A method for constructing a multi-field coupling model of concrete and a solving method thereof

Abstract

The application provides a kind of concrete multi-field coupling model construction method and its solving method, respectively constructs hydration reaction equation, temperature field control equation, humidity field control equation, adsorption / desorption isotherm equation, mechanical field equation, thermal-humidity-force-chemical coupling process is expressed and calculated in finite element, and the problem is solved by using Gaussian orthogonal space integration method and backward Euler time integration implicit algorithm.The application can accurately predict the temperature and humidity inside the concrete in complex service environment, and can simulate the deformation and stress characteristics of hydraulic concrete caused by temperature and humidity factors, providing support for durability judgment, safety evaluation, life prediction and the like of hydraulic concrete structure.

Description

Technical Field

[0001] This invention belongs to the field of concrete materials, specifically relating to a method for constructing and solving a multi-field coupled model of concrete. Background Technology

[0002] The increasing service life of modern concrete structures places higher demands on their durability. Concrete durability is closely related to its cracking degree, and temperature and humidity changes are significant factors inducing cracking. Therefore, studying the internal temperature and humidity changes of concrete during service is crucial. However, the evolution of temperature and humidity within concrete is driven by the hydration process and the external environment, and in turn, affects the hydration reaction, thus creating a complex coupled process. Therefore, studying concrete durability requires a comprehensive consideration of physical fields such as the hydration reaction field, temperature field, and humidity field. Summary of the Invention

[0003] This invention is made to solve the above-mentioned problems. Its purpose is to provide a method for constructing and solving a multi-field coupled model of concrete, which can accurately predict the internal temperature and humidity of concrete in a complex service environment, and provide support for the durability assessment of concrete structures.

[0004] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0005] A method for constructing a multi-field coupled model of concrete includes the following steps:

[0006] Step A1. Construct the hydration reaction equation;

[0007] Step A2. Construct the temperature field governing equations;

[0008] Step A3. Construct the governing equations for the humidity field;

[0009] Step A4. Construct the adsorption / desorption isotherm equations;

[0010] Step A5. Construct the mechanical field equations;

[0011] Step A6. Provide a coupled solution method for the thermo-humidity-mechanical-chemical multi-field coupled model.

[0012] Furthermore, the specific process of constructing the hydration reaction equation in step A1 is as follows:

[0013] A1.1, Degree of water hydration α c The hydration process can be defined as follows:

[0014]

[0015] A1.2 According to Arrhenius's law, the hydration process that changes with time can be expressed by the following formula:

[0016]

[0017] In the formula, A is the hydration rate, 1 / s; c (α c ) is the chemical affinity function, 1 / s, which is a function of the degree of hydration; E ac ρ is the activation energy of hydration, J / mol; R is the universal gas constant; T is the absolute temperature, K; E is the temperature. ac The value of / R can be determined experimentally;

[0018] The chemical affinity function takes the form shown below:

[0019]

[0020] In the formula, β1, β2, and β3 are material parameters, and η c Viscosity is the viscosity produced by the micro-diffusion of free water through the formation of hydrates. The final degree of hydration of cement is expressed as follows:

[0021]

[0022] In the formula: w / c is the water-cement ratio of concrete;

[0023] A1.3 The hydration rate will gradually slow down, and may even stop as the relative humidity decreases. The effect of relative humidity on the hydration rate can be considered by the improved formula (2), as shown below:

[0024]

[0025] In the formula, To account for the effect of relative humidity on the hydration rate, 1 / s; B h (h) is the empirical hydration function, h is the relative humidity, and a is a free parameter ranging from 5.5 to 12.5;

[0026] Furthermore, the specific process of constructing the temperature field control equation in step A2 is as follows:

[0027] A2.1 When the temperature does not exceed 100℃, Fourier's law can be used to describe the heat conduction phenomenon in concrete, expressed as:

[0028]

[0029] In the formula, q is the heat flux; λ is the thermal conductivity; and T is the absolute temperature in K. For temperature gradient, i.e.

[0030] A2.2 From the enthalpy balance equation, we can obtain:

[0031]

[0032]

[0033] In the formula, ρ is the density of concrete, kg / m³. 3 C p The isobaric heat capacity of concrete is J / (kg·K). The heat flux divergence, i.e. denoted as , where is the heat generation rate of cement hydration per unit volume; and 'c' is the cement content in concrete per unit volume, in kg / m³. 3 Q ∞ Enthalpy of hydration, kJ / kg;

[0034] A2.3 Combining equations (6) to (8), the overall governing equations of the temperature field can be obtained:

[0035]

[0036] The governing equation (9) must be completed by combining appropriate initial conditions and boundary conditions. The initial conditions refer to the temperature inside the concrete at the initial moment; while the boundary conditions are the heat transfer conditions of the heat transfer boundary, which can be represented by Cauchy-type boundary conditions:

[0037]

[0038] In the formula, T(t)| Ω The initial temperature of the computational domain; T (t = 0) is the temperature value at the initial moment; n| Γ α is the normal vector of the heat transfer boundary; T T is the heat transfer coefficient at the boundary; ext Let K be the external temperature.

[0039] Furthermore, the specific process of constructing the humidity field control equation in step A3 is as follows:

[0040] A3.1. Based on Fick's law, the water mass flux J per unit time is proportional to the spatial gradient of h:

[0041]

[0042] In the formula, D h (h) is the moisture diffusion coefficient, which is a nonlinear function related to the relative humidity h;

[0043] A3.2 For isothermal conditions, a unified expression for the moisture diffusivity coefficient can be used to describe the moisture transfer during the wetting and drying processes of concrete:

[0044]

[0045] In the formula, D d1 α and H represent the water diffusion coefficient when the relative humidity h is 100% during the water diffusion process. d And n are free parameters;

[0046] The increase in internal temperature of concrete will accelerate the rate of moisture diffusion, therefore equation (12) needs to be modified:

[0047]

[0048] In the formula, D d Q is the moisture diffusivity of concrete at an internal temperature of 20°C. ac R is the activation energy for water to migrate along the adsorption layer in the capillary pores; R is the universal gas constant.

[0049] A3.3, Moisture mass balance requires that the change in water mass w per unit volume of concrete over time equals the divergence of the water mass flux J, that is:

[0050]

[0051] In the formula, the water content w is the evaporable water w e and non-evaporable water w n The sum, assuming that evaporable water is the relative humidity h and the degree of hydration α c The function, i.e., w e =w e (h,α c Non-evaporable water (w) n The following formula can be used for calculation;

[0052] w n (α c )=ξ c α c c (15)

[0053] In the formula, ξ c The mass ratio of non-evaporable water required for complete hydration;

[0054] A3.4 Combining equations (11) to (15), the governing equations of the humidity field can be obtained:

[0055]

[0056] In the formula, The rate of change of non-evaporable water over time, i.e.

[0057] The governing equations must be completed by combining appropriate initial and boundary conditions. The initial condition refers to the relative humidity inside the concrete at the initial moment; while the boundary conditions refer to the diffusion conditions of the moisture transfer boundary, which can be represented by Dirichlet-type boundary conditions.

[0058]

[0059] In the formula, h(t=0)| Ω h(t=0)| Γ These represent the initial relative humidity inside the concrete and at the moisture transfer boundary, respectively.

[0060] Furthermore, the specific process of constructing the adsorption / desorption isotherm equation in step A4 is as follows:

[0061] A4.1 Adsorption and desorption isotherms, using Norling Mjornell's semi-empirical model, can be expressed as:

[0062]

[0063] In the formula, the first term on the right-hand side represents gel water, and the second term represents capillary water; the material parameter g1 controls the shape of the isotherm, G1(α c ) and K1(α c The numbers () represent the water content in the gel pores and capillaries at 100% relative humidity, respectively, which can be calculated according to equations (19) and (20):

[0064] G1(α c )=k c α c c (19)

[0065]

[0066] In the formula, w0 is the initial moisture content of the concrete, kg / m³. 3 ;k c Material parameters for saturated gel pore water content;

[0067] A4.2 Considering the different stages of concrete moisture development, it is necessary to modify the Norling Mjornell adsorption isotherm model, as shown in equations (21) to (24):

[0068]

[0069] w s ≈0.065c(α c -α c,d ) (twenty two)

[0070]

[0071]

[0072] In the formula, w s While maintaining saturation, the amount of water required to compensate for chemical shrinkage is [kg / m]. 3 ;α c,d The critical degree of hydration is defined as the point at which the relative humidity inside the concrete begins to decrease from 100%; K1' represents the capillary water content under corrected saturation conditions; w e 'This is the corrected amount of evaporable water;

[0073] Furthermore, the specific process of constructing the mechanical field equations in step A5 is as follows:

[0074] A5.1 The constitutive relation of elastic concrete can be expressed by the following formula:

[0075]

[0076] In the formula, ε, ε e ε t ε sh These are the total strain, elastic strain, temperature strain, and humidity shrinkage strain, respectively. Here, ε is the elastic stiffness matrix; where the expression for temperature strain is ε. t =α t (T-T0), α t T is the coefficient of thermal expansion; T and T0 are the current temperature and the initial temperature, respectively.

[0077] A5.2 The development of concrete humidity is divided into two stages: a humidity saturation period and a humidity decline period. A model is established to show the relationship between internal humidity changes and shrinkage deformation during these two periods. The relationship between the internal relative humidity h and humidity shrinkage deformation ε of concrete is described. sh The relationship between them can be represented by the following model:

[0078]

[0079] In the formula, E is the elastic modulus of concrete, which is related to the degree of hydration. The calculation expression is shown in formula (27), Pa; k1 and k2 are material parameters related to the elastic modulus; V cs V0 and V0 are the volumetric strains of concrete at a certain moment and at the initial setting time due to chemical shrinkage, respectively, which can be calculated according to equation (28); ε shc S represents the shrinkage deformation at the critical moment when the concrete moisture begins to decrease; a The saturation fraction, representing the volume percentage of water in the pores of hardened cement paste, can be expressed by equation (29); vp The porosity influence coefficient can be calculated according to equation (30); ρ w Let M be the density of water; M be the molar mass of water; K be the bulk modulus of concrete, and its relationship with the elastic modulus E and Poisson's ratio μ is shown in equation (31); K s This is the bulk modulus of concrete when it contains no pores.

[0080]

[0081] V(α c )=0.2(1-z)α c (28)

[0082]

[0083] v p =1-exp{-k0·r·[A p exp(v·α c (30)

[0084]

[0085] In the formula, E(α) c,u Let E(α) be the elastic modulus at the final moment of hydration. c,u ) = 1.05E 28 E 28 α is the elastic modulus of concrete at 28 days. c,1 The degree of hydration at the initial setting point; α c,u The degree of hydration at the critical point of humidity (when humidity begins to decrease); β E The shape parameter ρ describes how the elastic modulus changes with the degree of hydration. w ρ is the density of cement. c The density of cement; k0, A p v is the porosity influence coefficient. p The material parameters are: r is the inner radius of the capillary pore; μ is the Poisson's ratio of the concrete.

[0086] Furthermore, the specific process of step A6 is as follows:

[0087] To represent and calculate the coupled thermo-humidity-mechanical-chemical process in the finite element method, the Gaussian orthogonal space integration method and the implicit algorithm of backward Euler time integration were used to solve the problem. The main variables of the hydration reaction equation, temperature field control equation, and humidity field control equation can be discretized as follows:

[0088]

[0089] The hydration reaction equation (5) can be discretized as follows:

[0090]

[0091]

[0092] According to the principle of virtual work, the temperature field control equation (9) and the humidity field control equation (16) can be written as:

[0093]

[0094]

[0095] By discretizing equation (32), equations (35) and (36) can be further written as:

[0096]

[0097]

[0098] Equations (37) and (38) can be rewritten as:

[0099]

[0100]

[0101] In the formula, C p K, Q, C h D h W n These are heat capacity, thermal conductivity, hydration heat release rate, water capacity, water diffusion coefficient, and chemically bound water matrix, respectively.

[0102] The specific calculation process is as follows: First, input the initial values, including the initial time step δt and the initial temperature T. i Initial humidity h i Initial value C of the heat capacity matrix p,i Initial value of thermal conductivity matrix K i Initial value C of the water capacity matrix h,i Initial value D of the moisture diffusion coefficient matrix h,i Next, set an appropriate temperature increment value dT. i and humidity increment value dh i By combining the boundary conditions, the temperature T at the next time step can be obtained. t+δt and humidity h t+δt The degree of hydration α at the next time step can be obtained by solving equation (34) using the Newton-Raphson iterative method. c,t+δt Then the heat capacity matrix C for the next time step can be calculated. p,t+δt Thermal conductivity matrix K t+δt Hydration heat release rate matrix Q, water capacity matrix C h,t+δtMoisture diffusion coefficient matrix D h,t+δt Chemically bound water matrix W n It then determines whether an equilibrium state has been reached; if not, it resets the temperature increment value dT. i and humidity increment value dh i If an equilibrium state is reached, the final temperature T will be output. t+δt Humidity h t+δt α degree of hydration c,t+δt Heat capacity matrix C p,t+δt Heat conduction matrix K t+δt Moisture capacity matrix C h,t+δt Moisture diffusion coefficient matrix D h,t+δt Humidity deformation ε sh,t+δt Temperature deformation ε t,t+δt .

[0103] This invention also provides a solution method for a thermo-humid-mechanical-chemical multi-field coupling model, comprising the following steps:

[0104] B1. Acquire test data and establish a finite element model based on the actual dimensions of the concrete specimens to be tested, and set the boundary conditions of each physical field according to the actual curing conditions.

[0105] B2. Determination of Basic Model Parameters: Based on the actual mix proportions of the concrete specimens, the basic parameters of the model are determined. Based on the actual mix proportions and curing conditions of the concrete specimens, the material parameters of the model are preliminarily determined. The basic parameters include the water-cement ratio, concrete density, and final degree of hydration. The material parameters include the isotherm shape parameter g1 and the saturated gel pore water content parameter k. c Chemical affinity parameters β1, β2, β3, η c ;

[0106] B3. Preliminary calculations of the multi-field coupling model;

[0107] B4. Sensitivity analysis of model material parameters;

[0108] B5. Output the final simulation results;

[0109] By adjusting step B4, the final material parameter values ​​and simulation results can be obtained.

[0110] Further, step B3 includes the following sub-steps:

[0111] B3.1 Using the finite element calculation model established in step B1 and the model parameters initially determined in step B2, perform sensitivity analysis on mesh and relative tolerance.

[0112] B3.2 Using the finite element calculation model established in step B1, the model parameters initially determined in step B2, and the mesh density and relative tolerance determined in step B3.1, perform preliminary calculations of the thermo-humidity-mechanical-chemical multi-field coupling model.

[0113] Furthermore, step B4 includes the following sub-steps:

[0114] B4.1 Compare the relative humidity simulation results obtained in step B3.2 with the relative humidity test values ​​in step B1. If the relative humidity development pattern obtained by numerical simulation matches the test values, you can directly proceed to step B5; otherwise, you need to execute step B4.2.

[0115] B4.2 Since the development pattern of the simulation results obtained in step B3.2 does not match the experimental values, it is necessary to perform a sensitivity analysis on the material parameters initially determined in step B2.2. The main parameters affecting the development pattern of the simulation results are the chemical affinity parameters β1, β2, β3, and η. c Isotherm shape parameter g1, saturated gel pore water content parameter k c If a reasonable development model simulation result is obtained through simple sensitivity analysis, proceed to step B5; otherwise, step B4.3 must be executed.

[0116] B4.3. Based on step B4.2, a comprehensive sensitivity analysis of multiple material parameters is further performed. The values ​​of each material parameter can be determined through the sensitivity analysis.

[0117] Compared with the prior art, the present invention has the following beneficial effects:

[0118] 1. This invention uses a numerical model method that couples physical fields such as hydration reaction field, temperature field, and humidity field to investigate the temperature and humidity changes of concrete during service, avoiding the need for a large number of time-consuming and labor-intensive indoor physical tests.

[0119] 2. The multi-field coupling numerical method used in this invention can consider the coupling effect between the main variables of each physical field, overcoming the shortcomings of indoor physical experiments on concrete that mostly study a single dependent variable or physical field.

[0120] 3. The multi-field coupling numerical method used in this invention can be implemented using the finite element method, and can be used to solve the multiphysics problem of concrete quickly using the Gaussian orthogonal space integration method and the backward Euler time integration implicit algorithm.

[0121] 4. The multi-field coupling numerical method used in this invention can accurately predict the temperature and humidity changes of concrete in complex environments, taking into account various factors such as water-cement ratio, curing humidity, age, and distance from the drying surface.

[0122] 5. This invention improves the adsorption isotherm equation. First, the influence of the amount of water used to compensate for chemical shrinkage during different humidity development stages of concrete is analyzed; second, the calculation formula for evaporable water at different humidity development stages is modified to compensate for the amount of water; finally, the capillary water content in the adsorption isotherm is improved. The improvement to the adsorption isotherm equation enables the multi-field coupled model to simulate the humidity saturation period of concrete.

[0123] 6. Based on the coupling of the hydration reaction field, temperature field, and humidity field, this invention introduces a temperature deformation field and a wet-dry deformation field, and establishes the relationship between temperature, relative humidity and deformation, so that the multi-field coupling model can explore the deformation and stress characteristics caused by temperature and humidity factors.

[0124] In summary, this method can simulate the deformation and stress characteristics of hydraulic concrete caused by temperature and humidity factors through numerical simulation, providing support for the safety evaluation and life prediction of hydraulic concrete structures. Attached Figure Description

[0125] Figure 1 This is a flowchart illustrating the solution steps of the improved concrete thermo-hygroscopic-mechanical-chemical multi-field coupling model involved in this invention.

[0126] Figure 2 This is a schematic diagram of the self-drying and self-shrinkage test of a concrete specimen in an embodiment of the present invention;

[0127] Figure 3 The graph shows the test data of self-drying and self-shrinkage of concrete specimens in the embodiments of the present invention.

[0128] Figure 4 This is a finite element model of a concrete specimen established for the numerical implementation of a multi-field coupling model using the finite element method in this embodiment of the invention.

[0129] Figure 5 This is a graph showing the relative tolerance sensitivity analysis of the mesh of a multi-field coupled model under initially determined model parameters in an embodiment of the present invention.

[0130] Figure 6 This is a sensitivity analysis diagram of the material parameters of each model in the embodiments of the present invention on the numerical simulation results of the self-drying test;

[0131] Figure 7 This is a joint sensitivity analysis diagram of the numerical simulation results of the self-drying test for the four main model material parameters in the embodiments of the present invention;

[0132] Figure 8 This is a numerical simulation result diagram of the self-drying test in an embodiment of the present invention;

[0133] Figure 9This is a sensitivity analysis diagram of the material parameters of each model in the embodiments of the present invention on the numerical simulation results of the self-shrinkage test;

[0134] Figure 10 This is a joint sensitivity analysis diagram of the three main model material parameters in this embodiment of the invention on the numerical simulation results of the self-shrinkage test;

[0135] Figure 11 The figure shows the numerical simulation results of the self-shrinkage test in the embodiment of the present invention;

[0136] Figure 12 The figure shows the final numerical simulation results of the self-drying and self-shrinkage tests in the embodiments of the present invention.

[0137] Figure 13 The figure shows a comparison between the simulation results of the self-drying test of concrete specimens with different water-cement ratios using the improved concrete thermo-humidity-mechanical-chemical multi-field coupling model of the present invention and the simulation results of other multi-field coupling models in the comparative example.

[0138] Figure 14 The figure shows a comparison between the simulation results of the uniaxial diffusion drying test of concrete specimens with the same water-cement ratio and different ambient humidity using the improved concrete thermo-humidity-mechanical-chemical multi-field coupling model of the present invention and the simulation results of other models. Detailed Implementation

[0139] To make the technical problems, technical solutions, and beneficial effects of the embodiments of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0140] It should be understood that the terms "length", "width", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", and "outer" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the present invention.

[0141] In the description of this invention, unless otherwise stated, the term "connection" should be interpreted broadly, and may refer to a fixed connection, a detachable connection, or an integral connection. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0142] The implementation process of the present invention will be further described in detail below with reference to specific accompanying drawings and examples.

[0143] This embodiment provides a method for constructing a multi-field coupling model of concrete, including the following steps:

[0144] A1. Hydration reaction equation:

[0145] A1.1 The hydration process mainly uses the degree of hydration α c It can be defined as follows:

[0146]

[0147] In the formula, w n The mass of bound water formed by the hydration reaction at a certain moment, in kg / m³ 3 ; The final mass of bound water under ideal conditions, kg / m³ 3 ;

[0148] A1.2 According to Arrhenius's law, the hydration process that changes with time can be expressed by the following formula:

[0149]

[0150] In the formula, A is the hydration rate, 1 / s; c E is a chemical affinity function, 1 / s, which is a function of the degree of hydration. ac ρ is the activation energy of hydration, J / mol; R is the universal gas constant, with a value of 8.31441 J / (mol·K); T is the absolute temperature, K; E ac The value of / R can be determined experimentally. For concrete, the value is generally 3000 to 8000K.

[0151] Preferably, the free energy of a thermochemical system can be divided into three parts: thermal contribution, thermochemical coupling contribution, and chemical contribution. In this model, the chemical contribution is considered a quartic function rather than a cubic function, and the chemical affinity function takes the form shown below:

[0152]

[0153] In the formula, β1, β2, and β3 are material parameters, and η c Viscosity is the viscosity produced by the micro-diffusion of free water through the formation of hydrates. This represents the final degree of hydration of cement. Since the ideal hydration conditions are rarely met in reality, its value is always less than 1 and can be calculated using the following formula:

[0154]

[0155] In the formula, w / c is the water-cement ratio of the concrete;

[0156] A1.3. It is generally known from experiments that the hydration rate gradually slows down, and may even stop as the relative humidity decreases. The effect of relative humidity on the hydration rate can be considered using a modified formula, as shown below:

[0157]

[0158] In the formula, To account for the effect of relative humidity on the hydration rate, 1 / s; B h (h) is the empirical hydration function, h is the relative humidity, and a is a free parameter ranging from 5.5 to 12.5;

[0159] A2. Temperature field governing equations:

[0160] A2.1 When the temperature does not exceed 100℃, Fourier's law can be used to describe the heat conduction phenomenon in concrete, expressed as:

[0161]

[0162] In the formula, q is the heat flux; λ is the thermal conductivity.

[0163] A2.2 From the enthalpy balance equation, we can obtain:

[0164]

[0165]

[0166] In the formula, ρ is the density of concrete, kg / m³. 3 C p This refers to the isobaric heat capacity of concrete, which is generally 840–1170 J / (kg·K). The heat flux divergence, i.e. denoted as , where is the heat generation rate of cement hydration per unit volume; and 'c' is the cement content in concrete per unit volume, in kg / m³. 3 Q ∞ It is the enthalpy of hydration, with a typical value of 400–550 kJ / kg, which can be obtained experimentally.

[0167] A2.3 Combining equations (6) to (8), the overall governing equations of the temperature field can be obtained:

[0168]

[0169] Preferably, the governing equation (9) must be completed by combining appropriate initial conditions and boundary conditions. The initial conditions refer to the temperature inside the concrete at the initial moment; while the boundary conditions are the heat transfer conditions of the heat transfer boundary, which can be represented by Cauchy-type boundary conditions:

[0170]

[0171] In the formula, T(t)| Ω The initial temperature of the computational domain; T (t = 0) is the temperature value at the initial moment; n| Γ α is the normal vector of the heat transfer boundary; T T is the heat transfer coefficient at the boundary; ext Let K be the external temperature.

[0172] A3. Humidity field governing equation:

[0173] A3.1 The internal moisture in concrete is divided into two categories: non-evaporable water, which is bound water retained in the hydration products through the chemical reaction of cement and generally does not participate in diffusion; and evaporable water, which includes capillary water, adsorbed water, etc., and exhibits moisture diffusion, but the diffusion mechanisms of different types of evaporable water are different. Based on Fick's law, the water mass flux J per unit time is proportional to the spatial gradient h:

[0174]

[0175] In the formula, D h (h) is the moisture diffusion coefficient, which is a nonlinear function related to the relative humidity h;

[0176] A3.2 The moisture transfer mechanism of concrete differs during wetting and drying processes, but from a simplification perspective, a unified expression for the moisture diffusion coefficient can be used for isothermal conditions:

[0177]

[0178] In the formula, D d1 α and H represent the water diffusion coefficient when h is 100% during the water diffusion process. d And n are free parameters;

[0179] Preferably, the increase in internal temperature of the concrete will also accelerate the rate of moisture diffusion, so equation (12) needs to be modified:

[0180]

[0181] In the formula, D d Q is the moisture diffusivity of concrete at an internal temperature of 20°C. ac Let Q be the activation energy for water migration along the adsorption layer in the capillary pores, and R be the universal gas constant, which can generally be taken as Q. ac / R = 2700K;

[0182] A3.3, Moisture mass balance requires that the change in water mass w per unit volume of concrete over time equals the divergence of the water mass flux J, that is:

[0183]

[0184] In the formula, the water content w is the evaporable water w e and non-evaporable water w n The sum of the relative humidity h and the degree of hydration α. ​​Assume that evaporable water is the sum of the relative humidity h and the degree of hydration α. c The function, i.e., w e =w e (h,α c Non-evaporable water (w) n The following formula can be used for calculation;

[0185] w n (α c )=ξ c α c c (15)

[0186] In the formula, ξ c To determine the mass ratio of non-evaporable water during complete hydration, ξ can generally be taken as... c =0.253;

[0187] A3.4 Combining equations (11) to (15), the governing equations of the humidity field can be obtained:

[0188]

[0189] In the formula, The rate of change of non-evaporable water over time, i.e.

[0190] Preferably, the governing equations must be completed by combining appropriate initial and boundary conditions. The initial condition refers to the relative humidity inside the concrete at the initial moment; while the boundary conditions refer to the diffusion conditions of the moisture transfer boundary, which can be represented by Dirichlet-type boundary conditions.

[0191]

[0192] In the formula, h(t=0)| Ω h(t=0)| Γ These represent the initial relative humidity inside the concrete and at the moisture transfer boundary, respectively.

[0193] A4. Adsorption / Desorption Isotherm Equations:

[0194] A4.1 The relationship between evaporable water and relative humidity as relative humidity increases is called the "adsorption isotherm"; conversely, the relationship between evaporable water and relative humidity as relative humidity decreases is called the "desorption isotherm". Although adsorption and desorption isotherms do not completely coincide, their differences are usually ignored. Because hydration processes are involved, Norling Mjornell's semi-empirical model can be used, which can be expressed as:

[0195]

[0196] In the formula, the first term on the right-hand side represents gel water, and the second term represents capillary water; the material parameter g1 controls the shape of the isotherm. G1(α) c ) and K1(α c The numbers () represent the water content in the gel pores and capillaries at 100% relative humidity, respectively, which can be calculated according to equations (19) and (20):

[0197] G1(α c )=k c α c c (19)

[0198]

[0199] In the formula, w0 is the initial moisture content of the concrete, kg / m³. 3 ;k c Material parameters for saturated gel pore water content;

[0200] A4.2 The development of relative humidity inside concrete is divided into two stages. The first stage is the water vapor saturation stage. As the hydration reaction proceeds, the degree of hydration increases and the water saturation decreases. However, the connection of liquid water in the concrete is not broken, resulting in the relative humidity remaining at 100%. The evaporable water in this stage is the difference between the initial water content and the chemically bound water. When hydration reaches the critical degree of hydration, the development of relative humidity enters a new stage. In order to maintain the saturation state, the evaporable water in this stage should also include the amount of water to compensate for chemical shrinkage. Therefore, considering the different stages of concrete humidity development, it is necessary to modify the adsorption isotherm model based on Norling Mjornell, as shown in equations (21) to (24):

[0201]

[0202] w s ≈0.065c(α c -α c,d ) (twenty two)

[0203]

[0204]

[0205] In the formula, w s While maintaining saturation, the amount of water required to compensate for chemical shrinkage is [kg / m]. 3 ;α c,d The critical degree of hydration is defined as the point at which the relative humidity inside the concrete begins to decrease from 100%; K1' represents the capillary water content under corrected saturation conditions; w e 'This is the corrected amount of evaporable water;

[0206] A5. Mechanical Field:

[0207] A5.1 The constitutive relation of elastic concrete can be expressed by the following formula:

[0208]

[0209] In the formula, ε, ε e ε t ε sh These are the total strain, elastic strain, temperature strain, and humidity shrinkage strain, respectively. Here, ε is the elastic stiffness matrix; where the expression for temperature strain is ε. t =α t (T-T0), α t T is the coefficient of thermal expansion; T and T0 are the current temperature and the initial temperature, respectively.

[0210] A5.2 Preferably, as numerous scholars have shown, changes in the relative humidity inside concrete cause humidity shrinkage deformation. The humidity development of concrete is divided into two stages: a humidity saturation period and a humidity decline period. Therefore, to predict the humidity shrinkage inside concrete, it is necessary to establish a model relating internal humidity changes and shrinkage deformation during these two periods. As shown by Zhang Jun et al., the relative humidity h inside concrete is related to the humidity shrinkage deformation ε. sh The relationship between them can be represented by the following model:

[0211]

[0212] In the formula, E is the elastic modulus of concrete, which is related to the degree of hydration. The calculation expression is shown in formula (27), Pa; k1 and k2 are material parameters related to the elastic modulus; V cs V0 and V0 are the volumetric strains of concrete at a certain moment and at the initial setting time due to chemical shrinkage, respectively, which can be calculated according to equation (28); ε shc S represents the shrinkage deformation when the concrete begins to decrease in moisture (critical moment); a The saturation fraction, representing the volume percentage of water in the pores of hardened cement paste, can be expressed by equation (29); vp The porosity influence coefficient can be calculated according to equation (30); ρ w Where is the density of water, 1000 kg / m³; M is the molar mass of water, 0.01802 kg / mol; K is the bulk modulus of concrete, and its relationship with the elastic modulus E and Poisson's ratio is shown in equation (31); K s This is the bulk modulus of concrete when it contains no pores, and it can generally be taken as 40.5 GPa;

[0213]

[0214] V(α c )=0.2(1-z)α c (28)

[0215]

[0216] v p =1-exp{-k0·r·[A p exp(v·α c (30)

[0217]

[0218] In the formula, E(α) c,u Let E(α) be the elastic modulus at the final moment of hydration. c,u ) = 1.05E 28 E 28 α is the elastic modulus of concrete at 28 days. c,1 The degree of hydration at the initial setting point; α c,u The degree of hydration at the critical point of humidity (when humidity begins to decrease); β E The shape parameter ρ describes how the elastic modulus changes with the degree of hydration. w ρ is the density of cement. c The density of cement; k0, A p v is the porosity influence coefficient. p The material parameters are: r is the inner radius of the capillary pore; μ is the Poisson's ratio of the concrete.

[0219] A5.3. Through statistical analysis of a large amount of experimental data, approximate calculation formulas can be obtained for the initial setting time and the degree of hydration of concrete with a water-cement ratio between 0.30 and 0.62:

[0220]

[0221] In the formula, α c,1 α c,d These represent the degree of hydration at the initial setting time and the critical setting time, respectively.

[0222] Step A6. Discretize the main variables of the hydration reaction equation, temperature field control equation, and humidity field control equation. After inputting the initial values, set an appropriate temperature increment value dT. i and humidity increment value dh i The solution is obtained by combining the boundary conditions and using the Newton-Raphson iterative method. It is then determined whether an equilibrium state has been reached. If an equilibrium state has not been reached, the temperature increment and humidity increment values ​​are reset. If an equilibrium state has been reached, the final value is output.

[0223] The specific process is as follows:

[0224] To represent and calculate the coupled thermo-humidity-mechanical-chemical process in the finite element method, the Gaussian orthogonal space integration method and the implicit algorithm of backward Euler time integration were used to solve the problem. The main variables of the hydration reaction equation, temperature field control equation, and humidity field control equation can be discretized as follows:

[0225]

[0226] The hydration reaction equation (5) can be discretized as follows:

[0227]

[0228]

[0229] According to the principle of virtual work, the temperature field control equation (9) and the humidity field control equation (16) can be written as:

[0230]

[0231]

[0232] By discretizing equation (33), equations (36) and (37) can be further written as:

[0233]

[0234]

[0235] Equations (38) and (39) can be rewritten as:

[0236]

[0237]

[0238] In the formula, C p K, Q, C h D h W nThese are heat capacity, thermal conductivity, hydration heat release rate, water capacity, water diffusion coefficient, and chemically bound water matrix, respectively.

[0239] The specific calculation process is as follows: First, input the initial values, including the initial time step δt and the initial temperature T. i Initial humidity h i Initial value C of the heat capacity matrix p,i Initial value of thermal conductivity matrix K i Initial value C of the water capacity matrix h,i Initial value D of the moisture diffusion coefficient matrix h,i Next, set an appropriate temperature increment value dT. i and humidity increment value dh i By combining the boundary conditions, the temperature T at the next time step can be obtained. t+δt and humidity h t+δt The degree of hydration α at the next time step can be obtained by solving equation (34) using the Newton-Raphson iterative method. c,t+δt Then the heat capacity matrix C for the next time step can be calculated. p,t+δt Thermal conductivity matrix K t+δt Hydration heat release rate matrix Q, water capacity matrix C h,t+δt Moisture diffusion coefficient matrix D h,t+δt Chemically bound water matrix W n It then determines whether an equilibrium state has been reached; if not, it resets the temperature increment value dT. i and humidity increment value dh i If an equilibrium state is reached, the final temperature T will be output. t+δt Humidity h t+δt α degree of hydration c,t+δt Heat capacity matrix C p,t+δt Heat conduction matrix K t+δt Moisture capacity matrix C h,t+δt Moisture diffusion coefficient matrix D h,t+δt Humidity deformation ε sh,t+δt Temperature deformation ε t,t+δt .

[0240] like Figure 1 As shown, this embodiment provides a solution method for a thermo-humidity-mechanical-chemical multi-field coupling model, including the following steps:

[0241] B1. Data Acquisition:

[0242] B1.1 In this embodiment, see Figure 2 This study selects self-drying tests on concrete specimens as the research object. Taking the self-drying test as an example, the relative humidity and drying shrinkage values ​​during the self-drying process are used as experimental data. (See attached data). Figure 3 ;

[0243] B1.2. Establish a finite element model based on the actual dimensions of the concrete specimens used in the self-drying test. See [reference needed]. Figure 4 And set the boundary conditions for each physical field according to the actual maintenance conditions;

[0244] B2. Determination of basic model parameters:

[0245] B2.1. Based on the actual mix proportions of the concrete specimens used in the self-drying test, determine the basic parameters in the model, such as the water-cement ratio w / c, the concrete density ρ, and the final degree of hydration. Degree of hydration α at initial setting time c,1 The degree of hydration α at the critical moment of humidity decrease c,d Basic parameters such as the thermal conductivity of concrete are shown in Table 1.

[0246] Table 1. Basic Parameters of the Model

[0247]

[0248] B2.2. Based on the actual mix proportions and curing conditions of the concrete specimens, the material parameters of the model are preliminarily determined, such as the adsorption isotherm parameter g1, which is generally taken as 1.2–1.8, and k. c The typical value for β is 0.2 to 0.4; the typical value for the chemical affinity parameter β1 is 1 × 10⁻⁶. 8 ~9×10 8 h -1 η c The general value is 8.0 to 10.0; the initial material parameters are shown in Table 2.

[0249] Table 2 Material Parameters for Preliminary Model Design

[0250]

[0251] B3. Preliminary calculations of the multi-field coupling model:

[0252] B3.1. Using the finite element calculation model established in step B1.2 and the initial model parameters determined in step B2, perform a sensitivity analysis of the mesh and relative tolerance. The analysis results are shown in […]. Figure 5 , Figure 5 The hydration rate and humidity change rate in (a) and (b) are the results of the 2nd and 7th days of the self-drying test, respectively. The final grid number and relative tolerance can be determined as 2400 and 0.01%, respectively.

[0253] B3.2 Using the finite element calculation model established in step B1.2 and the model parameters initially determined in step B2, as well as the mesh density and relative tolerance determined in step B3.1, perform preliminary calculations of the thermo-humidity-mechanical-chemical multi-field coupling model;

[0254] B4. Sensitivity analysis of model material parameters:

[0255] B4.1 Compare the relative humidity simulation results obtained in step B3.2 with the relative humidity test values ​​in step B1.1. If the relative humidity development pattern obtained by numerical simulation matches the test values, you can directly proceed to step B5; otherwise, you need to execute step B4.2.

[0256] B4.2 Since the development pattern of the simulation results obtained in step B3.2 does not match the experimental values, it is necessary to perform a sensitivity analysis on the material parameters initially determined in step B2.2. The main parameters affecting the development pattern of the simulation results are the chemical affinity parameters β1, β2, β3, and η. c Isotherm shape parameter g1, saturated gel pore water content material parameter k c If a reasonable development model simulation result is obtained through simple sensitivity analysis, proceed to step B5; otherwise, step B4.3 must be executed. Figure 6 This is the result of the sensitivity analysis of each material parameter to the self-drying test. From the figure, we can see β1, η... c g1 and k c The effect on the self-drying results is significant and requires further analysis.

[0257] B4.3. Based on step B4.2, a comprehensive sensitivity analysis of multiple material parameters is further performed. The values ​​of each material parameter can be determined through this sensitivity analysis. Figure 7 It can be seen that, with other parameters constant, the decrease of β1 and η c The increase in β1 will prolong the moisture saturation period of concrete, and the increase in η will lead to a greater increase in β1 and η. c The decrease of g1, the increase of k c The greater the change, the lower the final relative humidity.

[0258] Preferably, according to Figure 7 After adjusting the values ​​of various material parameters, the final self-drying test material parameter values ​​and simulation results are shown in Table 3 and 3, respectively. Figure 8 .

[0259] Table 3. Material Parameters for Self-Drying Test

[0260]

[0261] B4.4. Based on step S4.3, further sensitivity analysis of the material parameters in the self-shrinkage test is performed, see... Figure 9 .Depend on Figure 9 It can be seen that k1, k2 and β E The main factors affecting the early-stage autogenous shrinkage deformation of concrete are k1, k2, and β. E The larger the value, the greater the early self-shrinkage deformation; k0, A p V and r primarily affect the autogenous shrinkage deformation of concrete in the later stages, manifested as k0 and A. p The larger v and r are, the greater the self-shrinkage deformation in the later stage.

[0262] Preferably, in Figure 9 Based on this, sensitivity analysis of multiple material parameters is performed, such as... Figure 10 As shown, based on Figure 10 The parameters of the self-shrinking material were adjusted, and the final values ​​of the self-shrinking test material parameters and simulation results are shown in Table 4 and [Table 4 is missing in the original text]. Figure 11 .

[0263] Table 4. Material Parameters for Self-Shrinkage Test

[0264]

[0265]

[0266] B5. Output the final simulation results.

[0267] By adjusting step B4, the final material parameter values ​​and simulation results of the self-drying test can be obtained.

[0268] Based on step B4, the final numerical simulation results and final material parameter tables for the self-drying and self-shrinkage tests can be obtained, as shown below. Figure 12 See Table 5.

[0269] Table 5 Final Material Parameters of the Model

[0270]

[0271] <Comparative Example>

[0272] This comparative example verifies the simulation effect of the thermo-humid-mechanical-chemical multi-field coupling model in the above embodiments through self-drying test and uniaxial diffusion drying test of concrete, and compares it with other existing models.

[0273] The experimental test environment consisted of an AMD Ryzen 7 5800H CPU @ 3.20GHz, 16GB of RAM, and a Windows 10 operating system. The improved thermo-humid-mechanical-chemical multi-field coupling model of this invention was compared and analyzed with the multi-field coupling model proposed by Luzio, Shen, and others.

[0274] In this embodiment, the improved multi-field coupling model of this invention and the multi-field coupling model proposed by Luzio et al. are used to simultaneously simulate the self-drying test of concrete specimens with different water-cement ratios. The simulation results are compared with those of... Figure 13 As shown; however, using the improved multi-field coupling model of this invention and the multi-field coupling model proposed by Shen et al. to simultaneously simulate the uniaxial diffusion drying test of concrete specimens with the same water-cement ratio and different environmental humidity, the simulation results are, for example, Figure 14 As shown.

[0275] Depend on Figure 13 and Figure 14 The simulation results show that the improved thermo-humidity-mechanical-chemical multi-field coupled model presented in this paper has a significantly higher simulation capability for concrete self-drying tests and uniaxial diffusion drying tests than other comparative models. Based on tests with different water-cement ratios and environmental conditions, it can quickly and accurately simulate the development pattern of relative humidity in concrete self-drying and uniaxial diffusion drying tests. Therefore, the improved thermo-humidity-mechanical-chemical multi-field coupled model provided by this invention can be used to investigate the deformation and stress characteristics of hydraulic concrete caused by temperature and humidity factors, serving practical engineering applications.

[0276] The above are merely preferred embodiments of the present invention and are not intended to limit the implementation methods and scope of protection of the present invention. Those skilled in the art should recognize that any equivalent substitutions and obvious changes made based on the content of this specification should be included within the scope of protection of the present invention.

Claims

1. A method for constructing a multi-field coupled model of concrete, characterized in that, Includes the following steps: Step A1. Construct the hydration reaction equation; the specific process is as follows: A1.1 Degree of water hydration The hydration process can be represented by: （1） In the formula, The mass of bound water formed by the hydration reaction at a certain moment, in kg / m³ 3 ; The final mass of bound water under ideal conditions, kg / m³ 3 ; A1.2 According to Arrhenius's law, the hydration process that changes with time can be expressed by the following formula: （2） In the formula, The hydration rate is 1 / s; is a chemical affinity function, 1 / s, which is a function of the degree of hydration; The activation energy for hydration is J / mol. R This is the universal gas constant; T K represents absolute temperature. E ac / R The value can be determined experimentally; The chemical affinity function takes the form shown below: （3） In the formula, , , For material parameters, Viscosity is the viscosity produced by the micro-diffusion of free water through the formation of hydrates. The final degree of hydration of cement is expressed as follows: （4） In the formula, The water-cement ratio of concrete; A1.3 The hydration rate will gradually slow down, and may even stop as the relative humidity decreases. The effect of relative humidity on the hydration rate can be considered by the improved formula (2), as shown below: （5） In the formula, To account for the effect of relative humidity on the hydration rate, 1 / s; For hydration empirical functions, h Relative humidity, The free parameters are in the range of 5.5 to 12.5; Step A2. Construct the temperature field governing equations; the specific process is as follows: A2.1 When the temperature does not exceed 100°C, Fourier's law can be used to describe the heat conduction phenomenon in concrete, expressed as: (6) In the formula, For heat flux; Thermal conductivity; T K represents absolute temperature. For temperature gradient, i.e. ; A2.2 From the enthalpy balance equation, we can obtain: (7) (8) In the formula, The density of concrete, kg / m³ 3 ; The isobaric heat capacity of concrete is J / (kg·K). The heat flux divergence, i.e. ; The heat generation rate of cement hydration per unit volume; c The cement content per unit volume of concrete, in kg / m³ 3 ; Enthalpy of hydration, kJ / kg; A2.3 Combining equations (6) to (8), the overall governing equations of the temperature field can be obtained: (9) The governing equation (9) must be completed by combining appropriate initial conditions and boundary conditions. The initial conditions refer to the temperature inside the concrete at the initial moment; while the boundary conditions are the heat transfer conditions of the heat transfer boundary, which can be represented by Cauchy-type boundary conditions: (10) In the formula, The initial temperature of the computational domain; The initial temperature value; This is the normal vector of the heat transfer boundary; The heat transfer coefficient at the boundary; T ext Let K be the external temperature. Step A3. Construct the governing equations for the humidity field; the specific process is as follows: A3.

1. Based on Fick's Law, the water mass flux per unit time With relative humidity h It is proportional to the spatial gradient: (11) In the formula, The water diffusion coefficient is related to relative humidity. h Related nonlinear functions; A3.2 For isothermal conditions, a unified expression for the moisture diffusivity coefficient can be used to describe the moisture transfer during the wetting and drying processes of concrete: (12) In the formula, Relative humidity during moisture diffusion h The water diffusion coefficient at 100%; , and These are free parameters; The increase in internal temperature of concrete will accelerate the rate of moisture diffusion, therefore equation (12) needs to be modified: (13) In the formula, The water diffusion coefficient is given when the internal temperature of the concrete is 20 °C. The activation energy for water to migrate along the adsorption layer in the capillary pores; R This is the universal gas constant; A3.3, Moisture balance requirements: Water mass per unit volume of concrete The change over time equals the water mass flux The divergence, i.e.: (14) In the formula, water content That is, evaporable water and non-evaporable water The sum, assuming that evaporable water is relative humidity h and degree of hydration The function, i.e. Non-evaporable water The following formula can be used for calculation: (15) In the formula, The mass ratio of non-evaporable water required for complete hydration; A3.4 Combining equations (11) to (15), the governing equations of the humidity field can be obtained: (16) In the formula, The rate of change of non-evaporable water over time, i.e. ; The governing equations must be completed by combining appropriate initial and boundary conditions. The initial condition refers to the relative humidity inside the concrete at the initial moment; while the boundary condition refers to the diffusion conditions of the moisture transfer boundary, which can be represented by Dirichlet-type boundary conditions. (17) In the formula, , These represent the initial relative humidity inside the concrete and at the moisture transfer boundary, respectively. Step A4. Construct the adsorption / desorption isotherm equations; Step A5. Construct the mechanical field equations; Step A6. The specific process of the coupled solution method for the thermo-humidity-mechanical-chemical multi-field coupled model is as follows: To represent and calculate the thermo-humidity-mechanical-chemical coupled process in the finite element method, the Gaussian orthogonal space integration method and the implicit algorithm of backward Euler time integration were used to solve the problem. The main variables of the hydration reaction equation, temperature field control equation, and humidity field control equation can be discretized as follows: (32) The hydration reaction equation (5) can be discretized as follows: (33) (34) According to the principle of virtual work, the temperature field control equation (9) and the humidity field control equation (16) can be written as: (35) (36) By discretizing equation (32), equations (35) and (36) can be further written as: (37) (38) Equations (37) and (38) can be rewritten as: (39) (40) In the formula, These are heat capacity, thermal conductivity, hydration heat release rate, water capacity, water diffusion coefficient, and chemically bound water matrix, respectively. The specific calculation process is as follows: First, input the initial values, including the initial time step. Initial temperature Initial humidity Initial values ​​of the heat capacity matrix Initial values ​​of thermal conductivity matrix Initial values ​​of the water capacity matrix Initial values ​​of the moisture diffusion coefficient matrix Next, set an appropriate temperature increment value. and humidity increment value The temperature at the next time step can be obtained by combining the boundary conditions. and humidity The degree of hydration at the next time step can be obtained by solving equation (34) using the Newton-Raphson iterative method. Then the heat capacity matrix for the next time step can be calculated. Thermal conductivity matrix Hydration heat release rate matrix Moisture capacity matrix Moisture diffusion coefficient matrix Chemically bound water matrix It then determines whether an equilibrium state has been reached; if not, it resets the temperature increment value. and humidity increment value If an equilibrium state is reached, the final temperature will be output. ,humidity hydration degree Heat capacity matrix Heat conduction matrix Moisture capacity matrix Moisture diffusion coefficient matrix Humidity deformation Temperature deformation .

2. The method for constructing a multi-field coupled model of concrete according to claim 1, characterized in that, The specific process of constructing the adsorption / desorption isotherm equation in step A4 is as follows: A4.1 Adsorption and desorption isotherms, using Norling Mjornell's semi-empirical model, can be expressed as: (18) In the formula, the first term on the right-hand side represents gel water, and the second term represents capillary water; material parameters Controlling the shape of the isotherms, and These represent the water content in the gel pores and capillaries at 100% relative humidity, respectively, which can be calculated according to equations (19) and (20): (19) (20) In the formula, This refers to the initial moisture content of the concrete, in kg / m³. 3 ; Material parameters for saturated gel pore water content; A4.2 Considering the different stages of concrete moisture development, it is necessary to modify the Norling Mjornell adsorption isotherm model, as shown in equations (21) to (24): (21) (22) (23) (24) In the formula, While maintaining saturation, the amount of water required to compensate for chemical shrinkage is [kg / m]. 3 ; This is the critical degree of hydration. When hydration reaches this point, the relative humidity inside the concrete begins to decrease from 100%. This represents the corrected capillary water content under saturated conditions. This is the corrected amount of evaporable water.

3. The method for constructing a multi-field coupled model of concrete according to claim 1, characterized in that, The specific process of constructing the mechanical field equations in step A5 is as follows: A5.1 The constitutive relation of elastic concrete can be expressed by the following formula: (25) In the formula, , , , These are the total strain, elastic strain, temperature strain, and humidity shrinkage strain, respectively. Here is the elastic stiffness matrix; where the expression for temperature strain is: , The coefficient of thermal expansion; , These are the current temperature and the initial temperature, respectively. A5.2 The development of concrete humidity is divided into two stages: the humidity saturation stage and the humidity decline stage. A model is established to show the relationship between internal humidity changes and shrinkage deformation during these two stages. The internal relative humidity of the concrete... h Shrinkage and deformation due to humidity The relationship between them can be represented by the following model: (26) In the formula, E The elastic modulus of concrete is related to the degree of hydration. The calculation expression is shown in equation (27), Pa; , Material parameters related to the elastic modulus; , These are the volumetric strains of concrete at a certain moment and at the initial setting moment due to chemical shrinkage, respectively, which can be calculated according to formula (28); This refers to the shrinkage deformation at the critical moment when the moisture content of the concrete begins to decrease. The saturation fraction represents the volume percentage of water in the pores of hardened cement paste, which can be expressed as equation (29). The porosity influence coefficient can be calculated according to formula (30); The density of water; M The molar mass of water; K The bulk modulus of concrete is related to its elastic modulus. E The relationship between the ratio and Poisson's ratio is shown in equation (31); This is the bulk modulus of concrete when it contains no pores. (27) (28) (29) (30) (31) In the formula, The elastic modulus at the final moment of hydration can be taken as... ,in The elastic modulus of concrete at 28 days; The degree of hydration at the initial setting point; The degree of hydration is the critical point of humidity, i.e., when humidity begins to decrease. A shape parameter describing how the elastic modulus changes with the degree of hydration; This refers to the density of cement. This refers to the density of cement. , and Porosity influence coefficient Material parameters; The inner radius of the capillary pore; is the Poisson's ratio of concrete.

4. A method for solving a thermo-humid-mechanical-chemical multi-field coupled model, applied to the method for constructing a multi-field coupled concrete model according to any one of claims 1-3, characterized in that, Includes the following steps: B1. Acquire test data and establish a finite element model based on the actual dimensions of the concrete specimens to be tested, and set the boundary conditions of each physical field according to the actual curing conditions. B2. Determination of Basic Model Parameters: Based on the actual mix proportions of the concrete specimens, the basic parameters of the model are determined. Based on the actual mix proportions and curing conditions of the concrete specimens, the material parameters of the model are preliminarily determined. The basic parameters include the water-cement ratio, concrete density, and final degree of hydration; the material parameters include isotherm shape parameters. saturated gel pore water content parameters Chemical affinity parameters , , , ; B3. Preliminary calculations of the multi-field coupling model; B4. Sensitivity analysis of model material parameters; B5. Output the final simulation results; By adjusting step B4, the final material parameter values ​​and simulation results can be obtained.

5. The solution method for a thermo-humid-mechanical-chemical multi-field coupling model according to claim 4, characterized in that, Step B3 includes the following sub-steps: B3.1 Using the finite element calculation model established in step B1 and the model parameters initially determined in step B2, perform sensitivity analysis on mesh and relative tolerance. B3.2 Using the finite element calculation model established in step B1, the model parameters initially determined in step B2, and the mesh density and relative tolerance determined in step B3.1, perform preliminary calculations of the thermo-humidity-mechanical-chemical multi-field coupling model.

6. The solution method for a thermo-humid-mechanical-chemical multi-field coupling model according to claim 4, characterized in that, Step B4 includes the following sub-steps: B4.1 Compare the relative humidity simulation results obtained in step B3.2 with the relative humidity test values ​​in step B1. If the relative humidity development pattern obtained by numerical simulation matches the test values, you can directly proceed to step B5; otherwise, you need to execute step B4.

2. B4.2 Since the development pattern of the simulation results obtained in step B3.2 does not match the experimental values, a sensitivity analysis of the material parameters initially determined in step B2.2 is required. The main parameters affecting the development pattern of the simulation results include the chemical affinity parameter. , , , Isotherm shape parameters saturated gel pore water content parameters If a reasonable development model simulation result is obtained through simple sensitivity analysis, proceed to step B5; otherwise, step B4.3 must be executed. B4.

3. Based on step B4.2, a comprehensive sensitivity analysis of multiple material parameters is further performed. The values ​​of each material parameter can be determined through the sensitivity analysis.

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