Comparative shrinkage behavior of ultra-high-performance fiber-reinforced concrete under ambient and heat curing conditions

Construction and Building Materials 162 (2018) 406–419

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Comparative shrinkage behavior of ultra-high-performance fiberreinforced concrete under ambient and heat curing conditions Doo-Yeol Yoo ⇑, Soonho Kim, Min-Jae Kim Department of Architectural Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea

g r a p h i c a l a b s t r a c t


Mechanical properties of UHPFRC are

Age (day) 0

10

20

30

40

50

60

0

Strain (με)

-100 -200

Autogenous shrinkage Total shrinkage Drying shrinkage

-300

Age (day) 0

10

20

30

40

50

60

0

-400

Test data Proposed model

-100

-500

-200 -600

Age (day) 0

Vinyl

10

20

30

40

50

60

0

Embedded strain gauge

-300

Ambient curing

-400 -500

-100

Thermocouple

Nylon line

(a)

-600

Strain (με)

improved by applying steam curing with heat.
The ultimate autogenous and drying shrinkage of UHPFRC are about 450 le and 45 le, respectively.
The ultimate autogenous shrinkage of UHPFRC is not affected by curing condition.
Most of micropores in UHPFRC are disappeared after steam curing, causing marginal increase of shrinkage afterward.
A prediction model for autogenous shrinkage of UHPFRC is proposed by considering equivalent age.

Strain (με)

h i g h l i g h t s

-200 -300

Autogenous shrinkage Total shrinkage Drying shrinkage

Heat curing

-700

-400 -500

Vinyl

-600

(b)

a r t i c l e

i n f o

Article history: Received 15 August 2017 Received in revised form 12 October 2017 Accepted 5 December 2017

Keywords: Ultra-high-performance fiber-reinforced concrete Autogenous shrinkage Drying shrinkage Curing condition Equivalent age

⇑ Corresponding author. E-mail address: [email protected] (D.-Y. Yoo). https://doi.org/10.1016/j.conbuildmat.2017.12.029 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.

a b s t r a c t This study aims to investigate the effect of curing conditions on the free shrinkage behaviors of ultrahigh-performance fiber-reinforced concrete (UHPFRC). For this study, a number of exposed and sealed prismatic UHPFRC samples for drying and autogenous shrinkage measurements were fabricated and tested using two different types of embedded strain gauges. Several other tests, including mechanical tests, X-ray diffraction (XRD), and mercury intrusion porosimetry analyses, were also performed. Test results indicate that steam curing with heat (90 °C, referred to as heat curing) was effective to improve the mechanical properties of UHPFRC at an early age in terms of strength, elastic modulus, and fracture energy absorption capacity. The larger quantities of C-S-H and much smaller total cumulative pore volume were obtained for the steam-cured specimens, compared to those for the ambient-cured specimens. The ultimate autogenous shrinkage of UHPFRC was insignificantly affected by the curing conditions, whereas heat curing accelerated the shrinkage development as compared to ambient curing. In particular, there was no increase of shrinkage strains for UHPFRC after heat curing was finished. The ultimate drying and autogenous shrinkage of UHPFRC were found to be approximately 45 le and 450 le, respectively. Based on literature review, an optimized model was suggested, and the autogenous shrinkage developments of UHPFRC at both ambient and heat curing conditions were successfully predicted based on the equivalent age method. Ó 2017 Elsevier Ltd. All rights reserved.

D.-Y. Yoo et al. / Construction and Building Materials 162 (2018) 406–419

1. Introduction Reactive powder concrete (RPC), which is the forerunner of various types of ultra-high-performance fiber-reinforced concrete (UHPFRC) developed in many countries (i.e., France, US, Japan, and South Korea) [1–4], was first introduced by Richard and Cheyrezy [5] in the mid-1990s. In accordance with ACI Committee 239 [2], this special material is considered to be concrete having a minimum compressive strength of 150 MPa and satisfying the specified durability, ductility, and toughness values. In order to increase the compressive strength of UHPFRC, an extremely low water-to-binder (W/B) ratio (less than 0.2) was adopted along with fine admixtures, such as silica fume and flour. To improve the ductility and toughness, a high volume (normally 2%) of short straight steel fibers were incorporated [6]. Even though this material has excellent mechanical properties and durability, its practical application has been limited thus far due to several reasons, such as high production price, high possibility of early age shrinkage cracks, significant variations of tensile performance according to fiber orientation, etc. Therefore, to accelerate its practical application, extensive studies have been carried out and published. In order to reduce the production cost of UHPFRC, several methods, e.g., adding coarse aggregate and reducing the steel fiber content, have been recently introduced [7–12]. First, Ma et al. [10] reported that, by including a coarse aggregate in UHPFRC, the amount of fine powders can be reduced, and a more flowable mixture and shorter mixing time can be obtained. Consequently, a lower production cost is achieved as compared to the conventional UHPFRC mixture without a coarse aggregate. The compressive strength was insignificantly influenced by the coarse aggregate [7,10], whereas a noticeably lower flexural strength was observed in UHPFRC with a coarse aggregate [13], owing to the lower bond strength of the steel fibers. By adding a coarse aggregate, the amount of shrinkage is reduced since it restrains the cement paste shrinkage, so that a lower bond strength is obtained [7]. Accordingly, methods including coarse aggregates in the UHPFRC mixture have not been widely adopted by researchers and engineers, since the excellent ductility and energy absorption capacity under tension or flexure for UHPFRC are the main reasons why this special construction material has attracted attention. Another method to reduce the production cost is to use a smaller amount of highstrength steel fibers without significantly deteriorating the tensile and flexural performance of UHPFRC [8,9,11,12]. Wille et al. [11] developed a strain-hardening UHPFRC including small amounts of hooked-end and twisted steel fibers. In their study [11], relatively higher tensile strength and strain capacity were obtained by using the hooked and twisted fibers as compared with using straight fibers at a low volume content. Ryu et al. [9] reported that 0.5% by volume of steel fibers in conventional UHPFRC can be reduced by the hybrid use of 16.3-mm and 19.5-mm straight steel fibers at respective volumes of 0.5% and 1% without any decrease of flexural strength. In addition, Yoo et al. [8,12] very recently developed a new type of UHPFRC with hybrid uses of steel fibers, and they reduced the total price of steel fibers for the commercially available UHPFRC by as much as 32–35% by reducing the fiber content. Likewise, a method to reduce the production cost was successfully introduced, mainly based on reducing the amount of steel fibers required. A special steam-heat treatment has been normally applied for the commercial UHPFRC [6] in order to accelerate its strength development, although this curing method also obviously increases its production costs. Since UHPFRC exhibits very high compressive strength more than 150 MPa, it requires a long curing time to develop its ultimate strength under water curing condition. It definitely delays construction period. Thus, to accelerate strength development and to shorten construction period, precast

407

UHPFRC products, which are fabricated under steam-heat curing, have been mostly adopted [14] along with a few cast-in-place UHPFRC with ambient curing. Accordingly, the other methods, mentioned above, have been considered by previous studies to reduce its production costs, instead of changing the curing method. Another important issue limiting the practical application of UHPFRC is early age shrinkage cracking during fabrication [15]. Since UHPFRC includes a low water-to-binder ratio and high fineness admixtures, it exhibits a very steep increase of autogenous shrinkage at very early ages. Furthermore, it is mostly used for thin plate structures, i.e., bridge decks, roofs, and walls, because of its excellent strength and post-cracking ductility, so a higher tensile stress is obtained by restraining shrinkage in the cross-section of these structures. Thus, several studies [15–18] have been carried out to improve the resistance to shrinkage cracks for UHPFRC. From free and steel-bar restrained shrinkage test results, Yoo et al. [16] reported that the addition of a shrinkage reducing admixture (SRA) was effective in reducing the amount of autogenous shrinkage and cracking potential of UHPFRC. Approximately 15.2% and 28.4% of autogenous shrinkage strains for UHPFRC were reduced by adding 1% and 2% SRA, respectively. Park et al. [17] also examined shrinkage behaviors of UHPFRC with SRA and expensive admixture (EA) and reported that the combined use of SRA and EA was more efficient in improving the shrinkage performance of UHPFRC than with SRA or EA alone. Based on their test results [17], Yoo et al. [15] performed restrained shrinkage tests of UHPFRC with and without SRA and EA using full-scale slab structures. Interestingly, although the combined use of SRA and EA effectively reduced the amount of free shrinkage and shrinkage crack width, it could not prevent the formation of shrinkage cracks. Rather, the shrinkage cracks in thin UHPFRC slabs were effectively controlled by increasing the slab thickness and using expanded polystyrene at the edges [18]. Based on these numerous preliminary mechanical and shrinkage test results, the Korea Institute of Civil Engineering and Building Technology has proposed an UHPFRC mixture containing 1.5 vol% hybrid straight steel fibers and minimized chemical admixture (only 1% SRA). This is because the prices of the steel fibers and admixtures, i.e., SRA and EA, are quite expensive, and the cracking formed by the restraint of shrinkage is mainly controlled by applying expanded polystyrene. Therefore, to practically use the proposed UHPFRC mixture, its comprehensive free shrinkage behaviors including ultimate value need to be examined. Furthermore, in order to perform its numerical construction step analysis, the development of free shrinkage, including autogenous and drying shrinkage, need to be evaluated and modeled properly. Accordingly, this study examines the autogenous and drying shrinkage behaviors of the UHPFRC developed at ambient and heat curing conditions because they can be applied for both in-situ concrete and precast products. Several other tests, i.e., mechanical tests, X-ray diffraction (XRD), and mercury intrusion porosimetry (MIP) analyses, were also performed to investigate its fundamental properties. Finally, the autogenous shrinkage development of UHPFRC was simulated with numbers from previous models in literature, and an optimized model was suggested to predict the autogenous shrinkage at both ambient and heat curing conditions by using the equivalent age concept. 2. Experimental program 2.1. Materials, mix proportions, and specimen preparation for mechanical tests In order to fabricate UHPFRC, Type I Portland cement and zirconium (Zr) silica fume (SF) were used as cementitious materials. The chemical compositions and physical properties of the cement and

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Zr SF are summarized in Table 1. As a fine aggregate, silica sand with a diameter of 0.2–0.3 mm was adopted, while silica filler (SSIL10) with a median diameter of 4.2 lm was incorporated to increase packing density. A coarse aggregate was not used in the present study since it is known that the coarse aggregate greatly deteriorates the tensile or flexural performance of UHPFRC [7]. In accordance with Collepardi et al. [7], the existence of a coarse aggregate resulted in the restraint of a great portion of the matrix shrinkage, leading to a reduced fiber bond strength, and a reduced homogeneity. Consequently, the flexural strength of UHPFRC having coarse aggregates was clearly smaller than that without coarse aggregates. A W/B ratio of 0.2 was applied, and the amount of Zr SF was 25% by weight of cement. Since the mixture of UHPFRC has a high volume of cement and high fineness admixtures, its viscosity is high, making it difficult to mix and cast into a mold. Thus, to achieve adequate flowability, a polycarboxylate superplasticizer (SP), including 30% solid and 70% water, was added into the mixture. The solid content was as much as 0.7% by weight of cement. The amount of SP required to provide proper flowability of UHPFRC was reduced as compared with previous studies [8] since the Zr SF with a specific surface area of 15,064 cm2/g has much larger grain size than the conventional SF with a specific surface area of 200,000 cm2/g, creating a more flowable mixture. The fluidity of the UHPFRC mixture was evaluated based on a slump flow test as per ASTM C1611 [19], and as shown in Fig. 1, a very flowable UHPFRC mixture with an average flow value of 625 mm was obtained. It has been reported that UHPFRC is susceptible to early age cracking when its shrinkage is restrained [15]. Thus, in order to reduce the amount of shrinkage for UHPFRC, a shrinkage reducing admixture (SRA) was additionally included at 1% of the cement weight. The detailed mixture proportions are given in Table 2. In order to improve the post-cracking tensile performance, high strength smooth steel fibers were added into the ultra-highperformance concrete (UHPC) mixture. According to the previous test results performed by Ryu et al. [9], the hybrid use of two smooth steel fibers with diameters of 0.2 mm and lengths of 16.3 mm and 19.5 mm provided the best post-cracking flexural performance compared to that of single fibers. In particular, the UHPFRC beams including hybrid use of 19.5-mm and 16.3-mm smooth steel fibers at 1% and 0.5%, respectively, exhibited better flexural performance as compared to UHPFRC including 2% short smooth steel fibers with an identical diameter but a shorter length of 13 mm (commercially available), even though 0.5% fewer steel fibers were used. Accordingly, the use of 1.5% hybrid smooth steel fibers was determined as a reference mixture for UHPFRC, and the properties of the smooth steel fibers used here are summarized in Table 3. Since UHPFRC includes high fineness admixtures and steel fibers but no coarse aggregate, its mixing sequence is different than that of ordinary concrete. First, all of the dry components, including cement, Zr SF, silica sand, filler, and SRA were included into a

Table 1 Compositions and physical properties of cementitious materials.

y

Hobart-type mixer with a capacity of 20 L and pre-mixed for approximately 5 min. Then, water pre-mixed with SP was added into the dry components and mixed for another 5–7 min. Once the mixture became flowable, 1.5 vol% steel fibers were carefully added and additionally mixed for 2 min. Finally, before removing the mixture from the mixer, it was very slowly mixed for an additional 1 min. In order to examine the compressive and tensile behaviors of UHPFRC according to the curing condition, a number of cylindrical and dog-bone shaped specimens were fabricated. Since UHPFRC has a very low W/B ratio and high fineness admixtures, water evaporation at the exposed surface is much faster than bleeding. Therefore, the exposed surface of UHPFRC dries very quickly even though the inner concrete is still fresh [20]. To prevent such a problem, the exposed surfaces of all of the cylindrical and dog-bone specimens were covered with a plastic sheet immediately after casting them. Once they had enough stiffness (after 2 days), the samples were removed from the molds and cured under both ambient and heat curing conditions. For the heat curing condition, steam and heat (approximately 90 °C) were applied for 3 days, and then, the specimens were cured at the ambient temperature equally. The temperature and relative humidity histories are shown in Fig. 2. Since the shrinkage measurements were carried out during monsoon season in South Korea, the relative humidity measured was quite fluctuated. In addition, a sudden change of temperature from about 20 °C to 90 °C was obtained for the case of heating curing. The temperature was measured using thermocouples, which were connected to a data logger, while the relative humidity was measured from I-button. For the heat curing condition, the data for relative humidity was not obtained due to a failure of the sensor (I-button). However, since steam was applied during curing, the relative humidity can be simply assumed to be 100% maintained. 2.2. Test setup for shrinkage measurements

Composition % (mass)

Cement*

Zr SFy

CaO Al2O3 SiO2 Fe2O3 MgO SO3 K2O Specific surface area (cm2/g) Density (g/cm3)

61.33 6.40 21.01 3.12 3.02 2.30 – 3413 3.15

0.04 0.43 94.3 0.01 – – – 15,064 2.50

* Type 1 Portland cement. Zr SF = zirconium silica fume.

Fig. 1. Slump flow test result for UHPFRC (unit: mm).

In order to evaluate the autogenous and drying shrinkage of UHPFRC under normal conditions, a number of prismatic beams with a cross-section of 100 mm  100 mm and a length of 400 mm were prepared. First, to prevent the restraint of shrinkage by friction between the UHPFRC and inner surface of the mold, a Teflon sheet was used. Then, for the specimens measuring autogenous shrinkage, vinyl was also included in order to prevent water evaporation, as shown in Fig. 3a. Aïtcin [21] reported that autogenous shrinkage of high-performance concrete (HPC) is developed during the hardening process, so measurements need to start at

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D.-Y. Yoo et al. / Construction and Building Materials 162 (2018) 406–419 Table 2 UHPFRC mix proportions. W/By

0.2

Unit weight (kg/m3)

Steel fibers (kg/m3) *

Water

Cement

Zr SF

Silica sand

Filler (S-SIL10)

SRA

SP

175.0

799.5

199.9

879.5

239.9

8.0

18.4

S1

S2

78.0

39.0

Note: Zr SF = zirconium silica fume, S-SIL10 = silica filler with a median particle size of 4.2 lm, SRA = shrinkage reducing admixture, SP = superplasticizer, S1 = smooth steel fiber with a diameter of 0.2 mm and a length of 19.5 mm, and S2 = smooth steel fiber with a diameter of 0.2 mm and a length of 16.3 mm. * Superplasticizer includes 30% solid (=5.52 kg/m3) and 70% water (=12.88 kg/m3). y W/B is calculated by dividing total water content (175.0 kg/m3 + 12.88 kg/m3 + a) by total amount of binder (799.5 kg/m3 + 199.9 kg/m3). Herein, a indicates certain amount of water in SRA.

Table 3 Properties of steel fibers. Name

df (mm)

lf (mm)

Aspect ratio (lf/df)

Density (g/cm3)

ft (MPa)

Ef (GPa)

S1 S2

0.20 0.20

19.5 16.3

97.5 81.5

7.9 7.9

2500 2500

200 200

Note: df = fiber diameter, lf = fiber length, ft = tensile strength of fiber, and Ef = elastic modulus of fiber.

Fig. 2. Temperature and relative humidity behaviors according to exposure time.

the setting time of concrete or before. Yoo et al. [16] also reported that if the autogenous shrinkage of UHPFRC is measured from the initial or final setting times, approximately 25% and 55% lower 30day autogenous shrinkage is obtained, respectively, compared to the actual value because the time of shrinkage stress development is faster than the setting times. Therefore, in order to measure the shrinkage strains and internal temperature variation of UHPFRC immediately after concrete casting, embedded strain gauge and thermocouple were installed at the center and middle height of

the mold before casting (Fig. 3a). Therefore, all the data was measured before casting through a data logger system (TDS 530). In this study, two different embedded strain gauge sensors were adopted for measuring the free shrinkage strains of UHPFRCs, as shown in Fig. 4. In order to achieve good bond performance between the gauge and UHPFRC, a dumbbell shape was applied for both strain gauges. Gauge #1, which was made of special plastic having a very small elastic modulus below about 2 GPa, was used for measuring the shrinkage under the ambient curing condition. Since the strain gauge #1 has very small elastic modulus than that of UHPFRC, it could precisely measure its very early age shrinkage behavior [16]. However, usable temperature range of the strain gauge #1 is from 20 to +60 °C, it couldn’t be used for the shrinkage measurements of steam-cured UHPFRC. Therefore, strain gauge #2, which was specially made to precisely measure the strain at a high temperature of approximately 90 °C, was alternatively used for measuring the shrinkage of UHPFRC under the heat curing condition. Since gauges #1 and #2 were made of different materials, the initial shrinkage behaviors of UHPFRC measured using the different gauges will vary. To verify this, the initial shrinkage strains measured from gauges #1 and #2 were compared in Section 3.2 below. In addition, to accurately compare the magnitude of shrinkage strains measured from gauges #1 and #2, they need to be used and analyzed at the identical curing condition. However, due to experimental limitations (i.e., limited budget and experimental period), the gauge #2 was only used for measuring the shrinkage strains at the steam-heat curing condi-

Gauge #2

Gauge #1 Fig. 3. Pictures for autogenous shrinkage measurement: (a) before casting, (b) immediately after casting with sealing.

Fig. 4. Pictures of gauges #1 and #2 for free shrinkage measurement.

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tion, while the gauge #1 was applied at the ambient curing condition. Since the UHPFRC mixture used in this study includes a high amount of SP, its initial set was delayed, and thus, the samples were demolded after initial 2-day curing in a room at ambient temperature. Both steam- and ambient-cured samples were all cured at the same room, and its temperature and relative humidity variations are given in the initial part of Fig. 2. In order to examine the effect of the curing conditions, i.e., heat curing and ambient curing, half of the specimens were then placed in a special chamber for steam-heat curing at 90 °C, while the rest were cured in a room at ambient temperature. The temperature histories for these curing conditions are given in Fig. 2. Steam curing with heat was applied for 3 days, and after that, all of the steam-cured specimens were cured in a room under identical conditions as the ambient-cured specimens until the end of the shrinkage measurement. In addition, to evaluate the autogenous and drying shrinkage, half of the specimens were covered with aluminum adhesive tape immediately after demolding, while the rest were exposed without any sealing. For the sealed samples, no water evaporation was generated, causing an occurrence of self-desiccation. Thus, autogenous shrinkage was evaluated by subtracting the thermal strain from the real concrete shrinkage strain of the sealed samples, using the following equation: eas ¼ est  aDT, where eas is the autogenous shrinkage, est is the measured concrete strain, a is the coefficient of thermal expansion, and DT is the temperature variation. Herein, the measured concrete strain indicates the actual strain of concrete excluding temperature effect of gauges, based on gauge manuals. In addition, the drying shrinkage was evaluated from the exposed prismatic samples. The measured shrinkage strains of exposed samples contained autogenous, drying, and thermal shrinkage strains. Thus, to obtain the drying shrinkage only, the autogenous and thermal strains were subtracted from the measured concrete strains of the exposed samples. 2.3. Test setup for mechanical properties For the compressive test, several cylindrical specimens with a diameter of 100 mm and height of 200 mm were fabricated and tested according to ASTM C39 [22]. Before applying the axial force, the casting surface of the cylinders was ground using a diamond blade to minimize the eccentric effect. A uniaxial load was applied to the specimens using a universal testing machine (UTM) with a maximum load capacity of 300 tons. To measure the compressive stress-strain curves, which provides information about the elastic modulus and strain capacity, a compressometer with three linear variable differential transformers (LVDTs) was adopted. The detailed test setup can be found elsewhere [23]. Direct tensile tests were also carried out to investigate the curing effect on the tensile strength and fracture energy absorption capacity of UHPFRC. To do this, several dog-bone-shaped specimens with notches at the center were fabricated and tested. The cross-sectional area of the specimens where the crack is formed by a notch was 50 mm  25 mm. The detailed geometry of the dog-bone specimen and test setup are shown in Fig. 5. To apply a uniaxial load, a UTM with a maximum load capacity of 25 tons was used, and the loading rate applied was 1 mm/min. Clip gauges were applied at the notch points to measure the crack mouth opening displacement (CMOD). A pin-fixed support condition was adopted to minimize the secondary moment. For both the compressive and direct tensile tests, at least three specimens were used for each variable to obtain average results. In addition, the compressive and tensile tests were performed immediately after heat curing was finished to evaluate the heat curing effect on the development of the compressive and tensile strengths, as well as after 28 days.

P Cross head

Load cell

Clip gauge

Notch

Pin

Dog-bone specimen Fixed end

(a)

(b)

Fig. 5. Direct tensile test setup; (a) test picture, (b) geometry of specimen.

2.4. X-ray diffraction analysis In order to examine the implications of the curing condition and age on the chemical composition of UHPFRC, XRD analysis was performed. For this, several cube specimens with a length of 50 mm were fabricated using the mortar without fibers. The specimens were cured for 6 days and 28 days like the mechanical specimens and placed into a desiccator for 1 day to remove the residual water. Then, the specimens were crushed in order to make powder samples. A high power X-ray diffractometer, based on Bragg-Brentano geometry, was used for XRD analysis with a 2h scanning range from 5 to 70°. This test was performed at room temperature. 2.5. Mercury intrusion porosimetry analysis The pore structures of UHPFRC cured at both ambient and high temperatures were examined using a mercury porosimeter (Autopore IV 9500 series). For this, cubic samples made of the mortar without fibers were prepared identically with those for XRD analysis. The samples were cured for 28 days and placed in the desiccator for 1 day to eliminate residual water. A low pressure of mercury (Hg) was first applied up to 0.51 psia using nitrogen gas to evaluate macroporosity, and the maximum pressure gradually increased up to 33,000 psia to measure microporosity. The diameter of the pores was calculated based on a Washburn equation by assuming a cylindrical pore, as follows:

d¼

4ccosh P

ð1Þ

where d is the pore diameter, c is the surface tension of mercury, h is the contact angle between mercury and the solid, and P is the pressure. Although the MIP analysis was used in this study for thoroughly investigating the shrinkage behavior of UHPFRC according to pore size distribution, some limitations of using it needs to be mentioned. According to Diamond [24], the MIP analysis has a limitation to evaluate pore size distribution of hydrated cement based on the Washburn equation, because the actual shape of pores is not cylindrical but they are visibly convoluted and most of the pore volume are not directly accessible to the mercury. Nevertheless, the MIP analysis has been most widely used for analyzing the pore

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size distribution of cement paste and mortar because of its simplicity [24,25].

3. Experimental results and discussion 3.1. Effect of the curing condition on the mechanical and microstructural properties of UHPFRC The compressive stress versus strain curves of all UHPFRC cylinders tested at 6 days are shown in Fig. 6a, and several important results are summarized in Table 4. Due to a problem with the LVDTs, the stress-strain curves at 28 days could not be measured. It is obvious that the development of compressive strength and elastic modulus for UHPFRC were accelerated under heat curing as compared to that under ambient curing. This is due to the acceleration of cement hydration, which is consistent with the findings from Graybeal [6] and Koh et al. [26]. Thus, the steam-cured cylinders provided higher compressive strengths and elastic moduli at all ages compared to the ambient-cured cylinders. As the UHPFRC cylinders are steam cured at a high temperature of 90 °C for 3 days, their full strength is developed. Therefore, no noticeable increase in compressive strength was observed for the steam-cured UHPFRC from 6 days (immediately after steam curing with heat finished) to 28 days. In contrast, the ambient-cured UHPFRC cylinders clearly showed an increase in compressive strength according to age. For example, the average compressive strengths of the

steam-cured cylinders at 6 days and 28 days were found to be 154.9 MPa (standard deviation of 8.5 MPa) and 157.3 MPa (standard deviation of 6.8 MPa), respectively, which are approximately 40% and 18% higher than those of the ambient-cured cylinders. The steam-cured UHPFRC cylinders also provided greater linear stress and strain behaviors up to the peak point compared to that of the ambient-cured ones. Similarly, Khan et al. [27] also reported that more linear and brittle compressive behaviors were obtained for higher strength concrete and when concrete was cured for a longer time. Therefore, it can be considered that the steam-cured specimens showed more linear and brittle compressive behaviors than their counterparts because of their higher strengths. The strain capacity of UHPFRC was insignificantly affected by the curing condition and was found to be 0.0037–0.0038. The tensile stress versus CMOD curves for all specimens are given in Fig. 6b. In addition, the tensile strengths and fracture energies are summarized in Table 4. Similar to the compressive test results, the steam-cured UHPFRC specimens provided higher tensile strengths than those of the ambient-cured ones due to the acceleration of hydration. For example, the tensile strengths of steam-cured UHPFRC were found to be 16.9 MPa on average, approximately 49% and 13% higher than those of the ambientcured specimens at 6 days and 28 days, respectively. The increased tensile strengths of steam-cured UHPFRC at early ages might be also caused by accelerated autogenous shrinkage development as compared to those of ambient-cured one. It has been reported that a higher amount of shrinkage of cement matrix results in a higher radial confinement pressure, leading to higher bond strength and pullout work of straight steel fibers embedded in UHPC [28]. Therefore, the accelerated shrinkage development, from steamheat curing, could improve the tensile performance of UHPFRC by enhancing the fiber pullout resistance. All the dog-bone specimens made of UHPFRC cured at both the ambient and heat curing conditions exhibited a higher load carrying capacity after matrix cracking. Since the post-cracking tensile strength is closely related to the fiber bridging capacity as compared to the matrix cracking strength [29], the higher tensile strength denotes a better fiber bridging capacity, mainly caused by an enhanced fiber pullout resistance. It was also reported by Yunsheng et al. [30] and Yoo and Banthia [31] that a much higher interfacial bond strength between the steel fibers and matrix was obtained for steamcuring at 90 °C than for water curing at 20 °C. The tensile strength increased with age for the ambient-cured specimens, whereas no increase of tensile strength was observed for the steam-cured specimens, which is similar to the compressive behavior. Since the clip gauge capacity was approximately 6 mm, we could not measure the CMOD values up to the ultimate point where zero tensile stress is obtained. Therefore, in order to calculate the fracture energy, a free-form model, based on a rational function, was adopted [32,33] as follows:

rt ðwÞ ¼ Fig. 6. Mechanical test results: (a) compression (at only 6 days), (b) tension.

1þ

ft
p

ð2Þ

w w0

Table 4 Mechanical properties.

Ambient-cured UHPFRC Steam-cured UHPFRC

Curing age (day)

fc 0 (MPa)

Ec (GPa)

ec ()

ft (MPa)

GF* (kNmm)

6 28 6 28

110.3 133.7 154.9 157.3

41.4 –a 50.9 –a

0.0038 –a 0.0037 –a

11.3 14.9 16.8 16.9

30.9 61.5 86.1 84.1

Note: fc0 = compressive strength, Ec = elastic modulus, ec = compressive strain capacity, ft = tensile strength, and GF = fracture energy. * Fracture energy is calculated based on Eq. (2). a Data is not available.

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where rt(w) is the tensile stress, ft is the tensile strength, w is the crack opening displacement (COD), w0 is the COD at 50% of the tensile strength, and p is the shape parameter. The comparative post-cracking tensile behaviors obtained from experiments and Eq. (2) are shown in Fig. 7. The shape parameters were determined by a non-linear regression analysis based on least square error method, and for all cases, the coefficient of determination (R2) was higher than 0.9. Since the longest steel fiber length used was 19.5 mm, it was simply assumed that the tensile stress suddenly drops to zero as the CMOD reaches 9.75 mm, which is a half of the longest steel fiber length. This assumption is quite reasonable because, due to the flattening of smooth steel fibers at the end, which is generated by the cutting process, higher shear stress at the interface between the fiber and matrix is obtained near the normalized slip, S/Le, of 1 [34,35]. This results in a sudden decrease of the pullout load of the fiber when it was almost completely pulled out. Herein, S is the end slip of the fiber and Le is the initial embedment length of the fiber. For this reason, a sudden drop of tensile stress at a CMOD of 9.75 mm (half of the fiber length) can be obtained. The fracture energies calculated based on Eq. (2) are given in Table 4. Much higher fracture energy was achieved for the steam-cured specimens due to the higher tensile strength than for the ambient-cured ones. For example, the fracture energy of the steam-cured specimens was found to be 86.1 kNmm at 6 days, which is approximately 2.8 times higher than that of the ambient-cured specimens at the same age. The fracture energy was greatly increased with the curing age increasing from 6 days to 28 days for the ambient-cured specimens, whereas there was no increase of fracture energy with age for the steam-cured specimens. Synthetically, applying the steam curing with heat (90 °C) led to improved mechanical properties for UHPFRC, including strength, elastic modulus, and fracture energy absorption capacity. The diffractograms obtained from the XRD analyses for all test series are shown in Fig. 8. The quantity of portlandite, Ca(OH)2, was much smaller for the steam-cured samples, compared to that of ambient-cured ones. This is caused by the fact that, due to the acceleration of pozzolanic reaction under heat curing, a great amount of the portlandite was consumed and converted to strong C-S-H (calcium silicate hydrate) at an early age. A greater quantity of C-S-H, leading to a higher strength, was observed for the steamcured samples than that of the ambient-cured samples after 6 days. The absent of portlandite peaks for UHPFRC was also observed by Reda et al. [36]. For the ambient-cured samples, the quantity of the portlandite decreased with time, meaning that the pozzolanic reaction was continuous activated from 6 to 28 days. This is consis-

tent with the findings from Zanni et al. [37] for UHPFRC cured at 20 °C. However, only a minor change in the quantity of the portlandite was observed for the steam-cured samples after finishing the heat curing process. This indicates that the pozzolanic reaction was almost completed during the heat curing process, consistent with the mechanical test results. For the samples cured at both ambient and heat curing conditions, abundant quartz peaks were obtained, caused by the existence of unreacted silica fume and silica powders, such as sand and flour. This is consistent with the findings from Prem et al. [38]. In the steam-cured samples, higher quantity of quartz was obtained after 6 days than after 28 days unexpectedly, which might be due to a limitation of XRD analysis, i.e., using a very small part of specimen. Since it was impossible to perfectly disperse silica powders during mixing the UHPFRC, the earlier XRD sample (at 6 days) might have higher amount of silica sand and flour when it was prepared for the XRD analysis as compared to that of the later sample (at 28 days). In contrast, the quantity of quartz in the ambient-cured samples decreased with time as was expected, because of the continuously activated pozzolanic reaction, causing a decrease of the amount of portlandite. Certain amounts of dicalcium and tricalcium silicates (C2S and C3S) still existed for both ambient- and steam-cured samples after 6 and 28 days, as was also reported by Prem et al. [38], but smaller quantities of C2S and C3S were obtained in the steam-cured ones, because of their more matured hydration stage. 3.2. Effect of the embedded strain gauge type on the initial shrinkage behaviors The initial shrinkage and temperature behaviors of sealed UHPFRC using two different embedded strain gauges are shown in Fig. 9. Two specimens were used to measure the shrinkage and temperature behaviors. At the very beginning (up to approximately 0.5 days), even though UHPFRC was not cast, the strains decreased due to the decrease of temperature since the strain gauges #1 and #2 have coefficient of thermal expansions (CTEs). In the case of the gauge #2, a constant CTE value of 10.2 le/°C was provided and the temperature effect of the gauge itself was excluded by considering calibration coefficient and CTE of the gauge #2. On the other hand, a constant CTE value was not given for the gauge #1 but instead the temperature effect of strain gauge #1 was recommended to be excluded by subtracting the apparent strain from the measured strain, based on a gauge manual provided by a manufacturer. Interestingly, the strains measured from gauge #1 changed more drastically compared with those from

Fig. 7. Comparative post-cracking tensile stress versus CMOD curves from experiments and Eq. (1) (Note: AC = ambient curing and HC = heat curing).

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413

Fig. 8. XRD analytical results.

Fig. 9. Initial shrinkage and temperature behaviors measured from (a) gauge #1 and (b) gauge #2.

gauge #2, meaning that the former is more susceptible to temperature variation. After approximately 0.55 days, both the temperatures and strains measured were very steeply increased up to the peak points. This is because the temperature of the fresh UHPFRC mixture was higher than the ambient temperature. At this point, the mixture of UHPFRC is very fresh (almost like liquid), so that the strain variations were attributed to the temperature variations rather than the actual shrinkage. After reaching the peak points, all measured temperatures decreased to the ambient temperature, causing a decrease in the strains. Once they reached the lowest points (approximately after 1.23 days), the temperature started to increase due to a hydration heat, but the measured strains steeply decreased. In a previous study [16], the point where the measured strain behaved differently with the inner temperature was compared with the time when a tensile stress is developed in UHPFRC by restraint of shrinkage, and they verified that the point where the measured strain and temperature behave differently is close to the time of shrinkage stress development. Therefore, the starting point of deviation between the strain and temperature was determined as a time-zero for UHPFRC in this study. It is interesting to note that the time-zero of UHPFRC was quite similar for both strain gauges, meaning that the point of time-zero is not influenced by the type of embedded strain gauge. The shrinkage strains were only measured from the gauges when they were deformed by the concrete shrinkage. In particular, at a very early age, since the elastic modulus of concrete is low, the magnitude of the measured strain can be differed according to the stiffness of the strain gauges. In other words, the softer gauge will be more easily deformed by the shrinkage of early age concrete than the harder gauge. As shown in Fig. 4, gauge #1 was made of plastic having much smaller elastic modulus than that of UHPFRC, while gauge #2 was made of steel with a high elastic modulus. Thus, as shown in Fig. 10, the strains measured from gauge #1

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were higher than those from gauge #2. This is similar to the findings from Yoo et al. [39] reporting that the magnitude of early age deformation of reinforcements embedded in UHPFRC by its shrinkage is influenced by the elastic moduli of reinforcements: the one with smaller elastic modulus is deformed more greatly. In the same vein, Chen and Choi [40] denoted that the shrinkage stress level in concrete reinforced with glass fiber reinforced polymer bar is approximately one-fifth of that with steel bar, because the former can deform more than the latter. In addition, the difference between the strains was mainly generated at an early age when the elastic modulus of UHPFRC was quite low. For example, the average strains measured at 0.3 days were found to be -185 le for gauge #1, which is approximately 27% higher than that of gauge #2, while the average strains measured at 1.5 days were found to be -255 le for gauge #1, which is approximately 20% higher than that of gauge #2. Thus, it was concluded that the initial shrinkage strain of UHPFRC can vary with the type of embedded strain gauges, and approximately 40 le smaller strains were measured from gauge #2 with a higher elastic modulus than those from gauge #1 with smaller elastic modulus. Synthetically, the strain gauge #1 is more appropriate to measure the early age shrinkage deformation of UHPFRC than its counterpart (gauge #2), so that shrinkage strain of UHPFRC measured from the gauge #2 was modified by adding 40 le. Similar to the previous test results [16,23], the shrinkage strain of UHPFRC was steeply increased at a very early age after the timezero up to approximately 0.3 days. After that, the increase rate of shrinkage strains was significantly reduced and there was even a slight expansion. The main reason for the increased rate of shrinkage suddenly reducing after this point is that both the chemical shrinkage and positive pressure applied to the capillary pores by water desiccation are self-restrained by UHPFRC because of its sufficient stiffness developed. 3.3. Free shrinkage behaviors (total, autogenous, and drying shrinkage) of UHPFRC under ambient and heat curing conditions Fig. 11 shows the summaries of the total, autogenous, and drying shrinkage of UHPFRC under ambient and heat curing conditions. Two prismatic specimens were used for obtaining the average curve for all test series, excepting the case of total shrinkage under heat curing. It was obvious that, regardless of the curing condition, the difference between total shrinkage and autogenous shrinkage for UHPFRC was minor, which is consistent with the findings from a previous study [41]. This means that a significant portion of the total shrinkage for UHPFRC is caused by the autoge-

Fig. 10. Initial shrinkage behavior of UHPFRC measured from gauges #1 and #2 (Note: G1 = gauge #1 and G2 = gauge #2).

Fig. 11. Free shrinkage behaviors of UHPFRC under (a) ambient curing and (b) heat curing.

nous shrinkage instead of the drying shrinkage. This is dissimilar with the trend of ordinary concrete exhibiting much higher drying shrinkage than autogenous shrinkage [42]. For example, based on test results obtained by Zhang et al. [42], the ratio of autogenous shrinkage and total shrinkage was found to be only 10% for plain concrete with a W/B ratio of 0.35. This is caused by the fact that, since UHPFRC had a low W/B ratio of 0.2, a much smaller amount of pore water might exist as compared to that of ordinary concrete, causing a decrease in drying shrinkage. It is well known that the amount of drying shrinkage increases with an increase in the W/ B ratio [43], because a higher amount of water is lost due to evaporation caused by a disequilibrium between the relative humidity inside concrete and the atmosphere, and thus, concrete shrinks more with a higher W/B ratio. Tam et al. [44] also reported that a long-term volume stability of concrete, i.e., drying shrinkage and creep, is affected by a W/B ratio and a higher drying shrinkage of concrete with a higher W/B ratio of 0.5 is obtained as compared with those having lower W/B ratios from 0.35 to 0.45. Furthermore, since UHPFRC included high fineness admixtures, such as Zr SF and filler, it has very densified micro-structures with smaller sized pores. The capillary pressure, which is caused by self-desiccation of pore water, is inversely proportional to the radius of the pores, based on a Laplace law for circular cylindrical pores [45], and thus, the smaller capillary pores caused higher autogenous shrinkage in UHPFRC. For these two reasons, UHPFRC exhibited much higher autogenous shrinkage than drying shrinkage, as shown in Fig. 11. In accordance with Mehta and Monteiro [46], the pore size distribution of cement paste is affected by a W/B ratio: for the low W/ B ratio pastes, the capillary voids may range from 10 to 50 nm,

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while those may range from 3 to 5 lm for the high W/B ratio pastes. They [46] also denoted that capillary pores smaller than 50 nm, which are referred to as micropores, mainly influence the shrinkage and creep. As shown in Fig. 12, almost there was no capillary pores with sizes ranging from 3 to 5 lm for the UHPFRC, whereas most of its capillary pores had the pore sizes between 10 and 100 nm under ambient curing, similar to the findings from Mehta and Monteiro [46]. Thus, the volumetric percentage of the micropores to the total pore volume is important factor affecting the autogenous shrinkage [47]. First, the total intrusion volume of ambient-cured UHPFRC at 28 days was found to be 0.0298 mL/ g, while that of 28-day concrete with a W/B ratio of 0.3 was obtained as approximately 0.035 mL/g [48]. The amount of the micropores with sizes between 5 and 50 nm occupies approximately 73.6% of a total pore volume for the ambient-cured UHPFRC at 28 days, which was higher than that (65.6%) of cement paste (mixture A1) with a W/B ratio of 0.3, which was reported by Li et al. [47]. Thus, higher autogenous shrinkage was obtained for the UHPFRC, compared to that of mixture A1 [47]. Based on the pore size distribution, thus, it is concluded that the UHPFRC exhibits higher autogenous shrinkage than normal and highperformance concretes, due to its higher amounts of micropores. The autogenous shrinkage strains of UHPFRC after 60 days were found to be approximately 450 le for both the ambient and heat curing conditions. This means that the ultimate autogenous shrinkage of UHPFRC was insignificantly affected by the curing conditions, which is consistent with the findings from Koh et al. [49]. However, the development of autogenous shrinkage was very accelerated at an early age for the case of heat curing compared to ambient curing, as shown in Fig. 11b. This is caused by the fact that, since the hydration process of cement paste was accelerated under heat curing condition, the pore water self-dried more quickly, leading to a steeper increase of autogenous (or selfdesiccation) shrinkage. Interestingly, there was no increase of total, autogenous, and drying shrinkage for UHPFRC after the heat curing finished for 3 days, as shown in Fig. 11b. This strongly indicates that, after the heat curing process is finished, there will be no shrinkage cracks occurring in the UHPFRC structures. Similarly, the AFGC recommendations [1] also noted that no autogenous shrinkage of UHPFRC is developed after a completion of heat treatment. Therefore, the high possibility of generating restrained shrinkage cracking in thin UHPFRC structures, such as slabs, decks, and wall, is only obtained at an early age. In reality, the shrinkage cracks in large-sized thin UHPFRC structures only occurred at a very early age, as reported by Yoo et al. [15]. As shown in Fig. 12, much smaller porosity and amount of micropores were obtained for the steam-cured UHPFRC, as compared with those of ambient-cured one. The total intrusion pore volume of the

Fig. 12. Pore size distributions of UHPFRC.

415

steam-cured UHPFRC was found to be 0.0099 mL/g, approximately 67% smaller than that of the ambient-cured one. This might be mainly caused by the accelerated filling effects of silica fume from pozzolanic reaction and fillers during the heat curing process. Thus, no shrinkage increase after the heat curing finished was mainly caused by the fact that 1) most of the micropores, which mainly cause the shrinkage, were filled with hydration and pozzolanic products at an early age and consequently almost disappeared (Fig. 12), and 2) most of pore water were already consumed during the heat curing process. On the contrary, the total and autogenous shrinkage of ambient-cured UHPFRC continuously increased until approximately 20 days, and after that, there was a minor increase in that shrinkage. Similar drying shrinkages of approximately 45 le was obtained for UHPFRC after 60 days under both ambient and heat curing conditions, as shown in Fig. 11. However, at an early age (before 10 days), smaller drying shrinkage was obtained for the case of heat curing than its counterpart due to the steam applied. Since the relative humidity surrounding the specimens was approximately 100% during the heating curing process, almost zero drying shrinkage was expected to be obtained, whereas pore water was quickly evaporated from UHPFRC at an early age under ambient curing since it had a higher water content in the pores than atmosphere. After approximately 8 days, the drying shrinkage of UHPFRC under ambient curing was somehow slightly reduced. This might be caused by a high relative humidity during the shrinkage measurement because it was monsoon season in South Korea at that time, but to more reasonably explain this observation, further study on the drying shrinkage behavior of UHPFRC at constant temperature and humidity needs to be carried out. 3.4. Prediction models for the autogenous shrinkage of UHPFRC Since shrinkage strains were only measured at certain ages discontinuously, it is important to suggest a proper model to continuously predict the shrinkage strains with time for simulating shrinkage cracking behaviors. In particular, numerous previous studies [50–56] have suggested various models for predicting the autogenous shrinkage behavior of high-performance concrete (HPC) because total shrinkage was mostly attributed to the autogenous shrinkage for HPC or UHPFRC rather than the drying shrinkage. Thus, in order to examine if the previously suggested models are appropriate for UHPFRC, the experimental results obtained in this study were compared with the six most widely used theoretical models from the literature. The Japan Society of Civil Engineers (JSCE) standard specification recommended use of the following equations to predict the autogenous shrinkage of concrete, based on Tazawa and Miyazawa’s model [51]:

eas ðtÞ ¼ ceas1 bðtÞ

ð3Þ

eas1 ¼ 3070 exp ½7:2ðW=BÞ for 0:2 6 W=B 6 0:5

ð4Þ

eas1 ¼ 80 for 0:5 < W=B

ð5Þ

bðtÞ ¼ 1  exp½aðt  t s Þb 

ð6Þ

where t is a time, c is a coefficient to consider the effects of the cement and admixture types, eas1 is the ultimate autogenous shrinkage, b(t) is the development function of autogenous shrinkage, W/B is the water-to-binder ratio, ts is the initial setting time, and a and b are the regression coefficients to represent the characteristic of progress of the autogenous shrinkage. The initial setting time, ts, of 0.3 days was adopted according to a previous study

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[16], and the coefficients, a and b, were adopted as 1.2 and 0.4, respectively, for a W/B of 0.2. The European CEB-FIP Model Code 90 [52] also proposed the following equations to predict autogenous shrinkage strains of concrete mainly based on 28-day compressive strength:

eas ðtÞ ¼ eas1 ðf cm ÞbðtÞ eas1 ðf cm Þ ¼ aas

6

f cm f cm0 cm þ ffcm0

ð7Þ !2:5 ð8Þ


pffiffiffiffiffiffiffiffiffi bðtÞ ¼ 1  exp 0:2 t=t 1

ð9Þ

where fcm is the compressive strength of a concrete cylinder at 28 days, fcm0 is 10 MPa, aas is a coefficient depending on the type of cement (700 for ordinary Portland cement), and t1 is 1 day. Based on a Le Roy’s empirical model [53], Eurocode 2 (EN-1992) [54] suggested equations for autogenous shrinkage prediction, as follows:

eas ðtÞ ¼ eas1 bðtÞ

ð10Þ

eas1 ¼ 2:5ðf ck  10Þ

ð11Þ

pffiffi bðtÞ ¼ 1  expð0:2 t Þ

ð12Þ

where fck is the mean compressive strength of concrete cubes at 28 days. Dilger and Wang [50] proposed prediction models for autogenous shrinkage of SF and non-SF concrete with various W/B ratios from 0.15 to 0.4. Their proposed models are as follows:

eas ðt; ts Þ ¼ eas ðtÞ  eas ðts Þ

ð13Þ

eas1 ¼ 700 exp½3:5ðW=BÞ  120 for SF concrete

ð14Þ

eas1 ¼ 700 exp½3:5ðW=BÞ for non-SF concrete

ð15Þ

eas ðtÞ ¼ eas1

t 0:7 16:7ð1  aas Þ þ aas t 0:7

ð16Þ

W=B 3

ð17Þ

aas ¼ 1:04 

for 0:15 6 W=B 6 0:4

where ts is the age of concrete when shrinkage starts. Jonasson and Hedlund [55] also empirically suggested the following equations for predicting autogenous shrinkage behaviors of HPC with a W/B ratio below 0.4 and SF:

eas ðtÞ ¼ eas1 bðtÞ

ð18Þ

eas1 ¼ ½0:6 þ 1:2ðW=BÞ  103

ð19Þ

"  bðtÞ ¼ 1:14 exp 

t s0 t  ts

0:3 # ð20Þ

where ts0 is a time parameter (a constant value of 5 days is applied for all types of HPC) and ts is the time to normalize the autogenous shrinkage strain as zero (1 day). Thus, concrete prior to the time, ts, is assumed to be at a plastic condition. Lee et al. [56] empirically proposed equations for simulating the autogenous shrinkage behaviors of concretes with various W/B ratios and ground granulated blast-furnace slag (GGBFS), based on Tazawa and Miyazawa’s model [51], as follows:

eas ðtÞ ¼ ce28 bðtÞ

ð21Þ

e28 ¼ 2080 exp ½7:4ðW=BÞ

ð22Þ

( "

 b #) 28  t 1500 bðtÞ ¼ exp a 1  t  t1500

ð23Þ

where e28 is the autogenous shrinkage strain at 28 days, c is a coefficient to describe to the effect of GGBFS, t1500 is the time at an ultrasonic pulse velocity (UPV) of 1500 m/s, and a and b are constants depending on the replacing ratio of GGBFS. The authors [56] selected a UPV value of 1500 m/s for the starting time of the autogenous shrinkage measurement because an initial setting time was similar to the time when the UPV value reached roughly 1500 m/s. Therefore, t1500 can simply be replaced with the initial setting time. In recent years, two international recommendations (i.e., AFGC [1] and Federal Highway Administration (FHWA) [57]) proposed prediction models for autogenous shrinkage of UHPFRC. The ultimate autogenous shrinkage of UHPFRC was proposed to be 525 le from the AFGC recommendations, and they proposed the following prediction equation.



B tþC

eas ðtÞ ¼ A  exp pffiffiffiffiffiffiffiffiffiffiffi

 ð24Þ

where A, B, and C are coefficients of 525 le, 2.5, and 0.5, respectively. FHWA report [57] also proposed a prediction model for autogenous shrinkage of UHPFRC, based on Graybeal’s study. Their formula was based on a modification of the equation recommended by ACI 209R-92 [58]. They reported that, although the coefficient of A was recommended to be 35 by ACI 209R-92, it can be changed to define the shape of shrinkage development curve. The ultimate autogenous shrinkage of untreated UHPFRC was suggested to be 555 le [57], and the prediction equation of FHWA is as follows:

eas ðtÞ ¼

t eas1 Aþt

ð25Þ

where A is a coefficient defining the shape of curve. Based on a nonlinear regression analysis, the value of A was obtained to be 3.7 with a coefficient of determination of 0.682, in this study. Comparisons of the autogenous shrinkage strains of UHPFRC and predictive values from previous Eqs. (3)–(25) are summarized in Fig. 13. Since most of the previous models were suggested based on test results performed at constant temperature of 20 °C, an equivalent age, te, was adopted from the Arrhenius maturity function in order to precisely predict the autogenous shrinkage behavior of UHPFRC under varied ambient temperatures, as follows:

Z te ¼



t

exp 0

  Ea ðTÞ 1 1 dt  R T ref þ 273 TðtÞ þ 273

ð26Þ

where Ea(T) is the activation energy, which can be determined as per ASTM C1074 [59] or alternatively uses a value of 40,000 J/mol or 45,000 J/mol [60], R is the ideal gas constant (8.315 J/molK), Tref is the reference temperature of 20 °C, and T(t) is the actual temperature. It is obvious that the predictive values were completely different according to the suggested models. Tazawa and Miyazawa’s model [51] provided the largest predictive values, while the CEBFIP model [52] exhibited the smallest values at all ages. In addition, Tazawa and Miyazawa’s model [51], Dilger and Wang’s model [50], and FHWA model [57] overestimated the autogenous shrinkage of UHPFRC, whereas the others [1,52,54–56] underestimated it. Although AFGC model [1] was proposed based on a mixture of UHPFRC, it greatly underestimated the autogenous shrinkage development. Among the others, the models suggested by Dilger and Wang [50], Lee et al. [56], and FHWA [57] simulated the development of autogenous shrinkage and its ultimate value for UHPFRC relatively well. The initial shrinkage behavior was better predicted

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417

Fig. 13. Comparative autogenous shrinkage behaviors of UHPFRC obtained from experiments and prediction models considering equivalent age.

based on Lee’s model [56] and FHWA model [57], while the later behavior was better simulated with Dilger’s model [50]. Even though the Lee’s and Dilger’s models quite similarly predicted the ultimate autogenous shrinkage strain of UHPFRC, their development function of autogenous shrinkage, b(t), was not well fitted with the test data. Furthermore, the ultimate autogenous shrinkage strain suggested by FHWA [57] (555 le) was higher than the measured value because the UHPFRC mixture developed contains 1% SRA. Therefore, although the coefficient A, defining the shape of curve, was suggested based on a non-linear regression analysis, the FHWA model [57] did not predict the development of autogenous shrinkage successfully. As shown in Fig. 13, the shape of actual autogenous shrinkage development curve was more close to that calculated by CEB-FIP model [52]. From these observations, thus, the following model was newly proposed by non-linear regression analyses, based on a least square error method:

eas ðtÞ ¼ ceas1 bðtÞ

ð27Þ

eas1 ¼ 2300 exp ½7:2ðW=BÞ

ð28Þ

pffiffi bðtÞ ¼ 1  expð0:65 tÞ

ð29Þ

where c is a coefficient to describe to the effect of SRA. For the UHPFRC mixture contained SRA, the coefficient c was suggested to be 0.85, based on a previous study [16]. In their study [16], the 30-day autogenous shrinkage of UHPFRC was approximately reduced as much as 15% by including 1% SRA. The comparative autogenous shrinkage behavior of UHPFRC obtained from experiments and proposed model, Eqs. (27)–(29), is shown in Fig. 13. As can be seen, the autogenous shrinkage behavior of UHPFRC was quite precisely simulated with the proposed model. It is also known that the hydration of cement clinker, mainly alite (C3S), and the development of early age shrinkage are accelerated under higher temperatures [61,62]. Thus, to accurately predict the autogenous shrinkage behavior of steam-cured UHPFRC at a high temperature of 90 °C, the equivalent age, te, was considered from the Eq. (26). The measured and predicted autogenous shrinkage behaviors of UHPFRC under ambient and heat curing conditions are also shown in Fig. 14. The proposed model, Eqs. (27)– (29), considering the equivalent age precisely simulated both the autogenous shrinkage behaviors of ambient- and steam-cured UHPFRCs. In particular, the two special features of steam-cured UHPFRC, i.e., (1) the much steeper increase of shrinkage at an early age during heat curing and (2) the insignificant increase of shrinkage after heat curing, were well simulated by considering the

Fig. 14. Comparison of autogenous shrinkage behaviors of UHPFRC under ambient and heat curing obtained from experiments and proposed model [Eqs. (27)–(29)] considering equivalent age.

equivalent age from Eq. (26). Synthetically, it was concluded that the proposed Eqs. (27)–(29) with a consideration of equivalent age can be properly applied to predict the autogenous shrinkage behaviors of the UHPFRC mixture introduced in the current study at both ambient and heat curing conditions. 4. Conclusions This study examined the free shrinkage behaviors of UHPFRC under ambient and heat curing conditions. The effect of the curing condition on the mechanical properties, microstructure, and pore structural distribution of UHPFRC was also analyzed to obtain fundamental data. Several prediction models from literature were adopted to simulate the autogenous shrinkage development of UHPFRC, and an optimized model was suggested. Based on the above discussions, the following conclusions are drawn: 1) By applying steam curing with heat (90 °C), the mechanical properties of UHPFRC in terms of strength, elastic modulus, and fracture energy absorption capacity were significantly improved as compared to the ambient-cured UHPFRC. In addition, higher quantity of C-S-H and smaller quantity of portlandite were obtained in the steam-cured UHPFRC than those of the ambient-cured one. 2) The magnitude of the initial shrinkage strains of UHPFRC was influenced by the type of embedded strain gauge: the

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3)

4)

5)

6)

softer gauge type provided higher shrinkage strains than the harder one. Approximately 10% of the ultimate autogenous shrinkage was differed according to the strain gauge type. A significant portion of the total shrinkage of UHPFRC was caused by the autogenous shrinkage instead of the drying shrinkage. The ultimate autogenous and drying shrinkage of UHPFRC were found to be approximately 450 le and 45 le, respectively. The ultimate autogenous shrinkage of UHPFRC was not affected by the curing condition, whereas the development of autogenous shrinkage was very accelerated at an early age under heat curing relative to that under ambient curing. No increase of shrinkage strains was observed for UHPFRC after heat curing, while there was a continuous increase of shrinkage strains up to about 20 days for ambient curing. Total cumulative pore volume of the steam-cured UHPFRC was approximately 67% smaller than that of the ambientcured one. Most of micropores in UHPFRC were disappeared by applying steam curing with heat due to filling effect, causing marginal increase of the autogenous shrinkage after finishing the heat curing. The six most widely used prediction models were used for simulating the autogenous shrinkage behavior of UHPFRC. The previous models exhibited significantly different predictive values, and they all overestimated or underestimated it. The autogenous shrinkage developments of both ambientand steam-cured UHPFRC were well simulated based on the proposed model, Eqs. (27)–(29), by considering the equivalent age.

Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2017R1C1B2007589).

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