Structural thermal-mechanical coupling analysis method for leakage state of heat distribution pipeline of shield tunnel

Abstract

The invention discloses a structural thermal-mechanical coupling analysis method for a leakage state of a heat distribution pipeline of a shield tunnel, which comprises the following steps of: constructing a three-dimensional finite element model of a soil layer, a duct piece, a ballast bed, accumulated water and air of the thermal shield tunnel according to an actual size of a structure, and respectively setting mechanical and thermodynamic attributes and calculation parameters of each part of solid and fluid; pushing a multi-physical field control equation of flow guide-solid coupling heat transfer and heat-force coupling elastic-plastic mechanics, and applying temperature fields and stress fields to all parts of the solid and the fluid; the method comprises the following steps: setting two typical working condition depths of high-temperature water accumulation according to a planned position of a pipeline leakage point in a thermal tunnel, and applying boundary conditions and initial conditions of temperature and stress to each part of solid and fluid; and setting an increment step length and an analysis time length, carrying out transient solution, outputting temperature and stress spatio-temporal evolution values of concrete structures such as duct pieces and ballast beds, and analyzing the safety and stability of the structures in a pipeline thermal leakage state.

Description

Technical Field

[0001] This invention relates to the field of structural safety analysis technology for thermal shield tunnels, and is particularly applicable to structural thermo-mechanical coupling analysis methods for leakage conditions of thermal pipelines in shield tunnels. Background Technology

[0002] Thermal shield tunnels are utility tunnel structures used to lay urban centralized heating pipelines. They can effectively transfer waste heat from power plants over long distances for urban centralized heating, reducing the need for coal-fired heating facilities, optimizing urban energy supply and demand, and achieving energy conservation, emission reduction, and green, low-carbon sustainable development. However, this structure faces the risk of internal thermal pipeline rupture and leakage. Large amounts of hot water cannot be drained in time, leading to thermal stress damage to the tunnel structure and seriously endangering the safety and stability of the tunnel segments, track bed, and other concrete structures. A thorough understanding of the spatiotemporal evolution of temperature and stress in tunnel segments, track bed, and other concrete structures under thermal pipeline leakage conditions is of significant practical importance for assessing the degree of structural damage and developing emergency repair measures.

[0003] Current research on this type of problem mainly adopts the method of constant temperature rise of the entire tunnel, and analyzes the temperature stress of the tunnel concrete structure in the form of steady-state uniform temperature distribution. However, it does not consider the transient heat conduction process of high temperature water accumulation on the concrete structure, cannot reflect the non-uniform temperature distribution of the structure over time and space, cannot reveal the transient coupling mechanism of temperature and stress, and is difficult to accurately assess the risk of structural thermal stress damage under the condition of leakage of thermal pipes in shield tunnels. Summary of the Invention

[0004] The purpose of this invention is to provide a structural thermo-mechanical coupling analysis method for the leakage state of thermal pipelines in shield tunnels, which can solve the problem of difficulty in accurately assessing the structural thermal stress damage risk under leakage state of thermal pipelines in shield tunnels.

[0005] To achieve the above objectives, the structural thermo-mechanical coupling analysis method for leakage state of thermal pipelines in shield tunnels according to the present invention includes the following steps: S1, based on the geological soil layer distribution and the size and shape of the concrete structure, construct an overall structural finite element model consisting of each soil layer, shield tunnel segments, heating pipes, track bed, water accumulation, and air finite element models; divide the mesh and set the temperature, stress properties and related parameters of each part; S2, respectively, introduce the temperature and stress set by each mesh element of the solid model and the fluid model into the temperature field control equation of fluid-solid coupling heat transfer and the stress field control equation of thermo-mechanical coupling elastoplastic mechanics, and construct the physical model of the temperature field and stress field of the overall structure; S3 sets the temperature and stress boundary conditions and initial conditions for each soil layer, shield tunnel segment, track bed, water accumulation, and air; S4: Select the numerical calculation and analysis method, set the incremental step size and analysis time, perform transient calculations of the structure, and output the spatiotemporal evolution laws of temperature and stress of shield tunnel segments and track bed concrete structures.

[0006] Furthermore, the grid division specifically involves arranging four layers of grid nodes radially for the shield tunnel segments and uniformly arranging several grid nodes circumferentially; based on the grid node situation of the shield tunnel segments, grid nodes are divided for each layer of soil, track bed, water accumulation, and air; along the direction of shield tunnel advance, a sweeping method is used to select regular hexahedrons to divide the grid.

[0007] Furthermore, the solid model mentioned in step S2 includes finite element models of each soil layer, shield tunnel segments, and track bed; the fluid model includes finite element models of water and air.

[0008] Furthermore, the temperature field governing equation for the fluid-structure interaction heat transfer is: ; ;in: Density of solids and fluids; For constant-pressure heat capacity of solids and fluids; Temperature of solids and fluids; The thermal convection rate of the fluid; Thermal conductivity is the coefficient of thermal conductivity of solids and fluids. For Hamiltonian operators; For divergence operators; For heat flux vectors of solids and fluids; For solids and fluids, the external heat source is t, which is a time variable.

[0009] Furthermore, the stress field governing equation of the thermo-mechanical coupled elastoplastic mechanics is as follows: ; ;in: The temperature of the solid structure; The elastic entropy of the solid structure; It is a heat source for solid structures; The coefficient of thermal expansion of the solid structure; , , For solid structures in x , y , z Normal stress in the direction; For Hamiltonian operators; It is a divergence operator.

[0010] Furthermore, the temperature boundary conditions described in step S3 include setting the top surface of the soil layer as a natural convection heat transfer condition; setting the sides and bottom of the soil layer as a constant temperature condition; setting the soil layer, air, pipe segments, and track bed at the end face where the heat pipe leak point is located as a thermal insulation condition; and setting the pipe segments, track bed, accumulated water, and air away from the end face where the heat pipe leak point is located as a constant temperature condition.

[0011] Furthermore, the stress boundary conditions described in step S3 include setting the side and bottom surfaces of the soil layer as fixed constraint conditions; setting the top surface of the soil layer as a free boundary condition; and setting the end face where the heat pipe leak point is located and the end face far from the heat pipe leak point as symmetrical constraint conditions.

[0012] Furthermore, the temperature and stress of each soil layer, shield tunnel segment, track bed, water accumulation, and air space within the overall structural finite element model are transmitted through the boundary deformation coordination matrix of the finite element.

[0013] Furthermore, the numerical calculation and analysis method described in step S4 is the direct method for sparse matrix linear equations.

[0014] The advantages of this invention lie in considering the heat conduction process of hot water and air to solid segments, track bed, and soil layers, and constructing a temperature field control equation for fluid-structure interaction heat transfer; analyzing the temperature stress of segments, track bed, and soil layers in the shield tunnel and the overall soil structure, and constructing a stress field control equation for thermo-mechanical coupling elastoplastic mechanics; eliminating the need for pre-assuming the overall temperature rise of the tunnel structure and uniform temperature distribution, and enabling transient calculation of heat conduction and thermal stress in tunnel structures under leaking thermal pipeline conditions; and calculating and outputting the quantitative variation laws of temperature and stress of water, air, segments, track bed, and soil layers with time and space. Attached Figure Description

[0015] Figure 1 This is an overall model of the shield tunnel soil layer, segments, track bed, water accumulation, and air in an embodiment of the present invention.

[0016] Figure 2 This is a finite element mesh division of shield tunnel segments, track bed, water accumulation, and air in an embodiment of the present invention.

[0017] Figure 3 This is a schematic diagram of the stress field boundary conditions of a shield tunnel according to an embodiment of the present invention. (a) is the symmetrical boundary condition at the leakage point of the thermal pipeline, (b) is the free boundary condition of the top surface of the soil layer, and (c) is the fixed constraint condition of the side surface of the soil layer.

[0018] Figure 4 This is a schematic diagram of the temperature field boundary conditions of a shield tunnel according to an embodiment of the present invention. (a) shows the convective heat transfer at the top of the soil layer, (b) shows the thermal insulation conditions at the leakage point of the thermal pipeline, and (c) shows the constant temperature conditions on the side of the soil layer.

[0019] Figure 5 These are the temperature distribution calculation results of the shield tunnel segments according to the embodiments of the present invention. (a) is the initial state, (b) is the temperature distribution calculation results of the shield tunnel segments after 1 day, (c) is the temperature distribution calculation results after 5 days, and (d) is the temperature distribution calculation results of the shield tunnel segments after 10 days.

[0020] Figure 6 These are the radial stress calculation results of shield tunnel segments according to embodiments of the present invention. (a) is the initial state, (b) is after 10 days, (c) is after 20 days, and (d) is after 30 days.

[0021] Figure 7 These are the temperature distribution calculation results of the shield tunnel track bed in the embodiments of the present invention. (a) is the initial state, (b) is the temperature distribution calculation results of the shield tunnel track bed after 2 days, (c) is the temperature distribution calculation results after 5 days, and (d) is the temperature distribution calculation results of the shield tunnel track bed after 10 days.

[0022] Figure 8 The results are the calculation results of the normal stress in the x-direction of the shield tunnel track bed according to the embodiments of the present invention. (a) is the initial state, (b) is after 5 days, (c) is after 10 days, and (d) is after 20 days. Detailed Implementation

[0023] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0024] Example 1 The structural thermo-mechanical coupling analysis method for leakage state of thermal pipelines in shield tunnels according to the present invention includes the following steps: S1, based on the actual geological conditions of the project, including soil layer distribution and the dimensions and shape of the concrete structure, and considering the influence range of the structural-thermal coupling effect under the leakage state of the heating pipe, a finite element model is constructed, including each soil layer, shield tunnel segments, heating pipe, and the track bed, water accumulation, and air inside the shield tunnel. These finite element models are then assembled to form the overall finite element model of the shield tunnel heating pipe structure. Figure 1 As shown. Figure 1 'a' represents the overall structural finite element model of the thermal pipeline in the shield tunnel, whose internal structure is not visible. Figure 1 b is the perspective view, which clearly shows the overall structural finite element model of various structures such as soil layers and shield tunnels.

[0025] Mesh the finite element model for each part. First, the finite element model for each part can be divided into a solid model and a fluid model. The solid model includes the soil layers, the concrete structural segments that make up the shield tunnel (i.e., the shield tunnel segments), and the track bed finite element model. The fluid model includes the water and air finite element models.

[0026] The mesh generation process involves arranging four layers of mesh nodes radially along the segments and a number of mesh nodes evenly distributed circumferentially for each soil layer, shield tunnel segment, and track bed in the solid model, as well as for the water and air in the fluid components. A sweeping method is used along the tunnel's forward direction, selecting regular hexahedral elements for finite element mesh generation. Temperature and stress properties and parameters are set for each solid element (soil layer, shield tunnel segment, track bed, etc.), and temperature properties and parameters are set for the fluid elements (water, air, etc.). Figure 2 a shows the finite element division of the shield tunnel along its length. Figure 2 This demonstrates the finite element element division of the shield tunnel cross-section. It includes the concrete structural segments that make up the shield tunnel, the air and water inside the tunnel, and the track bed.

[0027] Step 2: The temperature and stress of the mesh elements set for the solid model and fluid model are introduced into the temperature field control equation of fluid-solid coupled heat transfer and the stress field control equation of thermo-mechanical coupled elastoplastic mechanics, respectively. The temperature field and stress field physical model of the overall finite element model are constructed to realize the transition and transformation of the overall structural geometric model, finite element model and physical model, and to establish a transient analysis method for temperature and stress of the overall structural mesh elements.

[0028] The temperature field governing equations for fluid-structure interaction heat transfer are as follows: in: Density of solids and fluids; For constant-pressure heat capacity of solids and fluids; Temperature of solids and fluids; The thermal convection rate of the fluid; Thermal conductivity is the coefficient of thermal conductivity of solids and fluids. For Hamiltonian operators; For divergence operators; For heat flux vectors of solids and fluids; For solids and fluids, the external heat source is t; t is the time variable.

[0029] The stress field governing equations of thermo-mechanical coupled elastoplastic mechanics are as follows: in: The temperature of the solid structure; The elastic entropy of the solid structure; It is a heat source for solid structures; The coefficient of thermal expansion of the solid structure; , , For solid structures in x , y , z Normal stress in the direction; For Hamiltonian operators; is the divergence operator; t is the time variable.

[0030] The aforementioned temperature and stress field control equations are applied to the mesh elements of each part of the solid and fluid models of the overall finite element model of the shield tunnel thermal pipeline. The temperature, stress, and parameters of the solid and fluid models are then substituted into the corresponding mesh elements and control equations to construct the physical model of the temperature and stress fields of the shield tunnel thermal pipeline.

[0031] Step 3: Set the temperature and stress boundary conditions and initial conditions for each soil layer, shield tunnel segment, track bed, water accumulation, and air. Specifically, for the overall structural model, set temperature boundary conditions and initial temperatures for the soil layer, air, tunnel segments, track bed, and water accumulation. The initial temperature is set on the end face where the thermal pipeline leak point is located. For the solid model, set stress boundary conditions and initial stress conditions for each soil layer, shield tunnel segment, and track bed. The initial stress is set on the end face where the thermal pipeline leak point is located. This establishes the basic conditions required for the calculation and analysis of the temperature and stress fields of the shield tunnel's thermal pipeline.

[0032] The specific temperature boundary conditions are as follows: the top surface of the soil layer is set to natural convection heat transfer conditions; the sides of the soil layer and the ground surface are set to constant temperature conditions; the soil layer, air, pipe segments, and track bed at the end face where the heat pipe leak point is located are set to thermal insulation conditions; and the pipe segments, track bed, accumulated water, and air far away from the end face where the heat pipe leak point is located are set to constant temperature conditions.

[0033] The stress boundary conditions are as follows: the side and bottom surfaces of the soil layer are set as fixed constraint conditions; the top surface of the soil layer is set as a free boundary condition; and the end face where the heat pipe leak point is located and the end face far away from the heat pipe leak point are set as symmetrical constraint conditions.

[0034] In specific calculation formulas, the water and air zones within the tunnel space can be divided according to actual conditions to calculate the spatiotemporal evolution of temperature and stress in the shield tunnel segments and track bed concrete structure under different working conditions. For example, if the high-temperature water from a leaking thermal pipeline submerges one-third of the tunnel cross-section or fills the entire tunnel cross-section, the spatiotemporal evolution of temperature and stress in the shield tunnel segments and track bed concrete structure under these conditions can be calculated.

[0035] The specific temperature boundary conditions are as follows: Assuming the surface of the soil layer in contact with the air is under natural convection heat transfer conditions, the expression is as follows: Assuming the pipe segments, track bed, accumulated water, and air are at constant temperature conditions away from the end face where the thermal pipeline leak point is located, the expression is as follows: Assuming the side and bottom surfaces of the soil layer are at constant temperatures, the expression is as follows: Assuming the soil layer, air, pipe segments, and track bed at the end face where the thermal pipeline leaks are under thermal insulation conditions, the expression is as follows: in, This is the normal vector of the surface where the top of the soil layer contacts the air. This refers to the heat flux within the soil layer. For the convective heat flux at the boundary between the soil layer and the air; The convective heat transfer coefficient between the top surface of the soil layer and the air; The air temperature at the top surface of the soil layer; Temperature of solids and fluids; The water temperature at the leak point in the heating pipe; The temperature of the soil at the far end is constant.

[0036] Initial temperature conditions are ,in The initial temperature of the entire structure, excluding leaks in the heating pipes; The initial temperature is set.

[0037] The specific stress boundary conditions are as follows: Set the top surface of the soil layer as a free boundary condition.

[0038] The sides and bottom of the soil layer are set as fixed constraints, as shown in the following expression: The end face where the leak point in the heating pipe is located and the end face far from the leak point are defined as symmetrical constraints, as shown in the following expression: initial stress conditions , ; in, For structural displacement; The structural displacement rate; This is the normal vector between the end face and the far face of the leaking thermal pipeline.

[0039] In the shield tunnel thermal pipeline model, the temperature and stress between various parts such as soil, segments, track bed, water accumulation, and air can be transmitted through the boundary deformation synergy matrix of the finite element, so there are no boundary conditions between the parts.

[0040] Step 4: Within the overall structural domain of the tunnel, based on the temperature and stress field control equations and their boundary and initial conditions established in the preceding steps, select a numerical calculation and analysis method, set the incremental step size and analysis time, perform transient structural calculations, and output the temperature of the concrete structures such as tunnel segments and track bed. ,stress , , The spatiotemporal evolution law can be used to analyze the safety and stability of the tunnel structure under the condition of pipeline thermal leakage. At the same time, the spatiotemporal evolution law of soil temperature and stress, water temperature and air temperature can also be output.

[0041] Example 2 like Figure 1 , 2 As shown, based on the on-site geological survey results, the soil covering layers of the shield tunnel are set to six layers, with a total height of 101.5m. Considering the influence range of the structural thermal coupling effect under the leakage state of the heating pipeline, representative length and width sections are established, with length and width values ​​of 100m and 120m respectively. The overall effective dimensions of the tunnel's overall structural model are set to 100m×120m×101.5m (length×width×height). Based on the actual on-site conditions of the shield tunnel's burial depth and the structural dimensions of its segments and track bed, two working conditions are set: an inner diameter of 6m, an outer diameter of 6.7m, a segment thickness of 0.35m, a track bed height of 1.1m, and water accumulation depths of 0.9m and 4.9m. The lengths of the segments, track bed, water accumulation, and air are all 100m. Finite element models of each soil layer, segment, track bed, water accumulation, and air of the shield tunnel and heating pipeline are constructed to form the overall structural finite element model of the tunnel.

[0042] Then, four layers of grid nodes were arranged radially for the segment structure, and fifty-two grid nodes were evenly arranged circumferentially. Based on the segment grid node situation, grid nodes were divided for each layer of soil, track bed, water accumulation, and air in the surrounding area. Along the tunnel advance direction, a sweep method was used to select regular hexahedral elements to complete the finite element mesh division of the geometric model. The number of elements was 64,583, the number of nodes was 47,236, the stress field degree of freedom was 513,423, and the temperature field degree of freedom was 146,332.

[0043] Finally, temperature, stress and related parameters were set for each solid unit such as soil layer, segment, and track bed, and temperature and related parameters were set for fluid units such as water accumulation and air. The various indicators are shown in Table 1 and Table 2.

[0044] Table 1 Mechanical and thermodynamic parameters of various parts of the solid and fluid Table 2 Soil mechanical parameters and indices The temperature field control equation for fluid-structure interaction heat transfer and the stress field control equation for thermo-mechanical coupling elastoplastic mechanics are applied to the mesh elements of the solid model and fluid model of the finite element model of the thermal pipeline of the shield tunnel, respectively. The temperature, stress and related parameters of the solid model and fluid model set in step 1 are substituted into the corresponding mesh elements and control equations to construct the physical model of the temperature field and stress field of the overall tunnel structure finite element model.

[0045] Define the boundary conditions and initial conditions for the temperature and stress fields of each part of the overall tunnel structure finite element model. For example... Figure 3 , Figure 4 As shown, two working conditions are set for the water accumulation depth above the track bed in the tunnel: 0.9m and 4.9m. Temperature and stress boundary conditions are also set. The surface of the soil layer in contact with the air is set to natural convection heat transfer conditions; the end face away from the heat pipe leak point is set to constant temperature conditions; the sides, bottom, and far-end segments of the soil layer, track bed, water surface, and air are set to constant temperatures; the soil layer, air, segments, and track bed at the end face of the heat pipe leak point are set to thermal insulation conditions. Simultaneously, the initial temperature of the entire tunnel structure, excluding the heat pipe leak point, is also set.

[0046] Then, stress boundary conditions are set. The top surface of the soil layer is set as a free boundary condition; the sides and bottom of the soil layer are set as fixed constraints; the end face where the heat pipe leak point is located and the end face far away from the heat pipe leak point are set as symmetrical constraints, as well as initial stress conditions.

[0047] Within the finite element model of the overall tunnel structure, temperature and stress among the various components such as soil layers, tunnel segments, track bed, water accumulation, and air can be transferred through the boundary deformation synergy matrix of the finite elements; therefore, there are no boundary conditions between the components. This completes the construction of the basic conditions required for the calculation and analysis of the temperature and stress fields of the overall tunnel structure finite element model.

[0048] Based on the aforementioned steps, the governing equations, boundary conditions, and initial conditions for the temperature and stress fields established in various soil layers, tunnel segments, track bed, water accumulation, and air within the tunnel are determined. A direct solution method using sparse matrix linear equations is selected, with an incremental step size of 1 day and an analysis duration of 40 days. Transient structural calculations are then performed, outputting the temperature values ​​of the concrete structures such as tunnel segments and track bed. ,stress , , The spatiotemporal evolution law is analyzed to assess the safety and stability of the tunnel structure under the condition of pipeline thermal leakage, such as... Figure 5-8 As shown.

Claims

1. A structural-thermal coupling analysis method for leakage conditions of thermal pipelines in shield tunnels, characterized in that, Includes the following steps: S1, based on the geological soil layer distribution and the size and shape of the concrete structure, construct an overall structural finite element model consisting of each soil layer, shield tunnel segments, heating pipes, track bed, water accumulation, and air finite element models; divide the mesh and set the temperature, stress properties and related parameters of each part; S2, respectively, introduce the temperature and stress set by each mesh element of the solid model and the fluid model into the temperature field control equation of fluid-solid coupling heat transfer and the stress field control equation of thermo-mechanical coupling elastoplastic mechanics, and construct the physical model of the temperature field and stress field of the overall structure; S3 sets the temperature and stress boundary conditions and initial conditions for each soil layer, shield tunnel segment, track bed, water accumulation, and air; S4: Select the numerical calculation and analysis method, set the incremental step size and analysis time, perform transient calculations of the structure, and output the spatiotemporal evolution laws of temperature and stress of shield tunnel segments and track bed concrete structures.

2. The structural thermo-mechanical coupling analysis method for leakage state of thermal pipeline in shield tunnel according to claim 1, characterized in that: The grid division specifically involves arranging four layers of grid nodes radially for the shield tunnel segments and uniformly arranging several grid nodes circumferentially; based on the grid node situation of the shield tunnel segments, grid nodes are divided for each layer of soil, track bed, water accumulation, and air; along the direction of shield tunnel advance, a sweeping method is used to select regular hexahedrons to divide the grid.

3. The structural thermo-mechanical coupling analysis method for leakage state of thermal pipelines in shield tunnels according to claim 1, characterized in that: The solid model mentioned in step S2 includes finite element models of each soil layer, shield tunnel segments, and track bed; the fluid model includes finite element models of water and air.

4. The structural thermo-mechanical coupling analysis method for leakage state of thermal pipeline in shield tunnel according to claim 1, characterized in that: The temperature field governing equation for the fluid-structure coupled heat transfer is: ; ;in: Density of solids and fluids; For constant-pressure heat capacity of solids and fluids; Temperature of solids and fluids; The thermal convection rate of the fluid; Thermal conductivity of solids and fluids; For Hamiltonian operators; For divergence operators; For heat flux vectors of solids and fluids; For solids and fluids, the external heat source is t, which is a time variable.

5. The structural thermo-mechanical coupling analysis method for leakage state of thermal pipeline in shield tunnel according to claim 1, characterized in that: The stress field governing equations of the thermo-mechanical coupled elastoplastic mechanics are as follows: ; ;in: The temperature of the solid structure; The elastic entropy of the solid structure; A heat source for solid structures; The coefficient of thermal expansion of the solid structure; , , For solid structures in x , y , z Normal stress in the direction; For Hamiltonian operators; It is a divergence operator.

6. The structural thermo-mechanical coupling analysis method for leakage state of thermal pipeline in shield tunnel according to claim 1, characterized in that: The temperature boundary conditions described in step S3 include setting the top surface of the soil layer as a natural convection heat transfer condition; setting the sides and bottom of the soil layer as a constant temperature condition; setting the soil layer, air, pipe segments, and track bed at the end face where the heat pipe leak point is located as a thermal insulation condition; and setting the pipe segments, track bed, accumulated water, and air at the end face far from the heat pipe leak point as a constant temperature condition.

7. The structural thermo-mechanical coupling analysis method for leakage state of thermal pipeline in shield tunnel according to claim 1, characterized in that: The stress boundary conditions described in step S3 include setting the side and bottom surfaces of the soil layer as fixed constraints; setting the top surface of the soil layer as a free boundary condition; and setting the end face where the heat pipe leak point is located and the end face far from the heat pipe leak point as symmetrical constraints.

8. The structural thermo-mechanical coupling analysis method for leakage state of thermal pipeline in shield tunnel according to claim 1, characterized in that: The temperature and stress of each soil layer, shield tunnel segment, track bed, water accumulation, and air space within the overall structural finite element model are transmitted through the boundary deformation coordination matrix of the finite element.

9. The structural thermo-mechanical coupling analysis method for leakage state of thermal pipeline in shield tunnel according to claim 1, characterized in that: The numerical calculation and analysis method described in step S4 is the direct method for sparse matrix linear equations.

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