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Experimental study on interior relative humidity development in early-age concrete mixed with shrinkage-reducing and expansive admixtures
Construction and Building Materials 232 (2020) 117204
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Experimental study on interior relative humidity development in early-age concrete mixed with shrinkage-reducing and expansive admixtures Shuo Chen a,⇑, Haitao Zhao a,*, Yu Chen a,b, Donghui Huang c, Yuzhi Chen c, Xiaodong Chen a a b c
College of Civil and Transportation Engineering, Hohai University, Nanjing 210000, China Jiangnan Project Management Co., Ltd., Hangzhou 310000, China College of Civil Engineering and Architectural, Jinling Institute of Technology, Nanjing 210000, China
h i g h l i g h t s Effects of tested SRA and EA on RH development of early-age concrete was studied. A model for critical time considering SRA and EA dosages was proposed. A development model is proposed for the RH in early-age concrete with SRA and EA.
a r t i c l e
i n f o
Article history: Received 3 July 2019 Received in revised form 3 October 2019 Accepted 9 October 2019
Keywords: Relative humidity Development model Early-age concrete Shrinkage-reducing admixture Expansive admixture
a b s t r a c t Early age concrete may crack due to volumetric shrinkage caused by a decrease in the interior relative humidity (RH) in the self-desiccation process. Shrinkage-reducing admixtures (SRAs) and expansive admixtures (EAs) are utilized to mitigate the volumetric shrinkage. Using a self-developed wireless and automatic relative-humidity monitoring system, a series of experiments for the measurement of the RH within concrete specimens was conducted. A systematic analysis was conducted in the aspects of the setting time, critical time and interior RH development in early-age concrete with different dosages of the polymer-type SRA and CaO-type EA. On the basis, a critical time model and a two-stage RH development model considering the effects of the water to binder ratio, SRA and EA dosages were established. Both of the models are in good agreement with the experimental data. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Cracks in concrete, especially in high performance concrete, can cause significant adverse impacts on the long-term performance and durability of a structure. Published studies indicate that the initial conditions, i.e., the temperature and interior relative humidity (RH), have very large impacts on early-age cementitious material behaviours involving cracking [1,2]. Among all the non-loads, volumetric shrinkage under restraint conditions is one of the most important contributors [3,4]. Moisture loss is one of the most important influence factors for volumetric shrinkage and can be caused by self-desiccation [5,6]. When the water to binder (w/b) ratio is lower than a specific value (e.g., 0.36–0.48 depending on the cement type [7]), the amount of ⇑ Corresponding authors. E-mail addresses: [email protected] (S. Chen), [email protected] (H. Zhao). https://doi.org/10.1016/j.conbuildmat.2019.117204 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
water is inadequate to meet the requirement for complete hydration. In a sealed system, the water in the concrete pores can be consumed along with hydration, and the phenomenon of moisture loss (i.e., self-desiccation) occurs. In addition, according to Kelvin’s equation [8], a decrease in the RH could cause a decrease in the curvature radius of the capillary water surface, which would lead to an increase in the capillary stress and surface tension. Volumetric shrinkage occurs in turn, and cracks within the concrete occur with a high probability. Targeted chemical additives have been adopted to mitigate the self-desiccation induced shrinkage at an early age, including shrinkage-reducing admixtures (SRA) [9], expansive admixtures (EA) [10] or a mixture of both [11,12]. Through reducing the surface tension of the water in the capillary pores [13] and generating a limited volume expansion [14], the above two admixtures can compensate for volume shrinkage individually or together. Although a synergistic effect was observed by Meddah et al. [15],
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its mechanism was not thoroughly clarified. Therefore, it is still worth more effort to investigate the relationships among the variability of the RH and the effects of SRA and/or EA on cracking resistance. The measurement, analysis and establishment of development model of the RH change in early-age concrete is critically needed as a foundation for shrinkage calculations and structural cracking prediction. The measurement of the interior relative humidity is ordinarily adopted to quantify the RH change in a closed system [16–18], and a number of references are found in the literature on investigating the development of the interior RH in young concrete. For example, Persson established a model [19], which could accurately fit the RH variation in the decline segment. Zhang et al. [20] developed a two-stage moisture distribution model for earlystage concrete through the degree of cement hydration, which could well reproduce the results from their experiments. However, there are few studies on the RH of concrete containing SRAs and/or EAs. In addition, the traditional cabled RH measurement methods have a disadvantage of being inconvenient. Therefore, there are urgent demands for convenient and reliable in situ real-time monitoring of RH.
2. Materials and methods 2.1. Materials According to the American Society for Testing Materials (ASTM) standard C1157/C1157 M-17 [21], the cement used in this study was classified as original Portland cement (Cement II 52.5R) with a Blaine fineness of 375 m2/kg. The detailed material properties are presented in Table 1. The mud and clay contents of the original natural river sand were less than 1.5% and 0.5% in weight, respectively. Through cleaning, drying, screening and other pre-treatments, the sand was used as a fine aggregate. In addition, the particle size was less than 2.5 mm. The mud content of the crushed limestone was less than 0.5% in weight. In addition, the gradation was continuous, and the particle size was between 5 mm and 30 mm. The limestone was cleaned, dried and utilized as the coarse aggregate. The fitness of the CaO-type EA was verified by a sieve with a pore diameter of 1.18 mm, and the residue was less than 0.5% in weight, which met the requirement of the ASTM standard C688-14 [22]. In addition, detailed material properties of the
EA are presented in Table 2. The polymer-type SRA used in this paper were manufactured by the Sobute New Materials Company, and its detailed properties were reported in the paper [23]. 2.2. Mixture proportions This paper involved the evaluation of seven different concrete mixtures. Based on the study conducted by Powers and Brownyard [24], while the w/b ratio was lower than 0.42, significant self-desiccation induced shrinkage could be observed. Hence, all the designed w/b ratios in this paper are lower than 0.4. The details of the mix proportion designs are presented in Table 3. In the table, cSRA and cEA represent the mass fractions of the SRA and EA, respectively. In the evaluation, three plain concrete mixtures with varying w/b ratios were set as benchmarks (0.3, 0.35 and 0.4 for mixtures W30, W35 and W40, respectively), and the w/b ratio was kept constant at 0.35 for all the other mixtures. In addition, the cement was replaced by the SRA, and the alternative proportions were 2% and 3% in weight. These mixtures were correspondingly described as W35S2 and W35S3. The cement was further replaced by the EA in the W35S2 mixture by 2% and 3% in weight, and they were designated as W35S2E2 and W35S2E3, respectively. 2.3. Specimen preparation In this paper, steel molds with net inner dimensions of 100 mm 100 mm 515 mm were adopted for the RH measurements. The layout of the mold and the sensor arrangement is presented in Fig. 1(a). To form a sealed specimen, every inner side was greased and covered with plastic film to minimize moisture evaporation. During the mixing procedure, the sand and gravel were mixed in advance, and then the cement with different dosages of the admixtures and water were successively added into the agitator. The mixing process lasted 3 min, during which the predefined stirring rate varied with time. Furthermore, the slump of the mixtures was tested according to the ASTM standard C143/C143 M-15a [25], and the values met the requirements of the code. Finally, the mixtures were poured into specimens and compacted on a shaker. During the vibration process, a patented polyvinyl chloride (PVC) tube (as shown in Fig. 1(b)) with an inside steel bar was placed into the specimen, and its end was set at the geometric centre of the specimen. The top surface of every specimen was sealed with plastic film promptly after mixing. 2.4. Equipment preparation and experimental procedure An SHT35 digital sensor was adopted for simultaneously measuring the interior RH in this experiment. The measurement range for the RH was between 0 and 100%, and the typical accuracy was ±1.5%. The sensor was connected to a wireless sensing board, which was developed by the authors on a credit-card-size platform with a 1.4 ARM Cortex-A53 processor and wireless communication capability. A digital
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
Table 2 Chemical composition of EA. Chemical composition
CaO
Al2O3
SO3
SiO2
MgO
Fe2O3
Loss on ignition
EA (unit: %)
84.32
4.93
2.57
3.38
1.26
1.2
2.34
Table 3 Mixture proportions of different concretes. Mixture ID
w/b
cSRA (%)
cEA (%)
W30 W35 W40 W35S2W35S3W35S2E2W35S2E3-
0.3 0.35 0.4 0.35 0.35 0.35 0.35
0 0 0 2 3 2 2
0 0 0 0 0 2 3
Unit weight (kg/m3) Water
Cement
SRA
EA
Sand
Gravel
168 168 168 168 168 168 168
559.65 480 420.48 470.4 465.6 460.8 456
0 0 0 9.6 14.4 9.6 9.6
0 0 0 0 0 9.6 14.4
626.85 613 600 613 613 613 613
1165.5 1139 1115.52 1139 1139 1139 1139
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(a) Steel mold dimensions and sensor arrangement
(b) PVC tube
Fig. 1. Schematic diagram of the RH measurement apparatus.
Fig. 4. Casting specimen with a PVC tube installed.
Fig. 2. Layout of the WARMS design.
The experiments were carried out at an ambient temperature of 20 ± 2 °C and an RH of 50 ± 5%. During the test, different mixtures were made strictly according to the mix proportions, and a penetrator was implemented to measure the initial and final setting time for each mixture according to the ASTM C807-13 standard [27]. After the final set, the steel bar was removed from every PVC tube, and the inner surface was cleaned, as shown in Fig. 4. The calibrated digital sensor was inserted thereafter, and the nozzle was sealed with film and tin foil. Subsequently, the sensor was connected to the WARMS. Every 10 min, the RH data were measured. The data were automatically uploaded to a cloud database, displayed on web pages simultaneously and also saved locally in the TF card of the WARMS as a backup.
3. Experimental results and discussion 3.1. Setting time
Fig. 3. Calibration of the digital sensors using saturated salt solutions.
sensor and wireless sensing board together constituted the wireless and automatic relative-humidity monitoring system (WARMS, as shown in Fig. 2) with characteristics of low cost, real time data display and remote control. During the preparation of the sensors, a validation and calibration test was carried out using three different saturated salt solutions (i.e., NaCl, KCl and K2SO4) in sealed glass chambers in the lab with ambient temperature at 20 ± 2 °C. The experiment was performed according to the ASTM standard E104-02 (2012) [26]. The measurement results matched the recommended RH values provided by the standard well, and the accuracy of the sensors was verified. The layout of the calibration apparatus is presented in Fig. 3. After calibration, the sensors were placed on the top surfaces of the sealed specimens to keep the temperature synchronized to avoid condensation during subsequent measurements.
Setting time is a critical parameter for the application of concrete mixed with SRA and EA in the engineering. The initial and final setting times of the different mixtures is exhibited in Fig. 5. Setting times of the different mixtures (time differences shown in parentheses) In Fig. 5, the initial setting times of the W30, W35 and W40 mixtures were 238 min, 255 min and 280 min, respectively. With an increasing w/b ratio and compared to the W30 mixture, the initial times of W35 and W40 mixtures was delayed by 17 min and 42 min. As the w/b ratio increased, the cement content and hydration products decreased per unit volume. Hence, it was difficult for the product concentrations to reach saturation, and the follow-up hydration reaction could have been affected. Compared with benchmark W35 mixture, the initial setting times of W35S2 and W35S3mixtures were delayed 47 min and 80 min, respectively. In addition, the corresponding final setting times were delayed
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Fig. 5. The differences in the setting times is also calculated and presented in parentheses.
65 min and 110 min. It can be inferred that adding SRA could affect initial and final setting times, and both initial and final setting times delay as dosage increases. And the trend was in agreement with the one in Han et al.’s report [28]. For the group of W35S2E2, W35S2E3 and benchmark W35S2 mixtures, the initial setting times of the W35S2E2 and W35S2E3 mixtures were 20 min and 34 min advanced, respectively, compared to that of W35S2 mixture. Therefore, replacing the cement with the EA could lead to an acceleration of the archiving of the setting state. This phenomenon showed that the EA has a positive effect on expediting the hydration process, and similar conclusions can be obtained in Mo et al.’s paper [29].
3.2. Critical time The relation curves between the RH and the age of different concretes under varying influence factor values of w/b ratio, SRA
and EA dosage are presented in Fig. 6 (a)-(c), respectively. In each curve of every figure, a two-stage RH development characteristic can be clearly observed. During the initial flat stage (Stage I), the RH did not decrease apparently and remained constant at 100%, which indicated that the pores in the mixtures were saturated by the water vapour. In the course of time, the initial RH decreased sharply, and the trend slowed down afterwards (Stage II). Duration of Stage I since casting is defined as a critical time [30]. In Fig. 6(a), critical time can be affected by the w/b ratio and extends considerably with an increasing w/b ratio. In addition, the critical times for mixtures W30, W35 and W40 are measured as 3.5, 4.9 and 6.8 days, respectively, which was in agreement with the trend in Wyrzykowski and Lura’s paper [31]. For a sealed specimen, critical time could be mainly affected by both w/b ratio and hydration rate. On one hand, for mixtures with different w/b ratios, the initial size of the pores varied, and lower w/b ratio resulted in smaller pores [32]. Since casting, volume of water content yielded to the size of initial pores. For a given water loss rate, water can be consumed faster in the mixtures with lower w/b ratio, which would lead to reach critical time faster. On the other hand, for a certain volume of water in the fine pores, its reduction with time was controlled by water loss rate. Based on Zhang et al.’s study [33], a notable relationship between w/b ratio and the water loss rate could be observed. A lower w/b ratio would cause a higher water loss rate under the sealed condition and ultimately lead to an earlier achievement of critical time. Fig. 6(b) shows the effect of the SRA dosage on the RH development. In the figure, the critical times for the W35 (benchmark), W35S2 and W35S3 mixtures were 4.9, 6.3 and 7.6 days, respectively. A slight increase in the critical time could be attributed to the slow-down of water consumption in the fine pores in the concrete, which could also indicate that adding the SRA had an adverse effect on hydration [32]. In contrast, Fig. 6(c) shows that the EA has a positive effect on the RH evolution. Adding 2% and 3% EA in weight (i.e., the W35S2E2 and W35S2E3 mixtures) led to 1.3 and 2.2 days decrease, respectively,
Fig. 6. Relationship between the RH and age with different: (a) w/b ratio; (b) SRA dosage and (c) EA dosage.
S. Chen et al. / Construction and Building Materials 232 (2020) 117204
compared to that of the benchmark W35S2 mixture. When the EA compounded with the cement and was brought into contact with water, it competed with the cement for water, enriched the solution concentration of the Ca2+ in the mixture pores, generated Ca (OH)2 and retarded the crystallization of ettringite [33]. This process could significantly shorten the induction period of the hydration reaction and promote the subsequent hydration process [34], which appeared as a critical time reduction with the increase dosage of the EA.
3.3. RH decreasing rate The decreasing rate was introduced in this paper to study the law of RH development. It was defined and presented as follows:
aRH ¼
dRH dt
dropped by 0.58 and 0.66%/day, respectively compared to that of the W30 mixture. In Fig. 7(b), for the W35, W35S2 and W35S3 mixtures, the peak decreasing rate decreased with increasing SRA dosage, and it dropped by 0.29 and 0.36%/day for the W35S2 and W35S3 mixtures, respectively, compared to that of the W35 mixture. Based on Zuo et al.’s study [23] and the analysis in Section 3.1, the presence of SRA can cause hydration retardation and reduce surface tension of the solution in the pore of concrete. On one hand, the hydration retardation phenomenon could lead to a potential of reduction of water consumption at same age and cause a reduction of RH decreasing rate. On the other hand, according to Kelvin equation [8] (see Eq. (2)), the decrease of surface tension caused by SRA could also lead to a reduction of the internal RH at same hydration degree, which could also explain the trend of reduction in RH decreasing rate after adding SRA.
ð1Þ lnðRHÞ ¼
where aRH is the RH decreasing rate, dRHis the reduction of the RH during a certain time interval, dt. Based on the analysis in Section 3.2, during the initial watervapour saturated stage (i.e. Stage I), the RH was stable at 100%, and the decreasing rate was constant at 0%/day. Therefore, the curves corresponding with Stage I are omitted, and the graphical results of daily average RH decreasing rate for Stage II is presented in Fig. 7(a)–(c). In Fig. 7(a)–(c), decreasing rate varied significantly over time, which indicated that many of the pores were in an unsaturated porous state. The peak values of decreasing rate were 1.46, 0.88, 0.80, 0.59, 0.52, 0.73 and 0.75%/day, respectively, for the W30, W35, W40, W35S2, W35S3, W35S2E2 and W35S2E3 mixtures. In Fig. 7(a), the peak decreasing rate increased with a decreasing w/ b ratio, and the peak decreasing rate of the W35 and W40 mixtures
5
2ccoshV m RTr
ð2Þ
where c is the surface tension of the solution in the pore of concrete, h is the contact angle of free surface between solution and air, V m is the molar volume of the pore solution, R is the gas constant, T is the absolute temperature, and r is the menisci curvature radius. In Fig. 7(c), replacing the cement with more EA could lead to a slight increase in the peak decreasing rate. The values increased by 0.14 and 0.16%/day when the cement was replaced with 2% and 3% EA (i.e., in the W35S2E2 and W35S2E3 mixtures), compared to the peak value of the W35S2 mixture. This phenomenon indicated that the EA could promote the cement hydration process, which could confirm the results discussed in Section 3.2. Subsequently, decreasing rate decreased slowly after reaching the peak and tended to be stable after 7 days. For each curve, decreasing rate tended towards stability and was approximately
Fig. 7. Relationship between daily average RH decreasing rate and age with different: (a) w/b ratio; (b) SRA dosage and (c) EA dosage.
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S. Chen et al. / Construction and Building Materials 232 (2020) 117204
is presented in Table 4. In the table, the error, d, is calculated according to Eq. (7).
between 0.3–0.4%/day at 28 days, which was consistent with the literature [35]. Under sealed conditions, the evaporation between the ambient air and the surface of the concrete was blocked. In addition, based on Zhang et al.’s study [36], the temperature variation caused by the hydration heat mainly occurred during Stage I, so the temperature had nearly no influence on the change of RH, which occurred during Stage II. Hence, self-desiccation becomes the sole critical factor affecting the RH. The drop of the RH could legitimately be attributed to the consumption of water during the hydration process [37], and the slowdown was related to the completion of the major hydration process.
w2 w þ 5:6 þ 84:1 cSRA 81:62 cEA tcri ¼ 100 37 b b
ð6Þ d¼
Based on above Kelvin equation and Young-Laplace equation (Eq. (3)), it could be noted that with the hydration process and water consumption, water in a pore decreases and leads to a drop in RH. Simultaneously, the decrease of water could also lead to the reduction of menisci curvature radius and result in an increase of capillary pressure. Therefore, the variation of RH can be closely linked to the dying shrinkage and the potential of shrinkageinduced cracking. An accurate quantitative description of RH development can be helpful for the calculation of the shrinkageinduced stresses and prediction of formation cracking. Based on the experimental data and previous analysis, a two-stage model considering critical time for mixtures with different dosages of SRA and EA is established in this paper.
2ccosh r
where
rcap is the capillary pressure.
4.2. RH development Based on Persson’s study [19], a hyperbolic time function can well describe the relationship between the measured RH versus time during Stage II. However, it cannot take Stage I into consideration. In this paper, considering both Stage I and II, a modified model for mixtures W30, W35 and W40 was proposed and formulated as follows:
(
RHp ¼
According to Shen’s paper [38], the critical time of concrete without any SRA or EA (i.e., the benchmark critical time t bm ) is only influenced by the w/b ratio and can be expressed as follows:
w2 w þ cbm þ bbm b b
100
ap 1 bp lnðtÞ wb dp ½1þcp lnðtÞ
t tcri t cri < t 28
ð8Þ
where RHp indicates the RH considering the wb ratio and age; ap , bp , dp and cp are the fitting parameters; and t cri is the critical time and yields to Eq. (6). From Fig. 6(a), all of the fitting parameters are obtained through regression analysis, and they are 111.9, 0.03156, 0.00311 and 10.97, respectively. A comparison between the model and experimental data with different dosages of the SRA and EA is presented in Fig. 8. In Fig. 8, it can be observed that the calculated R2 for the W30, W35 and W40 mixtures at Stage II are 0.988, 0.988 and 0.996, respectively which are higher than 0.988. In addition, the RMSE values of the RH are 0.91%, 0.49% and 0.59%, respectively which are small compared with the RH values which are over 85%. There-
ð3Þ
4.1. Critical time
t bm ¼ abm
ð7Þ
where t cri; regression and t cri; test are critical times of the regression and the test, respectively. From Table 4, it can be found that the maximum value of the error between the test and regression results was 4.55%. This indicates that the model proposed above is in good agreement with the experimental data.
4. Models for critical time and RH development
rcap ¼
t cri; regression t cri; test 100% t cri; test
ð4Þ
where abm , bbm and cbm are the fitting parameters. According to the measurement results as illustrated in Fig. 6(a), abm , bbm and are obtained by a regression analysis, and they are 100, 37 and 5.6, respectively. When the SRA and EA are involved, based on an analysis of the critical time change regularity, the mass fraction parameters, cSRA and cEA , and the corresponding coefficients, aSRA and aEA , are introduced. Eq. (4) is revised, and critical time considering the effect of the SRA and EA can be expressed as:
t cri ¼ tbm þ aSRA; t cSRA þ aEA; t cEA
ð5Þ
where aSRA; t and aEA; t are the parameters, which can be obtained through a regression analysis. Based on the calculation, they are 84.1 and 81:62, respectively. The R2 and RMSE are 0.98 and 0.24, respectively. By combining Eqs. (4) and (5) and inputting in the values, the critical time correction formula can be expressed as in Eq. (6). A comparison between the test and regression results
Fig. 8. Comparison between the model and test data with different w/b ratio.
Table 4 Comparison between the test and regression results for the critical time. Mixture ID Results (day) d (%)
Test Regression
W30
W35
W40
W35S2
W35S3
W35S2E2
W35S2E3
3.5 3.5 0
4.9 4.9 0
6.8 6.8 0
6.3 6.6 4.55
7.6 7.4 2.7
5 4.9 2.04
4.1 4.1 0
S. Chen et al. / Construction and Building Materials 232 (2020) 117204
7
model developed for all compositions. Therefore, follow-up research work will be continued in the future. 5. Conclusions Based on the materials used in this study and measurement results, the following conclusions can be made:
Fig. 9. Comparison between the model and test data with different dosages of SRA and EA.
fore, it can be concluded that the equation, which is presented as Eq. (8) and illustrated in Fig. 8, is applicable to representing the variation of the RH versus age for the mixtures, taking no influence of the EA and SRA into account in this experiment. For mixtures with the CaO-type EA and polymer-type SRA added and based on Eq. (8), a modified model is proposed as follows:
RH ¼
100
t t cri
a RHp þ b tcri < t 28
1. The polymer-type SRA and CaO-type EA have a significant impact on the relationship between RH and age. In this study, the SRA can cause a delay of initial setting time, an extension of the critical time and an increase in the RH at 28 days after casting. In contrast, the addition of EA can cause a reduction in the critical time and a significant decrease of RH at 28 days. 2. A development model for the critical time, which considers the influence factors of w/b ratio, polymer-type SRA and CaO-type EA dosages, is established in early-age concrete under sealed condition. In addition, results from proposed model is consistent with the experimental ones. 3. Comprehensively considering the w/b ratio, critical time, polymer-type SRA and CaO-type EA dosages, a universal twostage model is proposed for the RH development in early-age concrete. The proposed model shows a good agreement with the experimental data.
ð9Þ
where RHp conforms with Eq. (6). In addition, a and b are the values of parametric equations, which are defined as presented in Eqs. (10) and (11), respectively.
a ¼ 1 ðaSRA cSRA þ aEA cEA Þ
ð10Þ
b ¼ bSRA cSRA þ bEA cEA
ð11Þ
Through a regression analysis, aSRA , aEA , bSRA and bEA are calculated and optimized using the quasi-Newton method [39]. The values are 5.30, 6.33, 621.11 and 705.36, respectively. The values are brought into Eqs. (10) and (11). A comparison between the model and experimental data for mixtures containing either SRA or EA (i.e., the W35S2, W35S3, W35S2E2 and W35S2E3 mixtures) at Stage II are presented in Fig. 9. In Fig. 9, the R2 value is calculated for the curves of the model and measured RH values versus age. The values are 0.990, 0.988, 0.996 and 0.994, respectively. In other words, the shape and trend of the development model are close to those of the measured ones. In addition, the RMSE values are all less than 0.41%, which are negligible compared to the RH values which are over 87% at 28 days. On the basis of the analysis above, a good agreement can be validated between the model and experimental data for the mixtures containing either SRA or EA in this experiment. Furthermore, the W30, W35 and W40 mixtures have neither SRA nor EA; therefore, cSRA and cEA are equal to 0. Accordingly, Eq. (9) can be simplified to Eq. (8). The results using Eq. (9) for the W30, W35 and W40 mixtures are identical to those presented in Fig. 8. Consequently, Eq. (9) can also be applied to all the mixtures without SRA or EA. Overall, the proposed model can accurately describe the development process of the RH with age for the fully sealed specimens with different dosages of the admixtures in this experiment. The proposed models target to describe the RH development for early-age concrete under sealed condition with a w/b ratio between 0.3 and 0.4 and EA/SRA dosages between 0 and 3% in weight, and is also suggested that the calculated RH should not be lower than 70% at 28 days. The generalizability of suggested development model remains a challenge due to the limited test data and undefined physical meaning. In addition, there is not a
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work has been supported by the China Postdoctoral Science Foundation Funded Project (No. 2018M632217). The authors also gratefully acknowledge the financial support from the National Natural Science Foundation of China under Grant No. 51878245 and 51708265. This research is also sponsored by the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (No. 16KJB560004), the Fund for Postgraduate Research & Practice Innovation Program of Jiangsu Province (SJCX18_0186) and the Fundamental Research Fund for the Central Universities (2018B760X14). References [1] T. Voigt, G. Ye, Z. Sun, S.P. Shah, K. van Breugel, Early age microstructure of Portland cement mortar investigated by ultrasonic shear waves and numerical simulation, Cem. Concr. Res. 35 (5) (2005) 858–866. [2] Z. Jun, H. Dongwei, C. Haoyu, Experimental and theoretical studies on autogenous shrinkage of concrete at early ages, J. Mater. Civ. Eng. 23 (3) (2011) 312–320. [3] X. Hu, Z. Shi, C. Shi, Z. Wu, B. Tong, Z. Ou, G. de Schutter, Drying shrinkage and cracking resistance of concrete made with ternary cementitious components, Constr. Build. Mater. 149 (2017) 406–415. [4] K. Kovler, S. Zhutovsky, Overview and Future Trends of Shrinkage Research, Mater. Struct. 39 (9) (2006) 827–847. [5] B.T. Bissonnette, P. Pierre, M. Pigeon, Influence of key parameters on drying shrinkage of cementitious materials, Cem. Concr. Res. 29 (10) (1999) 1655– 1662. [6] T. Ayano, F.H. Wittmann, Drying, moisture distribution, and shrinkage of cement-based materials, Mater. Struct. 35 (3) (2002) 134–140. [7] H.F.W. Taylor, Cement Chemistry, 2nd edition., Thomas Telford Publishing, London, 1997. [8] A.M. Neville, Properties of Concrete, 4th edition., John Wiley and Sons, London, 1996. [9] J. Saliba, E. Rozière, F. Grondin, A. Loukili, Influence of shrinkage-reducing admixtures on plastic and long-term shrinkage, Cem. Concr. Compos. 33 (2) (2011) 209–217.
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[10] L. Mo, M. Deng, A. Wang, Effects of MgO-based expansive additive on compensating the shrinkage of cement paste under non-wet curing conditions, Cem. Concr. Composites 34 (3) (2012) 377–383. [11] V. Corinaldesi, Combined effect of expansive, shrinkage reducing and hydrophobic admixtures for durable self compacting concrete, Constr. Build. Mater. 36 (2012) 758–764. [12] T. Francesca, G. Chiara, M. Saveria, Combined use of shrinkage reducing admixture and CaO in cement based materials, IOP Conf. Ser.: Mater. Sci. Eng. 245 (2) (2017) 022093. [13] Q. Ran, N. Gao, J. Liu, Q. Tian, J. Zhang, Shrinkage action mechanism of shrinkage-reducing admixtures based on the pore solution, Mag. Concr. Res. 65 (18) (2013) 1092–1100. [14] R. Polat, R. Demirbog˘a, W.H. Khushefati, Effects of nano and micro size of CaO and MgO, nano-clay and expanded perlite aggregate on the autogenous shrinkage of mortar, Constr. Build. Mater. 81 (2015) 268–275. [15] M.S. Meddah, M. Suzuki, R. Sato, Influence of a combination of expansive and shrinkage-reducing admixture on autogenous deformation and self-stress of silica fume high-performance concrete, Constr. Build. Mater. 25 (1) (2011) 239–250. [16] M.H. Zhang, C.T. Tam, M.P. Leow, Effect of water-to-cementitious materials ratio and silica fume on the autogenous shrinkage of concrete, Cem. Concr. Res. 33 (10) (2003) 1687–1694. [17] H. Samouh, E. Rozière, V. Wisniewski, A. Loukili, Consequences of longer sealed curing on drying shrinkage, cracking and carbonation of concrete, Cem. Concr. Res. 95 (2017) 117–131. [18] A. Hajibabaee, M.T. Ley, Impact of wet and sealed curing on curling in cement paste beams from drying shrinkage, ACI Mater. J. 112 (1) (2015) 79–84. [19] B. Persson, Moisture in concrete subjected to different kinds of curing, Mater. Struct. 30 (9) (1997) 533–544. [20] J. Zhang, D. Hou, Y. Gao, S. Wei, Determination of moisture diffusion coefficient of concrete at early age from interior humidity measurements, Drying Technol. 29 (6) (2011) 689–696. [21] ASTM, Standard Performance Specification for Hydraulic Cement, C1157/ C1157M-17, West Conshohocken, PA, USA, 2017. [22] ASTM, Standard Specification for Functional Additions for Use in Hydraulic Cements, C688-14, West Conshohocken, PA, USA, 2014. [23] W. Zuo, P. Feng, P. Zhong, Q. Tian, N. Gao, Y. Wang, C. Yu, C. Miao, Effects of novel polymer-type shrinkage-reducing admixture on early age autogenous deformation of cement pastes, Cem. Concr. Res. 100 (2017) 413–422. [24] T.C. Powers, T.L. Brownyard, Studies of the physical properties of hardened Portland cement paste, J. Am. Concr. Inst. Proc. 43 (9) (1946) 469–504.
[25] ASTM, Test Method for Hydraulic-Cement Concrete, C143/C143M-15a, West Conshohocken, PA, USA, 2015. [26] ASTM, Standard Practice For Maintaining Constant Relative Humidity By Means Of Aqueous Solutions, E104-02(2012), West Conshohocken, PA, USA, 2002. [27] ASTM, Standard Test Method for Time of Setting of Hydraulic Cement Mortar by Modified Vicat Needle, C807-18, West Conshohocken, PA, USA, 2018. [28] M.C. Han, C.G. Han, Use of maturity methods to estimate the setting time of concrete containing super retarding agents, Cem. Concr. Compos. 32 (2) (2010) 164–172. [29] L. Mo, M. Deng, M. Tang, A. Al-Tabbaa, MgO expansive cement and concrete in China: Past, present and future, Concr. Res. 57 (3) (2014) 1–12. [30] Y. Han, J. Zhang, Y. Luosun, T. Hao, Effect of internal curing on internal relative humidity and shrinkage of high strength concrete slabs, Constr. Build. Mater. 61 (3) (2014) 41–49. [31] M. Wyrzykowski, P. Lura, Effect of relative humidity decrease due to selfdesiccation on the hydration kinetics of cement, Cem. Concr. Res. 85 (2016) 75–81. [32] X. Ma, J. Liu, Z. Wu, C. Shi, Effects of SAP on the properties and pore structure of high performance cement-based materials, Constr. Build. Mater. 131 (2017) 476–484. [33] G. Sant, B. Lothenbach, P. Juilland, G. Le Saout, J. Weiss, K. Scrivener, The origin of early age expansions induced in cementitious materials containing shrinkage reducing admixtures, Cem. Concr. Res. 41 (3) (2011) 218–229. [34] F. Rajabipour, G. Sant, J. Weiss, Interactions between shrinkage reducing admixtures (SRA) and cement paste’s pore solution, Cem. Concr. Res. 38 (5) (2008) 606–615. [35] D. Shen, M. Wang, Y. Chen, T. Wang, J. Zhang, Prediction model for relative humidity of early-age internally cured concrete with pre-wetted lightweight aggregates, Constr. Build. Mater. 144 (2017) 717–727. [36] J. Zhang, K. Qi, Y. Huang, Calculation of moisture distribution in early-age concrete, J. Eng. Mech. 135 (8) (2009) 871–880. [37] J. Zhang, Y. Huang, K. Qi, Y. Gao, Interior relative humidity of normal- and highstrength concrete at early age, J. Mater. Civ. Eng. 124 (6) (2012) 615–622. [38] D. Shen, M. Wang, Y. Chen, W. Wang, J. Zhang, Prediction of internal relative humidity in concrete modified with super absorbent polymers at early age, Constr. Build. Mater. 149 (2017) 543–552. [39] D.F. Shanno, Conditioning of quasi-Newton methods for function minimization, Math. Comput. 111 (24) (1970) 647–656.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Experimental study on interior relative humidity development in early-age concrete mixed with shrinkage-reducing and expansive admixtures Shuo Chen a,⇑, Haitao Zhao a,*, Yu Chen a,b, Donghui Huang c, Yuzhi Chen c, Xiaodong Chen a a b c
College of Civil and Transportation Engineering, Hohai University, Nanjing 210000, China Jiangnan Project Management Co., Ltd., Hangzhou 310000, China College of Civil Engineering and Architectural, Jinling Institute of Technology, Nanjing 210000, China
h i g h l i g h t s Effects of tested SRA and EA on RH development of early-age concrete was studied. A model for critical time considering SRA and EA dosages was proposed. A development model is proposed for the RH in early-age concrete with SRA and EA.
a r t i c l e
i n f o
Article history: Received 3 July 2019 Received in revised form 3 October 2019 Accepted 9 October 2019
Keywords: Relative humidity Development model Early-age concrete Shrinkage-reducing admixture Expansive admixture
a b s t r a c t Early age concrete may crack due to volumetric shrinkage caused by a decrease in the interior relative humidity (RH) in the self-desiccation process. Shrinkage-reducing admixtures (SRAs) and expansive admixtures (EAs) are utilized to mitigate the volumetric shrinkage. Using a self-developed wireless and automatic relative-humidity monitoring system, a series of experiments for the measurement of the RH within concrete specimens was conducted. A systematic analysis was conducted in the aspects of the setting time, critical time and interior RH development in early-age concrete with different dosages of the polymer-type SRA and CaO-type EA. On the basis, a critical time model and a two-stage RH development model considering the effects of the water to binder ratio, SRA and EA dosages were established. Both of the models are in good agreement with the experimental data. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Cracks in concrete, especially in high performance concrete, can cause significant adverse impacts on the long-term performance and durability of a structure. Published studies indicate that the initial conditions, i.e., the temperature and interior relative humidity (RH), have very large impacts on early-age cementitious material behaviours involving cracking [1,2]. Among all the non-loads, volumetric shrinkage under restraint conditions is one of the most important contributors [3,4]. Moisture loss is one of the most important influence factors for volumetric shrinkage and can be caused by self-desiccation [5,6]. When the water to binder (w/b) ratio is lower than a specific value (e.g., 0.36–0.48 depending on the cement type [7]), the amount of ⇑ Corresponding authors. E-mail addresses: [email protected] (S. Chen), [email protected] (H. Zhao). https://doi.org/10.1016/j.conbuildmat.2019.117204 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
water is inadequate to meet the requirement for complete hydration. In a sealed system, the water in the concrete pores can be consumed along with hydration, and the phenomenon of moisture loss (i.e., self-desiccation) occurs. In addition, according to Kelvin’s equation [8], a decrease in the RH could cause a decrease in the curvature radius of the capillary water surface, which would lead to an increase in the capillary stress and surface tension. Volumetric shrinkage occurs in turn, and cracks within the concrete occur with a high probability. Targeted chemical additives have been adopted to mitigate the self-desiccation induced shrinkage at an early age, including shrinkage-reducing admixtures (SRA) [9], expansive admixtures (EA) [10] or a mixture of both [11,12]. Through reducing the surface tension of the water in the capillary pores [13] and generating a limited volume expansion [14], the above two admixtures can compensate for volume shrinkage individually or together. Although a synergistic effect was observed by Meddah et al. [15],
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its mechanism was not thoroughly clarified. Therefore, it is still worth more effort to investigate the relationships among the variability of the RH and the effects of SRA and/or EA on cracking resistance. The measurement, analysis and establishment of development model of the RH change in early-age concrete is critically needed as a foundation for shrinkage calculations and structural cracking prediction. The measurement of the interior relative humidity is ordinarily adopted to quantify the RH change in a closed system [16–18], and a number of references are found in the literature on investigating the development of the interior RH in young concrete. For example, Persson established a model [19], which could accurately fit the RH variation in the decline segment. Zhang et al. [20] developed a two-stage moisture distribution model for earlystage concrete through the degree of cement hydration, which could well reproduce the results from their experiments. However, there are few studies on the RH of concrete containing SRAs and/or EAs. In addition, the traditional cabled RH measurement methods have a disadvantage of being inconvenient. Therefore, there are urgent demands for convenient and reliable in situ real-time monitoring of RH.
2. Materials and methods 2.1. Materials According to the American Society for Testing Materials (ASTM) standard C1157/C1157 M-17 [21], the cement used in this study was classified as original Portland cement (Cement II 52.5R) with a Blaine fineness of 375 m2/kg. The detailed material properties are presented in Table 1. The mud and clay contents of the original natural river sand were less than 1.5% and 0.5% in weight, respectively. Through cleaning, drying, screening and other pre-treatments, the sand was used as a fine aggregate. In addition, the particle size was less than 2.5 mm. The mud content of the crushed limestone was less than 0.5% in weight. In addition, the gradation was continuous, and the particle size was between 5 mm and 30 mm. The limestone was cleaned, dried and utilized as the coarse aggregate. The fitness of the CaO-type EA was verified by a sieve with a pore diameter of 1.18 mm, and the residue was less than 0.5% in weight, which met the requirement of the ASTM standard C688-14 [22]. In addition, detailed material properties of the
EA are presented in Table 2. The polymer-type SRA used in this paper were manufactured by the Sobute New Materials Company, and its detailed properties were reported in the paper [23]. 2.2. Mixture proportions This paper involved the evaluation of seven different concrete mixtures. Based on the study conducted by Powers and Brownyard [24], while the w/b ratio was lower than 0.42, significant self-desiccation induced shrinkage could be observed. Hence, all the designed w/b ratios in this paper are lower than 0.4. The details of the mix proportion designs are presented in Table 3. In the table, cSRA and cEA represent the mass fractions of the SRA and EA, respectively. In the evaluation, three plain concrete mixtures with varying w/b ratios were set as benchmarks (0.3, 0.35 and 0.4 for mixtures W30, W35 and W40, respectively), and the w/b ratio was kept constant at 0.35 for all the other mixtures. In addition, the cement was replaced by the SRA, and the alternative proportions were 2% and 3% in weight. These mixtures were correspondingly described as W35S2 and W35S3. The cement was further replaced by the EA in the W35S2 mixture by 2% and 3% in weight, and they were designated as W35S2E2 and W35S2E3, respectively. 2.3. Specimen preparation In this paper, steel molds with net inner dimensions of 100 mm 100 mm 515 mm were adopted for the RH measurements. The layout of the mold and the sensor arrangement is presented in Fig. 1(a). To form a sealed specimen, every inner side was greased and covered with plastic film to minimize moisture evaporation. During the mixing procedure, the sand and gravel were mixed in advance, and then the cement with different dosages of the admixtures and water were successively added into the agitator. The mixing process lasted 3 min, during which the predefined stirring rate varied with time. Furthermore, the slump of the mixtures was tested according to the ASTM standard C143/C143 M-15a [25], and the values met the requirements of the code. Finally, the mixtures were poured into specimens and compacted on a shaker. During the vibration process, a patented polyvinyl chloride (PVC) tube (as shown in Fig. 1(b)) with an inside steel bar was placed into the specimen, and its end was set at the geometric centre of the specimen. The top surface of every specimen was sealed with plastic film promptly after mixing. 2.4. Equipment preparation and experimental procedure An SHT35 digital sensor was adopted for simultaneously measuring the interior RH in this experiment. The measurement range for the RH was between 0 and 100%, and the typical accuracy was ±1.5%. The sensor was connected to a wireless sensing board, which was developed by the authors on a credit-card-size platform with a 1.4 ARM Cortex-A53 processor and wireless communication capability. A digital
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
Table 2 Chemical composition of EA. Chemical composition
CaO
Al2O3
SO3
SiO2
MgO
Fe2O3
Loss on ignition
EA (unit: %)
84.32
4.93
2.57
3.38
1.26
1.2
2.34
Table 3 Mixture proportions of different concretes. Mixture ID
w/b
cSRA (%)
cEA (%)
W30 W35 W40 W35S2W35S3W35S2E2W35S2E3-
0.3 0.35 0.4 0.35 0.35 0.35 0.35
0 0 0 2 3 2 2
0 0 0 0 0 2 3
Unit weight (kg/m3) Water
Cement
SRA
EA
Sand
Gravel
168 168 168 168 168 168 168
559.65 480 420.48 470.4 465.6 460.8 456
0 0 0 9.6 14.4 9.6 9.6
0 0 0 0 0 9.6 14.4
626.85 613 600 613 613 613 613
1165.5 1139 1115.52 1139 1139 1139 1139
3
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(a) Steel mold dimensions and sensor arrangement
(b) PVC tube
Fig. 1. Schematic diagram of the RH measurement apparatus.
Fig. 4. Casting specimen with a PVC tube installed.
Fig. 2. Layout of the WARMS design.
The experiments were carried out at an ambient temperature of 20 ± 2 °C and an RH of 50 ± 5%. During the test, different mixtures were made strictly according to the mix proportions, and a penetrator was implemented to measure the initial and final setting time for each mixture according to the ASTM C807-13 standard [27]. After the final set, the steel bar was removed from every PVC tube, and the inner surface was cleaned, as shown in Fig. 4. The calibrated digital sensor was inserted thereafter, and the nozzle was sealed with film and tin foil. Subsequently, the sensor was connected to the WARMS. Every 10 min, the RH data were measured. The data were automatically uploaded to a cloud database, displayed on web pages simultaneously and also saved locally in the TF card of the WARMS as a backup.
3. Experimental results and discussion 3.1. Setting time
Fig. 3. Calibration of the digital sensors using saturated salt solutions.
sensor and wireless sensing board together constituted the wireless and automatic relative-humidity monitoring system (WARMS, as shown in Fig. 2) with characteristics of low cost, real time data display and remote control. During the preparation of the sensors, a validation and calibration test was carried out using three different saturated salt solutions (i.e., NaCl, KCl and K2SO4) in sealed glass chambers in the lab with ambient temperature at 20 ± 2 °C. The experiment was performed according to the ASTM standard E104-02 (2012) [26]. The measurement results matched the recommended RH values provided by the standard well, and the accuracy of the sensors was verified. The layout of the calibration apparatus is presented in Fig. 3. After calibration, the sensors were placed on the top surfaces of the sealed specimens to keep the temperature synchronized to avoid condensation during subsequent measurements.
Setting time is a critical parameter for the application of concrete mixed with SRA and EA in the engineering. The initial and final setting times of the different mixtures is exhibited in Fig. 5. Setting times of the different mixtures (time differences shown in parentheses) In Fig. 5, the initial setting times of the W30, W35 and W40 mixtures were 238 min, 255 min and 280 min, respectively. With an increasing w/b ratio and compared to the W30 mixture, the initial times of W35 and W40 mixtures was delayed by 17 min and 42 min. As the w/b ratio increased, the cement content and hydration products decreased per unit volume. Hence, it was difficult for the product concentrations to reach saturation, and the follow-up hydration reaction could have been affected. Compared with benchmark W35 mixture, the initial setting times of W35S2 and W35S3mixtures were delayed 47 min and 80 min, respectively. In addition, the corresponding final setting times were delayed
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Fig. 5. The differences in the setting times is also calculated and presented in parentheses.
65 min and 110 min. It can be inferred that adding SRA could affect initial and final setting times, and both initial and final setting times delay as dosage increases. And the trend was in agreement with the one in Han et al.’s report [28]. For the group of W35S2E2, W35S2E3 and benchmark W35S2 mixtures, the initial setting times of the W35S2E2 and W35S2E3 mixtures were 20 min and 34 min advanced, respectively, compared to that of W35S2 mixture. Therefore, replacing the cement with the EA could lead to an acceleration of the archiving of the setting state. This phenomenon showed that the EA has a positive effect on expediting the hydration process, and similar conclusions can be obtained in Mo et al.’s paper [29].
3.2. Critical time The relation curves between the RH and the age of different concretes under varying influence factor values of w/b ratio, SRA
and EA dosage are presented in Fig. 6 (a)-(c), respectively. In each curve of every figure, a two-stage RH development characteristic can be clearly observed. During the initial flat stage (Stage I), the RH did not decrease apparently and remained constant at 100%, which indicated that the pores in the mixtures were saturated by the water vapour. In the course of time, the initial RH decreased sharply, and the trend slowed down afterwards (Stage II). Duration of Stage I since casting is defined as a critical time [30]. In Fig. 6(a), critical time can be affected by the w/b ratio and extends considerably with an increasing w/b ratio. In addition, the critical times for mixtures W30, W35 and W40 are measured as 3.5, 4.9 and 6.8 days, respectively, which was in agreement with the trend in Wyrzykowski and Lura’s paper [31]. For a sealed specimen, critical time could be mainly affected by both w/b ratio and hydration rate. On one hand, for mixtures with different w/b ratios, the initial size of the pores varied, and lower w/b ratio resulted in smaller pores [32]. Since casting, volume of water content yielded to the size of initial pores. For a given water loss rate, water can be consumed faster in the mixtures with lower w/b ratio, which would lead to reach critical time faster. On the other hand, for a certain volume of water in the fine pores, its reduction with time was controlled by water loss rate. Based on Zhang et al.’s study [33], a notable relationship between w/b ratio and the water loss rate could be observed. A lower w/b ratio would cause a higher water loss rate under the sealed condition and ultimately lead to an earlier achievement of critical time. Fig. 6(b) shows the effect of the SRA dosage on the RH development. In the figure, the critical times for the W35 (benchmark), W35S2 and W35S3 mixtures were 4.9, 6.3 and 7.6 days, respectively. A slight increase in the critical time could be attributed to the slow-down of water consumption in the fine pores in the concrete, which could also indicate that adding the SRA had an adverse effect on hydration [32]. In contrast, Fig. 6(c) shows that the EA has a positive effect on the RH evolution. Adding 2% and 3% EA in weight (i.e., the W35S2E2 and W35S2E3 mixtures) led to 1.3 and 2.2 days decrease, respectively,
Fig. 6. Relationship between the RH and age with different: (a) w/b ratio; (b) SRA dosage and (c) EA dosage.
S. Chen et al. / Construction and Building Materials 232 (2020) 117204
compared to that of the benchmark W35S2 mixture. When the EA compounded with the cement and was brought into contact with water, it competed with the cement for water, enriched the solution concentration of the Ca2+ in the mixture pores, generated Ca (OH)2 and retarded the crystallization of ettringite [33]. This process could significantly shorten the induction period of the hydration reaction and promote the subsequent hydration process [34], which appeared as a critical time reduction with the increase dosage of the EA.
3.3. RH decreasing rate The decreasing rate was introduced in this paper to study the law of RH development. It was defined and presented as follows:
aRH ¼
dRH dt
dropped by 0.58 and 0.66%/day, respectively compared to that of the W30 mixture. In Fig. 7(b), for the W35, W35S2 and W35S3 mixtures, the peak decreasing rate decreased with increasing SRA dosage, and it dropped by 0.29 and 0.36%/day for the W35S2 and W35S3 mixtures, respectively, compared to that of the W35 mixture. Based on Zuo et al.’s study [23] and the analysis in Section 3.1, the presence of SRA can cause hydration retardation and reduce surface tension of the solution in the pore of concrete. On one hand, the hydration retardation phenomenon could lead to a potential of reduction of water consumption at same age and cause a reduction of RH decreasing rate. On the other hand, according to Kelvin equation [8] (see Eq. (2)), the decrease of surface tension caused by SRA could also lead to a reduction of the internal RH at same hydration degree, which could also explain the trend of reduction in RH decreasing rate after adding SRA.
ð1Þ lnðRHÞ ¼
where aRH is the RH decreasing rate, dRHis the reduction of the RH during a certain time interval, dt. Based on the analysis in Section 3.2, during the initial watervapour saturated stage (i.e. Stage I), the RH was stable at 100%, and the decreasing rate was constant at 0%/day. Therefore, the curves corresponding with Stage I are omitted, and the graphical results of daily average RH decreasing rate for Stage II is presented in Fig. 7(a)–(c). In Fig. 7(a)–(c), decreasing rate varied significantly over time, which indicated that many of the pores were in an unsaturated porous state. The peak values of decreasing rate were 1.46, 0.88, 0.80, 0.59, 0.52, 0.73 and 0.75%/day, respectively, for the W30, W35, W40, W35S2, W35S3, W35S2E2 and W35S2E3 mixtures. In Fig. 7(a), the peak decreasing rate increased with a decreasing w/ b ratio, and the peak decreasing rate of the W35 and W40 mixtures
5
2ccoshV m RTr
ð2Þ
where c is the surface tension of the solution in the pore of concrete, h is the contact angle of free surface between solution and air, V m is the molar volume of the pore solution, R is the gas constant, T is the absolute temperature, and r is the menisci curvature radius. In Fig. 7(c), replacing the cement with more EA could lead to a slight increase in the peak decreasing rate. The values increased by 0.14 and 0.16%/day when the cement was replaced with 2% and 3% EA (i.e., in the W35S2E2 and W35S2E3 mixtures), compared to the peak value of the W35S2 mixture. This phenomenon indicated that the EA could promote the cement hydration process, which could confirm the results discussed in Section 3.2. Subsequently, decreasing rate decreased slowly after reaching the peak and tended to be stable after 7 days. For each curve, decreasing rate tended towards stability and was approximately
Fig. 7. Relationship between daily average RH decreasing rate and age with different: (a) w/b ratio; (b) SRA dosage and (c) EA dosage.
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S. Chen et al. / Construction and Building Materials 232 (2020) 117204
is presented in Table 4. In the table, the error, d, is calculated according to Eq. (7).
between 0.3–0.4%/day at 28 days, which was consistent with the literature [35]. Under sealed conditions, the evaporation between the ambient air and the surface of the concrete was blocked. In addition, based on Zhang et al.’s study [36], the temperature variation caused by the hydration heat mainly occurred during Stage I, so the temperature had nearly no influence on the change of RH, which occurred during Stage II. Hence, self-desiccation becomes the sole critical factor affecting the RH. The drop of the RH could legitimately be attributed to the consumption of water during the hydration process [37], and the slowdown was related to the completion of the major hydration process.
w2 w þ 5:6 þ 84:1 cSRA 81:62 cEA tcri ¼ 100 37 b b
ð6Þ d¼
Based on above Kelvin equation and Young-Laplace equation (Eq. (3)), it could be noted that with the hydration process and water consumption, water in a pore decreases and leads to a drop in RH. Simultaneously, the decrease of water could also lead to the reduction of menisci curvature radius and result in an increase of capillary pressure. Therefore, the variation of RH can be closely linked to the dying shrinkage and the potential of shrinkageinduced cracking. An accurate quantitative description of RH development can be helpful for the calculation of the shrinkageinduced stresses and prediction of formation cracking. Based on the experimental data and previous analysis, a two-stage model considering critical time for mixtures with different dosages of SRA and EA is established in this paper.
2ccosh r
where
rcap is the capillary pressure.
4.2. RH development Based on Persson’s study [19], a hyperbolic time function can well describe the relationship between the measured RH versus time during Stage II. However, it cannot take Stage I into consideration. In this paper, considering both Stage I and II, a modified model for mixtures W30, W35 and W40 was proposed and formulated as follows:
(
RHp ¼
According to Shen’s paper [38], the critical time of concrete without any SRA or EA (i.e., the benchmark critical time t bm ) is only influenced by the w/b ratio and can be expressed as follows:
w2 w þ cbm þ bbm b b
100
ap 1 bp lnðtÞ wb dp ½1þcp lnðtÞ
t tcri t cri < t 28
ð8Þ
where RHp indicates the RH considering the wb ratio and age; ap , bp , dp and cp are the fitting parameters; and t cri is the critical time and yields to Eq. (6). From Fig. 6(a), all of the fitting parameters are obtained through regression analysis, and they are 111.9, 0.03156, 0.00311 and 10.97, respectively. A comparison between the model and experimental data with different dosages of the SRA and EA is presented in Fig. 8. In Fig. 8, it can be observed that the calculated R2 for the W30, W35 and W40 mixtures at Stage II are 0.988, 0.988 and 0.996, respectively which are higher than 0.988. In addition, the RMSE values of the RH are 0.91%, 0.49% and 0.59%, respectively which are small compared with the RH values which are over 85%. There-
ð3Þ
4.1. Critical time
t bm ¼ abm
ð7Þ
where t cri; regression and t cri; test are critical times of the regression and the test, respectively. From Table 4, it can be found that the maximum value of the error between the test and regression results was 4.55%. This indicates that the model proposed above is in good agreement with the experimental data.
4. Models for critical time and RH development
rcap ¼
t cri; regression t cri; test 100% t cri; test
ð4Þ
where abm , bbm and cbm are the fitting parameters. According to the measurement results as illustrated in Fig. 6(a), abm , bbm and are obtained by a regression analysis, and they are 100, 37 and 5.6, respectively. When the SRA and EA are involved, based on an analysis of the critical time change regularity, the mass fraction parameters, cSRA and cEA , and the corresponding coefficients, aSRA and aEA , are introduced. Eq. (4) is revised, and critical time considering the effect of the SRA and EA can be expressed as:
t cri ¼ tbm þ aSRA; t cSRA þ aEA; t cEA
ð5Þ
where aSRA; t and aEA; t are the parameters, which can be obtained through a regression analysis. Based on the calculation, they are 84.1 and 81:62, respectively. The R2 and RMSE are 0.98 and 0.24, respectively. By combining Eqs. (4) and (5) and inputting in the values, the critical time correction formula can be expressed as in Eq. (6). A comparison between the test and regression results
Fig. 8. Comparison between the model and test data with different w/b ratio.
Table 4 Comparison between the test and regression results for the critical time. Mixture ID Results (day) d (%)
Test Regression
W30
W35
W40
W35S2
W35S3
W35S2E2
W35S2E3
3.5 3.5 0
4.9 4.9 0
6.8 6.8 0
6.3 6.6 4.55
7.6 7.4 2.7
5 4.9 2.04
4.1 4.1 0
S. Chen et al. / Construction and Building Materials 232 (2020) 117204
7
model developed for all compositions. Therefore, follow-up research work will be continued in the future. 5. Conclusions Based on the materials used in this study and measurement results, the following conclusions can be made:
Fig. 9. Comparison between the model and test data with different dosages of SRA and EA.
fore, it can be concluded that the equation, which is presented as Eq. (8) and illustrated in Fig. 8, is applicable to representing the variation of the RH versus age for the mixtures, taking no influence of the EA and SRA into account in this experiment. For mixtures with the CaO-type EA and polymer-type SRA added and based on Eq. (8), a modified model is proposed as follows:
RH ¼
100
t t cri
a RHp þ b tcri < t 28
1. The polymer-type SRA and CaO-type EA have a significant impact on the relationship between RH and age. In this study, the SRA can cause a delay of initial setting time, an extension of the critical time and an increase in the RH at 28 days after casting. In contrast, the addition of EA can cause a reduction in the critical time and a significant decrease of RH at 28 days. 2. A development model for the critical time, which considers the influence factors of w/b ratio, polymer-type SRA and CaO-type EA dosages, is established in early-age concrete under sealed condition. In addition, results from proposed model is consistent with the experimental ones. 3. Comprehensively considering the w/b ratio, critical time, polymer-type SRA and CaO-type EA dosages, a universal twostage model is proposed for the RH development in early-age concrete. The proposed model shows a good agreement with the experimental data.
ð9Þ
where RHp conforms with Eq. (6). In addition, a and b are the values of parametric equations, which are defined as presented in Eqs. (10) and (11), respectively.
a ¼ 1 ðaSRA cSRA þ aEA cEA Þ
ð10Þ
b ¼ bSRA cSRA þ bEA cEA
ð11Þ
Through a regression analysis, aSRA , aEA , bSRA and bEA are calculated and optimized using the quasi-Newton method [39]. The values are 5.30, 6.33, 621.11 and 705.36, respectively. The values are brought into Eqs. (10) and (11). A comparison between the model and experimental data for mixtures containing either SRA or EA (i.e., the W35S2, W35S3, W35S2E2 and W35S2E3 mixtures) at Stage II are presented in Fig. 9. In Fig. 9, the R2 value is calculated for the curves of the model and measured RH values versus age. The values are 0.990, 0.988, 0.996 and 0.994, respectively. In other words, the shape and trend of the development model are close to those of the measured ones. In addition, the RMSE values are all less than 0.41%, which are negligible compared to the RH values which are over 87% at 28 days. On the basis of the analysis above, a good agreement can be validated between the model and experimental data for the mixtures containing either SRA or EA in this experiment. Furthermore, the W30, W35 and W40 mixtures have neither SRA nor EA; therefore, cSRA and cEA are equal to 0. Accordingly, Eq. (9) can be simplified to Eq. (8). The results using Eq. (9) for the W30, W35 and W40 mixtures are identical to those presented in Fig. 8. Consequently, Eq. (9) can also be applied to all the mixtures without SRA or EA. Overall, the proposed model can accurately describe the development process of the RH with age for the fully sealed specimens with different dosages of the admixtures in this experiment. The proposed models target to describe the RH development for early-age concrete under sealed condition with a w/b ratio between 0.3 and 0.4 and EA/SRA dosages between 0 and 3% in weight, and is also suggested that the calculated RH should not be lower than 70% at 28 days. The generalizability of suggested development model remains a challenge due to the limited test data and undefined physical meaning. In addition, there is not a
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work has been supported by the China Postdoctoral Science Foundation Funded Project (No. 2018M632217). The authors also gratefully acknowledge the financial support from the National Natural Science Foundation of China under Grant No. 51878245 and 51708265. This research is also sponsored by the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (No. 16KJB560004), the Fund for Postgraduate Research & Practice Innovation Program of Jiangsu Province (SJCX18_0186) and the Fundamental Research Fund for the Central Universities (2018B760X14). References [1] T. Voigt, G. Ye, Z. Sun, S.P. Shah, K. van Breugel, Early age microstructure of Portland cement mortar investigated by ultrasonic shear waves and numerical simulation, Cem. Concr. Res. 35 (5) (2005) 858–866. [2] Z. Jun, H. Dongwei, C. Haoyu, Experimental and theoretical studies on autogenous shrinkage of concrete at early ages, J. Mater. Civ. Eng. 23 (3) (2011) 312–320. [3] X. Hu, Z. Shi, C. Shi, Z. Wu, B. Tong, Z. Ou, G. de Schutter, Drying shrinkage and cracking resistance of concrete made with ternary cementitious components, Constr. Build. Mater. 149 (2017) 406–415. [4] K. Kovler, S. Zhutovsky, Overview and Future Trends of Shrinkage Research, Mater. Struct. 39 (9) (2006) 827–847. [5] B.T. Bissonnette, P. Pierre, M. Pigeon, Influence of key parameters on drying shrinkage of cementitious materials, Cem. Concr. Res. 29 (10) (1999) 1655– 1662. [6] T. Ayano, F.H. Wittmann, Drying, moisture distribution, and shrinkage of cement-based materials, Mater. Struct. 35 (3) (2002) 134–140. [7] H.F.W. Taylor, Cement Chemistry, 2nd edition., Thomas Telford Publishing, London, 1997. [8] A.M. Neville, Properties of Concrete, 4th edition., John Wiley and Sons, London, 1996. [9] J. Saliba, E. Rozière, F. Grondin, A. Loukili, Influence of shrinkage-reducing admixtures on plastic and long-term shrinkage, Cem. Concr. Compos. 33 (2) (2011) 209–217.
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