## 3 The Establishment of a Numerical Model
### Establishment of a Calculation Model of Freezing Body Temperature Field
In order to avoid the influence of a boundary effect on the numerical calculation results of the temperature field, the model range (X, Y, Z) was selected as (44, 15, 35 m), and considering the aspects of calculation accuracy and solution time, through the grid sensitivity analysis, we chose a set of grid configurations that can guarantee the calculation accuracy and control the calculation cost as the final simulation settings. The simulation results in this grid configuration are convergent and reliable enough to support our research conclusions. The upper surface of the tunnel and frozen tube model is free, and the displacement of the lower surface and four side surfaces is completely constrained. The load is generated from top to bottom according to the gradient of gravity field considering only the action of gravity. The Mohr-Coulomb elastoplastic model was used as the soil element in the model. To make the calculation results more realistic, the model was subdivided into two layers, namely plain-filled soil and silty clay. The obtained rock and soil samples were brought back to the laboratory for various physical and mechanical tests, such as a density test, water content test, compression test, shear test, etc., in order to obtain the physical and mechanical parameters of rock and soil bodies, such as density, water content, compression modulus, internal friction angle, cohesion force, etc. The physical and mechanical parameters and thermophysical parameters of each soil layer are shown in Table 1. The elastic model was adopted for shield tunnel segment elements. The elastic modulus of the shield segment was set at 33.5 GPa, Poisson's ratio at 0.2, thermal conductivity at 0.5 W/(m \({}^{\circ}\)C), specific heat capacity at 1 kJ/(kg \({}^{\circ}\)C), and density at 2500 kg/m\({}^{3}\). Thermal conductivity of surface air and air in tunnel was 0.025 W/(m \({}^{\circ}\)C), and specific heat capacity was 1 kJ/(kg \({}^{\circ}\)C). In the actual freezing method construction process, the active freezing period of the interval contact channel is 40 d, and the numerical calculation time of the temperature field is also 40 d. Because the freezing pipe is arranged in an inclined radial shape, the freezing pipe layout on the upper and lower lines is not the same. It is a common and important step to arrange temperature measuring holes on site to monitor the temperature development of the freezing curtain during the construction of a freezing method of a subway contact passage. For the measurement of the temperature hole, there are usually repeated measurements to ensure the accuracy and reliability of the data. The instru \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Rock and Soil** & **Natural Density** & **Cohesion** & **Angle of Friction** & **Void** & **Permeability** & **Coefficient** & **Modulus** & **Poisson’s** & **Thermal** & **Specific Heat** \\
**Stratification** & **(g/cm\({}^{3}\))** & **(kPa)** & **Friction** & **Rating** & **Coefficient** & **Lateral** & **Elasticity** & **Ratio** & **(W/m/\({}^{\circ}\)C)** & **Capacity** \\ \hline Plain fill soil & 1.96 & 15 & 10 & 0.752 & 3 & 0.35 & 4.5 & 0.35 & / & / \\ Silty clay & 1.98 & 38 & 13 & 0.710 & 0.006 & 0.33 & 6.5 & 0.33 & 1.85 & 1.46 \\ \hline \end{tabular}
\end{table} 
Table 1: Physical and mechanical parameters of rock and soil layer. ments used to collect temperature data are usually high-precision temperature sensors or thermometers. These instruments can be installed in a temperature measuring hole and transmit temperature data wired or wirelessly to a data acquisition system or monitoring center. The temperature sensors in the temperature measurement holes must be installed and arranged according to the design requirements. At the same time, in order to ensure the accuracy of the measurement data, the front end of the temperature measurement tube should be welded and sealed, and no water should be permeated in the tube.