30, 35 and 40 mm were 0.45, 0.49 and 0.56 kN, respectively, at 12% moisture content, and the pull-out resistances of those with 35 and 40 mm diameters were 1.089 and 1.254 times that of 30 mm anchors, respectively. The ultimate pull-out resistance values of anchors with diameters of 30, 35 and 40 mm were 0.426, 0.464 and 0.513 kN, respectively, at a moisture content of 14%. The pull-out resistances for diameters of 35 and 40 mm were 1.091 and 1.248 times that of 30 mm anchors, respectively. An appropriate increase in the diameter of the anchor will have a good effect on increasing the anchorage force. 3. The displacement corresponding to the ultimate pull-out force was basically the same for anchors with the three diameters and the same moisture content, i.e., the inflection point where the force-displacement curve tended to be flat remained the same. The displacement at the ultimate force for the 10% water content condition was 2.67 mm, while the displacements at the ultimate force for 12% and 14% water contents were 1.91 and 1.87 mm, respectively. This was because the soil properties determined the shear strength of the anchor-soil interface.