# Three-Dimensional Numerical Modeling of Artificially Freezing Ground in Metro Station Construction
## 1 Introduction  
A subway connecting passage, also known as the bypass channel or escape channel, is built in the middle of each subway tunnel section (sometimes with a pump house). The shape of the section may be circular, rectangular, or a straight wall arch. The most common form in construction is the straight wall arch, with a wall height of 2.5-3.5 m and a span of 2.0-3.0 m. The construction of the connecting passage is a key aspect of the construction of the subway. It can be constructed by using construction methods such as the 'open-cut' method, the 'undercut' method, the 'first open-cut and then undercut' method, and the 'pipe jacking' method. Due to above-ground traffic restrictions, the undercut method is often used. The decision as to which surrounding soil reinforcement method should be chosen is a technical problem that is frequently encountered [1, 2, 3]. The surrounding soil layer is reinforced by grouting in the tunnel, freezing in the tunnel, deep ground mixing, or rotary jet blasting [4, 5, 6]. When encountering a water-rich sandy soil layer, grouting in the tunnel is unstable and the quality is not easy to guarantee. Worse still, it is often impossible to carry out ground deep mixing or rotary jet reinforcement due to above-ground traffic restrictions. Therefore, the soil layer around the connecting passage is often reinforced using the 'freezing in the tunnel' method [7]. The common construction methods for connecting passages of metro station are summarized in Table 1. Water leakage likelyoccurs during construction phase of these methods, and the artificial ground freezing technique can be adopted to address this water leakage problem. Many researchers have studied the soil layer construction methods around connecting passages reinforced by the freezing method and combined these with practical engineering examples and reported much useful experience. [PERSON] and [PERSON] [8] used three-dimensional finite element simulation to study the construction mechanical behavior of the complex space structure composed of the shield tunnel and the connecting passage under the condition of the freezing method. It was pointed out that the design of the intersecting segment not only needs to satisfy the lateral internal force but also must meet the requirement for longitudinal structural strength. In combination with the Nanjing Metro Mochou Lake Station/Hanzhongmen Station Intersection Passage Project, [PERSON] et al. [9] used numerical methods to simulate the leakage of the mid-bottom angle, arch angle, and vault of the frozen wall and studied the effect of seepage on the structure of frozen soil. [PERSON] et al. [10] carried out on-the-spot research measurements during the whole process of freezing construction on an ultra-long connecting passage (the net length of the channel was 13.8 m) for the Nanjing Metro and concluded that it was completely feasible to achieve simultaneous freezing by setting freezing holes and two freezing stations in the tunnels on both sides. [PERSON] et al. [11] proposed a numerical model for thermal and mechanical analysis and selected a minimum pre-freezing time according to the criteria of code that the maximum surface settlement should be less than 30 mm. [PERSON] et al. [12] presented a coupled thermal hydraulic finite element model for freezing soils integrated within an optimization algorithm to optimize ground freezing in tunneling by finding the optimal positions of the frozen pipe. [PERSON] et al. [13] developed a thermal model to study the complete heat transfer problem that can be easily used in field applications. The developed model can be used to conduct  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  
parametric studies on operating conditions, refrigerant type, system geometry, or ground properties. [PERSON] et al. [14; 15; 16] described in detail the monitoring design of the freezing and reinforcement project of the Shanghai Yangtze River Tunnel and conducted an in-depth analysis of the freezing monitoring data.