Optimization of Compressive Strength and Drying Shrinkage of Calcium-Based Alkali-Activated Mortars Using Expansive and Shrinkage-Reducing Agents

Abstract

Alkali-activated materials can significantly reduce carbon dioxide emissions compared with cement. However, their durability remains insufficiently understood. This study investigated the effects of calcium hydroxide (Ca(OH)₂, CH), an expansion agent (calcium sulfoaluminate, CSA), and a shrinkage-reducing agent (SRA) on the compressive strength and length change and determined the optimal content levels for each agent. Experiments were conducted to evaluate the compressive strength and length change of 17 mortar mixtures containing CH, CSA, and SRA. The substitution ratios of CH, CSA, and SRA were fixed at three predefined levels for each factor. The microstructural changes induced by the use of each agent were analyzed using pH measurements, porosity analysis, and X-ray diffraction. In addition, the water desorption behaviors associated with CSA and SRA were assessed. Experimental and statistical analyses demonstrated that the optimal contents of CH, CSA, and SRA for simultaneously improving the compressive strength and length change were 8.54, 10.0, and 0.76 wt.%, respectively. The use of CSA significantly enhanced the compressive strength development and dimensional stability of the mortar. This improvement was associated with a reduction in the porosity, which was attributed to ettringite formation. Furthermore, while the SRA slightly reduced the compressive strength, it significantly improved the dimensional stability.

1. Introduction

Generally, alkali-activated materials (AAM) are manufactured using blast furnace slag (BFS), fly ash, and rice husk ash as binders and high-pH alkaline activators, such as Na₂SiO₂, NaOH, Ca(OH)₂, Na₂CO₃, K₂SO₄, K₂CO₃, Na₂SO₄, and fiber, either alone or in combination [1,2,3,4,5,6,7,8,9,10]. As these AAM are industrial byproducts, their manufacturing process differs from that of cement, which emits large amounts of CO₂ during the firing process [11]. Therefore, AAM can reduce CO₂ emissions during manufacturing and conserve natural resources.

From the point of view of engineering applications, various studies have reported that AAM and CAAM have a lower resistance to drying shrinkage than ordinary cement [12,13,14,15,16,17]. This high rate of length change increases cracking and facilitates the ingress of deteriorating agents that cause steel corrosion. Therefore, the use of CSA and SRA has been considered essential for improving the drying shrinkage resistance of alkali-activated cement.

Polyether-based shrinkage-reducing admixtures (SRA) have been employed to mitigate shrinkage, but their use is often accompanied by retardation of reaction kinetics and reduced strength development, leaving the trade-off between shrinkage reduction and mechanical performance as a critical challenge [16,17]. Meanwhile, MgO, CaO or CSA can compensate for shrinkage through the formation of expansive reaction products. However, inappropriate dosage or reaction kinetics may lead to increased porosity and strength loss, and some expansive sources exhibit limited effectiveness in long-term shrinkage mitigation [18,19,20]. While previous studies have primarily investigated the effects of expansive agents or SRA individually [21,22], their combined application on compressive strength and drying shrinkage of alkali-activated mortars, and to provide practical mix-design guidance for effective shrinkage mitigation without compromising mechanical performance, has not been fully investigated.

To develop AAM for low-carbon construction, the effects of sodium carbonate (Na₂CO_3, NC) or CH addition to BFS and rice husk ash on the durability, including the mechanical strength, drying shrinkage, and water permeability, were examined [23,24,25]. Moreover, fundamental performance changes owing to the use of CSA and SRA were experimentally investigated [25]. Consequently, the incorporation of NC and CSA was reported to delay the development of initial strength within the initial 7 d of curing. Furthermore, the use of SRA was more effective than that of CSA in reducing mortar length changes. Furthermore, in mortars composed of CH and BFS powder (Calcium-based Alkali-Activated Mortar, CAAM), a CH substitution ratio within the range of 5–10 wt.% was reported to have little effect on the compressive strength. Meanwhile, decreased dimensional stability due to water evaporation during the drying process remains a disadvantage of CAAM because of differences in the hydration products formed in CAAM compared with ordinary cement. Moreover, previous studies showed that the dimensional stability of mortar based on CH and BFS significantly improved when combined with CSA and SRA [25]. However, systematic statistical evaluations quantifying the individual and interactive effects of CSA and SRA, as well as their optimal replacement ratios for achieving dimensional stability comparable to or exceeding that of ordinary cement, remain limited.

The central composite design (CCD) approach enables quantitative analysis of the relationship between material variables and performance using a limited number of experiments. Reliable mathematical models can be built and used to derive the optimal material conditions for targeted performance properties [26]. This approach reduces the time and labor required to obtain reliable results [27,28].

The main purpose of this study was to optimize the compressive strength and drying shrinkage of alkali-activated cement using BFS as the primary binder and CH as a hydration accelerator. The detailed test procedure can be seen in Figure 1. Using the CCD, a response-surface-based statistical method, the effects of BFS powder, CH, CSA, and SRA on the compressive strength and drying shrinkage were systematically examined. The CH content relative to BFS was set at 5, 7.5, and 10 wt.%, the CSA at 0, 5, and 10 wt.%, and the SRA at 0, 1, and 2 wt.%. Using the CCD, approximately 17 material design combinations were generated. These designs were applied to determine the optimal conditions for improving the compressive strength and drying shrinkage of CAAM. X-ray diffraction (XRD), dynamic vapor sorption (DVS), porosity, pH, and ignition loss measurements were also performed to elucidate the mechanisms underlying the observed changes in compressive strength and drying shrinkage. This study therefore proposed an effective strategy for mitigating drying shrinkage, a well-recognized limitation of CAAM.

2. Materials and Methods

2.1. Raw Materials

In this study, gypsum-free BFS, with a density and specific surface area of 2.91 g/cm³ and 4310 cm²/g, respectively, was used. CH with a purity of 95.0% or higher (Hayashi Pure Chemical Industry, Ltd., Osaka City, Osaka, Japan) was used to activate the hydration of BFS. To improve the drying shrinkage resistance of the CAAM, a CSA, Denka CSA (CSA#20), and an SRA (Master Life^® SRA 900; Pozzolith Solutions, Ltd., Chigasaki City, Kanagawa, Japan) were used. To establish target drying shrinkage values for the CAAM, ordinary Portland cement and blast-furnace slag cement (BB) were purchased and used as reference materials in the experiments. To confirm the chemical composition and crystal structure of each material used, XRD and SEM–EDS analyses were performed. To determine the chemical composition and crystal structure of each material, XRD and SEM–EDS analyses were performed, and the results are shown in Figure 2 and Figure 3 and

Table 1. Chemical composition (%) from SEM–EDS.

Oxides	BFS	CH	CSA
CaO	52.3	98.6	64.0
SiO2	28.9	0.1	1.2
Al2O3	10.7	0.4	5.4
MgO	4.3	0.3	0.7
Fe2O3	0.6	0.4	0.8
SO3	2.1	0.1	27.9
Total (%)	98.9	99.9	99.9

. The XRD analysis results are shown in Figure 2. As shown, BFS exhibits no sharp crystalline peaks and is composed of an amorphous material. Furthermore, CH, used as a stimulant for blast furnace slag, exhibits a CH peak at approximately 18 °C. Furthermore, CSA exhibited Yeelimite peaks (Y) and anhydrite peaks (An).

2.2. CCD and Sample Preparation

In this study, the CCD was conducted using Minitab software (Minitab 22.2.1, LLC, 2021, State College, PA, USA), which is widely used to optimize material designs involving multiple factors.

Table 2. Level of each factor.

Level of Factor	CH	CSA	SRA
	(wt.%)	(wt.%)	(wt.%)
−1	5	0	0
0	7.5	5	1
1	10	10	2

and

Table 3. Mixture designations.

No.	CH	CSA	SRA	No.	CH	CSA	SRA
	(wt.%)	(wt.%)	(wt.%)		(wt.%)	(wt.%)	(wt.%)
1	5	10	0	10	7.5	5	0
2	5	0	2	11	7.5	10	1
3	10	0	0	12	10	5	1
4	10	10	2	13	5	10	2
5	5	5	1	14	5	0	0
6	7.5	0	1	15	10	10	0
7	7.5	5	1	16	10	0	2
8	7.5	5	2	17	7.5	5	1
9	7.5	5	1

show the experimental design for obtaining the three types of CH, CSA, and SRA using Minitab 22 software. This design yielded eight cubic points, one cubic center point, six axial points, and two axial center points, resulting in 17 experimental runs. Each design was selected randomly.

The water-to-binder ratio (W/B, B = BFS + CH + CSA) was 0.45. CH and CSA were defined as weight percentages relative to the binder, with BFS constituting the remainder. The sand content was set to 1.5 times the binder mass. These materials were mixed, and the compressive strength and drying shrinkage were subsequently measured. For the compressive strength test, a 50 mm × 100 mm cylindrical mold was used. The mortar was mixed twice for 2 min, poured into a cylindrical mold, and covered with glass to prevent water evaporation. The mold was removed after 4 d of curing, after which the specimens were sealed and cured until the intended curing age.

For the length-change test, the mortar specimens were fabricated as 40 mm × 40 mm × 160 mm prisms. After 4 d, the test specimens were demolded, sealed, cured, and then stored at 20 °C and 55 ± 5% relative humidity (RH). Length-change measurements were conducted for 35 d, starting from 7 d of age.

2.3. Test Methods

In this study, the compressive strength and drying shrinkage were tested using sand-mortar specimens. In addition, hydration heat, pH, porosity, water desorption behavior, ignition loss, and XRD analyses were also performed on the paste specimens.

2.3.1. Mortar Test Methods

• Compressive Strength
• Compressive strength tests were conducted to evaluate the mechanical performance of the materials. The mortar was poured into a cylindrical mold, and the specimens were demolded after 4 d. The samples were then sealed and cured until the measured ages were attained. The compressive strength was measured at 4, 7, and 28 d in accordance with JIS R 5201 [29]. The compressive strength test equipment is presented in Figure 4. At least two specimens were tested for each condition, and the average values were recorded.

• Drying Shrinkage

1.

After mortar casting, the mortar samples under investigation were sealed and cured in the laboratory at 20 °C for 4 d, then stored in a curing room at 20 ± 2 °C and 55 ± 5% RH. The changes in length was measured according to JIS A 1129 [30], as shown in Figure 5. The length measurements were performed using a digital micrometer (resolution: 0.001 mm, standard bar: 150 mm). The changes in length were calculated before and after drying.

2.3.2. Paste Test Methods

• Heat of Hydration

2.

Heat-of-hydration tests were conducted to evaluate the hydration reaction rates of the CAAM. This experiment was conducted with reference to the existing literature [31,32]. All materials were placed in a chamber at 22 °C for approximately 24 h before use. Approximately 30 g of the binder and distilled water were mixed by hand mixer for 2–3 min. Approximately 20 g of the paste was placed in a polyethylene (PP) container and inserted into the heat-of-hydration measuring device. Subsequently, the voltage was measured for 48 h using a data logger (TDS-540; Tokyo Measuring Instruments Laboratory, Tokyo, Japan). The time interval between measurements was 3 min. The baseline for each sensor was measured as follows: The calibration coefficient was obtained by filling the polyethylene container with distilled water and measuring the voltage for 24 h. The calibration coefficient was obtained using 100 Ω resistors and an external voltage supply. At least three measurements were taken for each paste, and the average values were used.

• pH Value

3.

To determine the effect of each material design on the alkalinity of the liquid, pH tests were conducted. These tests were conducted based on the authors’ previous research methods [23]. The paste was mixed for approximately 5 min using a hand mixer, placed in a 75 × 75 × 5 mm silicone mold, and stored in a polyethylene bag to prevent water evaporation. After 3 d, the paste was demolded and sealed for curing. After 4, 7, 14, and 28 d of curing, the samples were dried in an oven at 40 °C for 3 d. The paste was then ground to a size of 150 µm or less. A liquid-to-solid ratio of 10 was used, with 1–2 g of ground paste in this experiment. The paste was mixed with distilled water for approximately 2 min and the pH was measured after 5 min using a pH meter (DKK-TOA Co., HM-30P; DKK-TOA Co., Tokyo, Japan).

• Porosity

4.

The Archimedean porosity was measured to evaluate changes in paste porosity induced by each additive. This test was conducted based on the authors’ previous research methods [23]. The paste was prepared using the same method as that used for the pH measurement and then sealed and cured. Before measurement, the hydration of the paste was stopped using ethanol. All samples were dried at 40 °C for 3 d to remove residual ethanol, and the absolute dry weight was measured. The paste was then immersed in water for 1 d using a vacuum pump, and the submerged dry weight and surface dry weight were measured.

• Ignition Loss

5.

The ignition loss was measured to evaluate the changes in the hydration reaction with various mixtures. The paste preparation method was identical to that used for the pH tests. Hydration of the paste was stopped using ethanol, and the paste samples were dried at 40 °C for 3 d. The dried paste samples were then ground to a particle size of less than 150 µm, and 1–2 g of paste was placed in an electric furnace at 350 °C for 60 min [23]. The temperature varied from 40 °C to 350 °C, and the ignition loss was calculated using the formula (m₄₀ − m₃₅₀)/m₄₀ × 100, where m₄₀ and m₃₅₀ represent the sample masses at 40 °C and 350 °C, respectively.

• Water Desorption Behavior

6.

To evaluate the effects of the CSA and SRA on the water desorption behavior, DVS (AQUADYNE DVS1, Quantachrome Instruments, Aton-Paar, Boynton Beach, FL, USA) was measured. Paste specimens sealed and cured for 28 d were used. Before the analysis, all the pastes were cut to approximately 1 mm thickness [33] using a water-cooled cutter. The samples were then slowly exposed to RHs of 96%, 95%, 90%, 80%, 70%, 60%, 50%, 40%, 30%, 20%, and 15% and mass changes were recorded. The mass loss rate and equivalent temperature were adjusted to 0.0001% min⁻¹ and 25 °C, respectively.

• XRD Analyses

7.

Hydration reactions of the paste specimens, which were sealed and cured for 28 d, were stopped using ethanol. The samples were then vacuum-dried at 20 °C for 24 h. The hydration products of the pastes were then evaluated using a SmartLab X-ray diffractometer (Rigaku Corporation, Tokyo, Japan) using paste samples with particle sizes smaller than 150 µm.

3. Results

3.1. Compressive Strength and Length-Change Results

Mortar samples were manufactured according to the CCD using CH, CSA, and SRA, and their compressive strengths were evaluated after curing in water for 4, 7, and 28 d. In addition, the length change was measured for 28 d under the drying conditions of 20 °C and 55 ± 5% RH, using the specimens that were sealed and cured for 7 d.

Table 4. Compressive strength and length-change measurements and predictions using the central composite design.

No.	Factors			Compressive Strength (MPa)						Length Change (10−6)
	CH	CSA	SRA	Measured Value			Predicted Value			Measured	Predicted
	wt.%	wt.%	wt.%	4	7	28	4	7	28
1	5	10	0	15.2	20.5	23.8	15.4	19.8	23.1	−719	−925
2	5	0	2	7.8	13.5	15.6	7.6	13.2	15.5	−731	−1065
3	10	0	0	10.2	13.8	17.7	10.0	13.7	17.7	−2342	−2636
4	10	10	2	14.4	19.4	24.2	14.4	18.6	24.4	−613	−885
5	5	5	1	11.9	16.5	17.4	11.5	18.3	22.8	−1221	−1023
6	7.5	0	1	8.3	13.7	15.9	8.7	14.3	19.8	−2159	−1795
7	7.5	5	1	12.0	17.0	24.6	11.5	18.7	24.9	−1077	−1006
8	7.5	5	2	10.9	16.0	19.4	10.9	17.9	22.9	−750	−426
9	7.5	5	1	11.6	19.1	24.5	11.5	18.7	24.9	−1152	−1006
10	7.5	5	0	12.7	17.9	19.8	12.5	19.4	24.9	−1336	−1234
11	7.5	10	1	14.7	16.7	22.1	14.1	19.4	26.8	−1036	−974
12	10	5	1	12.0	16.7	19.5	12.2	18.2	22.7	−1556	−1327
13	5	10	2	12.8	18.6	26.3	13.1	17.3	22.7	−786	−703
14	5	0	0	9.8	15.8	23.3	9.9	15.1	19.5	−2270	−2209
15	10	10	0	14.9	20.9	28.0	15.2	19.8	24.5	−1480	−1357
16	10	0	2	9.2	13.8	16.8	9.1	13.1	13.9	−1236	−1242
17	7.5	5	1	11.3	19.0	25.9	11.5	18.7	24.9	−1137	−1006

lists the measured and predicted values for the compressive strength and length change obtained using the CCD. From the results in Figure 6, the coefficients of determination between the measured values and the predicted equations for compressive strength at 4, 7, and 28 d were 0.994, 0.9951, and 0.9809, respectively. Similarly, as shown in Figure 7, the coefficient of determination between the measured values and the predicted equation for the length change was 0.9978. These results indicate that the compressive strength and length change in CAAM were reliably predicted using Equations (1)–(4).

Compressive strength (4d)
= 12.31 − 0.715 CH + 0.628 CSA − 2.173 SRA + 0.0482 CH × CH − 0.0059 CSA × CSA + 0.151 SRA × SRA − 0.0050 CH × CSA + 0.1450 CH × SRA + 0.0025 CSA × SRA

(1)

Compressive strength (7d)
= 12.99 + 0.79 CH + 1.055 CSA − 1.43 SRA − 0.072 CH × CH − 0.0735 CSA × CSA − 0.092 SRA × SRA + 0.0291 CH × CSA + 0.133 CH × SRA − 0.0296 CSA × SRA

(2)

Compressive strength (28d)
= 4.0 + 4.81 CH + 0.682 CSA − 0.12 SRA − 0.344 CH × CH − 0.0643 CSA × CSA − 0.99 SRA × SRA + 0.0642 CH × CSA + 0.022 CH × SRA + 0.181 CSA × SRA

(3)

Length change
= −3136 + 321 CH + 280.3 CSA + 94 SRA − 27.1 CH × CH − 15.14 CSA × CSA + 176.1 SRA × SRA − 0.10 CH × CSA + 25.1 CH × SRA − 46.1 CSA × SRA

(4)

3.2. Analysis of Variance

The analysis of variance (ANOVA) results are summarized in

Table 5. ANOVA of compressive strength at 4 d.

Source	Sum of Squares	Degree of Freedom	Mean Square	F Value	p-Value
					Prob > F
Model	11	79.8362	7.2578	34.24	0.001
Blocks	2	0.2587	0.1293	0.61	0.579
Linear	3	78.242	26.0807	123.03	0.000
CH	1	1.024	1.024	4.83	0.079
CSA	1	71.289	71.289	336.29	0.000
SRA	1	5.929	5.929	27.97	0.003
Square	3	0.2993	0.0998	0.47	0.716
CH × CH	1	0.2025	0.2025	0.96	0.373
CSA × CSA	1	0.0493	0.0493	0.23	0.650
SRA × SRA	1	0.0511	0.0511	0.24	0.644
2-Way Interaction	3	1.0838	0.3613	1.70	0.281
CH × CSA	1	0.0313	0.0313	0.15	0.717
CH × SRA	1	1.0513	1.0513	4.96	0.076
CSA × SRA	1	0.0013	0.0013	0.01	0.942
Error	5	1.0599	0.212
Lack-of-Fit	4	0.9696	0.2424	2.68	0.425
Pure Error	1	0.0903	0.0903
Total	16	80.8962

,

Table 6. ANOVA of compressive strength at 7 d.

Source	Sum of Squares	Degree of Freedom	Mean Square	F Value	p-Value
					Prob > F
Model	11	84.2192	7.6563	5.63	0.035
Blocks	2	7.7717	3.8859	2.86	0.149
Linear	3	70.4199	23.4733	17.25	0.005
CH	1	0.0144	0.0144	0.01	0.922
CSA	1	64.4869	64.4869	47.4	0.001
SRA	1	5.9187	5.9187	4.35	0.091
Square	3	8.8768	2.9589	2.18	0.209
CH × CH	1	0.4502	0.4502	0.33	0.59
CSA × CSA	1	7.5373	7.5373	5.54	0.065
SRA × SRA	1	0.0189	0.0189	0.01	0.911
2-Way Interaction	3	2.1115	0.7038	0.52	0.688
CH × CSA	1	1.0573	1.0573	0.78	0.418
CH × SRA	1	0.8794	0.8794	0.65	0.458
CSA × SRA	1	0.1749	0.1749	0.13	0.735
Error	5	6.8019	1.3604
Lack-of-Fit	4	4.6461	1.1615	0.54	0.755
Pure Error	1	2.1558	2.1558
Total	16	91.0211

,

Table 7. ANOVA of compressive strength at 28 d.

Source	Sum of Squares	Degree of Freedom	Mean Square	F Value	p-Value
					Prob > F
Model	11	216.471	19.679	2.93	0.123
Blocks	2	69.391	34.696	5.17	0.061
Linear	3	133.771	44.59	6.64	0.034
CH	1	0.006	0.006	0.00	0.977
CSA	1	122.99	122.99	18.31	0.008
SRA	1	10.774	10.774	1.60	0.261
Square	3	23.192	7.731	1.15	0.414
CH × CH	1	10.334	10.334	1.54	0.270
CSA × CSA	1	5.763	5.763	0.86	0.397
SRA × SRA	1	2.208	2.208	0.33	0.591
2-Way Interaction	3	11.72	3.907	0.58	0.652
CH × CSA	1	5.152	5.152	0.77	0.421
CH × SRA	1	0.025	0.025	0.00	0.954
CSA × SRA	1	6.543	6.543	0.97	0.369
Error	5	33.581	6.716
Lack-of-Fit	4	33.579	8.395	6466.37	0.009
Pure Error	1	0.001	0.001
Total	16	250.052

and

Table 8. ANOVA of length change.

Source	Sum of Squares	Degree of Freedom	Mean Square	F Value	p-Value
					Prob > F
Model	11	4,617,188	419,744	18.88	0.002
Blocks	2	302,998	151,499	6.82	0.037
Linear	3	3,535,218	117,8406	53.02	0.000
CH	1	225,525	225,525	10.15	0.024
CSA	1	1,683,727	1,683,727	75.75	0.000
SRA	1	1,625,967	1,625,967	73.15	0.000
Square	3	446,911	148,970	6.70	0.033
CH × CH	1	63,777	63,777	2.87	0.151
CSA × CSA	1	319,394	319,394	14.37	0.013
SRA × SRA	1	69,148	69,148	3.11	0.138
2-Way Interaction	3	456,599	152,200	6.85	0.032
CH × CSA	1	12	12	0.00	0.982
CH × SRA	1	31,422	31,422	1.41	0.288
CSA × SRA	1	425,165	425,165	19.13	0.007
Error	5	111,138	22,228
Lack-of-Fit	4	108,281	27,070	9.47	0.238
Pure Error	1	2857	2857
Total	16	4,728,326

. In general, the statistical significance of a model is assessed when the p-value is less than 0.05. As shown in Table 4, Table 5 and Table 6, the p-values associated with CH for compressive strength at 4, 7, and 28 d were 0.079, 0.922, and 0.977, respectively. Because the p-values were greater than 0.05, it was confirmed that the amount of CH did not significantly affect the compressive strength of the CAAM. In contrast, the p-values associated with the CSA ranged between 0.00 and 0.01. Because the p-values were less than 0.05, these results indicated that the CSA had a statistically significant effect on the compressive strength of the CAAM. The p-values of the SRA were 0.00, 0.09, and 0.26 at 4, 7, and 28 d, respectively. The p-value was slightly higher at day 28. Based on these results and p-values, the CSA was found to contribute more strongly to compressive-strength development than CH and SRA.

Furthermore, as shown in Table 7, the p-values for the length change were 0.024, 0.000, and 0.000 for CH, CSA, and SRA, respectively, all of which were below 0.05. This indicates that all three parameters significantly affected the length change.

3.3. Main Effects

Figure 8 and Figure 9 show the main effects of each factor on the compressive strength and length change. These graphs were generated with CH, CSA, and SRA values fixed at 7.5, 5.0, and 1.0 wt.%, respectively.

As shown in Figure 8, no clear trend in compressive strength was observed with increasing CH content. Meanwhile, increasing the amounts of CSA and SRA resulted in either an increase or a decrease in the compressive strength. This behavior may be attributed to the acceleration of BFS hydration due to CSA replacement and the slight delay in the hydration of BFS and CH caused by SRA addition.

The length-change results are shown in Figure 9. The minus sign (−) indicates drying shrinkage. The figure indicated that as the CH substitution ratio in the BFS increased, the length change decreased further. In addition, the use of CSA and SRA resulted in an increase in the length change, confirming that they help in reducing the drying shrinkage of the mortar.

3.4. Interaction Effects

Figure 10 and Figure 11 present contour plots illustrating the interaction effects of the investigated factors on the compressive strength and length change, respectively. These plots correspond to conditions where the CH, CSA, and SRA were fixed at 7.5, 5.0, and 1.0 wt.%, respectively. As shown in Figure 10a, the compressive strength increased with increasing CSA content. In contrast, in Figure 10b, a slight decrease in compressive strength was observed with increasing SRA content.

Furthermore, as shown in Figure 10c, the compressive strength increased with increasing CSA content and decreasing SRA content. This behavior was attributed to ettringite formation induced by CSA, as reported in previous studies, and the delayed hydration reaction associated with SRA addition.

Figure 11 presents the interactive effects of each factor on length change as a contour graph. As shown in Figure 11a, higher CSA content resulted in a greater magnitude of expansion-related length change. Similarly, in Figure 11b, the change in length increased with increasing SRA content. Furthermore, as shown in Figure 11c, the change in length increased with increasing CSA content and decreasing SRA content. These results suggested that the combined use of CSA and SRA synergistically improved the dimensional stability of CAAM.

3.5. Optimization and Verification of Compressive Strength and Length Change

The optimal parameters for the compressive strength and length change were obtained using the CCD-derived equations, considering CH, CSA, and SRA as the parameters. The compressive strength at 28 d was set to the highest value. In addition, the target value of the length change was determined by measuring the length change in mortar samples made with ordinary cement with water–cement ratios of 0.45 and 0.55, which are commonly used in practice. The change in length of ordinary cement with water-cement ratios of 0.45 and 0.55 was measured to be −1100 × 10⁻⁶ to −1259 × 10⁻⁶ at the start of the 28-day drying period. Therefore, the target value of length change was set to −1100 × 10⁻⁶. The optimized replacement ratios of CH, CSA and SRA to optimize the compressive strength and drying shrinkage were calculated and are summarized in

Table 9. Optimum design of CH, CSA and SRA.

Factors	Value
CH (wt.%)	8.54
CSA (wt.%)	10.00
SRA (wt.%)	0.76
Predicted compressive strength (MPa)	28.0
Measured compressive strength (MPa)	26.7
Predicted drying shrinkage (×10−6)	−1100
Measured drying shrinkage (×10−6)	−1033

. These results confirmed that the CH, CSA, and SRA contents were 8.54, 10.0, and 0.76 wt.%, respectively. Based on these optimal values, compressive strength and length change tests were performed repeatedly, and the results showed close agreement between the measured and predicted values.

3.6. Hydration Heat of Paste

The heat of hydration was measured to evaluate the effects of the CSA and SRA on the hydration reaction of the CAAM. The results of the heat of hydration measurements are shown in Figure 12. This study focused on the hydration exothermic peak occurring within approximately 12 to 24 h, which is related to the acceleration of the hydration reaction of BFS. As shown in Figure 12a,b, as the CH substitution rate in BFS increases, the hydration exothermic peak (12–14 h) increases, and the total heat released up to 48 h also increases. This is due to the acceleration of the hydration reaction of BFS by CH. As shown in Figure 12c,d, the hydration exothermic peak appears to increase even when CSA is added. However, the hydration exothermic peak is slightly lower in the paste containing 10% CSA compared to the sample containing 5% CSA, but this result requires further investigation. As shown in Figure 12e,f, the hydration exothermic peak decreases as the amount of SRA increases.

From the above results, it appears that CH and CSA accelerate the reaction of blast furnace slag. Furthermore, SRA appears to slightly delay the hydration reaction between CH and BFS, which is similar to the measured heat of hydration of conventional cement with SRA [34].

3.7. Results of pH, Porosity, and Ignition Loss of Paste

The effects of CH on porosity, ignition loss, and pH are shown in Figure 13. The porosity and ignition loss results in Figure 13a,b show that despite increasing the CH substitution ratio, the porosity decreased slightly and the ignition loss slightly increased with increasing curing age. Therefore, the use of CH did not appear to have a significant effect on the porosity or ignition loss of the paste. Furthermore, as shown in Figure 13c, the overall pH increased with increasing CH content, owing to the presence of a large amount of unreacted CH.

The effects of the CSA on porosity, ignition loss, and pH are shown in Figure 14. As the replacement ratio of the CSA increased, the porosity decreased and ignition loss increased throughout the curing age. This suggests that CSA addition promotes the hydration reaction of pastes containing CH and BFS. In particular, it was observed that the porosity decreased and ignition loss increased within the first 14 d of curing, indicating that the CSA primarily contributes to early-age hydration. In addition, as shown in Figure 14c, the addition of the CSA slightly decreased the pH.

The effects of the SRA on porosity, ignition loss, and pH are shown in Figure 15. As the amount of SRA increased, the porosity decreased and the ignition loss increased. Furthermore, as shown in Figure 15c, the pH decreased slightly as the curing time increased.

3.8. XRD Analysis

An XRD analysis was conducted to determine the differences in the hydration products affecting the compressive strength and drying shrinkage of mortars made with CH, CSA, and SRA. Figure 16 shows the XRD results.

In Figure 16a, diffraction peaks were observed at approximately 10.7°, 11.4°, and 18.0°. The peaks at 10.7° and 11.4°, although unclear, were attributed to the formation of hemicarbonate, monocarbonate, and hydrotalcite. As shown in Figure 16b, a peak at 9.05° was observed in the paste containing the CSA, which was attributed to the formation of ettringite owing to the use of the CSA. However, no clear differences were observed in the paste containing the SRA as the amount of SRA increased (Figure 16c).

These results suggest that the use of CSA promotes the formation of ettringite, whereas the use of SRA does not affect the hydration reaction of the paste composed of CH and BFS.

3.9. DVS Results

DVS analysis was performed to evaluate the effect of CSA and SRA on water desorption behavior. Pastes aged for 28 d were used, and all samples were cut to a thickness of less than 1 mm. Figure 17 shows the results of water desorption analysis. As shown in Figure 17a, as the CSA and SRA replacement ratios increased, the total water content at 96% RH decreased. Specifically, the water evaporation rate was low in the RH range between 60% and 96%. Below 60% RH, no consistent trend in the water desorption curve was observed with increasing CSA and SRA contents. On the other hand, as shown in Figure 17b, the addition of an SRA reduced the overall water content compared to the sample without it.

In addition, DVS was also used to evaluate the pore structure distribution and its modification in the paste samples, so that the influence of CSA and SRA on the change in pore structure volume in the studied samples can be examined. Several research papers have reported using the DVS method to determine the pore structure of cement. One method is to assess the type of hydrate within a specific humidity range [35], and the Barrett–Joyner–Halenda (BJH) [36] method is also widely used [36]. Recently, Houng et al. [33] investigated the water-to-binder ratio and the nano pore structure of supplementary cementitious materials by means of DVS and they evaluated the pore size distribution by means of the BJH method, which is commonly used to evaluate the pore size distribution by means of nitrogen adsorption and water vapor adsorption. They proposed [33] that the pore structure of pastes is composed of interlayer water, small gel pores in ink bottles, large gel pores, and capillary pores. In this study, the BJH method was also used to examine the effects of CSA and shrinkage-reducing agents on pore structure. Figure 18 shows the pore size distribution results of the paste samples calculated using the BJH method. It can be seen from Figure 18a that two peaks were observed in the CH7.5 and CSA5 samples ranged between approximately 2 to 4 nm and 4 to 10 nm, respectively. These two samples indicate that the pores are composed of small and large gel pores. Moreover, in comparison to CH7.5 and CSA5 samples, the CSA10 sample has a lower amount of pore volume ranging from approximately 5 to 10 nm. It is observed that the pore volume decreases to approximately 7 nm for SRA1 and SRA2. These observations suggest that the use of CSA and SRA may cause pore structure change, which corresponds to large gel pores.

4. Discussion

4.1. Effect of CSA

Based on the CCD method, the compressive strength and length change in mortars containing different amounts of CH, CSA and SRA were evaluated. The effects of each parameter on the compressive strength and drying shrinkage of the mortar were investigated. Furthermore, an optimal material design method for achieving high compressive strength and improved dimensional stability was proposed and verified. The results demonstrated good agreement between the measured and predicted values.

Analysis of the effects of each material on the compressive strength revealed that CH had little or no statistically significant effect on the compressive strength, but as the CSA replacement ratio increased, the compressive strength improved throughout the entire curing period. Furthermore, the use of CSA increased the heat of hydration of the paste and decreased its porosity, which is related to the hydration reaction induced by CSA. Recently, other researchers have also studied the effects of CSA on the hydrates and mechanical properties and reported that the use of CSA resulted in the formation of ettringite, monosulfate, C-S-H gibbsite, and strätlingite [37,38,39]. In this study, the formation of ettringite, the primary hydration product of CSA, was also confirmed, leading to an increase in the compressive strength of the mortar.

Furthermore, the dimensional stability evaluation results showed that the replacement of CSA reduced length change. This improvement of the drying shrinkage was also confirmed by the water desorption analysis results. In the case of pastes containing CSA, the amount of gel pores was found to decrease. Generally, when CSA is added to cement, the pore volume increases from around 10 nm to several hundred nm or more [40,41], which corresponds to capillary pores. Therefore, the hydration products corresponding to the pore volume water desorption measurement (Figure 12), which may be due to the formation of C-S-H gel by promoting the hydration reaction of the BFS with CSA.

4.2. Effect of SRA

The use of an SRA in CAAM slightly delayed the heat of hydration, leading to a decrease in compressive strength. Several studies have reported the effects of SRA on compressive strength. This study found that the use of SRA in CAAM slightly delayed the heat of hydration and slightly reduced the compressive strength of mortar. This trend is similar to that observed in other studies [42]. The reasons for this are explained as the inhibition of dissolution of alkaline components in pore fluid during the hydration reaction [43] and the adsorption of SRA on anhydrous or hydrated phases [44]. Therefore, the delay in the hydration reaction and changes in the pore structure may be closely related to the reduction in compressive strength.

Generally, SRA reduces drying shrinkage by lowering the surface tension of the pore solution, thereby reducing capillary tension [45]. From the CCD results, it can be seen that the use of SRA significantly improved the dimensional stability of mortar. This trend was also confirmed by the DVS measurements of pastes using SRA. These findings provide further evidence that SRA effectively mitigates drying shrinkage by reducing moisture loss, ultimately improving the dimensional stability of CAAM. Furthermore, SRA reduces the pore volume corresponding to the relative humidity of the C-S-H ratio. In a previous paper by the authors, the effect of SRA on pore distribution was investigated using a nitrogen adsorption pore test, and a reduction in pore volume of 10 to 50 nm was observed [42]. Furthermore, using mercury intrusion porosimetry, it was reported that the volume of pores measuring approximately 5 nm decreased with increasing SRA content, while the volume of 15 nm pores increased [44]. In this study, it was also found that the pore volume of C-S-H gel decreased, a trend partially consistent with previous studies. Therefore, the SRA used in this study appears to affect small pores, and the presence of these pores helps suppress drying shrinkage.

5. Conclusions

This study investigated the effects of the relative proportions of CH, CSA, and SRA on the compressive strength and length change in CAAM. Based on these parameters, 17 types of mortar mixtures were manufactured using a CCD method, and their compressive strengths and length changes were measured. In addition, the heat of hydration, loss on ignition, porosity, and water-desorption behavior were investigated. Based on the experimental results, the following conclusions were drawn.

(a)

Analysis of variance for compressive strength revealed that the CH content exhibited higher p-values than the CSA and SRA. In contrast, the CSA showed lower p-values, which contributed to the improvement in the compressive strength of the CAAM. Analysis of variance for length change revealed that both CSA and SRA exhibited lower p-values than CH, indicating that these ingredients positively contributed to the improvement in drying shrinkage of the CAAM.

(b)

Using a CCD and ANOVA, prediction equations for the compressive strength and length change in mortar composed of CH, CSA and SRA were proposed. The optimal contents of CH, CSA and SRA for improving the compressive strength and length change were calculated to be 8.54, 10.0, and 0.76 wt.%, respectively. The compressive strength and length changes were measured again under these material conditions, showing that the experimental values closely matched the predicted values, confirming the reliability of the optimization approach.

(c)

Compressive strength measurements showed that the compressive strength increased with increasing CSA replacement ratio. This enhancement was associated with higher CSA replacement ratios. Conversely, increasing the SRA content resulted in a reduction in the compressive strength, consistent with the delayed hydration behavior observed in the paste.

(d)

Length-change measurements demonstrated that the use of CSA and SRA significantly improved the dimensional stability. Furthermore, the DVS analysis results were correlated with a reduction in water desorption at RH above 60% and revealed the presence of large gel pores, which may be related to the observed shrinkage-mitigation behavior. The use of CSA and SRA therefore represents a potentially effective strategy for overcoming the well-recognized drying shrinkage limitations of CAAM.