# 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
#### 3.2.3 Effects of Freezing and Swelling on the Extraction Force  
The shear strength of the anchor-soil interface was enhanced by the increase in the surrounding pressure on the anchor rod after the soil froze, and the anchor rod pull-out force vs. axial displacement under different temperature conditions is shown in Figure 15.  
Analysis of Figure 15 yielded the following insights:  
Figure 14: Schematic diagram of the bolt force under different temperature gradients. Figure 15: Pull-out force vs. displacement at different temperatures. 1. The ultimate value of the anchor pull-out force at each water content condition increased with decreasing temperature. Taking the moisture content of 10% as an example, the ultimate pull-out force at room temperature was 0.49 kN, and the ultimate values of the pull-out force under freezing to 0, \(-\)3 and \(-\)7 \({}^{\circ}\)C were 1.96, 8.35 and 8.87 kN, which were 4, 17.04 and 18.1 times higher than those at room temperature, respectively. This behaviour can be explained as follows: the soil entered a frozen state under the negative temperature load, the water in the soil froze and expanded in situ, the condensed ice crystals filled the gaps between the soil particles and tightly squeezed them, the compactness of the soil increased, the normal stress on the anchor rod body increased, the shear strength of the anchorage interface was enhanced, and the load-bearing capacity of the anchor rod in frozen soil could reach more than ten times that in unfrozen conditions. 2. When the centre of the anchor was at 0 \({}^{\circ}\)C, the surrounding soil was about to freeze, and some of the unfrozen water still maintained a small amount of mobility between the soil particles. The liquid phase in the soil was in an ice-water mixture, and the pull-out resistance underwent a small increase due to partial freezing of water. At the stage from 0 to \(-\)3 \({}^{\circ}\)C, the soil moisture around the rod basically entered the frozen state, the interstices of soil particles were filled with ice crystals, and the pull-out resistance and soil strength grew rapidly. At the stage from \(-\)3 to \(-\)7 \({}^{\circ}\)C, only a small amount of water in the soil had not frozen, the pull-out force growth potential was small, and thus, the limiting value of the pull-out force at this stage had only a small increase compared with the former. 3. At the same temperature, the limiting value of the pull-out force increased with increasing water content. Taking the working condition of \(-\)3 \({}^{\circ}\)C as an example, the limiting values of the pull-out forces of 10, 12 and 14% water content were 8.25, 9.74 and 11.39 kN, respectively. Compared with the working conditions of 10, 12 and 14% water content, the pull-out force increased by 1.49 and 3.14 kN, respectively, with increases of 18.06% and 38.06%, respectively. With the increase in soil moisture content, there was more liquid water between particles. The freezing expansion increased with increasing water content. The greater the degree of compaction of soil particles and ice crystals was, the greater the ability of the anchor to withstand confining pressure and shear resistance. 4. The stress displacement curve of the frozen soil anchor rod could also be divided into three stages: \"rapid growth\", \"slow growth\" and \"maintain the same\". Unlike the normal temperature condition, the stress growth stage of the freezing condition was longer before entering the failure stage. In the first stage, the drawing force increased rapidly with displacement, and the stress displacement increased linearly. In the second stage, the slope of the curve was gradually attenuated from 2 to 7 mm, and the relationship between the drawing force and the displacement was nonlinear. In the third stage, the curve entered the horizontal development stage between 7 and 8 mm, at which time the pull-out force basically reached the limit state. The pull-out force did not change with increasing displacement, and thus, the anchoring force was considered invalid.