Properties prediction of ultra high performance concrete using blended cement hydration model

Construction and Building Materials 64 (2014) 1–10

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Properties prediction of ultra high performance concrete using blended cement hydration model Xiao-Yong Wang ⇑ Department of Architectural Engineering, College of Engineering, Kangwon National University, Chuncheon 200-701, Republic of Korea

h i g h l i g h t s  Proposed a hydration model of ultra high performance concrete (UHPC).  Considered both cement hydration and silica fume reaction.  Predicted degree hydration of cement, CH contents and mechanical properties.  Proposed model is valid for both ordinary strength concrete and UHPC.

a r t i c l e

i n f o

Article history: Received 30 November 2013 Received in revised form 1 April 2014 Accepted 8 April 2014

Keywords: Ultra high performance concrete Silica fume Blended cement Hydration model

a b s t r a c t Ultra high performance concrete (UHPC) consists of cement, silica fume (SF), sand, fibers, water and superplasticizer. Typical water/binder-ratios are 0.15–0.20 with 20–30% of silica fume. The development of properties of hardening UHPC relates with both hydration of cement and pozzolanic reaction of silica fume. In this paper, by considering the production of calcium hydroxide in cement hydration and its consumption in the pozzolanic reaction, a numerical model is proposed to simulate the hydration of UHPC. The degree of hydration of cement and degree of reaction of silica fume are obtained as accompanied results from the proposed hydration model. The properties of hardening UHPC, such as degree of hydration of cement, calcium hydroxide contents, and compressive strength, are predicted from the contribution of cement hydration and pozzolanic reaction. The proposed model is verified through experimental data on concrete with different water-to-binder ratios and silica fume substitution ratios. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Concrete or cementitious composites with compressive strength over 150 MPa are generally described as ultra-high performance concrete (UHPC); if fibers are added in order to decrease brittleness and increase energy absorption capacity the term ultrahigh performance fiber reinforced concrete (UHP-FRC) is used. UHPC’s high compressive strength, obtained through dense particle packing, implies high durability, improved resistance against freeze–thaw cycles and various chemicals as well as higher penetration resistance [1,2]. Many experimental studies have been done on the development of properties and proportioning mixtures of UHPC. Morin et al. [3] found that for reactive powder concrete (RPC), a long dormant period of about 30 h after water addition which was attributed to the high amount of superplasticizer. Then, the hydration started and

⇑ Tel.: +82 33 250 6229; fax: +82 33 250 6211. E-mail address: [email protected] http://dx.doi.org/10.1016/j.conbuildmat.2014.04.084 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.

was characterized by a strong heat release, which lasted for about 12 h. Bentz et al. [4] and Chung [5] reported that silica fume (SF) fulfils some functions in UHPC: it fills voids between cement grains, it enhances the rheological characteristics and it forms hydration products by pozzolanic activity. Another important effect of the silica fume is the improvement of the interfacial transition zones between binder and steel fibers. Thus, the mechanical strengths are increased and microstructure and packing efficiency of the UHPC are enhanced. Loukili et al. [6] investigated the hydration kinetics, change of relative humidity, and autogenous shrinkage of ultra-high-strength concrete. They found that the degree of hydration of cement is only 0.58 at 28 days due to the lower water to binder ratio in ultra high strength concrete, and the autogeneous shrinkage of ultra high strength concrete were much higher than ordinary strength concrete because of high self-desiccation at an early age due to both a very low w/c ratio and a high silica fume content. Besides experimental investigations on chemical and physical properties of UHPC [3–6], there are some theoretical models for

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X.-Y. Wang / Construction and Building Materials 64 (2014) 1–10

Nomenclature

a m

degree of cement hydration stoichiometric ratio by mass of water to cement wg physically bound water in C–S–H gel qw density of water S Blaine surface area qc density of the cement r0 radius of unhydrated cement particles Sw effective surface area of the cement particles in contact with water S0 total surface area if the surface area develops unconstrained B the parameter controls the rate of the initial shell formation C the parameter controls the rate of the initial shell decay kd cement hydration rate coefficient in the initial dormant period kr cement hydration rate coefficient in the phase boundary reaction period De effective diffusion coefficient of water in cement hydration products De0 initial value of De B20, C20, kr20, and De20 values of B, C, kr, and De0 at 20 °C, respectively b1, b2, E/R, and b3 temperature sensitivity coefficients of B, C, kr, and De0, respectively C0 mass of cement in the mix proportion W0 mass of water in the mix proportion Cw-free amount of water at the exterior of the C–S–H gel r empirical parameter considering the accessibility of water into an inner anhydrous part CHCE(t) mass of produced calcium hydroxide from the hydration of cement SF silica fume

predicting properties of silica fume blended concrete or UHPC. Based on a simplified scheme describing the activity of silica fume and fly ash in terms of chemical reactions, Papadakis [7] evaluated the final chemical and volumetric composition of supplementary cementing materials (SCM) concrete. Furthermore, carbonation of the SCM concrete was predicted. Ishida et al. [8] proposed a model to predict the micro–hygro–physical properties of high strength blended concrete and ordinary strength concrete. Mechanical properties, water desorption, moisture loss and drying shrinkage behaviors were determined by an enhanced intrinsic porosity model. Zelic et al. [9] developed a mathematical model to predict the development of compressive strength in cement–silica fume blends. Knudsen’s dispersion models were applied in fitting both the degree of hydration and the compressive strength experimental data as a function of time. It was found that the degree of hydration—the compressive strength dependence, for replacement levels varying from 0% to 15% mass of silica fume, indicates a linear mathematical function. Using semi-adiabatic heat of hydration tests, Habel et al. [10] proposed a kinetic hydration model for ultra high performance concrete, and evaluated mechanical properties of hardening UHPC. Compressive strength, tensile strength, fracture energy and secant modulus were evaluated from degree of reaction. It was observed that for the UHPC, the rate of development of mechanical properties was highest for the secant modulus, followed by the compressive and then the tensile strength. As shown in Refs. [8–10], the development of properties of silica fume blended concrete or UHPC relates with degree of hydration. On the other hand, Papadakis [7] proposed that the development of properties of silica fume blended concrete relates with both

CH

calcium hydroxide degree of reaction of the glass (active) phase of silica fume msilica0 silica fume mass in mixing proportion cs mass percentage of glass silica in silica fume Wcap and Wchem masses of capillary water and chemically bound water, respectively mCH(t) mass of calcium hydroxide in hydrating cement–silica fume blends vsi stoichiometry ratio by mass of CH to silica fume rsi0 radius of silica fume particle Desi reaction rate coefficient of silica fume in the diffusion period Desi0 initial value of Desi krsi reaction rate coefficient of silica fume during the phase boundary reaction period Desi20 and krsi20 values of Desi0, and krsi at 293 K, respectively besi and Esi/R temperature sensitivity coefficients of Desi0, and krsi, respectively u capillary porosity in hydrating silica fume–cement paste aCEc and aSFc critical reaction degrees of cement and silica fume corresponding to percolation threshold of capillary porosity, respectively xfc gel/space ratio of blended cement pastes fc compressive strength of blended concrete A intrinsic strength of cement and silica fume blends a and b contributions of cement and silica fume to the intrinsic strength, respectively n strength exponent c and d contributions of cement and silica fume to the strength exponent, respectively

asilica

cement hydration and silica fume pozzolanic reaction. In this paper, a numerical model is proposed to simulate the hydration of UHPC. The degree of hydration of cement and degree of reaction of silica fume are obtained as accompanied results from the proposed hydration model. The properties of hardening UHPC are predicted from the contribution of cement hydration and pozzolanic reaction. 2. Hydration model of Portland cement The shrinking-core model, which was originally developed by Tomosawa [11], is used in this study to simulate the development of cement hydration. This model is expressed as a single equation consisting of three coefficients: kd the reaction coefficient in the induction period; De the effective diffusion coefficient of water through the C–S–H gel; and kr a coefficient of the reaction rate of cement as shown in Eq. (1). These coefficients determine the rate of mass transport through the initial shell layer, the rate of phase boundary reaction process, and the rate of diffusion controlled process. The modeled cement particles are assumed to be spheres surrounded by hydration product. Based on this theory, the rate of cement hydration is derived as follows:

da 3ðSw =S0 Þqw C w-free 1   ¼ 1 2 r0 r0 1 dt ðv þ wg Þr 0 qc  De þ De ð1  aÞ 3 þ k1r ð1  aÞ 3 k

ð1Þ

d

where a is the degree of cement hydration; m is the stoichiometric ratio by mass of water to cement (= 0.25); wg is the physically bound water in C–S–H gel (= 0.15); qw is the density of water;

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X.-Y. Wang / Construction and Building Materials 64 (2014) 1–10

Cw-free is the amount of water at the exterior of the C–S–H gel; and r0 is the radius of unhydrated cement particles. In Eq. (1), the cement particles are assumed to be spherical and of uniform size with an average radius of r0 = 3/(Sqc) [12]. The terms S and qc stand for the Blaine surface area and density of the cement, respectively. As the hydration progresses, the hydration rate decreases with a reduction in the contact area between cement particles and the surrounding water because of the increase in interconnections among cement particles. This effect is accounted for by the term (Sw/S0) in Eq. (1) where Sw is the effective surface area of the cement particles in contact with water and S0 is the total surface area if the surface area develops unconstrained. The reaction coefficient kd is assumed to be a function of the degree of hydration as shown in Eq. (2) where B and C are the coefficients determining this factor; B controls the rate of the initial shell formation and C controls the rate of the initial shell decay.

kd ¼

B

a1:5

þ C a3

ð2Þ

The effective diffusion coefficient of water is affected by the tortuosity of the gel pores as well as the radii of the gel pores in the hydrate. This phenomenon can be described as a function of the degree of hydration and is expressed as follows:

De ¼ De0 ln

  1

a

ð3Þ

In addition, free water in the capillary pores is depleted as hydration of cement minerals progresses. Some water is bound in the gel pores, and this water is not available for further hydration, an effect that must be taken into consideration in every step of the progress of the hydration. Therefore, the amount of water in the capillary pores Cw-free is expressed as a function of the degree of hydration in the previous step as shown in Eq. (4).

C w-free ¼

 r W 0  0:4  a  C 0 W0

ð4Þ

where C0 and W0 are the mass fractions of cement and water in the mix proportion, and r is a empirical parameter considering the accessibility of water into an inner anhydrous part through an outer hard shell of the cement particles [4]. The effect of temperature on these reaction coefficients is assumed to follow Arrhenius’s law as shown in Eqs. (5)–(8):

   1 1 B ¼ B20 exp b1  T 293    1 1  C ¼ C 20 exp b2 T 293    E 1 1  kr ¼ kr20 exp  R T 293    1 1  De ¼ De20 exp b3 T 293

3. Hydration model for cement blended with silica fume 3.1. The amount of calcium hydroxide (CH) during the hydration process Using the hydration model and the stoichiometry of the reaction of silica fume proposed by Papadakis [7], the amounts of calcium hydroxide in cement–silica fume blends during hydration can be determined with the following equations:

CH ¼ CHCEðtÞ  1:85  asilica  msilica0  cs

ð9Þ

In Eq. (9), CHCE(t) is the mass of produced calcium hydroxide from the hydration of cement; asilica is the degree of hydration of the glass (active) phase of silica fume; msilica0 is the silica fume mass in mixing proportion; cs is the mass percentage of glass silica in silica fume. In this equation, the term CHCE(t) considers the producing of calcium hydroxide from cement hydration and the term 1:85  asilica  msilica0  cs considers the consumption of it in pozzolanic reaction. Similar with the hydration of cement, with the proceeding of pozzolanic reaction, the water is physically adsorbed in the hydration products of silica fume. Jensen and Hansen [13] proposed that for the silica fume pozzolanic reaction, when 1 g silica fume reacts, 0.5 g gel water and 0 g chemical water [7,13] are consumed. Hence the mass of capillary water and chemically bound water in hydrating cement–SF blends can be rewritten as following Eqs. (10.1) and (10.2):

W cap ¼ W 0  0:4  C 0  a  0:5  asilica  msilica0  cs

ð10:1Þ

W chem ¼ 0:25  C 0  a

ð10:2Þ

where Wcap and Wchem are the mass of capillary water and chemically bound water, respectively. In Eqs. (10.1) and (10.2), the term 0.4  C0  a considers the reduction of capillary water due to cement hydration. The term 0:5  asilica  msilica0  cs considers the reduction of capillary water due to pozzolanic reaction. Compared with Portland cement, the physically bound water within silica fume hydration products is much higher. This maybe comes from the relatively higher CSH content in silica fume hydration products [13]. On the other hand, there are also some minor components (about 10%) in silica fume, such as Al2O3, Fe2O3, CaO, and SO3. The influences of these minor components on the stoichiometries of silica fume needs more investigations. 3.2. The simulation of pozzolanic reaction in cement–silica fume blends

ð5Þ ð6Þ ð7Þ ð8Þ

where b1, b2, E/R, and b3 are temperature sensitivity coefficients and B20, C20, kr20, and De20 are the values of B, C, kr, and De at 20 °C. By using the proposed Portland cement hydration model, Tomosawa [11] evaluated the heat evolution rate, chemically bound water, and compressive strength of hardening concrete. Park et al. [12] predicted the temperature distribution in high strength concrete using this hydration model. High strength concrete with a water to cement ratio 0.27 was experimentally placed in a three-story reinforced concrete building having a basement floor with a building area and total floor area 615 m2 and 1353 m2, respectively. A good correlation was found between the analysis results and experimental results.

Because of the high specific surface of silica fume and great pozzolanic activity, in this paper it is assumed that the hydration of silica fume includes two processes: phase-boundary reaction process and diffusion process. Considering these points, based on the proposed method by Saeki and Monteiro [14], the hydration equation of silica fume can be written as Eqs. (11.1) and (11.2):

dasilica mCH ðtÞ 3qw 1 ¼ ð11:1Þ msilica0 v si r si0 qsi rsio ð1  asilica Þ13  rsi0 þ 1 ð1  asilica Þ23 dt krsi Desi Desi   1 Desi ¼ Desi0  ln ð11:2Þ

asilica

where mCH(t) is the calcium hydroxide mass in a unit volume in hydrating cement–silica fume blends and can be obtained from Eq. (9). vsi is the stoichiometry ratio by mass of CH to silica fume. rsi0 is the radius of silica fume particle. qsi is the density of silica fume. Desi0 is the initial diffusion coefficient and krsi is the reaction rate coefficient. The influence of temperature on hydration is considered by Arrhenius law as following Eqs. (11.3) and (11.4):

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X.-Y. Wang / Construction and Building Materials 64 (2014) 1–10

krsi ¼ krsi20 exp½Esi =Rð1=T  1=293Þ

ð11:3Þ

Desi0 ¼ Desi20 exp½besi ð1=T  1=293Þ

ð11:4Þ

where krsi20 and Desi20 are reaction coefficients at 20 °C; Esi/R and besi are activation energies. The heat evolution rate of hydrating cement–silica fume blends consists of contribution from two parts: the heat generated from Portland cement hydration and the heat generated from pozzolanic reaction between silica fume and calcium hydroxide. The outline of modeling is shown in Fig. 1. The proposed procedure has considered the effects of silica fume replacement ratios, water to binder ratios, and curing temperatures on the hydration of ultra high performance concrete. At each time step, the calcium hydroxide contents, capillary water contents, chemically bound water contents, gel–space ratio, and compressive strength of hardening ultra high performance concrete are determined using cement hydration degree and silica fume reaction degree. 4. Evaluation of properties of hardening UHPC The mean diameter of silica fume (the size for which there is 50% of the volume of particles passing) is about 0.15 lm [15], and the mean diameter of cement with a Baline surface 450 m2/ kg is 13.7 lm [15]. Due to the size of silica fume is much finer than that of cement, silica fume particles can effectively fill the voids among cement particles, and the packing efficiency of cement– silica fume blends is higher that of cement alone. Using

Setting of initial conditions and calculating time, tend

t=t+ t

Hydration model:

Δα = f ce (T , t ); Δα silica = f SF (T , t ) Calculating a degree of hydration:

α = α + Δα ; α silica = α silica + Δα silica

compressible packing model proposed by de Larrard [2], the effects of fine/coarse size ratio on packing density of binary mixture are calculated and shown in Fig. 2. X axis represents volume fraction of finer particles (x = 0 means no finer particles and x = 1 means all the particles are finer particles). Y axis represents calculated packing density of binary mixture. As shown in Fig. 2, the optimum packing density (peak point of each curve) increases when the fine/ coarse size ratio decreases. Also, volume fraction of finer class at the optimum tends to decrease, which is logical: the less the sizes are comparable, the less the fractions are interchangeable [2,4,5]. On the other hand, UHPC has theoretical optimum water contents [2]. The theoretical optimum water contents of UHPC can be analyzed using relative density (the ratio between density of the concrete at demoulding and the solid density of the granular mixture). As the water to binder ratio is increased above the 0.08 minimum, water replaces air without increasing the volume of the mixture up to water to binder ratio of about 0.13. If the water to binder ratio is increased beyond this point, additional water increases the volume and thus decreases the density of the mixture. The mixtures represented by the descending branch (water to binder ratio higher than 0.13) have a superior performance and workability to those represented by the ascending branch (water to binder ratio less than 0.13). Hence, the practical optimal water to binder ratio used is chosen slightly biased towards the higher values of water to binder ratio to ensure that the water to binder ratio of the actual mixture is slightly higher than the theoretical optimum [2,15]. Nguyen [15] made experimental investigations of development of properties of silica fume blended ordinary concrete and ultra high performance concrete. Specimens with three main w/b ratios of 0.18, 0.25 and 0.40 and different amounts of silica fume additions, from 10% to 30%, were cured at 20 °C. The specimens with water/binder ratios of 0.25 and 0.4 (paste specimens) were sealed curing in a plastic lid, and the UHPC mortar specimens with water/ binder ratio of 0.18 were cured in a fog room until the day of testing. The mixing proportions of UHPC specimens are shown in Table 1. For UHPC mortar specimens, silica sand with a particle size ranging from 100 to 300 lm, was employed. Based on experimental investigations and theoretical calculations of packing density of sand-binder binary systems, Nguyen [15] found that optimized packing density can be achieved at a sand/(sand + binder) ratio of 0.5. Hence, UHPC mixtures were designed with a sand/(sand + binder) ratio of 0.50. For the specimens with water to binder ratios

The amount of calcium hydroxide:

CH = CHCE (t ) − 1.85 * α silica * msilica 0 * γ s The amount of capillary water: Wcap = W0 − 0.4 * C0 * α − 0.5* α silica * ms ilica 0 * γ s

The amount of chemically bound water:

Wchem = 0.25* C0 * α The amount of gel-space ratio and compressive strength:

f c = Ax fc n

No

t>tend

END Fig. 1. The outline of modeling.

Fig. 2. Effects of fine/coarse size ratio on packing density of the binary mix: d1 and d2 are diameters of larger particles and finer particles respectively (d1 > d2).

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X.-Y. Wang / Construction and Building Materials 64 (2014) 1–10 Table 1 Mixing proportions of UHPC. Amount of cement (kg/m3)

Water/binder ratio (by weight)

Sand to binder ratio (by weight)

Silica fume (% by weight)

Superplasticizer (solid% by weight of binder)

1140 1010 885 765

0.18 0.18 0.18 0.18

1 1 1 1

0 10 20 30

0.9 0.6 0.7 1.25

0.25 and 0.18, polycarboxylic type superplasticizer was used to achieve a flow value from 210 mm to 230 mm. The workability of all mixtures was determined by means of the flow table test. Experimental procedures of flow table tests are shown as follows: first, the flow table is wetted; second, the cone is placed in the center of the flow table and filled with fresh concrete in two equal layers. Each layer is tamped 10 times with tamping rod. Wait 30 s before lifting the cone; third, the cone is lifted, allowing the concrete to flow; fourth, the flow table is then lifted up 40 mm and then dropped 15 times, causing the concrete to flow; fifth, the diameter of the concrete is measured. The studies on scanning electron microscope (SEM), thermal gravimetric analysis (TGA) and compressive strengths were performed on specimens. In this study, for SEM tests, backscattered electron (BSE) mode was used to determine the amount of anhydrous cement by image analysis. Furthermore, degree of hydration of cement can be calculated from the amount of anhydrous cement. The amount of calcium hydroxide (CH) of samples was determined by TGA. In this study, the CH content was determined from the weight loss curve during thermal analysis by a graphical technique originally proposed by Marsh and Day [16]. The degree of hydration of cement, calcium hydroxide amount and compressive strength of specimens were determined at different ages, i.e. 6 h, 1, 3, 7, 28 and 91 days. 4.1. Evaluation of hydration degree of cement in Portland cement paste 4.1.1. Effect of moist curing on cement hydration When UHPC specimens are cured in a fog room with relative humidity (RH) > 95%, extra free water is maintained on the surfaces of specimens [15]. The extra free water can facilitate the hydration of cement through imbibition of capillary water from surfaces of specimens (imbibitions means the absorption of liquid (water) of a hardening concrete from surfaces of concrete covered with extra free water). The amount of imbibition of capillary water related with the chemical shrinkage of hardening paste. As hydration occurs, depending on the initial water to cement (w/c) ratio, a point maybe reached where the capillary porosity is no longer connected and the transport of imbibed water must then occur through the much smaller gel pores in the calcium silicate hydrate (CSH) gel. Bentz et al. [4] proposed that percolation threshold of capillary porosity was 0.17. In this study, it is assumed when the capillary porosity in hydrating paste is higher than 0.17, the amount of imbibed capillary water equals the amount of chemically shrinkage of hydrating blends, and when the capillary porosity in paste is less than 0.17, the amount of imbibed capillary water equals zero due to the slower transport rate of imbibed water through gel pores [4]. Considering the influence of imbibitions from surrounding environments, calculations of capillary water are shown as follows:

u ¼ ðW 0  1:06  C 0  a=qc  1:52  asilica  msilica0  cs =qsi Þ=ðW 0 =qw þ C 0 =qc þ msilica0 =qsi Þ

ð12:1Þ

W cap ¼ W 0  0:4  C 0  a  0:5  asilica  msilica0  cs þ 0:0625  C 0  a þ 0:22  asilica  msilica0  cs ðu P 0:17Þ

ð12:2Þ

W cap ¼ W 0  0:4  C 0  a  0:5  asilica  msilica0  cs þ 0:0625  C 0  aCEc þ 0:22  aSFc  msilica0  cs ðu < 0:17Þ

ð12:3Þ

Eq. (12.1) calculates the evolution of capillary porosity u in hydrating silica fume–cement paste. For Portland cement pastes, it is approximately assumed that 1 ml of hydrated cement occupies 2.06 ml, and for SF pozzolanic reaction, 1 ml of reacted SF is considered to occupy 2.52 ml of space [17]. The term 1.06  C0  a/qc in the numerator considers the reduction of capillary porosity due to cement hydration, and the term 1:52  asilica  msilica0  cs =qsi in the numerator considers the reduction of capillary porosity due to silica fume reaction. Eq. (12.2) calculates the amount of capillary water when capillary porosity of hydrating paste is higher than 0.17. Due to the connectivity of capillary pores, the amount of imbibed capillary water equals the amount of chemically shrinkage. The term 0.0625  C0  a considers the imbibition of capillary water due to chemical shrinkage of cement hydration, and the term 0:22  asilica  msilica0  cs considers the imbibition of capillary water due to chemical shrinkage of silica fume reaction [5,13]. Eq. (12.3) shows that when capillary porosity is less than percolation threshold, due to the slower transport rate of imbibed water through gel pores, the imbibition of capillary water from surrounding environments is approximately assumed to be zero. aCEc and aSFc represent critical reaction degrees of cement and silica fume corresponding to percolation threshold of capillary porosity, respectively. On the other hand, it should be noticed that in this study, the transport of water vapor is not specifically considered. It is simply assumed that for a UHPC specimen with moist curing, from the surface part to the inner part, the moisture contents are uniform and do not vary with depths of specimen. 4.1.2. Effect of superplasticizer on cement hydration When a superplasticiser is used in mixing concrete, the initial dormant period generally is prolonged. To consider the influence of the superplasticiser on the initial dormant period, the coefficient B20, which relates to the initial dormant period of cement hydration, is multiplied by a empirical factor of 0.3, which means that the hydration rate of Portland cement in the initial dormant period is reduced and the initial dormant period is prolonged correspondingly [17]. On the other side, it should be noticed that when the dosage of polycarboxylate type superplasticizer is high, it not only extends the dormant period, but also reduces the second peak of the heat generation rate [8]. Currently the proposed model is specifically applicable to normal ranges of organic admixtures dosage. For high range of organic admixtures, more investigations are necessary to clarify the relations between organic admixtures contents and the variations of reaction rate coefficient kr (kr relates with the second peak of hydration heat). In addition, the polycarboxylate type superplasticizer has a comb-like molecule structures. Inhibition of reactive sites through dispersion is the dominating work

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X.-Y. Wang / Construction and Building Materials 64 (2014) 1–10

mechanism of polycarboxylate type superplasticizer [2]. By changing the chemical structure of polycarboxylate type superplasticizer, it is possible to control the rate of slump loss of fresh concrete [8]. The value of coefficient B (the coefficient of formation of initial impermeable layer) may relate with chemical structure of polycarboxylate type superplasticizer. Based on the degree of hydration of cement in Portland cement paste, reaction coefficients B, C, kr, and De0 of the Portland cement hydration model can be obtained and shown in Table 2. The values of empirical parameter r in Eq. (4) are calibrated as 1.0, 1.4 and 5.0 for different water to binder ratios 0.4, 0.25 and 0.18, respectively. The increasing of parameter r means increasing of constrictivity and tortuosity of a pore network and less pore connectivity, and less accessibility of water into an inner anhydrous part through an outer hard shell of the cement particles [18]. On the other hand, as shown in Fig. 3, due to the addition of superplasticizer for water to cement ratios 0.25 and 0.18, the initial dormant periods is prolonged compared to that of water to cement ratio 0.4. Given a certain age, the cement paste with a lower water to cement ratio shows a lower degree of hydration. This is because of the limitation in the capillary water and deposition spaces necessary for hydration in case of lower water to cement ratios. Fig. 4 shows the relationship between degree of hydration of cement and calcium hydroxide contents. When looking at the very early ages, Fig. 4 reveals a threshold in the appearance of crystallized Ca(OH)2, showing a significant precipitation of this product in the cement paste. This threshold appears at the same degree of hydration (a  19%) for all the cement pastes investigated here. Moreover, from this threshold the Ca(OH)2 content is linearly linked to the degree of hydration. The threshold is because that the precipitation of Ca(OH)2 is not immediate and occurs only a few hours after cement and water contact (when the calcium ion concentration of the interstitial phase reaches a maximum [19]). Considering the linear relationship between degree of hydration and CH contents, the CH contents in Portland cement paste can be calculated as follows:

CHCEðtÞ ¼



0 ð0:334  a  0:063Þ  C 0

a < 0:19 a P 0:19

Fig. 3. Evaluation of degree of hydration of cement in Portland cement paste.

ð13Þ

As shown in Fig. 5, the calculation results about CH contents generally agree with experimental results. CH contents increase rapidly in early-age as a result of rapid hydration of Portland cement, and show a plateau in late age due to the decreasing of rate of hydration. On the other hand, it should be noticed that Eq. (13) is only a parameter fitting equation and is specifically applicable to the Portland cement used in this study. For different type of Portland cement, the relation between calcium hydroxide and degree of hydration may be different from Eq. (13). 4.2. Evaluation of reaction degree of silica fume in silica fume–cement paste In the hydration of ordinary Portland cement, the amount of calcium hydroxide increases until it reaches a steady state. In the hydration of cement–silica fume blends, the evolution of the amount of CH depends on two factors: such as the Portland cement hydration that produces CH and the pozzolanic reaction that consumes CH. In the initial period the production of CH is the dominant process and then the consumption of CH is the dominant process. In the experiment range [15], the CH amount initially

Fig. 4. Relationship between degree of hydration and calcium hydroxide (CH) contents in Portland cement paste.

increases, reaches a maximum value and then decreases. Based on the amount of calcium hydroxide, the reaction coefficients krsi and Desi0 of silica fume reaction model can be obtained and shown in the Table 2. The evolution of the CH amount is shown as a function of the hydration time in Fig. 6. As shown in Fig. 6, the simulation results overall agree well with experimental results. The calculated reaction degree of silica fume is shown in Fig. 7. As shown in Fig. 7(1), given a certain silica fume replacement ratio, with an increase of water to binder ratio, there is more space available for hydration products to form, hence the reactivity of silica fume increases correspondingly. Fig. 7(2) shows that given a certain water to binder ratio, with an increasing of the replacement level of silica fume, the alkaline activating effect of the cement would be weaker, so that the reactivity of silica fume decreases. Lam et al. [20] also found the similar results for fly ash blended cement paste. The reaction degree of fly ash decreases with the increasing of fly ash replacement ratios and decreasing of water to binder ratios.

Table 2 Reaction coefficients of proposed hydration model. B (cm/h)

C (cm/h)

kr (cm/h)

De0 (cm2/h)

krsi (cm/h)

Desi0 (cm2/h)

4.310  107

0.035

8.584  105

1.094  109

3.204  108

3.160  1013

X.-Y. Wang / Construction and Building Materials 64 (2014) 1–10

Fig. 5. Evaluation of calcium hydroxide contents in Portland cement paste.

(6-1) calcium hydroxide contents: water to binder ratio 0.4 with 10% and 20% silice fumes

7

Fig. 8 shows evaluation of hydration degree of cement in silica fume–cement paste with different water to binder ratios and silica fume replacement ratios. Given a certain water to cement ratio, an increase in the amount of mineral admixtures involves a decrease in the amount of cement and consequently an increase in the water/cement ratio. This dilution effect results in a higher degree of hydration. On the other hand, it should be noticed that in Fig. 8(1), for water to binder 0.25 with 20% silica fume replacements, the calculation results are slightly less than experimental results in early age. This comes from the ignorance of nucleation effects of silica fume on cement hydration in the proposed model (silica fume can form the nucleation sites for calcium hydroxide to accelerate the hydration of cement). Fig. 9 shows the evolution of phase volume fractions of hardening cement–silica fume paste as a function of curing time (water to binder ratio 0.18 and silica fume replacement ratio 0.20). As shown in Fig. 9, with the proceeding of hydration, the volumes of cement and silica fume decrease and the volumes of cement hydration products and silica fume reaction products increase. With the increasing of curing time, due to losses in the capillary water,

(6-2) calcium hydroxide contents: water to binder ratio 0.25 with 10% and 20% silice fumes

(6-3) calcium hydroxide contents: water to binder ratio 0.18 with 20% silice fume Fig. 6. Evaluation of calcium hydroxide contents in silica fume–cement paste.

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(7-1) reaction degree of silica fume: water to binder ratios 0.4, 0.25 and 0.18 with 20% silica fume

(7-2) reaction degree of silica fume: water to binder ratio 0.18 with 10%, 20% and 30% silica fumes

Fig. 7. Evaluation of reaction degree of silica fume in silica fume–cement paste.

(8-1) hydration degree of cement : water to binder ratio 0.25 with 10% and 20% silica fumes

(8-2) hydration degree of cement: water to binder ratio 0.18 with 20% silica fume

Fig. 8. Evaluation of hydration degree of cement in silica fume–cement paste.

decreasing of available deposition spaces for hydration products, and changing of hydration rate determining process to a diffusion-controlled stage, the rate of hydration becomes slower. In this study, the input coefficients of proposed model, such as B, C, kr and De0 of Portland cement hydration model, and krsi and Desi0 of silica fume reaction model, are calibrated from experimental results of degree of hydration of cement in Portland cement paste and calcium hydroxide contents in silica fume blended paste. To extend this model to other kinds of material systems such as different types of Portland cement, more investigations are necessary to find the dependence of hydration coefficients B, C, kr and De0 on the mineral compositions of cement C3S, C2S, C3A, and C4AF. The relation between silica fume reaction coefficients krsi and Desi0 and size of silica fume particle rsi0 also needs further study.

4.3. Evaluation of compressive strength of UHPC It is well-known that the compressive strength of concrete depends on the gel/space ratio determined from degree of cement hydration and w/c ratio. A gel/space ratio is defined as the ratio of the volumes of the hydrated cement to the sum of the volumes of the hydrated cement and of the capillary pores [11,12]. For Portland cement pastes, it is approximately assumed that 1 ml of hydrated cement occupies 2.06 ml, and for silica fume pozzolanic reaction, 1 ml of reacted silica fume is considered to occupy 2.52 ml of space [17]. So the gel/space ratio of silica fume–cement paste is given by

xfc ¼

2:06ð1=qÞaC 0 þ 2:52ð1=qsi Þcs asilica msilica0 ð1=qÞaC 0 þ ð1=qsi Þcs asilica msilica0 þ W 0

ð14Þ

X.-Y. Wang / Construction and Building Materials 64 (2014) 1–10

9

where xfc is the gel/space ratio of blended cement pastes. It is noted that the volume change of silica fume is larger than the anhydrous cement (2.52 vs. 2.06). This may be partially due to the lower density of the pozzolanic hydration products, and may indicate that pozzolanic reaction products are more effective in filling pores [17]. On the other hand, in very low or higher w/c cement pastes, the ratios of low density C–S–H (outer hydration products) and high density C–S–H (inner hydration products) are different [8]. For an accurate modeling of hydration of Portland cement, the volumetric stoichiometries of hydration of Portland cement should be expressed as a function of water to cement ratio. So Eq. (14) is only a simplified equation to determine gel/space ratio. Furthermore, the development of compressive strength of blended concrete can be evaluated through Powers’ strength theory, as

fc ¼ Axnfc C0 msilica0 þb C 0 þ msilica0 C 0 þ msilica0 C0 msilica0 þd n¼c C 0 þ msilica0 C 0 þ msilica0 A¼a Fig. 9. Evolution of phase volume fractions of cement–silica fume paste (water to binder ratio 0.18 with 20% silica fume).

(10-1) control concrete

(10-3) water to binder ratio 0.18 with 20% silica fume

(10-2) water to binder ratio 0.18 with 10% silica fume

(10-4) water to binder ratio 0.18 with 30% silica fume

Fig. 10. Evaluation of compressive strength of UHPC.

ð15:1Þ ð15:2Þ ð15:3Þ

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where fc is the compressive strength of blended concrete. A is the intrinsic strength of the material and can be expressed as a function of the weight fractions of cement and mineral admixture in the mixing proportion. The coefficients a and b in Eq. (15.2) represent the contributions of cement and mineral admixture to the intrinsic strength of materials, respectively, and the units of a and b are MPa. n is the exponent and also can be expressed as a function of the weight fractions of cement and mineral admixture in the mixing proportion. The coefficients c and d in Eq. (15.3) represent the contributions of cement and mineral admixture, respectively. On the basis of the compressive strength of UHPC with different silica fume replacement ratios [15], the values of the coefficients of a, b, c, d are given as a = 267.49, b = 166.05, c = 2.04, and d = 1.48. The comparisons between the experimental results and the prediction results are shown in Fig. 10. It is shown that the prediction results generally agree with the experimental results. The compressive strength of SF modified samples is highest with 10% SF content. The addition of higher SF contents, especially beyond 20%, gives a reduction to the compressive strength of UHPC. This is due to the reduction of reaction degree with increasing of silica fume replacement ratios, and another reason may be the agglomeration because of the very large specific surface of SF. Agglomeration reduces the positive effects of SF in terms of filler and pozzolanic effects in UHPC and results in a reduction of the compressive strength of SF modified samples. As far as the compressive strength is concerned, Habel et al. [10] evaluated the development of mechanical properties of UHPC using degree of isothermal heat evolution. When silica fume replacement ratio varies, hydration reaction coefficients change correspondingly [10]. In this paper, the development of compressive strength of UHPC is predicted from the physical aspect, i.e. the development of compressive strength of UHPC with different mixing proportions is expressed as a function of gel–space ratio, as shown in the Eq. (15). The coefficients do not change with silica fume replacement ratios. In addition, it should be noticed that the dependence of volume stoichiometries of the hydration reactions on curing temperature, the dependence of intrinsic strength of material on curing temperature and mineral components of cement, and the influence of air contents and packing density on compressive strength of UHPC are not considered in the current proposed model. As an experimental fact, the compressive strength of ultra-high strength concrete depends on the kinds of aggregates. This model may be applicable only for the aggregate examined. More improvements are necessary to modify the proposed model. This study focuses on modeling of hydration behavior of UHPC. The effect of addition of fibers on properties of UHPC is not considered in this study. However, in construction practice, to increase the tensile toughness, compared with UHPC, UHP-FRC is more widely used. Graybeal and Tanesi [1] made systematic investigations on the durability of UHP-FRC. They reported that UHP-FRC can exhibit compressive strength of 193 MPa, tensile strength of 9.0 MPa, significant tensile toughness, elastic modulus of 52.4 GPa, and minimal long-term creep or drying shrinkage. It can also resist freeze–thaw and scaling conditions with virtually no damage and is nearly impermeable to chloride ions. On the other hand, Larrard [2] and Nguyen [15] found that UHPC exhibits large shrinkage values, but, unlike normal concrete, autogenous shrinkage makes up a larger portion of the total shrinkage in UHPC than drying shrinkage. Due to the fact that the very dense microstructure of UHPC enables only very slow water ingress into the interior of concrete members, mitigation of autogenous shrinkage using external curing is not effective. Because of this, internal water curing is considered to be an effective solution to counteract selfdesiccation and autogenous shrinkage for the low permeability of the low w/b ratio cementitious system, thereby reducing the likelihood of early-age cracking [2,15].

5. Conclusions This paper presents a general procedure to evaluate the development of properties of hardening UHPC. First, by considering the production of calcium hydroxide in cement hydration and its consumption in the pozzolanic reaction, a numerical model is proposed to simulate the hydration of concrete containing silica fume (SF). The reaction coefficients of SF are obtained from the experimental results of calcium hydroxide contents of SF blended concrete. The degree of hydration of cement and degree of reaction of SF are obtained as accompanied results from the proposed hydration model. Second, on the basis of the volume stoichiometries, mixing proportions, and the degree of reactions of cement and SF, the gel–space ratio of hydrating UHPC is calculated. Finally, the development of compressive strength of UHPC is evaluated through Powers’ strength theory considering the contributions of cement hydration and SF reaction. Predicted compressive strength curves were compared with experimental data and a good correlation was found. Acknowledgement This paper is financially supported by National Research Foundation of Korea (Grant No.: NRF-2013R1A1A2060231; Project Name: An integrated program for predicting chloride penetration into reinforced concrete structures by using a Cement Hydration Model). References [1] Graybeal B, Tanesi J. Durability of an ultrahigh-performance concrete. J Mater Civil Eng 2007;19:850–4. [2] de Larrard F. Concrete mixing proportioning, a scientific approach. London and New York: E&FN Spon.; 1999. [3] Morin V, Tenoudji FC, Feylessoufi A, Richard P. Superplasticizer effects on setting and structuration mechanisms of ultrahigh-performance concrete. Cem Concr Res 2001;31:63–71. [4] Bentz DP, Stutzman PE, Garboczi EJ. Experimental and simulation studies of the interfacial zone in concrete. Cem Concr Res 1992;22:891–902. [5] Chung DDL. Review: improving cement-based materials by using silica fume. J Mater Sci 2002;37:673–82. [6] Loukili A, Khelidj A, Richard P. Hydration kinetics, change of relative humidity, and autogenous shrinkage of ultra-high-strength concrete. Cem Concr Res 1999;29:577–84. [7] Papadakis VG. Experimental investigation and theoretical modeling of silica fume activity in concrete. Cem Concr Res 1999;29:79–86. [8] Ishida T, Luan Y, Sagawa T, Nawa T. Modeling of early age behavior of blast furnace slag concrete based on micro-physical properties. Cem Concr Res 2011;41:1357–67. [9] Zelic J, Rusic D, Krstulovic R. A mathematical model for prediction of compressive strength in cement–silica fume blends. Cem Concr Res 2004;34:2319–28. [10] Habel K, Viviani M, Denarié E, Brühwiler E. Development of the mechanical properties of an Ultra-High Performance Fiber Reinforced Concrete (UHPFRC). Cem Concr Res 2006;36:1362–70. [11] Tomosawa F. Development of a kinetic model for hydration of cement. In: Proceedings of the 10th international congress on the chemistry of cement. Gothenburg: Harald Justnes Publisher; 1997. p. 51–8. [12] Park KB, Jee NY, Yoon IS, Lee HS. Prediction of temperature distribution in high-strength concrete using hydration model. ACI Mater J 2008;105:180–6. [13] Jensen OM, Hansen PF. Water-entrained cement-based materials: I. Principles and theoretical background. Cem Concr Res 2001;31:647–54. [14] Saeki T, Monteiro PJM. A model to predict the amount of calcium hydroxide in concrete containing mineral admixture. Cem Concr Res 2005;35:1914–21. [15] Nguyen VT. Rice husk ash as a mineral admixture for ultra high performance concrete. Netherlands: Delft University of Technology, PhD thesis; 2011. [16] Marsh BK, Day RL. Pozzolanic and cementitious reactions of fly ash in blended cement pastes. Cem Concr Res 1988;18:301–10. [17] Wang XY, Lee HS. Evaluation of the mechanical properties of concrete considering the effects of temperature and aging. Constr Build Mater 2012;29:581–90. [18] Oh BH, Cha SW. Nolinear analysis of temperature and moisture distributions in early-age concrete structures based on degree of hydration. ACI Mater J 2003;100:361–70. [19] Mounanga P, Khelidj A, Loukili A, Bouny VB. Predicting Ca(OH)2 content and chemical shrinkage of hydrating cement pastes using analytical approach. Cem Concr Res 2004;34:255–65. [20] Lam L, Wong YL, Poon CS. Degree of hydration and gel/space ratio of highvolume fly ash/cement systems. Cem Concr Res 2000;30:747–56.