# Study of the Load-Bearing Characteristics of Bolts under Asymmetric Freezing Conditions
## 4 Discussion and Conclusions  
In this study, we conducted indoor pull-out model tests on anchor rods with different moisture contents and freezing temperatures, quantitatively described the changes in anchor rod pull-out force before and after freezing, plotted load-displacement curves, observed and recorded the freezing displacement of the anchor rod and stress evolution of the surrounding soil under asymmetric negative temperature loading, and reached the following main conclusions:  
1. The pull-out force of the anchor increased with increasing axial displacement, and the change process was divided into three stages: \"fast growth\", \"slow growth\" and \"constant growth\". The pull-out force increased with increasing anchorage diameter, and the pull-out forces for 35 and 40 mm diameters were 1.102 and 1.306, 1.089 and 1.254, and 1.091 and 1.248 times that of 30 mm for the three water content conditions, respectively. The shear strength and pull-out force at the anchor interface decreased with increasing water content. When the water content increased from 10 to 12 and 14% for 30 mm diameter anchorages, the anchor pull-out force decreased by 0.039 and 0.064 kN, or 7.96% and 13.1%, respectively.
2. The test soil entered the frozen state by the negative temperature load, and the frozen area continued spreading from the cold source at the upper right through the whole soil specimen with increased freezing time. The anchor rods were in an asymmetric stress state for a long time due to the influence of the single-side freezing method, and they were displaced under the action of the freezing expansion force. Taking the moisture content of 10% as an example, the lateral displacements of anchors at 0, \(-\)3 and \(-\)7 \({}^{\circ}\)C were 2.9, 3.2 and 3.5 mm, and the vertical displacements were 0.2, 3.5 and 4.3 mm, respectively. The total displacement increased with increasing moisture content; the maximum horizontal displacements were 3.5, 3.65 and 3.8 mm under 10,  
Figure 18: Schematic diagram of freeze–thaw moisture migration.  
12 and 14% moisture content working conditions, and the vertical displacements were 4.3, 5.1 and 5.5 mm, respectively.
* The shear strength of the anchor-soil interface increased as the temperature decreased, and the ultimate value of the pull-out force increased as the temperature decreased and the moisture content increased. The pull-out force of the frozen anchor increased with increasing water content.
* After freezing and thawing. the ultimate pull-out forces were 71, 68 and 52% of that before freezing under 10, 12 and 14% moisture content working conditions, respectively.  
Conceptualization, J.D.; Methodology, J.D.; Validation, X.Y. and Z.-Q.L.; Formal analysis, J.D., X.Y. and Z.-Q.L.; Investigation, X.Y.; Resources, J.D. and Y.-H.Z.; Data curation, J.D., X.Y., Z.-Q.L. and Y.L.; Writing--original draft, X.Y.; Writing--review & editing, K.F.; Visualization, Y.-H.Z.; Supervision, Y.L., Y.-H.Z. and K.F.; Project administration, Y.L.; Funding acquisition, J.D. All authors have read and agreed to the published version of the manuscript.  
The research described in this paper was financially supported by the Natural Science Foundation of China (NO. 51878242), the Natural Science Foundation of Hebei Province of China (NO. E2020404007), the Doctoral Research Start-up Fund Project (B-202101), the Research Project of Basic Scientific Research Business Fund for Higher Education Institutions in Hebei Province (2021 QNJS07), the Research Project on Basic Research Funds for Higher Education Institutions in Hebei Province (2021 QNJS02), Hebei Provincial Department of Education Innovative Ability Training Program for graduate students (CXZZSS202063).  
Not applicable.  
Data Availability Statement: Data will be made available on request.  
The authors declare no conflict of interest.