# Study of the Load-Bearing Characteristics of Bolts under Asymmetric Freezing Conditions
## 3 Results and Analyses
### Study on the Bearing Characteristics of Bolts in a Cold Environment
#### 3.2.2 Influence of Frost Heaving on Bolt Displacement  
The horizontal frost heaving force and the longitudinal frost pulling force generated during the soil freezing process affect the spatial position of the anchor bolt. Under different freezing temperatures, the horizontal and vertical displacements of the anchor bolt are shown in Figures 12 and 13. The temperature was that at the anchor bolt centre. The analysis of Figure 12 shows that the horizontal displacement of the anchor rod under the same water content condition increased to varying degrees with decreasing temperature. For the same freezing temperature, the frost heave displacement increased slightly with increasing water content. For every 2% increase in water content, the displacement increased by from 3% to 7%. For the sample with 10% water content, when the  
Figure 12: Horizontal displacement of the anchor rod at different temperatures. Figure 13: Vertical displacement of bolts at different temperatures. soil mass dropped from room temperature to 0 \({}^{\circ}\)C, the anchor rod had a large horizontal displacement of 0.29 mm. When the temperature dropped to \(-3\)\({}^{\circ}\)C and \(-7\)\({}^{\circ}\)C, the horizontal displacement increased by 0.03 and 0.06 mm, which were 10.3 and 20.6% of the displacement when the temperature dropped to 0 \({}^{\circ}\)C, respectively. The reason for this behaviour can be explained as follows. The soil mass on the right side of the rod body froze and further expanded before the temperature at the centre of the bolt dropped to zero. During this process, water continuously migrated to the right and condensed, the strength of the soil on the right side constantly improved, and the frost heaving force on the rod was exerted to the left. As the soil on the left side of the anchor had not yet entered frozen, it was softer than the frozen soil and had poor resistance to the load on the right side, and the anchor was displaced under the action of the horizontal thrust. During the process from 0 to \(-3\)\({}^{\circ}\)C, the strength of the soil mass on the left side of the anchor bar gradually increased as it entered the negative temperature state. The soil gradually developed the ability to resist the load on the right side and produce the frost heaving force on the anchor bar to the right, but the force on the left side was still smaller than the horizontal resultant force on the right side, and the overall direction was still to the left. Although the soil stress values on both sides still maintained a certain gap, the left side had a certain strength after freezing, and the soil changed from soft to hard. Therefore, the displacement change at this stage kept increasing, but the increase was greatly reduced. During the process from 3 to \(-7\)\({}^{\circ}\)C, the frozen soil on both sides of the bolt simultaneously developed to reach a lower temperature, the frost heaving effect continued to have an effect, and the displacement was similar to that during the previous stage and underwent a small amount of development. Due to the free interface above the model, the bolt was vertically dislocated with the free expansion of the frozen soil in the vertical direction. The analysis of Figure 13 shows that the vertical displacement of the bolt increased with increasing moisture content and decreasing freezing temperature, and the increase was related to the longitudinal distribution of the gradient of freezing temperature. The vertical displacement of the bolt under the same freezing temperature conditions increased with increasing moisture content. Taking the working condition of 10% moisture content as an example, the freezing displacement value of the rod body was 0.2 mm when the core temperature of the bolt was reduced from room temperature to 0 \({}^{\circ}\)C. When the temperature dropped to \(-3\)\({}^{\circ}\)C, the displacement increased by 3.2 mm, a 15-fold increase. From \(-3\) to \(-7\)\({}^{\circ}\)C, the displacement continued to increase by 0.8 mm.