Sensitivity Analysis of Different Factors in the New Pipe Curtain Freezing Method under Seepage Conditions

Abstract

This paper takes the freezing project of the North Arch Tunnel of the Hong Kong–Zhuhai–Macao Bridge as an example. Based on Darcy’s law and the theory of heat transfer in porous media, using the coupled module of the temperature field and seepage field in the COMSOL Multiphysics software, numerical simulations of the freezing reinforcement of the new pipe curtain freezing method are conducted to study the influence of different factors on this method under seepage conditions. The research shows that an increase in the groundwater flow velocity will affect the development of frozen soil curtains, prolonging the formation time of frozen soil curtains. A rise in the initial ground temperature will increase the time required for the formation of frozen soil curtains during the freezing process, resulting in a slight increase in the temperature of the final frozen soil curtains. With an increase in the salinity of the groundwater, the temperature at the temperature measurement point upstream of the freezing pipe increases, while the temperature at the temperature measurement point downstream of the freezing pipe decreases. The average temperature of the frozen soil curtain also increases with an increase in the salinity of the groundwater. This study is expected to provide a valuable reference for similar projects in the future.

1. Introduction

The development of underground public spaces is considered a major contributor to urban sustainable development [1]. The selection of auxiliary methods in tunnel construction is particularly important [2]. The method of combining pipe curtains with artificial freezing represents a new tunnel excavation method suitable for water-rich environments, and it was successfully applied for the first time in the North Arch Tunnel of the underground excavation section of the Hong Kong–Zhuhai–Macao Bridge [3].

Regarding the pipe curtain method, Japan has conducted extensive research in this direction and was the first to propose combining pipe curtain steel pipes with freezing methods for construction [4,5,6]. In the construction of the North Arch Tunnel using this method, the team, led by Hu Xiangdong [7,8,9], conducted theoretical analysis, indoor physical experiments, studies on the freezing and water sealing effects and composite structural support effects, on-site in situ tests, and other research on the innovative “pipe curtain freezing method”, providing a technical reference for engineering construction and achieving good practical results. Hu Jun et al. [10] improved the pipe curtain freezing method for the Gongbei Tunnel of the Hong Kong–Zhuhai–Macao Bridge and proposed a new patented technology for the pipe curtain freezing method, studying its cooling effect. Compared to the traditional pipe curtain freezing method, this construction method places the freezing pipes outside the steel pipes of the pipe curtain. The freezing pipes and steel pipes are arranged alternately. According to the structural shape of the underground engineering project being constructed, the supporting structure can be arranged in a rectangular or circular shape or in any other shape.

However, in the field of civil engineering, the introduction of construction techniques often follows practice before theoretical research. The pipe curtain freezing method is no exception. The existing research works and reports on the pipe curtain freezing method are mainly based on engineering examples, with relatively little theoretical research.

In frozen engineering in permeable soil layers, the impact of the groundwater flow on frozen soil curtains needs further research. Groundwater seepage carries heat, and the velocity of the groundwater flow plays a decisive role in whether frozen engineering projects can be completed smoothly [11,12,13]. In order to conduct in-depth research on the coupling of the seepage field and temperature field, domestic and foreign researchers have used various research methods, such as field measurement, indoor physical model tests, and numerical finite element analysis [14,15,16]. Many achievements have been obtained on the issue of water–heat coupling and relevant industry standards have been formulated [17,18,19,20]. However, the research has focused more on mine and rock fissure flows. The study of the temperature field of frozen pipes under seepage conditions often uses numerical simulations combined with physical model experiments to study single-row and multi-row frozen pipes. There is relatively little research on the new pipe curtain freezing method under seepage conditions.

This study combines the theory of heat transfer in porous media and Darcy’s law. Based on the actual engineering of the Gongbei Tunnel, a new pipe curtain freezing model under seepage conditions is established using the COMSOL 6.0 finite element software. The study investigates the influence of different factors on the new pipe curtain freezing method under seepage conditions, aiming to provide a reference for similar projects in the future.

2. Project Overview

The construction of the North Arch Tunnel of the Hong Kong–Zhuhai–Macao Bridge is the most difficult and significant engineering stage of the entire bridge project. The dark excavation section of the North Arch Tunnel is 225 m long. When viewed from above, the plan of the North Arch Tunnel presents a curved shape, with a curvature radius of R = 885.8~906.2 m. The excavation width and height of the section are 18.8 m × 21.0 m. A working well is set at the connection of the dark excavation section with other open excavation sections.

2.1. Freeze Pipe Deployment

A segment of the Guangbei Tunnel’s bored pile casing is composed of 36 steel pipes, which are divided into single-digit and double-digit pipes. The thickness of the single-digit pipes (24 mm) is different from that of the double-digit pipes (20 mm). The pipe spacing is approximately 35.6 mm. The single-digit pipes are solid-bottomed and concrete-filled, a circular freezing pipe arrangement inside. The circular freezing pipe is a 108 mm diameter round steel pipe. The double-digit pipes are open-bottomed, and, within them, two irregular freezing pipes are placed. These irregular pipes form a sector-shaped cross-section by surrounding the empty space of the steel pipe with 30 mm × 30 mm angle steel. The tunnel cross-section is illustrated in Figure 1.

2.2. Temperature Measurement Point Layout

The entire pipe curtain freezing project of the Gongbei Tunnel is equipped with a total of 32 temperature measurement sections, with spacing of 8 m between them. The arrangement of the temperature measurement holes in each temperature measurement section is consistent, and the overall layout of the temperature measurement points in a certain temperature measurement section is shown in Figure 2 [6].

Each curtain wall steel pipe is equipped with temperature measurement points, with seven temperature measurement points arranged in odd-numbered pipes and six in even-numbered pipes. The number of temperature measurement points on the outer side of the steel pipe is between three and seven.

3. Numerical Simulation

Due to the bidirectional coupling effect of the seepage field and temperature field, a complete freezing process is formed. Only by combining the joint action of the seepage field and temperature field can the variation law of the temperature field under seepage conditions be fully and comprehensively understood. This study simplifies the calculation of water–heat coupling and makes the following assumptions.

(1)

Assuming an initial soil layer temperature of 20 °C, the soil is considered to exhibit groundwater flow characteristics, and it is assumed to be uniformly distributed within the model, with the material properties varying uniformly with the temperature and with the change process solely influenced by the temperature.

(2)

The model is set up with the inflow and outflow at the left and right sides as groundwater flow zones, while the other surfaces are impermeable. The flow within the model is a unidirectional horizontal groundwater flow, with fixed head conditions upstream and downstream, in line with Darcy’s law.

(3)

The temperature load is directly applied to the freezing walls of the circular and irregular freezing pipes in the model. Heat loss during heat exchange between the refrigerant and the soil, as well as water migration during the freezing process, is neglected in the calculation.

(4)

The soil is assumed to start freezing when its temperature drops below −1 °C, with heat transfer during the freezing process considered only through conduction and convection.

(5)

The computational model developed in this research is a fully coupled water–heat model, disregarding the influence of stress fields on the temperature field in practical engineering scenarios.

3.1. Temperature Field Heat Transfer Equation

Based on the heat transfer principle in porous media, the differential equation governing the freezing temperature field under the groundwater influence can be expressed as [22]

$$C_{eff}\frac{\partial T}{\partial t}-\nabla ({\lambda }_{eff}\nabla T)+C_f\overrightarrow{u}\nabla T=\epsilon {\rho }_{w}L\frac{\partial {\theta }_w}{\partial t}+Q_G$$

In the above equation,

$C_{eff}$—equivalent volume heat capacity ($\mathrm{J}\cdot (\mathrm{kg}\cdot \mathrm{K}{)}^{-1}$);

$T$—temperature (°C);

$C_f$—equivalent fluid heat capacity ($\mathrm{J}\cdot (\mathrm{kg}\cdot \mathrm{K}{)}^{-1}$);

$\epsilon$—soil porosity;

${\rho }_w$—water density ($\mathrm{kg}\cdot {\mathrm{m}}^{-3}$);

$\overrightarrow{u}$—fluid darcy flow velocity vector ($\mathrm{m}\cdot {\mathrm{s}}^{-1}$), controlled by Darcy’s law;

$L$—latent heat of ice–water phase change ($\mathrm{kJ}\cdot \mathrm{k}{\mathrm{g}}^{-1}$)—this study adopts a value of 333 ($\mathrm{kJ}\cdot \mathrm{k}{\mathrm{g}}^{-1}$);

${\theta }_w$—water content ratio or moisture content;

${\lambda }_{eff}$—effective thermal conductivity coefficient ($\mathrm{W}\cdot (\mathrm{m}\cdot \mathrm{K}{)}^{-1}$);

$Q_G$—heat source ($\mathrm{W}\cdot {\mathrm{m}}^{-3}$).

3.2. Darcy Flow Equation in a Porous Medium Field

This study assumes a groundwater flow in a single direction, setting the Reynolds number range for the groundwater flow as [1,10] to ensure a laminar flow, in accordance with Darcy’s law [23]. The governing equations for the flow in the porous medium under the temperature field influence are as follows:

$${\rho }_w[{\alpha }_w\varphi +{\alpha }_s(1-\varphi )]\frac{\partial p}{\partial t}+\nabla \cdot ({\rho }_w\overrightarrow{u})=Q_m$$

where the expression of Darcy’s law is

$$\overrightarrow{u}=-\frac{k}{{\rho }_{w}g}\nabla p$$

In the above equation,

$\varphi$—porosity of soil;

$p$—hydraulic head or hydraulic pressure ($\mathrm{kPa}$);

$k$—hydraulic conductivity ($\mathrm{m}\cdot {\mathrm{s}}^{-1}$)—its value varies with the temperature changes;

${\alpha }_w,{\alpha }_s$—coefficients of expansion for water and soil particles, respectively ($1/\mathrm{K}$);

$Q_m$—mass source in the flow field ($\mathrm{W}\cdot {\mathrm{m}}^{-3}$).

3.3. Equation for the Phase Transition of Ice and Water

As the soil temperature decreases, the water within the soil freezes, leading to the continuous formation of a permafrost layer. This process releases substantial latent heat during freezing, which in turn affects the development of the permafrost barrier. In addition to latent heat, other physical parameters of the material also change with the decreasing temperature. To simplify the model calculations, we disregard any discontinuities in these changes and employ the Heaviside function [24] for a simplified representation of the parameter variation process. This is denoted by H(T), with the following expression:

H(T) = flc2hs(T − T, dT)

In the equation, T—soil temperature (°C);

Td—phase change temperature of water (°C);

dT—range of phase change temperature values adopted in this paper [−1 °C, 0 °C].

During the freezing of the soil, the permeability approaches zero, and there is no flow velocity within the soil. This change can also be represented using the Heaviside function, with the expression as follows:

$$K(T)=(K_u-K_f)\times H(T)+K_f\times H(T)$$

In the equation,

$K_u$—permeability coefficient of soil at room temperature ($\mathrm{m}\cdot {\mathrm{d}}^{-1}$);

$K_f$—permeability coefficient of frozen soil ($\mathrm{m}\cdot {\mathrm{d}}^{-1}$), assigned a numerical value of $1\times {10}^{-20}\mathrm{m}\cdot {\mathrm{d}}^{-1}$.

3.4. Geometric Model, Mesh Division, and Observation Path Layout

Finite element analysis is widely used in geotechnical engineering [25,26,27,28,29,30], and the commercial finite element software COMSOL is used in this study. When conducting the three-dimensional modeling of the new pipe curtain freezing method, the width and height of the excavation area within the pipe curtain freezing pipe are 18.8 m × 21 m. The odd-numbered pipes are solid top pipes filled with concrete and arranged with circular freezing pipes; the even-numbered pipes are freezing pipes with irregular freezing pipes arranged inside. The solid top pipes and empty top pipes are alternately arranged with spacing of 36 mm. The diameter of the curtain steel pipe is 1.62 m, and the diameter of the freezing pipe is 108 mm, with spacing of 791.6 mm between the curtain steel pipe and the freezing pipe. The thickness of the overlying soil is set to 5 m. According to the freezing range and considering the influence of the groundwater flow on the frozen soil curtain, the entire model dimensions (Y) × width (X) × height (Z) = 100 m × 20 m × 50 m. The model is meshed using a free tetrahedral model, defined with appropriate mesh sizes to ensure the convergence and accuracy of the computational model. The model boundaries use a larger mesh density to simplify the model calculations, while a smaller mesh density is used for the freezing zone of the freezing pipe. This study calculates a total of 899,432 grid cells for the final partition, with the smallest cell size being 0.1522. A schematic diagram of the model’s mesh division is shown in Figure 3. Taking the smallest grid size computationally feasible as a reference, the smallest cell size is increased to 0.03926, resulting in a total of 535,172 grid cells for the final partition. A finite element model with two different grid sizes is computed, and the simulation outcomes show deformation values within a 5% range. The test results confirm the grid independence. The grid partition after increasing the smallest cell size is depicted in Figure 4. The new pipe curtain freezing model also sets the front side (y = 0 m) and back side (y = 100 m) positions in the model length direction as constant-temperature permeable boundaries, while the remaining model boundaries are adiabatic impermeable boundaries. The dimensions of the three-dimensional model are length (Y) × width (X) × height (Z) = 100 m × 20 m × 50 m. The model boundaries use a larger mesh density to simplify the model calculations, while a smaller mesh density is used for the freezing zone of the freezing pipe. A schematic diagram of the boundary settings for the new pipe curtain freezing model under seepage conditions is shown in Figure 5.

3.5. Selection of Relevant Parameters

According to the ‘Geological Survey Report of the Gongbei Tunnel Project’, the soil material parameters are assigned. It is assumed that the thermal physical parameters of the concrete in the top pipe and within the top pipe do not change with the temperature. The material parameters in the three-dimensional model of the new pipe curtain method are taken from

Table 1. Thermal physical parameters of each soil layer.

Soil Layer		Density Kg/m3	Moisture Content %	Thermal Conductivity W/(m·K)	Specific Heat J/(kg·K)	Latent Heat of Phase Change KJ/m3	Permeability Coefficientcm M/d
Artificial fill soil	Unfrozen soil	1600	16.05	1.398	1420	36.32	2.97 × 10−2
	Frozen soil			1.690	1360
Medium gravel sand	Unfrozen soil	2000	13.54	1.217	1410	31.48	2.86 × 101
	Frozen soil			1.758	1340
Silty clay with silt	Unfrozen soil	1820	47.6	1.485	1510	41.26	1.98 × 10−4
	Frozen soil			1.772	1450
Fine clay	Unfrozen soil	2010	26.37	1.537	1560	56.24	1.50 × 10−4
	Frozen soil			1.824	1470
Medium sand	Unfrozen soil	2020	17.92	1.439	1430	32.87	3.98 × 100
	Frozen soil			1.756	1360
Gravelly clay	Unfrozen soil	1890	31.98	1.442	1580	48.25	5.78 × 10−4
	Frozen soil			1.790	1470

[31].

4. The Influence of Different Factors on the Development of Temperature Field Patterns

A quantitative analysis was conducted along path DGJ-3 perpendicular to the direction of the groundwater flow and path DGJ-4 along the direction of the groundwater flow. Figure 6 shows a schematic diagram of the path at X = 10 m.

4.1. The Influence of Different Seepage Velocities on the Temperature Field of the New Pipe Curtain Freezing Method

In order to study the influence of different seepage velocities on the temperature field of the new pipe curtain freezing method under seepage conditions, different seepage velocities were set according to the step length for multiple numerical simulations. The initial seepage velocity was 0.27 m/d, increasing by 1 m/d each time. The freezing times of the soil curtain and the final frozen soil curtain formed under different seepage velocities were analyzed to obtain the influence of the seepage velocity changes on the new pipe curtain freezing method, providing a reference for similar projects in the future. Seepage velocities of 0.27 m/d, 2.27 m/d, 4.27 m/d, and 6.27 m/d were selected for the overall frozen soil curtain cloud map analysis. Figure 7 shows the influence of the different seepage velocities on the new pipe curtain freezing method. Under the initial seepage velocity, the new pipe curtain freezing method initially formed a frozen soil curtain after 25 days of freezing, and the frozen soil curtain steadily developed with the passage of the freezing time. When the seepage velocity increased to 2.27 m/d, at 25 days of freezing, the development of the frozen soil curtain was significantly slower than that under the initial seepage velocity. The water flow could still be seen within the area enclosed by the frozen soil curtain, indicating that the frozen soil curtain was not fully closed at this point. With the continuous application of cooling from the freezing pipes, the new pipe curtain freezing method formed a stable frozen soil curtain. When the seepage velocity increased to 4.27 m/d, the influence of the groundwater on the new pipe curtain freezing method under this seepage condition became increasingly apparent. The development of the frozen soil curtain was slow; in particular, the frozen soil curtains on the upstream and downstream faces of the new pipe curtain structure had not closed, even after 70 days of freezing. By the end of freezing (90 days), there was a layer of a weaker frozen soil curtain. When the seepage velocity increased to 6.27 m/d, it was evident that the groundwater flow had a significant impact on the formation of the frozen soil curtain under the new pipe curtain freezing method. A complete frozen soil curtain was not formed throughout the entire freezing period. Gaps in freezing still existed on the upstream and downstream faces of the new pipe curtain freezing structure, and the water flow passed through the excavation area enclosed by the steel pipes and freezing pipes. In practical engineering, this would pose a significant safety hazard for subsequent construction and excavation.

4.2. Effect of Initial Ground Temperature

In order to investigate the influence of different initial ground temperatures on the new pipe curtain freezing method under seepage conditions, the initial ground temperature is set as the only variable under typical parameters. Different models with varying initial ground temperatures are numerically obtained to analyze their respective outcomes. Six different initial ground temperatures ranging from 10 °C to 35 °C are set at intervals of 5° C to study the effects of different initial temperatures on the new pipe curtain freezing method.

Based on the previously set temperature measurement paths DGJ-3 and DGJ-4, two temperature measurement points are selected along the paths: one located directly between the freezing pipes and the other positioned 1 m away. Figure 8 shows the cooling curves of the different temperature measurement points on the two different paths. From Figure 8, it can be observed that with the increase in the initial ground temperature, the time required for the new pipe curtain freezing method to form a frozen soil curtain under seepage conditions is prolonged, and the final temperature of the frozen soil curtain also increases. The time taken for each point on the path to reach −1 °C (freezing temperature) is also extended with the increase in the original ground temperature. Moreover, the cooling curve of the temperature measurement point becomes more susceptible to the influence of the increase in the initial temperature as the distance from the freezing pipe increases. Taking point DGJ-3-5 as an example, when the original ground temperature is 10 °C, the time required for point DGJ-3-5 to reach −1 °C is 28 days. When the original ground temperature increases to 25 °C, the time required for point DGJ-3-5 to reach −1 °C is 46 days, extending the freezing time by 18 days. When the original ground temperature increases to 35 °C, the time required for point DGJ-3-5 to reach −1 °C is 58 days, extending the freezing time by 30 days. At the same time, the final freezing temperature of temperature measurement point DGJ-3-5 also increases with the rise in the initial temperature. When the initial temperature increases from 10 °C to 35 °C, the final freezing temperature increases from −16.77 °C to −8.66 °C, with a rise of 8.11 °C. The frozen soil engineering design stipulates that the final frozen soil curtain temperature should not exceed −10 °C, which is not met when the initial ground temperature is 35 °C.

Through a horizontal comparison, on the same path, it is found that the temperature decrease at the temperature measurement points farther from the freezing pipes reacts more slowly to the increase in the initial ground temperature, and it is more influenced by the rise in the original ground temperature. Through a vertical comparison, it is found that the temperature measurement points at the same position on the two paths are both affected by the increase in the initial ground temperature. However, the temperature decrease at point 2 on DGJ-4, located on the upstream side, is slower than that at point 4 on temperature measurement path DGJ-3 on the downstream side of the curtain due to the influence of the groundwater flow. Similarly, due to the partial removal of cold energy by the groundwater flow, the cooling curve at point 5 on path DGJ-3 differs from that at point 3 on path DGJ-4.

According to the engineering design requirements, in order to meet the construction excavation requirements, the thickness of the frozen soil curtain should be greater than 2 m and the average temperature should be less than −10 °C. Based on the final freezing temperature calculation at the temperature measurement point DGJ-3-5, located 1 m away from the freezing pipe, for every 5 °C increase in the original ground temperature, the final freezing temperature increases by 1.62 °C. When the initial ground temperature is greater than 35 °C, it significantly affects the formation of the frozen soil curtain in permeable conditions. Therefore, in practical frozen soil engineering, it is crucial to enhance the monitoring of the initial ground temperature.

4.3. The Impact of the Salt Content on the New Pipe Curtain Freezing Method

In frozen engineering in coastal formations, not only does the impact of the groundwater flow need to be considered, but the influence of changes in the salt content in the underground soil layers caused by seawater infiltration on frozen engineering also needs to be taken into account. In order to study the influence of different salt content in various soil layers on the new pipe curtain freezing method under seepage conditions, this study adopts four different salt content values of 0%, 2%, 4%, and 6% and conducts a numerical analysis on models with different salt content. The calculated results provide a reference for similar engineering projects.

In frozen engineering, specific attention needs to be paid to the freezing effect in predominantly water-rich sand layers or in formations with flowing water. In order to simplify the model calculations, only sand layers are used in this model to simulate the permeable layers with different salt content. Additionally, to enhance the display of the calculation results, a seepage velocity of 4.27 m/d is set. Based on the experimental research by Lin [17], the thermal physical parameters of salt solutions with different salt content are obtained. The thermal physical parameters are listed in

Table 2. Thermal physical parameters of salt solution with different salt content.

Salt Content /%	Density Kg/m3	Thermal Conductivity W/(m·K)	Specific Heat Capacity J/(kg·K)	Freezing Point Temperture °C
0	1000	0.630	4180	0
2	1013	0.598	4074	−1.47
4	1027	0.594	3958	−3.01
6	1041	0.591	3894	−4.02

.

Table 3. Parameters of ice after phase transition.

Ice	Density Kg/m3	Thermal Conductivity W/(m·K)	Specific Heat Capacity J/(kg·K)	Latent Heat Kg/m
	918	2.31	2050	330

shows the parameters of ice after a phase change [32,33,34,35].

A temperature curve analysis is conducted on temperature measurement point DGJ-4-2 located in the freezing interval of temperature measurement path DGJ-4, as well as temperature measurement points DGJ-4-1 and DGJ-4-3 located at 1 m on each side of DGJ-4-2.

Figure 9 shows the temperature variation curves of the temperature measurement points with different salt content. The curves clearly indicate that temperature measurement point DGJ-4-1 upstream of the freezing pipe is most affected by the salt content. The freezing time of the measurement point increases with higher salt content, and the final freezing temperature also rises. The different salt content also affects the encircling time of the frozen soil curtain in the new pipe curtain freezing method, with the freezing time of DGJ-4-2 increasing with the salt content. In contrast, the freezing condition at temperature measurement point DGJ-4-3, located downstream of the freezing pipe, shows the opposite result to that of DGJ-4-1, which is upstream. As the salt content increases, the freezing time at DGJ-4-3 decreases, and the final temperature also drops. This indicates that the variation in the salt content not only affects the final freezing effect of the frozen soil curtain but also influences the formation process of the frozen soil curtain. Before the temperature reaches the freezing point, due to the flow of the groundwater and the presence of large ions in the salt solution, the free ions freeze only when they reach the downstream region, disrupting the normal formation of the frozen soil curtain.

In frozen engineering, an important indicator when measuring the frozen soil curtain is its average temperature, so it is also necessary to consider the effect of changes in salt content on the average temperature of the frozen soil curtain. Figure 10 shows the average temperature of the final frozen soil curtain formed under different salt content. From the figure, when the salt concentration is below 4%, the gradient of the temperature increase in the frozen soil curtain is substantial and relatively consistent. However, as the salt content increases further, the gradient of the temperature rise exhibits significant variation, with the gradient decreasing.

In conclusion, the salinity of the groundwater has a significant impact on the freezing temperature field in frozen engineering, especially in coastal areas. When conducting construction using the freezing method in underground engineering, attention should be paid to the groundwater and its salinity.

5. Conclusions

This study is based on the construction of a geometric model of the pipe curtain freezing method in the Gongbei Tunnel. The empty top pipe in the pipe curtain structure is replaced by a freezing pipe, and a new type of pipe curtain freezing method is formed by the alternate combination of the pipe curtain and the freezing pipe. A three-dimensional numerical calculation model of the new pipe curtain freezing method under seepage conditions was established according to the actual material parameters of the Gongbei Tunnel. Firstly, the three-dimensional model was cut at different positions to analyze the temperature field cloud map and isotherms of the new pipe curtain freezing method under seepage conditions. Secondly, the cooling curve of symmetric points upstream and downstream of the freezing pipe was analyzed, and the influence of the groundwater flow on the freezing temperature field was studied. Finally, in order to investigate the effects of different factors on the new pipe curtain freezing method under seepage conditions, calculation models with different seepage velocities, different initial ground temperatures, and different salt content were established, and the results were analyzed through single-factor analysis.

This study mainly draws the following conclusions.

(1) An increase in the groundwater flow rate will affect the development of frozen soil curtains, prolonging the formation time of frozen soil curtains. When the seepage velocity reaches 4.27 m/d, the “tail” formed by the groundwater flow at the downstream position of the new pipe curtain freezing structure increases, and the encirclement time of the frozen soil curtain shows “explosive” growth. When the seepage velocity reaches 5.27 m/d, the frozen soil curtain does not close, and with the increase in the seepage velocity, a certain number of “frozen gaps” are formed.

(2) An increase in the initial ground temperature will lead to an increase in the time taken for the formation of frozen soil curtains during the freezing process. The temperature of the frozen soil curtain formed in the end will slightly rise with the increase in the initial ground temperature. For every 5 °C increase in the initial ground temperature, the temperature of the frozen soil curtain increases by 1.6 °C. When the initial temperature is greater than 35 °C, it significantly affects the formation of the frozen soil structure under seepage conditions, necessitating the enhanced monitoring of the original ground temperature in practical freezing engineering projects.

(3) With an increase in the groundwater salinity, different temperature measurement points undergo varying changes. The temperature at the temperature measurement point located upstream of the freezing pipe increases with an increase in salinity, while the temperature at the temperature measurement point downstream of the freezing pipe decreases with an increase in salinity. The average temperature of the frozen soil curtain also increases with an increase in the groundwater salinity. The salinity of the groundwater has an impact on the development of the freezing temperature field in frozen engineering, especially in coastal areas; thus, attention needs to be paid to the groundwater and its salinity during construction using the freezing method in underground engineering.