Cold region tunnel water thermal coupling numerical modeling method and system

Abstract

The invention belongs to the technical field of tunnel engineering, and particularly relates to a cold region tunnel water thermal coupling numerical modeling method and system. The method comprises the following steps: establishing an equal-proportion tunnel geometric model; defining equation variables, and setting various parameters, boundaries and initial conditions of materials; performing grid division to obtain a tunnel numerical calculation model; based on the tunnel numerical calculation model, solving a pre-constructed tunnel hydrothermal-thermal coupling mathematical model to obtain tunnel temperature field, moisture field and stress field distribution data; the tunnel water thermal-mechanical coupling mathematical model comprises a temperature field control equation, a moisture field control equation and a stress field control equation; and visualizing the distribution data of the temperature field, the moisture field and the stress field of the tunnel to obtain the change conditions of the temperature field, the moisture field and the stress field of the tunnel in winter. The method can effectively simulate and analyze the distribution conditions of moisture, temperature and stress of the tunnel in the cold region under the multi-field coupling condition, and provides scientific basis for design and maintenance of tunnel engineering in the cold region.

Description

Technical Field

[0001] The present invention belongs to the technical field of tunnel engineering, and particularly relates to a numerical modeling method and system for water-heat-stress coupling in cold-region tunnels. Background Art

[0002] Highway and railway transportation road networks are being continuously improved, and more and more highway tunnel projects are being built in high-altitude or high-latitude frigid regions. Most of the existing tunnels in these regions are located in frozen soil areas with inaccessible locations and extremely harsh climate conditions, and tunnel frost damage is widespread. Through the investigation of tunnel diseases in cold regions, it is found that 80% of the tunnels in cold regions have varying degrees of frost damage problems, which are usually manifested as deterioration of lining materials, tunnel deformation and cracking, concrete spalling, water seepage, icing, etc., seriously affecting the operation and normal use of the tunnels. Frost damage is mainly caused by the combined action of multiple factors such as moisture, temperature, and stress in the tunnel, which is a complex water-heat-stress coupling process.

[0003] Currently, the research on the water-heat-stress coupling method in cold regions is in a stage of continuous development, and most of them take frozen soil as the research object. There are many defects in carrying out the water-heat-stress coupling research on cold-region tunnels based on this, such as the differences in the boundary conditions between frozen soil and tunnels, the different control equations, and the differences in model assumptions, etc. Moreover, the frozen soil model cannot well describe the coupling effects between tunnel engineering and temperature, unfrozen water, and deformation. Summary of the Invention

[0004] The purpose of the present invention is to provide a numerical modeling method for water-heat-stress coupling in cold-region tunnels, which solves the problem of inaccuracy existing in the existing water-heat-stress coupling methods in cold regions.

[0005] The present invention is realized through the following technical solutions: A numerical modeling method for water-heat-stress coupling in cold-region tunnels includes the following steps: (1) Establish an equal-proportion tunnel geometric model according to the actual working conditions of the tunnel project; (2) Based on the tunnel geometric model, define equation variables, set various parameters of materials, temperatures at each boundary, and initial conditions; (3) Conduct refined mesh division on each region of the tunnel geometric model to obtain a tunnel numerical calculation model; (4) Solve the pre-constructed tunnel water-heat-stress coupling mathematical model based on the tunnel numerical calculation model to obtain distribution data of the tunnel temperature field, moisture field, and stress field; the tunnel water-heat-stress coupling mathematical model includes a temperature field control equation, a moisture field control equation, and a stress field control equation; (5) Visualize the distribution data of the tunnel temperature field, moisture field, and stress field to obtain the variation conditions of the tunnel temperature field, moisture field, and stress field in winter.

[0006] Furthermore, in step (2), the temperatures at each boundary are set according to the on-site measured data. The two side boundaries of the tunnel are subject to horizontal displacement constraints and are set as impermeable boundaries; the bottom boundary is a vertical fixed constraint, and the upper boundary is a free boundary.

[0007] Furthermore, in step (4), the temperature field control equation is expressed as:

[0008] In the formula, is the volumetric heat capacity of the tunnel insulation layer; is the thermal conductivity of the lining; is the temperature of the surrounding rock; is the specific heat capacity of water; is the seepage velocity of the water flux; is the latent heat of ice-water phase change; , are the densities of ice and water respectively; is the volume content of pore ice; is the Hamiltonian operator; t is the time.

[0009] Furthermore, in the calculation of heat conduction problems accompanied by phase change, the apparent heat capacity method is adopted. It is assumed that the phase change occurs within a temperature range near the phase change temperature . When constructing the equivalent heat capacity, the influence of is taken into account. The expressions for the constructed volumetric heat capacity and thermal conductivity are:

[0010]

[0011] In the formula, is the assumed phase change; the subscripts represent the frozen and melting states respectively; C f is the volumetric heat capacity in the frozen state; C u is the volumetric heat capacity in the melting state; T p is the phase change temperature; λ f represents the thermal conductivity in the frozen state; λ u represents the thermal conductivity in the melting state; T represents the temperature.

[0012] Furthermore, in step (4), the moisture field control equation is expressed as:

[0013] In the formula, is the specific water capacity; is the matric potential; and are the volume contents of unfrozen water and ice respectively; 、 are the densities of ice and water respectively; is the isothermal hydraulic conductivity under the influence of the hydraulic gradient; is the non-isothermal hydraulic conductivity under the influence of the temperature gradient; is the unit vector along the gravity direction; is the Hamiltonian operator; T represents temperature; t represents time.

[0014] Furthermore, the VG matric suction model is adopted to describe the soil-water characteristic curve, and the relationship expression between the effective saturation and the matric potential is expressed as:

[0015] In the formula, is the effective saturation; 、 are the saturated water content and the residual water content respectively; According to Mualem's pore distribution model, the impedance factor is introduced to determine and , and their expressions are as follows:

[0016]

[0017] Among them,

[0018]

[0019]

[0020] In the formula: is the hydraulic conductivity of the saturated soil mass; is the permeability of the unsaturated soil; is the hydraulic diffusion coefficient in frozen soil; 、 、 are all fitting parameters determined by the soil properties; is the gain factor related to the soil temperature; is the surface tension of soil water, ; is the surface tension value of soil water at 25°C; Impedance factor represents the hindrance effect of the presence of pore ice on the migration of unfrozen water.

[0021] Furthermore, in step (4), the stress field control equation is expressed as:

[0022] wherein, is the differential operator; is the total stress tensor; is the body force vector; , is the displacement tensor; is the strain tensor; is the temperature-dependent elastic matrix; , , , respectively represent the total strain increment vector, elastic strain increment vector, plastic strain increment vector, and frost heave strain increment vector.

[0023] Furthermore, in step (3), refined mesh division is performed on each region of the tunnel geometric model, specifically: The tunnel surrounding rock, primary support, insulation layer, and secondary lining regions are meshed using free triangular meshes.

[0024] Furthermore, in step (4), the MUMPS transient solver is used to perform non-linear coupled solution on the tunnel hydro-thermal-mechanical coupling mathematical model; Dependent variables are configured in the MUMPS transient solver, and the dependent variables include temperature, moisture, and stress; In step (5), specifically, the post-processing module of COMSOL software is used to perform visualization processing on the distribution data of the tunnel temperature field, moisture field, and stress field, and obtain the distribution contour maps of the tunnel temperature field, moisture field, and stress field.

[0025] The present invention also discloses a numerical modeling system for tunnel hydro-thermal-mechanical coupling in cold regions, including: A model establishment module for establishing a scaled tunnel geometric model according to the actual working conditions of the tunnel project; A setting module for defining equation variables, setting various parameters of materials, boundaries, and initial conditions; A mesh division module for performing refined mesh division on each region of the tunnel geometric model to obtain a tunnel numerical calculation model; A solution module for solving the pre-constructed mathematical model of tunnel hydro-thermal-mechanical coupling based on a tunnel numerical calculation model, and obtaining distribution data of the tunnel temperature field, moisture field and stress field; the tunnel hydro-thermal-mechanical coupling mathematical model includes a temperature field control equation, a moisture field control equation and a stress field control equation. A post-processing module for visualizing the distribution data of the tunnel temperature field, moisture field and stress field to obtain the changes in the temperature field, moisture field and stress field in winter in the tunnel.

[0026] Compared with the prior art, the present invention has the following beneficial technical effects: The present invention discloses a numerical modeling method for hydro-thermal-mechanical coupling of cold-region tunnels, constructs a moisture field control equation and a temperature field control equation suitable for cold-region tunnels, and imports them into the PDE module in COMSOL for secondary development, improving the accuracy of numerical results. First, based on the temperature field control equation, the moisture field control equation, and the relationship equations of temperature, unfrozen water and pore ice, a full coupling analysis between the moisture field and the temperature field is realized. Secondly, considering the influence of the self-weight of the rock and soil mass and the expansion effect of ice-water phase change on deformation as the stress-strain relationship equation, a one-way coupling between hydro-thermal and force is realized, thus realizing a three-field coupling analysis of hydro-thermal-mechanical. Description of the Drawings

[0027] Figure 1 is a schematic diagram of the calculation process based on COMSOL of the present invention; Figure 2 is a schematic diagram of the tunnel inner contour of the present invention; Figure 3 is a multi-physics field interface setting diagram of the present invention; Figure 4a is a tunnel cross-section mesh division diagram of the present invention; Figure 4b is a tunnel longitudinal-section mesh division diagram of the present invention; Figure 5 is a schematic diagram of the tunnel temperature field distribution of the present invention; Figure 6 is a schematic diagram of the tunnel volume ice content distribution of the present invention; Figure 7 is a schematic diagram of the tunnel stress field distribution of the present invention. Detailed Embodiments

[0028] In order to make the purpose, technical solutions and advantages of the present invention clearer, the following further detailed description is given in conjunction with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments.

[0029] The components described and illustrated in the accompanying drawings and embodiments of the present invention can be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of the present invention provided in the following drawings is not intended to limit the scope of the claimed invention, but merely represents a selected embodiment of the present invention. Based on the accompanying drawings and embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative efforts belong to the protection scope of the present invention.

[0030] It should be noted that the term "comprising", "including" or any other variant is intended to cover non-exclusive inclusion, so that a process, element, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent in the process, element, method, article or device.

[0031] The features and performance of the present invention will be further described in detail below in conjunction with embodiments.

[0032] Embodiment 1 The present invention discloses a numerical modeling method for water-heat-mechanical coupling in cold-region tunnels. The specific process is as Figure 1 shown. The method includes the following steps: S1. Establish an equal-proportion tunnel geometric model in COMSOL software according to the actual working conditions of the tunnel project, as Figure 2 shown.

[0033] S2. Define equation variables, set various parameters of materials, boundaries and initial conditions, and establish a water-heat-mechanical coupling mathematical model of the tunnel according to the on-site investigation and instrument measurement results.

[0034] S3. Conduct refined mesh division for each region of the tunnel geometric model.

[0035] S3. Set the solver to solve the water-heat-mechanical coupling mathematical model of the tunnel, and obtain the distribution data of the tunnel temperature field, moisture field and stress field.

[0036] S5. Use the post-processing module of COMSOL to visually process the calculated data information, and obtain the distribution contour maps of the temperature field, moisture field and stress field of the tunnel, where the distribution law of the moisture field is reflected by the change of the volume ice content.

[0037] Embodiment 2 Mainly introduce the construction process of the water-heat-mechanical coupling mathematical model of the tunnel.

[0038] The water-heat-mechanical coupling mathematical model of the tunnel includes a temperature field control equation, a moisture field control equation and a stress field control equation.

[0039] The temperature field control equation can be expressed as:

[0040] In the formula: is the volumetric heat capacity of the tunnel insulation layer ; is the thermal conductivity of the lining 、 are the temperatures of the surrounding rock (°C); is the seepage velocity of the water flux ; is the latent heat of ice-water phase change, with a value of ; 、 are the densities of ice and water respectively ; is the volume content of pore ice; is the Hamiltonian operator; t is time; is the specific heat capacity of water.

[0041] Furthermore, in the calculation of heat conduction problems accompanied by phase change, the apparent heat capacity method is adopted, assuming that the phase change occurs in a small temperature range near (phase change temperature), so the influence of must be taken into account when constructing the equivalent heat capacity. The expressions for the constructed volumetric heat capacity and thermal conductivity are expressed as:

[0042]

[0043] In the formula: The subscripts represent the frozen and melted states respectively; C f is the volumetric heat capacity in the frozen state; C u is the volumetric heat capacity in the melted state; T p is the phase change temperature; λ f represents the thermal conductivity in the frozen state; λ u represents the thermal conductivity in the melted state; T represents temperature.

[0044] The water content field control equation can be expressed as:

[0045] In the formula: is the specific water capacity; is the matrix potential; and are the volume contents of unfrozen water and ice, respectively ; and are the densities of ice and water, respectively ; is the isothermal hydraulic conductivity under the influence of the hydraulic gradient; is the non-isothermal hydraulic conductivity under the influence of the temperature gradient; is the unit vector along the direction of gravity.

[0046] Furthermore, the VG (Van Genuchten) matrix suction model is used to describe the soil-water characteristic curve, and the relationship between the effective saturation and the matrix potential can be expressed as:

[0047] where: is the effective saturation; and are the saturated water content and the residual water content, respectively.

[0048] Furthermore, according to Mualem's pore distribution model, an impedance factor (indicating the hindrance effect of the presence of pore ice on the migration of unfrozen water) is introduced to determine and , and their expressions are as follows:

[0049]

[0050]

[0051]

[0052]

[0053] where: is the hydraulic conductivity of the saturated soil mass; is the permeability of the unsaturated soil; is the hydraulic diffusivity in frozen soil; and and are all fitting parameters determined by the properties of the soil mass, where is generally taken as 0.5; is the gain factor related to the soil temperature, generally taken as 7; is the surface tension of soil water (related to temperature), ; is the value of the surface tension of soil water at 25°C.

[0054] The stress field control equation can be expressed as:

[0055] Where: is the differential operator (divergence div); is the total stress tensor; is the body force vector; , are the displacement tensors; is the strain tensor; is the temperature-dependent elastic matrix; , , , respectively represent the total strain increment vector, elastic strain increment vector, plastic strain increment vector, and frost heave strain increment vector.

[0056] Example 3 Give a specific example to illustrate a numerical modeling method for thermo-hydro-mechanical coupling of tunnels in cold regions according to the present invention. The specific process is as Figure 1 shown, and this method includes the following steps: S1. Establish a scaled tunnel geometric model in the COMSOL software according to the actual working conditions of the tunnel project, as Figure 2 shown. The size of the surrounding rock geometric model is 40m×30m, the calculated inner diameter of the tunnel is 11.8m, including an initial support thickness of 26cm, a secondary lining thickness of 50cm, and a thermal insulation layer thickness of 5cm.

[0057] S2. As Figure 3 shown, import the constructed temperature field control equation and moisture field control equation into the partial differential equation interface of the COMSOL software, and import the stress field control equation into the solid mechanics interface of the COMSOL software.

[0058] S3. Mesh the areas of the tunnel surrounding rock, initial support, thermal insulation layer, secondary lining, etc. using free triangular meshes to obtain a tunnel numerical calculation model, as Figure 4a , Figure 4b shown.

[0059] S4. Set the solver to solve the thermo-hydro-mechanical coupling model of the tunnel. In the solver configuration, the dependent variables include temperature, moisture, and stress. The transient solver selects MUMPS for non-linear coupling solution, and the distribution data of the tunnel temperature field, moisture field, and stress field are obtained by solving.

[0060] S5. Use the post-processing module of CSOML to visually process the calculated data information to obtain as Figures 5 - 7The variation of the temperature field, moisture field, and stress field of the tunnel shown in winter, where the distribution law of the moisture field is reflected by the change in the volumetric ice content.

[0061] Figure 5 , Figure 6 , Figure 7 are the measured distribution of the hydro-thermodynamic field of the tunnel. It can be seen from the figure that the results are roughly the same as those obtained from the measured values at each hole position. Therefore, overall, the consistency between the measured results and the calculated results verifies the accuracy of the hydro-thermal numerical model of the tunnel established in the present invention.

[0062] The present invention discloses a numerical modeling method for hydro-thermal coupling of tunnels in cold regions, which has the following effects: 1. Improved accuracy of hydro-thermal coupling: By constructing the control equations of the moisture field and temperature field unique to tunnels in cold regions and importing them into the COMSOL PDE module for secondary development, the accuracy of the simulation results is significantly improved. The full-coupling analysis between the moisture field and the temperature field effectively reflects the hydro-thermal transfer characteristics of the tunnel in a cold environment.

[0063] 2. Coupling relationship between the temperature field and the moisture field: The coupling analysis results of the temperature field and the moisture field show that in tunnels in cold regions, temperature changes directly affect the phase change of moisture, especially the transformation between unfrozen water and pore ice. This coupling relationship reveals the influence of temperature fluctuations on moisture migration and distribution, helps identify areas in the tunnel where condensation, frost heave, etc. may occur, and further assesses the potential threats to structural safety.

[0064] 3. Influence of frost heave and swelling effects: Considering the self-weight of the rock and soil mass and the influence of the expansion effect of ice-water phase change on tunnel deformation, the frost heave phenomenon is accurately captured in the hydro-thermal coupling analysis. The simulation results show that the freezing of moisture will cause local expansion in the tunnel structure, which may lead to cracks or other structural damages. This analysis helps predict the possible structural deformation of the tunnel under severe winter conditions and provides a scientific basis for preventing damages caused by frost heave.

[0065] 4. Unidirectional coupling characteristics of hydro-thermal coupling analysis: In the three-field coupling analysis of hydro-thermal, by combining the stress-strain equation with the hydro-thermal process, the unidirectional coupling relationship between hydro-thermal and force is simulated. The results show that the volume expansion and contraction caused by moisture changes have an important impact on the change of the stress field of the tunnel, especially at low temperatures, the freezing and melting of water play a decisive role in the stress state of the tunnel structure.

[0066] 5. Tunnel Safety and Stability Assessment: Through the comprehensive assessment of the results of the coupled analysis of water, heat, and stress fields, the moisture, temperature, and stress states of the tunnel in the cold season can be comprehensively understood, thus accurately predicting problems such as frost heave, cracks, and deformation that the tunnel may face. Combining these analysis results, an optimized plan can be provided for the design, construction, and maintenance of the tunnel to ensure the safety and long-term stability of the tunnel in the cold region environment.

[0067] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications or equivalent replacements can still be made to the specific implementation manners of the present invention, and any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention should be covered by the protection scope of the claims of the present invention.

Claims

1. A numerical modeling method for thermo-hydro-mechanical coupling in cold region tunnels, characterized in that It includes the following steps: (1) Establish an equal-proportion tunnel geometric model according to the actual working conditions of the tunnel project; (2) Based on the tunnel geometric model, define equation variables, and set various parameters of the materials, temperatures at each boundary, and initial conditions; (3) Conduct refined mesh division for each region of the tunnel geometric model to obtain a tunnel numerical calculation model; (4) Solve the pre-constructed tunnel hydro-thermo-mechanical coupling mathematical model based on the tunnel numerical calculation model to obtain distribution data of the tunnel temperature field, moisture field, and stress field; the tunnel hydro-thermo-mechanical coupling mathematical model includes a temperature field control equation, a moisture field control equation, and a stress field control equation; (5) Perform visualization processing on the distribution data of the tunnel temperature field, moisture field, and stress field to obtain the variation conditions of the tunnel temperature field, moisture field, and stress field in winter.

2. A numerical modeling method for water-heat coupling in cold region tunnels according to claim 1, characterized in that In step (2), the temperatures at each boundary are set according to on-site measured data. The two side boundaries of the tunnel are subject to horizontal displacement constraints and are set as water-proof boundaries; the bottom boundary is a vertical fixed constraint, and the upper boundary is a free boundary.

3. A numerical modeling method for water-thermal coupling in cold region tunnels according to claim 1, characterized in that In step (4), the temperature field control equation is expressed as: In the formula, is the volumetric heat capacity of the tunnel insulation layer; is the thermal conductivity of the lining; is the temperature of the surrounding rock; is the specific heat capacity of water; is the seepage velocity of water flux; is the latent heat of ice-water phase change; , are the densities of ice and water respectively; is the volume content of pore ice; is the Hamiltonian operator; t is time.

4. A numerical modeling method for water-thermal coupling in cold region tunnels according to claim 3, characterized in that In the calculation of heat conduction problems accompanied by phase change, the apparent heat capacity method is adopted, assuming that the phase change occurs within a temperature range near the phase change temperature . When constructing the equivalent heat capacity, the influence of is taken into account. The expressions for the constructed volumetric heat capacity and the thermal conductivity are as follows: ​ where is the assumed phase change; the subscripts represent the frozen and melted states, respectively; C f is the volumetric heat capacity in the frozen state; C u is the volumetric heat capacity in the melted state; T p is the phase change temperature; λ f represents the thermal conductivity in the frozen state; λ u represents the thermal conductivity in the melted state; T represents the temperature.

5. A numerical modeling method for water-thermal coupling in cold region tunnels according to claim 1, characterized in that In step (4), the moisture field control equation is expressed as: In the formula, is the specific water capacity; is the matrix potential; and are the volume contents of unfrozen water and ice respectively; 、 are the densities of ice and water respectively; is the isothermal hydraulic conductivity under the influence of the hydraulic gradient; is the non-isothermal hydraulic conductivity under the influence of the temperature gradient; is the unit vector along the direction of gravity; is the Hamiltonian operator; T represents temperature; t represents time.

6. A numerical modeling method for thermo-hydro-mechanical coupling in cold region tunnels according to claim 5, characterized in that, The VG matrix suction model is used to describe the soil-water characteristic curve, and the relationship expression between the effective saturation and the matrix potential is: In the formula, is the effective saturation; , are the saturated water content and the residual water content respectively; According to Mualem's pore size distribution model, the impedance factor is introduced simultaneously to determine and , and their expressions are as follows: Among them, Wherein: is the hydraulic conductivity of the saturated soil; is the permeability of the unsaturated soil; is the hydraulic diffusivity in frozen soil; 、 、 are all fitting parameters determined by the soil properties; is the gain factor related to the soil temperature; is the surface tension of soil water, ; is the value of the surface tension of soil water at a temperature of 25°C; Impedance factor It represents the hindrance effect of the presence of pore ice on the migration of unfrozen water.

7. A numerical modeling method for thermo-hydro-mechanical coupling in cold region tunnels according to claim 1, characterized in that, In step (4), the stress field control equation is expressed as: In the formula, is the differential operator; is the total stress tensor; is the body force vector; and are the displacement tensors; is the strain tensor; is the temperature-dependent elastic matrix; and and and respectively represent the total strain increment vector, elastic strain increment vector, plastic strain increment vector, and frost heave strain increment vector.

8. A numerical modeling method for water-thermal coupling in cold region tunnels according to claim 1, characterized in that, In step (3), the refined mesh division for each region of the tunnel geometric model is specifically as follows: The tunnel surrounding rock, primary support, insulation layer, and secondary lining regions are meshed using free triangular meshes.

9. A numerical modeling method for thermo-hydro-mechanical coupling in cold region tunnels according to claim 1, characterized in that In step (4), the MUMPS transient solver is used to perform non-linear coupling solution on the tunnel hydro-thermo-mechanical coupling mathematical model; Dependent variables are configured in the MUMPS transient solver, and the dependent variables include temperature, moisture, and stress; In step (5), specifically, the post-processing module of the COMSOL software is used to perform visualization processing on the distribution data of the tunnel temperature field, moisture field, and stress field to obtain the distribution cloud maps of the tunnel temperature field, moisture field, and stress field.

10. A numerical modeling system for coupled hydro-thermal-mechanical processes in cold region tunnels, characterized in that, It includes: A model establishment module for establishing an equal-proportion tunnel geometric model according to the actual working conditions of the tunnel project; A setting module for defining equation variables, setting various parameters of the materials, boundaries, and initial conditions; A mesh division module for performing refined mesh division on each region of the tunnel geometric model to obtain a tunnel numerical calculation model; A solution module for solving the pre-constructed tunnel hydro-thermo-mechanical coupling mathematical model based on the tunnel numerical calculation model to obtain distribution data of the tunnel temperature field, moisture field, and stress field; the tunnel hydro-thermo-mechanical coupling mathematical model includes a temperature field control equation, a moisture field control equation, and a stress field control equation; A post-processing module for performing visualization processing on the distribution data of the tunnel temperature field, moisture field, and stress field to obtain the variation conditions of the tunnel temperature field, moisture field, and stress field in winter.

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