Prediction method for early cracking index and spatial and temporal distribution of mass concrete based on maturity theory

Abstract

The invention discloses a maturity theory-based mass concrete early cracking index and spatial and temporal distribution prediction method. According to the method, the cracking possibility of the mass concrete is evaluated by uniformly adopting the cracking index and the spatial and temporal distribution thereof. In order to improve the calculation precision of the cracking index and the spatial and temporal distribution of the mass concrete, the reaction heat of a cementing material at 20 DEG C, 40 DEG C, 60 DEG C and 80 DEG C, and the tensile strength, the elastic modulus and the porosity of the concrete are tested, and the tensile strength and the elastic modulus under high-temperature damage are corrected through a porosity test result; a temperature field, a temperature strain field, a shrinkage strain field, an elastic modulus field, a stress field and a tensile strength field of the mass concrete are calculated based on a maturity theory and spatial and temporal distribution, and meanwhile, a relaxation coefficient is introduced to consider the influence of creep on stress, so that the accuracy of predicting the cracking index and the spatial and temporal distribution of the mass concrete is improved.

Description

Technical Field

[0001] The invention relates to a method for calculating a mass concrete cracking index and its temporal and spatial distribution, and belongs to the technical field of building structure analysis and calculation. Background Art

[0002] With the increasing investment in large-scale infrastructure such as water conservancy, construction and transportation in my country, the application of mass concrete is becoming more and more common. However, in the early stage, concrete generates a large amount of hydration heat due to the hydration reaction, resulting in drastic changes in internal temperature. This temperature change easily causes temperature shrinkage deformation, which leads to cracking. Cracks not only affect the appearance of the building, but also reduce the bearing capacity of structural components, and may cause leakage, steel corrosion, accelerated concrete carbonization and reduced strength. In severe cases, it may even endanger the normal service life of the building. Therefore, the calculation of the cracking index and its temporal and spatial distribution in the early stage is of great significance in the design and construction of mass concrete structures.

[0003] The most representative volume deformations in large-volume concrete structures include: (1) temperature deformation caused by heat release from the hydration reaction of cementitious materials; (2) shrinkage deformation caused by water consumption due to the hydration reaction of cementitious materials. At present, the heat source function used by domestic and foreign scholars in numerical simulations of temperature cracking is mainly based on the reaction heat released from the adiabatic temperature rise test, which cannot truly reflect the actual heat release of concrete. In addition, most previous studies only involve temperature field calculations, and the calculations of parameters such as cracking driving force, tensile strength, and elastic modulus do not involve the concept of space. In addition, the temperature evolution history of different points in large-volume concrete is different, which makes the hydration degree of concrete at different locations at the same time different. Therefore, the maturity theory must be used to calculate the performance development of various parts of concrete space. At present, "cracking risk" is usually used to evaluate whether large-volume concrete is cracked, but in fact, the cracking risk is the probability density of several cracking indices. Therefore, the present invention uniformly uses "cracking index" and its spatiotemporal distribution to evaluate the cracking possibility of large-volume concrete. In order to improve the calculation accuracy of the cracking index of large-volume concrete and its spatiotemporal distribution, the present invention tests the reaction heat of cementitious materials at 20°C, 40°C, 60°C and 80°C, and the tensile strength, elastic modulus and porosity of concrete, corrects the tensile strength and elastic modulus under high-temperature damage by the porosity test results, and calculates the temperature field, temperature strain field, shrinkage strain field, elastic modulus field, stress field and tensile strength field of large-volume concrete based on maturity theory and spatiotemporal distribution, and introduces a relaxation coefficient to consider the influence of creep on stress, thereby improving the accuracy of the prediction of the cracking index of large-volume concrete and its spatiotemporal distribution. Summary of the invention

[0004] The technical problem to be solved by the present invention is that, in view of the fact that the current calculation of the cracking index of large-volume concrete and its temporal and spatial distribution cannot simultaneously consider the influence of time variation, temperature variation and different spatial positions, thereby causing different heat release of hydration reaction, mechanical properties and shrinkage deformation, a method for predicting the early cracking index of large-volume concrete and its temporal and spatial distribution based on maturity theory is provided, and the results are more accurate and reliable.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a method for predicting the early cracking index of mass concrete and its temporal and spatial distribution based on maturity theory, comprising the following steps:

[0006] Step 1: Establish a solid model of mass concrete in ABAQUS. The size of the concrete is 76.1m×74.1m×5.5m, and the concrete grade is C50.

[0007] Step 2: Mesh division, using DC3D8 heat conduction cube unit. Due to the large number of mesh divisions in the calculation process, reduced integration is used;

[0008] Step 3: Establish the heat conduction equation. Heat source function in Where Q is the heat emitted per unit volume per unit time, J / (m 3 ·h); c is specific heat capacity, J / (kg·℃); ρ is concrete density, kg / m 3 ; m is the amount of cementitious material in unit volume of concrete, kg / m 3 ; q is the heat released per unit mass of cementitious material per unit time, J / (kg.h); Q' is the heat released per unit mass of cementitious material, J / kg;

[0009] Step 4: Establish the equation of maturity theory:

[0010] Where Q'(t,T') is the heat released by unit mass of cementitious material at time t under the influence of temperature; A is the pre-exponential factor; R is the gas constant, 8.314 J / (mol·K); T' is the constant temperature, ℃; E a is the activation energy, J / mol, t is the age; t0 is the initial time; Q' max is the cumulative heat release of concrete cementitious materials when t→∞;

[0011] Step 5, setting the boundary conditions and initial conditions of the temperature field;

[0012] Step 6: The expression of concrete temperature strain is dε T =α T ·dT, where ε T is the temperature strain, α Tis the coefficient of thermal expansion, dT is the temperature increment;

[0013] Step 7: Early shrinkage strain of concrete ε w It can be calculated by the following formula:

[0014]

[0015] Among them, η is the stiffness influence coefficient, and C50 concrete takes 9.5×10 -3 ; α is the degree of hydration; w / c is the water-cement ratio, ρ c and ρ w are the density of powder and water respectively; M is the molar mass of water; R is the gas constant; T is the temperature; K is the bulk modulus of the porous material; K s The bulk modulus of the non-porous material is 44 GPa; where K = E / 3 (1-2v), E is the elastic modulus; ρ is the density of water; v is the Poisson's ratio of 0.209; RH in is the relative humidity inside the concrete; v p is the total pore volume;

[0016] Step 8, the degree of hydration α(t,T) is obtained by the following formula: M s (t,T') can be obtained by the following formula Where M1(t,105℃) is the mass of the sample at 105℃ at time t; M2(t,950℃) is the mass of the sample at 950℃ at time t; car (t,600~750℃) is the mass of the sample at 600℃~750℃ at time t; M smax is the amount of bound water in a fully hydrated sample;

[0017] Step 9. In fact, concrete materials do not strictly obey Hooke's law. Its stress-strain relationship does not strictly conform to the linear relationship of σ=E·ε. The relationship between relaxation stress and elastic stress is expressed as: σ relax (t, τ) = σ elas (τ)ψ(t, τ), where σ relax (t,τ) is the relaxation stress, σ elas (t,τ) is the elastic stress, ψ(t,τ) is the relaxation coefficient, and τ is the final setting time of concrete;

[0018] Step 10: The concrete cracking index and its temporal and spatial distribution are calculated as follows:

[0019] Where η(t,T,x,y,z)= is the cracking index of any point inside the concrete affected by temperature at time t; σelax (t,τ,T,x,y,z) is the deformation tensile stress (cracking driving force) of any point inside the concrete affected by temperature at time t, MPa; ψ(t,τ,T,x,y,z) is the relaxation coefficient; f t (t,T,x,y,z) is the tensile strength (cracking resistance) of any point inside the concrete affected by temperature at time t, MPa; E(t,T,x,y,z) is the elastic modulus of any point inside the concrete affected by temperature at time t, MPa; ε S is the shrinkage strain of any point inside the concrete affected by temperature at time t; ε T is the temperature strain of any point inside the concrete affected by temperature at time t; R is the constraint degree, which is approximately 1 for the embedded foundation slab structure.

[0020] Based on the reaction heat of the cementitious material at four temperatures measured under constant temperature, the three unknown parameters Q' are calculated using the nonlinear least squares method. max , A and E a .

[0021] According to the calculation process of step eight, the hydration degree at different times and temperatures is obtained.

[0022] In order to avoid cracking caused by rapid cooling of large-volume concrete, it is usually kept in a closed and water-tight environment and is always in a humidity saturation period. To this end, the shrinkage strain of concrete at four temperatures is measured in a water bath constant temperature environment to verify the correctness of the calculation results.

[0023] The relaxation coefficient is The creep coefficient Calculated by the following formula:

[0024] Among them, α(t,T) is the degree of hydration affected by time and temperature; ω is the water-cement ratio; n is the relaxation factor, whose value is 0.3 based on the experience recommended by Wang Tiemeng; d is a constant, which is 0.35; τ is the final setting time of concrete; and T is the temperature.

[0025] Due to the rapid hydration at high temperature, the formed slurry structure is relatively loose, resulting in low strength. Therefore, the present invention takes 70°C as the critical damage temperature, and based on the test results of porosity at high temperature, introduces the damage factor to obtain the elastic modulus and tensile strength of concrete considering high temperature damage:

[0026] E=E0-ζφ;f t =f t0 -ζφ

[0027] Where, E is the elastic modulus of concrete when there is temperature damage; E0 is the elastic modulus of concrete when there is no temperature damage; f tis the tensile strength of concrete when temperature damage exists; f t0 is the tensile strength of concrete without temperature damage; ζ is the damage factor related to temperature; φ is the porosity of concrete with temperature damage. The porosity of concrete is obtained by low-field nuclear magnetic resonance testing.

[0028] When η(t,T,x,y,z)>1.0, concrete will definitely crack; when 0.7<η(t,T,x,y,z)≤1.0, there is a possibility of concrete cracking; when η(t,T,x,y,z)≤0.7, concrete will basically not crack.

[0029] Beneficial Effects

[0030] The present invention discloses a method for predicting the early cracking index of mass concrete and its spatiotemporal distribution based on maturity theory. Compared with the existing methods, the method proposed by the present invention provides a method for accurately predicting the performance and deformation of concrete at any temperature history and any age, which improves the accuracy of predicting the cracking index of mass concrete and its spatiotemporal distribution and saves a lot of time and labor costs. More importantly, it is possible to assume a series of concrete mix proportions, assume a variety of construction and maintenance boundary conditions, and assume different mixture temperatures that may be regulated to predict the temperature field, strain field, stress field, tensile strength field and cracking index of actual mass concrete and its spatiotemporal distribution, thereby reversely designing the anti-cracking concrete formula, construction and maintenance methods, and mold temperature control. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is the relationship between concrete hydration water consumption and hydration degree.

[0032] Figure 2 The relationship between concrete porosity and hydration degree.

[0033] Figure 3 is the relationship between elastic modulus and degree of hydration.

[0034] Figure 4 is the relationship between tensile strength and degree of hydration.

[0035] Figure 5 Comparison between the predicted values ​​of concrete shrinkage model and the experimental values.

[0036] Figure 6 Comparison between the predicted value and the experimental value of hydration heat release of cementitious materials.

[0037] Figure 7 The results are the prediction of temperature field and temperature strain field of mass concrete at 28 days.

[0038] Figure 8 These are the prediction results of the hydration water consumption field and shrinkage strain field of large-volume concrete at 28 days.

[0039] Fig. 9 These are the prediction results of the tensile strength field and elastic modulus field of 28d mass concrete.

[0040] Fig.10 This is the prediction result of the stress relaxation coefficient field of large-volume concrete at 28 days.

[0041] Fig.11 This is the prediction result of the stress field of large-volume concrete at 28 days.

[0042] Fig.12 The prediction results of the cracking index and its temporal and spatial distribution of mass concrete at a mold entry temperature of 35°C at 28 days.

[0043] Fig.13 The prediction results of the cracking index and its temporal and spatial distribution of mass concrete at a mold entry temperature of 30℃ at 28 days.

[0044] Fig.14 The cracking index and its temporal and spatial distribution prediction results of mass concrete when the amount of cementitious materials is reduced by 10%.

[0045] Fig.15 is the cracking index and its distribution probability of the mass concrete at the section y=0. DETAILED DESCRIPTION

[0046] The present invention will be further described with respect to the following examples, but it should be understood that these examples are only for illustration and should not be construed as limiting the implementation of the present invention. The present invention will be further described in detail below with respect to specific examples.

[0047] The present invention discloses a method for predicting the early cracking index of mass concrete and its spatiotemporal distribution based on maturity theory. Most previous studies only involved temperature field calculations, and the calculations of parameters such as cracking driving force, tensile strength, and elastic modulus did not involve the concept of space. In addition, the "cracking risk" is currently commonly used to assess whether mass concrete is cracking, but in fact the cracking risk is the probability density of several cracking indices. Therefore, the present invention uniformly uses the "cracking index" and its spatiotemporal distribution to assess the possibility of cracking of mass concrete. In order to improve the calculation accuracy of the cracking index of large-volume concrete and its spatiotemporal distribution, the present invention tests the reaction heat of cementitious materials at 20°C, 40°C, 60°C and 80°C, and the tensile strength, elastic modulus and porosity of concrete, corrects the tensile strength and elastic modulus under high-temperature damage by the porosity test results, and calculates the temperature field, temperature strain field, shrinkage strain field, elastic modulus field, stress field and tensile strength field of large-volume concrete based on maturity theory and spatiotemporal distribution, and introduces a relaxation coefficient to consider the influence of creep on stress, thereby improving the accuracy of the prediction of the cracking index of large-volume concrete and its spatiotemporal distribution.

[0048] More specifically, a method for predicting the early cracking index of mass concrete and its temporal and spatial distribution based on maturity theory comprises the following steps:

[0049] (1) First, a solid model of large-volume concrete is established in ABAQUS. The dimensions of the concrete are 76.1 m × 74.1 m × 5.5 m, and the concrete grade is C50.

[0050] (2) Grid division was performed and DC3D8 heat conduction cube unit was selected. Due to the large number of grid divisions in the calculation process, reduced integration was selected.

[0051] (3) Establish the heat conduction equation, Heat source function in Q' is the heat released per unit mass of cementitious material.

[0052] (4) Establish the equation of maturity theory:

[0053] Where Q'(t,T') is the heat released by unit mass of cementitious material at time t under the influence of temperature; A is the pre-exponential factor; R is the gas constant, 8.314 J / (mol·K); T' is the constant temperature, ℃; E a is the activation energy, J / mol;

[0054] (5) Furthermore, the temperature field boundary conditions and initial conditions are set. At the initial moment, the temperature field distribution of the mass concrete is set to a constant of 35°C or 30°C. The third type of boundary conditions are adopted, assuming that the heat flux passing through the concrete surface is proportional to the concrete surface temperature T and the ambient temperature T a is proportional to the difference, that is Where β is the heat convection coefficient, W / (m 2 K). The fourth type of boundary condition is used at the bottom of the concrete λ1 and λ2 are the thermal conductivities of concrete and bedrock, respectively.

[0055] (6) Furthermore, the expression of concrete temperature strain is dε T =α T ·dT, where ε T is the temperature strain, α T is the thermal expansion coefficient and dT is the temperature increment.

[0056] (7) Furthermore, the relationship between creep stress and elastic stress is expressed as: σ relax (t,τ)=σ elas (τ)ψ(t,τ), where σ relax (t,τ) is the creep stress, σ elas(t,τ) is the elastic stress and ψ(t,τ) is the relaxation coefficient. The creep coefficient It can be calculated by the following formula:

[0057] Where α(t,T) is the degree of hydration affected by time and temperature; ω is the water-binder ratio; n is the relaxation factor, whose value is 0.3 based on the experience recommended by Wang Tiemeng; d is a constant, whose value is 0.35.

[0058] (8) Furthermore, the hydration water consumption of concrete can be obtained by the following formula: Among them, M s (t,T) is the hydration water consumption of concrete at time t affected by temperature T; M smax is the bound water content of the fully hydrated sample; A is the pre-exponential factor; R is the gas constant, 8.314 J / (mol·K); E a is the activation energy, J / mol. M1(t,105℃) is the mass of the sample at 105℃ at time t; M2(t,950℃) is the mass of the sample at 950℃ at time t; M car (t, 600℃~750℃) is the mass of the sample at 600℃~750℃ at time t; the present invention uses a muffle furnace to measure M1(t, 105℃), M2(t, 950℃) and M at 3d, 7d and 28d corresponding to 20℃, 40℃, 60℃ and 80℃ car (t, 600℃~750℃), and the corresponding hydration water consumption is calculated. Finally, based on the nonlinear least squares method, the unknown parameter M is obtained. smax , A and E a .

[0059] (9) Furthermore, the degree of hydration of concrete α(t,T) can be obtained by the following formula: Among them, M s (t,T) is the hydration water consumption of concrete at time t affected by temperature T; M smax is the amount of bound water in a fully hydrated sample.

[0060] (10) Furthermore, the early shrinkage strain of concrete can be calculated by the following formula:

[0061]

[0062] Among them, η is the stiffness influence coefficient, and C50 concrete takes 9.5×10 -3 ; α is the degree of hydration; w / c is the water-cement ratio, ρ c and ρ ware the density of powder and water respectively; M is the molar mass of water; R is the gas constant; T is the temperature; K is the bulk modulus of the porous material; K s The bulk modulus of the non-porous material is 44 GPa; where K = E / 3 (1-2v), E is the elastic modulus; ρ is the density of water; v is the Poisson's ratio of 0.209; RH in is the relative humidity inside the concrete; v p is the total pore volume.

[0063] (11) Furthermore, the concrete cracking index and its temporal and spatial distribution are calculated as follows:

[0064] , where σ elax (t,τ,T,x,y,z) is the deformation tensile stress (cracking driving force) of any point inside the concrete affected by temperature at time t, MPa; ψ(t,τ,T,x,y,z) is the relaxation coefficient; f t (t,T,x,y,z) is the tensile strength (cracking resistance) of any point inside the concrete affected by temperature at time t, MPa; E(t,T,x,y,z) is the elastic modulus of any point inside the concrete affected by temperature at time t, MPa; ε S is the shrinkage strain of any point inside the concrete affected by temperature at time t; ε T is the temperature strain of any point inside the concrete affected by temperature at time t. R is the degree of constraint, which can be approximated to 1 for the embedded foundation slab structure.

[0065] Example

[0066] 1. Based on the results of the 20℃ isothermal calorimetry test, Q'(24h, 293.15K), Q'(72h, 293.15K), Q'(168h, 293.15K) at t=1d, 3d and 7d can be obtained; Based on the results of the 40℃ isothermal calorimetry test, Q'(24h, 313.15K), Q'(72h, 313.15K)Q'(168h, 313.15K) at t=1d, 3d and 7d can be obtained. ; Based on the results of the 60℃ isothermal calorimetry test, Q'(24h, 333.15K), Q'(72h, 333.15K), Q'(168h, 333.15K) at t=1d, 3d and 7d can be obtained; Based on the results of the 80℃ isothermal calorimetry test, Q'(24h, 353.15K), Q'(72h, 353.15K), Q'(168h, 353.15K) at t=1d, 3d and 7d can be obtained.

[0067] 2. Use a bellows shrinkage tester to test the shrinkage strain of concrete at 20℃, 40℃, 60℃ and 80℃ in a water bath constant temperature environment; the elastic modulus, tensile strength and Poisson's ratio of concrete are tested in accordance with the current national standard GB / T 50081 "Standard for Test Methods of Mechanical Properties of Ordinary Concrete"; the thermal expansion coefficient of concrete is tested by direct length measurement method

[0068] 3. Solve Q' based on nonlinear least squares method max 、M smax , A and E a

[0069] Four, Among them, y i is the actual measured value, S max Can be Q' max and M smax , and set the constraint to 350 <Q’ max <500; 20 <M smax <25;10 8 <A<10 12 ; 30000 <E a <60000

[0070] 5. Based on the Gauss-Newton method and the trust region reflection algorithm, the above model is solved using Python language, Q' max =400, M smax =21.58, A=5.90×10 8 、E a =59224.13

[0071] 6. The degree of hydration α(t,T) is calculated by the following formula:

[0072] 7. The expression of concrete temperature strain is dε T =α T ·dT, where ε T is the temperature strain, α T is the coefficient of thermal expansion, dT is the temperature increment

[0073] 8. The early shrinkage strain of concrete can be calculated by the following formula:

[0074]

[0075] Among them, η is the stiffness influence coefficient, and C50 concrete takes 9.5×10 -3 ; α is the degree of hydration; w / c is the water-cement ratio, ρ c and ρ ware the density of powder and water respectively; M is the molar mass of water; R is the gas constant; T is the temperature; K is the bulk modulus of the porous material; K s The bulk modulus of the non-porous material is 44 GPa; where K = E / 3 (1-2v), E is the elastic modulus; ρ is the density of water; v is the Poisson's ratio of 0.209; RH in is the relative humidity inside the concrete; v p is the total pore volume

[0076] IX. Based on the test results of porosity and hydration degree at high temperature, the damage factor is introduced to obtain the elastic modulus and tensile strength of concrete considering high temperature damage: E = E0-ζφ; f t =f t0 -ζφ

[0077] Where, E is the elastic modulus of concrete when there is temperature damage; E0 is the elastic modulus of concrete when there is no temperature damage; f t is the tensile strength of concrete when temperature damage exists; f t0 is the tensile strength of concrete without temperature damage; ζ is the damage factor related to temperature; φ is the porosity of concrete with temperature damage. The porosity of concrete is obtained by low-field nuclear magnetic resonance testing.

[0078] 10. The calculation formula of concrete relaxation coefficient is: Creep coefficient It can be calculated by the following formula:

[0079] Where α(t,T) is the degree of hydration affected by time and temperature; ω is the water-binder ratio; n is the relaxation factor, whose value is 0.3 according to the experience recommended by Wang Tiemeng; d is a constant, which is 0.35; τ is the final setting time of concrete

[0080] 11. The calculation formula of concrete cracking index and its temporal and spatial distribution is:

[0081] , where σ elax (t,τ,T,x,y,z) is the deformation tensile stress (cracking driving force) of any point inside the concrete affected by temperature at time t, MPa; ψ(t,τ,T,x,y,z) is the relaxation coefficient; f t (t,T,x,y,z) is the tensile strength (cracking resistance) of any point inside the concrete affected by temperature at time t, MPa; E(t,T,x,y,z) is the elastic modulus of any point inside the concrete affected by temperature at time t, MPa; ε S (t,T,x,y,z) is the shrinkage strain of any point inside the concrete affected by temperature at time t; ε T(t,T,x,y,z) is the temperature strain of any point inside the concrete affected by temperature at time t; R is the constraint degree, and the embedded foundation slab structure can be approximated as 1

[0082] The following is a calculation of the mass concrete cracking index and its temporal and spatial distribution based on maturity theory and stress relaxation:

[0083] The size of a large volume of concrete is 76.1m×74.1m×5.5m, the concrete grade is C50, and the concrete mix ratio is shown in Table 1. It is poured in summer and maintained from bottom to top with "plastic film + geotextile + quilt + rain cloth" in a closed and water-proof environment.

[0084] Firstly, the relationship between concrete hydration water consumption, porosity, elastic modulus, tensile strength and hydration degree was calculated, and the predicted values ​​of concrete shrinkage strain and hydration heat release were compared with the experimental values. Figure 1 to Figure 6 shown.

[0085] Then, the temperature field and temperature strain field of the mass concrete are calculated based on the heat conduction equation, boundary conditions and initial conditions, such as Figure 7 As shown. Since the temperature evolution history of each point inside the concrete is different, the development of parameters such as hydration degree, tensile strength, elastic modulus, etc. at each point is different. Accordingly, the present invention predicts the hydration water consumption of large-volume concrete, the development of tensile strength and elastic modulus at each point based on maturity theory and spatiotemporal distribution, thereby obtaining the hydration water consumption field, shrinkage strain field, elastic modulus field, stress relaxation coefficient field, stress field, and tensile strength field of large-volume concrete, as shown in FIG. Figure 8 to Figure 11 Finally, according to the cracking index and its distribution calculation formula, the cracking index of mass concrete and its spatiotemporal distribution prediction results are calculated. In addition, the cracking index and its spatiotemporal distribution prediction results of mass concrete under different mold entry temperatures and different cementitious material dosages are compared, as shown in Figure 1. Figure 12 to Figure 14 shown.

[0086] When the mold entry temperature drops from 35°C to 30°C, the maximum temperature in the center of the large-volume concrete can be reduced by about 10°C, and the probability of a cracking index greater than 0.7 can be reduced from 0.71 to 0, significantly reducing the risk of concrete cracking. In addition, when the amount of cementitious materials is reduced by 10%, the maximum temperature in the center of the large-volume concrete can be reduced by about 8°C, and the probability of a cracking index greater than 0.7 can be reduced from 0.71 to 0.17, and there is still a certain possibility of cracking of the concrete. Among the above two control methods, lowering the mold entry temperature has the most significant effect on reducing the center temperature and cracking index of concrete.

[0087] From the above calculation and analysis, it can be seen that by reducing the temperature of concrete entering the mold and reducing the amount of cementitious materials, the cracking index of mass concrete can be significantly reduced by 11% to 20%. In addition, the surface and edge cracking index of mass concrete and its temporal and spatial distribution are larger than those in the center. Insulation materials should be covered on the surface, and the curing film time should be appropriately extended to reduce the cooling rate of the concrete surface.

[0088] Table 1 C50 concrete mix proportions with different cementitious material dosages

[0089]

[0090] Table 2Q' max 、M smax , A and E a The value of

[0091]

[0092] The above embodiments describe the present invention and its implementation methods, which are not restrictive. The embodiments listed are only some of the implementation methods of the present invention, and the actual implementation methods are far from being limited thereto. Therefore, without departing from the purpose of the invention, any manufacturing method and embodiment similar to the technical solution of the present invention without creative design shall fall within the protection scope of the present invention.

Claims

1. A method for predicting the early cracking index of mass concrete and its temporal and spatial distribution based on maturity theory, characterized in that: The following steps are involved: Step 1: Establish a solid model of mass concrete in ABAQUS. The size of the concrete is 76.1m×74.1m×5.5m, and the concrete grade is C50. Step 2: Mesh division, using DC3D8 heat conduction cube unit. Due to the large number of mesh divisions in the calculation process, reduced integration is used. Step 3: Establish the heat conduction equation. Heat source function in Where Q is the heat emitted per unit volume per unit time, J / (m 3 ·h); c is specific heat capacity, J / (kg·℃); ρ is concrete density, kg / m 3 ; m is the amount of cementitious material in unit volume of concrete, kg / m 3 ; q is the heat released per unit mass of cementitious material per unit time, J / (kg.h); Q' is the heat released per unit mass of cementitious material, J / kg; Step 4: Establish the equation of maturity theory: Where Q'(t,T') is the heat released by unit mass of cementitious material at time t under the influence of temperature; A is the pre-exponential factor; R is the gas constant, 8.314 J / (mol·K); T' is the constant temperature, ℃; E a is the activation energy, J / mol, t is the age; t0 is the initial time; Q' max is the cumulative heat release of concrete cementitious materials when t→∞; Step 5, setting the boundary conditions and initial conditions of the temperature field; Step 6: The expression of concrete temperature strain is dε T =α T ·dT, where ε T is the temperature strain, α T is the coefficient of thermal expansion, dT is the temperature increment; Step 7: Early shrinkage strain of concrete ε w It can be calculated by the following formula: Among them, η is the stiffness influence coefficient, and C50 concrete takes 9.5×10 -3 ; α is the degree of hydration; w / c is the water-cement ratio, ρ c and ρ w are the density of powder and water respectively; M is the molar mass of water; R is the gas constant; T is the temperature; K is the bulk modulus of the porous material; K s The bulk modulus of the non-porous material is 44 GPa; where K = E / 3 (1-2v), E is the elastic modulus; ρ is the density of water; v is the Poisson's ratio of 0.209; RH in is the relative humidity inside the concrete; v p is the total pore volume; Step 8, the degree of hydration α(t,T) is obtained by the following formula: M s (t,T') can be obtained by the following formula Where M1(t,105℃) is the mass of the sample at 105℃ at time t; M2(t,950℃) is the mass of the sample at 950℃ at time t; car (t,600~750℃) is the mass of the sample at 600℃~750℃ at time t; M smax is the amount of bound water in a fully hydrated sample; Step 9. In fact, concrete materials do not strictly obey Hooke's law. Its stress-strain relationship does not strictly conform to the linear relationship of σ=E·ε. The relationship between relaxation stress and elastic stress is expressed as: σ relax (t, τ) = σ elas (τ)ψ(t, τ), where σ relax (t,τ) is the relaxation stress, σ elas (t,τ) is the elastic stress, ψ(t,τ) is the relaxation coefficient, and τ is the final setting time of concrete; Step 10: The concrete cracking index and its temporal and spatial distribution are calculated as follows: ， Where η(t,T,x,y,z)= is the cracking index of any point inside the concrete affected by temperature at time t; σ elax (t,τ,T,x,y,z) is the deformation tensile stress (cracking driving force) of any point inside the concrete affected by temperature at time t, MPa; ψ(t,τ,T,x,y,z) is the relaxation coefficient; f t (t,T,x,y,z) is the tensile strength (cracking resistance) of any point inside the concrete affected by temperature at time t, MPa; E(t,T,x,y,z) is the elastic modulus of any point inside the concrete affected by temperature at time t, MPa; ε S is the shrinkage strain of any point inside the concrete affected by temperature at time t; ε T is the temperature strain of any point inside the concrete affected by temperature at time t; R is the constraint degree, which is approximately 1 for the embedded foundation slab structure.

2. The method for predicting the early cracking index of mass concrete and its temporal and spatial distribution based on maturity theory according to claim 1, characterized in that: Based on the reaction heat of the cementitious material at four temperatures measured under constant temperature, the three unknown parameters Q' are calculated using the nonlinear least squares method. max , A and E a .

3. The method for predicting the early cracking index of mass concrete and its temporal and spatial distribution based on maturity theory according to claim 1, characterized in that: According to the calculation process of step eight, the hydration degree at different times and temperatures is obtained.

4. The method for predicting the early cracking index of mass concrete and its temporal and spatial distribution based on maturity theory according to claim 1, characterized in that: In order to avoid cracking caused by rapid cooling of large-volume concrete, it is usually kept in a closed and water-tight environment and is always in a humidity saturation period. To this end, the shrinkage strain of concrete at four temperatures is measured in a water bath constant temperature environment to verify the correctness of the calculation results.

5. The method for predicting the early cracking index of mass concrete and its temporal and spatial distribution based on maturity theory according to claim 1, characterized in that: The relaxation coefficient is ψ(t,τ,T), = The creep coefficient Calculated by the following formula: Among them, α(t,T) is the degree of hydration affected by time and temperature; ω is the water-cement ratio; n is the relaxation factor, whose value is 0.3 based on the experience recommended by Wang Tiemeng; d is a constant, which is 0.35; τ is the final setting time of concrete; and T is the temperature.

6. The method for predicting the early cracking index of mass concrete and its temporal and spatial distribution based on maturity theory according to claim 1, characterized in that: Due to the rapid hydration at high temperature, the formed slurry structure is relatively loose, resulting in low strength. Therefore, the present invention takes 70°C as the critical damage temperature, and based on the test results of porosity at high temperature, introduces the damage factor to obtain the elastic modulus and tensile strength of concrete considering high temperature damage: E=E0-ζφ;f t =f t0 -zf Where, E is the elastic modulus of concrete when there is temperature damage; E0 is the elastic modulus of concrete when there is no temperature damage; f t is the tensile strength of concrete when temperature damage exists; f t0 is the tensile strength of concrete without temperature damage; ζ is the damage factor related to temperature; φ is the porosity of concrete with temperature damage. The porosity of concrete is obtained by low-field nuclear magnetic resonance testing.

7. The method for predicting the early cracking index of mass concrete and its temporal and spatial distribution based on maturity theory according to claim 1, characterized in that: When η(t,T,x,y,z)>1.0, concrete will definitely crack; when 0.7<η(t,T,x,y,z)≤1.0, there is a possibility of concrete cracking; when η(t,T,x,y,z)≤0.7, concrete will basically not crack.

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