An Integrated Hydration and Property Evaluation Model for Coral Powder–Cement Binary Blends

Abstract

With the rise in the marine industry and marine tourism, coral powder is increasingly used to make concrete for marine islands. This study proposes a three-parameter hydration model and a hydration kinetic model to predict the performance of coral powder concrete based on previous experimental data. The process of the proposed prediction model is as follows: 1. The input parameters of the three-parameter hydration model are calibrated for the first 7 days using the cumulative hydration heat per gram of cement. The maximum cumulative hydration heat (455.87 J/g cement) and the shape coefficient (−0.87) remain constant. In this study, the hydration rate coefficients for 0%, 10%, and 20% coral powder were 6.91, 6.19, and 5.55, respectively, showing decreases of 10.41% and 19.68% compared with the specimens without coral powder. 2. At 28 days, the cumulative heat release values per gram of cement for 0%, 10%, and 20% coral powder were 389.77, 395.69, and 401.62 J/g, showing increases of 1.52% and 3.04% for the specimens containing 10% and 20% coral powder, respectively. Meanwhile, the hydration degrees for 0%, 10%, and 20% coral powder were 0.855, 0.868, and 0.881, respectively, showing increases of 1.52% and 3.04%. Furthermore, the cumulative heat release values per gram of binder were 389.77, 356.12, and 321.29 J/g, showing decreases of 8.63% and 17.56% for specimens containing 10% and 20% coral powder, respectively. 3. Properties such as compressive strength, ultrasonic pulse velocity (UPV), and surface electrical resistivity were evaluated using the power function and the cumulative hydration heat per gram of binder. 4. At 28 days, the chemically bound water contents for samples with 0%, 10%, and 20% coral powder were 0.2402, 0.2197, and 0.1981 g/g binder, respectively. Moreover, the calcium hydroxide contents were 0.1848, 0.1690, and 0.1524 g/g binder, showing reductions of 8.53% and 17.52% in bound water and 8.54% and 17.53% in calcium hydroxide. 5. A hydration kinetic model is proposed, which can distinguish between the dilution effect and the nucleation effect of coral powder, unlike the three-parameter model, which cannot distinguish between the two effects. Furthermore, the input parameters of the hydration kinetic model remain unchanged for different mixtures, while the input parameters of the three-parameter model must be varied among mixtures. Parameter analysis of the hydration kinetic model indicated that a low water–binder ratio and a high coral powder substitution rate significantly improve the relative reaction level of cement.

1. Introduction

As marine tourism and the marine industry advance, the use of concrete for constructing island buildings and infrastructure is increasing. Given the associated transportation expenses, using local materials for concrete structures on islands is a recommended practice to lower both material and overall construction costs [1]. Coral, a common ocean organism, primarily consists of calcium carbonate. When ground into powder, coral can partially replace cement, thereby reducing the costs of island concrete, enhancing its performance, and improving its environmental sustainability.

To date, experimental and theoretical studies on coral powder concrete have been limited. Building on these studies, this study aimed to develop a hydration model for coral powder concrete. Given that the primary component of coral powder is calcium carbonate, the following literature review focuses mainly on theoretical prediction models for calcium carbonate concrete. Poppe and Schutter [2,3] measured the hydration heat of calcium carbonate concrete and examined the accelerating effect of calcium carbonate on the cement’s hydration heat. Based on the isothermal–exothermic hydration heat curve, they proposed a hydration model for calcium carbonate concrete, considering the replacement amount of calcium carbonate and the type of cement. The activation energy of the hydration reaction was derived from regression analysis, allowing the prediction of the concrete’s adiabatic temperature rise curve. Bentz [4] introduced a hydration model that accounted for the spatial distribution of hydration products, applicable to different water–binder ratios and varying amounts of limestone filler. Bentz et al. [5] utilized Powers’ hydration model, treating calcium carbonate powder as a chemically inert filler. They calculated the product’s composition and the strength development of concrete, discovering that using limestone powder in concrete with a low water–binder ratio mitigates the strength loss caused by the addition of limestone powder. Maekawa et al. [6] found that limestone powder accelerates the cement hydration reaction, particularly during the phase boundary reaction period and the diffusion period. By adjusting the cement hydration model’s parameters, they incorporated the acceleration effect of limestone powder. Ye et al. [7] proposed a microscopic pore development model for limestone powder concrete and validated the hydration model through cumulative hydration heat experiments, pore size distribution experiments, and hydration product analysis. Ouyang et al. [8] analyzed the hydration and lattice models of filler-blended concrete, finding that limestone powder exhibited a better bonding performance than quartz powder, potentially because of electrostatic interactions or ionocovalent forces. The hydration model proposed by Lothenbach et al. [9] and Lothenbach and Zajac [10] included the chemical reaction of limestone powder. They simulated the reaction between limestone powder and the aluminum phase in cementitious materials, resulting in the formation of carbonaluminate. The concentrations of various ions in the pore solution were then calculated using the thermodynamic equilibrium method.

When conducting this literature review, several shortcomings in previous studies can be identified. First, calcium carbonate exists in three crystalline forms: calcite, aragonite, and vaterite. Calcite is the most stable form, but in marine organisms such as coral, calcium carbonate predominantly appears as aragonite [11]. Although both aragonite and calcite share calcium carbonate as their main chemical component, their crystal structures differ [11]. Research on aragonite, compared with calcite, is very limited, particularly for the hydration model of aragonite. Second, previously proposed hydration models require numerous input parameters, adding to their complexity and limiting their practical application [3,6,11]. Simpler models with comprehensive functions are more practical and desirable. Third, earlier models primarily focused on general experimental results, such as compressive strength, hydration heat, and hydration product content [6], for predicting concrete properties. Recently, non-destructive testing methods such as ultrasonic pulse velocity and surface electrical resistivity have gained popularity [1]. There is a need for further research on using hydration models to predict non-destructive testing results.

To address the gaps in previous research, this paper proposes a comprehensive hydration model and a performance prediction model for coral powder concrete. The hydration model is straightforward, requiring only three input parameters. It predicts both general test results and non-destructive testing results for concrete, such as its strength, hydration heat, chemically bound water content, calcium hydroxide content, ultrasonic pulse velocity, and surface electrical resistivity. Additionally, based on this three-parameter hydration model, this study introduces a hydration kinetic model. The input parameters of this kinetic model remain constant regardless of changes in the concrete mixing ratio. The influence of coral powder on the relative reaction level of cement is elucidated through parameter analysis.

The novelties of this study can be summarized as follows: First, the focus on simulations in this study is unique. Previous studies have primarily examined concrete containing limestone powder, which is mainly composed of calcite, while the main component of coral powder is aragonite. Second, the simulation method employed in this study is innovative. To address the limitations of the three-parameter hydration model, a new hydration kinetic model is proposed to simulate the hydration reaction of cement–coral powder binary concrete. The three-parameter hydration model and the hydration kinetic model complement each other effectively. Finally, the proposed hydration kinetic model not only predicts experimental results but also facilitates parameter analysis, uncovers new trends in these experimental data, and supports the design of coral powder concrete.

This study was a theoretical research project focused on the development of a hydration model rather than an experimental one. This paper is structured as follows: Section 1 is the introduction, concluding here, which has reviewed previous hydration models of calcium carbonate concrete and proven the necessity of studying the hydration model of coral powder concrete. Section 2 presents experimental details from previous research [1] and introduces a three-parameter hydration model. Section 3 proposes a hydration kinetic model, showcasing prediction results and parameter studies using this model. Section 4 discusses both the three-parameter hydration model and the hydration kinetic model, elucidating their connections and differences. Finally, Section 5 offers the conclusions and summarizes the key findings of this study.

2. Development of Hydration Model and Prediction of Concrete Properties

2.1. Materials and Methods

The experimental results used in this study were taken from previous research [1], which focused on materials based on coral powder cement. The cement used was Portland cement, and the coral powder was primarily composed of aragonite (calcium carbonate). In engineering practice, to avoid excessive strength losses, the maximum replacement amount of limestone powder is typically 20%. Given that the main chemical component in coral powder is calcium carbonate, its maximum substitution amount was similarly set at 20%. To assess the impact of different substitution levels on the experimental results, previous studies [1] also included coral powder substitution amounts of 10% and 0%.

2.1.1. Raw Materials and Mixtures

Figure 1a illustrates the cumulative particle size distribution of the binder materials, with average particle sizes of 10.71 μm and 6.54 μm, respectively. Figure 1b then confirms that the primary component of coral powder is aragonite.

Table 1. Chemical composition of the cement and coral powder [1].

Chemical Composition (mass%)	Coral Powder	Cement
CaO	53.68	63.1
MgO	0.31	2.31
Al2O3	0.25	4.96
SiO2	0.75	21.0
P2O5	0.02	0.116
SO3	0.57	2.31
K2O	0.03	0.910
Cl	0.03	-
TiO2	-	0.278
MnO	0.6	0.0877
Fe2O3	0.13	2.77
ZnO	-	0.0646
Loss on ignition	43.62	2.06

presents the chemical composition of the cement and coral powder, noting that the ignition loss of coral powder is significantly higher than that of cement. This higher ignition loss is due to the decomposition of calcium carbonate, the main component of coral powder, at high temperatures.

Table 2. Mixing proportions of the cement blends [1].

	Coral Powder	Cement	W/B	S/B
CP0	0	100	0.5	2.75
CP10	10	90	0.5	2.75
CP20	20	80	0.5	2.75

details the mixing ratios of the mortar specimens, with a sand-to-binder mass ratio of 2.75.

2.1.2. Methodology of Macroscopic Tests

Macroscopic measurements of compressive strength, surface electrical resistivity, and ultrasonic pulse velocity were conducted on three specimens according to the relevant standards, and the average result was recorded as the final value [1].

For compressive strength testing, three mortar specimens, each sized 5 × 5 × 5 cm, were used following ASTM C109 standards, with curing intervals of 3, 7, and 28 days (including 24 h in molds). An AGX-600 universal material testing machine was utilized for these tests, and the compressive strength was calculated as the average of the three results. Coral powder replacement rates were set at 10% and 20% [1].

Ultrasonic pulse velocity (UPV) measurements adhered to AASHTO T 358 standards, with the specimen placed between the ultrasonic transmitter and receiver. A coupling agent was applied uniformly to ensure proper surface contact [1].

Surface electrical resistivity was evaluated using RILEM TC154-EMC guidelines, employing a four-point probe tester. The samples were 4 × 4 × 16 cm in size, and their surfaces were cleaned before testing [1].

Table 3. Strength test results (MPa) [1].

Age (days)	CP0	CP10	CP20
3	29.8	25.8	18.3
7	36.9	28.7	21.9
28	54.3	40.9	30.5

,

Table 4. Electrical resistivity test results of (kΩ*cm) [1].

Age (days)	CP0	CP10	CP20
3	15.5	14.3	13.1
7	22.3	20.2	19
28	38.2	37.3	32.5

and

Table 5. UPV test results (m/s) [1].

Age (days)	CP0	CP10	CP20
3	4113	4061	3865
7	4338	4231	4035
28	4497	4396	4199

present the test results for compressive strength, resistivity, and ultrasonic pulse velocity, respectively. The overall trend is that as the amount of coral powder increased, the compressive strength, resistivity, and ultrasonic pulse velocity all decreased [1].

2.1.3. Microscopic Test Methodology

For the microscopic measurements—specifically, the heat of hydration and TGA—one sample was used per experiment according to the referenced method [1]. Microscopic experiments typically exhibit less variability compared with macroscopic experiments.

A multichannel isothermal calorimeter was employed to track the heat release of the slurry and investigate how coral powder (CP) affects the hydration kinetics of ordinary Portland cement (OPC). The cement slurry was prepared at 20 °C, approximately 5 g of which was sealed in an ampoule and placed in separate channels of the calorimeter. The test was carried out under isothermal conditions at 20 ± 0.02 °C for 168 h [1].

Figure 2 displays the hydration heat per gram of cementitious material and per gram of cement, respectively. It was observed that as the substitution of coral powder increased, the hydration heat per gram of cementitious material decreased while the hydration heat per gram of cement increased [1].

After 28 days, the paste samples that had undergone sealing and curing were crushed and ground to a particle size of less than 63 μm. Following this, the samples were immersed in an isopropyl alcohol solution to halt the reaction. The treated samples were then filtered and placed in a vacuum chamber to dry in preparation for phase identification. A thermogravimetric analysis (TGA) of the dried paste powder was performed using a TG analyzer, using approximately 20 mg of powder per run. The tests were conducted under a nitrogen purge, using a temperature range of 50–1050 °C and a heating rate of 10 °C/min.

The combined water content and CH content are determined based on TGA as follows [1]:

Combined water content = (m50 − m550)/m550

(1)

CH content = (m400 − m500)/m550 × (74/18)

(2)

where m50, m400, m500, and m550 represent the masses at 50, 400, 500, and 550 degrees, respectively, and (74/18) represents the molar mass ratio of calcium hydroxide to water.

Figure 3 presents the results of the TGA test. As the amount of coral powder increased, the weight loss at 1000 degrees Celsius also increased because of the decomposition of coral powder at high temperatures [1].

2.2. Determination of Hydration Model Parameters

The use of coral powder has both physical and chemical impacts. When examining hydration heat, the physical effects of coral powder are primarily influential. These physical effects include the dilution effect and the nucleation effect. The dilution effect refers to an increase in capillary water concentration when coral powder partially replaces cement, which in turn raises the cement’s reaction rate. The nucleation effect involves the formation of hydration products on the surface of the coral powder, which also speeds up the hydration process. Collectively, these effects result in an accelerated rate of cement hydration. To better observe the acceleration effect of coral powder on cement hydration, the experimentally measured cumulative hydration heat was divided by the mass of cement in the paste.

The reactivity of coral powder is very low. Bentz [12] found that after 180 days, the reaction level of calcium carbonate was approximately 5%, which is significantly lower compared with other mineral admixtures [6]. While the impact of chemical reactions on the hydration heat is minimal compared with physical effects, it is important to note that the chemical reaction of coral powder can influence the composition of the solid hydration products and the ion concentrations in the capillary pore solution. Products of chemical reactions of coral powder, such as carbonaluminate, can be detected using microscopic techniques such as X-ray diffraction. In summary, while coral powder does react, it has only a minor effect on hydration heat.

The red lines in Figure 4a–c illustrate the cumulative hydration heat test results per gram of cement from the start of mixing up to 168 h. As noted earlier, the isothermal hydration heat per gram of cement increased with a greater replacement of coral powder, which can be attributed to the physical effects of the coral powder.

The three-parameter hydration model is widely employed to predict the characteristics of cement-based materials. Prior research has demonstrated that the cumulative hydration heat is directly proportional to the reaction level of cement [4]. Consequently, this study utilized the cumulative hydration heat as an indicator of the cement’s hydration degree. Based on references [13,14,15], the cumulative hydration heat of cement can be predicted using the following Equation (3):

H(t) = Hmax × exp(−ra × t^sp)

(3)

In Equation (3), t denotes time, H(t) signifies the cumulative hydration heat as a function of time, and Hmax represents the maximum hydration heat. When the hydration period is sufficiently long, the cumulative hydration heat, H(t), approaches the maximum hydration heat, Hmax. The term ra represents the hydration rate coefficient of the cement, while sp denotes the shape coefficient of the hydration heat curve [16,17].

As illustrated in Equation (3), the hydration heat equation involves three input parameters: the maximum hydration heat (Hmax), the hydration rate coefficient of cement (ra), and the shape coefficient of the hydration heat curve (sp). These parameters can be determined from the cumulative hydration heat curve. Initially, the parameters for the pure cement sample—namely, the maximum hydration heat (Hmax), the hydration rate coefficient (ra0), and the shape coefficient (sp), as listed in

Table 6. Input parameters of three-parameter hydration model.

Hmax	sp	ra0	ra10	ra20
455.87	−0.58	6.91	6.19	5.55

—were calibrated using the isothermal hydration heat test results for the sample without coral powder (Figure 5a). Subsequently, the hydration rate coefficients for the 10% (ra10) and 20% (ra20) coral powder samples (also shown in Table 6) were calibrated by keeping the maximum hydration heat (Hmax) and shape coefficient (sp) constant based on the hydration heat test results for samples containing 10% and 20% coral powder (Figure 5b). The thin blue lines in Figure 5a–c represent the predictions made using Equation (3). These subfigures show that the predicted results closely matched the experimental findings. However, in the early stages of the hydration heat test (from mixing start to about 5 h), the predicted values were slightly lower than the experimental results. This discrepancy is attributed to Equation (3) not accounting for the rapid heat release from C₃A and C₃S reactions during the early phase of cement hydration [18]. In summary, the input parameters for the three-parameter hydration model varied with different mixtures, such as varying water-to-binder ratios and coral powder replacements. Therefore, recalibration of these parameters is necessary when altering the concrete mixture. This recalibration requirement is a notable limitation of the three-parameter hydration model, indicating the need for further improvements.

In Equation (3), the maximum cumulative hydration heat and the shape coefficient remained constant across different samples. As the coral powder content increased to 0%, 10%, and 20%, the hydration rate coefficient gradually decreased. This observation supports the hypothesis that coral powder primarily exerts a physical effect: it accelerates the exothermic reaction of cement without altering its final heat release (Hmax) or the fundamental progression of the hydration reaction (sp). The validity of the hydration model proposed in this paper was confirmed through both quantitative and qualitative approaches. The quantitative validation was based on experimental results from prior research [1], while the qualitative validation was derived from the established literature in this field [4].

2.3. Prediction of Coral Powder Concrete’s Properties

2.3.1. Prediction of Long-Term Hydration Heat and Long-Term Hydration Degree

After determining the model’s input parameters using Equation (3), the long-term hydration heat of the coral powder concrete and the cement’s long-term hydration degree were calculated. The results for the cumulative hydration heat from the start of mixing to 28 days are depicted in Figure 6a. During the initial week of mixing, the hydration heat increased rapidly. Following this, the rate of increase in hydration heat significantly slowed. By the end of the 28-day curing period, there was no notable difference in the hydration heat release across different mixing ratios. This observation further supports the idea that the addition of coral powder primarily has a physical effect, enhancing the cement’s hydration reaction without altering the final hydration heat release per gram of cement. The hydration degree of cement can be determined by dividing the cumulative hydration heat, H(t), by the maximum cumulative hydration heat, Hmax [19,20], as shown in Equation (4) and Figure 6b.

α(t) = H(t)/Hmax

(4)

The following figures indicate that the trend in the degree of hydration closely mirrors that of the hydration heat. At 28 days, the cumulative heat release values per gram of cement for specimens containing 0%, 10%, and 20% coral powder were 389.77, 395.69, and 401.62 J/g cement, respectively (see Figure 6a). Correspondingly, the hydration degrees of the cement were 0.855, 0.868, and 0.881 (refer to Figure 6b). This suggests that by 28 days, the majority of the cement had undergone a reaction, with only a minimal increase in the reaction level beyond this point. Hence, using the 28-day test results to evaluate the performance of coral powder concrete is justified.

Figure 6a displays the hydration heat release per gram of cement. However, in concrete engineering, hydration heat release is more commonly expressed per gram of binder. Thus, Figure 7 presents the hydration heat release per gram of binder. At 28 days, the cumulative heat release values per gram of binder for specimens with 0%, 10%, and 20% coral powder were 389.77, 356.12, and 321.29 J/g binder, respectively. This decrease in heat release over time is attributed to the dilution effect of the coral powder, which reduced the cement content and, consequently, the cumulative hydration heat. Conversely, from the start of mixing up to approximately 50 h, there was no significant difference in the cumulative hydration heat per gram of binder across different coral powder contents. This is due to the fact that, during the early stage, the nucleation effect of the coral powder accelerated the hydration reaction and increased the hydration heat, compensating for the reduction caused by the dilution effect. Generally, in coral powder concrete, both nucleation and dilution effects are present. During the early stages of hydration, nucleation predominates and increases hydration heat, while in the later stages, dilution becomes dominant and reduces hydration heat [12].

As the replacement level of coral powder reached 30%, the cement’s reaction level increased, raising the heat of hydration per gram of cement because of the accelerated hydration caused by the nucleation effect of the coral powder. Conversely, the heat of hydration per gram of binder decreased because the dilution effect of the coral powder diminished the total heat of hydration. The overall cumulative heat of hydration was influenced by these effects, with the reduction due to dilution being more prominent in the later stages of hydration, while the increase due to nucleation was mainly observed in the early stages.

2.3.2. Prediction of Compressive Strength

As hydration progresses, its products accumulate continuously in the capillary spaces, gradually increasing the concrete’s compressive strength. The latter reflects the mechanical aspect of the hydration reaction, while hydration heat represents its thermal aspect; thus, the compressive strength and hydration heat may be correlated. The hydration model was employed to calculate the cumulative hydration heat at 3, 7, and 28 days, and compressive strength was measured at these intervals. In the strength tests, coral powder replacement levels were set at 10% and 20%. A power function was used to analyze the relationship between cumulative hydration heat and compressive strength. As illustrated in Figure 8, the correlation coefficient for the power function regression was 0.8568.

2.3.3. Prediction of Surface Electrical Resistivity

As the hydration reaction advances, the capillary water content in concrete specimens diminishes, increasing surface electrical resistivity. This resistivity can serve as an indirect measure of concrete’s durability. In reinforced concrete, as corrosion of steel reinforcement begins, an increase in concrete resistivity corresponds to a reduction in the corrosion rate of the steel bars, thereby enhancing their durability and extending their service life. This study utilized a power function to analyze the relationship between the experimentally measured surface electrical resistivity and the calculated cumulative hydration heat at 3, 7, and 28 days. As depicted in Figure 9, the power function regression yielded a correlation coefficient of 0.8952.

2.3.4. Prediction of UPV

The ultrasonic pulse velocity (UPV) can serve as an indirect indicator of concrete strength. As the hydration reaction progresses, solid products build up in the capillary pores, increasing the UPV of the concrete. UPV reflects the volume of solid hydration products, while cumulative hydration heat directly measures the heat released by these products; thus, UPV and hydration heat are likely correlated. A power function was applied to analyze the relationship between UPV test results and cumulative hydration heat calculations at 3, 7, and 28 days. As shown in Figure 10, the correlation coefficient for the power function regression between UPV and cumulative hydration heat was 0.9025.

The coral powder used is primarily made up of aragonite, but it also contains a small amount of softer organic matter. While these organic substances significantly affect the mechanical properties, they have minimal impact on the hydration heat. Consequently, when hydration heat was employed to predict strength, the correlation coefficient fell below 0.90. This discrepancy is not attributed to the choice of mathematical models, such as polynomial, power, or linear functions, but rather to the inadequate consideration of the effects of the organic matter in the coral powder.

The UPV and hydration heat both reflect aspects of cement hydration. As the hydration process advances, the formation of solid hydration products and the UPV both increase while hydration heat is released. The UPV represents hydration through the accumulation of solid products, whereas hydration heat represents it through thermal properties. Consequently, there is a strong relationship between the UPV and hydration heat, with the degree of hydration serving as the fundamental link connecting the two.

2.3.5. Prediction of Hydration Product Content

In a prior study, thermogravimetric analysis (TGA) was performed after 28 days of curing. From the TGA results, it was possible to ascertain both the amount of chemically bound water and the calcium hydroxide content. The chemically bound water content was determined by measuring the weight change in the paste specimen between 50 and 550 °C [21], while the calcium hydroxide content was calculated from the weight loss peak observed in the range of 400 to 500 °C [22]. In this temperature range, calcium hydroxide decomposes into calcium oxide and water.

In this study, when utilizing the hydration model, the reaction levels of cement after 28 days of curing were determined to be 0.855, 0.868, and 0.881 for the control specimen, the specimen with 10% coral powder, and that with 20% coral powder, respectively (as shown in Figure 6b). The formula used to calculate the chemically bound water per gram of cement is as follows:

W(t) = Wmax × α(t)

(5)

In this study, W(t) denotes the amount of chemically bound water, Wmax represents the chemically bound water content when 1 g of cement is fully hydrated, and α(t) indicates the degree of hydration of the cement (as depicted in Figure 6b). Using the measured chemically bound water content of the control sample at 28 days and the computed degree of hydration, Wmax was determined to be 28.09 g/g of cement. This value is slightly higher than the 25 g/g of cement reported in previous hydration models [23,24]. This discrepancy may be attributed to the fact that previous studies measured chemically bound water starting from 50 °C, whereas earlier hydration models [23,24] began their measurements at 105 °C. Since ettringite, which decomposes at temperatures starting from 50 °C and contains a significant amount of chemically bound water, was included in this study’s calculations, the value of Wmax was slightly higher compared with previous models that did not account for this decomposition [23,24].

The calculated values for chemically bound water are presented in Figure 11a. For the control sample, the calculated and experimental values for chemically bound water were both approximately 0.240 g/g binder. However, for the samples with 10% and 20% coral powder, the calculated values were slightly lower than the experimental measurements. Specifically, for the 10% coral powder sample, the calculated value was 0.219 g/g binder, while the experimental value was 0.224 g/g binder. For the 20% coral powder sample, the calculated value was 0.198 g/g binder compared with the experimental value of 0.212 g/g binder. The calculated values for samples with coral powder were somewhat lower than the experimentally measured values. This discrepancy is likely due to the omission of the chemical reactions involving coral powder in the model. The chemical reaction of coral powder, which produces carbon aluminate, contributes to an increased amount of chemically bound water [21,25].

Similar to the approach used for calculating chemically bound water, the content of calcium hydroxide can also be estimated based on the degree of hydration. The formula for calculating the amount of calcium hydroxide per gram of cement is as follows:

CH(t) = CHmax × α(t)

(6)

In this context, CH(t) denotes the quantity of calcium hydroxide produced at time t, while CHmax represents the amount of calcium hydroxide formed when 1 g of cement has fully reacted. The value of CHmax was determined using the calcium hydroxide measurement from the control sample at 28 days along with the calculated hydration degree, resulting in CHmax = 21.61 g/g cement. Typically, the amount of calcium hydroxide generated when 1 g of cement reacts completely ranges from approximately 0.2 to 0.3 g [26,27,28]. The CHmax value obtained in this study fell within this range.

The results of the calcium hydroxide calculations are illustrated in Figure 11b. For the control sample, the calculated calcium hydroxide content closely matched the experimental findings, with both being approximately 0.185 g/g binder. In contrast, for the samples containing 10% and 20% coral powder, the calculated values were somewhat higher than the experimental results. Specifically, for the 10% coral powder sample, the calculated calcium hydroxide was 0.169 g/g binder compared with the experimental value of 0.157 g/g binder. Similarly, for the 20% sample, the calculated value was 0.152 g/g binder, while the experimental value was 0.142 g/g binder. The calculated calcium hydroxide for the coral powder samples was slightly higher than the experimentally measured amounts. This discrepancy is likely due to the model not accounting for the chemical reactions involving coral powder, which consumes calcium hydroxide and thus reduces its content [21,22,29].

This study did not account for the chemical reactions of coral powder. The impact of these reactions varies across different properties. First, the chemical reactions of coral powder can refine the pore structure of concrete, notably increasing the electrical resistivity. Second, the byproducts of these reactions can fill the pores, thereby enhancing both the strength and ultrasonic pulse velocity of the concrete. Finally, while the chemical reactions of coral powder contribute to hydration heat, the effect is minimal because of the low reactivity of the powder. In summary, while the chemical reactions of coral powder can enhance electrical resistivity, strength, ultrasonic pulse velocity, and hydration heat, the degree of increase differs: electrical resistivity shows the most significant increase, followed by strength and ultrasonic pulse velocity, with hydration heat showing the smallest increase.

3. Combining the Hydration Kinetic Model with the Three-Parameter Hydration Model

3.1. Necessity of the Hydration Kinetic Model

Although the three-parameter hydration model could predict both the hydration heat and various properties of the concrete, the parameter for the hydration reaction rate (ra in Equation (3)) varied with different amounts of coral powder. Additionally, changes in the water-to-binder ratio could also affect the other two parameters: the maximum heat release of the cement (Hmax in Equation (3)) and the shape coefficient of the heat release curve (sp in Equation (3)). Consequently, since the model did not account for the fundamental mechanisms of coral powder concrete, its generalizability was notably limited.

To enhance the generalizability of the three-parameter hydration model, it was integrated with the hydration kinetic model. This combination preserved the model’s strong predictive capability while improving its adaptability, so it became more suitable for varying water-to-binder ratios and different levels of coral powder replacement.

3.2. Hydration Kinetic Model for Cement–Coral Powder Blends

3.2.1. Hydration Kinetic Model for Cement

In previous research, the authors introduced a hydration kinetic model designed to simulate the hydration reaction process of Portland cement with water. The equation for this hydration kinetic model is as follows [30,31]:

$$\alpha (t)={\displaystyle {\int }_0^t\frac{d\alpha }{dt}}$$

(7)

$$\begin{array}{ll}{\displaystyle \frac{d\alpha }{dt}}=& {\displaystyle \frac{3{\rho }_w}{(v+w_g)r_0{\rho }_c}}\left[{\displaystyle \frac{W_0-0.4C_0\alpha }{W_0}}\right]\left[{\displaystyle \frac{S_w}{S_0}}\right]\\ & {\displaystyle \frac{1}{(\frac{1}{\raisebox{1ex}{$B$}\!\left/ \!\raisebox{-1ex}{${\alpha }^{1.5}$}\right.+C{\alpha }^3}-\frac{r_0}{D_{e0}\ln (\frac{1}{\alpha })})+\frac{r_0}{D_{e0}\ln (\frac{1}{\alpha })}{(1-\alpha )}^{\frac{-1}{3}}+\frac{1}{k\mathrm{r}}{(1-\alpha )}^{\frac{-2}{3}}}}\end{array}$$

(8)

In Equations (7) and (8), α represents the degree of hydration, and t denotes time. The term dα/dt indicates the rate at which cement hydration occurs. Equation (7) illustrates that the degree of hydration can be determined by numerically integrating the hydration rate. In Equation (8), the parameters B, C, kr, and De₀ are variables that describe different stages of the cement hydration process. Specifically, parameter B and parameter C relate to the initial dormant period: B is linked to the rapid heat release at the beginning of hydration, while C pertains to the gradual increase in heat toward the end of the initial dormant period. Parameter kr describes the phase boundary reaction during hydration, and De₀ is associated with the diffusion process. The term De₀ln(1/α) signifies that as the hydration reaction approaches completion (α = 1), the rate of hydration heat release diminishes to nearly zero. The parameters B, C, kr, and De₀ can either be derived from the mineral composition of the cement or calibrated using experimental results for ρ hydration heat [32].

Equation (8) integrates various physical and chemical factors involved in cement hydration. First, it considers specific physical parameters of both cement and water: r₀ represents the average particle size of the cement, ρ_c denotes the density of cement, and ρ_w indicates the density of water. Second, it incorporates chemical reaction constants related to the hydration process: ν signifies the chemically bound water per gram of cement (with ν = 0.25); w_g represents the physically bound water per gram of cement (with w_g = 0.15); and ν + w_g represents the total mass of water consumed during the reaction of 1 g of cement with water (totaling 0.40 g, i.e., 0.25 g + 0.15 g). Moreover, Equation (8) addresses the influence of capillary water and pore structure formation on the hydration rate. W₀ represents the initial mass of mixed water; C₀ denotes the initial mass of cement in the mix; W₀ − 0.4C₀α indicates the mass of capillary water remaining during hydration; and (W₀ − 0.4C₀α)/W₀ represents the ratio of the remaining capillary water to the initial water mass. At the beginning of hydration α = 0, this ratio is 1, but it decreases as hydration progresses. Additionally, S₀ represents the initial contact area between cement particles and water, while S_W indicates the contact area during hydration. Initially, S_W/S₀ is 1, but it diminishes as hydration continues. Generally, S_W/S₀ is a function of the degree of hydration, illustrating how pore structure formation impacts the reduction in the hydration rate.

3.2.2. Effect of Coral Powder on Cement Hydration

The addition of coral powder has a notable influence on the physical characteristics of cement hydration, particularly through the dilution effect and the nucleation effect. The contribution of coral powder to the hydration kinetic model is as follows.

When coral powder is used as a partial replacement for cement, the water-to-cement mass ratio increases, which accelerates the cement hydration process. This acceleration, known as the dilution effect of coral powder, is incorporated into the model through the term (W₀ − 0.4C₀α)/W₀.

In the cement hydration process, coral powder acts similarly to an inert filler. It allows some of the hydration products to form on its surface, thereby decreasing the thickness of the hydration layer on the cement’s surface. This reduction in layer thickness lowers the resistance that capillary water faces when interacting with unhydrated cement, thereby accelerating the diffusion process of the hydration reaction. The nucleation effect of coral powder is represented by Equation (9), as follows:

$$D{\mathrm{e}}_0\prime =D{\mathrm{e}}_0\left(1+\mathrm{nu}\times {\displaystyle \frac{C{P}_0}{{\mathrm{CP}}_0+{\mathrm{C}}_0}}\right)$$

(9)

Here, $D{\mathrm{e}}_0\prime$ represents the diffusion parameter that accounts for the nucleation effect of coral powder, CP₀ denotes the mass of coral powder in the mix, and nu is the nucleation effect parameter for coral powder. The term CP₀/(CP₀ + C₀) reflects the replacement ratio of coral powder. When the coral powder substitution amount is zero, $D{\mathrm{e}}_0\prime$ equals De₀. As illustrated in Equation (9), an increase in the coral powder content leads to a higher cement hydration reaction rate, which aligns with the trend observed in the three-parameter hydration model.

3.3. Calibration of Input Parameters of Hydration Kinetic Model

The parameters of the cement–coral powder hydration model, including B, C, kr, De₀, and nu, can be determined using experimental results from the isothermal hydration heat. The heat released during the complete hydration of 1 g of cement is 455.87 J/g (as obtained from the three-parameter hydration model). The values for B, C, kr, and De0 can be calibrated based on the isothermal hydration heat results of the control specimen. Additionally, the nucleation effect parameter, nu, can be adjusted using isothermal hydration heat data from the 20% coral powder specimen in conjunction with the calibrated values of B, C, kr, and De₀.

Table 7. The values of input parameters of the hydration kinetic model.

B (cm/h)	C (cm/h)	kr (cm/h)	De0 (cm2/h)	nu
7.70 × 10−9	0.0016	5.32 × 10−5	1.12 × 10−10	8

presents the values for the input parameters of the hydration kinetic model.

It is important to note that these input parameters remained constant across different mixtures, whereas in the three-parameter hydration model, the input parameters varied with changes in the mixtures. In this regard, the hydration kinetic model addresses the limitations of the three-parameter model. In other words, once the input parameters for the hydration kinetic model are calibrated, they can be applied to various mixing proportions without needing further adjustments.

The calibration and experimental results are displayed in Figure 12. The hydration kinetic model demonstrated better alignment with these experimental data compared with the three-parameter hydration model. In the initial stage of hydration, the three-parameter hydration model’s simulation results were somewhat lower than the experimental results (as shown in Figure 5). In contrast, the hydration kinetic model’s simulation results closely matched these experimental data. This improved accuracy is attributed to the hydration kinetic model’s incorporation of the rapid heat release during the early stages of hydration, which the three-parameter model did not account for.

3.4. Analysis of Property Development in Hardening Cement–Coral Powder Blends

The long-term degree of cement hydration (illustrated in Figure 13a) was determined using the hydration kinetic model. Additionally, with the hydration degree of the cement, the cumulative hydration heat, combined water, and calcium hydroxide content per gram of cement were computed using Equations (10), (11) and (12), respectively. The long-term hydration heat per gram of binder (shown in Figure 13b) was also calculated. The trends observed in these results were consistent with those in the results of the three-parameter hydration model. Specifically, with an increase in the coral powder content, the cement’s degree of hydration increased while the heat release per gram of binder decreased.

H(t) = Hmax × α(t)

(10)

W(t) = Wmax × α(t)

(11)

CH(t) = CHmax × α(t)

(12)

The properties of mortar at various ages were estimated using the hydration heat per gram of binder. The results are presented in detail in Figure 14. The trends observed in these results were comparable to those from the three-parameter hydration model. For samples with coral powder, the computed values for chemically combined water were slightly lower than the experimental values, whereas the calculated calcium hydroxide content was slightly higher than the experimental measurements.

3.5. Parameter Study Using Hydration Kinetic Model

3.5.1. Parameter Study of Reaction Degree of Cement in Cement–Coral Powder Blends

It is important to note that the three-parameter hydration model could not be used for parameter analysis because its input parameters vary for different mixtures. In contrast, the hydration kinetic model is suitable for parameter analysis since its input parameters remain constant across various mixtures. This model accounts for the effects of both the water–binder ratio and the amount of coral powder replacement, allowing it to not only replicate experimental results but also facilitate parameter analysis. Previous research has demonstrated that the hydration kinetic model is effective for assessing various concrete properties, including hydration heat and the amount of chemically bound water, for different mixing proportions, such as normal-strength and high-strength concrete [30,31,32]. In this study, a parameter analysis of the hydration model was conducted by calculating the hydration degree of cement at different ages, considering two water–binder ratios (0.50 and 0.35) and two levels of coral powder replacement (10% and 20%).

The results of the parameter analysis are illustrated in Figure 15. For a fixed amount of coral powder, reducing the water–binder ratio from 0.50 to 0.35 led to a decrease in the cement’s degree of hydration, attributable to the reduced concentration of capillary water. Conversely, for a constant water–binder ratio, increasing the coral powder content from 10% to 20% resulted in a higher degree of cement hydration. This increase is attributed to the physical effects of the coral powder.

3.5.2. Parameter Study about Relative Reaction Level of Cement in Cement–Coral Powder Blends

The relative reaction level of cement is defined as the ratio of the cement’s reaction level in the sample with coral powder to the reaction level of cement without coral powder, given the same water–binder ratio. As depicted in Figure 16, the relative reaction level of the cement rose with an increasing coral powder content and decreasing water–binder ratio. In concrete, unreacted cement serves as an expensive filler. By increasing the relative reaction level of the cement, the amount of unreacted cement is reduced, thereby achieving material cost and energy savings. This trend in the parameter analysis results mirrors the findings reported by Bentz [4].

The primary advantage of the hydration kinetic model over the three-parameter hydration model is not necessarily an improvement in calculation accuracy but rather its ability to conduct parameter analysis and determine the reaction level of cement across various mixing proportions. This capability allows the hydration kinetic model to guide material design for coral powder concrete, thereby reducing material waste and enhancing sustainability.

4. Discussions of the Three-Parameter Hydration Model and Hydration Kinetic Model

The primary equations utilized in this paper are provided in

Table 8. Equations for the three-parameter hydration model.

Aim of Equation	Equation Expression	Equation Number
Determine cumulative hydration heat	H(t) = Hmax × exp(−ra × tsp)	(3)
Determine degree of hydration	α(t) = H(t)/Hmax	(4)
Determine combined water	W(t) = Wmax × α(t)	(5)
Determine calcium hydroxide	CH(t) = CHmax × α(t)	(6)
Evaluate macro properties	Power functions based on hydration heat calculated from Equation (3) and the other equations are shown in Figure 8, Figure 9 and Figure 10	-

and

Table 9. Equations for the hydration kinetic model.

Aim of Equation	Equation Expression	Equation Number
Determine degree of hydration	$\alpha (t)={\displaystyle {\int }_0^t\frac{d\alpha }{dt}}$	(7)
Determine rate of hydration	$\begin{array}{ll}{\displaystyle \frac{d\alpha }{dt}}=& {\displaystyle \frac{3{\rho }_w}{(v+w_g)r_0{\rho }_c}}\left[{\displaystyle \frac{W_0-0.4C_0\alpha }{W_0}}\right]\left[{\displaystyle \frac{S_w}{S_0}}\right]\\ & {\displaystyle \frac{1}{(\frac{1}{\raisebox{1ex}{$B$}\!\left/ \!\raisebox{-1ex}{${\alpha }^{1.5}$}\right.+C{\alpha }^3}-\frac{r_0}{D_{e0}\ln (\frac{1}{\alpha })})+\frac{r_0}{D_{e0}\ln (\frac{1}{\alpha })}{(1-\alpha )}^{\frac{-1}{3}}+\frac{1}{k\mathrm{r}}{(1-\alpha )}^{\frac{-2}{3}}}}\end{array}$	(8)
Determine nucleation effect of coral powder	$D{\mathrm{e}}_0’=D{\mathrm{e}}_0\left(1+\mathrm{nu}\times {\displaystyle \frac{C{P}_0}{{\mathrm{CP}}_0+{\mathrm{C}}_0}}\right)$	(9)
Determine hydration heat	H(t) = Hmax × α(t)	(10)
Determine combined water	W(t) = Wmax × α(t)	(11)
Determine calcium hydroxide	CH(t) = CHmax × α(t)	(12)
Evaluate macro properties	Power functions based on hydration heat calculated using Equation (10), and the other equations are shown in Figure 14a–c	-

.

4.1. Three-Parameter Hydration Model

The three-parameter hydration model offers several advantages: First, it allows for the exploration of the physical effects of coral powder. Second, it provides accurate determinations of the ultimate hydration heat release (Hmax in Equation (3)), ultimate combined water (Wmax in Equation (5)), and ultimate calcium hydroxide (CHmax in Equation (6)) when 1 g of cement is fully hydrated. Currently, no universal formula exists for calculating Hmax, Wmax, and CHmax [30,31,32], but these values can be estimated using the hydration kinetic model (Equations (10)–(12)). Third, the three-parameter model is straightforward and user-friendly, making it accessible and easy to apply for researchers.

However, this model also has limitations. The primary drawback is that the input parameters must be recalibrated whenever the concrete mixtures are altered. This is due to the model’s inability to differentiate between the dilution effect and the nucleation effect.

4.2. Connections between the Hydration Kinetic Model and Three-Parameter Hydration Model

The main connections between the hydration kinetic model and the three-parameter hydration model are as follows: The three-parameter hydration model simplifies the hydration reaction to a diffusion process, with the addition of coral powder primarily affecting the hydration rate coefficient (ra in Equation (3)). However, this model does not clearly differentiate between the dilution effect and the nucleation effect. In contrast, the hydration kinetic model views cement hydration as comprising three stages: the initial dormant period, the phase boundary reaction process, and the diffusion process. This model incorporates the dilution effect through the capillary water content term (W₀ − 0.4C₀α in Equation (8)) and accounts for the nucleation effect using the nucleation effect parameter, nu, in Equation (9). The hydration kinetic model explicitly differentiates between the dilution and nucleation effects of coral powder, which means that the input parameters do not need to be adjusted for different mixtures. This is a significant advantage of the hydration kinetic model over the three-parameter hydration model. Nevertheless, the former does not account for the chemical reactions involving coral powder, and it cannot accurately determine the composition of hydration products or pore solutions.

4.3. Can the Hydration Kinetic Model Be Used Alone?

Although the hydration kinetic model offers more comprehensive functions than the three-parameter hydration model, it cannot be used independently. As indicated in Equations (10)–(12), the hydration kinetic model requires the values of Hmax, Wmax, and CHmax. Currently, there are no established formulas for precisely calculating these values. Thus, these parameters must be determined through regression using the three-parameter hydration model. Then, once these reaction constants are established, they can be incorporated into Equations (10)–(12). In summary, at present, the hydration kinetic model must be utilized alongside the three-parameter hydration model.

4.4. Principles of Model Selection

The three-parameter hydration model is generally straightforward in its formulation, and it is particularly advantageous for research involving general-strength concrete, where the dilution effect of coral powder is not pronounced. In such cases, the simplicity of the three-parameter model is beneficial. Meanwhile, the hydration kinetic model is somewhat more complex. It becomes particularly advantageous when studying a range of water–binder ratios, such as in general-strength concrete (with a high water–binder ratio) and high-strength concrete (with a low ratio). Chiefly, the hydration kinetic model excels in distinguishing between the dilution and nucleation effects of coral powder. Overall, in terms of prediction accuracy, there is no significant difference between the two models. The key distinction lies in their ability to differentiate between the dilution and nucleation effects: the three-parameter model cannot, whereas the hydration kinetic model can.

4.5. Experimental Method to Determine the Degree of Hydration

In this study, the input parameters for both the three-parameter hydration model and the hydration kinetic model were calibrated using isothermal hydration heat experiments. These experiments are microscopic in nature and are highly sensitive to material preparation and experimental procedures. If isothermal hydration heat equipment is unavailable, alternative methods can be employed to characterize the degree of cement hydration. Some researchers suggest that the relative compressive strength of concrete can serve as an indicator of the hydration degree [33,34,35]. The relative compressive strength is calculated by dividing the concrete’s compressive strength at a specific age by its compressive strength at full curing (approximately one year) [28]. As with the degree of hydration, the relative compressive strength is a dimensionless variable [36]. After determining the changes in hydration degree over time, the input parameters for both the three-parameter hydration model and the hydration kinetic model can be identified. This allows for the calculation of the cement reaction level and the evaluation of the properties of hardening concrete. Additionally, for high-strength concrete, the use of a superplasticizer may influence the initial dormant period of cement hydration [37,38,39]. This effect can be incorporated using parameters B and C from the Portland cement hydration model [30,31].

4.6. Multi-Component Hydration Kinetic Model

In a prior study [31], a multi-component hydration model for Portland cement was introduced. This model allows users to input the cement’s physical properties, mineral composition (including the mass percentages of C₃S, C₂S, C₃A, and C₄AF), concrete mixing ratios, and curing conditions. Based on these inputs, the model can automatically determine the reaction levels of the cement’s mineral components and calculate the overall reaction degree of the cement. This reaction degree can then be used to predict various mechanical, chemical, thermal, and durability properties of the hardening concrete. Notably, the multi-component hydration model does not require the regression of input parameters. However, the model does have several limitations, such as neglecting the effects of the alkali content in the cement, the impact of small amounts of limestone powder used in Portland cement production, and the interactions between different mineral components of the cement. Consequently, the results obtained from the multi-component hydration model may differ from experimental findings [6,31].

5. Conclusions

This study presented both a three-parameter hydration model and a hydration kinetic model tailored for coral powder concrete based on previous experimental data. The key findings are as follows:

The input parameters for the three-parameter hydration model were calibrated using cumulative hydration heat measurements taken while mixing for up to 7 days. The values for the maximum cumulative hydration heat (Hmax = 455.87 J/g cement) and the shape coefficient of the hydration reaction curve (sp = −0.87) were kept constant. The hydration rate coefficients were determined to be 6.91, 6.19, and 5.55 for 0%, 10%, and 20% coral powder, respectively. This indicates that coral powder accelerates the cement hydration process without altering the final heat output or the fundamental hydration process. However, a limitation of this model is that its input parameters change with different mixtures, as it does not differentiate between the dilution and nucleation effects of coral powder.

At 28 days, the cumulative heat release values per gram of cement were 389.77, 395.69, and 401.62 J/g for 0%, 10%, and 20% coral powder, respectively. The corresponding hydration levels were 0.855, 0.868, and 0.881. Due to the dilution effect of coral powder, the cumulative heat release values per gram of binder were 389.77, 356.12, and 321.29 J/g, respectively. Additionally, the macro properties were assessed using the cumulative hydration heat and a power function.

At 28 days, the contents of chemically bound water were 0.2402, 0.2197, and 0.1981 g/g binder for 0%, 10%, and 20% coral powder, respectively. The model slightly underestimated these values for the coral powder samples. Meanwhile, the calculated contents of calcium hydroxide were 0.1848, 0.1690, and 0.1524 g/g binder, respectively, with the model slightly overestimating these values.

This study also introduced a hydration kinetic model, which maintains consistent input parameters across different mixtures by accounting for both the dilution and nucleation effects. The results from the hydration kinetic model were comparable to those of the three-parameter model. Parameter analysis revealed that a lower water–binder ratio and higher coral powder substitution significantly enhance the relative reaction level of cement.

In summary, the proposed models are effective for predicting the performance of coral powder concrete and may facilitate its use in marine construction.