# Three-Dimensional Numerical Modeling of Artificially Freezing Ground in Metro Station Construction
## 5 Conclusions  
This study reported the engineering background of using the ground freezing method to reinforce the No. 2 connecting passage of Binhu Road Station/Jinhu Square Station of Nanning Metro Line 3. A finite element software was used to establish a three-dimensional numerical model of the connecting passage and its surrounding soil layers. The development behavior of the soil curtain temperature field was monitored and the evolution of the frozen soil curtain was dynamically simulated. The following conclusions can be drawn based on the analysis.  
1. Measured values from the construction site and numerical modeling calculation results exhibited good agreement and the progression of the freezing process was similar in both instances. The work demonstrated that it is feasible to simulate the changing process of the frozen soil curtain temperature field of a connecting passage using a three-dimensional numerical model;
2. The weakest link in the frozen soil curtain is the top of the bell mouth where the downhole tunnel intersects the connecting passage. This feature was consistent with the findings of Ref. [3]. On the basis of the information obtained during the present study, it is recommended that a row of shorter freezing holes should be made at the top of the downline bell to enhance the freezing effect in this area and ensure safety during the construction of the connecting passages;Under the design freezing scheme, the frozen wall closure time was 14 days. As the freezing time increased, the thickness and average temperature (strength) of the frozen soil curtain gradually increased, eventually forming a completely closed and stable frozen soil curtain;
4. The thickness of the frozen soil curtains of C1 and C2, C4 and C5, and C6 and C7 reached 1.75 m or more, indicating that the entire frozen soil curtain met the design requirements and the conditions necessary for safe excavation and construction were achieved;
5. The freezing project started on 25 May 2018, and lasted until 3 July 2018 (40 days of freezing). The average thickness of the frozen soil curtain was 2.4 m, the average temperature was \(-\)10.7 \({}^{\circ}\)C, and the freezing effect met the design requirements. The successful excavation of the site project suggested that it was feasible to adopt the above-mentioned connecting passage freezing scheme, which may provide references for comparable projects using artificially freezing ground in metro station construction.  
As a limitation, in the current study, only the temperature field has been considered for waterproofing purposes. The soil's mechanical behavior (e.g. frost heave and moisture migration) under temperature change and heat transfer, as well as the possibilities of the numerical calculation program to optimize the number of freezing holes, their location and length will be examined as future work.  
Conceptualization, B.W.; methodology, X.L.; software, X.L.; validation, J.H., X.L. and H.Z.; formal analysis, X.L.; investigation, X.L.; resources, H.Z.; data curation, X.L.; writing--original draft preparation, B.W.; writing--review and editing, B.W.; visualization, X.L.; supervision, J.H.; project administration, H.Z.; funding acquisition, H.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Innovative Research Team Project of Natural Science Foundation of Hainan Province, P. R. China (522 CXTD511), High Technology Direction Project of the Key Research & Development Science and Technology of Hainan Province, P. R. China (Grant No. ZDYF2021 GXJS020), characteristic innovation (Natural Science) projects of scientific research platforms and scientific research projects of Guangdong Universities in 2021 (Grant No. 2021 KTSCX139), and Jiangmen Basic and Applied Basic Research Key Foundation (Grant No. JZ202214).  
Not applicable.  
The data used to support the findings of this study are available from the corresponding author upon request.  
The authors declare that they have no conflict of interest.