A calculation method for temperature stress and deformation of initial support structure of vertical shaft in cold regions

Abstract

The present invention provides a method for calculating the temperature stress and deformation of the initial support structure of a vertical shaft in cold regions, comprising the following steps: establishing a calculation model, dividing the surrounding rock into two stable temperature fields, a constant temperature zone and a variable temperature zone, and establishing a three-layer thick-walled cylinder finite ring elastic contact calculation model; solving an analytical solution for the temperature distribution, constructing a differential equation for the heat conduction of the shaft under temperature field conditions, and solving an analytical solution for the temperature distribution of the initial support structure; determining the temperature stress and deformation, based on the obtained analytical solution for the temperature distribution of the initial support structure and the theory of autogenous temperature stress of thick-walled cylinders. Compared with traditional methods, this method can provide a basic theory for cold-proof and thermal insulation design of vertical shafts in cold regions. The resulting "zoning-contact solution" concept solves the problem of determining the temperature value of the initial support structure. Not only is the calculation method consistent with structural reality and simple, but the calculation results are also scientific and reasonable, and have the value of further promotion and application.

Description

Technical Field

[0001] The invention belongs to the technical field of tunnel engineering, and in particular relates to a method for calculating the temperature stress and deformation of an initial support structure of a vertical shaft in cold regions. Background Art

[0002] Antifreeze and thermal insulation of engineering structures pose a severe challenge to transportation infrastructure construction. As the primary auxiliary structure of extra-long tunnels, vertical shafts play an irreplaceable role in assisting construction and operational ventilation. Therefore, clarifying the mechanical properties of the support structure is crucial. During the excavation of vertical shafts in cold regions, the surrounding rock's temperature field is disturbed, and the interior of the shaft exchanges heat with the surface environment, causing the initial support structure to experience thermal expansion and contraction. This process manifests as temperature stress and deformation in the structure. Therefore, clarifying the temperature stress and deformation values ​​of the initial support structure of the vertical shaft is crucial for the antifreeze and thermal insulation design of vertical shafts in cold regions.

[0003] At present, the research on temperature stress and deformation of shaft support structure mainly focuses on fire conditions, and the research method is mainly based on numerical simulation. There are no relevant reports on the calculation of temperature stress and deformation of initial support structure of shaft in cold regions. For example, Zhu Jie, Yang Tianyou, Zhang Lilong, et al., Engineering Mechanics, 2011, 08, studied the temperature variation law of fire smoke in shaft structure under the action of pure hot smoke buoyancy. The research method combined field experiments, theoretical analysis and field simulation was adopted. By setting up 8 different fire scenes, the temperature variation law of smoke in shaft structure was tested respectively, providing theoretical basis and practical guidance for the actual fire protection design and personnel evacuation of high-rise buildings. However, the temperature stress and deformation value of shaft support structure could not be quantitatively given. Luo Yanbin, Chen Jianxun, Highway, 2012, 01, three-dimensional numerical simulation and analysis of temperature stress of ventilation shaft in highway tunnel, used three-dimensional numerical simulation method to analyze and study the temperature stress of shaft with separated air supply and exhaust by partition in single shaft, revealing the seasonal variation law of temperature of shaft wall, partition and formation of ventilation shaft. It also did not involve the support structure. Structural stress and deformation calculation; Wan Liangyong, Guo Jiaqi, Wang Mengshu, China Civil Engineering Journal, 2015, June, Model Test Study on Temperature Distribution Characteristics of Shaft Ventilation Tunnels During Fires. Through small-scale (1:50) tunnel fire model tests under a shaft ventilation scheme, the temperature distribution characteristics at different heights of the tunnel vault and the tunnel centerline before and after the fire source were studied during fires. The calculation of the initial support structure stress and deformation was not involved. Wang Jianjun, Yang Linlin, Yang Wenbo et al., Modern Tunneling Technology, 2022, June, Study on Temperature Field Distribution and Freezing Prevention and Insulation of Ventilation Shafts in Cold Regions. Based on the Dongliangdi Tunnel ventilation shaft, the temperature field of the ventilation shaft in cold regions was monitored on-site during construction, and the temperature field during operation was analyzed using CFD simulation. However, the initial support structure stress and deformation values ​​were still not quantified. Therefore, determining the temperature stress and deformation of shafts in cold regions and clarifying the influence of temperature on the initial support structure of the shaft can effectively guide the cold protection and insulation of the shaft. Summary of the Invention

[0004] In view of the problems existing in the above-mentioned background technology, the present invention provides a method for calculating the temperature stress and deformation of the initial support structure of a vertical shaft in cold regions. First, the surrounding rock is regarded as a stable temperature field, and the surrounding rock temperature field is divided into two parts: a constant temperature zone and a variable temperature zone, and a three-layer thick-walled cylinder finite ring elastic contact calculation model is established; secondly, the shaft heat conduction differential equation under the temperature field condition is constructed, and the analytical solution of the temperature distribution of the surrounding rock and the initial support structure is solved respectively; finally, based on the theory of autogenous temperature stress of thick-walled cylinders, the autogenous temperature stress and deformation of the initial support structure are solved. The present invention forms a method for calculating the temperature stress and deformation of the initial support structure of a vertical shaft in cold regions, which can provide a theoretical basis for cold protection and heat preservation of extra-long tunnel shafts in cold regions. Not only does the calculation method have the characteristics of being in line with the actual and simple characteristics of the temperature field of the vertical shaft in cold regions, but the calculation results also have the advantages of being accurate, scientific and reasonable.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] The above-mentioned method for calculating the temperature stress and deformation of the initial support structure of a vertical shaft in cold regions comprises the following steps:

[0007] In the above-mentioned method for calculating the temperature stress and deformation of the initial support structure of a vertical shaft in cold regions, the calculation method includes the following steps:

[0008]

S1

[0009] The surrounding rock is regarded as a stable temperature field, and the surrounding rock temperature field is divided into two parts: constant temperature zone and variable temperature zone. A three-layer thick-walled cylindrical finite ring elastic contact calculation model is established, and calculation assumptions are made.

[0010]

S2

[0011] The differential equation of wellbore heat conduction under temperature field conditions is constructed, and the temperature boundary conditions are reasonably selected to obtain the analytical solutions of the temperature distribution of the surrounding rock and the initial support structure respectively.

[0012]

S3

[0013] Based on the obtained analytical solution of the initial support structure temperature distribution and according to the thick-walled cylinder temperature stress theory, the initial support structure temperature stress and deformation are determined.

[0014] The above-mentioned method for calculating the temperature stress and deformation of the initial support structure of a vertical shaft in cold regions is characterized in that the surrounding rock is regarded as a stable temperature field in step [S1] for the convenience of calculation, and the calculation method adopted is the finite ring thermal elastic deformation coordination method.

[0015] In the above-mentioned method for calculating the temperature stress and deformation of the initial support structure of a vertical shaft in cold regions, the three-point calculation assumptions in step [S1] are: the heat flow is always conducted in the direction of temperature decrease; the temperature field conforms to the one-dimensional temperature field; and the first to third categories and the temperature and heat flow continuity boundary conditions are met.

[0016] In the above-mentioned method for calculating the temperature stress and deformation of the initial support structure of a vertical shaft in cold regions, the differential equation for the heat conduction of the shaft under the temperature field conditions in step [S2] is as follows:

[0017]

[0018] Where dt is the temperature of the microelement; dr is the radial length of the microelement; and r is the shaft radius variable.

[0019] In the above-mentioned method for calculating the temperature stress and deformation of the initial support structure of a vertical shaft in cold regions, the analytical solution for the temperature distribution of the initial support structure in step [S2] is as follows:

[0020]

[0021] Where, t l is the analytical solution of the initial support structure temperature distribution; T0 is the boundary temperature when r=R; r is the radius variable; r0 is the wellbore radius; r1 is the contact surface radius between the initial support structure and the surrounding rock; R is the contact surface radius between the variable temperature zone and the constant temperature zone; λ l is the thermal conductivity of the initial support structure; s is the thermal conductivity of the shaft surrounding rock; h l is the convective heat transfer coefficient between water and the initial support structure.

[0022] In the above-mentioned method for calculating the temperature stress and deformation of the initial support structure of a vertical shaft in cold regions, the temperature stress and deformation of the initial support structure in step [S3] are as follows:

[0023]

[0024] Where σ r is the initial radial temperature stress of the supporting structure; σ θ is the initial tangential temperature stress of the supporting structure; σ z is the initial longitudinal (depth direction) temperature stress of the supporting structure; u r is the initial radial deformation of the supporting structure; α l Initial support structure linear expansion coefficient; E l is the elastic modulus of the initial support structure; μ l is the Poisson's ratio of the initial support structure; T l is the temperature at radius r.

[0025] The beneficial effects of the present invention are:

[0026] (1) The present invention regards the surrounding rock of the cold-region vertical shaft as a stable temperature field, and divides the temperature field into two parts: constant temperature and variable temperature zone. A three-layer thick-walled cylindrical finite ring elastic contact calculation model is established, and the calculation formula of the temperature stress and deformation of the initial support structure is obtained by theoretical deduction. Compared with the current numerical simulation research method, the seven key factors affecting the temperature stress and deformation of the initial support structure of the cold-region vertical shaft are clarified, namely the geometric dimensions of the initial support structure section, thermal conductivity, heat transfer coefficient, elastic constant, linear expansion coefficient, ambient temperature, and structure surface temperature; compared with the current experimental research method, the disadvantages of difficult on-site vertical high-altitude testing and distortion of the dynamic simulation of the indoor test environment temperature are avoided, which can provide a basic theory for the cold-proof and thermal insulation design of the cold-region vertical shaft.

[0027] (2) This invention draws on the elastic mechanics of multi-layer thick-walled cylinders and establishes a three-layer thick-walled cylinder finite ring elastic contact calculation model of "surrounding rock constant temperature zone - surrounding rock variable temperature zone - initial support structure". Based on the heat conduction equation of the stable temperature field, it realizes the solution of the temperature distribution of the initial support structure. The formed "partition-contact solution" concept solves the difficult problem of determining the temperature value of the initial support structure, and has the advantages of being more reasonable and in line with the actual characteristics of the structure.

[0028] (3) The present invention is based on the analytical solution of the temperature distribution of the initial support structure, adopts the theory of thermoelasticity, and uses the temperature stress and deformation theory of thick-walled cylinders to determine the initial support stress and deformation, establishes a connection between temperature, stress and deformation, avoids the tediousness of thermodynamic solutions, overcomes the defects of the software in calculating temperature with multiple boundary conditions and the accuracy of fluid-solid coupling solutions, and makes the calculation and solution more accurate, reasonable, simple and convenient. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments described in the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0030] Figure 1 Flow chart of the calculation method of the present invention;

[0031] Figure 2 Schematic diagram of the calculation model for the contact problem of three-layer thick-walled cylinders established by the present invention;

[0032] Figure 3 Schematic diagram of the calculation model of the thick-walled cylinder of the initial support structure established by the present invention;

[0033] Figure 4 a) is a schematic diagram of a numerical simulation calculation model established in the present invention;

[0034] Figure 4 b) is the radial displacement u of the initial support structure of the present invention r Numerical simulation cloud map;

[0035] Figure 4 c) is the initial radial stress σ of the supporting structure of the present invention r Numerical simulation cloud map;

[0036] Figure 4 d) is the initial tangential stress σ of the supporting structure of the present invention θ Numerical simulation cloud map;

[0037] Figure 4 e) is the initial z-direction stress σ of the supporting structure of the present invention zNumerical simulation cloud map.

[0038] The reference numerals are as follows:

[0039] 1-Inside the wellbore; 2-Initial support structure; 3-Variable temperature zone; 4-Constant temperature zone. DETAILED DESCRIPTION

[0040] In order to make those skilled in the art better understand the technical solution of the present invention, Figure 1-4 The present invention is further described in detail with reference to the accompanying drawings and embodiments to make the objectives, technical solutions and advantages of the present invention more clear.

[0041] Thermal expansion and contraction effects of initial support structures of vertical shafts in cold regions:

[0042] The average annual ambient temperature in cold regions is generally below 0°C, and permafrost exists above the surface freezing line. Shaft construction disturbs the thermal balance of the surrounding rock. The primary support structure 2 is in the permafrost heat exchange variable temperature zone 3 in the immediate vicinity of the surrounding rock, while the distal area is in the constant temperature zone 4. Furthermore, due to heat exchange with the surrounding environment, the temperature within the shaft reaches negative temperatures at a certain depth in winter, causing the primary support structure to contract. In spring and summer, the temperature reaches positive temperatures at a certain depth, causing the primary support structure to expand. The primary support structure is constructed of cast-in-place reinforced concrete, a temperature-sensitive material. Thermal expansion and contraction cause internal thermal stresses and deformations, exacerbating degradation. Therefore, determining the thermal stresses and deformations of the primary support structure is crucial.

[0043] like Figure 1 As shown, the present invention provides a method for calculating the temperature stress and deformation of the initial support structure of a vertical shaft in cold regions, comprising the following steps:

[0044]

S1

[0045] For vertical shafts in cold regions, the temperature field of a certain range of the surrounding rock is disturbed after excavation, resulting in variable temperature zones and constant temperature zones. Both zones are regarded as stable temperature fields, and a three-layer thick-walled cylindrical finite ring elastic contact calculation model of "constant temperature zone-variable temperature zone-initial support structure" is established, as shown in the following example: Figure 2 shown.

[0046] Three assumptions are made for the calculation model: heat flow is always conducted in the direction of decreasing temperature, that is, the direction of heat conduction is from high temperature to low temperature; the temperature field conforms to the one-dimensional temperature field, that is, the temperature of the medium changes only in one coordinate direction; the first to third categories and the temperature and heat flow continuity boundary conditions are met.

[0047]

S2

[0048] The surrounding rock constant temperature zone, variable temperature zone, and initial support structure can be regarded as a three-layer thick-walled cylinder contact problem. The first layer is the initial support structure (r0≤r≤r1); the second layer is the surrounding rock variable temperature zone (r1≤r≤R); and the third layer is the surrounding rock constant temperature zone (R≤r≤+∞). The calculation model is as follows: Figure 2 shown.

[0049] Using the cylindrical coordinate system, the heat conduction equation of "initial support structure-surrounding rock" under the stable temperature field is:

[0050]

[0051] Where dt is the temperature of the microelement; dr is the radial length of the microelement; and r is the shaft variable, m.

[0052] According to the temperature field boundary value condition, the inner interface of the initial support structure is a given convection heat transfer boundary condition, and the outer interface of the initial support structure is a contact boundary condition, that is,

[0053]

[0054] Where λ l is the thermal conductivity of the initial support structure; h l is the convective heat transfer coefficient between water and the initial support structure; t1 is the external interface temperature of the initial support structure, that is, the temperature of the contact surface with the surrounding rock, ℃; t is the temperature variable, ℃.

[0055] Using the boundary conditions of formula (2), solving the differential equation of formula (1), we can obtain the temperature distribution law of the initial support structure:

[0056]

[0057] Where C1 and D1 are constant coefficients of the differential equation; l is the analytical solution of the temperature distribution of the initial support structure, ℃; r0 is the shaft radius, m; r1 is the contact surface radius between the initial support structure and the surrounding rock, m;

[0058] For the variable temperature zone of the surrounding rock of the shaft (r1≤r≤R), the boundary temperature condition is

[0059]

[0060] Where R is the contact radius between the variable temperature zone and the constant temperature zone, m; T0 is the boundary temperature when r = R, °C; Using the boundary condition formula (5) to solve the differential equation (1), we can get the temperature distribution law of the variable temperature zone of the vertical shaft surrounding rock:

[0061]

[0062] Where C2 and D2 are constant coefficients of the differential equation; sis the analytical solution for the temperature distribution in the surrounding rock temperature change zone, ℃. According to the continuous heat flow condition at the contact surface between the initial support structure and the surrounding rock

[0063]

[0064] Where λ s is the thermal conductivity of the shaft surrounding rock.

[0065] Therefore, the temperature distribution law in the initial support structure can be obtained as shown in the following formula:

[0066]

[0067]

S3

[0068] Based on the obtained analytical solution of the temperature distribution of the initial support structure and according to the theory of autogenous temperature stress of thick-walled cylinders, the temperature stress and deformation of the initial support structure are determined.

[0069] The initial support structure of the shaft is equivalent to a thick-walled cylinder with an inner radius of r0 and an outer radius of r1, as shown in Figure 3 As shown, it is in an axisymmetric temperature field, and its axisymmetric temperature change is T = T(r). The boundary conditions are

[0070]

[0071] Where σ r is the radial temperature stress, MPa.

[0072] According to the thermoelastic physics equation

[0073]

[0074] Where, ε r is the radial strain; ε θ is the tangential strain; γ rθ is the shear strain; μ is the Poisson's ratio; E is the elastic modulus of the initial support structure, MPa; τ rθ is the tangential stress, MPa.

[0075] Using cylindrical coordinates, due to the axisymmetric problem, the shear stress τ rθ =0, so transforming (13) we can get

[0076]

[0077] Where, E is the elastic modulus of the thick-walled cylinder, MPa; μ is the Poisson's ratio of the thick-walled cylinder; α is the linear expansion coefficient of the thick-walled cylinder; T l is the temperature at radius r, ℃.

[0078] Substituting the boundary conditions of equation (12) into the equilibrium equation of the plane strain problem of equation (15)

[0079]

[0080] Available

[0081]

[0082] Geometric equations for plane strain problems

[0083]

[0084] Where du is the displacement of the microelement

[0085] Substituting into (16), we can get

[0086]

[0087] Formula (18) can be rewritten as

[0088]

[0089] Integrating formula (19), we can get

[0090]

[0091] Where A and B are the integral constants to be determined.

[0092] Substituting equation (20) into equation (17) and then into equation (14), we can get

[0093]

[0094] From formula (21)σ r And the boundary condition formula (12), we can get the integral constants A and B

[0095]

[0096] Where A and B are integral constant coefficients.

[0097] Substituting formula (22) into (21), we can get

[0098]

[0099] According to ε in formula (17) θ , formula (20), (22), we can get

[0100]

[0101] In formulas (16) to (24), T l Satisfy the following formula

[0102]

[0103] Where, is the initial temperature of the supporting structure itself, ℃.

[0104] Engineering example applications

[0105] The Tianshan Victory Tunnel, 22.1 km long and the world's longest highway tunnel under construction, utilizes a "3-hole + 4-shaft" construction scheme. The 2-2 shaft site is located at an altitude of 3,700 m, with an average annual temperature of -25°C, typical of a high-altitude, cold plateau. The shaft excavation radius is 6.1 m, and a double-layer formwork concrete support structure is employed. The initial support structure is 50 cm thick, and the secondary lining is 35 cm thick. The elastic modulus E of the initial support structure is 3.5 × 10 4 MPa, Poisson's ratio μ is 0.35, and the linear expansion coefficient α is 1.2×10 -2 / ℃, ambient temperature T l 0 The temperature is -35℃ (the lowest negative temperature in winter), and the thermal conductivity of the initial support structure is λ l is 1.5W / (m·K), the thermal conductivity of the surrounding rock is 2.5W / (m·K), and the convection heat transfer coefficient between water and the initial support structure is h l 40W / (m 2 ·K), the temperature of the surrounding rock constant temperature zone T0 is -5℃, and the temperature stress and deformation are determined by taking the interface between the initial support structure and the surrounding rock as an example.

[0106] Let r = 6.1, and calculate t according to formula (10) l

[0107]

[0108] t l =-2.02℃Substitute into formula (25) to calculate T l

[0109]

[0110] Finite element method was used to establish a two-dimensional stratum structure model, and the rationality of the calculation example was verified by applying a temperature field. The initial support structure adopted the extracted beam unit model, and the surrounding rock adopted a two-dimensional plane model. The numerical calculation model established is as follows: Figure 4 As shown in (a). Figure 4 (b) shows the displacement cloud diagram of the initial support structure, and the numerical simulation is very close to the calculated results. Figure 4 Figures (c) to (e) show the stress cloud diagrams of the initial support structure in the radial, tangential, and longitudinal directions, respectively. The numerical simulations are very close to the theoretical calculations, which shows that the calculation method proposed in this invention is reasonable.

[0111] In summary, the present invention provides a method for calculating the temperature stress and deformation of the initial support structure of a vertical shaft in cold regions. First, the surrounding rock is regarded as a stable temperature field, and the surrounding rock temperature field is divided into two parts: a constant temperature zone and a variable temperature zone, and a three-layer thick-walled cylinder finite ring elastic contact calculation model is established; secondly, the shaft heat conduction differential equation under the temperature field condition is constructed, and the analytical solution of the temperature distribution of the surrounding rock and the initial support structure is solved respectively; finally, based on the theory of autogenous temperature stress of thick-walled cylinders, the temperature stress and deformation of the initial support structure are solved. The present invention forms a method for calculating the temperature stress and deformation of the initial support structure of a vertical shaft in cold regions, which can provide a theoretical basis for cold protection and heat preservation of extra-long tunnel shafts in cold regions. Not only does the calculation method have the characteristics of being in line with the actual and simple characteristics of the temperature field of the vertical shaft in cold regions, but the calculation results are also accurate, scientific and reasonable, and have the value of further promotion and application.

Claims

1. A method for calculating temperature stress and deformation of initial support structure of vertical shaft in cold regions, characterized by: The following steps are involved: 【S1】Establishment of computational model The surrounding rock is regarded as a stable temperature field, and the surrounding rock temperature field is divided into two parts: constant temperature zone and variable temperature zone. A three-layer thick-walled cylinder finite ring elastic contact calculation model is established, and calculation assumptions are made. 【S2】Calculate the analytical solution of temperature distribution Construct the differential equation of heat conduction in the wellbore under the temperature field condition, reasonably select the temperature boundary conditions, and solve the analytical solutions of the temperature distribution of the surrounding rock and the initial support structure respectively; The differential equation for wellbore heat conduction under temperature field conditions is as follows: Where, dt is the temperature of the microelement; dr is the radial length of the microelement; r is the shaft radius variable; The analytical solution for the temperature distribution of the initial support structure is as follows: Where, t l is the analytical solution of the initial support structure temperature distribution; T0 is the boundary temperature when r=R; r is the radius variable; r0 is the wellbore radius; r1 is the contact surface radius between the initial support structure and the surrounding rock; R is the contact surface radius between the variable temperature zone and the constant temperature zone; λ l is the thermal conductivity of the initial support structure; s is the thermal conductivity of the shaft surrounding rock; h l is the convective heat transfer coefficient between water and the initial support structure; 【S3】Determine temperature stress and deformation Based on the analytical solution of the initial support structure temperature distribution and the thick-walled cylinder temperature stress theory, the initial support structure temperature stress and deformation are determined. The initial temperature stress and deformation of the supporting structure are as follows: Where, σ r is the initial radial temperature stress of the supporting structure; σ θ is the initial tangential temperature stress of the supporting structure; σ z is the longitudinal (depth direction) temperature stress of the initial support structure; u r is the initial radial deformation of the supporting structure; α l Initial support structure linear expansion coefficient; E l is the elastic modulus of the initial support structure; μ l is the Poisson's ratio of the initial support structure; T l is the temperature at radius r.

2. The method for calculating temperature stress and deformation of initial support structure of vertical shaft in cold regions according to claim 1 is characterized in that: In the step [S1], the surrounding rock is considered to be in a stable temperature field for the sake of calculation convenience, and the calculation method adopted is the finite ring thermoelastic deformation coordination method.

3. The method for calculating temperature stress and deformation of initial support structure of vertical shaft in cold regions according to claim 1 is characterized in that: In the step [S1], it is assumed that: the heat flow is always conducted in the direction of decreasing temperature; the temperature field conforms to a one-dimensional temperature field; and the first to third categories and temperature and heat flow continuity boundary conditions are met.

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