Methods, systems, and equipment for predicting the heat of hydration and adiabatic temperature of concrete with slag powder

Abstract

This application provides a method, system, and equipment for predicting the hydration heat and adiabatic temperature of concrete mixed with slag powder, belonging to the technical field of cement hydration and concrete simulation modeling. The method includes: expressing the total heat release of the silicate cement-slag system as the sum of the hydration heat release of silicate cement and slag, obtaining a silicate cement-slag hydration heat release prediction model; differentiating this model and multiplying it by the amount of cementitious material used per unit volume, using this as the internal heat source term in the concrete heat conduction differential equation; and solving the concrete heat conduction differential equation using the finite difference method to obtain the temperature field distribution of the concrete under adiabatic conditions. The hydration degree prediction model for silicate cement and slag is based on the hydration kinetic mechanism of silicate cement. This method does not require experimental determination of the concrete hydration heat; it only requires providing relevant parameters to accurately predict the hydration heat release law and adiabatic temperature rise behavior of the cement-slag system, providing support for the temperature control design of large-volume concrete.

Description

Technical Field

[0001] This application relates to the field of cement hydration and concrete simulation modeling technology, and in particular to a method, system and equipment for predicting the heat of hydration and adiabatic temperature of concrete mixed with slag powder. Background Technology

[0002] During the construction of large-volume concrete, the massive volume of concrete and the large amount of heat released during cement hydration, coupled with uneven heat dissipation and internal and external constraints, lead to temperature gradient-induced thermal stress and cracking, which is a major factor affecting the durability and safe use of concrete structures. Especially in marine engineering, large amounts of slag are often incorporated to enhance resistance to chloride ion attack. Slag not only reduces the heat of hydration but also solidifies chloride ions, significantly improving concrete durability. Therefore, accurately predicting the evolution of the heat of hydration and the temperature field distribution of slag-incorporated large-volume concrete is crucial for optimizing construction techniques and temperature control measures.

[0003] In existing technologies, scholars both domestically and internationally mostly use experimental methods to obtain hydration heat data of cementitious materials and combine it with the finite element method or finite difference method to predict the internal temperature changes of concrete. For example, some studies have measured the hydration heat of cementitious materials and recorded the ambient temperature, combining it with a finite element model to predict the temperature change of concrete over time; relevant standards have obtained the heat release at different ages through experiments to estimate the total heat release, and used experimental or empirical methods to estimate the temperature of cement with different admixtures; other studies have established temperature field prediction models based on the finite element or finite difference methods, considering multiple factors such as water-cement ratio, cement type, and admixtures, to calculate the temperature distribution law inside the concrete, and verified it with the measured results.

[0004] However, in actual large-volume concrete projects, a wide variety of cementitious materials are selected, such as low-heat cement or silicate cement with a large amount of mineral admixtures. If the hydration heat release process of each type of cement is measured one by one through experiments, it will not only be time-consuming and labor-intensive, but will also lead to a lag in temperature control.

[0005] Therefore, it is necessary to provide an improved technical solution that can accurately predict the heat release and temperature changes of hydration in large-volume concrete without relying on experimental data, so as to support the formulation and regulation of its temperature control measures. Summary of the Invention

[0006] The purpose of this application is to provide a method, system, and equipment for predicting the heat of hydration and adiabatic temperature of concrete with slag powder, so as to alleviate or solve the problems of time-consuming and labor-intensive methods and temperature control delay caused by relying on experiments to obtain hydration heat data in the prior art. By replacing experimental data with theoretical models, the application directly and accurately predicts the heat of hydration and concrete temperature evolution law of pure silicate cement system and silicate cement-slag composite cementitious system, providing a theoretical basis and technical support for temperature rise control of large volume concrete.

[0007] To achieve the above objectives, this application provides the following technical solution:

[0008] In a first aspect, this application provides a method for predicting the heat of hydration and adiabatic temperature of concrete mixed with slag powder, including:

[0009] The total heat release of the silicate cement-slag system is expressed as the sum of the heat release from the hydration of silicate cement and the heat release from the hydration of slag, thus obtaining a prediction model for the heat release from the hydration of silicate cement-slag.

[0010] The total heat release of the silicate cement-slag system calculated by the silicate cement-slag hydration heat release prediction model is multiplied by the amount of cementitious material used per cubic meter, and used as the internal heat source term in the concrete heat conduction differential equation. The finite difference method is then used to solve the concrete heat conduction differential equation to obtain the temperature field distribution of the concrete under adiabatic conditions.

[0011] The heat release from hydration of the silicate cement is calculated based on the degree of hydration of the silicate cement, which is predicted by a hydration degree prediction model. The hydration degree prediction model is based on the PK hydration kinetic model and comprehensively considers the effects of hydration time, water-cement ratio, specific surface area, relative humidity, and curing environment temperature on the hydration rate of silicate cement.

[0012] The heat release from slag hydration is calculated based on the degree of slag hydration. The degree of slag hydration is predicted by a slag hydration degree model, which comprehensively considers the effects of slag content, water-cement ratio, specific surface area, and curing environment temperature on the slag hydration process.

[0013] In conjunction with the first aspect, among some possible implementation methods, a hydration degree model for slag is constructed based on the hydration kinetic mechanism, including:

[0014] The hydration kinetics of slag is considered to be controlled by a diffusion reaction process. Based on the equation of diffusion reaction process in the hydration kinetics equation of silicate cement, the initial hydration kinetics equation of slag is written.

[0015] The initial hydration kinetic equation of the slag is modified by introducing the maximum hydration degree of the slag to obtain the final slag hydration kinetic equation. The final slag hydration kinetic equation is then integrated to obtain the first slag hydration degree prediction model.

[0016] In conjunction with the first aspect, in some possible implementations, the maximum degree of hydration of the slag is related to the slag activity index, and the effects of different water-cement ratios, slag content, specific surface area, and curing environment temperature on the hydration process are comprehensively considered.

[0017] In conjunction with the first aspect, in some possible implementations, the expression for the maximum degree of hydration of slag is as follows:

[0018] ,

[0019] The final equation for the slag hydration kinetics is expressed as follows:

[0020] ,

[0021] In the formula, This represents the maximum degree of hydration of the slag. The activity index of slag; This refers to the water-to-binder ratio; This refers to the amount of slag added. The specific surface area of ​​the slag; This is a reference value for the specific surface area of ​​slag. The apparent activation energy of slag; This is the universal gas constant; Reference temperature; To maintain the ambient temperature; The degree of slag hydration; This is the reaction rate constant for the slag diffusion reaction process, which is related to the water-cement ratio and the slag content. This refers to the hydration time, or hydration age.

[0022] In conjunction with the first aspect, among some possible implementations, the method further includes: obtaining a hydration degree model of slag through surface fitting based on statistical results of experimental data from different existing studies, as detailed below:

[0023] Obtain the test results of different researchers on the non-evaporation water content of the silicate cement-slag system and the corresponding test conditions;

[0024] Based on the expression for the non-evaporating water content of the silicate cement-slag system, a preliminary expression for the degree of slag hydration is determined; wherein, the non-evaporating water content of the silicate cement-slag system is expressed as the sum of the non-evaporating water content of silicate cement and the non-evaporating water content of slag;

[0025] Substituting the test results of the non-evaporating water content of the silicate cement-slag system from the different researchers into the preliminary expression of the slag hydration degree, the slag hydration degree under different test conditions was calculated.

[0026] The degree of slag hydration under different test conditions is fitted with a surface to obtain a surface-fitted expression for the degree of slag hydration; the surface-fitted expression for the degree of slag hydration is used to characterize the change law of the degree of slag hydration with hydration time under different water-cement ratios.

[0027] Taking into account the effects of effective water-cement ratio, hydration time, slag content, specific surface area and curing environment temperature on the slag hydration process, the slag hydration degree expression of the surface fitting is modified to obtain the second slag hydration degree prediction model.

[0028] The effective water-cement ratio is adjusted by using the slag activity index to determine the effective contribution of the slag.

[0029] In conjunction with the first aspect, in some possible implementations, the expression for the second slag hydration degree prediction model is as follows:

[0030] ,

[0031] In the formula, This refers to the hydration time, or hydration age. The degree of hydration of the slag; The activity index of slag; This refers to the amount of slag added. For an effective water-cement ratio; The specific surface area of ​​the slag; This is a reference value for the specific surface area of ​​slag. The apparent activation energy of slag; This is the universal gas constant; Reference temperature; To maintain the ambient temperature.

[0032] In conjunction with the first aspect, in some possible implementations, the slag activity index takes into account the influence of the two different forms of Al2O3 in the chemical composition of the slag—tetracoordinate and hexacoordinate—on the slag activity.

[0033] In conjunction with the first aspect, among some possible implementations, the finite difference method is used to solve the differential equation for heat conduction in concrete to obtain the temperature field distribution of concrete under adiabatic conditions, including:

[0034] Divide the concrete section into two-dimensional meshes;

[0035] Initial conditions and adiabatic boundary conditions are set, and the temperature of each node at each time moment is calculated in two-dimensional space using the finite difference method to obtain the predicted adiabatic temperature of concrete with slag powder.

[0036] The types of nodes include: internal nodes, boundary nodes, and corner nodes.

[0037] Secondly, this embodiment provides a system for predicting the heat of hydration and adiabatic temperature of concrete mixed with slag powder. This system is used to perform the steps of the method for predicting the heat of hydration and adiabatic temperature of concrete mixed with slag powder provided in any of the above embodiments, including:

[0038] The hydration heat prediction model building unit is configured to express the total heat release of the silicate cement-slag system as the sum of the hydration heat release of silicate cement and the hydration heat release of slag, thereby obtaining the silicate cement-slag hydration heat release prediction model.

[0039] The adiabatic temperature prediction unit is configured to multiply the total heat release of the silicate cement-slag system calculated by the silicate cement-slag hydration heat release prediction model by the amount of cementitious material used per cubic meter, and use it as the internal heat source term of the concrete heat conduction differential equation. The unit then uses the finite difference method to solve the concrete heat conduction differential equation to obtain the temperature field distribution of the concrete under adiabatic conditions.

[0040] The heat release from hydration of the silicate cement is calculated based on the degree of hydration of the silicate cement, which is predicted by a hydration degree prediction model. The hydration degree prediction model is based on the PK hydration kinetic model and comprehensively considers the effects of hydration time, water-cement ratio, specific surface area, relative humidity, and curing environment temperature on the hydration rate of silicate cement.

[0041] The heat release from slag hydration is calculated based on the degree of slag hydration; the degree of slag hydration is predicted by a slag hydration degree model, which is constructed based on the hydration kinetic mechanism.

[0042] Thirdly, this embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method for predicting the heat of hydration and adiabatic temperature of concrete mixed with slag powder provided in any of the above embodiments.

[0043] Beneficial effects:

[0044] The technical solution provided in this application is based on the hydration kinetic mechanism to predict the hydration degree of silicate cement (hereinafter referred to as cement) and slag respectively, and after modeling the hydration heat release of cement and slag respectively and coupling them, the total heat release of the silicate cement-slag system is obtained, and then the temperature field distribution is solved by the finite difference method. This scheme calculates the total heat release of the silicate cement-slag system by multiplying it by the amount of cementitious material used in the cementitious cement-slag hydration heat release prediction model. This product is then used as an internal heat source term and substituted into the concrete heat conduction differential equation to obtain the temperature field distribution of the concrete under adiabatic conditions. This allows for theoretical prediction of the entire process from hydration reaction to temperature field evolution, providing a scientific basis for the formulation of temperature control measures for large-volume concrete. Furthermore, this prediction process can obtain the heat release of cement and slag hydration without conducting hydration heat tests, reducing research and development costs and time. It distinguishes the hydration behavior of cement and slag, and considers the influence of factors such as slag content and water-cement ratio in the modeling, improving the accuracy and applicability of the composite system hydration heat prediction. In addition, since this method does not rely on the concrete's own experimental data, it only requires concrete-related material parameters and external parameters (such as mix proportion and curing environment temperature) to predict the heat of hydration and adiabatic temperature. Therefore, this method can be used to predict temperature rise during the mix design stage, enabling pre-emptive temperature control and providing technical support for optimizing construction schemes. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the structure of a computer device.

[0046] Figure 2 The diagram shows the hydration process of silicate cement, where (a) represents the crystal nucleation and crystal growth reaction process, (b) represents the diffusion reaction process, and (c) represents the process of forming a hydration shell or hydration film.

[0047] Figure 3 The time-varying pattern of non-evaporating water content under different slag admixtures is shown, where (a) represents the slag admixture content. =30% time-varying curve, (b) is the slag content =40% time-varying curve, (c) is the slag content =50% time-varying curve, (d) is the slag content =60% time-varying curve, (e) is the slag content =70% time-varying curve, (f) is the slag content =80% of the time-varying curve.

[0048] Figure 4 The time-varying pattern of non-evaporating water content under different water-to-binder ratios is shown, where (a) represents the water-to-binder ratio. The time-varying curve with a water-to-gel ratio of 0.3 is shown in (b). The time-varying curve with a water-to-gel ratio of 0.4, (c) represents the water-to-gel ratio. = 0.5 time-varying curve.

[0049] Figure 5 This is a schematic diagram comparing the simulated temperature and the monitored temperature at the center point and a quarter-thickness distance from the surface of a large-volume concrete specimen.

[0050] Figure 6 The diagram shows the fitted surface of the slag hydration degree, where (a) represents the curing temperature. The fitted surface at 20℃, (b) is the water-to-gel ratio. The fitted surface when = 0.3, (c) is the water-to-glue ratio The fitted surface when = 0.4, where (d) is the water-to-glue ratio. The fitted surface when = 0.5.

[0051] Figure 7 This is a schematic diagram comparing the test results and predicted results of the slag hydration degree.

[0052] Figure 8 The diagram shows a comparison between the predicted and experimental results of the cumulative heat release of different slag admixtures. (a) is a comparison with the experimental results of scholars such as Gruyaert et al., and (b) is a comparison with the experimental results of scholars such as Park et al.

[0053] Figure 9 This is a schematic diagram of the grid division of a concrete section.

[0054] Figure 10 Temperature field distribution cloud maps of concrete with a cross-sectional size of 1.5m×1.5m at hydration times of 1 day, 3 days and 7 days are shown. Among them, (a) is the temperature cloud map with hydration time of 1 day, (b) is the temperature cloud map with hydration time of 3 days and (c) is the temperature cloud map with hydration time of 7 days. Detailed Implementation

[0055] The embodiments of this application will now be described with reference to the accompanying drawings.

[0056] This embodiment provides a method for predicting the heat of hydration and adiabatic temperature of concrete containing slag powder. The concrete containing slag powder belongs to a silicate cement-slag composite cementitious system. This method can be executed by computer equipment and includes:

[0057] Step S1: By expressing the total heat release of the silicate cement-slag system as the sum of the heat release from the hydration of silicate cement and the heat release from the hydration of slag, a prediction model for the heat release from the hydration of silicate cement-slag is obtained.

[0058] Step S2: Multiply the total heat release of the silicate cement-slag system calculated by the silicate cement-slag hydration heat release prediction model by the amount of cementitious material used per cubic meter, and use it as the internal heat source term in the concrete heat conduction differential equation. Then, use the finite difference method to solve the concrete heat conduction differential equation to obtain the temperature field distribution of the concrete under adiabatic conditions.

[0059] The heat release from hydration of silicate cement is calculated based on the degree of hydration of silicate cement, which is predicted by a hydration degree prediction model. The hydration degree prediction model is based on the PK hydration kinetic model and comprehensively considers the effects of hydration time, water-cement ratio, specific surface area, relative humidity, and curing environment temperature on the hydration rate of silicate cement.

[0060] The technical solution of this embodiment is based on the hydration reaction kinetics mechanism of silicate cement, predicting the hydration degree of silicate cement and slag respectively, and then calculating the heat release of hydration for each of silicate cement and slag. Combined with the finite difference method, adiabatic temperature simulation is achieved. This solution breaks through the traditional two-stage temperature prediction method of first determining the heat of hydration experimentally and then inputting the experimental data into the finite element method for temperature field simulation. By embedding the prediction of the hydration degree of silicate cement and slag into the heat of hydration prediction process, the cumulative total heat release can be calculated using the silicate cement-slag hydration heat release prediction model without experimental data. Then, the temperature field is directly solved based on the concrete heat conduction differential equation, achieving high-precision temperature prediction.

[0061] The following section first introduces the steps for predicting the heat release during the hydration of silicate cement.

[0062] Silicate cement is a multi-mineral aggregate, mainly composed of four clinker minerals: tricalcium silicate (C3S), dicalcium silicate (C2S), tricalcium aluminate (C3A), and tetracalcium aluminoferrite (C4AF), as well as small amounts of free calcium oxide (f-CaO), magnesium oxide (f-MgO), SO3, etc. The heat of hydration of silicate cement is directly related to the above composition; therefore, the heat of hydration of silicate cement can be expressed as:

[0063] (1)

[0064] In the formula, yes The heat of hydration of silicate cement at any given time These are the serial numbers of each phase (i.e., mineral composition). It is the first time when cement is fully hydrated The maximum heat release of a certain phase (material composition); It is the first Mass fraction of the seed phase; It is the first silicate cement Species in The degree of hydration at any given time.

[0065] Based on existing research, the maximum heat release values ​​for each phase in formula (1) are shown in Table 1. Table 1 is as follows:

[0066] Table 1 Maximum heat release of each phase

[0067]

[0068] In formula (1), the mass fraction of the mineral composition for the four main clinker mineral phases C3S, C2S, C3A, and C4AF is... The mass fraction of each mineral component can be calculated using the modified Bogue equation in ASTM C 150; therefore, it is expressed as follows:

[0069] when At that time, mass fraction Calculate as follows:

[0070] (2)

[0071] (3)

[0072] (4)

[0073] (5)

[0074] when quality score Calculate as follows:

[0075] (6)

[0076] (7)

[0077] (8)

[0078] (9)

[0079] In the formula, , , , , These are the mass fractions of C3S, C2S, C3A, C4AF, and C2F, respectively. , , , and These are the mass fractions of CaO, SiO2, Al2O3, Fe2O3, and SO3 in cement clinker, respectively.

[0080] If no limestone or inorganic materials are added to the cement, use the above formulas (2) to (9) to calculate the mass fraction of each mineral component. That's it, no adjustments needed.

[0081] Furthermore, when limestone or inorganic processed materials, or both, are added to cement, the mineral composition needs to be modified. In this case, the contents of C3S, C2S, C3A, and C4AF can be adjusted according to the following equation:

[0082] (10)

[0083] In the formula, It refers to the content of C3S, C2S, C3A, and C4AF in limestone or inorganic processing additions. It refers to the content of C3S, C2S, C3A, and C4AF in basic cement (i.e., pure clinker cement without any added limestone or inorganic processed materials). It is the mass percentage of limestone. It is the percentage of the mass of inorganic processed materials.

[0084] It should be noted that since SO3, f-CaO (free calcium oxide) and f-MgO (free magnesium oxide) are present in low amounts in silicate cement, they can be considered to react fully during the hydration process, so the degree of hydration is considered to be 1. The degree of hydration of other mineral phases (such as C3S, C2S, C3A, C4AF) needs to be further calculated using a hydration kinetic model.

[0085] To calculate the degree of hydration of each mineral, we first introduce a hydration kinetic model for cement clinker minerals based on the classic PK model.

[0086] The degree of hydration of the four clinker minerals (C3S, C2S, C3A, and C4AF) in silicate cement depends on their chemical reaction kinetics, and their hydration process is as follows: Figure 2 As shown in the figure. Different colors and symbols represent the components. The hydration process of silicate cement can be described as three stages: (a) Nucleation and Growth: This stage represents the initial stage of the hydration reaction, where water molecules enter the cement surface and react chemically with clinker minerals to generate initial hydration products (i.e., CSH gel) and calcium hydroxide (CSH gel). (a) Hydration products form tiny crystal nuclei on the cement surface and gradually grow outward, covering part of the cement surface; (b) Diffusion reaction: This stage represents the middle stage of hydration. As hydration products (CSH gel) deposit on the cement surface, a dense hydration layer is formed, hindering water molecules from diffusing further inward. Water molecules need to bypass or diffuse through pores to the unreacted area, while mineral clinker migrates from the inside out through pores. Therefore, the hydration rate is controlled by diffusion; (c) Formation of hydration shell or hydration film: This stage represents the later stage of hydration. The hydration products (CSH gel) have completely encapsulated the cement, forming a continuous hydration shell. Water molecules find it difficult to enter the reaction zone, and the hydration reaction tends to slow down, eventually entering a stable period. Therefore, the hydration kinetics of the four clinker minerals can be represented by the PK model, and the expressions for the hydration rates in the three stages are as follows:

[0087] Crystallization nucleation and growth processes:

[0088] (11)

[0089] Diffusion process:

[0090] (12)

[0091] The process of forming a hydration shell or hydration film:

[0092] (13)

[0093] In the formula, The degree of hydration, Indicates the hydration rate, This indicates the hydration rate during the crystal nucleation and growth reaction processes. Indicates the hydration rate in the diffusion reaction process. This indicates the hydration rate during the formation of a hydration shell or hydration film. , , These are the reaction rate constants for the three stages; , These refer to the reaction orders of the crystallization nucleation and crystal growth processes, and the processes of forming a hydration shell or hydration film. Among them, , , , , These are collectively referred to as hydration reaction kinetic parameters.

[0094] Formulas (11), (12), and (13) are also known as the hydration kinetic equations for the three stages of crystal nucleation and crystal growth reaction, diffusion reaction, and formation of a hydration shell or hydration film. Integrating the above three hydration kinetic equations respectively, the relationship between the degree of hydration and hydration time is obtained, as shown in the following expression:

[0095] (14)

[0096] (15)

[0097] (16)

[0098] In the formula, , , These are hydration functions for the crystallization nucleation and crystal growth processes, diffusion processes, and the formation of hydration shells or hydration films, used to describe the reaction progress at each stage of the hydration process.

[0099] Based on the quantitative XRD analysis of silicate hydration samples with different clinker mineral contents by scholars Lothenbach et al. using the Rietveld method, the hydration reaction kinetic parameters of four clinker minerals in equations (11)~(13) and (14)~(16) are given in Table 2. Table 2 is as follows:

[0100] Table 2. Hydration reaction kinetic parameters required to describe the change in the degree of hydration of a single mineral over time.

[0101]

[0102] Based on the above description, it can be seen that in the hydration process of cement clinker single minerals shown in formulas (11) to (13), the hydration process is controlled by the minimum hydration rate. However, for finely ground cement, its hydration process is not only related to the water-cement ratio, but also to factors such as the specific surface area of ​​cement, relative humidity and temperature during hydration. Therefore, it is necessary to improve formulas (11) to (13) and comprehensively consider the influence of hydration time, water-cement ratio, specific surface area, relative humidity and temperature on the hydration rate of silicate cement, so as to form an improved cement hydration kinetic model describing the hydration rate of single minerals. The expression is as follows:

[0103] (17)

[0104] In the formula, For hydration time, For the first The degree of hydration of the species phase , , , These are the influence coefficients of water-cement ratio, specific surface area, relative humidity, and curing environment temperature on cement clinker minerals.

[0105] Among them, each influence coefficient , , , The calculation method is as follows:

[0106] The influence coefficient of water-cement ratio on cement clinker minerals The expression is as follows:

[0107] (18)

[0108] In the formula, Water-cement ratio; For the first The degree of hydration of a single phase; H is an empirical constant that needs to be determined experimentally based on the degree of hydration of a single mineral under different water-cement ratios.

[0109] Specific surface area influence coefficient The expression is as follows:

[0110] (19)

[0111] In the formula, It is the actual specific surface area of ​​cement; It is the surface area of ​​the reference cement. In this embodiment, it is taken as... =3850cm 2 / g.

[0112] Relative humidity influence coefficient The expression is as follows:

[0113] (20)

[0114] In the formula, It is the relative humidity of the pores in the hardened slurry.

[0115] The influence coefficient of the curing environment temperature on the hydration of a single mineral can be expressed as:

[0116] (twenty one)

[0117] In the formula, It is the apparent activation energy; It is the gas constant ( ); It is the reference temperature ( =293K); It refers to the actual maintenance environment temperature, or simply maintenance environment temperature.

[0118] Substituting formulas (11) to (13) and formulas (18) to (21) into formula (17), we can obtain an improved cement hydration kinetic model that comprehensively considers the effects of water-cement ratio, temperature, relative humidity and cement specific surface area on the hydration rate.

[0119] Based on this, the degree of hydration of silicate cement can be expressed by the hydration rate of each phase, as shown in the following expression:

[0120] (twenty two)

[0121] In the formula, , , , These are the hydration degrees of C3S, C2S, C3A, and C4AF, respectively. Formula (22) is based on the hydration kinetics mechanism of silicate cement and is also known as the hydration degree prediction model of silicate cement.

[0122] The empirical constants are introduced below. The calibration process.

[0123] To avoid experimental errors, the following was selected: The chemical composition and specific surface area of ​​silicate cement are shown in Table 3. Table 3 is as follows:

[0124] Table 3. Cement chemical composition and specific surface area

[0125]

[0126] For silicate cement, the non-evaporating water content is often used to characterize the degree of hydration. The test procedure is briefly as follows: The sample is placed in a drying oven and dried at 105℃ for 24 hours. After cooling in a desiccator, it is weighed and the mass is recorded as m1. Then, it is heated in a martensitic furnace to 1000℃ for 4 hours, cooled, and weighed, and the mass is recorded as m2. Considering that the cementitious material also has a loss on ignition at high temperatures, the change in the loss on ignition (LOI) of the cementitious material must be taken into account when calculating the non-evaporating water content. The cementitious material is dried and weighed, and the mass is recorded as m2. a After burning and cooling, the mass is recorded as m. b Three samples were weighed each time, and the results were calculated as the arithmetic mean. The LOI (Lowest Ignition Index) and non-evaporated water content were calculated based on the experimental data. Then calculate the degree of cement hydration. (Right now The relevant calculation formulas can be found in existing technologies, and will not be elaborated here. Statistical analysis of the calculation results yielded experimental results on the degree of hydration of silicate cement at different ages and water-cement ratios, as shown in Table 4. Table 4 is as follows:

[0127] Table 4. Hydration degree of silicate cement at different water-cement ratios (%)

[0128]

[0129] Substituting the experimental results from Table 4 into formula (18), we obtain the empirical constants for each phase under different water-cement ratios. The statistical results are shown in Table 5, which is as follows:

[0130] Table 5. Empirical constants H for different water-cement ratios

[0131]

[0132] Substituting Tables 4 and 5 into formula (22), the hydration degree of silicate cement with different water-cement ratios can be predicted. Substituting the prediction results into formula (1), any... The heat release during the hydration of silicate cement.

[0133] To verify the reliability of the predicted hydration degree of silicate cement, the experimental results of scholars Wong et al. and Liao et al. were compared and verified. The mineral composition and specific surface area of ​​silicate cement clinker used by the two scholars are shown in Table 6. Table 6 is as follows:

[0134] Table 6 Chemical composition and specific surface area of ​​cement and slag

[0135]

[0136] Substituting parameters such as the mineral composition of clinker, water-cement ratio, hydration age, curing temperature, and cement specific surface area into the hydration degree prediction model of silicate cement, i.e., formula (22), the prediction result of the hydration degree of silicate cement can be obtained. The prediction result is compared and analyzed with the experimental results given by scholars. The analysis results show that the prediction result is basically consistent with the experimental result. If the experimental result is taken as the benchmark, the maximum error between the prediction and the experimental result is 14.78%. This error range is relatively small for silicate cement with multiple mineral compositions, further proving that the prediction result of the hydration degree of silicate cement is reliable.

[0137] Furthermore, by substituting the predicted degree of hydration of silicate cement into formula (1), the heat of hydration of silicate cement can be obtained. The predicted results were verified by the following steps: The experiment used slurries with water-cement ratios of 0.35 and 0.50, and a TAMAIR eight-channel isothermal calorimeter from TA Instruments was used for testing. The test temperature was constant at 20 ± 1℃. The corresponding parameters were then substituted into formula (1) to predict the cumulative hydration heat release of the cement. The predicted results were obtained. Comparing and analyzing the experimental results with the predicted results reveals that the cumulative heat release of silicate cement... The predicted results and experimental results are basically consistent, both showing a trend of rapid growth in the early stage and slow growth in the later stage, with a maximum error of 6.31%, indicating that the heat of hydration of silicate cement in formula (1) is relatively stable. The predictions are accurate and reasonable.

[0138] After describing in detail the steps for predicting the degree of hydration and heat release of silicate cement, the following section introduces the steps for predicting the degree of hydration and heat release of silicate cement-slag system.

[0139] It should be noted that slag is a byproduct produced by water quenching during the blast furnace ironmaking process. The glass phase content is usually above 90%, and it exists in an irregular network form. It is often used as a cement admixture or a mineral admixture in concrete, and it is widely used in marine engineering large-volume concrete.

[0140] Considering the silicate cement-slag system, its hydration process is relatively complex, but its hydration heat release can be simply expressed as the sum of the hydration heat release of silicate cement and slag. Therefore, a prediction model for the hydration heat release of silicate cement-slag is established, as shown in the following expression:

[0141] (twenty three)

[0142] (twenty four)

[0143] (25)

[0144] In the formula, for The total heat release of the silicate cement-slag system at any given time and They are The cumulative heat release during the hydration of silicate cement (cement) and slag; It refers to the amount of slag added; and These are the theoretical heat releases from the complete hydration of cement and slag, respectively. , denoted as t, representing the degree of hydration of cement and slag at time t, respectively.

[0145] The aforementioned silicate cement-slag hydration exothermic prediction model decomposes the complex silicate cement-slag system into two subsystems: the cement subsystem and the slag subsystem. After modeling each subsystem separately, a weighted sum is performed, resulting in a formula with a clear structure, explicit physical meaning, and intuitive representation of the slag content. The regulation of total heat release enables a theoretical description of the hydration behavior of the composite cementitious system, solving the problem of poor applicability of existing models to cement-slag composite systems.

[0146] Among them, the theoretical heat release for complete hydration of each unit mass of slag is... The theoretical heat release from the complete hydration of cement is 630 J / g; Based on the maximum heat release of each phase Mass fraction of each phase The maximum heat release of each phase was calculated. Existing research results can be referenced, as shown in Table 1.

[0147] The cumulative heat release during the hydration of silicate cement The heat of hydration of silicate cement, also known as silicate cement, The hydration degree of silicate cement can be calculated according to formula (1) in the aforementioned embodiment, that is, the hydration degree of silicate cement is predicted by the silicate cement hydration degree prediction model; and the hydration heat release of silicate cement is calculated based on the hydration degree of silicate cement.

[0148] The following describes the heat release during slag hydration. The theoretical calculation process.

[0149] In this embodiment, the heat release from slag hydration is calculated based on the degree of slag hydration. The degree of slag hydration is predicted by a slag hydration degree model, which comprehensively considers the influence of slag content, water-cement ratio, specific surface area, and curing environment temperature on the slag hydration process.

[0150] Specifically, the degree of hydration of slag can be predicted in two ways. One is based on the hydration kinetics, which is called the first slag hydration degree prediction model. The other is based on the statistical results of experimental data from different researchers, which are then fitted and corrected to obtain the second slag hydration degree prediction model.

[0151] The following sections introduce two methods for predicting the degree of slag hydration.

[0152] First, we will explain the process of predicting the degree of slag hydration based on hydration kinetics.

[0153] In one embodiment, a slag hydration degree model is constructed based on the hydration reaction kinetics mechanism of silicate cement, including:

[0154] Step S11a: The hydration kinetics of slag is considered to be controlled by the diffusion reaction process. Based on the equation of the diffusion reaction process in the hydration kinetics equation of silicate cement, the initial hydration kinetics equation of slag is written.

[0155] Step S11b: The initial hydration kinetic equation of the slag is modified by introducing the maximum hydration degree of the slag to obtain the final slag hydration kinetic equation. The final slag hydration kinetic equation is then integrated to obtain the first slag hydration degree prediction model.

[0156] It should be noted that the hydration kinetics of slag is basically the same as that of silicate cement, and it is also divided into three stages: crystal nucleation and crystal growth reaction, diffusion reaction, and formation of hydration shell. Considering that the glass network structure of slag itself has lower early activity compared with the silicate clinker mineral components in a metastable state, and that the crystal nucleation and crystal growth process of slag is very slow and almost difficult to test, the hydration kinetics of slag is considered to be controlled by the diffusion reaction process. According to formula (12), that is, the equation of the diffusion reaction process, the initial hydration kinetics equation of slag can be expressed as:

[0157] (26)

[0158] In the formula, express The degree of hydration of the slag at all times It is the reaction rate constant of the slag diffusion reaction process, which is related to the water-cement ratio and the amount of slag added.

[0159] Since slag contains a certain amount of inert crystalline phase, its hydration reaction has an upper limit threshold. Therefore, the maximum hydration degree of slag (also known as the final hydration degree) is introduced. The hydration kinetics equation of slag, i.e., formula (26), is modified to obtain the final slag hydration kinetics equation, which is expressed as follows:

[0160] (27)

[0161] In the formula, It is the maximum degree of hydration when the slag is fully hydrated (i.e., the maximum degree of hydration of the slag).

[0162] Preferably, the maximum degree of hydration of the slag It is related to the activity index of slag and takes into account the effects of different water-cement ratios, slag content, specific surface area, and curing temperature on the hydration process.

[0163] Maximum hydration degree of slag Related to the activity index of slag, its preliminary expression is as follows:

[0164] (28)

[0165] In the formula, It refers to the amount of slag added; Indicates the activity index of slag; This indicates the water-to-binder ratio.

[0166] Furthermore, since the hydration of slag is related not only to the water-cement ratio but also to factors such as specific surface area and curing environment temperature, therefore, for The initial expression was improved. The final expression is as follows:

[0167] (29)

[0168] In the formula, This refers to the water-to-glue ratio. This represents the actual specific surface area of ​​the slag. The reference specific surface area; Indicates activation energy; It is the gas constant; The standard curing temperature, also known as the reference temperature. To maintain the ambient temperature. Therefore, The final expression comprehensively considers the effects of different water-cement ratios, slag content, specific surface area, and curing environment temperature on the hydration process.

[0169] Will Substituting the final expression, i.e. formula (29), into formula (27) and integrating, we can obtain the first slag hydration degree prediction model.

[0170] It should also be noted that in formula (27), the reaction rate constant of the slag diffusion reaction process is... Typically, the setting is based on temperature. However, considering the significant differences in water-cement ratio and slag content across various engineering scenarios (e.g., high slag content and low water-cement ratio are commonly used in marine engineering), if a fixed setting is still adopted... This may not accurately describe its hydration characteristics. Therefore, in this embodiment, as a further improvement, the test data of the degree of slag hydration, combined with the test results of different scholars, is fitted with the hydration kinetic model (i.e., formula (27)) to give the slag reaction rate constants at different slag admixtures and curing temperatures with water-cement ratios of 0.3, 0.4, and 0.5. The details are shown in Table 7, which is as follows:

[0171] Table 7. Slag Reaction Rate Constants under Different Conditions

[0172]

[0173] The above-mentioned reaction rate constant for slag In the determination process, the slag reaction rate constant is no longer regarded as a fixed value determined by temperature, but rather as a function of water-cement ratio, slag content, and temperature. By fitting experimental data with the model, the prediction of slag hydration degree can more realistically reflect the hydration behavior under actual working conditions, reduce errors caused by parameter simplification, and improve prediction accuracy.

[0174] In another implementation, based on the statistical results of experimental data from different existing studies, a hydration degree model for slag is obtained through surface fitting, including:

[0175] Step S12a: Obtain the test results of different researchers on the non-evaporation water content of the silicate cement-slag system and the corresponding test conditions.

[0176] Step S12b: Determine the preliminary expression for the degree of slag hydration based on the expression for the non-evaporation water content of the silicate cement-slag system; wherein, the non-evaporation water content of the silicate cement-slag system is expressed as the sum of the non-evaporation water content of silicate cement and the non-evaporation water content of slag.

[0177] In step S12c, the test results of the non-evaporation water content of the silicate cement-slag system by different researchers are substituted into the preliminary expression of the slag hydration degree to calculate the slag hydration degree under different test conditions.

[0178] Step S12d: Perform surface fitting on the slag hydration degree under different test conditions to obtain the surface-fitted expression for the slag hydration degree; the surface-fitted expression for the slag hydration degree is used to characterize the variation law of slag hydration degree with hydration time under different water-cement ratios.

[0179] Step S12e: Taking into account the effects of effective water-cement ratio, hydration age, slag content, specific surface area and curing environment temperature on the slag hydration process, the expression for the degree of slag hydration fitted by the surface is modified to obtain the second slag hydration degree prediction model.

[0180] The effective water-cement ratio is adjusted using the slag activity index to determine the effective contribution of the slag.

[0181] Specifically, the hydration degree model for slag can be predicted by testing changes in non-evaporating water content. Considering that the non-evaporating water content of the silicate cement-slag system is related to factors such as water-cement ratio, hydration age, slag content, specific surface area, and curing temperature, step S12a involves obtaining test data on the non-evaporating water content of the silicate cement-slag system from different researchers, and using these test results to verify the correlation between the slag hydration degree and the aforementioned factors. Specifically, this is based on statistical analysis of the time-varying pattern of non-evaporating water content under different slag contents and water-cement ratios (e.g.,...). Figure 3 , Figure 4As shown in Table 8, the corresponding test conditions, including slag content, water-cement ratio, specific surface area, and temperature, are given. Table 8 is as follows:

[0182] Table 8 Test conditions for non-evaporated water content

[0183]

[0184] The purpose of step S12b is to obtain a preliminary expression for the degree of slag hydration, which is related to the degree of slag hydration, the non-evaporating water content of the slag, and the degree of hydration of silicate cement. Specifically:

[0185] Because the hydration process of the cement-slag cementitious system is relatively complex, this embodiment assumes that the hydration of cement and slag is independent. Therefore, the non-evaporating water content of the silicate cement-slag system is... (i.e., total non-evaporating water content) can be expressed as the sum of the non-evaporating water content of cement and the non-evaporating water content of slag, as shown in the following expression:

[0186] (30)

[0187] In the formula, It is the non-evaporated water content when cement and slag are fully hydrated. It is related to the composition and structure of slag and is generally taken as 0.25-0.30. In this embodiment, the results of scholars Wang et al. are adopted and 0.30 is taken.

[0188] Transforming formula (30), the degree of hydration of slag can be expressed by the non-evaporated water content as follows:

[0189] (31)

[0190] According to formula (31), the degree of hydration of slag is related to the content of non-evaporating water and the degree of hydration of cement. The degree of hydration of cement and slag is related not only to their composition and structure but also to their chemical composition. The glass phase content of slag is above 90%. Under this premise, the activity of slag is expressed by the activity index. The result is as shown in formula (32):

[0191] (32)

[0192] In formula (32), the chemical composition of slag is considered to include two forms of Al2O3: tetracoordinate and hexacoordinate. Different forms have different effects on the activity of slag.

[0193] The prediction of the degree of slag hydration needs to be calculated based on the basic parameters of the raw materials. The slag composition, calcination vector and activity index calculated by formula (32) selected by different researchers (collectively referred to as slag parameters) are shown in Table 9. Table 9 is as follows:

[0194] Table 9 Slag Parameters

[0195]

[0196] In step S12c, the results of non-evaporation water content of slag used by different researchers are substituted into the preliminary expression of the degree of slag hydration, i.e. formula (31), to obtain the degree of slag hydration under different test conditions.

[0197] Next, in step S12d, the calculation results, i.e., the degree of slag hydration under different test conditions, are subjected to surface fitting, such as... Figure 6 As shown. Specifically, based on hydration time Slag admixture The degree of slag hydration is the independent variable. Using water-cement ratio and curing temperature as the dependent variable, surface fitting was performed: First, the calculation results were grouped according to different combinations of water-cement ratio and temperature. Then, for each group of data, a three-dimensional scatter plot was created with hydration time as the horizontal axis, slag content as the vertical axis, and hydration degree as the vertical axis. A smooth surface was generated using polynomial regression or empirical function fitting methods. Different surfaces represent the trend changes under different test parameter conditions, i.e., the change in slag hydration degree with hydration time under different water-cement ratios. Statistical fitting was performed on all the fitted slag hydration degrees to obtain an empirical expression for the slag hydration degree, i.e., the surface-fitted expression for the slag hydration degree, as follows:

[0198] (33)

[0199] In the formula, Indicates hydration time (hydration age). This indicates the water-to-binder ratio.

[0200] Formula (33) only reflects the influence of slag content, water-cement ratio, and hydration age on the degree of slag hydration. Studies have shown that the hydration reaction of slag is also related to its fineness (specific surface area) and curing environment temperature. In addition, in the silicate cement-slag composite system, the dilution effect of slag also causes changes in the effective water-cement ratio of cement. Considering the above factors, in order to further improve the accuracy of slag hydration degree prediction, formula (33) is further modified in step S12e to obtain the second slag hydration degree prediction model, the expression of which is as follows:

[0201] (34)

[0202] In the formula, For time; The degree of hydration of the slag; The activity index of slag; This refers to the amount of slag added. For an effective water-cement ratio; The specific surface area of ​​the slag; The reference value for the specific surface area of ​​slag is 4500 cm². 2 / g; The apparent activation energy of slag (50 kJ / mol - 60 kJ / mol); This is the universal gas constant; Reference temperature; To maintain the ambient temperature.

[0203] The effective water-cement ratio is adjusted for the effective contribution of slag using the slag activity index, as shown in the following expression:

[0204] (35)

[0205] In the formula, Indicates the amount of water used for mixing. This indicates the amount of cementitious material used.

[0206] Among them, the slag activity index takes into account the influence of two different forms of Al2O3 in the chemical composition of slag, namely tetracoordinate and hexacoordinate, on the slag activity. Its expression is shown in formula (32).

[0207] To verify the rationality of the slag hydration degree calculated by formulas (34) and (35), test results of the slag hydration degree published by other researchers in the literature (different from the literature on the aforementioned surface fitting process) were cited. The corresponding test conditions and parameters were substituted into formulas (34) and (35) to obtain the predicted results of the slag hydration degree. The fitting curve of the predicted results was compared with the test results, and the results are as follows. Figure 7 As shown in the figure, the test data and the fitting results show a consistent and good trend. Therefore, the second slag hydration degree prediction model represented by formulas (34) and (35) has high accuracy.

[0208] Based on the establishment of the first slag hydration degree prediction model and the second slag hydration degree prediction model and the verification of their calculated slag hydration degree, the slag hydration degree can be substituted into formula (25) to calculate the slag hydration heat release. This refers to the cumulative calorific value of the slag, and its rationality is verified.

[0209] For verifying the cumulative calorific value of slag, it is difficult to accurately separate the slag's calorific value from the total calorific value in the silicate cement-slag cement system. Therefore, this embodiment uses the total calorific value of the silicate cement-slag system for verification. Based on the cumulative calorific value test results of silicate cement-slag systems with a water-cement ratio of 0.5, a curing temperature of 20℃, and slag content of 0%, 30%, and 50% given by scholars Gruyaert et al. and Park et al. in published literature, the basic parameters in the literature are substituted into formulas (34) and (35) to calculate the degree of slag hydration. Then, the degree of slag hydration is substituted into formula (25) to predict the cumulative calorific value of the slag. The predicted results were compared with the experimental results in publicly available literature, and the results are as follows: Figure 8 As shown. From Figure 8 As can be seen from the results, the prediction results are basically consistent with the experimental results, with a maximum error of 9.47%, indicating that it is reliable and reasonable to predict the degree of slag hydration and thus the cumulative calorific value of slag based on (34) and (35).

[0210] The cumulative calorific value of the slag was predicted. Based on this, and combined with the heat release of silicate cement hydration predicted by the aforementioned formula (1), The total heat release of the silicate cement-slag system can be obtained by weighted summation of the two using formula (23). The prediction results.

[0211] The total heat release of the silicate cement-slag system Following the prediction model, step S2 will utilize this silicate cement-slag hydration heat release prediction model to calculate the concrete temperature field, specifically including the following steps:

[0212] First, based on the solid conduction theory and the law of conservation of energy, the differential equation for heat conduction in concrete temperature field calculation is derived.

[0213] It should be noted that the concrete temperature field refers to the temperature distribution pattern inside the concrete, that is, for any... Any point inside the concrete at any time Temperature at location .

[0214] According to the theory of solid conduction, concrete is a poor conductor of heat, and its temperature change is related to its composition, pore structure, and the external environment. In practical engineering, in addition to testing the heat from the center of the concrete to the surface layer, more emphasis is placed on analyzing the temperature distribution from the center of the concrete to the surface layer.

[0215] For calculating the temperature field of concrete after pouring, the differential equation of concrete heat conduction can be derived based on heat flow analysis. A micro-element exists within the concrete. The amount of heat released per unit volume of concrete per unit time is... Then the infinitesimal element The heat released per unit time is According to the law of conservation of energy, the heat generated by the change in concrete temperature is equal to the sum of the heat retained by the concrete through external heat transfer and internal heat release. Therefore:

[0216] (36)

[0217] In the formula, It is the temperature at a certain point inside the concrete; Hydration time; It is the thermal conductivity of concrete; It is the heat released by the cementitious materials in a unit volume of concrete per unit time; It is the specific heat capacity of concrete; It refers to the density of concrete.

[0218] Considering the heat of hydration, assuming the concrete is under adiabatic conditions, all the heat of hydration is used for temperature rise, and the rate of temperature change is determined only by the heat released per unit volume. Without considering the thermal conductivity term, the temperature rise of the concrete can be initially expressed as formula (37):

[0219] (37)

[0220] In the formula, It is the adiabatic temperature rise of concrete. It is the rate of temperature rise of concrete under adiabatic conditions. Equation (37) is integrally transformed, and the total heat release of the silicate cement-slag system calculated by the silicate cement-slag hydration heat release prediction model is combined with the amount of cementitious material per cubic meter. Multiply, we get The cumulative heat release of cementitious materials per unit volume of concrete at any given time, i.e. As the internal heat source term in the differential equation of concrete heat conduction, the formula for calculating the adiabatic temperature rise is as follows:

[0221] (38)

[0222] In the formula, Indicates the amount of cementitious material used per cubic meter; yes The total heat release of the silicate cement-slag system at any given time can be theoretically predicted using formulas (23) to (25).

[0223] Solving the differential equation for heat conduction in concrete using the finite difference method yields the temperature field distribution of concrete under adiabatic conditions, including the following sub-steps:

[0224] First, initial conditions and adiabatic boundary conditions are set. In this embodiment, it is assumed that the initial temperature distribution of the concrete is relatively uniform; therefore, At that time, the initial instantaneous temperature inside the concrete (i.e., the initial conditions) was:

[0225] (39)

[0226] In the formula, This represents the initial internal temperature of the concrete, which is a constant.

[0227] Assuming the concrete surface is adiabatic, the heat flux density at the boundary is zero, and the boundary conditions can be expressed as:

[0228] (40)

[0229] In the formula, n is the direction of the outer normal to the concrete surface.

[0230] Secondly, a two-dimensional mesh is generated for the concrete cross-section. This embodiment focuses on the temperature field analysis of the concrete in two-dimensional space (i.e., a certain cross-section of the concrete). Based on the finite difference method, the temperature of each node at each time step is calculated to solve for the concrete temperature field. Specifically:

[0231] Vertical space can be ignored in two-dimensional space. Since the heat conduction is oriented in the direction of heat transfer, equation (36) can be simplified to the following two-dimensional heat conduction differential equation:

[0232] (41)

[0233] Then, the concrete section is meshed to obtain a discrete mesh. Specifically, as follows: Figure 9 As shown, half of the concrete section is along shaft and axial direction with spacing and Divide into equal parts, and take the heat transfer time interval as . This yields a discrete mesh, and the coordinates of each node on the mesh. Temperature at the location express.

[0234] Subsequently, based on the mesh generation results, the finite difference method was used to calculate the temperature of each node at each time step in two-dimensional space, obtaining the predicted adiabatic temperature of the concrete with slag powder, i.e., solving for the temperature values ​​of internal nodes, boundary nodes, and corner nodes of the concrete. Different iterative formulas were used to solve for each type of node; the specific iterative formulas can be found in existing technologies, but for the sake of brevity, they will not be elaborated here.

[0235] As an example, the method provided in this embodiment, the prediction process for the heat release of hydration of composite cementitious materials and the internal temperature field of concrete can be executed according to the following procedure:

[0236] 1. Calculate the heat release of silicate cement hydration. The heat release of silicate cement hydration is obtained from formula (1). ;

[0237] 2. The mass fraction of each clinker mineral phase is obtained from formulas (2) to (9);

[0238] 3. The maximum heat release of each mineral phase is obtained from Table 1;

[0239] 4. Determine the mass fraction of cement in the cementitious system based on the actual mix proportion;

[0240] 5. The degree of hydration of the slag is calculated by integrating formula (27) or by formulas (34) and (35). ;

[0241] 6. Determine the theoretical heat release from complete hydration of slag. This value is derived from existing research results;

[0242] 7. Calculate the total heat release of the silicate cement-slag system using formulas (23) to (25). ;

[0243] 8. The temperature field distribution of concrete is calculated using formula (41) to obtain the temperature prediction result.

[0244] The experimental verification process of the concrete temperature field prediction results is described below.

[0245] The mix design examples for mass concrete are shown in Table 10. Table 10 is as follows:

[0246] Table 10 Concrete Mix Proportions

[0247]

[0248] The experiment adopted Cement was used, and the fine aggregate was river sand with a particle size distribution of Zone II. The coarse aggregate was basalt aggregate with a continuous gradation of 5mm to 20mm. The specimen size was 1.5m × 1.5m × 0.8m. Temperature rise tests were conducted based on these parameters. According to the concrete composition, the required concrete parameters for predicting the temperature field of mass concrete are as follows: thermal conductivity of concrete. Specific heat capacity of concrete density of concrete Initial temperature inside concrete The temperature is 20℃.

[0249] In the experiment, the internal temperature rise of the concrete was measured using an SCT2002 intelligent temperature controller (temperature sensor). The temperature measurement resolution was 0.1℃, the maximum test range was -55℃ to 125℃, and the temperature acquisition interval was 1 hour / time. The prepared concrete specimens were placed in a 2 cm thick insulated foam box for thermal protection. The temperature sensor was placed at the center point (point A) and one-quarter of the way from the surface of the concrete specimen (point B). The ambient temperature was maintained at 20 ± 1℃. Data acquisition was stopped when the concrete temperature equalized with the ambient temperature.

[0250] Figure 5 This diagram illustrates the comparison between simulated and monitored temperatures at the center point and a quarter-thickness distance from the surface of a large-volume concrete specimen. As shown, after concrete pouring, the internal temperature of the concrete rises rapidly, reaching its peak within one day. Due to the thickness and poor thermal conductivity of the large-volume concrete, heat is concentrated inside the concrete, with the highest temperature at the center (56.7℃). With increasing hydration time, the temperature at the center point decreases to 35.2℃ after 3 days. When hydration reaches 7 days, the rate of heat dissipation exceeds the rate of heat generation, and the overall temperature of the concrete structure approaches the ambient temperature. The measured temperature (i.e., monitored temperature) is in good agreement with the simulated temperature. If the measured results are used as the benchmark, the maximum error between the two is 10.26%, indicating that the model is reasonable and has high predictive accuracy.

[0251] Figure 10 The temperature field distribution cloud maps of 1.5m × 1.5m concrete with hydration times of 1 day, 3 days, and 7 days are shown. (a) is the temperature cloud map for 1 day of hydration, (b) is for 3 days of hydration, and (c) is for 7 days of hydration. The cloud maps clearly show that the temperature is highest at the center of the concrete, gradually decreasing outwards. By day 7 of hydration, the temperature difference between the center and surface is close to the ambient temperature.

[0252] In summary, the technical solution provided in this embodiment proposes a hydration degree prediction model for silicate cement and a hydration degree model for slag based on the hydration kinetic mechanism of silicate cement. Furthermore, it establishes hydration heat prediction models for silicate cement systems and cement-slag systems under different conditions. Finally, based on solid conduction theory and the finite difference method, it predicts the evolution of the central temperature of large-volume concrete in the silicate cement-slag system. This solution eliminates the need for experimental determination in predicting the hydration heat of large-volume concrete in the cement-slag system; only parameters such as the concrete mix proportion, thermal conductivity, and specific heat capacity are required to obtain the predicted concrete temperature field. Experimental results show that this solution can accurately predict the hydration heat release process and adiabatic temperature rise of cementitious materials.

[0253] Based on the same inventive concept, this embodiment provides a system for predicting the heat of hydration and adiabatic temperature of concrete mixed with slag powder. This system is used to perform the steps of the method for predicting the heat of hydration and adiabatic temperature of concrete mixed with slag powder provided in any of the above embodiments, including:

[0254] The hydration heat prediction model construction unit is configured to express the total heat release of the silicate cement-slag system as the sum of the hydration heat release of silicate cement and the hydration heat release of slag, thus obtaining the silicate cement-slag hydration heat release prediction model.

[0255] The adiabatic temperature prediction unit is configured to multiply the total heat release of the silicate cement-slag system calculated by the silicate cement-slag hydration heat release prediction model by the amount of cementitious material used per cubic meter, and use it as the internal heat source term of the concrete heat conduction differential equation. The unit then uses the finite difference method to solve the concrete heat conduction differential equation to obtain the temperature field distribution of the concrete under adiabatic conditions.

[0256] The heat release from hydration of the silicate cement is calculated based on the degree of hydration of the silicate cement, which is predicted by a hydration degree prediction model. The hydration degree prediction model is based on the PK hydration kinetic model and comprehensively considers the effects of hydration time, water-cement ratio, specific surface area, relative humidity, and curing environment temperature on the hydration rate of silicate cement.

[0257] The heat release from slag hydration is calculated based on the degree of slag hydration. The degree of slag hydration is predicted by a slag hydration degree model, which comprehensively considers the effects of slag content, hydration time, water-cement ratio, specific surface area, and curing environment temperature on the slag hydration process.

[0258] The hydration heat and adiabatic temperature prediction system for concrete with slag powder provided in this embodiment can realize the steps and processes of the hydration heat and adiabatic temperature prediction method for concrete with slag powder provided in any of the above embodiments, and achieve the same technical effect, which will not be described in detail here.

[0259] The embodiments of this application can be applied to Figure 1 The computer device 200 shown may include one or more of the following components: a processor 201, a memory 203, a communication interface 202, and a communication bus 204. The memory 203 can be connected to the processor 201 via the bus 204. The bus can transmit data between the processor 201 and the memory 203. The bus may be an address bus, a data bus, a control bus, etc. The memory 203 stores a computer program, and the processor 201 executes the computer program to implement the steps of the method for predicting the heat of hydration and adiabatic temperature of concrete mixed with slag powder provided in any of the above embodiments.

Claims

1. A method for predicting the heat of hydration and adiabatic temperature of concrete mixed with slag powder, characterized in that, include: The total heat release of the silicate cement-slag system is expressed as the sum of the heat release from the hydration of silicate cement and the heat release from the hydration of slag, thus obtaining a prediction model for the heat release from the hydration of silicate cement-slag. The total heat release of the silicate cement-slag system calculated by the silicate cement-slag hydration heat release prediction model is multiplied by the amount of cementitious material used per cubic meter, and used as the internal heat source term in the concrete heat conduction differential equation. The finite difference method is then used to solve the concrete heat conduction differential equation to obtain the temperature field distribution of the concrete under adiabatic conditions. The heat release from hydration of the silicate cement is calculated based on the degree of hydration of the silicate cement, which is predicted by a hydration degree prediction model. The hydration degree prediction model is based on the PK hydration kinetic model and comprehensively considers the effects of hydration time, water-cement ratio, specific surface area, relative humidity, and curing environment temperature on the hydration rate of silicate cement. The heat release from slag hydration is calculated based on the degree of slag hydration. The degree of slag hydration is predicted by a slag hydration degree model, which comprehensively considers the effects of slag content, hydration time, water-cement ratio, specific surface area, and curing environment temperature on the slag hydration process.

2. The method according to claim 1, characterized in that, The hydration degree model of the slag is constructed based on the hydration kinetic mechanism, including: The hydration kinetics of slag is considered to be controlled by a diffusion reaction process. Based on the equation of diffusion reaction process in the hydration kinetics equation of silicate cement, the initial hydration kinetics equation of slag is written. The initial hydration kinetic equation of the slag is modified by introducing the maximum hydration degree of the slag to obtain the final slag hydration kinetic equation. The final slag hydration kinetic equation is then integrated to obtain the first slag hydration degree prediction model.

3. The method according to claim 2, characterized in that, The maximum degree of hydration of the slag is related to the slag activity index, and the effects of different water-cement ratios, hydration time, slag content, specific surface area, and curing temperature on the hydration process are comprehensively considered.

4. The method according to claim 3, characterized in that, The expression for the maximum degree of hydration of the slag is as follows: ， The final equation for the slag hydration kinetics is expressed as follows: ， In the formula, This represents the maximum degree of hydration of the slag. The activity index of slag; This refers to the water-to-binder ratio; This refers to the amount of slag added. The specific surface area of ​​the slag; This is a reference value for the specific surface area of ​​slag. The apparent activation energy of slag; This is the universal gas constant; Reference temperature; To maintain the ambient temperature; The degree of slag hydration; This is the reaction rate constant for the slag diffusion reaction process, which is related to the water-cement ratio and the slag content. This refers to the hydration time.

5. The method according to claim 1, characterized in that, The method further includes: obtaining a hydration degree model of slag through surface fitting based on the statistical results of experimental data from different existing studies, as detailed below: Obtain the test results of different researchers on the non-evaporation water content of the silicate cement-slag system and the corresponding test conditions; Based on the expression for the non-evaporating water content of the silicate cement-slag system, a preliminary expression for the degree of slag hydration is determined; wherein, the non-evaporating water content of the silicate cement-slag system is expressed as the sum of the non-evaporating water content of silicate cement and the non-evaporating water content of slag; Substituting the test results of different researchers on the non-evaporation water content of the silicate cement-slag system into the preliminary expression of the slag hydration degree, the slag hydration degree under different test conditions was calculated. The degree of slag hydration under different test conditions is fitted with a surface to obtain the surface-fitted expression for the degree of slag hydration; the surface-fitted expression for the degree of slag hydration is used to characterize the change law of the degree of slag hydration with hydration time under different water-cement ratios. Taking into account the effects of effective water-cement ratio, hydration time, slag content, specific surface area and curing environment temperature on the slag hydration process, the slag hydration degree expression of the surface fitting is modified to obtain the second slag hydration degree prediction model. The effective water-cement ratio is adjusted by using the slag activity index to determine the effective contribution of the slag.

6. The method according to claim 5, characterized in that, The expression for the second slag hydration degree prediction model is as follows: ， In the formula, Hydration time; The degree of hydration of the slag; The activity index of slag; This refers to the amount of slag added. For an effective water-cement ratio; The specific surface area of ​​the slag; This is a reference value for the specific surface area of ​​slag. The apparent activation energy of slag; This is the universal gas constant; Reference temperature; To maintain the ambient temperature.

7. The method according to claim 3 or 5, characterized in that, The slag activity index takes into account the influence of two different forms of Al2O3 in the chemical composition of slag, namely tetracoordinate and hexacoordinate, on the slag activity.

8. The method according to claim 1, characterized in that, The finite difference method is used to solve the differential equation for heat conduction in concrete, yielding the temperature field distribution of concrete under adiabatic conditions, including: Divide the concrete section into two-dimensional meshes; Initial conditions and adiabatic boundary conditions are set, and the temperature of each node at each time moment is calculated in two-dimensional space using the finite difference method to obtain the predicted adiabatic temperature of concrete with slag powder. The types of nodes include: internal nodes, boundary nodes, and corner nodes.

9. A system for predicting the heat of hydration and adiabatic temperature of concrete mixed with slag powder, the system being used to perform the steps of the method for predicting the heat of hydration and adiabatic temperature of concrete mixed with slag powder according to any one of claims 1 to 8, comprising: The hydration heat prediction model construction unit is configured to express the total heat release of the silicate cement-slag system as the sum of the hydration heat release of silicate cement and the hydration heat release of slag, thus obtaining the silicate cement-slag hydration heat release prediction model. The adiabatic temperature prediction unit is configured to multiply the total heat release of the silicate cement-slag system calculated by the silicate cement-slag hydration heat release prediction model by the amount of cementitious material used per cubic meter, and use it as the internal heat source term of the concrete heat conduction differential equation. The unit then uses the finite difference method to solve the concrete heat conduction differential equation to obtain the temperature field distribution of the concrete under adiabatic conditions. The heat release from hydration of the silicate cement is calculated based on the degree of hydration of the silicate cement, which is predicted by a hydration degree prediction model. The hydration degree prediction model is based on the PK hydration kinetic model and comprehensively considers the effects of hydration time, water-cement ratio, specific surface area, relative humidity, and curing environment temperature on the hydration rate of silicate cement. The heat release from slag hydration is calculated based on the degree of slag hydration. The degree of slag hydration is predicted by a slag hydration degree model, which comprehensively considers the effects of slag content, hydration time, water-cement ratio, specific surface area, and curing environment temperature on the slag hydration process.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method for predicting the heat of hydration and adiabatic temperature of concrete with slag powder as described in any one of claims 1 to 8.

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