**1. Introduction**

Cement is an excellent and economical construction material, and to date, no construction material that can perfectly replace cement exists. As environmental problems emerge worldwide, however, efforts are being made to identify a suitable substitute for cement because it emits CO2 gas in large quantities [1,2]. It is difficult to completely replace cement in the construction industry because of its widespread usage, but some proportion may be replaceable provided binders suitable for different structural purposes are developed. Various materials that may serve as substitutes for cement have been investigated by many researchers [3–8]. Among them, ground granulated blast furnace slag (GGBFS) and fly ash (FA), which have been used to partially replace cement, can exhibit performances equal to those of ordinary Portland cement (OPC) if alkali-activated materials (AAMs) are used. AAMs are eco-friendly materials that can improve the performance of concrete because they have high initial strength and excellent durability. Thus, many researchers have studied the performance of AAM concrete in this regard [9]. Most studies on AAMs, however, have focused on the reactivity and physical performances of binders; the shrinkage characteristics of AAMs have hardly been

investigated. Cartwright et al. [10], however, reported that AAMs exhibited 3–6 times more shrinkage than OPC. Various previous studies have also reported that AAMs can cause serious problems when used in structures because their shrinkage is significantly higher than that of OPC [11,12]. However, the mechanisms and inferences relating to the high shrinkage of AAMs have not been comprehensibly summarized.

AAMs cause microcracks because they cause much shrinkage [13–16], as such microcracks may degrade the strength and durability of concrete [17–21], various methods have been proposed to reduce the shrinkage of AAMs. According to Chatterji [22], the use of the expansive additives containing alkali metal components can compensate for shrinkage because they generate many expansive hydrates, such as ettringite (3CaO·3Al2O3·CaSO4·32H2O) and calcium hydroxide (Ca(OH)2), and this expansion effect is affected by the mixing and curing conditions of concrete [23,24]. Palacios and Puertas [15] conducted research with various shrinkage-reducing agents to reduce the shrinkage of AAMs. In addition to these methods, which are materials-specific, other techniques for reducing shrinkage have been studied. Thomas et al. [25] proposed a curing method to reduce drying shrinkage, and Sakulich and Bentz [26] reported that use of lightweight aggregates subjected to pre-wetting can reduce autogenous shrinkage due to the internal curing effect. Summarizing the results of these previous studies reveals that the shrinkage caused by AAMs is determined by specific parameters, including the types and mix proportions of AAMs as well as the curing conditions [27–29].

With regard to the shrinkage of AAM mortar, structural problems can be caused simply by the generated shrinkage, but most issues are caused by shrinkage cracking, which occurs when the stress caused by shrinkage is higher than the mortar strength. The shrinkage stress acting on a structure increases with the amount of shrinkage and the modulus of elasticity. In general, the shrinkage of concrete is high at early ages and decreases over time, but the modulus of elasticity increases over time. Thus, in the long term, the shrinkage is low, but the shrinkage stress acting on the structure can be evaluated differently. In particular, AAM mortars show higher initial shrinkage than OPC and are also subject to continuous shrinkage over the long term. Therefore, it is necessary to accurately predict the shrinkage stress generated in AAM mortars by measuring the modulus of elasticity by age and to thereafter apply appropriate shrinkage-reducing technologies accordingly.

In this study, a calcium sulfoaluminate-based (CSA) expansive additive was used to compensate for the shrinkage of AAM mortar. The shrinkage characteristics of the AAM mortar were analyzed by age by measuring its autogenous and total shrinkage for 150 days according to the content of the CSA expansive additive, and a shrinkage model was proposed based on the results. In addition, the shrinkage stress of the AAM mortar was calculated by measuring its modulus of elasticity, and the shrinkage stress compensation effect of the mortar mixed with the CSA expansive additive was analyzed.

#### **2. Materials and Method**

#### *2.1. Materials and Mixture Proportions of AAM Mortar*

The AAM mortar used in this study contained a two-component binder, wherein GGBFS and FA were mixed in the ratio 7:3. Table 1 shows the analysis results of the major chemical components of the GGBFS and FA. The GGBFS was procured from Sampyo Cement Corp. (Dangjin, Korea). It had a density of 2.91 g/cm3 and a fineness of 4683 cm2/g. The GGBFS was composed of 41.9% CaO, 33.4% SiO2, 13.8% Al2O3, and 4.9% MgO, and thus, its basicity coefficient (Kb = (CaO + MgO)/(SiO2 + Al2O3)) was 1.00, which is similar to the neutral value of 1.0 for ideal alkali activation [30]. The hydration modulus of GGBFS according to a formula proposed in Ref. [31] (HM = (CaO + MgO + Al2O3)/SiO2) was 1.82. This value was higher than the required value of 1.4, which indicates good hydration properties of the GGBFS [31].

The FA was type 2 fly ash (KS L 5405) procured from Sampyo Cement Corp. (Boryeong, Korea) [30]. It had a density of 2.20 g/cm3 and a fineness of 3216 cm2/g. The FA was composed of 60.3% SiO2, 24.2% Al2O3, and 7.3% Fe2O3. Moreover, SiO2, Al2O3, and Fe2O3 accounted for 91.8% of the total, whereas M2O (K2O + Na2O) accounted for 1.9%. The alkali-activator was used to accelerate the reaction of the binder. The alkali-activator was in the form of white powder with a specific density of 1.026 g/cm3 and a molar ratio of 0.95. In addition, alkali-activators are manufactured separately by adjusting the chemical components. The SiO2/Na2O ratio of the alkali-activator (SiO2: 46.17%, Na2O: 50.18%) used in this study was 0.92.

To compensate for the shrinkage of the AAM mortar, a powdered CSA expansive additive was used. The CSA expansive additive contained lime, gypsum, and bauxite as its major components. The specific density of the CSA expansive additive was 2.86 g/cm3, and its Blaine fineness was 3754 cm2/g. River sand with a density of 2.53 g/cm3 and a water absorption rate of 1.08% was used as a fine aggregate. The maximum size of the fine aggregate was 4.76 mm, and the fineness modulus was 2.77.

**Table 1.** Chemical composition of ground granulated blast furnace slag (GGBFS), fly ash (FA), and calcium sulfoaluminate-based (CSA) expansion agent.

Table 2 summarizes the mix proportions of the AAM mortar. The water-to-binder (W/B) ratio was 45.1% and the sand-to-binder (S/B) ratio was 1.2. The activator-to-water ratio was 24.0%. Then, 0.0%, 2.5%, 5.0%, and 7.5% of CSA expansive additive based on the amount of the binder (GGBFS:FA = 7:3) was added. The AAM mortar was dry mixed for 30 s after inserting the binder as well as the powdered AAM and CSA expansive additive. Water was then added, and the mortar was mixed at a low speed (15 rpm) for 10 min. After inserting the fine aggregate, the mortar was mixed for 90 s at a speed of 30 rpm.

**Table 2.** Mix proportions of alkali-activated material (AAM) mortar.

#### *2.2. Test Methods*

Cube mortar specimens of dimensions 50 mm × 50 mm × 50 mm complying with ASTM C109-16a [32] were prepared. AAM mortar was poured into a cubic mold, cured for 1 d, and demolded. It was then cured in a chamber with constant temperature (20 ± 2 ◦C) and relative humidity (90 ± 2%). The compressive strength test was conducted at 1, 7, and 28 d of age. The modulus of elasticity of the concrete was calculated by applying loads up to 40% of the ultimate load at a rate of 0.25 MPa/s and obtaining the deformation values for the loads using an interpolation method in accordance with ASTM C469M-14 [33].

An embedded gauge (PMFL-50-2LT, Tokyo Sokki Kenkyujo Co., Ltd., Tokyo, Japan) was used to measure the shrinkage of the AAM mortar. Figure 1 shows the method for measuring the length change of the mortar due to shrinkage. An embedded gauge for the length change rate and a temperature sensor (Thermocouple t type, Tokyo Sokki Kenkyujo Co., Ltd., Tokyo, Japan) were installed at the center of 100 mm × 100 mm × 400 mm specimens. Before pouring the mortar, a Teflon sheet and polystyrene board were placed on the inner surface of the mold to minimize friction with the mold and provide restraint in the length direction. After pouring the mortar, a polyester film was installed on the specimen surface to prevent the evaporation and absorption of moisture on the surface. The AAM mortar specimens were cured for 1 d and demolded. The autogenous shrinkage specimen was sealed using a polyester film to control drying shrinkage. The specimen for measuring total shrinkage, namely the sum of drying shrinkage and autogenous shrinkage, was not sealed after demolding. Two specimens were prepared for the length change rate test to measure total shrinkage and autogenous shrinkage, and the measurement results were averaged. The test on the length change rate of the AAM mortar was conducted in a chamber with constant temperature (20 ◦C) and relative humidity (60%).

**Figure 1.** Measurement of length change.

#### **3. Results and Discussion**

### *3.1. Compressive Strength and Modulus of Elasticity*

Table 3 shows the tests results of the compressive strength and modulus of elasticity of the AAM mortar according to the content of the expansive additive. The target strength of the AAM mortar was 40 MPa, and all the mixtures met the target strength at 28 d of age. The compressive strength results at 1 d of age showed that the compressive strength of Expansive Additive (EA)-0.0 was 3.16 MPa, but the AAM mortar specimens mixed with the expansive additive exhibited compressive strengths exceeding 5 MPa, indicating a strength increase of more than 2 MPa compared to that for EA-0.0. In particular, EA-5.0 exhibited a compressive strength of 5.91 MPa, the highest observed strength, at 1 d of age. At 28 d of age, the strengths of EA-2.5 and EA-5.0 were respectively 12.6% and 13.7% higher than that of EA-0.0. The strength of EA-7.5, however, was only 8.4% higher. Therefore, it was found that AAM mortar exhibited the highest strength when the content of the expansive additive was 5%.

When the modulus of elasticity of the AAM mortar specimens mixed with the expansive additive were compared, it was found that the initial modulus of elasticity increased as the content of expansive additive increased. While the modulus of elasticity of EA-0.0 at 1 d of age was 1.21 GPa, that of EA-7.5 with the highest expansive additive content was 2.46 GPa, which was approximately two times higher. As the age increased, however, the effect of the addition of the expansive additive on the modulus of elasticity decreased. At 28 d of age, the modulus of elasticity of the AAM mortar ranged from 20.07 to 21.17 GPa, showing that the influence of the expansive additive was not significant.

**Table 3.** Compressive strength and modulus of elasticity of AAM mortar.

AAM mortar with the CSA expansive additive exhibited an increase in the modulus of elasticity at early ages, but there was no significant difference in the modulus of elasticity at 28 d of age. This means that the rate of increase of the modulus of elasticity may vary depending on the content of the expansive additive. Various prediction equations on the modulus of elasticity were applied to compare the moduli of elasticity of the AAM mortar according to the content of the expansive additive, but the model on the modulus of elasticity proposed by American Concrete Institute (ACI) 209, which can predict the modulus of elasticity of the AAM mortar most accurately, was used [34]. As a result, R2 between the modulus of elasticity measured from the experiment and that obtained by the ACI 209 model for AAM mortar was 98.89% or higher, indicating a high correlation.

$$E\_{\rm cntt} = E\_{\rm cm28} \sqrt{\frac{t}{a+bt}}\tag{1}$$

where *Ecmt* is the modulus of elasticity of the AAM mortar at *t* days of age, and *Ecm*28 is the compressive strength at 28 d of age. *a* and *b* are material constants related to the compressive strength. Figure 2 shows the experimental values of the modulus of elasticity of the AAM mortars and the prediction curves for the modulus of elasticity as per the ACI 209 model. Table 4 shows the results of the derivation of the values of *a* and *b* according to the content of the expansive additive by applying the ACI 209 model. Nagataki and Gomi [35] reported that if the content of CSA expansive additive exceeds a certain value, the strength may decrease but the modulus of elasticity and creep increase continuously. The experiment results also showed that the material constants of the modulus of elasticity did not change considerably when the content of the expansive additive was less than 5%, but they exhibited a different tendency when the content was 7.5% because the increment in the modulus of elasticity increased. When the content of the expansive additive was less than 5%, the value of *a*, which represents the increment in the modulus of elasticity, decreased, whereas the value of *b*, which denotes the rate of increase in the modulus of elasticity, showed a tendency to slowly increase as the content of the expansive additive increased at 1 d of age. This means that when the expansive additive is added, the initial modulus of elasticity is high and the modulus of elasticity rapidly increases, but there is no significant difference in the final modulus of elasticity. As a result, the prediction curves for the modulus of elasticity as per the ACI 209 model showed a tendency similar to the actually measured modulus of elasticity. Regarding the curves for the modulus of elasticity predicted by the ACI 209 model, EA-7.5 exhibited a somewhat high modulus of elasticity in the long term, but the AAM mortar specimens with the expansive additive content of less than 5% exhibited no significant difference in the modulus of elasticity.

**Figure 2.** Comparison of modulus of elasticity between the test results and the results of the ACI 209 model.

**Table 4.** Material constants of the modulus of elasticity of AAM mortar.

### *3.2. Shrinkage*

Figure 3 shows the shrinkage test results of the AAM mortars at 3 and 150 d of age according to the content of the expansive additive. In the AAM mortar shrinkage test, measurement was started based on the final setting time. According to the results of various studies on AAMs, OPC-based mortar has large initial autogenous shrinkage, which tends to decrease over time. However, AAM mortar has higher initial autogenous shrinkage than OPC mortar and involves high shrinkage in the long term [11,36]. In this experiment, the shrinkage test results of the AAM mortars also showed that rapid shrinkage occurred until approximately 0.5 d and continuous shrinkage occurred until 150 d. EA-0.0 exhibited the highest total shrinkage and autogenous shrinkage because it had no shrinkage compensation effect caused by the expansive additive. As the content of the expansive additive increased, the shrinkage of the AAM mortar decreased. The shrinkage compensation effect of the expansive additive was most clearly observed within 1 d of age. Moreover, the shrinkage curves for up to 150 d of age showed that the shrinkage compensation effect of the expansive additive was not significant for autogenous shrinkage, but the opposite was true for total shrinkage.

The total shrinkage of AAM mortar is the sum of autogenous and drying shrinkage. Thus, drying shrinkage can be calculated using the measured total and autogenous shrinkage. Table 5 summarizes the autogenous, total, and drying shrinkage of the AAM mortars at 1 and 150 d of age. When the shrinkage of AAM mortars was analyzed at 1 d of age, the autogenous shrinkage reduction rates of EA-2.5, EA-5.0, and EA-7.5 were 23.3%, 27.0%, and 35.3% respectively compared to the autogenous shrinkage of EA-0.0, and their corresponding drying shrinkage reduction rates were 65.0%, 65.9%, and 85.1%. This indicates that the addition of expansive additive to AAM mortar reduces both autogenous and drying shrinkage at 1 d of age, but the influence on drying shrinkage is higher. When the shrinkage of the AAM mortars was analyzed at 150 d of age, the autogenous shrinkage reduction rates of EA-2.5, EA-5.0, and EA-7.5 were 1.8%, 3.9%, and 7.5% respectively compared to the autogenous shrinkage of EA-0.0; thus, the reduction rates were lower compared to those at 1 d of age. The drying shrinkage reduction rates of EA-2.5, EA-5.0, and EA-7.5 were 38.0%, 67.4%, and 71.8% respectively compared to the drying shrinkage of EA-0.0, indicating that the reduction rates were lower compared to those at 1 d of age even though shrinkage was reduced by the expansive additive in the long term. This result can be attributed to the initial shrinkage compensation effect of the CSA expansive additive, and the shrinkage reduction rate decreased in the long term because the shrinkage compensation effect of the expansive additive was not significant after 3 d of age.

**Table 5.** εash\*, εtsh\*\*, εdsh\*\*\* of AAM mortar at 1 and 150 d of age.

\* εash: Autogenous shrinkage, \*\* εtsh: Total shrinkage, \*\*\* εdsh: Drying shrinkage.

**Figure 3.** Autogenous shrinkage curves of AAM mortars: (**a**) autogenous shrinkage for 3 d, (**b**) autogenous shrinkage for 150 d, (**c**) drying shrinkage for 3 d, (**d**) drying shrinkage for 150 d, (**e**) total shrinkage for 3 d, and (**f**) total shrinkage for 150 d.