Analyses of the Ground Surface Displacement under Reinforcement Construction in the Shield Tunnel End Using the Artificial Ground Freezing Method

Abstract

There are stringent requirements on the vertical movement of a ground surface when using artificial ground freezing method to reinforce a shield tunnel in a city. This paper focused on the tunnel of Nanjing Metro Line Two between Yixianqiao and Daxinggong. Based on the discrete element thermo-mechanical coupling theory, the horizontal freezing reinforcement project was numerically simulated. The numerical results of the soil temperature field and displacement field are approximately compatible with the field measurements. When the tunnel was frozen for 40 days, an effectively frozen soil wall was created and satisfied the construction requirements. During the freezing construction, both frost heave and thaw settlement obviously occurred. Above the tunnel, the vertical deformation of the ground surface was symmetrical about the center of the tunnel and decayed towards the ends. The maximum vertical displacement of ground surface frost heave was 8 mm, and the maximum vertical displacement of ground surface thaw settlement was 18 mm. Increasing the depth of the tunnel embedment can result in a decline in ground surface displacement. The study serves as a viable means of predicting ground surface displacements.

1. Introduction

Artificial freezing technology is a method of stabilizing the subsoil using an artificial refrigerant to freeze the water in the soil into ice, thereby cementing it to the soil to achieve a water-stopping and reinforcing effect for construction safety. The artificial freezing method has been widely used in the mining and tunneling industry for over 100 years [1,2,3]. This technology has been extensively used in the building of metro tunnels [4], connecting passages [5], and shield machine initiation [6]. However, when the tunnel reinforcement method of freezing is adopted, the ground will undergo an obvious frost heave, and there is thaw settlement movement [5,7,8,9], which will impact the serviceability performance of surface-sensitive buildings and surrounding pipelines as well as the tunnel construction.

The results of soil-freezing experiments indicate that the soil frost heave consists of ground displacement induced by water freezing into ice and fractionated frost heave due to water migration [9,10]. The studies of Everett [11] and Miller [12] provided important theoretical support for a better understanding of the soil freezing mechanism. The Soviet scholar Tsytovich [13] proved through indoor tests that soil melt settlement is composed of both hot melt settlement from melting ice and the settling of soil that has been compacted as a result of external and internal loads, laying the foundation for subsequent related research. Huang et al. [14] used the change in pore ratio as a criterion to establish a three-field coupled moisture–heat–stress model for frozen ground. However, considering the practicality of the artificially frozen ground heave and settlement movement, how to achieve effective prediction of ground surface movement when using the freezing method for reinforcement becomes a pressing issue that should be of greater concern.

To achieve an effective prediction of ground surface movement during freezing construction, many scholars have carried out model tests on the heave and settlement movement of frozen soil. Zhou et al. [15] derived and predicted the temperature field and thaw settlement displacement development for the artificial freezing method of thawing using centrifuge experiments. Tang et al. [16] studied the displacement change law of soft soil in Shanghai during the construction process of the freezing method using a self-designed freezing device. Model tests can provide a visual understanding of soil displacement patterns in freezing construction, but it is difficult to obtain more accurate and consistent conclusions with individual model tests. Furthermore, the conditions required to carry out multiple similar model tests are too demanding.

Numerical simulation allows researchers to obtain a better solution to this problem by performing multiple calculations on a model to predict soil displacement as a guidance of engineering applications. Cai et al. [17] analyzed the temperature distribution and freezing displacement of horizontal freezing by numerical simulation based on an example of a frozen Shanghai metro tunnel project. Based on the segregation potential approach, Konrad et al. [18,19] implemented a prediction of freezing soil with a two-dimensional thermodynamic coupling model, and applied it to the numerical simulation of freezing construction in an existing tunnel in Kobe, Japan. Yang et al. [20] proposed a frost heave prediction model for construction using the freezing method, a thermo-hydro-mechanical coupled model and applied it to engineering practice. Hou et al. [21] combined indoor experiments and numerical simulations to compare and analyze the displacement change patterns of soils during freezing and thawing. Zheng et al. [22] proposed a method to predict the surface displacement during the whole freezing process, and the validity of the method was verified by comparing numerical results with the measured data. Finite element software is mostly based on continuous theory, which does not take into account the discrete characteristics of multiple fine particles in frozen soil, thereby has certain limitations.

To overcome the aforementioned restrictions, the thermo-mechanical coupled theory of the Discrete Element Method (DEM) is used in this study to model the entire process of frost heave and thaw settlement of the soil during the freezing construction of a shield exit hole. The authors used field measurement date to verify the adaptability and accuracy of the model and analyze the effect of tunnel embedment depth on surface soil displacement during freezing construction. This study provides an idea for subsequent frost heave and thaw settlement prediction for freezing-method construction.

2. Project Overview

2.1. Engineering Background

The simulation refers to the freezing and strengthening of the tunnel between Daxinggong Station and Xi’anmen Station on Nanjing Metro Line 2. It is located between Xi’anmen Station and Yixian Bridge, with an under-crossing tunnel and the over-crossing Yixian Bridge. The stratum of this reinforcement project from top to bottom is artificial fill, silty clay, and silt. The depth to the water table is 1.35–1.80 m (elevation of about 8.00 m), and the soil is rich in water and weak in permeability, as seen in Figure 1. Ground surface displacement monitoring is provided at the shield exit to monitor the frost heave and thaw settlement displacement.

To ensure the shield machine safely going out of the ground, freezing pipes were installed at the exit to form a cup-shaped frozen soil wall [23,24]. The freezing pipes in the bottom of the cup are symmetrically positioned horizontally along the horizontal axis, as seen in Figure 2. One freezing tube was installed in the center of the opening, 7 inner ring freezing tubes were arranged in a circle along the opening diameter of 2.7 m, 14 middle ring freezing tubes were arranged in a circle along the opening diameter of 5.1 m, and 31 outer ring freezing tubes were arranged in a circle along the opening diameter of 7.5 m.

2.2. Monitoring Scheme

The project focused on brine temperature monitoring, freeze zone temperature monitoring, and ground displacement monitoring, with the following monitoring program:

(1) Brine temperature monitoring: Valves and temperature measurement points were provided on the brine piping and cooling water circulation piping. Every 3 or 4 freeze tubes in a series were a group, and each group of the series circuit was set as a temperature measurement point. Brine temperature monitoring data are shown in Figure 3.

(2) Freezing zone temperature monitoring: Temperature measurement hole C1 for the outer ring monitoring was located outside the outer ring freezing tube. Temperature measurement hole C2 for the middle ring temperature monitoring was located between the outer ring freezing tube and the middle ring freezing tube. Temperature measurement hole C3 for the inner ring temperature monitoring was located between the inner ring freezing tube and the middle ring freezing tube. Each temperature measurement hole was arranged in 2 to 3 measurement points; the specific layout of the temperature measurement holes is shown in Figure 2.

(3) Ground surface displacement monitoring: The original reference data for ground surface vertical displacement monitoring were established before the construction of horizontal holes. Monitoring began on the first day when the horizontal holes were constructed and continued until the frozen soil wall melts after the completion of the frozen construction. Monitoring displacement twice a day during drilling and once a day during freezing reinforcement can effectively reduce errors in monitoring ground surface frost heave displacement due to uncertainties.

3. Numerical Simulation

3.1. Mathematical Models

In tunnel construction, the freezing temperature field is a transient heat transmission issue with a water–ice phase change. The main form of heat transfer in DEM is contact heat transfer. The heat conduction law is discretized to derive its difference equation to enable the solution of material-specific heat conduction problems under operating conditions [25]. Neglecting the effect of deformation on temperature, the heat transfer equation is shown in Equation (1):

$$-\frac{\partial q_i}{\partial x_i}+q_v=p{C}_v\frac{\partial T}{\partial t}$$

(1)

where $q_i$ is the heat flux, $\mathrm{W}/{\mathrm{m}}^2$; $q_v$ is the heat source intensity per unit volume, $\mathrm{W}/{\mathrm{m}}^3$; $\rho$ is the material density, $\mathrm{kg}/{\mathrm{m}}^3$; $C_v$ is the specific heat capacity, $\mathrm{J}/\mathrm{kg}·°\mathrm{C}$; $T$ is the temperature, $°\mathrm{C}$.

The relationship between heat flux and temperature gradient satisfies Fourier’s law, as shown in Equation (2):

$$q_i=-k_{\mathrm{ij}}\frac{\partial T}{\partial x_{\mathrm{j}}}$$

(2)

where $k_{\mathrm{ij}}$ is the thermal conductivity tensor, $\mathrm{W}/\mathrm{m}·°\mathrm{C}$.

According to the sensible heat capacity method [26], the expressions for its equivalent volumetric specific heat ${\mathrm{C}}^{*}$ and equivalent thermal conductivity ${\mathrm{k}}^{*}$ when simulated are as follows:

$${\mathrm{C}}^{*}=\{\begin{array}{c} C_f , \hspace{1em}T<T_d\\ \frac{ C_f+C_u}{2}+\frac{L}{T_r-T_d}, \hspace{1em}{T}_d\le T\le T_r\\ C_u , \hspace{1em}T>T_r\end{array}$$

(3)

$${\mathrm{k}}^{*}=\{\begin{array}{c} k_f , \hspace{1em}T<T_d\\ k_f+\frac{k_u-k_f}{T_r-T_d}\left(T-T_d\right), \hspace{1em}{T}_d\le T\le T_r\\ k_u , \hspace{1em}T>T_r\end{array}$$

(4)

where

$C_f, C_u$—volumetric specific heat of frost and thawed soils, $\mathrm{kcal}/\left({\mathrm{m}}^3·°\mathrm{C}\right)$;

$k_f,k_u$—thermal conductivity of frost and thawed soils, $\mathrm{kcal}/\left(\mathrm{m}·\mathrm{d}·°\mathrm{C}\right)$;

$T_r,T_d$—melting and freezing temperatures of the soil, $°\mathrm{C}$.

Ice plays an important role in the frozen soil wall. The DEM uses a parallel bond constitutive model to simulate the cohesive action within ice. It can achieve the transfer of forces and moments between particles when frozen soil is stressed. It can also characterize the damage form of frozen soil [27,28]. The parallel bond constitutive model corresponds to alienated particles, which are bonded into a single unit by contact bonds between the particles. These contact bonds are similar to springs with constant stiffness on the contact surface, which act together with the sliding model to counteract the forces and moments generated. The specific intrinsic structure model is shown in Figure 4.

The forces and moments generated by the parallel bond constitutive model contact are shown in Equations (5) and (6):

$${\overline{F}}_i={\overline{F}}_i^n+{\overline{F}}_i^s$$

(5)

$${\overline{M}}_i={\overline{M}}_i^n+{\overline{M}}_i^s$$

(6)

where ${\overline{F}}_i^n, {\overline{F}}_i^s$ denote the normal and tangential components of the force ($\mathrm{N}$); ${\overline{M}}_i^n$,${\overline{M}}_i^s$ denote the normal and tangential components of the moment ($\mathrm{N}·\mathrm{m}$).

Soil freezing and thawing deformation can be regarded as a temperature-dependent transient volume strain problem [29,30], and the DEM can realize this transient change process of soil by particle radius expansion. DEM thermal coupling is achieved through the existence of temperature differences between particles or between particles and walls, where heat is transferred from one particle or wall to another through contact, causing a change in particle temperature, which in turn causes the particles to expand and generate thermal strain. The expression for the amount of change in particle radius is shown in Equation (7):

$$\Delta R=\alpha R\Delta T$$

(7)

where $\alpha$ is the particle linear shrinkage coefficient, $1/°\mathrm{C}$.

A change in temperature leads to a change in the normal contact force vector $\Delta {\overline{F}}_n$ between the particles, as shown in Equation (8):

$$\Delta {\overline{F}}_{\mathrm{n}}=-K\Delta U_{\mathrm{n}}=-{\overline{k}}_{\mathrm{n}}A\left(\overline{\alpha }\overline{L}\Delta T\right)$$

(8)

where ${\overline{k}}_n$ is the normal stiffness of the contact, $\mathrm{N}/{\mathrm{m}}^3$; $A$ is the cross-sectional area of the contact, ${\mathrm{m}}^2$; $\overline{\alpha }$ is the average linear shrinkage coefficient of the contact, $1/°\mathrm{C}$; $\overline{L}$ is the length of the contact, taken as the distance from the center of the particle shape, $\mathrm{m}$; $\Delta T$ is the temperature variation, taken as the average of the temperature variation, $°\mathrm{C}$.

As the particle changes with temperature lead to the breaking of old contacts and the creation of new ones between the particles, the number of heat pipes between the contacts changes constantly, which in turn affects the overall thermophysical properties of the soil. For example, the macroscopic thermal conductivity of the soil increases when new contacts are created; however, the macroscopic thermal conductivity of the soil decreases when the inter-particle contact breaks.

3.2. Material Parameters

The stratum at the location of the freezing project is mainly powdered silty clay, so the silty clay is selected in the simulation. Based on the macroscopic parameters such as elastic modulus and Poisson’s ratio of the actual pulverized clay, the calculation of elastic modulus and Poisson’s ratio based on the plane strain assumption mentioned by Potyondy [31] (as in Equations (9) and (10)).

$$v=\frac{1}{1+\frac{\Delta {\epsilon }_{\mathrm{y}}}{\Delta {\epsilon }_{\mathrm{x}}}}$$

(9)

$$E=\left(1-v^2\right)\frac{\Delta {\sigma }_{\mathrm{y}}}{\Delta {\epsilon }_{\mathrm{y}}}$$

(10)

The parameters characterized by the particles in the numerical simulation were calibrated by using a trial-and-error method, and the calibration of the microscopic parameters was completed when the error between the macroscopic parameter values derived from the simulation and the actual values of the soil was less than 2%.

3.3. Initial Boundary Conditions

The initial conditions of the temperature field at the beginning of freezing work, presuming a uniform initial temperature distribution in the ground, are as follows:

$${T|}_{t=0}=T_0$$

(11)

where $T_0$ is the beginning temperature of the ground, $°\mathrm{C}$.

Each frozen tube can be converted to a single particle in the DEM computation model, resulting in the following expression for the temperature of each frozen tube:

$${T|}_{\left(X_p,Y_p\right)}=T_c\left(t\right)$$

(12)

where ${T|}_{\left(X_p,Y_p\right)}$ are the Cartesian coordinates of each freezing tube particle; $T_c\left(t\right)$ is the temperature of the freezing tube particle, $°\mathrm{C}$, determined by the temperature of the brine in the project.

The frozen soil started to melt spontaneously following the completion of the tunnel segment’s construction. When the soil thaws, the temperature field’s initial conditions are as follows:

$${T|}_{t=0}=T\left(x,y\right)$$

(13)

where $T\left(x,y\right)$ is the freezing temperature, $°\mathrm{C}$, that exists just before the ground thaws.

3.4. Building a Computational Model

Assuming a constant atmospheric temperature of 22 °C and an initial soil temperature of 22 °C and taking into account the influence range of tunnel freezing and the speed of calculation, the specific simulation steps of this simulation are as follows:

(1) Soil generation: The minimum radius of soil particles in the simulation is 0.02 m and the maximum radius is 0.04 m; to study the impact of the frozen tube on the surrounding soil, the center of the tunnel is set as the origin of coordinates to establish a two-dimensional initial soil model of 20 m × 30 m size. The total number of particles is approximately 170,000. The model is given the mechanical parameters shown in

Table 1. Soil physical parameters (drained).

	Effective Modulus (MPa)	Normal-to-Shear Stiffness Ratio	Bond Effective Modulus (MPa)	Bond Normal-to-Shear Stiffness Ratio	Cohesion (kPa)	Tensile Strength (kPa)	Density (kg·m3)
silty clay	6	3	6	3	15	50	1801

, and the particles are given gravity to compact them to their natural state.

(2) Generating freeze tubes: We import 43 frozen pipes with a radius of 0.054 m into the soil, use the “ball delete” command to delete the soil particles at the location of the frozen pipes, and then create a frozen pipe wall with a radius of 0.054 m at that location. Finally, the internal forces of the soil are balanced to complete the model generation.

(3) Set initial conditions: We set the wall as a fixed unit with no displacement and use the “configure thermal” command to enable the program thermal calculation module. The particles were then given the unfrozen soil thermodynamic fine view parameters as in

Table 2. Soil thermophysical parameters.

	Specific Heat (J/(kg·°C−1))	Thermal Conductivity (W/(m·K))	Latent Heat (kJ/kg)	Frost Heave Coefficient (%)	Thaw Settlement Coefficient (%)
silty clay	1710	1.05	92	4.5	6.8

, and the boundary wall was set to a fixed 22 °C. According to the actual brine cooling curve of the project (Figure 2) in the freezing tube temperature of the brine temperature set, the beginning temperature of the ground is set to 22 °C.

(4) Thermal coupling calculation: The thermal coupling calculation module is enabled by the command “set thermal on mechanical on”. The inclusion of a judgment statement enables the particles to be given a coefficient of frost heave (thaw settlement) if the temperature of the soil particles meets the conditions for frost heave (thaw settlement) [32,33,34,35]. The specific calculation process is shown in Figure 5 below.

4. Results and Discussion

4.1. Frost Heave Simulation

Figure 6 shows a schematic diagram of the temperature field over time during the freezing of the tunnel. By the 5th day of freezing, the temperature of the part of the soil in direct contact with the freezing tube dropped below 0 °C, and the frozen soil wall was initially formed with the freezing tube as the center of the circle. By the 10th day of freezing, the radius of the circular frozen soil wall formed by the freezing tube gradually increased, and the soil temperature reached below 0 °C except for the part of the soil within the middle ring of the freezing tube. By 20 days of freezing, the soil inside the frozen pipe reached below −5 °C. The main body of the freeze began to change from the frozen soil between the pipes to the soil outside the pipes, and the freeze impact area began to increase. After 40 days of treatment, the soil inside the frozen tube reached below −10 °C, and the overall temperature of the soil outside the outer ring of the frozen tube dropped. The frozen soil wall thickness met the freezing design requirements, and the positive freezing work was completed.

To further verify the correctness of the development of the freezing temperature field in the DEM simulation of the soil, the temperature change curves of the middle and inner ring temperature measurement holes in the simulation were analyzed and compared with the actual temperature change curves. Figure 7 shows the simulated temperatures of the middle ring temperature measurement holes compared with the measured temperatures. Figure 8 shows the simulated temperatures of the inner ring temperature measurement hole compared with the measured temperatures. The simulated values and measured values are generally in good agreement. However, the heat transfer method in the numerical simulation only considers contact heat transfer, ignoring radiation heat transfer and convection heat transfer; therefore, some calibration corrections that are needed within the simulated values remain.

The computed ground displacement fields of soil frost heave are shown in Figure 9 and Figure 10. From the beginning of freezing to the 5th day of freezing, the main body of freezing is mainly the soil in direct contact with the freezing pipe, and the soil starts to change from the original ground temperature at this stage, so the total amount of frost heave is small and the vertical displacement grows slowly. From day 6 to day 20 of freezing, most of the soil between the frozen pipes freezes. This is the main stage when the soil freezes, and at this moment, the frost heave displacement of the soil grows more quickly. From the 21st day of freezing to the completion of freezing, a small amount of soil swelling occurred outside the outer ring of the frozen pipe, with a relatively slow increase in displacements. After freezing was completed, a maximum vertical soil frost heave displacement of 23 mm and a maximum vertical ground surface frost heave displacement of 8 mm occurred directly above the tunnel.

The ground surface frost heave displacement distributions are shown in Figure 11 and Figure 12. The ground surface displacement distributions are roughly symmetrical about the center of the tunnel. The highest vertical displacement occurs right above the tunnel center, and the displacement of the surface diminishes with increasing transverse distance from the tunnel center. The horizontal displacement of the ground surface increases initially with increasing distance from the tunnel’s center until it reaches a maximum value of 7 m, at which point it starts to decrease. The distribution of frost heave displacement from the top of the tunnel to the surface is shown in Figure 13. The soil displacement at the top of the tunnel is the largest, the freezing displacement decreases with decreasing distance from the surface, and the surface displacement is the smallest.

A comparison of the frost heave displacement monitoring values of the vertical displacement of the ground surface directly above the center of the tunnel for the first 20 days with the simulated values is shown in Figure 14. The figure confirms a strong correlation between the field results and the numerical simulation. This indicates that the application of this numerical simulation method for the analysis of the effect of artificial frozen soil on the displacement of the surrounding soil is accurate and consistent and can feasibly be used in theoretical and practical simulations. The displacement in the measured data shows a tendency of decreasing and then increasing, which occurs because the surface where the freezing project is located is an urban arterial road, on which there is often a vehicle load, resulting in a decreasing trend in the measured results. So, the method still needs some small refinements, as shown in Figure 7 and Figure 8.

4.2. Thaw Settlement Simulation

During the natural thawing process, the temperature of the frozen soil wall curtain rises gradually from the outside and the tunnel tube sheet to the inside of the frozen soil wall. The law of change in soil thawing temperature is similar to the law of change in frost heave temperature and is therefore not discussed specifically. The record of thaw settlement starts with the state of the shield tunnel tube sheet after it has been installed. The computed displacement field of soil thaw settling is shown in Figure 15 and Figure 16. From the start of thawing to 10 days of thawing, only a small part of the frozen soil wall is thawed at this stage due to the influence of the low-temperature frozen soil wall, and the soil thaw settlement displacement grows more slowly at this time. From 11 to 45 days after thawing, the frozen soil wall is gradually thawed from the outermost soil and the soil in contact with the tunnel, when the soil thaw settlement displacement grows at a faster rate. After 45 days of thawing, the frozen soil wall has been thawed and the natural thaw is complete.

The ground surface displacement distributions of the thaw settlement are shown in Figure 17 and Figure 18. The thaw settlement displacement increases with increasing natural thawing time, and the displacement is generally symmetrical about the center of the tunnel, which is the same as the frost heave shown in Figure 11. After the complete thawing of the frozen soil wall, the maximum surface thaw settlement displacement reached 18 mm, and the surface settlement displacement was significantly greater than the surface frost heave displacement. The distribution of thaw settlement displacement from the top of the tunnel to the surface is shown in Figure 19. The soil displacement at the top of the tunnel is the largest, which is the same as the frost heave shown in Figure 13.

A comparison of the thaw settlement displacement monitoring values of the vertical displacement of the ground surface directly above the center of the tunnel for the first 45 days with the simulated values is shown in Figure 20. The figure confirms the strong correlation between the field results and the numerical simulation. However, follow-up grouting was carried out during the thaw settlement process, limiting the development of ground surface displacements, and it is difficult for the numerical simulation to realize this process. There is still a little gap between the measured and simulated values, and the method still needs some small enhancements and refinements.

4.3. Effect of Burial Depth

To further study the effect of the depth of tunnel burial on the freezing construction of the project, four additional freezing options were selected for the tunnel burial depths of 15 m, 17 m, 21 m, and 23 m, respectively. The vertical displacement of the ground surface frost heave under different burial depth conditions is shown in Figure 21, and the maximum ground surface frost heave displacement is shown in Figure 22. The study’s findings indicated that it is decreasing for the frost heave displacement at each location while increasing the burial depth of the tunnel. This suggests that the frost heave displacement of the soil during the freezing-method construction is severely affected by the tunnel’s depth.

The ground surface thaw settlement displacement for different burial depths is shown in Figure 23, and the maximum ground surface thaw settlement displacement is shown in Figure 24. As can be seen from the graphs. The greater the depth of burial, the greater the overburden load on the soil, and the smaller the thaw settlement displacement is at each point. The reduction is greater compared to frost heave displacement. This suggests that the tunnel’s level of embedment has a significant inhibitory impact on the displacement of soil caused by thaw settlement during freezing-technique construction.

When the burial depth of the tunnel increases, the pressure load acting on the frozen wall increases, which inhibits the development of frost heave and thaw settlement movement of the soil. On the other hand, an increase in tunnel burial depth implies an increase in the distance to the surface, leading to a reduction in the displacement transmitted to the surface.

5. Summary and Conclusions

This study simulated the horizontal freezing and strengthening of the tunnel between the Yixianqiao and Daxinggong sections of Nanjing Metro Line 2 to create a thermo-mechanical coupling calculation model for the changes in the soil temperature and displacement fields during freezing construction. To forecast how much soil will undergo frost heave and thaw settlement, the authors employed the DEM simulation approach. The findings of the study demonstrate the following:

(1) The DEM numerical model developed can accurately simulate the freezing-method tunnel construction process and achieve an effective simulation of the ground surface deformation caused by the freezing-method construction, which offers fresh perspectives and direction for the forecasting of ground surface displacement in future projects.

(2) The frozen soil wall is initially formed with the freezing tube as the center of the circle at the beginning of the freezing cycle and thereafter expands with the increase in freezing time. After 40 days of freezing, a cup-shaped frozen soil wall was formed, meeting the design requirements for freezing reinforcement.

(3) As the freezing (thawing) days rises, the soil experiences larger frost heave (thaw settlement) displacement. Typically, the frost heave displacement is smaller than the thaw settlement displacement. The vertical displacement caused by frost heave and thaw settlement grows almost symmetrically around the tunnel’s center, gradually decreasing towards the ends until it reaches zero. The maximum surface frost heave displacement of 8 mm and the maximum thaw settlement displacement of 18 mm occur directly above the center of the tunnel for the case modeled. People can set up heating limit pipes and thawing grouting pipes right above the center of the tunnel to effectively reduce the displacement.

(4) The depth of tunnel embedment has a major influence on the frost heave and thaw settlement of the soil caused by the freezing construction. The greater the burial depth of the tunnel, the smaller the surface heave and settlement movement. If there is a need to reduce the amount of heave and settlement movement deformation in subsequent freezing work, the depth of tunnel embedment should be increased appropriately.