## 2 Experiment and Method
### Freezing Experiment  
This study mainly investigated the proposed new method; therefore, the main variables were the flow rate of cold gas and initial water content in the sand; other factors involved in the freezing process were not taken into account, such as frost heave and groundwater flow. The sand selected for the experiments is not sensitive to frost heave and has high strength; the specific parameters are shown in Table 1. The freezing pipe was filled with water-bearing sand and compacted. According to the initial water contents (0.2 and 0.4), water was mixed with sands and then loaded into the model and compacted. The experimental site is located in Fuyu City, Jilin Province, China, one of the cold regions in China, where winter can last 4-5 months, and the outdoor temperature is from \(-25\) to \(-10\)\({}^{\circ}\)C for most of the winter. Such an abundant natural cold source is convenient for artificial freezing construction. Considering that the underground temperature is generally about 3-10 \({}^{\circ}\)C, the initial temperature of the freezing pipe was controlled at approximately 5 \({}^{\circ}\)C, and then, the heat cable was stopped. In the experiments, cold gas was continuously supplied by a nitrogen cylinder with a pre-pressurized pressure of 10 MPa, which was placed outdoors in order to ensure that the gas temperature was equivalent to the outdoor temperature, and then the experiments started.  
After each experiment, the sand samples were collected at the point of the inlet, T2, T3, T4, and T5, and the outlet to calculate the total water content by weight; the specific calculation method was as follows. The wet and dry weights of the samples prior to experiments are \(M_{ow}\) and \(M_{od}\), respectively, and the initial water content of the freezing model is \(\theta_{0}\). After the experiments, the same values are weighed as \(M_{w}\) and \(M_{d}\). The water content \(\theta\) of the samples after the experiment can be calculated by the following formula:  
\[\theta=\theta_{0}\times\frac{(M_{w}-M_{d})\times M_{od}}{(M_{ow}-M_{od})\times M _{d}}. \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Sand** \\ **Type** \\ \end{tabular} & **Mesh Size** & **Packed Porosity** & \begin{tabular}{c} **Density** \\ **(Kg/m3)** \\ \end{tabular} & \
\begin{tabular}{c} **Thermal** \\ **Conductivity** \\ **(W/(m\(\cdot\)K))** \\ \end{tabular} &
\begin{tabular}{c} **Specific Heat** \\ **(KJ/(Kg\({}^{\circ}\)C))** \\ \end{tabular} \\ \hline Ceramsite sand & 40–70 & 0.39 & 1100 & 1.15 & 0.961 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical properties of sand.  
Figure 2: Principle diagram of freezing model and experimental device.  
In order to preliminarily study the evolution of temperature in the freezing model during natural cold gas injection and to verify the feasibility of the new method, four groups of experiments were carried out. The initial water content was 0.2 and 0.4; in addition, we optimized and used the two gas flow rates, 15 L/min and 25 L/min. We also tested the gas flow rate intermittently by the dewatering method in each experiment [18], and it was verified that the flow fluctuation was not more than 0.2 L/min. The specific experimental conditions were as shown in Table 2.