Effect of Superabsorbent Polymers and Presoaked Coarse Recycled Shale Lightweight Aggregates on Relative Humidity Development in Early-Age Concrete

Abstract

Self-desiccation-induced shrinkage may result in cracking at an early age, which is averse to the durability of concrete. Internal curing (IC) agents, such as superabsorbent polymers (SAP), are normally used for moisture regulation and shrinkage reduction. In addition, the make-up of recycled shale lightweight aggregate (RSLA) results in a good absorbing capacity, which makes it a potential candidate for IC. In this paper, the synergistic effect of SAP and RSLA on the relative humidity (RH) variation in early-age concrete under sealed conditions is investigated experimentally in terms of the setting time, relative humidity, and autogenous shrinkage. The results indicate that adding SAP and presoaked RSLA can significantly postpone the initial and final setting times. The initial setting time of RSLA30 and SAP06 is delayed by 127 and 171 min, respectively, compared to the benchmark mixture. In addition, increasing the amounts of SAP and presoaked RSLA can effectively extend the duration of the vapour-saturated stage, reducing the decrease in RH and autogenous shrinkage at 28 days. When the RSLA dosage increases from 0 to 10%, 20%, and 30%, the duration of the vapour-saturated stage is extended by 2, 9.4, and 26 days, respectively. Moreover, due to different water desorption behaviours, more IC water released by RSLA during the initial stage can slow the water release of SAP and lead to a higher RH level at 28 days.

1. Introduction

Early cracks in high-performance cementitious materials are detrimental to the durability of concrete structures over the long term [1]. Cracks allow moisture and other harmful substances (e.g., deicing salt and carbon dioxide) to seep into the concrete to cause reinforcement corrosion, leading to structure deterioration [2]. Hence, the construction community urgently needs to minimise the risk of cracking at an early age through effective approaches [3]. Conventional approaches, such as watering the concrete surface and surface coverage with plastic sheeting, are usually less effective in application [4]. With the development of materials science, internal curing (IC) is currently well known as one of the most effective approaches. Benefiting from the application of IC agents, such as superabsorbent polymers (SAP) and porous lightweight aggregates (LWAs), additional water is introduced into the concrete to regulate moisture to reduce autogenous shrinkage mitigation.

SAP is a type of functional polymer material that can absorb water up to thousands of times of its weight and release water during hydration to help maintain a high RH. However, it has undesirable characteristics in practice, such as poor dispersion after wetting [5] and low density, which brings problems such as uneven dispensability in mixing and difficulty in controlling the curing effect. In addition, macrovoids may form after SAP particles dry out. These features may lead to a counterproductive effect on concrete durability and mechanical properties. LWAs, on the other hand, are porous materials, such as expanded shale, leca, and zeolite. In particular, to alleviate environmental pressure, much effort has been made to use recycled construction waste as LWA, for example, recycled shale lightweight aggregate (RSLA). Commonly, in practice, LWAs are presoaked and used as a partial replacement of normal aggregates to provide IC water. However, because of their low-intensity character, excessive addition of LWAs may cause a substantial decrease in the mechanical strength of the cement matrix skeleton (for example, up to 32% according to Khatib’s research [6]).

In most instances, early cracks in cementitious materials are closely related to shrinkage during self-desiccation [7,8,9]. Prior investigations [10,11] indicate that moisture loss, represented by a decrease in interior relative humidity (RH), is one of the key factors controlling the magnitude of shrinkage. Large amounts of instructive research have demonstrated that SAP and conventional LWAs are individually effective in RH retention and autogenous shrinkage reduction. However, considering their merits and shortcomings, a mixture of both may produce mutual complementarity, and the synergistic effect mechanism has not been thoroughly clarified. Furthermore, RSLA has the characteristics of large porosity and high-water absorption, which makes it a potential substitute for conventional LWAs. Therefore, more effort toward improving the knowledge of the combined effect on RH development using SAP and RSLA remains worthwhile in increasing waste resource reuse efficiency and improving shrinkage mitigation of early-age concrete.

2. Materials and Methods

2.1. Materials

Ordinary Portland cement (Cement II 52.5R) was used in accordance with the American Society for Testing Materials (ASTM) standard C1157/C1157 M-17 [12]. The density and specific surface area of the cement are 3170 kg/m³ and 380 m²/kg, respectively. Detailed chemical components are presented in

Table 1. Chemical composition of the cement.

Chemical Composition	SiO2	Al2O3	Fe2O3	CaO	MgO	Na2O	K2O	SO3	TiO2	Loss on Ignition
Ordinary Portland cement (unit: %)	19.53	4.31	2.89	63.84	1.25	0.13	0.64	3.25	0.26	3.04

. Natural river sand with a particle size of less than 2.5 mm was used as a fine aggregate after pretreatments of cleaning, drying, and screening. Crushed limestone with a particle size of 5–25 mm was used as the coarse aggregate after washing and drying. Polycarboxylate-type superplasticiser was also adopted to improve the workability of concrete with different mixture proportions.

The SAP used in this test was a structurally cross-linked hydrophilic polymer and could store a considerable amount of water within its semi-open cells without dissolution. The particle size of SAP is between 90 and 120 μm. Adopting Jensen and Hansen’s approach [13], the water absorption capacity of SAP was tested, and it was 14 g water per gram of SAP in pure water.

Referring to guidelines from the American Concrete Institute [14], RSLA was produced by following a six-step procedure, as presented in Figure 1a. First, a mechanical surface treatment was conducted to remove the cement mortar remains. Then, the larger aggregates were successively crushed through primary and secondary jaw-type crushers. After being sieved and washed twice, the RSLAs were dried and collected. The RSLA had a dry-bulk density of 2024 kg/m³. Figure 1b,c is a photograph and the sieving curve of the RSLA used in the experiments, respectively. To determine the water absorption capacity of the RSLA, an experiment was conducted according to ASTM standard C1761/C1761M-17 [15]. The RSLA in a dry state was placed in a gauze bag and weighed to record the initial weight G₀. Following immersion in deionised water for a specific time t, the bag was lifted and weighed after no more dripping, and the weight G_t was recorded. The water absorption in weight at t is calculated using Equation (1). The water absorption curve has been reported previously [16] and is as presented in Figure 1d. The curve becomes flat after 3 days. Hence, a water absorption ratio of 15.5% at 3 days is adopted for the mixture design in this test.

$$Q_t=\left(M_t-M_0\right)/M_0$$

(1)

where $Q_t$ is the water absorption ratio in weight at time t, $M_t$ is the total weight after soaking for time t, and M₀ is the initial weight of the RSLA in a dry state and the gauze bag.

2.2. Mixture Proportions

This paper involved the evaluation of nine concrete mixtures. Based on Powers and Brownyard’s study [17], when the w/c ratio was lower than 0.42, substantial self-desiccation-induced shrinkage could be observed. Hence, as a continuation of previous work, the w/c ratio of the benchmark mixture was designed at 0.35, and the details of the mixture proportion design are presented in

Table 2. Mixture proportions of different concretes.

Mixture ID		WC 35	RSLA10	RSLA15	RSLA20	RSLA30	SAP 02	SAP 04	SAP 06	R10S02
w/c		0.35	0.35	0.35	0.35	0.35	0.35	0.35	0.35	0.35
Mass fraction of RSLA (%)		0	10	15	20	30	0	0	0	10
Mass fraction of SAP (%)		0	0	0	0	0	0.2	0.40	0.60	0.20
Mass in per 1 m3 of concrete (kg)	Water	168	168	168	168	168	168	168	168	168
	Cement	480	480	480	480	480	480	480	480	480
	Sand	613	613	613	613	613	613	613	613	613
	Gravel	1139	1025	968	911	797	1139	1139	1139	1025
	RSLA	0	88.3	132.4	176.6	264.9	0	0	0	88.3
	SAP	0	0	0	0	0	0.95	1.89	2.85	0.95
	IC water	0	13.69	20.53	27.37	41.06	13.69	27.37	41.06	27.37

.

For the design of a mixture with IC using RSLA, the theoretical quantity of IC water to eliminate self-desiccation can be calculated using Equation (2) [18]:

$$M_{\mathrm{IC}}=C_f{\alpha }_{\max }\mathrm{CS}$$

(2)

where $M_{\mathrm{IC}}$ is the theoretical quantity of IC water, $C_f$ denotes the cement content per unit volume of concrete (480 kg/m³ in this paper), ${\alpha }_{\max }$ is the theoretical maximum hydration degree, which can be estimated as (w/c)/0.36 (0.972 in this paper), and CS denotes the chemical shrinkage of the cement at complete hydration (0.08 in this paper).

For a given w/c ratio and specific amount of cement, the required quantity of IC water can be calculated. The required RSLA amount for mixture design ($M_{\mathrm{LWA}}$) is calculated using Equation (3):

$$M_{\mathrm{LWA}}=\frac{M_{\mathrm{IC}}}{S\beta {\phi }_{\mathrm{LWA}}}$$

(3)

where S is the degree of saturation of aggregate (0 to 1), which is set to 1 owing to RSLA is soaked in advance; $\beta$ denotes the fraction of effective water to counteract self-desiccation in IC water (0 to 1), and $\beta$ = 1 is employed with the assumption that all water in RSLA can be released; ${\phi }_{\mathrm{LWA}}$ is the absorbed water by weight in a unit weight of RSLA (0.155 kg/kg of RSLA in this paper). Based on a calculation, the required IC water quantity per unit volume of concrete is 37.33 kg, and the quantity of dry RSLA is 240.86 kg. To better study the effect of RSLA on the development of the RH, in this paper, gravel was replaced by RSLA by 10%, 15%, 20%, and 30% in weight, and these specimens were designated RSLA10, RSLA15, RSLA20, and RSLA30 (i.e., mixture No. 2–5 in Table 2), respectively.

For the design of a mixture with IC using SAP, based on Jensen and Hansen’s theory [19], 0.23 g chemical combined water and 0.19 g gel water are required for 1 g cement to finish the process of complete hydration. When w/c is lower than 0.42, cement particles imbibe water from the surroundings and cause chemical shrinkage. To avoid this behaviour, internal curing is necessary. Based on Powers’ theory [17], the required quantity of IC water can be calculated using Equation (4):

$$M_{\mathrm{IC},\mathrm{SAP}}=\left\{\begin{array}{ll}0.19\times \left(w/c\right)\times M_{\mathrm{cement}}& w/c\le 0.36\\ \left[0.42-\left(w/c\right)\right]\times M_{\mathrm{cement}}& w/c>0.36\end{array}\right.$$

(4)

where $M_{\mathrm{IC},\mathrm{SAP}}$ is the theoretical quantity of IC water, and $M_{\mathrm{cement}}$ denotes the unit weight of cement. Based on the test result of the water absorption capacity of SAP, the amount of SAP can be calculated. To keep consistent with mixtures of RSLA on the quantity of IC water, mixtures No. 6–8 in Table 2 are 0.2%, 0.40%, and 0.60% SAP by weight, respectively. Ultimately, to be consistent with mixtures of RSLA and SAP on the quantity of IC water, mixture No. 9 is designed, and the details regarding the mix proportion design are presented in Table 2.

2.3. Sensor Calibration

For continuous interior RH measurement, SHT35 digital sensors from Sensirion were adopted, with typical RH measurement accuracy at ±1.5% and a measurement range from 0 to 100%. In the experiment, sensors were connected to a self-developed sensing device with the features of wireless communication and compact and real-time monitoring. Its detailed design has been reported previously [3]. Before the experiment, a calibration test of the RH sensors was conducted using three saturated salt solutions (i.e., NaCl, KCl, and K₂SO₄) under a constant temperature of 22 °C. The test was conducted according to ASTM standard E104-02 (2012) [20], and the layout is presented in Figure 2a. Each sensor was calibrated at three humidity levels. Figure 2b shows calibrating curves of the RH sensors. The root-mean-square errors between the benchmark curve and curves of the four sensors are calculated as 1.46%, 1.83%, 1.75%, and 0.95. The correlation coefficients between the benchmark and measurement curves are 0.997, 0.997, 0.999, and 0.999. The obtained numbers indicate that the sensors can accurately record the variation in RH. To obtain more accurate data, the measured RH data were revised based on the calibration results.

2.4. Concrete Mixing and Experimental Procedures

RSLA was soaked in water for 3 days, and its surface was dried using a wet towel. During the mixing procedure, the sand and gravel were mixed in advance. Then, cement was added to the agitator followed by both required amounts of water with a superplasticiser, and the mixing process was continued for 2.5 min with a 30 s pause in the middle. For mixtures containing RSLA alone, presoaked RSLA was added to the agitator for 1 min. For SAP mixtures, SAP and the corresponding amount of IC water were added to the mixtures, and the continuous mixing time was 1 min. For the mixture with SAP and RSLA components, SAP, the designed quantity of IC water, and presoaked RSLA were added successively, and mixing continued for another 1 min. Afterwards, the slumps and initial casting temperatures of the fresh concrete were measured and recorded according to ASTM standard C143/C143 M-15a [21].

The experiments were conducted in a lab with an ambient temperature of 20 ± 2 °C. Steel moulds with net inner dimensions of 100 mm × 100 mm × 100 mm were adopted for the RH measurements. Every side of the mould was covered with film and tinfoil to minimise moisture evaporation. The layout of the mould and the sensor arrangement are presented in Figure 3. After being fully mixed, different mixtures were cast into the moulds and consolidated by a mini vibrator. During the vibration process, a patented polyvinyl chloride (PVC) tube [22] was inserted into each specimen with an inside steel bar as a space filler. After vibration, the surface of every specimen was also sealed. Moreover, the initial and final setting time for each specimen was determined by Vicat needle penetration according to the ASTM standard C807-13 [23]. After the final set, the steel bar was replaced with a calibrated RH sensor. The nozzle was sealed with a plug, and the gap between the sealing plug and PVC tube was smeared with Vaseline. Subsequently, RH data were automatically measured every 10 min. The data were wirelessly transmitted to the terminal and saved locally in the TF card as a fail-safe backup.

3. Results and Discussion

3.1. Setting Time

Setting time is a critical parameter for the study of autogenous shrinkage. In addition, it is crucial for the application of concrete mixed with RSLA and SAP in engineering. In this paper, setting time measurements were conducted on the same batch of concrete. The initial and final setting times of the different mixtures are presented in parentheses in Figure 4. In addition, mixtures are symbolised by different colours to distinguish different quantities of IC water.

In Figure 4, the initial setting time of the benchmark mixture WC35 was 417 min. Compared to the benchmark mixture, the initial setting times of RSLA10, RSLA15, RSLA20, and RSLA30 were delayed by 54 min, 68 min, 86 min, and 127 min, respectively. A substantial delay in the initial setting can be observed with an increased quantity of presoaked RSLA. The same trend can be observed in the WC35, SAP02, SAP04, and SAP06 groups. With increasing dosage of SAP, the initial setting times were delayed by 56 min, 109 min, and 171 min. On the other hand, for different mixtures with the same quantity of IC water, the initial and final setting times were largely the same. For the RSLA10 and SAP02 groups, the time differences were 2 min (initial setting) and 3 min (final setting), respectively. For the RSLA30 and SAP06 groups, the time differences were 44 min (initial setting) and 6 min (final setting), respectively. For the RSLA20, SAP40, and R10S02 groups, the maximum time differences were 23 min (between RSLA20 and SAP04).

Similar results have been reported previously [24], and IC water quantity is one of the most crucial factors contributing to these results. By introducing more IC water into the mixtures, the effective w/c ratio decreases, which leads to an increase in the effective water content for hydrating the cement. On the other hand, paper [25] also reported that a small amount of IC water may be released into fresh mixtures before the initial setting. Hence, with an additional amount of water, hydration products achieve saturation concentration with difficulty, and the subsequent hydration process will be affected [26]. The dosage of SAP could be another factor. Numerous papers indicate that adding SAP could prolong the induction stage of hydration, which could lead to a reduction in heat release in the acceleration stage and result in a delay in the initial setting [27]. An error brought by testing methods could also be a factor. For the preparation of presoaked RSLA, surfaces were cleaned with a damp cloth. Saturated dry conditions for RSLA are precisely achieved with difficulty, and additional water may be introduced to cause a deviation in the setting time, which requires more research to fully understand the role of the above factors in the global progress of the setting.

3.2. Effect of SAP on the Development of the RH

The RH is plotted against the age of different mixtures containing different SAP dosages in Figure 5a. A significant two-stage RH evolution characteristic can be observed in each curve. During the initial water vapour saturation stage (stage I), the curves of RH are relatively stable, and the values remain constant at 100%, which indicates that the pore inside the mixtures is saturated by water. For mixtures WC35, SAP02, SAP04, and SAP06, stage I lasts 2, 6.2, 8.9, and 20.9 days, respectively. In comparison, the duration of stage I for different mixtures with and without SAP is displayed in Figure 5b. In addition, the correlation coefficient (R²) and root-mean-square error (RMSE) between the experimental data and the corresponding linear regression curve are calculated as 0.893 and 3.24%, respectively. A substantial effect of adding SAP can be observed, and the duration increases significantly with the quantity of IC water. After stage I, the RH starts to decrease for each mixture considered in Figure 5a. At 7 days, the RHs are 97.15%, 99.69%, 100%, and 100% for mixtures WC35, SAP02, SAP04, and SAP06, respectively. In addition, at 28 days, the RHs of the corresponding mixtures are 95.0%, 97.76%, 98.84%, and 99.37%, respectively. A trend of the reduction in the RH is delayed with the addition of more IC water over time, which agrees well with the literature [13]. The daily average rate of decrease in the RH of mixtures WC35, SAP02, SAP04, and SAP06 is 0.026, 0.032, 0.044, and 0.061%/day, respectively.

Concrete is a heterogeneous multiphase material, and the measured RH is the RH of the pores, which are in a water vapour equilibrium state [28]. At the early age from casting, the fine pores are filled with an admixture of cemental material particles, liquid water, and trace amounts of air [29], which lead to an initial RH at or near 100%. With the consumption of initial water in the pores, more pores convert into an unsaturated porous state, which ultimately leads to a decrease in the measured RH. Therefore, the water loss rate and amount of water in the pores are two crucial factors that affect the duration of the initial water vapour saturation stage (stage I) and govern the evolution of the RH. Regarding water loss, the mixtures in this paper are under sealed conditions; thus, water loss caused by evaporation from the top surface is blocked. Therefore, water consumption in the fine pores is mainly caused by the hydration process of cemental material particles. The amount of water in the pores is generally affected by the size of the pores from casting, which is mainly controlled by the w/c ratio. However, because of the water desorption characteristics of SAP, additional water is released at an early age to replenish water consumption due to hydration, leading an increase in the duration of stage I upon adding more SAP, as shown in Figure 5a. As the hydration process continues, the water content in the fine pores dwindles, and the vapour becomes unsaturated, which is manifested as a decrease in the RH.

3.3. Effect of RSLA on the Development of the RH and Autogenous Shrinkage

Experimental data on RH development of mixtures with added RSLA are presented in Figure 6, which have been reported in the literature [16]. The addition of RSLA leads to a prolonged saturation period, and the RH increases progressively with higher RSLA content during the unsaturation stage.

In this section, the reduction rate of RH (${\alpha }_{\mathrm{RH}}$) is used to study the effect of adding RSLA on the evolution of RH, which is defined as follows:

$${\alpha }_{\mathrm{RH}}=\Delta RH/\Delta t$$

(5)

where ${\alpha }_{\mathrm{RH}}$ denotes the RH reduction rate, and $\Delta RH$ is the change in the RH in time frame $\Delta t$. Based on Equation (5), graphical results of the daily average rate of decrease in RH for mixtures containing RSLA are presented in Figure 7.

In Figure 7, for the mixture RSLA30, the RH was constant at 100% over 28 days; consequently, the RH reduction rate was 0% throughout the experiment. For the curves of other mixtures in the group, a significant two-stage characteristic can be observed. During stage I, the RH was stable, which led to a constant RH reduction rate of 0%/day. For the mixtures WC35, RSLA10, RSLA15, and RSLA20, stage I lasts 2, 4, 9.9, and 11.4 days, respectively. The duration of the initial stage increases with the amount of IC water.

The autogenous deformation test for mixtures with/without RSLA was conducted using cylindrical PVC tube moulds with deformation sensors installed at the geometric centre, i.e., the vibration wire method. Details of the experimental setup and testing procedures were reported in previous work [16]. In many papers, different methods have been proposed for determining the starting time point for the analysis of autogenous deformation, such as the initial or final setting time [30], time for reaching peak expansion [31], and initial changing time of the measured ultrasonic velocity [32]. In this paper, considering the factors of unity in the analysis and definition of autogenous deformation [33], the initial setting time is selected as time zero for the analysis of autogenous deformation evolution. For better analysis, the influence of thermal deformation is calculated using the approach recommended by the Japan Concrete Institute [34] and eliminated from the measured deformation. The specific calculation formula is as follows:

$$\epsilon (t)={\epsilon }_{total}(t)-\alpha (t)\cdot \left[T(t)-T_0\right]$$

(6)

where $\epsilon (t)$ is the autogenous deformation strain of the concrete at t days, με; ${\epsilon }_{total}(t)$ is the deformation data of concrete measured at t days, με; $\alpha (t)$ is the thermal expansion coefficient of concrete, and the recommended value of 10 µε/°C as suggested by the Japan Concrete Institute [34] is adopted; $T(t)$ is the temperature of the concrete at t days, °C; $T_0$ is the initial temperature of the concrete, °C; and $t$ is the age, in days.

The relationship between age and autogenous deformation of concrete with different RSLA content is displayed in Figure 8. The autogenous deformation of concrete incorporating RSLA exhibits an initial expansion followed by shrinkage and then gradually stabilises. The larger the RSLA content, the larger the maximum expansion and the longer the corresponding age. Moreover, the autogenous shrinkage of concrete significantly decreases with the increase in RSLA content throughout the testing period.

The relationship between autogenous shrinkage and RH at 28 days is presented in Figure 9. In Figure 9, different patterns can be observed, and they will be discussed separately. The mixture of plain concrete (i.e., WC35) has an L-shaped curve that shows a distinct two-stage variety characteristic at 28 days. As previously analysed regarding RH evolution, the mixture is in a vapour-saturated stage after casting; hence, the initial curve is vertical. Along with hydration, the RH begins to decrease (stage II), and mixture WC35 continues to contract. In addition, during stage II, the value of autogenous shrinkage increases from 37 με to 123 με with contraction. Linear correlations can be observed between ln(RH) and autogenous shrinkage ($\epsilon$), which matches the trend in the literature [35]. The linear relationship can be expressed as follows:

$$\epsilon =a\ln \left(RH\right)+b$$

(7)

where a and b are parameters related to the mixture proportion.

For the mixtures RSLA10 and RSLA15, an “expansion–contraction” pattern can be observed in the curve. After the initial setting, the mixtures begin to expand and reach expansion peaks of 35 με and 50 με at 10 h and 12 h, respectively. Subsequently, shrinkage deformation occurs. At 28 days, the autogenous shrinkages are −50 με and −5 με, respectively, which are 59.3% and 95.6% reductions compared to the autogenous shrinkage value of WC35 at the same age. For mixtures RSLA20 and RSLA30, the curves show a continuous expansion pattern. For mixture RSLA20, the autogenous shrinkages at the beginning of stage II and at 28 days are 63 με and 70 με, respectively. In addition, the curve of mixture RSLA30 shows no discernible turning point. The autogenous shrinkage value at 28 days is 85 με, which is 21% higher than that of RSLA20 at the same age.

For the mixture RSLA30, linear correlations can be observed between ln(RH) and $\epsilon$ in Figure 9. Based on Equation (7), fitting parameters are obtained through a regression analysis for mixtures other than RSLA30, and fitting formulas are presented in Figure 9. Correlation coefficients (r) and root-mean-square errors (RMSEs) are calculated between fitting and test data. The minimum correlation coefficient is 0.927, and the maximum RMSE is 5.7 με. The calculated results show the linear correlations between ln(RH) and $\epsilon$ for mixtures with added RSLA at stage II.

Different factors can contribute to the experimental behaviour of mixtures at stage II. For RSLA30, reabsorption of the bleeding water [36] and growth of hydration products (i.e., ettringite, calcium hydroxide, etc.) [37] can be two major factors for its continuing expansion. For other mixtures, according to the literature, autogenous shrinkage is closely connected to the variation in internal RH, which can be explained by the evolution mechanism of the microstructure of cement paste. Its process is shown schematically in Figure 10. From casting, the cement particles are saturated in the water (as presented in Figure 10a). With the formation and development of hydration products, pores varied in size and differed in direction, and local connectivity began to form. When the pore water is separated from the water network and the hydration process continues, the internal RH begins to decrease (as presented in Figure 10b), menisci are formed, and capillary stress occurs. According to the Kelvin and Laplace equation [38], the capillary stress ($\sigma$) and menisci curvature radius (r) can be calculated as follows:

$$\sigma =\left(-\rho RT/M\right)\cdot \ln \left(RH\right)$$

(8)

$$r=-2\gamma M/\left[\rho RT\cdot \ln \left(RH\right)\right]$$

(9)

where $M$, $\rho$, and $\gamma$ are the molar weight, density, and surface tension of the pore solution, respectively. R is the universal gas constant, and T is the absolute temperature. Considering the equivalence and superposition principle introduced by Mackenzie and the micromechanical model established by Jun Zhang [39], the total strain in a porous material can be expressed as follows:

$${\epsilon }_w=-\frac{v_{\mathrm{p}}\rho RT}{3M}\left(\frac{1}{K}-\frac{1}{K_{\mathrm{s}}}\right)\cdot \ln \left(RH\right)$$

(10)

where K and K_s are the bulk moduli of the porous body and solid skeleton of the material, respectively.

In Equation (10), the parameter (i.e., $-\frac{v_{\mathrm{p}}\rho RT}{3M}\left(\frac{1}{K}-\frac{1}{K_{\mathrm{s}}}\right)$) is closely connected to the pore characteristics in the mixture. Under ideal circumstances, the properties change slightly with the hydration process, and the parameter is a constant value. Thus, the resulting strain from the capillary force has a linear relationship with ln(RH), which matches well with the trend in Figure 9. Although several factors could contribute to this experimental behaviour (e.g., surface free energy [40] and disjoining pressure [41]), capillary stress could be one of the most important factors. The above calculation results related to capillary stress could well explain the experimental results under ideal circumstances. However, how each factor is involved in the macroscopic shrinkage performance of each mixture still needs further research.

3.4. Synergistic Effect of RSLA and SAP on the Development of RH

To study the combined effect of RSLA and SAP on RH development in mixtures, presoaked RSLA and SAP were added to mixture R10S02 according to the designed proportion in Table 2. For the group of mixtures of SAP04, RSLA20, and R10S02, the quantity of internal curing water was identical. RH data are compared in Figure 11 with reference to benchmark mixture WC35.

In Figure 11, the curves of different mixtures also show a clear two-stage trend. For the mixtures SAP04, RSLA20, and R10S02, stage I lasts 8.9, 11.4, and 9.2 days, respectively. Compared to 2 days of plain mixture WC35, the durations of stage I mixtures with internal curing are substantially extended. In addition, in terms of RH development, at 14 days and for the corresponding mixtures, the RHs are 99.8%, 99.5%, and 99.6%, respectively. At 28 days, the corresponding RHs are 98.8%, 98.5%, and 99.1%. Compared to the plain mixture WC35 at the same age, the RHs of mixtures with internal curing at 14 and 28 days are substantially increased. The significant delay in RH reduction and slower decrease in the RH value in stage II can be attributed to the internal curing water released by SAP and/or RSLA. Based on the analysis in Section 3.3, a slower decrease in RH benefits the reduction in autogenous shrinkage, which possibly leads to a low risk of cracking.

However, RH development varies slightly for the SAP04, RSLA20, and R10S02 mixtures. The stage I duration of R10S02 is longer than that of SAP04 but shorter than that of RSLA20. In addition, the RH value of R10S02 is intermediate to those of SAP04 and RSLA20 most of the time because the RH decreases. Research indicates [42] that this phenomenon might be related to the different water desorption behaviours of SAP and presoaked RSLA during hydration. Because of different structural characteristics, RSLA typically released water faster than SAP under identical conditions [4], which would cause changes in the total water-to-cement (w_t/c) ratios [43]. The RH development curves in Figure 11 indicate that the sequence of w_t/c ratios for mixtures is as follows: RSLA20, R10S02, and SAP04. On one hand, for a lower w_t/c ratio, smaller initial pores are formed in the mixtures, which can store less water. For a given water loss rate, a smaller amount of water is consumed faster and therefore stage II is reached sooner [44]. On the other hand, a lower w_t/c ratio leads to a higher water loss rate under sealed conditions and stage I is briefer [45]. For a certain amount of pore water, an increase in the water consumption rate also makes stage I briefer.

In particular, for mixture R10S02, half of the IC water is designed to be provided by presoaked RSLA, and the other half is from SAP. In this experiment, the synergism of RSLA and SAP is primarily exhibited as a superposition effect in water desorption behaviour. Notably, after 24 days, the RH of mixture R10S02 is higher than that of mixture SAP04. This phenomenon might also be related to the synergistic effect. According to Wang et al. [46], the RH gradient is a major factor affecting the desorption behaviour in cement paste. From casting, more IC water is released from the RSLA than from the SAP, which leads to a smaller RH gradient near the SAP particles in mixture R10S02. Hence, IC water is released slowly by SAP because of the insufficient driving force in diffusion. During the hydration process, more water is consumed. With the increase in the RH gradient, more water is released, which leads to a high level of RH at 28 days in mixture R10S02. Experimental error caused by data acquisition inaccuracy could also be too large to neglect, especially when the RH is high. To ensure the reliability of the research in this paper, for each mixture proportion, two parallel experiments were conducted. The measured RH has the same trend as discussed in this paper with a slight difference in value. However, the influence of experimental accuracy could not be completely excluded. More discussion on the analysis of influencing factors and further research on the synergistic effect between RSLA and SAP are still needed.

4. Conclusions

Based on the materials used in this study and the measurement results, the following conclusions can be drawn:

• SAP and RSLA have a substantial effect on the setting. With increasing dosages of SAP and RSLA, a significant delay in the initial and final setting times can be observed. Moreover, the extent of the delay is less influenced by the proportion of SAP and RSLA but depends on the IC water quantity. The initial setting time of RSLA30 and SAP06 is delayed by 127 and 171 min, respectively, compared to the benchmark mixture.
• SAP and RSLA have a great influence on the RH development of early-age concrete. Specifically, the addition of both can significantly extend the duration of the vapour-saturated stage in a hydration process and increase the RH level at 28 days after casting. When the RSLA dosage increases from 0 to 10%, 20%, and 30%, the duration of the vapour-saturated stage is extended by 2, 9.4, and 26 days, respectively. Furthermore, both substances are effective in alleviating the early-age shrinkage based on the reduction in capillary stress caused by the decrease in RH, which benefits mitigating cracking at an early age.
• SAP and RSLA interact with each other and change each other’s desorption behaviour. Because most IC water is released by RSLA in a preliminary stage, the RH gradient near IC agents decreases, which leads to a decline in water desorption until more water is consumed with hydration. Hence, a substantial increase in RH at 28 days can be observed in the mixture of SAP and presoaked RSLA.