Study on Hydration Heat Release Model and Its Influence Coefficient of Addition Concrete

Abstract

The concrete of the main structure of subway stations is highly constrained, so the temperature effect and shrinkage effect generated during the construction process often cause large restraint stress, thus causing the problem of structural cracking. Therefore, low-heat-of-hydration cements are usually used in such construction work to reduce the temperature during the aging of concrete. Therefore, based on the hydration heat release subprogram of concrete, an effective numerical simulation was carried out, and compared with the semi-adiabatic temperature rise test, a method of numerical calculation and parameter fitting to solve the influence coefficient of the hydration heat model was proposed, and the sensitivity of the hydration heat release model and the influence coefficient for several concrete mixtures with additives was studied. The main conclusions are as follows: (1) Combined with the measured temperature curves of several types of mineral-admixed concrete, the composite exponential exothermic model of several types of mineral-admixed concrete can be obtained by adjusting the parameter fitting to solve the influence coefficient of the exothermic hydration model proposed in this paper. (2) One can adjust the influencing coefficient a to control the maximum temperature of concrete. Similarly, the temperature curve of concrete can be adjusted by modifying the influencing coefficient b.

1. Introduction

China’s economy and urban rail transportation infrastructure are growing in tandem and at a nearly equal and rapid rate. Simultaneously, the subway stations are also getting bigger, more practical, and safer [1]. As a crucial link in the process of urban railroad construction, the environmental protection and structural safety issues arising at metro station construction sites need to be given serious consideration. The concrete of the main structure of the subway station is highly constrained, so the temperature effect [2] and shrinkage effect [3] generated during the construction process often cause large constraint stress, which leads to the problem of structural cracking. It is generally believed that the early constraint stress of concrete mainly includes two types, namely, the temperature stress caused by the temperature change of concrete and the shrinkage stress induced by the shrinkage of concrete [4]. The temperature restraining stresses mainly include two types. The temperature confining stress has two components, viz., (1) the self-confining stress generated by the temperature gradient between the surface and the interior of the structure, and (2) the external confining stress generated by the constraints of neighboring members and the substrate in the process of the cooling and shrinkage of the structure. Extensive research has already been completed on the cracking factors and crack generation mechanism of concrete, and hereunder a detailed review of the current status of such research is presented. Pettersson [5] investigated the crack development caused by different types of concrete structures under different boundary conditions, and concluded that there exists a relatively significant influence of the boundary conditions on the length and size of cracks due to temperature stresses, etc. Muneer K. Saeed [6] conducted heat generation experiments on mass concrete specimens and measured the temperature distribution at the center and both sides of the specimens. Subsequently, numerical simulations were used to investigate the influence of the specimen size, concrete placement temperature, ambient temperature, solar radiation, and formwork type on the temperature rise and associated cracking potential of mass concrete specimens. Visagie J. Wdeng [7] investigated the effect of surface curing time on the plastic cracking of concrete, and the results established that curing time has an important effect on the cracking of the concrete surface; longer curing times lead to less cracking on the concrete surface. Nikolay Aniskin [8] predicted the temperature field and thermal stresses of concrete structures under particular construction conditions, assessed the risk of thermal cracking in concrete structures under various construction conditions, and compared them with the criteria used in actual construction practice. Substantial research on the subject has been completed indigenously as well, and a detailed review of such works follows hereunder. Yue Zhuwen [9] analyzed the heat of hydration of a mass concrete footing using Midas finite element analysis software (https://product.midasit.cn/index, accessed on 3 March 2024), and the results showed that during the hydration process the tensile stress alternately affected the inner and outer concrete leading to cracks. After the on-site monitoring and numerical simulation calculations, Zhang Wenbo [10] concluded that mass concrete is prone to temperature cracks owing to the trapping of the heat of hydration within its interior in the initial stages, thereby producing a steep temperature gradient between the interior and exterior surfaces; they proposed the use of a fly-ash mineral admixture as a means to reduce the heat of hydration. Taking the Nanchang Rail Transit Line 2 station as an example, Zhan Jianjun [11] used the BP neural network method to determine the mean influence volume (MIV) of each factor on the concrete cracking on the side wall; the MIV-BP neural network model was established to validate the effect of the influence of each factor on the concrete cracking on the side wall. Gan Mingwei [12] applied the ABAQUS subroutine to a four-scale concrete multiscale model to obtain parameters such as the modulus of elasticity and strength of early concrete and evaluated the cracking of mass concrete based on the stress-strength ratio.

In summary, clarifying the heat of hydration model of concrete is crucial for studying the temperature–stress characteristics of concrete. To accomplish this, an effective numerical simulation has been carried out based on the hydration exothermic subroutine of concrete and compared with the semi-adiabatic temperature rise test for validation. Further, a method of numerical computation of tuned-parameter fitting to solve the influence coefficients of the heat of hydration model has been investigated to carry out a sensitivity study of the hydration exothermic model of several types of multi-admixed mineral-admixture concretes and their influence coefficients.

2. Concrete Hydration Exothermic Model and Its Finite Element Analysis Method

To optimize the semi-adiabatic temperature rise test using numerical simulation analysis and to solve the adiabatic temperature rise model of concrete, it is necessary to scientifically and reasonably conduct finite element analysis of the exothermic process of concrete. To accomplish this purpose, it is necessary to gain a clear understanding of the hydration exothermic principle of concrete, select a reasonable hydration exothermic model, and implement it in ABAQUS 2021 finite element analysis software.

2.1. Introduction to Exothermic Modeling of Concrete Hydration

Currently, three types of exothermic concrete hydration models are commonly used in engineering research: mono-exponential, hyperbolic, and composite exponential models. In this section, these three exothermic hydration models are briefly introduced, and the related calculation formulas and parameters are provided to compare and select the most suitable calculation model.

• Mono-exponential model

The mono-exponential model was proposed by the U.S. Bureau of Reclamation, and use of the exponential function can be more accurate and better suits the requirements of the adiabatic temperature-rise model in engineering. However, the formula has only one variable parameter; therefore, its accuracy may be reduced when calculating the heat of hydration of different types of concrete. The formula is expressed as follows:

$$Q(t)=Q_0(1-e^{mt})$$

(1)

where Q(t) is the total amount of heat of hydration released when the age of the concrete is t (kJ/kg); Q₀ is the maximum value of concrete hydration heat release; t is the age of the concrete; and m is the specific calculation parameter, which is specific for the type of cement.

2.

Hyperbolic model

The hyperbolic model proposed by Cai Zhengyuan [13] introduces the concept of half-age when the concrete hydration exotherm is half so that the model is closer to reality. However, before applying the model for any specific application, it is necessary to know in advance the age the concrete will be when it reaches half of the total amount of exotherm. Thus, there are some limitations to the application of this formula. The specific model calculation formula is expressed as follows:

$$Q(t)=\frac{Q_{0}t}{n+t}$$

(2)

where n is the age at which half of the total exothermic heat is reached; corresponding to the setting of n, the values of other parameters are determined according to the following expressions: when t = 0, Q(t) = 0; when t = n, Q(t) = Q₀/2; and when t = ∞, Q(t) = Q₀.

3.

Composite exponential model

The composite exponential model was proposed by Zhu Bofang [14], an academic at the Academy of Engineering, China. The formula is optimized for the single exponential model and two parameters are introduced to the age t for calculation, which greatly improves the accuracy of the model and can be applied to various types of high-performance concrete. The specific model calculation formula is expressed as follows:

$$Q(t)=Q_0\left(1-e^{-a{t}^b}\right)$$

(3)

where a and b are the model influence coefficients related to the type of cementitious material involved in the hydration reaction. The specific values are listed in

Table 1. Composite exponential model coefficients corresponding to different cement grades.

Cement Varieties	Q0	a	b
CEM I 42.5 CHN	330	0.69	0.56
CEM I 52.5 CHN	350	0.36	0.74
CEM II/A 42.5 CHN	270	0.79	0.70
CEM II/A 52.5 CHN	285	0.29	0.76

Note: The values in the table refer to research by Zhu Bofang [14].

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4.

Selection of hydration exothermic models

From the foregoing discussion on the three hydration exothermic models, it is evident that the composite exponential model is the best hydration exothermic model with the best calculation accuracy and applicability. Therefore, the subsequent calculations are based on the composite exponential model, which has three main parameters, i.e., Q₀, a, and b. Among them, the availability of information on the influence of coefficients a and b is relatively low, especially for different multi-mixed additions of concrete, and there is a lack of relevant experimental support data as well. For the Q₀ of different additions, the value can be obtained empirically according to the value method in GB 50496-2018 [15], and the calculation formula is as follows:

$$Q_g=k·Q_0$$

(4)

where Q_g is the total exothermic hydration of concrete with multiple additions, Q₀ is the total exothermic hydration of OPC with the same content, and k is the adjustment coefficient of the exothermic hydration of different additions. The coefficient k is expressed using the following formula:

k = k₁·k₂·k₃·k₄

(5)

where k₁, k₂, k₃, and k₄ are the corresponding hydration heat adjustment coefficients of fly-ash, slag, limestone powder, and metakaolin, respectively. These values are listed in

Table 2. Adjustment factor for heat of hydration corresponding to different additions.

Mineral Admixture	0	10%	20%	30%	40%
Fly-ash (k1)	1	0.96	0.95	0.93	0.82
Slag (k2)	1	1	0.93	0.92	0.84
Limestone powder (k3)	1	0.95	0.90	0.85	0.80
Metakaolin (k4)	1	1	0.97	0.95	0.90

Note: The values in the table refer to the GB/T 51028-2015 [16].

, below:

2.2. Finite Element Analysis Method for Exothermic Hydration of Concrete

In this study, ABAQUS 2021 was used with the HETVAL subroutine for heat generation analysis. The analysis of the hydration exothermic temperature field of concrete is equivalent to adding a heat source inside which varies with concrete age. Because there is no direct function in ABAQUS to simulate a time-varying heat source, it is necessary to borrow the HETVAL subroutine to realize the time-varying heat source function and couple it with the calculation of the concrete temperature field. The exothermic hydration curve is complex, and a simplified empirical fitting expression is generally used in engineering. In this study, a composite exponential exothermic model is used to calculate the temperature field. To realize the hydration exotherm of concrete in the HETVAL subroutine, it is necessary to first set the exothermic rate FLUX(1) of the heat source in the subroutine. FLUX(1) is derived from Equation (6) as follows:

$$\mathrm{F}\mathrm{L}\mathrm{U}\mathrm{X}(1)=q_v=\frac{ab{Q}_0}{24}{\left(\frac{t}{24}\right)}^{b-1}{e}^{-a{\left(\frac{t}{24}\right)}^b}$$

(6)

where q_v is the heat source exothermic rate, Q₀ is the maximum value of the concrete hydration exothermic rate, and a and b are exothermic model parameters.

The Fortran language is used in the subroutine to write the above equation such that FLUX(1) is equal to q_v. The statev result state variable is used to store it so that it is convenient to view the output during postprocessing. The HETVAL subroutine is used to provide the heat source for the heat transfer analysis model, which varies with time such that time t in q_v is defined as the age of the concrete, and time(2) is entered as the total time at the end of the increment. Time(2) is the input and time(2) is the total time at the end of the increment. Using this finite element analysis method for the exothermic hydration of concrete, the temperature fields of different concrete structures at different ages can be obtained.

3. Numerical Calculation Model and Its Accuracy Verification

The traditional semi-adiabatic temperature rise test does not specify properties such as the thickness and type of the insulation material and the size of the concrete specimen block. However, to carry out the semi-adiabatic temperature rise test in an economical and reasonable manner, the test needs to be optimized and improved to determine the specific test plan. Therefore, the finite element analysis method of the hydration exotherm described in Section 2.2 is used in this section to change the test conditions, simulate the exothermic process of the concrete test blocks, and study the hydration heat model of mineral-adulterated concrete.

3.1. Numerical Calculation Model

Based on the ABAQUS numerical calculation and analysis program, a three-dimensional model diagram of the semi-adiabatic temperature-rise test device was established, as shown in Figure 1. It comprised an insulation layer and a concrete test block, with the individual components demarcated by discretizing the geometric units. The concrete test block was initially set up as a cube with 20 cm sides that was completely wrapped by a layer of insulation, thereby forming a box like cover. The different heat transfer modes existing in the semi-adiabatic temperature rise test are considered in the finite element software as follows: (1) Thermal conduction behavior: This occurs within the concrete specimen block, within the thermal insulation material, and between the concrete specimen block and the thermal insulation material. This is realized by setting the thermal conduction coefficients of the materials in the property module. (2) Thermal convection behavior: this occurs on the surface of the insulation layer that is exposed to the ambient air and realized by setting the heat dissipation coefficient of the membrane layer in the contact module. (3) Thermal radiation behavior: This occurs in the process of thermal radiation exchange between the entire semi-adiabatic warming device and the external environment. This is realized by setting the emissivity property in the contact module, in addition to defining the magnitude of absolute zero and the Stefan–Boltzmann constant.

3.2. Semi-Adiabatic Temperature Rise Test

The semi-adiabatic test device comprises a concrete mold and an insulation box. The interior of the insulation box with internal dimensions 31 cm × 31 cm × 31 cm is lined with a 10-cm-thick polyurethane composite insulation board. Inside this arrangement, an internal concrete mold box with 21 cm × 21 cm × 21 cm sides with 1 cm thick polypropylene-sheet liner is set such that there is clear 20 cm × 20 cm × 20 cm internal space. For the accurate measurement of the core temperature of the concrete specimen block, temperature sensors with accuracies of ±0.25 °C are embedded in the core part of the concrete specimen block during testing. An integrated test system is used to monitor the temperature change of the concrete continuously and automatically store the temperature data of the concrete specimen. The time interval setting for the temperature measurement command is set to 20 min. The test setup and arrangement of the monitoring instruments (CHN) are illustrated in Figure 2.

In large-volume concrete projects, additions are generally used to replace 20–70% of the cement [17], so in order to explore the influence of different additions on the temperature rise characteristics of concrete, the additions in this test are set to replace 40% of the cement. The concrete test block adopts the material ratio of common C40 concrete. Fly ash is a mineral admixture commonly used to reduce the heat of hydration in engineering [18]. The test was based on fly-ash, and the three remaining additive materials, viz., blast-furnace slag, limestone powder, and metakaolin, were added in various combinations. Different concrete specimens with double, triple, and quadruple additions were cast and the semi-adiabatic temperature rise tests were conducted separately for each specimen. The marking scheme for the specimens is as follows: F (fly-ash), S (blast-furnace slag), L (limestone powder), and K (kaolin); the number after the letter represents the percentage of cement replacement. For example, F20S20L0K0 indicates a concrete test-specimen block with 20% fly-ash and 20% blast-furnace slag, and the specific coordinates of all the test specimen blocks are listed in

Table 3. Concrete mixing ratios for multiple additions.

Serial Number	Cement (kg)	Fly-Ash (kg)	BF Slag (kg)	Limestone Powder (kg)	Metakaolin (kg)	Medium Sand (kg)	Coarse Aggregates (Stone) (kg)	Water (kg)	Superplasticizer (kg)	Volume (m3)
F0S0L0K0	420.0	0.0	0.0	0.0	0.0	745.0	1117.0	168.0	2.5	0.008
F20S20L0K0	252.0	84.1	84.1	0.0	0.0	745.0	1117.0	168.0	2.5	0.008
F20S0L20K0	252.0	84.1	0.0	84. 1	0.0	745.0	1117.0	168.0	2.5	0.008
F20S0L0K20	252.0	84.1	0.0	0.0	84.1	745.0	1117.0	168.0	2.5	0.008
F15S12.5L12.5K0	252.0	63.0	52.5	52.5	0.0	745.0	1117.0	168.0	2.5	0.008
F15S12.5L0K12.5	252.0	63.0	52.5	0.0	52.5	745.0	1117.0	168.0	2.5	0.008
F15S0L12.5K12.5	252.0	63.0	0.0	52.5	52.5	745.0	1117.0	168.0	2.5	0.008
F10S10L10K10	252.0	42.0	42.0	42.0	42.0	745.0	1117.0	168.0	2.5	0.008

Note: The mass values (in kg) in the table correspond to a specific volume of 0.008 m³.

.

Conduct of the semi-adiabatic temperature-rise test involved the following six steps: (1) Assembly of the customized polyurethane-lined insulation box and polypropylene concrete mold. (2) Accurate measurement of the ingredients according to the design ratios of different concrete test specimens and adequate mixing according to the mixing procedure and the test criteria. (3) The prepared concrete mix was poured into the polypropylene concrete mold and vibrated sufficiently. (4) Temperature sensors were embedded in the cores of the concrete specimens at predetermined intermediate locations. (5) Place the concrete specimens together with the mold in the preset insulated box and seal it. (6) The real-time monitoring system was connected to the monitoring system and the temperature data were extracted every 20 min. The concrete specimens were continuously monitored for a period of approximately seven days, and the semi-adiabatic temperature-rise curve of the concrete specimens during the aging period was obtained.

3.3. Validation of the Accuracy of the Numerical Method

Combined with the above finite element analysis method, the exothermic analysis of the F0S0L0K0 specimen (using OPC 425), based on the data presented in Table 1, permits the direct adjustment of exothermic model coefficients within the subroutine as follows: Q₀ = 330 kJ/kg, a = 0.69, and b = 0.56. The measured and simulated temperature curves of the specimens after the simulation are shown in Figure 3. From the figure, it can be observed that the trends of the measured and simulated curves are nearly the same and the extent of difference is insignificant. Moreover, the maximum temperature difference is only 0.5 °C. To reduce the error value, the optimization of the simulation was performed as follows: (1) the thermal conductivity of the insulation layer was adjusted to eliminate the effect of the gap between the test concrete specimen and the insulation layer; (2) the simulation of the beginning of the aging and the accelerated rate of temperature rise was changed from the beginning of the calculation period to eliminate the effect of the induction period. After continuous debugging, the thermal conductivity of the insulation layer was adjusted to 0.045 W/m·K, and the starting age of the exothermic simulation was adjusted to 6 h; other parameters remained unchanged. Calculations were carried out and the optimized simulation curve was obtained for comparison with the measured curve, as shown in Figure 4. As can be seen from the figure, the simulation value and the measured value curves are in good agreement after adjustments, and the overall deviation of the two curves is within 5%, greatly improving the simulation accuracy. Therefore, the adjusted model parameters were chosen as the basis for subsequent analysis.

4. Modeling of Heat of Hydration of Mineral Admixture Concrete

4.1. Sensitivity Analysis of Impact Coefficients of Hydration Exotherm Models

To fit the composite exponential hydration exothermic model by adjusting the influence coefficient, it is necessary to carry out a sensitivity analysis of the influence coefficient of the composite exponential hydration exothermic model. As shown in Figure 5, the influence coefficient a was set to 0.49, 0.69, and 0.89 and the temperature curves show the corresponding changes. It is evident that the smaller the influence coefficient a, the lower the maximum temperature that can be reached and the lower the temperature change. However, there is no significant change in the effect of the influence coefficient a on the time it takes for concrete to reach the maximum temperature. Accordingly, it is clear that the maximum temperature of the concrete can be adjusted by adjusting the influence coefficient, a.

Similarly, the changes to the temperature curves when the influence coefficients b were set to 0.56, 0.96, and 1.36 are shown in Figure 6. It is evident that the smaller the influence coefficient b, the lower the maximum temperature that can be reached. Moreover, when the influence coefficient b is smaller, it takes less time to reach the maximum temperature; thus, the time to attain the maximum temperature can be fine-tuned through the adjustment of the influence coefficient b. It is also worth noting here, the higher the influence coefficient b, the steeper the temperature curve, and the smaller the influence coefficient b, the shallower the temperature curve becomes.

4.2. Data Fitting to Solve the Hydration Exothermic Model for Impact Coefficients

The temperature curves of the concrete test block mixed with two additions and the conventional concrete test block were obtained, as shown in Figure 7. It can be seen from the figure that the maximum temperature of the core part of the concrete decreases significantly after the two additions, which indicates that different combinations of double additions have a certain effect on reducing the temperature of the concrete during aging. Different combinations of double-doped additions have different effects on the temperature of concrete.

According to the experimental analysis, F20S0L20K0 is the concrete specimen with the lowest heat release. Therefore, taking F20S0L20K0 as an example, the above finite element analysis method of the hydration exotherm was used to continuously adjust the influence coefficients a and b of the composite exponential hydration exotherm model in the subroutine. The iterative adjustment of the coefficients was performed such that the temperature curve of the model is constantly in good alignment with the measured temperature curve of F20S0L20K0, and thus, the hydration exotherm model of F20S0L20K0 evolved.

Table 4. Heat of hydration of concrete with different additions.

Specimen Number	Heat of Hydration Adjustment Factor k	Total Exothermic Hydration Q0 (kJ/kg)	Specimen Number	Heat of Hydration Adjustment Factor k	Total Exothermic Hydration Q0 (kJ/kg)
F0S0L0K0	1	330.0	F15S12.5L12.5K0	0.87	287.0
F20S20L0K0	0.88	290.4	F15S0L12.5K12.5	0.92	303.6
F20S0L20K0	0.82	270.5	F15S12.5L0K12.5	0.95	313.5
F20S0L0K20	0.92	303.6	F10S10L10K10	0.91	300.3

shows the adjustment coefficients of the heat of hydration and the total amount of heat of hydration of concrete with different additions according to Equation (5). Total heat of hydration (Q₀) of F20S0L20K0 is 270.5 kJ/kg.

Figure 8 shows the process of fitting the influence coefficient of the composite exponential hydration exothermic model of F20S0L20K0. Initially, the model impact coefficients a and b are set to the same impact coefficients as in the F0S0L0K0 model, and Q₀ is set to 270.5 kJ/kg. Post simulation curves are presented in Figure 8a, and it can be observed that the simulated values have deviated away from the measured value, and there is a need to “squash” the simulated curves. According to the sensitivity analysis law, the values of the impact coefficients a and b are adjusted to 0.59 and 0.66, respectively, and the numerical simulations are repeated. From Figure 8b it can be observed that the simulation curve is in close alignment with the measured curve. The influence coefficients a and b are repeatedly adjusted so that the simulation curve and the measured curve gradually approach the final curve, as shown in Figure 8f, at which point both curves nearly overlap. This approximates the composite exponential hydration exothermic model for F20S0L20K0 with influence coefficients a and b equal to 0.52 and 0.62, respectively. Therefore, the hydration exothermic model for F20S0L20K0 can be expressed as follows: $Q(t)=270.5-\left(1-e^{-0.52t^{0.62}}\right)$.

Combined with the measured temperature curves of several other types of mineral admixture concrete and using the above method of tuning parameter fitting to solve the influence coefficient of the hydration exothermic model, simulations and analyses were performed to obtain the composite exponential hydration exothermic model of several other types of mineral admixture concrete, as listed in

Table 5. Exothermic model of hydration of concrete with different additions.

Specimen Number	Composite Exponential Hydration Exothermic Model	Specimen Number	Composite Exponential Hydration Exothermic Model
F0S0L0K0	$Q(t)=330.0-\left(1-e^{-0.69t^{0.56}}\right)$	F15S12.5L12.5K0	$Q(t)=287.0-\left(1-e^{-0.50t^{0.75}}\right)$
F20S20L0K0	$Q(t)=290.4-\left(1-e^{-0.59t^{0.66}}\right)$	F15S0L12.5K12.5	$Q(t)=303.6-\left(1-e^{-0.72t^{0.54}}\right)$
F20S0L20K0	$Q(t)=270.5-\left(1-e^{-0.52t^{0.62}}\right)$	F15S12.5L0K12.5	$Q(t)=313.5-\left(1-e^{-0.70t^{0.53}}\right)$
F20S0L0K20	$Q(t)=303.6-\left(1-e^{-0.70t^{0.58}}\right)$	F10S10L10K10	$Q(t)=300.3-\left(1-e^{-0.69t^{0.51}}\right)$

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5. Conclusions

With the aim of developing a hydration heat model for concrete with different additions and their influence coefficient, the hydration exothermic subroutine of concrete was used to carry out an effective numerical simulation. The results were compared with a semi-adiabatic temperature rise test to verify the method of numerical calculation by parameter fitting. To optimize the influence coefficient of the hydration heat model, it was proposed to determine the hydration exothermic model of several types of concrete with additions and test the sensitivity of their influence coefficients. The following is a summary of the outcomes and corresponding findings:

(1)

The smaller the influence coefficient a, the smaller the maximum temperature that can be reached, and the smaller the temperature change. However, there is no significant change in the effect of the influence coefficient a on the time it takes for concrete to reach the maximum temperature. Therefore, the maximum temperature of the concrete can be controlled by adjusting the influence coefficient a.

(2)

The smaller the influence coefficient b, the lower the maximum temperature that can be reached and the shorter is the time required to reach the maximum temperature. Therefore, the temperature profile of concrete can be adjusted by adjusting the influence coefficient b. The larger the influence coefficient b is, the “steeper” the temperature profile will be, and the smaller the influence coefficient b is, the more “shallow” the temperature profile will be.

(3)

Combined with the measured temperature curves of several types of mineral-adulterated concrete, a composite exponential hydration exothermic model of several types of mineral-adulterated concrete was obtained by simulation and analysis using the tuning parameter fitting method to solve the influence coefficient of the proposed hydration exothermic model.