A stress analysis calculation method for hydraulic engineering structures under combined action of temperature and humidity

Abstract

This invention provides a stress analysis and calculation method for hydraulic engineering structures considering humid and thermal conditions, comprising the following steps: Step 1, determining the heat conduction equation and the moisture diffusion equation, and establishing a mathematical model for the coupled heat and moisture transport of concrete; Step 2, considering the boundary conditions for heat conduction and relative humidity diffusion under natural conditions; Step 3, determining the elastic constitutive equation of concrete for humid and thermal deformation; Step 4, determining the geometric parameters and boundary conditions of the hydraulic engineering structure, and obtaining the stress distribution after coupled analysis based on the results of Steps 1-3. This method can be used to understand the internal stress conditions and variation patterns of hydraulic engineering structures under different environments, providing a reference for the design, construction, and maintenance of future hydraulic engineering structures.

Description

Technical Field

[0001] This invention relates to the field of water conservancy engineering technology, and in particular to a method for stress analysis and calculation of water conservancy engineering structures considering humid and thermal conditions. Background Technology

[0002] Hydraulic engineering structures include numerous hydraulic buildings, such as dams, weirs, canals, and aqueducts. Aqueducts are water conveyance structures spanning mountains, valleys, and roads, and are widely used in agricultural irrigation and other water conveyance projects, playing a vital role in my country's water conservancy projects. The outer surface of an aqueduct is exposed to a complex natural environment. Influenced by factors such as solar radiation, diurnal temperature variations, annual temperature variations, and cold currents, the temperature of the aqueduct's outer surface is constantly changing. Meanwhile, the interior of the aqueduct is filled with flowing water, and its inner surface remains relatively stable due to contact with the flowing water. Under the interaction of the constantly changing outer surface and the relatively stable inner surface, the temperature at various points within the aqueduct is constantly changing, gradually leading to a non-uniform temperature distribution within the aqueduct.

[0003] Furthermore, aqueducts have a large contact area with water, and the water transport process is intermittent with water level changes, resulting in non-uniform humidity variations within the aqueduct. This uneven distribution of the humid heat field within the aqueduct structure leads to varying degrees of humid heat deformation, causing changes in the internal forces and deformation of the aqueduct. This generates tensile stress on the aqueduct's surface and may lead to cracks, posing a significant threat to thin-walled structures like aqueducts. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a stress analysis and calculation method for hydraulic engineering structures considering humid and thermal conditions. Using this method, the internal stress conditions and variation laws of hydraulic engineering structures under different environments can be understood, providing a reference for the design, construction and maintenance of hydraulic engineering structures in the future.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a stress analysis and calculation method for hydraulic engineering structures considering hygrothermal conditions, comprising the following steps:

[0006] Step 1: Determine the heat conduction equation and the moisture diffusion equation, and establish a mathematical model for the coupled heat and moisture transport in concrete;

[0007] Step 2: Consider the boundary conditions of heat conduction and relative humidity diffusion under natural conditions;

[0008] Step 3: Determine the elastic constitutive equation of concrete for wet-heat deformation;

[0009] Step 4: Determine the geometric parameters and boundary conditions of the hydraulic engineering structure, and obtain the stress-strain distribution by performing a coupled analysis based on the results of Steps 1 to 3.

[0010] In the preferred embodiment, in step one, according to Fourier's law, the heat conduction equation is expressed as:

[0011]

[0012]

[0013] Among them, (ρC P ) eff T represents the effective heat capacity of the concrete; T represents the temperature of the concrete. t is the temperature gradient; t is time; Q is the heat source; k eff L is the effective thermal conductivity of concrete. V The latent heat of vaporization of concrete; δ p φ represents the vapor permeability of concrete; φ represents the relative humidity of concrete; p sat This is the saturated vapor pressure of the concrete.

[0014] In the preferred embodiment, the effective thermal conductivity k in the heat conduction equation is... eff The calculation formula is:

[0015] k eff (T, φ) = k0·F1(T)·F2(φ)

[0016] Where k0 is the reference thermal conductivity of concrete; F1(T) represents the function of temperature on the effective thermal conductivity, and F2(φ) represents the function of relative humidity on the effective thermal conductivity;

[0017] F1(T) = 1 - a(TT) ref )

[0018] 'a' represents the temperature coefficient; 'T' represents the concrete temperature; ref The initial temperature of the concrete;

[0019]

[0020] w c This indicates the internal moisture content of the concrete; b is the humidity addition coefficient; ρ s This indicates the density of concrete.

[0021] In the preferred embodiment, the effective heat capacity of concrete material is calculated using the following formula in the heat conduction equation:

[0022] (ρC p ) eff =ρ s C p，s +w c C p，w

[0023] Among them, (ρCp ) eff For effective heat melting of concrete; w c C represents the moisture content of the concrete. p，s C represents the constant-pressure heat capacity of dry concrete. p，w This indicates the specific heat capacity of water.

[0024] In the preferred embodiment, in step one, according to Fick's second law, the concrete moisture diffusion equation is expressed as:

[0025]

[0026]

[0027]

[0028] Where φ is the relative humidity of the concrete; w c D represents the moisture content of the concrete. w G is the diffusion coefficient of concrete; G is the moisture source; p sat This is the saturated vapor pressure of the concrete.

[0029] The relative humidity of concrete is converted into the internal moisture content of concrete:

[0030]

[0031] In the formula, W uni It represents the mass of a single water molecule layer adsorbed on the surface of the hydration product; C is a thermal performance parameter; Q, P, and M represent equation coefficients.

[0032] In the preferred embodiment, the formula for calculating the diffusion coefficient in the concrete moisture diffusion equation is:

[0033] D w (φ, T) = D0·F3(φ)·F4(T)

[0034] Where D0 is the humidity diffusion coefficient of saturated concrete; F3(φ) represents the function of relative humidity on the diffusion coefficient; and F4(T) represents the function of temperature on the diffusion coefficient.

[0035]

[0036] φ represents the relative humidity of the concrete. c denoted as the initial relative humidity of the concrete; n represents the regression coefficient of the nonlinear humidity diffusion equation; a0 is an empirical coefficient.

[0037]

[0038] Q is the enthalpy of vaporization of water at 20℃; R is the gas constant; T0 represents the initial temperature of the concrete; T represents the current temperature of the concrete.

[0039] In the preferred embodiment, the boundary conditions for concrete heat conduction in step two are divided into the following three categories:

[0040] (1) Given the boundary temperature function, the formula is as follows:

[0041] T(t)| Γ =f(t)

[0042] In the formula, f(t) is a known temperature function; Γ is the boundary of the object;

[0043] (2) Given the boundary heat flux density function, the formula is as follows:

[0044]

[0045] In the formula, k is the thermal conductivity; n is the normal direction of the concrete surface; q(t) is a known heat flux density function;

[0046] (3) Given the boundary heat exchange law, the formula is expressed as:

[0047]

[0048] In the formula, h is the heat transfer coefficient; T Γ (t) represents the surface temperature of the concrete material; T a (t) represents the ambient temperature.

[0049] In the preferred embodiment, the boundary condition for concrete moisture diffusion in step two is expressed as follows:

[0050] φ(t)| Γ =φ(t)

[0051]

[0052] In the formula, φ(t) is a known function of ambient relative humidity; T is the boundary of the concrete; D w β is the diffusion coefficient; n is the normal direction of the concrete surface; β p φ represents the water migration coefficient. Γ (t) represents the relative humidity of the concrete surface; φ amb (t) represents the ambient relative humidity.

[0053] In the preferred embodiment, in step three, the elastic constitutive equation of the concrete material is expressed as:

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] In the formula, E0 is the initial elastic modulus of concrete; μ is Poisson's ratio; σ x σ y σ z τ xy τ yz and τ zz For stress; ε x ε y ε z γ xy γ yz and γ zx For strain; ε th ε represents the temperature strain of the concrete. hs The value represents the humidity strain of the concrete; E(w, T) represents the elastic modulus of the concrete after the effects of humidity and temperature.

[0061] Concrete temperature strain ε th It can be represented as:

[0062] ε th =α(TT) ref )

[0063] In the formula, α is the coefficient of linear expansion; T ref This refers to the initial temperature of the concrete.

[0064] Concrete humidity strain ε hs It manifests as:

[0065] ε hs =β h (w c -w ref )

[0066] In the formula, β h w is the coefficient of hygroscopic expansion. ref This refers to the initial moisture content of the concrete; w c This refers to the internal moisture content of the concrete.

[0067] The elastic modulus E(w, T) of concrete is a function of temperature and relative humidity:

[0068] E(w, T) = E0·F5(w)·F6(T)

[0069] Where F5(w) represents the effect function of humidity on the elastic modulus of concrete; F6(T) represents the effect function of temperature on the elasticity of concrete;

[0070] F5(w) = 24.31 + 130w

[0071] F6(T)=1-0.00094T 20C<T<800C

[0072] w = w c (φ) / ρ s

[0073] Where w is the moisture content of the concrete, w c ρ represents the water content of concrete. s This refers to the density of the concrete.

[0074] In the preferred embodiment, in step four, the stress-strain distribution is obtained by performing a coupled analysis of the temperature field, humidity field, and stress field in COMSOL Multiphysiscs software.

[0075] This invention provides a stress analysis and calculation method for hydraulic engineering structures considering hygrothermal conditions. It establishes a coupling relationship for hygrothermal transmission in bridges using thermal conductivity and diffusion coefficient, and determines a method for calculating the boundary conditions of the hygrothermal field in concrete aqueducts under natural environmental conditions. Considering hygrothermal deformation, a numerical model for coupled calculation of concrete hygrothermal-mechanical forces is established, which facilitates subsequent analysis of non-uniform hygrothermal fields and hygrothermal effects in hydraulic engineering structures. Attached Figure Description

[0076] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0077] Figure 1 This is a flowchart of an analytical calculation method for the stress of hydraulic engineering structures under hygrothermal conditions, according to the present invention.

[0078] Figure 2 This is a mesh diagram of the aqueduct in the embodiment;

[0079] Figure 3 This is a humidity distribution diagram of the mid-span section of the aqueduct in the embodiment;

[0080] Figure 4 This is a distribution diagram of the stress on the surface of the aqueduct in the embodiment;

[0081] Figure 5 This is a displacement distribution diagram of the mid-span section of the aqueduct in the embodiment; Detailed Implementation

[0082] Based on the data of the aqueduct project in Kashgar, Northwest my country, a finite element model of a rectangular aqueduct was established to simulate the influence of humid heat on the stress and deformation of the aqueduct under full water conveyance conditions.

[0083] The aqueduct is 10m long and has 5 tie rods spaced 2.45m apart. The aqueduct is simply supported at both ends. The mid-span cross-section is a rectangular section measuring 5.0m × 3.45m (width × height), with a shell wall thickness of 0.2m. The top of the shell is thickened to form side beams, and the bottom is thickened to form longitudinal beams. End ribs, 0.3m thick, are provided at both ends of the aqueduct. The aqueduct runs north-south. As a rectangular open aqueduct, it is a thin-walled spatial structure, and in the numerical model, it is meshed using hexahedral 8-node 3D solid elements. To ensure computational accuracy, a 10-layer mesh was created along the thickness direction of the aqueduct. The mesh generation of the aqueduct is shown in [link to mesh generation details]. Figure 2 .

[0084] This invention is achieved through the following technical solution:

[0085] A method for stress analysis and calculation of hydraulic engineering structures considering hygrothermal conditions, such as Figure 1 As shown, the steps include: Step 1: Determine the heat conduction equation and the moisture diffusion equation, and establish a mathematical model of concrete moisture-heat coupling transport.

[0086] The mathematical model for the coupled heat and moisture transport in concrete includes a heat conduction equation, which represents the process of temperature change through conduction in space. In this invention, the heat conduction equation represents the heat exchange process between the ambient temperature and the concrete temperature. According to Fourier's law, the heat conduction equation is expressed as:

[0087]

[0088]

[0089] Among them, (ρC P ) eff is the effective heat capacity of concrete; T is the temperature of concrete. For temperature gradient; t is time; Q is the heat source (considered as 0 here); k eff L is the effective thermal conductivity of concrete. V The latent heat of vaporization of concrete; δ p φ represents the vapor permeability of the concrete; φ represents the relative humidity of the concrete, typically taken as 0.5; p sat This is the saturated vapor pressure of the concrete.

[0090] In the heat conduction equation, the effective thermal conductivity k eff The calculation formula is:

[0091] k eff (T, φ) = k0·F1(T)·F2(φ)

[0092] Where k0 is the reference thermal conductivity of concrete; it is generally taken as 1.74; F1(T) represents the function of temperature on the effective thermal conductivity, and F2(φ) represents the function of relative humidity on the effective thermal conductivity.

[0093] F1(T) = 1 - a(TT) ref )

[0094] 'a' represents the temperature coefficient; it is generally taken as a = 1.017 × 10⁻⁶. -3 T represents the concrete temperature; T ref The initial temperature of the concrete is 20℃.

[0095]

[0096] w c This indicates the internal moisture content of the concrete; b is the humidity additional coefficient, generally taken as b = 20; ρ s This indicates the density of concrete.

[0097] In the heat conduction equation, the formula for calculating the effective heat capacity of concrete is:

[0098] (ρC p ) eff =ρ s C p，s +w c C p，w

[0099] Among them, (ρC p ) eff For effective heat melting of concrete; w c C represents the moisture content of the concrete. p，s C represents the constant-pressure heat capacity of dry concrete. p，w This indicates the specific heat capacity of water.

[0100] Step one includes the concrete moisture diffusion equation in hydraulic engineering structures. The moisture diffusion equation represents the process of moisture from the environment diffusing into the concrete. According to Fick's second law, the concrete moisture diffusion equation is expressed as:

[0101]

[0102]

[0103]

[0104] Where φ is the relative humidity of the concrete; w c D represents the moisture content of the concrete. w G is the diffusion coefficient of concrete; G is the moisture source; psat This is the saturated vapor pressure of the concrete.

[0105] Moisture content represents the percentage of water in concrete. Since the equation above requires the moisture content of the concrete, and we only know the relative humidity, I can use a modified BET model to convert the relative humidity of the concrete into its internal moisture content: Converting the relative humidity of the concrete into its internal moisture content:

[0106]

[0107] In the formula, W uni W uni =0.009 represents the mass of a single water molecule layer adsorbed on the surface of the hydration product; C=6.669 is a thermal performance parameter; Q, P, and M can be obtained from the isothermal adsorption-desorption curves of the concrete specimen, representing equation coefficients of 4.875, 0.348, and 1.08, respectively.

[0108] The key to humidity-heat coupling lies in the fact that the coefficients in the heat transfer and moisture transfer equations are affected by temperature and humidity, respectively. The effective thermal conductivity is a function of both temperature and relative humidity.

[0109] In the concrete moisture diffusion equation, the formula for calculating the diffusion coefficient is:

[0110] D w (φ, T) = D0·F3(φ)·F4(T)

[0111] Where D0 is the moisture diffusion coefficient of saturated concrete, and the saturated diffusion coefficient is generally taken as 3 × 10⁻⁶. -9 F3(φ) represents the function of relative humidity on the diffusion coefficient; F4(T) represents the function of temperature on the diffusion coefficient.

[0112]

[0113] φ represents the relative humidity of the concrete. c The initial relative humidity of the concrete is denoted by ; n represents the regression coefficient of the nonlinear diffusion equation of humidity, typically taken as 6–16, but 15 in this invention; a0 is an empirical coefficient, typically taken as 0.5.

[0114]

[0115] Q is the enthalpy of vaporization of water at 20℃, 45KJ / mol; R is the gas constant, 8.314J / (mol·K); T0 represents the initial temperature of the concrete; here T0=20℃, and T represents the current temperature of the concrete.

[0116] Step 2: Consider the boundary conditions of heat conduction and relative humidity diffusion under natural conditions.

[0117] In step two, the influence analysis of the boundary conditions of the temperature field shows that the heat exchange between the concrete aqueduct structure and the external environment can be divided into three forms: heat conduction, radiation heat transfer, and convection heat transfer.

[0118] The boundary conditions for heat conduction in concrete can be categorized into the following three types:

[0119] (1) Given the boundary temperature function, the formula is as follows:

[0120] T(t)| Γ =f(t)

[0121] In the formula, f(t) is a known temperature function; Γ is the boundary of the object.

[0122] (2) Given the boundary heat flux density function, the formula is as follows:

[0123]

[0124] In the formula, k is the thermal conductivity; n is the normal direction of the concrete material surface; and q(t) is a known heat flux density function.

[0125] (3) Given the boundary heat exchange law, the formula is expressed as:

[0126]

[0127] In the formula, h is the heat transfer coefficient; T Γ (t) represents the surface temperature of the concrete material; T a (t) represents the ambient temperature.

[0128] The boundary condition for moisture diffusion in concrete is expressed as follows:

[0129] φ(t)| Γ =φ(t)

[0130]

[0131] In the formula, φ(t) is a known function of ambient relative humidity; Γ is the boundary of the concrete; D w m is the diffusion coefficient. 2 / s; n is the normal direction of the concrete surface; β p The value m represents the water transport coefficient. 2 / s;φ Γ (t) represents the relative humidity of the concrete surface; φ amb (t) represents the ambient relative humidity. The relative humidity of the concrete surface remains close to 1, i.e., φ. Γ (t) = 1. The humidity distribution at the mid-span of the concrete can be obtained by using the ambient humidity and the relative humidity of the concrete for moisture exchange, see [reference needed]. Figure 3 .

[0132] Step 3: Determine the elastic constitutive equation of concrete for wet-heat deformation.

[0133] The elastic constitutive equation of concrete is expressed as:

[0134]

[0135]

[0136]

[0137]

[0138]

[0139]

[0140] In the formula, E0 is the initial elastic modulus of concrete; μ is Poisson's ratio; σ x σ y σ z τ xy τ yz and τ zx For stress; ε x ε y ε z γ xy γ yz and γ zx For strain; ε th ε represents the temperature strain of the concrete. hs denoted as , where is the humidity strain of the concrete; E(w, T) is the elastic modulus of the concrete after the effects of humidity and temperature.

[0141] Concrete temperature strain ε th It can be represented as:

[0142] ε th =α(TT) ref )

[0143] In the formula, α is the coefficient of linear expansion; T ref This refers to the initial temperature of the concrete.

[0144] Concrete humidity strain ε hs It manifests as:

[0145] ε hs =β h (w c -w ref )

[0146] In the formula, β hw is the coefficient of hygroscopic expansion. ref This refers to the initial moisture content of the concrete; w c This refers to the internal moisture content of the concrete.

[0147] After the effects of humidity and temperature, the elastic modulus E(w, T) of concrete becomes a function of temperature and relative humidity:

[0148] E(w, T) = E0·F5(w)·F6(T)

[0149] Where F5(w) represents the effect function of humidity on the elastic modulus of concrete; F6(T) represents the effect function of temperature on the elasticity of concrete;

[0150] F5(w) = 24.31 + 130w

[0151] F6(T)=1-0.00094T 20C<T<800C

[0152] w = w c (φ) / ρ s

[0153] Where w is the moisture content of the concrete, w c ρ represents the water content of concrete. s This refers to the density of the concrete.

[0154] Step 4: Determine the geometric parameters and boundary conditions of the hydraulic engineering structure. Based on the results of steps 1-3, perform a coupled analysis to obtain the stress-strain distribution. Specifically, use COMSOL Multiphysics software to perform a coupled analysis of the temperature field, humidity field, and stress field to obtain the stress-strain distribution.

[0155] Step four involves determining the geometric parameters and boundary conditions of the aqueduct structure, and then performing coupled analysis of the temperature field, humidity field, and stress field equations in COMSOL Multiphysics software to obtain the stress distribution of the aqueduct. Figure 4 and displacement distribution at mid-span section Figure 5 Through observation Figure 4 We can observe that the stress is greatest on both sides of the bottom of the aqueduct, with a maximum tensile stress of 6.5 MPa; through observation... Figure 5 The maximum displacement was found at the bottom plate of the aqueduct, with a maximum displacement of 2.72 mm.

[0156] This invention obtains a calculation model of a hydraulic engineering structure considering the coupling effect of moisture, heat, and force through finite element analysis. The calculation method can then be used to analyze the stress of the hydraulic engineering structure, which is of great significance for the design and construction of concrete aqueducts.

Claims

1. A method for stress analysis and calculation of hydraulic engineering structures considering hygrothermal conditions, characterized in that, Includes the following steps: Step 1: Determine the heat conduction equation and the moisture diffusion equation, and establish a mathematical model for the coupled heat and moisture transport in concrete; According to Fourier's law, the heat conduction equation is expressed as: ； in, The effective heat capacity of concrete; The temperature of the concrete; For temperature gradient; For time; As a heat source; The effective thermal conductivity of concrete; The latent heat of vaporization of concrete; For the vapor permeability of concrete; The relative humidity of the concrete; This is the saturated vapor pressure of the concrete. Effective thermal conductivity The calculation formula is: ； in, The reference thermal conductivity of concrete; A function representing the effect of temperature on the effective thermal conductivity. A function representing the effect of relative humidity on the effective thermal conductivity; ； This represents the temperature coefficient. This indicates the temperature of the concrete; The initial temperature of the concrete; ； This indicates the internal moisture content of the concrete; Humidity factor; Indicates the density of concrete; The formula for calculating the effective heat capacity of concrete is: ； in, For effective heat melting of concrete; This refers to the moisture content of the concrete. This represents the constant-pressure heat capacity of dry concrete. This indicates the specific heat capacity of water; Step 2: Consider the boundary conditions of heat conduction and relative humidity diffusion under natural conditions; Step 3: Determine the elastic constitutive equation of concrete for wet-heat deformation; Step 4: Determine the geometric parameters and boundary conditions of the hydraulic engineering structure, and obtain the stress-strain distribution after performing a coupled analysis based on the results of Steps 1 to 3.

2. The stress analysis and calculation method for hydraulic engineering structures considering hygrothermal conditions according to claim 1, characterized in that, In step one, according to Fick's second law, the concrete moisture diffusion equation is expressed as: ； in, The relative humidity of the concrete; This refers to the moisture content of the concrete. The diffusion coefficient of concrete; It is a source of moisture; This is the saturated vapor pressure of the concrete. The relative humidity of concrete is converted into the internal moisture content of concrete: ； In the formula, W uni It represents the mass of a single water molecule layer adsorbed on the surface of hydration products; C These are thermal performance parameters; P, M Represents the coefficients of the equation.

3. The stress analysis and calculation method for hydraulic engineering structures considering hygrothermal conditions according to claim 2, characterized in that, In the concrete moisture diffusion equation, the formula for calculating the diffusion coefficient is: ； in, The humidity diffusion coefficient of saturated concrete; A function representing the effect of relative humidity on the diffusion coefficient; It represents a function of the effect of temperature on the diffusion coefficient; ； The relative humidity of the concrete. The initial relative humidity of the concrete; n Represents the regression coefficients of the nonlinear humidity diffusion equation; This is an empirical coefficient; ； The enthalpy of vaporization of water at 20°C; It is the gas constant; Indicates the initial temperature of the concrete; This indicates the current temperature of the concrete.

4. The stress analysis and calculation method for hydraulic engineering structures considering hygrothermal conditions according to claim 1, characterized in that, In step two, the boundary conditions for concrete heat conduction are divided into the following three categories: (1) Given the boundary temperature function, the formula is as follows: ； In the formula, A known temperature function; The boundary of the object; (2) Given the boundary heat flux density function, the formula is as follows: ； In the formula, Thermal conductivity; The direction of the normal to the surface of the concrete material; The heat flux density function is known. (3) Given the boundary heat exchange law, the formula is expressed as: ； In the formula, The heat transfer coefficient; The temperature of the concrete surface; The ambient temperature.

5. The stress analysis and calculation method for hydraulic engineering structures considering hygrothermal conditions according to claim 1, characterized in that, In step two, the boundary condition for concrete moisture diffusion is expressed as follows: ； In the formula, Given a known function of ambient relative humidity; The boundary of the concrete; The diffusion coefficient is denoted as . The direction of the normal to the concrete surface; Indicates the water migration coefficient; Indicates the relative humidity of the concrete surface; This refers to the relative humidity of the environment.

6. The stress analysis and calculation method for hydraulic engineering structures considering hygrothermal conditions according to claim 1, characterized in that, In step three, the elastic constitutive equation of the concrete material is expressed as: ； In the formula, This is the initial elastic modulus of concrete; Poisson's ratio; , , , , and For stress; , , , , and In response to the situation; For the temperature strain of concrete; For the humidity strain of concrete; The elastic modulus of concrete after the effects of humidity and temperature. Concrete temperature strain Represented as: ； In the formula, The coefficient of linear expansion; This refers to the initial temperature of the concrete. Concrete humidity strain It manifests as: ； In the formula, This is the coefficient of moisture expansion; This refers to the initial moisture content of the concrete. This refers to the internal moisture content of the concrete. elastic modulus of concrete It is a function of temperature and relative humidity: ； in, This represents the function that describes the effect of humidity on the elastic modulus of concrete. This represents the effect of temperature on the elasticity of concrete; ； in, This refers to the moisture content of the concrete. This refers to the moisture content of the concrete. This refers to the density of the concrete.

7. The stress analysis and calculation method for hydraulic engineering structures considering hygrothermal conditions according to claim 1, characterized in that, In step four, the stress-strain distribution is obtained by performing coupled analysis of the temperature field, humidity field, and stress field in COMSOL Multiphysiscs software.

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