Method for calculating damp-heat coupling strain and cracking index of cement-based material

Abstract

The invention discloses a method for calculating a damp-heat coupling strain and a cracking index of a cement-based material. The method comprises the following steps: firstly, deducing a damp-heat coupling control equation, and establishing a damp-heat coupling strain formula considering steel bar constraint, a concrete creep effect and a structural constraint condition, so as to obtain a calculation method of a cracking index; secondly, key parameters are measured, an engineering concrete finite element model is constructed, an initial value and boundary conditions are input, a partial differential equation is solved through an implicit difference method, and a concrete temperature and humidity coupling field is obtained; and then, through temperature and humidity changes at different time and positions, combining the thermal expansion coefficient and the moisture shrinkage coefficient, calculating actual temperature and humidity coupling strain, and comparing the actual temperature and humidity coupling strain with field monitoring data to verify that the actual temperature and humidity coupling strain is well matched with the field monitoring data. The method is suitable for a concrete structure with an obvious damp-heat coupling effect, such as a large-area long side wall, a pipe piece needing steam curing and water curing, mass concrete containing a cooling water pipe and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of cement concrete, in particular to a method for predicting the coupled thermal and moisture strain and cracking index of cement-based materials based on the maturity theory calculation. Background Art

[0002] In the practical application of concrete structures, cracks caused by non-load account for more than 80% of the total number of cracks. Among them, the strain caused by the coupled thermal and moisture effect is the main reason for non-load cracking. The interaction between the humidity and temperature fields inside the concrete material (coupled thermal and moisture) exacerbates the formation of internal stress. When the stress accumulation exceeds the tensile strength limit of the material, cracks will occur, significantly affecting the durability and service life of the concrete. Therefore, accurately describing the coupled thermal and moisture strain is crucial for crack control and cracking index prediction.

[0003] However, existing research mainly focuses on plain concrete as the research object, and usually does not fully consider the influence of steel bar restraint, creep effect, and structural restraint on the coupled thermal and moisture strain, making it difficult for the calculation results to accurately reflect the actual engineering situation. In practical engineering applications, the restraint effect of steel bars will significantly change the free expansion or contraction state of concrete, thereby affecting the evolution process of the coupled thermal and moisture strain. In addition, the creep characteristics of cement-based materials cause the strain to change slowly over time, and this long-term effect is particularly significant in high-temperature and high-humidity environments. The geometric restraint of the structure further affects the distribution of the thermal and moisture strain, which may lead to local stress concentration and exacerbate the cracking risk. Therefore, the applicability of existing calculation methods in complex structural environments still has limitations.

[0004] The accurate prediction of the coupled thermal and moisture strain first depends on establishing a reasonable coupled thermal and moisture control equation. This equation synthesizes the processes of heat conduction and moisture migration inside the concrete, and describes the evolution laws of the temperature field and humidity field. The key lies in how to determine the parameters required in the coupled thermal and moisture process, such as the moisture diffusion coefficient, thermal conductivity, etc. These parameters often have a non-linear relationship under the interaction of humidity and temperature. Therefore, based on an accurate parameter acquisition method and combined with the numerical solution of the control differential equation, it is the premise for analyzing the coupled thermal and moisture strain.

[0005] Considering the coupled thermal and moisture strain simultaneously requires accurately knowing each key parameter and solving complex partial differential equations. Therefore, in most current studies, mature concrete is mostly used to obtain key parameters (such as moisture diffusion coefficient, heat source function, etc.), and the coupled thermal and moisture strain is usually calculated by separately calculating the temperature strain and humidity strain. In practical engineering, the non-linearity and complexity of the coupled thermal and moisture effect are far more significant than the separate analysis. Therefore, this separated treatment method may lead to inaccurate stress evaluation, making it difficult to truly reflect the stress state of concrete materials in complex environments, resulting in a deviation between the calculation results and the engineering reality.

[0006] In view of the above problems, based on the maturity theory, this study proposes a new method for calculating the hygrothermal coupling strain of cement-based materials. The maturity theory can reflect the parameter growth law of concrete under different temperature and humidity conditions and consider the effects of temperature and humidity in a unified framework. This method not only makes the acquisition of key parameters in hygrothermal coupling more reasonable but also integrates the coupling effect of humidity and temperature at the initial stage of analysis, which will help to more accurately describe the deformation evolution and cracking risk of cement-based materials in complex environments. This can not only improve the engineering applicability of hygrothermal coupling strain calculation but also provide more scientific theoretical support for the prediction of the service performance of concrete structures. Summary of the Invention

[0007] Technical Problem: The object of the present invention is to address the problems of low engineering applicability, unreasonable calculation parameter values, low degree of hygrothermal coupling, difficulty in quantitative evaluation, and inability to accurately predict in the prediction equations for the hygrothermal coupling strain and cracking index of concrete, and proposes a method for calculating the hygrothermal coupling strain and cracking index of cement-based materials.

[0008] Technical Solution: A method for calculating the hygrothermal coupling strain and cracking index of cement-based materials according to the present invention includes the following steps:

[0009] Step 1: Derive the hygrothermal coupling control equation, hygrothermal coupling strain, and actual cracking index calculation equations of cement-based materials;

[0010] Step 2: Give the key parameters based on the hygrothermal coupling control equation; the key parameters include: moisture content M; D is the moisture diffusion coefficient; water consumption for hydration reaction M s ; thermal conductivity λ; specific heat capacity c p ; heat release per unit mass of cementitious material per unit time q; elastic modulus E of concrete c ; tensile strength f of concrete s ;

[0011] Step 3: Prepare test blocks according to the engineering concrete mix ratio and test and measure the values of the key parameters under standard conditions, and convert them to the values under any conditions using the maturity theory;

[0012] Step 4: Establish a finite element model according to the engineering structure size, input the hygrothermal coupling key parameters, initial values, and boundary conditions, and calculate the temperature and humidity coupling field of concrete using the hygrothermal coupling module;

[0013] Step 5: Based on the temperature and humidity coupling field and its distribution, couple the thermal expansion coefficient and shrinkage coefficient to calculate the temperature and humidity coupling strain; the temperature and humidity coupling field is the temperature and humidity characteristics at different positions and different ages;

[0014] The process of calculating the temperature-humidity coupling strain based on the temperature-humidity coupling field is to first calculate the temperature-humidity coupling field, then consider the steel bar constraint, creep effect and structural constraint, and then couple the thermal expansion coefficient and the wet deformation coefficient to obtain the temperature-humidity coupling strain;

[0015] Step 6: Based on the results of the coupled thermal and moisture strain, couple the elastic modulus of concrete and the splitting tensile strength value to predict the cracking index; the elastic modulus is measured based on the ultrasonic method, and the tensile strength is measured by the splitting method; the variation range of the cracking index is 0-1.

[0016] Step 7: Compare the monitored values and calculated values of the temperature-humidity field data and the coupled thermal and moisture strain data to verify the correctness of the calculation method.

[0017] Among them,

[0018] The coupled thermal and moisture control equation in Step 1 is:

[0019]

[0020] where M is the moisture content; D is the moisture diffusion coefficient; M s is the water consumption for hydration reaction; λ is the thermal conductivity; c p is the specific heat capacity; q is the heat release per unit mass of cementitious material per unit time; h lv is the latent heat of water evaporation; x, y, z are the coordinate positions of characteristic points in the specimen, T is the temperature; t is the age; ρ is the density; m is the amount of cementitious material.

[0021] When not considering the steel bar constraint, creep effect and structural constraint, the calculation formula for the coupled thermal and moisture strain in Step 1 is:

[0022] ε coupled (t,T,M,x,y,z) = ε T (t e ,τ) + ε M (t e ,τ) = α T ·(T(t e ) - T(τ)) + β sh ·(M(t e ) - M(τ))

[0023] where ε coupled (t,T,M,x,y,z) is the coupled thermal and moisture strain without considering constraints and creep; ε T (t e ,τ) is the temperature strain; α T is the temperature expansion coefficient; T(t e ) is the temperature at the equivalent age t e and T(τ) is the temperature at the final setting; εM (t e , τ) is the humidity strain; β sh is the wet deformation coefficient; M(t e ) is the wet content at the equivalent age t e , and M(τ) is the wet content at the final setting.

[0024] When only considering the reinforcement constraint, the calculation formula for the thermo - hygro - mechanical coupling strain in the first step is:

[0025]

[0026] Where: is the thermo - hygro - mechanical coupling strain under only considering the reinforcement constraint; η s is the reinforcement constraint coefficient; E s is the elastic modulus of the reinforcement; E c is the elastic modulus of the concrete; ρ s is the reinforcement ratio; α s is the thermal expansion coefficient of the reinforcement, taking 1.2×10 -5 / ℃; α T is the thermal expansion coefficient of the concrete; T(t e ) is the temperature at the equivalent age t e , and T(τ) is the temperature at the final setting; β sh is the wet deformation coefficient; M(t e ) is the wet content at the equivalent age t e , and M(τ) is the wet content at the final setting; ΔT is the change in temperature;

[0027] When only considering the creep effect, the calculation formula for the thermo - hygro - mechanical coupling strain in the first step is:

[0028]

[0029] Where: is the thermo - hygro - mechanical coupling strain under only considering the creep effect; is the creep coefficient; f c is the axial compressive strength of the concrete; RH is the environmental relative humidity (0 - 1); h0 is the characteristic size of the component, defined as the ratio of the cross - sectional area to the cross - sectional perimeter; α T is the thermal expansion coefficient of the concrete; T(t e ) is the temperature at the equivalent age t e , and T(τ) is the temperature at the final setting; β sh is the wet deformation coefficient; M(t e ) is the wet content at the equivalent age t e , and M(τ) is the wet content at the final setting;

[0030] When only considering the structural constraints, the calculation formula for the coupled thermo-hygroscopic strain in the first step is:

[0031]

[0032] Where: is the coupled thermo-hygroscopic effect when only considering the structural constraints; R s is the degree of structural constraint (0 - 1); L is the length of the structure; H is the height of the structure; h is the height from the ground of the considered point; α T is the thermal expansion coefficient of concrete; T(t e ) is the temperature at the equivalent age t e , and T(τ) is the temperature at the final setting time; β sh is the coefficient of wet deformation; M(t e ) is the moisture content at the equivalent age t e , and M(τ) is the moisture content at the final setting time;

[0033] When considering the reinforcement constraint, creep effect and structural constraint simultaneously, the calculation formula for the coupled thermo-hygroscopic strain in the first step is:

[0034]

[0035] Where, ε coupled,eff (t, T, M, x, y, z) is the actual coupled thermo-hygroscopic strain considering the reinforcement constraint, creep and structural constraint; η s is the reinforcement constraint coefficient, and its expression is E s is the elastic modulus of the reinforcement; E c is the elastic modulus of concrete; ρ s is the reinforcement ratio; α s is the thermal expansion coefficient of the reinforcement, taking 1.2×10 -5 / ℃; ε T (t e , τ) is the temperature strain; α T is the temperature expansion coefficient; T(t e ) is the temperature at the equivalent age t e , and T(τ) is the temperature at the final setting time; ε M (t e , τ) is the moisture strain; β sh is the coefficient of wet deformation; M(t e ) is the moisture content at the equivalent age t e , and M(τ) is the moisture content at the final setting time; ΔT is the temperature change of concrete, positive when increasing and negative when decreasing; is the creep coefficient, Where t eis the equivalent age, τ is the final setting time, representing the concrete age when creep starts, f c is the axial compressive strength of the concrete, RH is the relative environmental humidity (0 - 1), h0 is the characteristic dimension of the component, defined as the ratio of the cross-sectional area to the cross-sectional perimeter; R s is the degree of structural restraint, where L is the length of the structure, H is the height of the structure, and h is the height from the ground of the point under consideration.

[0036] When considering steel bar restraint, creep, and structural restraint simultaneously, the calculation method of the actual cracking index in Step 1 is as follows:

[0037]

[0038] where η(t, T, M, x, y, z) is the cracking index of the concrete; σ(t, T, M, x, y, z) is the internal tensile stress of the concrete, MPa; E c is the elastic modulus at any point inside the concrete, GPa; ε couple,eff (t, T, M, x, y, z) is the thermo - hygroscopic coupling effective strain at any point inside the concrete affected by temperature and humidity at time t, f s is the tensile strength of the concrete.

[0039] For the moisture content M, the testing methods include the drying method, nuclear magnetic resonance method, resistance method, and capacitance method;

[0040] When using the drying method, its calculation formula is: M = (m i - m d ) / m d , where: m i is the initial mass; m d is the mass after drying in an oven at 105°C for 24 h;

[0041] The testing method for the relationship between the moisture content M and the internal relative humidity H is obtained by acquiring the equilibrium moisture content of the test specimens at different relative humidities and is based on the Fagerlund model. Its calculation formula is M is the moisture content; M0 is the moisture content in the saturated state; RH c is the critical relative humidity; γ is a parameter related to the pore structure;

[0042] The determination methods of the moisture diffusion coefficient D include the water absorption method and the drying method;

[0043] When using the water absorption method, its specific testing process is as follows: Dry the test specimen at 105°C for 24 h and record the initial weight m1; Let the test specimen absorb water for 6 h and record the weight m2 at this time. Calculate the moisture diffusion coefficient according to the relationship between the absorbed water mass △m and time. Its expression is where D: moisture diffusion coefficient, m2 / s; Δm: mass change of the test piece, kg; S: cross-sectional area of the specimen, m 2 ; Δt: specimen interval, s; l: height of the specimen, m; ΔC: water content during the diffusion time, kg / m 3 ;

[0044] The expression of the wet diffusion coefficient D at any curing temperature, any internal temperature, any age, and any relative humidity inside the concrete is as follows:

[0045]

[0046] where R represents the gas constant, 8.314 J / (mol·K); T represents the temperature; T' is the internal temperature of the concrete; t represents the age, d; t e is the equivalent age; S is the maturity; E ad is the activation energy of water diffusion in the concrete; Δt is the age interval from 0 to t; α is the critical relative humidity, generally 0.92 for C35 concrete; M0 is the wet content in the initial state; γ is a parameter related to the pore structure;

[0047] The water consumption M s for the hydration reaction is tested by thermogravimetry, and its expression is where M smax is the maximum value of the chemically bound water per unit mass in the completely reacted cementitious material, g / g; M s (t, T) is the reaction water consumption at temperature T and time t, g / g; S is the maturity; E a is the activation energy of the cementitious material; A is the pre-exponential factor; T is the temperature; T0 is the standard reference temperature; t0 is the age at the start of the hydration reaction; R is taken as 8.314 J / (mol·K);

[0048] The thermal conductivity λ is measured by the steady-state flat plate method, and its measurement formula is and where θ is the heat flux density, W / m 2 ; d is the sample thickness, m; T1 and T2 are the temperatures on both sides of the sample, K; Q is the heat flow, W; S is the cross-sectional area of the test piece, m 2 ;

[0049] The specific heat capacity c p is tested by the calorimeter method;

[0050] Its calculation formula is where m is the mass of the concrete; T i is the initial temperature of the sample; T f is the final mixing temperature of the sample and water; m w is the mass of water; cw is the specific heat capacity of water; T w,i is the initial temperature of water;

[0051] The heat release rate q per unit mass of the cementitious material per unit time is the isothermal calorimetry method, and its determination formula is wherein, Q(t, T) is the heat release rate per unit mass of the cementitious material at age t at temperature T, Q max is the total heat release of the cementitious material per unit mass, K T is the hydration heat release rate constant, A is the pre-exponential factor, E a is the hydration activation energy, and R is the universal gas constant.

[0052] In the third step, the maturity theory is used to convert the key parameters into values under any conditions. The core of the maturity theory is that the key parameters of concrete are the same under the same degree of hydration, which is equivalent to the age under standard conditions; the calculation method of maturity is S=(t e -τ)·T0, where: S is the maturity, °C / d; t e is the equivalent age under the actual temperature history, d; τ is the final setting time of concrete, d; T0 is the reference temperature, °C; the calculation formula of the equivalent age is wherein, t e is the equivalent age; T is the average temperature; Ea is the activation energy of the cementitious material; t is the age at the time of testing; R takes 8.314 J / (mol·K), and Δt is the time of the hydration reaction.

[0053] Beneficial effects: The present invention obtains the coupled heat and moisture control equation of cement-based materials through Fick's law, the heat conduction law, the law of conservation of mass, and the law of conservation of energy. Then, based on the experimental method, the key parameters in the control equation are determined and transformed into their values under any conditions by combining the maturity theory and the equivalent age method. By establishing a finite element model, inputting key parameters, initial values, boundary conditions, etc., the implicit difference method is used to solve the partial differential equation to obtain the coupled temperature and humidity field, and then the coupled temperature and humidity strain is obtained. The present invention obtains the coupled heat and moisture control equation and key parameters based on the actual hydration process of concrete. According to the maturity theory, the simulation method is used to effectively calculate the actual coupled heat and moisture strain of concrete and compare it with the on-site monitoring data of the project. Further, the cracking index is predicted. The present invention not only makes the acquisition of key parameters in the coupled heat and moisture more reasonable, but also integrates the coupling effect of humidity and temperature at the initial stage of analysis, effectively improving the accuracy of strain prediction, and can provide a more scientific basis and guidance for crack prevention design in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is the overall calculation process of the present invention;

[0055] Figure 2 Relationship between moisture content and relative humidity of the present invention;

[0056] Figure 3 Relationship between moisture diffusion coefficient and maturity of the present invention;

[0057] Figure 4 Relationship between elastic modulus and maturity of the present invention;

[0058] Figure 5 Relationship between splitting tensile strength and maturity of the present invention;

[0059] Figure 6 Schematic diagram of the position of the monitoring point in the wall;

[0060] Figure 7 Modeling process of the finite element model of the present invention;

[0061] Figure 8 Relationship between steel bar restraint coefficient and maturity of the present invention;

[0062] Figure 9 Relationship between creep coefficient and maturity of the present invention;

[0063] Figure 10 Comparison between the coupled temperature and humidity strain calculated by the present invention and the monitoring data;

[0064] Figure 11 Cracking index calculated by the present invention at different monitoring points and different ages;

[0065] Figure 12 Temperature distribution calculated by the present invention at the Z = 1.65 m section at 2 d;

[0066] Figure 13 Moisture content distribution calculated by the present invention at the Z = 1.65 m section at 2 d;

[0067] Figure 14 Cracking index distribution calculated by the present invention at the Z = 1.65 m section at 28 d. Specific implementation mode

[0068] A method for calculating the coupled thermal and moisture strain and cracking index of cement-based materials adopted by the present invention includes the following steps:

[0069] Step 1: Derive the coupled thermal and moisture control equation of cement-based materials according to Fick's law, heat conduction law, mass conservation law, and energy conservation law;

[0070] Step 2: Obtain key parameters based on the coupled thermal and moisture control equation, and the key parameters include: M is the moisture content; D is the moisture diffusion coefficient; M s is the water consumption of the hydration reaction; λ is the thermal conductivity; cp c is the specific heat capacity; q is the heat release of per unit mass of cementitious material per unit time;

[0071] Step 3: Prepare specimens according to the engineering concrete mix ratio, test to obtain the key parameter values under standard conditions, and convert them to the values under any conditions by using the maturity theory;

[0072] Step 4: Establish a finite element model according to the engineering structure size, input the key parameters of hygrothermal coupling, as well as the initial values and boundary conditions, and calculate the temperature and humidity coupling field of concrete by using the hygrothermal coupling module;

[0073] Step 5: Based on the temperature and humidity coupling field and its distribution, couple the thermal expansion coefficient and the shrinkage coefficient, and calculate the temperature and humidity coupling strain;

[0074] Step 6: Based on the results of hygrothermal coupling strain, couple the elastic modulus and the splitting tensile strength value of concrete to predict the cracking index;

[0075] Step 7: Compare the monitored values and calculated values of the temperature and humidity field data and the hygrothermal coupling strain data to verify the correctness of the calculation method.

[0076] Preferably, the hygrothermal coupling control equation in Step 1 is:

[0077]

[0078] The meanings of each parameter are as follows: M is the moisture content; D is the moisture diffusion coefficient; M s is the water consumed by the hydration reaction; λ is the thermal conductivity; ρ is the density; c p is the specific heat capacity; T is the temperature; t is the age; m is the amount of cementitious material per unit volume of concrete; q is the heat release of per unit mass of cementitious material per unit time; h lv is the latent heat of evaporation; x, y, and z are the positions of the characteristic points in the specimen.

[0079] Preferably, when not considering the steel bar constraint, creep effect, and structural constraint in Step 1, the hygrothermal coupling strain calculation formula is:

[0080] ε coupled (t, T, M, x, y, z) = ε T (t e , τ) + ε M (t e , τ) = α T ·(T(t e ) - T(τ)) + β sh ·(M(t e ) - M(τ))

[0081] where ε coupled(t, T, M, x, y, z) is the coupled thermo - hygro - mechanical strain without considering constraints and creep; ε T (t e , τ) is the thermal strain; α T is the coefficient of thermal expansion; T(t e ) is the temperature at equivalent age t e , T(τ) is the temperature at the end of setting; ε M (t e , τ) is the moisture strain; β sh is the coefficient of moisture deformation; M(t e ) is the moisture content at equivalent age t e , M(τ) is the moisture content at the end of setting;

[0082] When only considering the steel bar constraint in the first step, the calculation formula for the coupled thermo - hygro - mechanical strain is:

[0083]

[0084] Where: is the coupled thermo - hygro - mechanical strain under only considering the steel bar constraint; η s is the steel bar constraint coefficient; E s is the elastic modulus of the steel bar; E c is the elastic modulus of the concrete; ρ s is the reinforcement ratio; α s is the coefficient of thermal expansion of the steel bar, taking 1.2×10 -5 / ℃; α T is the coefficient of thermal expansion of the concrete; T(t e ) is the temperature at equivalent age t e , T(τ) is the temperature at the end of setting; β sh is the coefficient of moisture deformation; M(t e ) is the moisture content at equivalent age t e , M(τ) is the moisture content at the end of setting;

[0085] When only considering the creep effect in the first step, the calculation formula for the coupled thermo - hygro - mechanical strain is:

[0086]

[0087] Where: is the coupled thermo - hygro - mechanical strain under only considering the creep effect; is the creep coefficient; f c is the axial compressive strength of the concrete; RH is the relative environmental humidity (0 - 1); h0 is the characteristic size of the component, defined as the ratio of the cross - sectional area to the cross - sectional perimeter; α T is the coefficient of thermal expansion of the concrete; T(t e ) is the temperature at equivalent age t eThe temperature at time t, T(τ) is the temperature at final setting; β sh is the coefficient of wet deformation; M(t e ) is the equivalent age t e when the wet content, M(τ) is the wet content at final setting;

[0088] When only considering structural constraints in the first step, the calculation formula for the coupled thermal and moisture strain is:

[0089]

[0090] Where: is the coupled thermal and moisture effect when only considering structural constraints; R s is the degree of structural constraint (0 - 1); L is the length of the structure; H is the height of the structure; h is the height from the ground of the point considered; α T is the thermal expansion coefficient of concrete; T(t e ) is the equivalent age t e when the temperature, T(τ) is the temperature at final setting; β sh is the coefficient of wet deformation; M(t e ) is the equivalent age t e when the wet content, M(τ) is the wet content at final setting;

[0091] When considering steel bar constraint, creep effect and structural constraint simultaneously in the first step, the calculation formula for the coupled thermal and moisture strain is:

[0092]

[0093] Where, ε coupled,eff (t, T, M, x, y, z) is the actual temperature and humidity coupled strain considering steel bar constraint, creep and structural constraint; η s is the steel bar constraint coefficient, and its expression is E s is the elastic modulus of the steel bar; E c is the elastic modulus of concrete; ρ s is the reinforcement ratio; α s is the thermal expansion coefficient of the steel bar, taking 1.2×10 -5 / ℃; ε T (t e ,τ) is the temperature strain; α T is the temperature expansion coefficient; T(t e ) is the equivalent age t e when the temperature, T(τ) is the temperature at final setting; ε M (t e ,τ) is the humidity strain; β sh is the coefficient of wet deformation; M(t e ) is the equivalent age t eThe moisture content at time τ, M(τ) is the moisture content at final setting; ΔT is the temperature change of the concrete, positive when increasing and negative when decreasing; is the creep coefficient, where t e is the equivalent age, τ is the final setting time, representing the concrete age when creep starts, f c is the axial compressive strength of the concrete, RH is the ambient relative humidity (0 - 1), h0 is the characteristic dimension of the member, defined as the ratio of the cross-sectional area to the cross-sectional perimeter; R s is the degree of structural restraint, where L is the length of the structure, H is the height of the structure, and h is the height from the ground of the point considered.

[0094] Preferably, the calculation method of the cracking index when simultaneously considering steel bar restraint, creep, and structural restraint in step one is:

[0095]

[0096] where η(t, T, M, x, y, z) is the cracking index of the concrete; σ(t, T, M, x, y, z) is the internal tensile stress of the concrete, MPa; E c is the elastic modulus at any point inside the concrete, GPa; ε couple,eff (t, T, M, x, y, z) is the hygrothermal coupling effective strain at any point inside the concrete affected by temperature and humidity at time t.

[0097] Preferably, the test method for the key parameter moisture content M in step three is the drying method, and its calculation formula is: M = (m i - m d ) / m d , where: m i is the initial mass; m d is the mass after drying in an oven at 105°C for 24 h;

[0098] The test method for the relationship between the key parameter moisture content M and the internal relative humidity H in step three is obtained by acquiring the equilibrium moisture content of the test block at different relative humidities and based on the Fagerlund model, and its calculation formula is M is the moisture content; M st is the moisture content in the saturated state; RH c is the critical relative humidity; γ is a parameter related to the pore structure;

[0099] The determination method of the key parameter wet diffusion coefficient D in Step 3 under specific conditions is the water absorption method, and its specific test process is as follows: Dry the test piece at 105 °C for 24 h and record the initial weight m1; Let the test piece absorb water for 6 h and record the weight m2 at this time. According to the relationship between the water absorption mass △m and time, calculate the wet diffusion coefficient, and its expression is where D: wet diffusion coefficient, m 2 / s; △m: mass change of the test piece, kg; S: cross-sectional area of the specimen, m 2 ; △t: test piece interval, s; l: height of the specimen, m; △C: water content during the diffusion time, kg / m 3 ;

[0100] The measurement of the key parameter thermal conductivity λ in Step 3 adopts the flat plate steady state method, and its measurement formula is and where θ is the heat flux density, W / m 2 ; d is the sample thickness, m; T1 and T2 are the temperatures on both sides of the sample, K; Q is the heat flow, W; S is the cross-sectional area of the test piece, m 2 ;

[0101] The test method for the key parameter specific heat capacity c p in Step 3 is the calorimeter method, and its calculation formula is where m is the mass of concrete; T i is the initial temperature of the sample; T f is the final mixing temperature of the sample and water; m w is the mass of water; c w is the specific heat capacity of water; T w,i is the initial temperature of water;

[0102] The key parameter heat release rate q of unit mass of cementitious material per unit time in Step 3 is the isothermal calorimetry method, and its determination formula is where, Q(t, T) is the heat release rate per unit mass of cementitious material at age t at temperature T, Q max is the total heat release per unit mass of cementitious material, K T is the hydration heat release rate constant, A is the pre-exponential factor, E a is the hydration activation energy, R is the universal gas constant;

[0103] The expression of the wet diffusion coefficient D at any curing temperature, any internal temperature, any age, and any relative humidity inside the concrete for the key parameter wet diffusion coefficient D in Step 3 is:

[0104]

[0105] where, E aRepresents the reaction activation energy of the hydration of the cementitious material; R represents the gas constant, 8.314 J / (mol·K); T represents the temperature; T' is the internal temperature of the concrete; t represents the age, d; t e is the equivalent age; S is the maturity; E ad is the water diffusion activation energy of the concrete; Δt is the age interval from 0 to t; α is the critical relative humidity, generally 0.92 for C35 concrete; M0 is the wet content in the initial state; γ is a parameter related to the pore structure. Among them, E a represents the reaction activation energy of the hydration of the cementitious material, kJ / mol;

[0106] The key parameter of step three, the water consumption of the hydration reaction M s The test method is thermogravimetry, and its expression is where M smax is the maximum value of the chemically bound water per unit mass in the completely reacted cementitious material, g / g; M s (t, T) is the water consumption of the reaction at temperature T and time t, g / g; S is the maturity; E a is the activation energy of the cementitious material; A is the pre-exponential factor; T is the temperature; T0 is the standard reference temperature; t0 is the age at the start of the hydration reaction; R takes 8.314 J / (mol·K);

[0107] Preferably, in step three, the maturity theory is used to convert the key parameters into values under any conditions. The core of the maturity theory is that the key parameters of concrete under the same degree of hydration are consistent and can be equivalent to the age under standard conditions. The calculation method of maturity is S = (t e - τ)·T0, where: S is the maturity, °C / d; t e is the equivalent age under the actual temperature history, d; τ is the final setting time of the concrete, d; T0 is the reference temperature, °C. The calculation formula for the equivalent age is where t e is the equivalent age; T is the average temperature; Ea is the activation energy of the cementitious material; t is the age at the time of testing; R takes 8.314 J / (mol·K), and Δt is the time of the hydration reaction;

[0108] Preferably, the methods for establishing the finite element model of the concrete described in step four include external import modeling, parametric modeling, equation-based geometric modeling, and multi-level geometric modeling; in this paper, the parametric modeling method is used;

[0109] The solution method for the coupled heat and moisture control equation described in step four is the implicit difference method, and its steps include time and space discretization, forming a discrete algebraic equation system, solving the algebraic equation system, setting boundary conditions and initial conditions, and iterative solution.

[0110] Preferably, the temperature and humidity coupling field in step five is the temperature and humidity characteristics at different positions and different ages.

[0111] The process of calculating the temperature and humidity coupling strain based on the temperature and humidity coupling field in step five is to first calculate the temperature and humidity coupling field, then consider the reinforcement constraint, creep effect and structural constraint, and then couple the thermal expansion coefficient and the wet deformation coefficient to obtain the temperature and humidity coupling strain.

[0112] Preferably, the elastic modulus in step six is measured based on the ultrasonic method, and the tensile strength is measured by the splitting method; the change range of the cracking index in step seven is 0-1.

[0113] Preferably, the monitoring method in step seven is remote coupling monitoring, and the specific steps include: embedding temperature and strain sensors and humidity sensors, connecting the sensors to a data acquisition box, keeping the acquisition box powered on and networked, and collecting data in the cloud.

[0114] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0115] As Figure 1 shown, a method for calculating the hygrothermal coupling strain and cracking index of cement-based materials includes the following steps:

[0116] Step 001: Prepare concrete specimens according to the concrete mix ratio of the actual project and place them in an environment with a temperature of 25°C and a relative humidity of 0.95 for 1 day of curing and then demold. Select a certain brand of Portland cement, and according to the provisions of "Portland Cement" GB175, its composition is shown in Table 1.

[0117] Table 1 Chemical composition of cement (%)

[0118]

[0119] Table 2 Mix ratio kg / m 3

[0120]

[0121] Make samples of the above Portland cement according to the mix ratio in Table 2.

[0122] Step 002: According to the hygrothermal coupling control equation, use the method described above to measure each key parameter, which are respectively: the relationship between the moisture content and the relative humidity ( Figure 2 ), the relationship between the moisture diffusion coefficient and the maturity ( Figure 3 ), the measurement of the key parameters of the heat source function (Table 3), the relationship between the elastic modulus and the maturity ( Figure 4 ), the relationship between the splitting tensile strength and the maturity ( Figure 5 ), and the measurement results of other parameters are shown in Table 4.

[0123] Table 3

[0124]

[0125] Table 4

[0126]

[0127] Step 003: Use an underground engineering wall panel as the research object. The main information of the wall panel is shown in Table 5, and the location information of the research points is shown in Table 6. The schematic diagram of the positions of each point in the wall is shown in Figure 6 .

[0128] Table 5

[0129]

[0130] Table 6

[0131]

[0132] Step 004: According to the engineering structure dimensions, the modeling process of the established finite element model is shown in Figure 7 .

[0133] Step 005: Calculate the relationship between the steel bar restraint coefficient and the maturity according to the formula, as shown in Figure 8 .

[0134] Step 006: Calculate the relationship between the creep coefficient and the maturity according to the formula, as shown in Figure 9 .

[0135] Step 007: Calculate the structural restraint coefficients at different positions according to the formula, as shown in Table 7.

[0136] Table 7

[0137]

[0138]

[0139] Step 008: Assign the above parameters to the finite element model, consider the strong coupling between heat and humidity, calculate the temperature and humidity fields and the thermo-hydro-mechanical coupling strains, and compare them with the monitoring data, as shown in Figure 10 .

[0140] Step 009: Couple the elastic modulus and the splitting tensile strength with the thermo-hydro-mechanical coupling strain data to obtain the prediction results of the cracking index, as shown in Figure 11 .

[0141] Step 010: Further, the temperature distribution at the Z = 1.65 m section at 2 d of the wall calculated by the present invention can be calculated, as shown in Figure 12 ; the moisture content distribution at the Z = 1.65 m section at 2 d, as shown inFigure 13 ; The cracking index distribution at the Z = 1.65 m section after 28 days calculated by the present invention is shown in Figure 14 .

[0142] In summary, the present invention discloses a method for calculating the hygrothermal coupling strain and predicting the cracking index of cement-based materials based on the maturity theory. The method includes: deriving the hygrothermal coupling control equation, giving the hygrothermal coupling strain formula considering steel bar restraint, creep effect and structural restraint conditions, and then obtaining the cracking index calculation method; measuring the key parameters for predicting the hygrothermal coupling strain and cracking index; constructing a finite element model of concrete for engineering structures; inputting key parameters, initial values and boundary conditions, etc., and using the implicit difference method to solve the partial differential equation to obtain the temperature and humidity coupling field of concrete; using the differences between the temperature and humidity of concrete at different times and positions and the initial temperature and humidity, coupling the thermal expansion coefficient and the wet shrinkage coefficient, calculating the temperature and humidity coupling strain under actual conditions, and comparing with the on-site monitoring results. Further, coupling the temperature and humidity coupling strain under actual conditions with the elastic modulus and the tensile strength, the cracking index is predicted. The present invention obtains the hygrothermal coupling control equation and key parameters based on the actual hydration process of concrete, and effectively calculates the actual hygrothermal coupling strain of concrete and predicts the cracking index by using a simulation method according to the maturity theory.

[0143] It should be understood that the application of the present invention is not limited to the above examples. For those of ordinary skill in the art, improvements or transformations can be made according to the above description, and all such improvements and transformations shall fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for calculating the hygrothermal coupling strain and cracking index of cement-based materials, characterized in that: The following steps are involved: Step 1: Derive the moisture-heat coupling control equation of cement-based materials, the moisture-heat coupling strain and the actual cracking index calculation equation; Step 2: Based on the wet-heat coupling control equation, key parameters are given; the key parameters include: moisture content M; D is the moisture diffusion coefficient; water consumption M for hydration reaction s ; Thermal conductivity λ; Specific heat c p ; The heat released per unit mass of cementitious material per unit time q; The elastic modulus of concrete E c ; tensile strength of concrete f s ; Step 3: Prepare test blocks according to the engineering concrete mix ratio and test the key parameter values ​​under standard conditions, and use maturity theory to convert them into values ​​under any conditions; Step 4: Establish a finite element model according to the dimensions of the engineering structure, input the key parameters of moisture-heat coupling, initial values ​​and boundary conditions, and use the moisture-heat coupling module to calculate the temperature and humidity coupling field of the concrete; Step 5: Based on the temperature and humidity coupling field and its distribution, the thermal expansion coefficient and the contraction coefficient are coupled to calculate the temperature and humidity coupling strain; the temperature and humidity coupling field is the temperature and humidity characteristics of different positions and different ages; The process of calculating the temperature-humidity coupling strain based on the temperature-humidity coupling field is to first calculate the temperature-humidity coupling field, then consider the steel constraint, creep effect and structural constraint, and then couple the thermal expansion coefficient and the moisture deformation coefficient to obtain the temperature-humidity coupling strain; Step 6: Based on the results of the hygrothermal coupling strain, the concrete elastic modulus and splitting tensile strength are coupled to predict the cracking index; the elastic modulus is measured based on the ultrasonic method, and the tensile strength is measured by the splitting method; the cracking index varies in the range of 0-1; Step 7: Compare the monitored values ​​and calculated values ​​of the temperature and humidity field data and the hygrothermal coupling strain data to verify the correctness of the calculation method.

2. The method for calculating the hygrothermal coupling strain and cracking index of cement-based materials according to claim 1, characterized in that: The heat-moisture coupling control equation of step 1 is: Where M is the moisture content; D is the moisture diffusion coefficient; M s is the water consumption of hydration reaction; λ is the thermal conductivity; c p is the specific heat capacity; q is the heat released per unit mass of cementitious material per unit time; h lv is the latent heat of water evaporation; x, y, z are the coordinates of the characteristic points in the test block, T is the temperature; t is the age; ρ is the density; m is the amount of cementitious material used.

3. The method for calculating the hygrothermal coupling strain and cracking index prediction of cement-based materials based on maturity theory according to claim 2 is characterized in that: When the steel bar constraint, creep effect and structural constraint are not considered, the calculation formula of the moisture-heat coupling strain in step 1 is: e coupled (t,T,M,x,y,z)=ε T (t e ,t)+e M (t e ,τ)=a T ·(T(t e )-T(τ))+β sh ·(M(t e )-M(τ)) where ε coupled (t, T, M, x, y, z) is the hygrothermal coupling strain without considering constraint and creep; ε T (t e ,τ) is the temperature strain; α T is the temperature expansion coefficient; T(t e ) is the equivalent age t e The temperature at the time of final setting is T(τ), and ε M (t e ,τ) is the humidity strain; β sh is the wet deformation coefficient; M(t e ) is the equivalent age t e M(τ) is the moisture content at final setting.

4. The method for calculating the moisture-heat coupling strain and cracking index prediction of cement-based materials based on maturity theory according to claim 2, characterized in that: When only the steel bar constraint is considered, the calculation formula of the moisture-heat coupling strain in step 1 is: in: is the hygrothermal coupling strain under the reinforcement constraint only; η s is the reinforcement constraint coefficient; E s is the elastic modulus of the steel bar; E c is the elastic modulus of concrete; ρ s is the reinforcement ratio; α s is the thermal expansion coefficient of the steel bar, which is 1.2×10 -5 / ℃;α T is the thermal expansion coefficient of concrete; T(t e ) is the equivalent age t e The temperature at the time of final setting is T(τ), β sh is the wet deformation coefficient; M(t e ) is the equivalent age t e The moisture content at the time of final setting is M(τ), and ΔT is the change in temperature.

5. The method for calculating the moisture-heat coupling strain and cracking index prediction of cement-based materials based on maturity theory according to claim 2, characterized in that: When only the creep effect is considered, the calculation formula for the moisture-heat coupling strain in step 1 is: in: Only the hygrothermal coupling strain under creep effect is considered; is the creep coefficient; f c is the axial compressive strength of concrete; RH is the relative humidity of the environment (0-1); h0 is the characteristic size of the component, defined as the ratio of the cross-sectional area to the cross-sectional perimeter; α T is the thermal expansion coefficient of concrete; T(t e ) is the equivalent age t e The temperature at the time of final setting is T(τ), β sh is the wet deformation coefficient; M(t e ) is the equivalent age t e M(τ) is the moisture content at final setting.

6. The method for calculating the moisture-heat coupling strain and cracking index prediction of cement-based materials based on maturity theory according to claim 2, characterized in that: When only the structural constraints are considered, the calculation formula for the moisture-heat coupling strain in step 1 is: in: is the moist-thermal coupling effect when only structural constraints are considered; R s is the degree of structural constraint (0-1); L is the length of the structure; H is the height of the structure; h is the height of the considered point from the ground; α T is the thermal expansion coefficient of concrete; T(t e ) is the equivalent age t e The temperature at the time of final setting is T(τ), β sh is the wet deformation coefficient; M(t e ) is the equivalent age t e M(τ) is the moisture content at final setting.

7. The method for calculating the hygrothermal coupling strain and cracking index prediction of cement-based materials based on maturity theory according to claim 2, characterized in that: When considering reinforcement constraint, creep effect and structural constraint at the same time, the calculation formula of the moisture-heat coupling strain in step 1 is: Among them, ε coupled,eff (t, T, M, x, y, z) is the actual temperature-humidity coupling strain considering reinforcement constraint, creep and structural constraint; η s is the reinforcement constraint coefficient, and its expression is E s is the elastic modulus of the steel bar; E c is the elastic modulus of concrete; ρ s is the reinforcement ratio; α s is the thermal expansion coefficient of the steel bar, which is 1.2×10 -5 / ℃;ε T (t e ,τ) is the temperature strain; α T is the temperature expansion coefficient; T(t e ) is the equivalent age t e The temperature at the time of final setting is T(τ), and ε M (t e ,τ) is the humidity strain; β sh is the wet deformation coefficient; M(t e ) is the equivalent age t e Moisture content at the time of setting, M(τ) is the moisture content at the time of final setting; ΔT is the temperature change of concrete, which is positive when it increases and negative when it decreases; is the creep coefficient, where t e is the equivalent age, τ is the final setting time, representing the age of concrete when creep begins, f c is the axial compressive strength of concrete, RH is the relative humidity of the environment (0-1), h0 is the characteristic size of the component, defined as the ratio of the cross-sectional area to the cross-sectional perimeter; R s is the degree of structural constraint, Where L is the length of the structure, H is the height of the structure, and h is the height of the considered point from the ground.

8. The method for calculating the hygrothermal coupling strain and cracking index of cement-based materials according to claim 2, characterized in that: The calculation method of the actual cracking index in step 1 when considering reinforcement constraint, creep and structural constraint at the same time is: Where, η(t,T,M,x,y,z) is the cracking index of concrete; σ(t,T,M,x,y,z) is the tensile stress inside concrete, MPa; E c is the elastic modulus of any point inside the concrete, GPa; ε couple,eff (t,T,M,x,y,z) is the effective strain of the thermal coupling at any point in the concrete affected by temperature and humidity at time t, f s is the tensile strength of concrete.

9. The method for calculating the hygrothermal coupling strain and cracking index of cement-based materials according to claim 2, characterized in that: The moisture content M can be tested by drying method, nuclear magnetic resonance method, resistance method and capacitance method; When the drying method is used, the calculation formula is: M = (m i -m d ) / m d , where: m i is the initial mass; m d It is the mass after drying in an oven at 105℃ for 24h; The test method for the relationship between the moisture content M and the internal relative humidity H is to obtain the equilibrium moisture content of the test block at different relative humidity, based on the Fagerlund model, and the calculation formula is: M is the moisture content; M0 is the moisture content under saturation; RH c is the critical relative humidity; γ is a parameter related to the pore structure; The methods for determining the wet diffusion coefficient D include a water absorption method and a drying method; When the water absorption method is used, the specific test process is as follows: dry the specimen at 105°C for 24 hours and record the initial weight m1; allow the specimen to absorb water for 6 hours and record the weight m2 at this time. According to the relationship between the water absorption mass △m and time, calculate the wet diffusion coefficient, which is expressed as follows: Where D: wet diffusion coefficient, m 2 / s; △m: mass change of the specimen, kg; S: cross-sectional area of ​​the specimen, m 2 ; △t: specimen interval, s; l: specimen height, m; △C: water content during diffusion time, kg / m 3 ; The expression of the moisture diffusion coefficient D at any curing temperature, any internal temperature, any age, and any relative humidity inside the concrete is: Where R is the gas constant, 8.314 J / (mol·K); T is the temperature; T' is the internal temperature of the concrete; t is the age, d; t e is the equivalent age; S is the maturity; E ad is the activation energy of water diffusion in concrete; △t is the age interval from 0 to t; α is the critical relative humidity, which is generally 0.92 for C35 concrete; M0 is the moisture content in the initial state; γ is a parameter related to the pore structure; The hydration reaction consumes water M s The test method is thermogravimetry, and its expression is Among them, M smax M is the maximum value of chemically bound water per unit mass in fully reacted cement-based materials, g / g; s (t,T) is the water consumption of the reaction at temperature T and time t, g / g; S is the maturity; E a is the activation energy of the cementitious material; A is the pre-exponential factor; T is the temperature; T0 is the standard reference temperature; t0 is the age at the beginning of the hydration reaction; R is 8.314 J / (mol·K); The thermal conductivity λ is tested by a plate steady-state method, and its measurement formula is: and Where θ is the heat flux, W / m 2 ; d is the sample thickness, m; T1 and T2 are the temperatures on both sides of the sample, K; Q is the heat flow, W; S is the cross-sectional area of ​​the specimen, m 2 ; The specific heat capacity c p The test method is the calorimeter method; The calculation formula is: Where m is the mass of concrete; T i is the initial temperature of the sample; T f is the final mixing temperature of the sample and water; m w is the quality of water; c w is the specific heat capacity of water; T w,i is the initial water temperature; The heat release q of the unit mass of the cementitious material per unit time is determined by isothermal calorimetry, and the formula is: in, Q(t, T) is the heat released per unit mass of the cementitious material at temperature T after age t. max is the total heat release per unit mass of the cementitious material, K T is the hydration exothermic rate constant, A is the pre-exponential factor, E a is the hydration activation energy, and R is the universal gas constant.

10. The method for calculating the hygrothermal coupling strain and cracking index of cement-based materials according to claim 1, characterized in that: In step 3, the maturity theory is used to convert the key parameters into values ​​under any conditions. The core of the maturity theory is that the key parameters of concrete under the same hydration degree are consistent, which is equivalent to the age under standard conditions. The calculation method of maturity is S = (t e -τ)·T0, where: S is maturity, ℃ / d; t e is the equivalent age under the actual temperature history, d; τ is the final setting time of concrete, d; T0 is the reference temperature, ℃; the calculation formula of the equivalent age is Among them, t e is the equivalent age; T is the average temperature; Ea is the activation energy of the cementitious material; t is the age at the time of the test; R is 8.314 J / (mol·K), and Δt is the time of the hydration reaction.

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