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Modeling of chloride diffusion in concrete containing low-calcium fly ash
Materials Chemistry and Physics 138 (2013) 917e928
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Modeling of chloride diffusion in concrete containing low-calcium fly ash Xiao-Yong Wang a, Han-Seung Lee b, * a b
Department of Architectural Engineering, College of Engineering, Kangwon National University, Chuncheon 200-701, Republic of Korea School of Architecture & Architectural Engineering, Hanyang University, Ansan 425-791, Republic of Korea
h i g h l i g h t s < A model to predict chloride ingress in fly ash blended concrete is proposed. < The model consists of a hydration model and a chloride diffusion model. < The evolution of properties of concrete is obtained from the hydration model. < The results from the hydration model are used for predicting chloride ingress. < The proposed model can be used for durability design of marine structures.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 August 2012 Received in revised form 20 November 2012 Accepted 28 December 2012
Low-calcium fly ash (FL) is a general product from the combustion of anthracite and bituminous coals and has been widely used as a mineral admixture to produce high strength and high performance concrete. And in marine and coastal environments, penetration of chloride ions is one of the main mechanisms causing concrete reinforcement corrosion. In this paper, we proposed a numerical procedure to predict the chloride diffusion in low-calcium fly ash blended concrete. This numerical procedure includes two parts: a hydration model and a chloride diffusion model. The hydration model starts with mix proportions of low-calcium fly ash blended concrete and considers Portland cement hydration and low-calcium fly ash reaction respectively. By using the hydration model, the evolution of properties of low-calcium fly ash blended concrete is predicted as a function of curing age and these properties are adopted as input parameters for the chloride penetration model. Furthermore, based on the modeling of physicochemical processes of diffusion of chloride ion into concrete, the chloride distribution in lowcalcium fly ash blended concrete is evaluated. The prediction results agree well with experiment results. Ó 2013 Elsevier B.V. All rights reserved.
Keywords: C: Computer modelling and simulation D: Corrosion D: Diffusion D: Microstructure
1. Introduction Fly ash is the combustion residue in coal-burning electric power plants. Viewed from significant differences in its mineralogical composition and properties, the fly ash can be divided into two categories based on their calcium content. The ash in the first category, low-calcium fly ash (FL), containing less than 10% of analytical calcium oxide (CaO), is a general product from the combustion of anthracite and bituminous coals. The ash in the second category, high-calcium fly ash (FH), typically containing 15e40% of analytical CaO, is a general product from the combustion
* Corresponding author. Tel./fax: þ82 31 400 5181. E-mail addresses: [email protected] hanyang.ac.kr (H.-S. Lee).
(X.-Y.
Wang),
ercleehs@
0254-0584/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matchemphys.2012.12.085
of lignite and subbituminous coals. The FL is categorized as a normal type of pozzolan that consists of silicate glass and is modified by aluminum and iron. Also, it has long been used as a mineral admixture to produce high strength and high performance concrete [1]. It is widely known that the ingress of chloride ions constitutes a major source of durability problems affecting reinforced concrete structures which are exposed to marine environments. Once a sufficient quantity of chloride ions has accumulated around the embedded steel, pitting corrosion of the metal is liable to occur unless the environmental conditions are strongly anaerobic. In the design of concrete structures, the influence of chloride ingress on service life must be considered [1]. The literature is rich in papers dealing with chloride attack of concrete. Papadakis [2,3] made experimental investigations and numerical modeling of chloride ingress into concrete incorporating
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fly ash. The physicochemical processes of diffusion of chloride ion in the aqueous phase of pores, their adsorption and binding in the solid phase of concrete were described by a nonlinear partial differential equation. Based on computed micro-pore structure [4], Yoon [5] proposed a simple approach to calculate the diffusivity of concrete considering carbonation. The parameters affecting the chloride diffusivity, such as the diffusivity in pore solution, tortuosity, micro-structural properties of hardened cement paste, and volumetric portion of aggregate, are taken into consideration in the calculation of chloride diffusivity. Han [6] proposed a modified diffusion coefficient that considers the effect of chloride binding and evaporable water on the diffusion coefficient. The evaporable water content was predicted from a hydration model of Portland cement. Based on mathematical derivation of microstructure of concrete, Song [7] built a procedure for predicting the diffusivity of high strength SF concrete. In this model the influence of water to binder ratio, SF replacement ratio, and degree of hydration on diffusivity was considered. Ishida [8] formulated the chloride diffusivity based on computed multi-scale micro-pore structure, which considers tortuosity and constrictivity of porous network as reduction factors in terms of complex micro-pore structure and electric interaction of chloride ions and pore wall. From references [2e8], we can see that based on a hydration model, the evolution of concrete properties, such as the content of evaporable water and porosity, can be described as a function of curing age. The diffusivity of chloride ions in concrete can be obtained from the microstructure of concrete [2e8]. Due to the pozzolanic reaction between calcium hydroxide and low-calcium fly ash, compared with ordinary Portland cement, hydration of concrete containing low-calcium fly ash is much more complex. It is difficult to build a chemical-based kinetic equation to quantitatively describe the evolution of properties of low-calcium fly ash blended concrete and only the final concentrations of reaction products, which apply after the Portland cement hydration and pozzolanic reaction are complete and a steady is established [3,9]. In this paper, a numerical procedure which can simulate chloride diffusion in low-calcium fly ash blended concrete is built. The flow chart of this procedure is shown in Fig. 1. As shown in Fig. 1, this numerical procedure includes a hydration model and a chloride diffusion model. In the hydration model, by considering the producing of calcium hydroxide in cement hydration and the consumption of it in pozzolanic reaction, a numerical model is
proposed to simulate the hydration of concrete containing lowcalcium fly ash. The contents of evaporable water, calcium hydroxide, and porosity were obtained as companied results of the hydration model and were used as input variables for the chloride diffusion model. Furthermore, in the chloride diffusion model, the physicochemical processes of diffusion of chloride ion in the aqueous phase of pores, the adsorption and binding in the solid phase of concrete, and the desorption are described by a nonlinear partial differential equation. The prediction results on chloride penetration profiles were verified with the experimental results. 2. Hydration model of ordinary portland cement 2.1. The assumptions of a hydration model In this hydration model, the influences of the water to cement ratio, cement particle size distribution, cement mineral components and curing temperature on the hydration reaction of Portland cement are considered. The assumptions of this model can be summarized as follows: 1. Cement particles are randomly cast in a representative unit cell space, as shown in Fig. 2. As proposed by Navi [10], the length of the edge of the representative unit cell is 100 micron. The amount of chemically bound water for each cement component, C3S, C2S, C3A, and C4AF, proposed by Park [11] is used for simulation in this paper. 2. The degree of hydration of cement components is the ratio of the volume of reacted cement components to the volume of initial cement components. The degree of the hydration of cement paste can be regarded as a weighted sum of cement particles and mineral components as shown in Fig. 3. The hydration at various temperatures is modeled by Arrhenius law [11]. 3. The liquid phase, which is assumed to be water, diffuses through a hydrate layer, reaches the surface of the cement particle and chemically reacts with cement. The hydrate formed by hydration adheres to the cement particles spherically. 4. Particle size distribution of cement can be approximated using the RosineRammler function [11].
Mixing proportion and curing condition of low-calcium fly ash blended concrete Hydration model considers both cement hydration and low-calcium fly ash reaction Evolution of porosity, evaporable water and other physical and chemical properties with ages Nonlinear partial differential equation for physicochemical process Chloride ion concentration in low-calcium fly ash blended concrete Fig. 1. The flow chart of predicting chloride ion concentration in low-calcium fly ash blended concrete.
Fig. 2. The cement particles distribute randomly in cell space.
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hydrate. This phenomenon can be expressed as a function of degree of hydration and is described by Eq. (3):
Dei ¼ Dei0 ln
1
! (3)
aji
When the cement is mixed with water, the hydration of each mineral component processes according to the model described in the previous section. The degree of the hydration of cement can be calculated as following Eq. (4):
P
P
j¼n i¼4 j i ¼ 1 a gi gj a ¼ Pj ¼j ¼1n Pi ¼ 4 i j¼1
i¼1
gi gj
(4)
where gi is the mass fraction in mineral components; gj is the mass fraction of individual particle in cement and n is the total number of cement particles in a cell space. As shown in Eq. (4), the different hydration reactions do not consume the same amount of water, so the computation of the total consumed water should be a weighted average of the consumed water for each elementary reaction.
Fig. 3. The schematic of multi-component hydration model.
2.2. Hydration mechanism 2.3. Water withdrawl mechanism In Park’s model [11], some improvements were achieved by incorporating size distribution of cement particles and the component of cement minerals, including C3S, C2S, C3A and C4AF. The basic hydration equation for each mineral composition in cement particles can be described as following Eq. (1), which is originally built by Tomosawa [12] to describe hydration of a single cement particle. This model is expressed as a single equation composed of four rate determining coefficients which consider the rate of formation and destruction of initial impermeable layer, the activated chemical reaction process and following diffusion-controlled process:
dai 3rw ¼ j dt vi þwag r0 ri j
!
1
1 1 2 1 3 3 1 aji þ 1 aji þ kd Dei kri Dei j r0
j r0
(1)
where ai denotes the hydration degree of the mineral component in given cement particle. i is the mineral component. j is the number of cement particles. vi is the stoichiometric ratio by the mass of water to mineral component. wag is the physically bound water that is approximately equal to 13% of the mass of reacted cement, ri is the density of the anhydrate cement mineral compoj nent, kd is the reaction coefficient in a dormant period, r0 is the radius of anhydrate cement particles, Dei is the effective diffusion coefficient of water in the hydration product for each mineral component and kri is the coefficient of reaction rate for each mineral component. rw is the density of water. The influence of temperature on the hydration rate is considered by Arrhenius law [12]. The activation energies of each compound are obtained from the cement hydration experiments performed under different curing temperatures. Whereas, kd is assumed to be a function of degree of hydration during the initial reaction period and it is expressed as Eq. (2): j
4 B kd ¼ 1:5 þ C r0j rtj
aji
(2)
The B and C in Eq. (2) denote reaction coefficients. The effective diffusion coefficient of water is affected by the tortuosity of the gel pore as well as the radius of the gel pore in
During the hydration period, at a certain time point after the initial setting time, due to the increasing interconnection among cement particles, the contact area between cement particle and surrounding water will be decreased. As a result, the slower hydration rate will be achieved. On the other hand, the water presenting in the paste can be classified into evaporable and non-evaporable fractions [11,12]. The former is the capillary water and the gel water that resides partially within the hydration product. The nonevaporable water is defined as the bound water which has chemically reacted with cement. During the hydration process, only the capillary water contributes to further hydration. With the hydration process proceeding, the capillary water will be consumed and the relative hydration rate will be decreased. Under sealed-curing condition, when water to cement ratio is less than 0.38, due to the limiting of capillary water, the cement hydration is not complete. (The mass of chemically bound water approximately equals to 25% of the mass of reacted cement and the mass of gel water approximately equals to 13% of the mass of reacted cement [11].) By considering these two points, as proposed by Park [11] and Maruyama [13], the modification of Eq. (1) can be expressed as Eq. (5):
daji dt
!0 ¼
daji freesurface j w0 0:38*Ce0 *a * * dt w0 totalsurface
(5)
In Eq. (5), the item (freesurface/totalsurface)j is the ratio between the free surface area (the area which contacts with water) and the total surface area, which can be determined by the proposed method in reference [10]. w0 is the water mass and Ce0 is the cement mass in a mixing proportion. The item (w00.38*Ce0*a)/w0 considers the decrease of the available capillary water for cement hydration. 3. Hydration model for cement blended with low-calcium fly ash 3.1. The amount of calcium hydroxide (CH) during the hydration process As proposed by Papadakis [14,15], during the hydration period, the chemical reactions of the mineral components of Portland cement can be expressed as following Eqs. (6a)e(6d):
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2C3 S þ 6H/C3 S2 H3 þ 3CH
(6a)
3.2. The simulation of pozzolanic reaction in cement-low-calcium fly ash blends
2C2 S þ 4H/C3 S2 H3 þ CH
(6b)
C3 A þ CSH2 þ 10H/C4 ASH12
(6c)
C4 AF þ 2CH þ 10H/C6 AFH12
(6d)
The addition of low-calcium fly ash has both physical and chemical effect on the hydration of cement. The physical effect includes retard effect and heterogeneous nucleation. The chemical aspect is pozzolanic activity of fly ash. As reported by Cyr [16], the addition of fly ash can retard hydration of the cement in early age. This retardation could be due to aluminate ions or organic matter dissolved from the fly ash into the aqueous phase, delaying the nucleation and crystallization of Ca(OH)2 and CeSeH. However, this delay can be partly compensated by heterogeneous nucleation. The fly ash particles can serve as nuclei sites of the cement particles and leads a chemical activation of the hydration of cement. Due to the coexistence of both retardation effect and acceleration effect, as reported by Papadakis [15], when aggregate is partly replaced by fly ash (the mixing proportions of these specimens are listed in Table 2, as FLA1, FLA2 and FLA3), in early age, the compressive strength, calcium hydroxide amount and released heat of the fly ash-cement paste (FLA paste) is not significantly different from that of the control cement paste. Compared with physical effect, the pozzolanic activity has dominate effect on long-term properties of FL-concrete. This paper focuses on the simulation of the pozzolanic activity in the hydration of fly ash blended cement. The simulation of physical effect is considered as a further research. Besides physical and chemical effect, when cement is replaced by the same quantity of fly ash, the amount of cement will decrease and the water to cementitious materials ratio will increase [14,15]. This effect is considered by the cement hydration model, as Eq. (5). The proposed model comes from the similarity in mechanism between cement hydration and pozzolanic activity: Firstly, the cement reacts with water and the glass phase of the pozzolanic material reacts with calcium hydroxide. The cement hydration process includes initial dormant period, phase-boundary reaction period and diffusion period. In the late age of cement hydration, diffusion is the control process. Some researchers reported that the pozzolanic activity was a diffusion-controlled process [13,15]. Secondly, based on analysis of the scanning electron micrographs (SEM) of Portland cement paste, silica fume-cement paste and fly ash-cement paste, Papadakis [2,3,9,14,15] reported that the cement hydration product adheres on surface of the cement particles and the pozzolanic product adheres on surface of the pozzolanic particles. Thirdly, the cement particle with small size has a highly reactivity with water and shows almost no initial dormant period and the cement particle with big size shows initial dormant period. Similarly, silica fume is a highly pozzolanic cement replacement material and shows only a short initial dormant period, like small cement particle. Fly ash shows a long initial dormant period, because the fly ash activation mainly lies in the breaking down of its glass phases. The alumina phase and silica phase in fly ash will not dissolve until the pH is higher than 13.3 [15]. On the other hand, there also exist some differences between cement hydration and pozzolanic activity. Cement hydration will produce calcium hydroxide and pozzolanic activity will consume it. As proposed in references [2,3,9,14,15], the hydration rate of the pozzolanic materials depends on the amount of calcium hydroxide in hydrating blends and the degree of hydration of mineral admixture. So we can derivate an equation from cement hydration to pozzolanic reaction by considering both similarity in kinetic reaction processes and difference in reaction affecting factors between two reactions. Compared with the silica fume, the hydration rate of the lowcalcium fly ash is much lower due to the larger particle size. In the early duration period of 0e21 days no traces of reaction among FL particles can be detected. In the simulation, it is assumed that the pozzolanic reaction is divided into three processes: initial dormant
By the aforementioned hydration model and Eqs. (6a)e(6d), the mass of the hydration product in a unit volume of Portland cement, such as calcium hydroxide, can be obtained from Eq. (7) as follows:
CH ¼
1:5gc3s ac3s þ 0:5gc2s ac2s 2gc4af ac4af *74:1*Ce0
(7)
Fly ash is a complex material that consists of a wide range of glass and crystalline compounds. In reaction form, there is the aluminosilicate (AeS) glass with a high content of S. The hydration product of an aluminosilicate glass/hydrated lime mixture should be a calcium silicate hydrate (CeSeH) gel incorporating significant amounts of A. The S of AeS glass is proposed to react with the CH without additional water binding and to form a calcium silicate hydrate described by the simplified formula of C3S2H3 as shown by using almost pure vitreous silica. The silicon presented as quartz or in crystalline aluminosilicate phases is inert. Based on the experimental results of the reaction stoichiometry among FL, chemically bound water and calcium hydroxide, Papadakis [14,15] proposed the pozzolanic reaction in cement-low-calcium fly ash blends which is written as following Eqs. (8a)e(8c):
2S þ 3CH/C3 S2 H3
(8a)
A þ CSH2 þ 3CH þ 7H/C4 ASH12
(8b)
A þ 4CH þ 9H/C4 AH13
(8c)
Based on the hydration model and pozzolanic reaction proposed in Eqs. (8a)e(8c), during the hydration period, the mass of calcium hydroxide CH and chemical bound water wchem can be rewritten as following Eqs. (9a) and (9b):
CH ¼
1:5gc3s ac3s þ 0:5gc2s ac2s 2gc4af ac4af *74:1*Ce0 1:85*gS *fS;P þ 2:907*gA *fA;P *aglass *P
(9a) wchem ¼ 0:25*Ce0 *a þ mH2 O *gA *fA;P *aglass *P
(9b)
In the Eqs. (9a) and (9b), fS,P and fA,P are the mass fraction of S and A in fly ash; gS and gA are their active (glass) part; aglass is the reacted degree of active (glass) part of fly ash; P is the fly ash mass in a mixing proportion; mH2O is the amount of chemically bound water in a unit mass of the reacted active (glass) part of fly ash. As shown in Eq. (9a), the evolution of calcium hydroxide mass is dependent on two aspects: the production of calcium hydroxide from the hydration of Portland cement and the consumption of it from the pozzolanic activity. As shown in Eq. (9b) both the hydration of Portland cement and pozzolanic activity will contribute to chemically bound water. As shown in Eqs. (9a) and (9b), in the simulation it is assumed that the active (glass) S and A, hydrate show equal rates.
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period, phase-boundary reaction process and diffusion process. By considering these points, based on the method proposed by Saeki [17], the hydration equation of the active (glass) part in FL can be written as Eqs. (10a)e(10c):
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In Eq. (12), the item (0.25*Ce0*a þ 0.13*Ce0*a) considers the consumption of capillary water from the hydration of cement; and the item ðmH2 O *gA *fA;P *aglass *P þ 0:15*aflyash *PÞ considers the consumption of capillary water from the reaction of fly ash.
daglass m ðtÞ 3rw 1 ¼ CH 1 1 2 P dt vFL rFL0 rFL 1 rFL0 rFL0 3 3 1 aglass þ 1 aglass þ kdFL DeFL krFL DeFL
kdFL ¼
3 BFL 1:5 þ CFL * aglass
(10b)
aglass
The porosity of hydrating blends is reduced due to the Portland cement hydration and pozzolanic activity during hydration period. As proposed by Papadakis [15], the porosity can be determined as Eq. (13): 3
DeFL ¼ DeFL0 *ln
1
! (10c)
aglass
Where mCH(t) is the calcium hydroxide mass in a unit volume of hydrating cement-low-calcium fly ash blends and can be obtained from Eq. (9a); P is the low-calcium fly ash mass in mixing proportion; vFL is the stoichiometry ratio by mass of CH to low-calcium fly ash; rFL0 is the radius of low-calcium fly ash particle; rFL is the density of fly ash; kdFL is the reaction rate coefficients in dormant period (BFL and CFL are coefficients); DeFL0 is the initial diffusion coefficient and krFL is the reaction rate coefficient. The influence of temperature on hydration can be considered by Arrhenius law. The activation energy of pozzolanic reactions in cement-FL blends can be obtained by the hydration experiments of cement-FL blends performed under different curing temperatures. The low-calcium fly ash includes both active part and inert part. The reacted ratio of the active part of fly ash can be calculated according to Eq. (10). The inert part is assumed as chemically inert and does not react. The reacted ratio of fly ash (includes both active part and inert part), can be obtained based on Eq. (10) and the mass compositions of fly ash. The reacted ratio of the fly ash can be calculated as following Eq. (11):
aflyash ¼ gs *fS;P þ gA *fA;P *aglass ¼
0:82*0:535 þ 0:82*0:204 *aglass ¼ 0:606*aglass (11)
Similar with the hydration of cement, with the proceeding of pozzolanic reaction, the water will be physically adsorbed in the hydration products of fly ash. Maekawa [18] proposed that for the fly ash pozzolanic reaction, when 1 g fly ash reacts, 0.15 g gel water will be consumed. Hence the mass of capillary water wcap in hydrating cement-FL blends can be calculated as follows:
wcap ¼ w0 ð0:25*Ce0 *a þ 0:13*Ce0 *aÞ mH2 O *gA *fA;P *aglass *P þ 0:15*aflyash *P
(12)
(10a)
¼
w0
rw
D3 h D3 p
(13)
Where D3 h is the porosity reduction due to hydration of Portland cement. It can be obtained from the amount of the chemically bound water which is consumed in hydration of the Portland cement. D3 p is the porosity reduction due to the pozzolanic activity and it can be obtained from the amount of chemically bound water which is consumed in the pozzolanic reaction. 4. Verification of hydration model 4.1. The degree of hydration of mineral components of ordinary Portland cement The results of this part in the experiments for regarding the hydration degree of ordinary Portland cement were used [19]. The water to cement ratio was 0.5 and curing temperature was 293 K. The hydration degree of the mineral components was measured at 1, 3, 7, 28, 91, 190 and 365 days. Powder X-Ray diffraction/Rietveld analysis was used to measure the degree of hydration of cement mineral components. The amount of chemically bound water determined by Rietveld analysis was verified by ignition loss [19]. By regression experiment results, the reaction coefficients of the multicomponents hydration model were obtained and listed in Table 1. Fig. 4 represents the comparison between the experiment results and the prediction results. Because the reaction rate of C3S and C3A is much quicker than C2S and C4AF, the hydration of C3S and C3A reaches a steady-state much earlier than C2S and C4AF. Most of C3A and C3S have reacted in the first 1000 h. As shown in Fig. 4, the prediction results overall agree well with experimental results. 4.2. The hydration of cement blended with low-calcium fly ash In this part, the experimental results of the hydration of cementFL blends [15] are adopted to verify the proposed hydration model. The mixing proportions for the specimens are shown in Table 2. In the control specimen, the water to cement ratio (W/C) was 0.5 and the aggregate to cement ratio (A/C) was 3. When FL replaces the volume of aggregates, three contents of FL were selected, such as
Table 1 The coefficients of the proposed hydration model. B (cm h1)
C (cm (cm4 h1))
krc3s (cm h1)
krc2s (cm h1)
krc3a (cm h1)
krc4af (cm h1)
Dec3s0 (cm2 h1)
Dec3a0 (cm2 h1)
Dec2s0 (cm2 h1)
Dec4af0 (cm2 h1)
2 109
1.5 1015
2.422 105
1.815 107
1.985 106
3.759 107
6.328 1010
9.568 108
6.328 1010
9.568 108
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Fig. 4. The comparison between experiment results [19] and simulation results of the hydration degree of cement mineral components: C3S,C2S,C3A and C4AF.
10%, 20%, and 30%, and added to the cement mass for the specimens FLA1, FLA2, and FLA3, respectively. For the cement replaced by FL, the same contents were also selected, such as 10%, 20%, and 30%, for replacing the control cement mass for the specimens FLC1, FLC2, and FLC3, respectively. The specimens were cured under a sealed condition with 20 C. The CH content, chemically bound water content and porosity at 3, 7, 14, 28, 49, 112, 182, and 364 days after casting was tested. For each test, the specimen was stripped, placed in a preweighed glass mortar, and pulverized. The mortar with the material was placed in an oven at 105 C until the weight was constant. These weight indications were used to determine the chemically bound water content and porosity.
mass depends on two factors: such as the Portland cement hydration that produces CH and the pozzolanic reaction that consumes CH. Because the low-calcium fly ash represents a low reaction rate, the CH content of FLA specimens in the initial period follows the CH content of its control, but the CH of FLA specimens is consumed at a slow rate after 14 days [15]. Based on the mass of calcium hydroxide, the reaction coefficients of pozzolanic reaction in Eqs. (10a)e(10c) can be obtained (as B ¼ 1.169 1012 cm h1, C ¼ 0.0426 cm h1, krFL ¼ 8.829 108 cm h1, DeFL0 ¼ 2.705 1011 cm2 h1). The evolution of the mass of CH is shown as a function of hydration time in Fig. 5. As shown in Fig. 5, the simulation results overall agree well with the experimental results.
4.2.1. The amount of calcium hydroxide during the hydration period In the hydration of ordinary Portland cement, the mass of calcium hydroxide will increase until a steady-state is reached. In the hydration of cement-low-calcium fly ash blends, the evolution of CH
4.2.2. The amount of bound water and porosity during the hydration period In the case of the cement-low-calcium fly ash blends, in its initial three months of hydration, there are two factors that affect the
Table 2 Mixture proportions for the specimens. Specimen
Cement (kg m3)
Water (kg m3)
Fly ash (kg m3)
Aggregate (kg m3)
Water to cement ratio
Fly ash to cement ratio
Aggregate to cement ratio
Control FLA1 FLA2 FLA3 FLC1 FLC2 FLC3
514.6 514.6 514.6 514.6 463.1 411.7 360.2
257.4 257.4 257.4 257.4 257.4 257.4 257.4
0.0 51.5 102.9 154.4 51.5 102.9 154.4
1543.8 1482.7 1421.7 1360.6 1526.6 1509.4 1492.3
0.5 0.5 0.5 0.5 0.556 0.625 0.715
0.0 0.1 0.2 0.3 0.111 0.250 0.429
3.0 2.88 2.76 2.64 3.30 3.67 4.14
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Fig. 5. The comparison between experiment results [15] and simulation results of CH amount.
bound water content. First is the selective reaction of the CH with S instead of its reaction with C3A and C4AF phases of cement. Second is the high content of aluminate in fly ash counterbalances losses in water content. The overall result is that the control specimen as well as all FLA specimens has almost the same water content in its initial three months. After three months, the chemically bound water content values for FLA specimens exceeded those of the controls. It seems that during this late period the remaining amounts of the C3A and C4AF phases of cement have reacted, binding additional water. In the current model, the selective reaction of the CH with S is not considered and it is assumed that the active (glass) S and A, hydrate show equal rates. By using the proposed model, the evolution of bound water amount and porosity is calculated and shown as a function of hydration time in Figs. 6 and 7 respectively. As shown in Figs. 6 and 7, the calculation results overall agree well with the experimental results. The difference between the calculation results and experimental results may comes from the ignorance of selective reaction of CH with S and the different reaction rates of active (glass) S and A in low-calcium fly ash. 5. Modeling of chloride diffusion and reaction in low-calcium fly ash blended concrete 5.1. Model of chloride diffusion-adsorption in concrete In most field cases, chloride ion may penetrate into concrete through a combined mechanism of hydraulic advection, capillary
suction, diffusion and thermal migration. Diffusion is the dominating mechanism in the case of saturated concrete, such as concrete submerged in seawater. In many papers, chloride transport in concrete is modeled using Fick’s second law of diffusion, neglecting the chloride interaction with the solid phase [1]. However, several field studies in recent years have indicated that the use of this law is not applicable to long-term chloride transport in concrete, very often calculating a decreasing chloride transport coefficient in time. It is widely accepted that the transport behavior of chloride ions in concrete is a more complex and complicated process than can be described by Fick’s law of diffusion. This approach, therefore, can be characterized as semi-empirical, resulting in the calculation of an apparent effective diffusivity. The binding of chloride ion by cementitious materials is very complicated, and is influenced by many factors including chloride concentration, cement composition, hydroxyl concentration, cation of chloride salt, temperature, supplementary cementing materials, carbonation, sulfate ions and electrical field etc. There is a generally good correlation between C3A content (or C4AF when there is lack of C3A phase) and chloride binding capacity. There is also evidence for the binding of chlorides in CeSeH gel, possibly in interlayer space. The Naþ ions can be bound in CeSeH gel lattice, especially when the C/S ratio is low [3]. Several secondary chlorideecalcium compounds have also been reported. In addition to the chemical binding, the effects of ionic interaction, lagging motion of cations, and formation of an electrical double layer on the solid surface all play an important role in the transport of chloride ions in concrete.
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Fig. 6. The comparison between experiment results [15] and simulation results of bound water.
The relationship between bound and free chlorides is nonlinear and may be expressed by the Langmuir equation, the Freundlich equation, or the modified Brunauer, Emmet and Teller (BET) equation. Of these, the Langmuir equation is both fundamental and easier to use in practical applications [6]. Pereira and Hegedus [20] were the first to identify and model chloride diffusion and reaction in fully saturated concrete as a Langmuirian equilibrium process coupled with Fickian diffusion. Furthermore, Papadakis et al. [21] generalized this pioneering model effort of Pereira and Hegedus and extended it to more general conditions, offering an alternative simpler, yet equally accurate, numerical and analytical solution. Papadakis proposed that the physicochemical processes of diffusion of Cl in the aqueous phase of pores, their adsorption and binding in the solid phase of concrete, and their desorption can be described by a nonlinear partial differential equation for the concentration of Cl in the aqueous phase [Cl(aq)] (kg m3 pore solution). The equations for calculating the Cl in the aqueous phase [Cl(aq)] and Cl bound in the solid phase [Cl(s)] (kg m3 concrete) are shown as follows:
2 De;Cl 1 þ Keq Cl aq v Cl aq v2 Cl aq ¼ 2 vt vx2 Keq Cl s þ 3 1 þ Keq Cl aq sat
(14a)
i h Keq Cl s sat Cl aq ¼ Cl s 1 þ Keq Cl aq
(14b)
With initial condition: [Cl(aq)] ¼ [Cl(aq)]in at t ¼ 0 (initial concentration); and boundary condition: [Cl(aq)] ¼ [Cl(aq)]0 at x ¼ 0 (concrete surface) and v[Cl(aq)]/vx ¼ 0 at x ¼ M (axis of symmetry). In Eqs. (14a) and (14b), x is the distance from the concrete surface (m); t is the time(s); D e,Cl is the intrinsic effective diffusivity of chloride ion in concrete (m2 s1); Keq is the equilibrium constant for chloride binding (m3 of pore solution/kg); and [Cl(s)]sat is the saturation concentration of chloride ion in the solid phase (kg m3 concrete). As observed from Eq. (14b), the chloride binding capacity depends both on [Cl(s)]sat (contents of sites that can bind chlorides) and Keq (ratio of adsorption to desorption rate constants). In a non-steady-state diffusion process, the gradient of the free chloride ions in the pore solution is the effective driving force; the diffusion coefficient derived from measured free chloride concentration profiles is the effective diffusion coefficient. The effective diffusion coefficients can also be derived from measured concentration profiles in existing structures and serve as a basis for estimates on the future progress of the chloride penetration. In this paper, by introducing a chlorideesolid phase interaction term, the effective diffusivity is named as an “intrinsic” effective diffusivity. The intrinsic effective diffusivity of chloride ion in concrete (m2 s1) can be estimated by the following semi-empirical equations:
Fig. 7. The comparison between experiment results [15] and simulation results of porosity.
X.-Y. Wang, H.-S. Lee / Materials Chemistry and Physics 138 (2013) 917e928
De;Cl ¼
2:4 1010 Ce0 þ kP
rc
3 eff
¼
w0
rw
þ
w0
2
3:5
3 eff
(14c)
rw
0:226 103 ðCe0 þ kPÞ a
(14d)
where rc is the density of cement; k is the efficiency factor of the low-calcium fly ash for chloride penetration (based on the fit of experimental results, Papadakis proposed that k ¼ 3 for lowcalcium fly ash); and 3 eff is the effective porosity for diffusion. In the original chloride diffusion model [3], Papadakis made an assumption that cement hydration and pozzolanic reaction have been completed, i.e. a ¼ 1. While in the extension model of this paper, the degree of hydration is obtained from the proposed hydration model. By using Eq. (14c) and Eq. (14d), it can be found that with the increasing of fly ash replacement, due to the pore restructuring from fly ash reaction and the finer gel pores of pozzolanic CeSeH, the chloride diffusivity will decrease and the chloride ingress will be retarded. Eq. (14b) shows the Langmuir chloride binding isotherm between the Cl in the aqueous phase [Cl(aq)] and Cl bound in the solid phase [Cl(s)]. In Eq. (14b), parameters [Cl(s)]sat and Keq can be determined from the slope and the intercept of straight lines fitted to test data on the steady-state values of the [Cl(aq)] and [Cl(s)] in concrete samples with known initial concentration. Papadakis determined parameters [Cl(s)]sat and Keq from chloride binding isotherms experiments [2,3]. The equilibrium constant for chloride binding was found fairly constant for all mixtures (Keq ¼ 0.1 m3 of pore volume/kg Cl). And the saturation concentration of chloride in the solid phase can be estimated by the following empirical equation:
h
i Cl s
sat
¼ 8:8 103 ðCe0 þ kPÞ
(14e)
As shown in Eqs. (14a)e(14e), the influences of fly ash on chloride ingress are considered through two aspects, the effect of fly ash on chloride effective diffusivity and the effect of fly ash on chloride binding capacity. With the increasing of fly ash replacement, due to the pore restructuring from fly ash reaction and the finer gel pores of pozzolanic CeSeH, the chloride diffusivity will decrease. Also with the increasing of fly ash replacement, the saturation concentration of chloride ion in the solid phase will increase, and the chloride binding capacity will increase. Consequently, the chloride ingress will be retarded due to the decreasing of chloride diffusivity and the increasing of chloride binding capacity. Eqs. (14a) and (14b), in space is a boundary-value problem and in time is an initial-value problem. In this paper, a one dimensional finite element method is adopted to solve this equation. For numerical time integration part, the Galerkin method is used to confirm the stability of numerical integration [22e24]. 5.2. Verification of the proposed model Papadkis made experimental investigations on chloride penetration in low-calcium fly ash blended concrete according to Nordtest method NT Build 443 [3]. The mixing proportions of specimens are shown in Table 2. The mortar specimens were cast in steel cylinders of 100-mm diameter and 200-mm height, vibrated for 30 s on a vibration table, and then hermetically sealed to minimize water evaporation. The molds were stripped after 24 h and the specimens were placed, separately for each mixture, underwater at 20 C for 1 year. This long-term curing period underwater ensures an advanced degree of both Portland cement hydration and pozzolanic activity. So the
925
specimens in the chloride penetration tests can be approximately regarded as hardened concrete. The slice specimen for chloride penetration tests, with 60 mm thick, was taken from the initially 200 mm specimens. Prior to immersion, the samples were coated with epoxy resin. And then the samples were immersed in a chloride solution (165 g NaCl/L) for 100 days. The temperature was kept constant at 20 C throughout the entire test period. At the end of the immersion period, the exposed surface was ground using a dry process by removing thin successive layers from different depths. The total chloride content of the powders was determined by the Volhard titration method in accordance with the method NT Build code. By using Eqs. (14a) and (14b), we predicted the total chloride concentration (3 ½Cl ðaqÞ þ ½Cl ðsÞ), as a function of the distance from the outer concrete surface. As shown in Fig. 8, both my extension model and Papadakis’ original model can generally reproduce the experimental results. It should be noticed that the calculation results from Papadakis’ original model are slightly lower than my extension model. This is because Papadakis’ original model assumed that cement hydration and pozzolanic reaction have been completed, and consequently the porosity and chloride diffusivity used in Papadakis’ original model is a little lower than my extension model. In addition, the analysis results show that the specimens incorporating fly ash, whether it substitutes aggregate of cement, exhibit significantly lower total chloride content for all depths from the surface than the control specimen. Given a certain water to binder ratio, with the increasing of fly ash amount, the ingress depth of chloride ions decreases significantly. Oh and Jang [25] made an experimental research on the effects of materials and environmental factors on chloride penetration profiles in concrete structures. The Type I (ordinary Portland cement) and Type V (sulphate resisting cement) were used and the content of fly ash in the mixture was 20% of total cementitious materials, respectively. The water to binder ratio of specimens was 0.38. The concrete specimens (phi10 20 cm) were continuously immersed in 3.5% chloride solutions for 15 weeks after 28-days water curing at 23 C. It should be noticed that the 28 days curing period can not ensure the advanced degree of cement hydration and fly ash reaction. Especially, in the case of fly ash blended concrete, the pozzolanic reaction of fly ash can proceed continuously until one year. So the densification of microstructure of specimens will occur during the following chloride penetration test. In the chloride penetration test, all surfaces of the concrete specimens except top and bottom sides were sealed by epoxy resin so that the chloride penetration can occur only in one-direction. The solution was replenished every week to maintain uniform concentration, even though the reservoir is large enough. After immersion period, the total (acid-soluble) chloride profiles were measured. By using the proposed model, the total chloride concentrations are predicted as a function of the distance from the outer concrete surface. As shown in Fig. 9, because of the consideration the dependence of chloride diffusivity and porosity on the age, my extension model can generally reproduce the experimental results. Contrastively, the analysis results from Papadakis’ original model are much lower than the experimental results. This is because of the ignorance of densification of microstructure of specimens during the chloride diffusion test. On the other hand, it should be noticed that the deviation degrees between Papadakis’ model results and experimental results vary with mixing proportions of concrete. In the case of fly ash blended concrete (Fig. 9b and c), the deviation degrees are much larger than that of Portland cement concrete (Fig. 9a). This is because the pozzolanic reaction of fly ash mainly occurs after 28 days, and the decreasing of chloride diffusivity and porosity of fly ash blended concrete is much larger than that of Portland cement concrete. Summarily, the original model is only valid for chloride diffusion in hardened concrete, while due to the combination of hydration model, the proposed extension model is valid for chloride diffusion in both hardened concrete and
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Fig. 8. The comparison between experimental results [3] and simulated results of chloride penetration profiles.
hardening concrete. Similarly with Papadakis’ report [2,3], the specimens incorporating fly ash exhibit lower total chloride content than the control specimen. The difference between experimental results and prediction results maybe come from the difference of reactivity of fly ash between Papadakis’ experiment [3] and Oh’s experiment [25]. The depassivation of steel bars takes place when molar concentration of dissolved Cl, [Cl(aq)], in their vicinity drops below
a certain percentage of the molar concentration of hydroxyls in the pore water, [OH]. The critical value of the [Cl(aq)]/OH] ratio which signals depassivation seems to be 0.3 [21]. The molar concentration of [OH] depends on the cation type and on whether concrete is carbonated or not. By using the proposed model, we can predict the chloride penetration/binding profiles and estimate the time required for the chloride concentration surrounding the reinforcement to increase over the threshold of depassivation of
X.-Y. Wang, H.-S. Lee / Materials Chemistry and Physics 138 (2013) 917e928
927
Fig. 9. The comparison between experimental results [25] and simulated results of chloride penetration profiles.
reinforcing bars. The protection measures against chloride induced depassivation of steel in concrete also can be achieved. The intrinsic contributions of this paper are shown as follows: First, Papadakis [2,3] proposed a series of models on the chemical reactions of fly ash blended concrete and chloride ingress into blended concrete. Papadakis’ model can be used to determine the stoichiometric ratio in the chemical reactions of fly ash blended concrete, such as the stoichiometric ratio of hydration of cement and the pozzolanic reaction of fly ash. However, until now Papadakis’ model does not consider the influences of water to binder ratio and fly ash replacement on the reactivity of fly ash. Comparatively, in this paper, the proposed hydration model can describe the increasing of reactivity of fly ash with an increase of water to binder ratio or with a reduction of the replacement level of mineral admixture. So the first intrinsic contribution of this paper is the improvement on the modeling of reactions of fly ash blended concrete. By using the hydration model, the evolution of properties of low-calcium fly ash blended concrete is predicted as a function of curing age and these properties are adopted as input parameters for the chloride penetration model. Second, this paper contributes on modeling the chloride diffusion and reaction in a hydrating concrete in presence of fly ash. Especially the case of modeling of chloride penetration in a concrete that simultaneously is being hydrated offers originality. Yoon [5], Han [6], Ishida’s [8] work can be used to model the simultaneous chloride diffusion & reaction in a hydrating Portland cement concrete. In the case of fly ash blended concrete, Yoon [5], Han [6],
Ishida’s [8] work is not valid currently. On the other hand, Song’s [7] work can model the chloride diffusion in hardened silica fume blended concrete. When chloride diffusion and reaction happen together, Song’s [7] work is not valid currently. So the second intrinsic contribution of this paper is on the modeling the chloride diffusion and reaction in a hydrating concrete in presence of fly ash. Third, the proposed model in this paper can be used to evaluate the evolution of degree of hydration of cement and degree of reaction of fly ash as a function of curing age. Based on the degree of hydration of cement and degree of reaction of fly ash, the contents of evaporable water, calcium hydroxide, and porosity of hardening fly ash blended concrete can be determined. Our former work has evaluated the mechanical properties material chemical properties and thermal factors of hardening fly ash blended concrete [26]. This paper focuses on the modeling chloride ingress into fly ash blended concrete. So the third intrinsic contribution of this paper is that we proposed an integrated model for evaluation both early-age properties and durability aspects for fly ash blended concrete. On the other hand, compared with low-calcium fly ash, highcalcium fly ash has higher free CaO and sulfur contents. It should be noticed that the proposed hydration model in this paper is only valid for low-calcium fly ash blended concrete. For high-calcium fly ash blended concrete, because of the coexistence of cement hydration, rapid free CaO reaction and the reaction of glass phase in high-calcium fly ash, the hydration of FH-cement blends is more complicated than that of FL-cement blends. The investigation of interaction mechanisms
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among cement hydration, rapid free CaO reaction and high-calcium fly ash glass phase reaction will be carried out in the further research. In addition, Papadakis’ previous research on the stoichiometry of highcalcium fly ash reaction is very valuable for the development of kinetic reaction model of FH-cement blends [27]. The chemical and volumetric compositions of FH concrete obtained from Papadakis’ model can be used for the evaluation of durability aspects of FH blended concrete, such as carbonation and chloride ingress [3]. 6. Conclusions In this paper, we proposed a numerical procedure to evaluate the chloride diffusion in low-calcium fly ash blended concrete. This numerical procedure consists of two sub models, i.e. a hydration model and a chloride diffusion model. First, based on the combination of Papadakis’ chemical-based steady-state model and the kinetic reaction mechanisms involved in cement hydration and the pozzolanic reaction, a kinetic model is proposed to describe the hydration process of FL-concrete. By considering the production of calcium hydroxide in cement hydration and its consumption in pozzolanic reaction, the pozzolanic reaction of FL is separated from cement hydration. The proposed model considers the dependence of pozzolanic activity on the mass of calcium hydroxide and the influence of FL on the hydration of Portland cement. The contents of evaporable water, calcium hydroxide, and porosity were obtained as companied results of the hydration model and were used as input parameters for evaluation of the penetration of chloride ion. Second, in the chloride diffusion model, the physicochemical processes of diffusion of chloride ion in the aqueous phase of pores, the adsorption and binding in the solid phase of concrete, and the desorption are described by a nonlinear partial differential equation. The prediction results on chloride penetration profiles generally agree with experimental results. Acknowledgment This study was supported by 2012 Research Grant from Kangwon National University. Nomenclature
aji
hydration degree of the mineral component in a given cement particle i mineral component of cement j number of cement particles t time stoichiometric ratio by the mass of water to mineral vi component physically bound water wag ri density of the anhydrate cement mineral component reaction coefficient in a dormant period kd radius of anhydrate cement particles r0j effective diffusion coefficient of water in the cement Dei hydration product coefficient of reaction rate for each mineral component kri rw density of water B and C reaction coefficients in a dormant period initial diffusion coefficient Dei0 mass fraction in mineral components gi mass fraction of individual particle in cement gj n total number of cement particles in a cell space a degree of hydration of cement freesurface/totalsurface ratio between the free surface area and the total surface area water mass in a mixing proportion w0
Ce0 cement mass in a mixing proportion fS,P and fA,P mass fraction of S and A in fly ash gS and gA active (glass) part of S and A aglass reacted degree of active (glass) part of fly ash P fly ash mass in a mixing proportion chemically bound water of fly ash. mH2O mCH(t) calcium hydroxide mass in the hydrating cement-fly ash blends stoichiometry ratio by mass of CH to low-calcium fly ash vFL radius of low-calcium fly ash particle rFL0 rFL density of fly ash reaction rate coefficients of fly ash in a dormant period kdFL BFL and CFL reaction coefficients of fly ash in a dormant period initial diffusion coefficient of fly ash DeFL0 reaction rate coefficient of fly ash krFL aflyash reacted ratio of the fly ash mass of capillary water wcap D3 h porosity reduction due to hydration of Portland cement D3 p porosity reduction due to the pozzolanic activity 3 porosity [Cle(aq)] Cl concentration in the aqueous phase [Cle(s)] Cl bound in the solid phase x distance from the concrete surface intrinsic effective diffusivity of chloride ion in concrete D e,Cl equilibrium constant for chloride binding Keq [Cl(s)]satsaturation concentration of chloride ion in the solid phase rc density of cement k efficiency factor of the low-calcium fly ash for chloride penetration 3 eff effective porosity for diffusion References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
[19]
[20] [21]
[22] [23] [24] [25] [26] [27]
V. Saraswathy, H.W. Song, Mater. Chem. Phys. 104 (2007) 356e361. V.G. Papadakis, M.N. Faradis, C.G. Vayenas, Chem. Eng. Sci. 51 (1996) 505e513. V.G. Papadakis, Cem. Concr. Res. 30 (2000) 291e299. K. Breugel, Cem. Concr. Res. 25 (1995) 319e331. I.S. Yoon, Comput. Concr. 6 (2009) 1e18. S.H. Han, Constr. Build. 21 (2007) 370e378. H.W. Song, J.C. Jang, V. Saraswathy, K.J. Byun, Build. Environ. 42 (2007) 1358e1367. T. Ishida, P.O.N. Iqbal, H.T.L. Anh, Cem. Concr. Res. 39 (2009) 913e923. V.G. Papadakis, M.N. Faradis, C.G. Vayenas, ACI Mater. J. 89 (1992) 119e130. P. Navi, C. Pignat, Adv. Cem. Base Mater. 4 (1996) 58e67. K.B. Park, T. Noguchi, J. Plawsky, Cem. Concr. Res. 35 (2005) 1676e1684. F. Tomosawa, in: S. Chandra (Ed.), Proceedings of Tenth International Congress Chemistry of Cement, Gothenburg, 1997, pp. 72e75. M. Ippei, M. Suzuki, R. Sato, in: Henry G. Russell (Ed.), ACI SP-228, Proc. of 7th Int. Symp on High Performance Concrete, 2005, pp. 1175e1186. V.G. Papadakis, Cem. Concr. Res. 29 (1999) 79e86. V.G. Papadakis, Cem. Concr. Res. 29 (1999) 1727e1736. M. Cyr, P. Lawrence, E. Ringot, Cem. Concr. Res. 35 (2005) 719e730. T. Saeki, P.J.M. Monteiro, Cem. Concr. Res. 35 (2005) 1914e1921. K. Maekawa, R. Chaube, T. Kishi, Modeling of Concrete Performance: Hydration, Microstructure Formation and Mass Transport, Routledge, London and New York, 1998. T. Matsushita, S. Hoshino, I. Maruyama, T. Noguchi, K. Yamada, in: J. Beaudoin (Ed.), Proceedings of 12th International Congress Chemistry of Cement, Montreal, pp. 1e12, 2007. TH2-07.3. C.J. Pereira, L.L. Hegedus, in: Proceedings of the 8th International Symposium of Chemical Reaction Engineering, Edinburgh, 1984, pp. 427e438. V.G. Papadakis, M.N. Faradis, C.G. Vayenas, in: R.K. Dhir, M.R. Jones (Eds.), Concrete Repair, Rehabilitation and Protection, E. & F.N. Spon, London, 1996, pp. 165e174. D. Logan, A First Course in the Finite Element Method, third ed., Brooks/Cole Thomson learning, United States, 2002. M. Koichi, T. Ishida, T. Kishi, Multi-scale Modeling of Structural Concrete, Taylor & Francis, London and New York, 2009. C. Hyun, Prediction of thermal stress of high strength concrete and massive concrete, PhD dissertation, The University of Tokyo, 1995. B.H. Oh, S.Y. Jang, Cem. Concr. Res. 37 (2007) 47e53. X.Y. Wang, H.S. Lee, J. Mater. Civil Eng. 23 (2011) 1113e1123. V.G. Papadakis, Cem. Concr. Res. 30 (2000) 1647e1654.
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Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Modeling of chloride diffusion in concrete containing low-calcium fly ash Xiao-Yong Wang a, Han-Seung Lee b, * a b
Department of Architectural Engineering, College of Engineering, Kangwon National University, Chuncheon 200-701, Republic of Korea School of Architecture & Architectural Engineering, Hanyang University, Ansan 425-791, Republic of Korea
h i g h l i g h t s < A model to predict chloride ingress in fly ash blended concrete is proposed. < The model consists of a hydration model and a chloride diffusion model. < The evolution of properties of concrete is obtained from the hydration model. < The results from the hydration model are used for predicting chloride ingress. < The proposed model can be used for durability design of marine structures.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 August 2012 Received in revised form 20 November 2012 Accepted 28 December 2012
Low-calcium fly ash (FL) is a general product from the combustion of anthracite and bituminous coals and has been widely used as a mineral admixture to produce high strength and high performance concrete. And in marine and coastal environments, penetration of chloride ions is one of the main mechanisms causing concrete reinforcement corrosion. In this paper, we proposed a numerical procedure to predict the chloride diffusion in low-calcium fly ash blended concrete. This numerical procedure includes two parts: a hydration model and a chloride diffusion model. The hydration model starts with mix proportions of low-calcium fly ash blended concrete and considers Portland cement hydration and low-calcium fly ash reaction respectively. By using the hydration model, the evolution of properties of low-calcium fly ash blended concrete is predicted as a function of curing age and these properties are adopted as input parameters for the chloride penetration model. Furthermore, based on the modeling of physicochemical processes of diffusion of chloride ion into concrete, the chloride distribution in lowcalcium fly ash blended concrete is evaluated. The prediction results agree well with experiment results. Ó 2013 Elsevier B.V. All rights reserved.
Keywords: C: Computer modelling and simulation D: Corrosion D: Diffusion D: Microstructure
1. Introduction Fly ash is the combustion residue in coal-burning electric power plants. Viewed from significant differences in its mineralogical composition and properties, the fly ash can be divided into two categories based on their calcium content. The ash in the first category, low-calcium fly ash (FL), containing less than 10% of analytical calcium oxide (CaO), is a general product from the combustion of anthracite and bituminous coals. The ash in the second category, high-calcium fly ash (FH), typically containing 15e40% of analytical CaO, is a general product from the combustion
* Corresponding author. Tel./fax: þ82 31 400 5181. E-mail addresses: [email protected] hanyang.ac.kr (H.-S. Lee).
(X.-Y.
Wang),
ercleehs@
0254-0584/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matchemphys.2012.12.085
of lignite and subbituminous coals. The FL is categorized as a normal type of pozzolan that consists of silicate glass and is modified by aluminum and iron. Also, it has long been used as a mineral admixture to produce high strength and high performance concrete [1]. It is widely known that the ingress of chloride ions constitutes a major source of durability problems affecting reinforced concrete structures which are exposed to marine environments. Once a sufficient quantity of chloride ions has accumulated around the embedded steel, pitting corrosion of the metal is liable to occur unless the environmental conditions are strongly anaerobic. In the design of concrete structures, the influence of chloride ingress on service life must be considered [1]. The literature is rich in papers dealing with chloride attack of concrete. Papadakis [2,3] made experimental investigations and numerical modeling of chloride ingress into concrete incorporating
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fly ash. The physicochemical processes of diffusion of chloride ion in the aqueous phase of pores, their adsorption and binding in the solid phase of concrete were described by a nonlinear partial differential equation. Based on computed micro-pore structure [4], Yoon [5] proposed a simple approach to calculate the diffusivity of concrete considering carbonation. The parameters affecting the chloride diffusivity, such as the diffusivity in pore solution, tortuosity, micro-structural properties of hardened cement paste, and volumetric portion of aggregate, are taken into consideration in the calculation of chloride diffusivity. Han [6] proposed a modified diffusion coefficient that considers the effect of chloride binding and evaporable water on the diffusion coefficient. The evaporable water content was predicted from a hydration model of Portland cement. Based on mathematical derivation of microstructure of concrete, Song [7] built a procedure for predicting the diffusivity of high strength SF concrete. In this model the influence of water to binder ratio, SF replacement ratio, and degree of hydration on diffusivity was considered. Ishida [8] formulated the chloride diffusivity based on computed multi-scale micro-pore structure, which considers tortuosity and constrictivity of porous network as reduction factors in terms of complex micro-pore structure and electric interaction of chloride ions and pore wall. From references [2e8], we can see that based on a hydration model, the evolution of concrete properties, such as the content of evaporable water and porosity, can be described as a function of curing age. The diffusivity of chloride ions in concrete can be obtained from the microstructure of concrete [2e8]. Due to the pozzolanic reaction between calcium hydroxide and low-calcium fly ash, compared with ordinary Portland cement, hydration of concrete containing low-calcium fly ash is much more complex. It is difficult to build a chemical-based kinetic equation to quantitatively describe the evolution of properties of low-calcium fly ash blended concrete and only the final concentrations of reaction products, which apply after the Portland cement hydration and pozzolanic reaction are complete and a steady is established [3,9]. In this paper, a numerical procedure which can simulate chloride diffusion in low-calcium fly ash blended concrete is built. The flow chart of this procedure is shown in Fig. 1. As shown in Fig. 1, this numerical procedure includes a hydration model and a chloride diffusion model. In the hydration model, by considering the producing of calcium hydroxide in cement hydration and the consumption of it in pozzolanic reaction, a numerical model is
proposed to simulate the hydration of concrete containing lowcalcium fly ash. The contents of evaporable water, calcium hydroxide, and porosity were obtained as companied results of the hydration model and were used as input variables for the chloride diffusion model. Furthermore, in the chloride diffusion model, the physicochemical processes of diffusion of chloride ion in the aqueous phase of pores, the adsorption and binding in the solid phase of concrete, and the desorption are described by a nonlinear partial differential equation. The prediction results on chloride penetration profiles were verified with the experimental results. 2. Hydration model of ordinary portland cement 2.1. The assumptions of a hydration model In this hydration model, the influences of the water to cement ratio, cement particle size distribution, cement mineral components and curing temperature on the hydration reaction of Portland cement are considered. The assumptions of this model can be summarized as follows: 1. Cement particles are randomly cast in a representative unit cell space, as shown in Fig. 2. As proposed by Navi [10], the length of the edge of the representative unit cell is 100 micron. The amount of chemically bound water for each cement component, C3S, C2S, C3A, and C4AF, proposed by Park [11] is used for simulation in this paper. 2. The degree of hydration of cement components is the ratio of the volume of reacted cement components to the volume of initial cement components. The degree of the hydration of cement paste can be regarded as a weighted sum of cement particles and mineral components as shown in Fig. 3. The hydration at various temperatures is modeled by Arrhenius law [11]. 3. The liquid phase, which is assumed to be water, diffuses through a hydrate layer, reaches the surface of the cement particle and chemically reacts with cement. The hydrate formed by hydration adheres to the cement particles spherically. 4. Particle size distribution of cement can be approximated using the RosineRammler function [11].
Mixing proportion and curing condition of low-calcium fly ash blended concrete Hydration model considers both cement hydration and low-calcium fly ash reaction Evolution of porosity, evaporable water and other physical and chemical properties with ages Nonlinear partial differential equation for physicochemical process Chloride ion concentration in low-calcium fly ash blended concrete Fig. 1. The flow chart of predicting chloride ion concentration in low-calcium fly ash blended concrete.
Fig. 2. The cement particles distribute randomly in cell space.
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919
hydrate. This phenomenon can be expressed as a function of degree of hydration and is described by Eq. (3):
Dei ¼ Dei0 ln
1
! (3)
aji
When the cement is mixed with water, the hydration of each mineral component processes according to the model described in the previous section. The degree of the hydration of cement can be calculated as following Eq. (4):
P
P
j¼n i¼4 j i ¼ 1 a gi gj a ¼ Pj ¼j ¼1n Pi ¼ 4 i j¼1
i¼1
gi gj
(4)
where gi is the mass fraction in mineral components; gj is the mass fraction of individual particle in cement and n is the total number of cement particles in a cell space. As shown in Eq. (4), the different hydration reactions do not consume the same amount of water, so the computation of the total consumed water should be a weighted average of the consumed water for each elementary reaction.
Fig. 3. The schematic of multi-component hydration model.
2.2. Hydration mechanism 2.3. Water withdrawl mechanism In Park’s model [11], some improvements were achieved by incorporating size distribution of cement particles and the component of cement minerals, including C3S, C2S, C3A and C4AF. The basic hydration equation for each mineral composition in cement particles can be described as following Eq. (1), which is originally built by Tomosawa [12] to describe hydration of a single cement particle. This model is expressed as a single equation composed of four rate determining coefficients which consider the rate of formation and destruction of initial impermeable layer, the activated chemical reaction process and following diffusion-controlled process:
dai 3rw ¼ j dt vi þwag r0 ri j
!
1
1 1 2 1 3 3 1 aji þ 1 aji þ kd Dei kri Dei j r0
j r0
(1)
where ai denotes the hydration degree of the mineral component in given cement particle. i is the mineral component. j is the number of cement particles. vi is the stoichiometric ratio by the mass of water to mineral component. wag is the physically bound water that is approximately equal to 13% of the mass of reacted cement, ri is the density of the anhydrate cement mineral compoj nent, kd is the reaction coefficient in a dormant period, r0 is the radius of anhydrate cement particles, Dei is the effective diffusion coefficient of water in the hydration product for each mineral component and kri is the coefficient of reaction rate for each mineral component. rw is the density of water. The influence of temperature on the hydration rate is considered by Arrhenius law [12]. The activation energies of each compound are obtained from the cement hydration experiments performed under different curing temperatures. Whereas, kd is assumed to be a function of degree of hydration during the initial reaction period and it is expressed as Eq. (2): j
4 B kd ¼ 1:5 þ C r0j rtj
aji
(2)
The B and C in Eq. (2) denote reaction coefficients. The effective diffusion coefficient of water is affected by the tortuosity of the gel pore as well as the radius of the gel pore in
During the hydration period, at a certain time point after the initial setting time, due to the increasing interconnection among cement particles, the contact area between cement particle and surrounding water will be decreased. As a result, the slower hydration rate will be achieved. On the other hand, the water presenting in the paste can be classified into evaporable and non-evaporable fractions [11,12]. The former is the capillary water and the gel water that resides partially within the hydration product. The nonevaporable water is defined as the bound water which has chemically reacted with cement. During the hydration process, only the capillary water contributes to further hydration. With the hydration process proceeding, the capillary water will be consumed and the relative hydration rate will be decreased. Under sealed-curing condition, when water to cement ratio is less than 0.38, due to the limiting of capillary water, the cement hydration is not complete. (The mass of chemically bound water approximately equals to 25% of the mass of reacted cement and the mass of gel water approximately equals to 13% of the mass of reacted cement [11].) By considering these two points, as proposed by Park [11] and Maruyama [13], the modification of Eq. (1) can be expressed as Eq. (5):
daji dt
!0 ¼
daji freesurface j w0 0:38*Ce0 *a * * dt w0 totalsurface
(5)
In Eq. (5), the item (freesurface/totalsurface)j is the ratio between the free surface area (the area which contacts with water) and the total surface area, which can be determined by the proposed method in reference [10]. w0 is the water mass and Ce0 is the cement mass in a mixing proportion. The item (w00.38*Ce0*a)/w0 considers the decrease of the available capillary water for cement hydration. 3. Hydration model for cement blended with low-calcium fly ash 3.1. The amount of calcium hydroxide (CH) during the hydration process As proposed by Papadakis [14,15], during the hydration period, the chemical reactions of the mineral components of Portland cement can be expressed as following Eqs. (6a)e(6d):
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2C3 S þ 6H/C3 S2 H3 þ 3CH
(6a)
3.2. The simulation of pozzolanic reaction in cement-low-calcium fly ash blends
2C2 S þ 4H/C3 S2 H3 þ CH
(6b)
C3 A þ CSH2 þ 10H/C4 ASH12
(6c)
C4 AF þ 2CH þ 10H/C6 AFH12
(6d)
The addition of low-calcium fly ash has both physical and chemical effect on the hydration of cement. The physical effect includes retard effect and heterogeneous nucleation. The chemical aspect is pozzolanic activity of fly ash. As reported by Cyr [16], the addition of fly ash can retard hydration of the cement in early age. This retardation could be due to aluminate ions or organic matter dissolved from the fly ash into the aqueous phase, delaying the nucleation and crystallization of Ca(OH)2 and CeSeH. However, this delay can be partly compensated by heterogeneous nucleation. The fly ash particles can serve as nuclei sites of the cement particles and leads a chemical activation of the hydration of cement. Due to the coexistence of both retardation effect and acceleration effect, as reported by Papadakis [15], when aggregate is partly replaced by fly ash (the mixing proportions of these specimens are listed in Table 2, as FLA1, FLA2 and FLA3), in early age, the compressive strength, calcium hydroxide amount and released heat of the fly ash-cement paste (FLA paste) is not significantly different from that of the control cement paste. Compared with physical effect, the pozzolanic activity has dominate effect on long-term properties of FL-concrete. This paper focuses on the simulation of the pozzolanic activity in the hydration of fly ash blended cement. The simulation of physical effect is considered as a further research. Besides physical and chemical effect, when cement is replaced by the same quantity of fly ash, the amount of cement will decrease and the water to cementitious materials ratio will increase [14,15]. This effect is considered by the cement hydration model, as Eq. (5). The proposed model comes from the similarity in mechanism between cement hydration and pozzolanic activity: Firstly, the cement reacts with water and the glass phase of the pozzolanic material reacts with calcium hydroxide. The cement hydration process includes initial dormant period, phase-boundary reaction period and diffusion period. In the late age of cement hydration, diffusion is the control process. Some researchers reported that the pozzolanic activity was a diffusion-controlled process [13,15]. Secondly, based on analysis of the scanning electron micrographs (SEM) of Portland cement paste, silica fume-cement paste and fly ash-cement paste, Papadakis [2,3,9,14,15] reported that the cement hydration product adheres on surface of the cement particles and the pozzolanic product adheres on surface of the pozzolanic particles. Thirdly, the cement particle with small size has a highly reactivity with water and shows almost no initial dormant period and the cement particle with big size shows initial dormant period. Similarly, silica fume is a highly pozzolanic cement replacement material and shows only a short initial dormant period, like small cement particle. Fly ash shows a long initial dormant period, because the fly ash activation mainly lies in the breaking down of its glass phases. The alumina phase and silica phase in fly ash will not dissolve until the pH is higher than 13.3 [15]. On the other hand, there also exist some differences between cement hydration and pozzolanic activity. Cement hydration will produce calcium hydroxide and pozzolanic activity will consume it. As proposed in references [2,3,9,14,15], the hydration rate of the pozzolanic materials depends on the amount of calcium hydroxide in hydrating blends and the degree of hydration of mineral admixture. So we can derivate an equation from cement hydration to pozzolanic reaction by considering both similarity in kinetic reaction processes and difference in reaction affecting factors between two reactions. Compared with the silica fume, the hydration rate of the lowcalcium fly ash is much lower due to the larger particle size. In the early duration period of 0e21 days no traces of reaction among FL particles can be detected. In the simulation, it is assumed that the pozzolanic reaction is divided into three processes: initial dormant
By the aforementioned hydration model and Eqs. (6a)e(6d), the mass of the hydration product in a unit volume of Portland cement, such as calcium hydroxide, can be obtained from Eq. (7) as follows:
CH ¼
1:5gc3s ac3s þ 0:5gc2s ac2s 2gc4af ac4af *74:1*Ce0
(7)
Fly ash is a complex material that consists of a wide range of glass and crystalline compounds. In reaction form, there is the aluminosilicate (AeS) glass with a high content of S. The hydration product of an aluminosilicate glass/hydrated lime mixture should be a calcium silicate hydrate (CeSeH) gel incorporating significant amounts of A. The S of AeS glass is proposed to react with the CH without additional water binding and to form a calcium silicate hydrate described by the simplified formula of C3S2H3 as shown by using almost pure vitreous silica. The silicon presented as quartz or in crystalline aluminosilicate phases is inert. Based on the experimental results of the reaction stoichiometry among FL, chemically bound water and calcium hydroxide, Papadakis [14,15] proposed the pozzolanic reaction in cement-low-calcium fly ash blends which is written as following Eqs. (8a)e(8c):
2S þ 3CH/C3 S2 H3
(8a)
A þ CSH2 þ 3CH þ 7H/C4 ASH12
(8b)
A þ 4CH þ 9H/C4 AH13
(8c)
Based on the hydration model and pozzolanic reaction proposed in Eqs. (8a)e(8c), during the hydration period, the mass of calcium hydroxide CH and chemical bound water wchem can be rewritten as following Eqs. (9a) and (9b):
CH ¼
1:5gc3s ac3s þ 0:5gc2s ac2s 2gc4af ac4af *74:1*Ce0 1:85*gS *fS;P þ 2:907*gA *fA;P *aglass *P
(9a) wchem ¼ 0:25*Ce0 *a þ mH2 O *gA *fA;P *aglass *P
(9b)
In the Eqs. (9a) and (9b), fS,P and fA,P are the mass fraction of S and A in fly ash; gS and gA are their active (glass) part; aglass is the reacted degree of active (glass) part of fly ash; P is the fly ash mass in a mixing proportion; mH2O is the amount of chemically bound water in a unit mass of the reacted active (glass) part of fly ash. As shown in Eq. (9a), the evolution of calcium hydroxide mass is dependent on two aspects: the production of calcium hydroxide from the hydration of Portland cement and the consumption of it from the pozzolanic activity. As shown in Eq. (9b) both the hydration of Portland cement and pozzolanic activity will contribute to chemically bound water. As shown in Eqs. (9a) and (9b), in the simulation it is assumed that the active (glass) S and A, hydrate show equal rates.
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period, phase-boundary reaction process and diffusion process. By considering these points, based on the method proposed by Saeki [17], the hydration equation of the active (glass) part in FL can be written as Eqs. (10a)e(10c):
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In Eq. (12), the item (0.25*Ce0*a þ 0.13*Ce0*a) considers the consumption of capillary water from the hydration of cement; and the item ðmH2 O *gA *fA;P *aglass *P þ 0:15*aflyash *PÞ considers the consumption of capillary water from the reaction of fly ash.
daglass m ðtÞ 3rw 1 ¼ CH 1 1 2 P dt vFL rFL0 rFL 1 rFL0 rFL0 3 3 1 aglass þ 1 aglass þ kdFL DeFL krFL DeFL
kdFL ¼
3 BFL 1:5 þ CFL * aglass
(10b)
aglass
The porosity of hydrating blends is reduced due to the Portland cement hydration and pozzolanic activity during hydration period. As proposed by Papadakis [15], the porosity can be determined as Eq. (13): 3
DeFL ¼ DeFL0 *ln
1
! (10c)
aglass
Where mCH(t) is the calcium hydroxide mass in a unit volume of hydrating cement-low-calcium fly ash blends and can be obtained from Eq. (9a); P is the low-calcium fly ash mass in mixing proportion; vFL is the stoichiometry ratio by mass of CH to low-calcium fly ash; rFL0 is the radius of low-calcium fly ash particle; rFL is the density of fly ash; kdFL is the reaction rate coefficients in dormant period (BFL and CFL are coefficients); DeFL0 is the initial diffusion coefficient and krFL is the reaction rate coefficient. The influence of temperature on hydration can be considered by Arrhenius law. The activation energy of pozzolanic reactions in cement-FL blends can be obtained by the hydration experiments of cement-FL blends performed under different curing temperatures. The low-calcium fly ash includes both active part and inert part. The reacted ratio of the active part of fly ash can be calculated according to Eq. (10). The inert part is assumed as chemically inert and does not react. The reacted ratio of fly ash (includes both active part and inert part), can be obtained based on Eq. (10) and the mass compositions of fly ash. The reacted ratio of the fly ash can be calculated as following Eq. (11):
aflyash ¼ gs *fS;P þ gA *fA;P *aglass ¼
0:82*0:535 þ 0:82*0:204 *aglass ¼ 0:606*aglass (11)
Similar with the hydration of cement, with the proceeding of pozzolanic reaction, the water will be physically adsorbed in the hydration products of fly ash. Maekawa [18] proposed that for the fly ash pozzolanic reaction, when 1 g fly ash reacts, 0.15 g gel water will be consumed. Hence the mass of capillary water wcap in hydrating cement-FL blends can be calculated as follows:
wcap ¼ w0 ð0:25*Ce0 *a þ 0:13*Ce0 *aÞ mH2 O *gA *fA;P *aglass *P þ 0:15*aflyash *P
(12)
(10a)
¼
w0
rw
D3 h D3 p
(13)
Where D3 h is the porosity reduction due to hydration of Portland cement. It can be obtained from the amount of the chemically bound water which is consumed in hydration of the Portland cement. D3 p is the porosity reduction due to the pozzolanic activity and it can be obtained from the amount of chemically bound water which is consumed in the pozzolanic reaction. 4. Verification of hydration model 4.1. The degree of hydration of mineral components of ordinary Portland cement The results of this part in the experiments for regarding the hydration degree of ordinary Portland cement were used [19]. The water to cement ratio was 0.5 and curing temperature was 293 K. The hydration degree of the mineral components was measured at 1, 3, 7, 28, 91, 190 and 365 days. Powder X-Ray diffraction/Rietveld analysis was used to measure the degree of hydration of cement mineral components. The amount of chemically bound water determined by Rietveld analysis was verified by ignition loss [19]. By regression experiment results, the reaction coefficients of the multicomponents hydration model were obtained and listed in Table 1. Fig. 4 represents the comparison between the experiment results and the prediction results. Because the reaction rate of C3S and C3A is much quicker than C2S and C4AF, the hydration of C3S and C3A reaches a steady-state much earlier than C2S and C4AF. Most of C3A and C3S have reacted in the first 1000 h. As shown in Fig. 4, the prediction results overall agree well with experimental results. 4.2. The hydration of cement blended with low-calcium fly ash In this part, the experimental results of the hydration of cementFL blends [15] are adopted to verify the proposed hydration model. The mixing proportions for the specimens are shown in Table 2. In the control specimen, the water to cement ratio (W/C) was 0.5 and the aggregate to cement ratio (A/C) was 3. When FL replaces the volume of aggregates, three contents of FL were selected, such as
Table 1 The coefficients of the proposed hydration model. B (cm h1)
C (cm (cm4 h1))
krc3s (cm h1)
krc2s (cm h1)
krc3a (cm h1)
krc4af (cm h1)
Dec3s0 (cm2 h1)
Dec3a0 (cm2 h1)
Dec2s0 (cm2 h1)
Dec4af0 (cm2 h1)
2 109
1.5 1015
2.422 105
1.815 107
1.985 106
3.759 107
6.328 1010
9.568 108
6.328 1010
9.568 108
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Fig. 4. The comparison between experiment results [19] and simulation results of the hydration degree of cement mineral components: C3S,C2S,C3A and C4AF.
10%, 20%, and 30%, and added to the cement mass for the specimens FLA1, FLA2, and FLA3, respectively. For the cement replaced by FL, the same contents were also selected, such as 10%, 20%, and 30%, for replacing the control cement mass for the specimens FLC1, FLC2, and FLC3, respectively. The specimens were cured under a sealed condition with 20 C. The CH content, chemically bound water content and porosity at 3, 7, 14, 28, 49, 112, 182, and 364 days after casting was tested. For each test, the specimen was stripped, placed in a preweighed glass mortar, and pulverized. The mortar with the material was placed in an oven at 105 C until the weight was constant. These weight indications were used to determine the chemically bound water content and porosity.
mass depends on two factors: such as the Portland cement hydration that produces CH and the pozzolanic reaction that consumes CH. Because the low-calcium fly ash represents a low reaction rate, the CH content of FLA specimens in the initial period follows the CH content of its control, but the CH of FLA specimens is consumed at a slow rate after 14 days [15]. Based on the mass of calcium hydroxide, the reaction coefficients of pozzolanic reaction in Eqs. (10a)e(10c) can be obtained (as B ¼ 1.169 1012 cm h1, C ¼ 0.0426 cm h1, krFL ¼ 8.829 108 cm h1, DeFL0 ¼ 2.705 1011 cm2 h1). The evolution of the mass of CH is shown as a function of hydration time in Fig. 5. As shown in Fig. 5, the simulation results overall agree well with the experimental results.
4.2.1. The amount of calcium hydroxide during the hydration period In the hydration of ordinary Portland cement, the mass of calcium hydroxide will increase until a steady-state is reached. In the hydration of cement-low-calcium fly ash blends, the evolution of CH
4.2.2. The amount of bound water and porosity during the hydration period In the case of the cement-low-calcium fly ash blends, in its initial three months of hydration, there are two factors that affect the
Table 2 Mixture proportions for the specimens. Specimen
Cement (kg m3)
Water (kg m3)
Fly ash (kg m3)
Aggregate (kg m3)
Water to cement ratio
Fly ash to cement ratio
Aggregate to cement ratio
Control FLA1 FLA2 FLA3 FLC1 FLC2 FLC3
514.6 514.6 514.6 514.6 463.1 411.7 360.2
257.4 257.4 257.4 257.4 257.4 257.4 257.4
0.0 51.5 102.9 154.4 51.5 102.9 154.4
1543.8 1482.7 1421.7 1360.6 1526.6 1509.4 1492.3
0.5 0.5 0.5 0.5 0.556 0.625 0.715
0.0 0.1 0.2 0.3 0.111 0.250 0.429
3.0 2.88 2.76 2.64 3.30 3.67 4.14
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Fig. 5. The comparison between experiment results [15] and simulation results of CH amount.
bound water content. First is the selective reaction of the CH with S instead of its reaction with C3A and C4AF phases of cement. Second is the high content of aluminate in fly ash counterbalances losses in water content. The overall result is that the control specimen as well as all FLA specimens has almost the same water content in its initial three months. After three months, the chemically bound water content values for FLA specimens exceeded those of the controls. It seems that during this late period the remaining amounts of the C3A and C4AF phases of cement have reacted, binding additional water. In the current model, the selective reaction of the CH with S is not considered and it is assumed that the active (glass) S and A, hydrate show equal rates. By using the proposed model, the evolution of bound water amount and porosity is calculated and shown as a function of hydration time in Figs. 6 and 7 respectively. As shown in Figs. 6 and 7, the calculation results overall agree well with the experimental results. The difference between the calculation results and experimental results may comes from the ignorance of selective reaction of CH with S and the different reaction rates of active (glass) S and A in low-calcium fly ash. 5. Modeling of chloride diffusion and reaction in low-calcium fly ash blended concrete 5.1. Model of chloride diffusion-adsorption in concrete In most field cases, chloride ion may penetrate into concrete through a combined mechanism of hydraulic advection, capillary
suction, diffusion and thermal migration. Diffusion is the dominating mechanism in the case of saturated concrete, such as concrete submerged in seawater. In many papers, chloride transport in concrete is modeled using Fick’s second law of diffusion, neglecting the chloride interaction with the solid phase [1]. However, several field studies in recent years have indicated that the use of this law is not applicable to long-term chloride transport in concrete, very often calculating a decreasing chloride transport coefficient in time. It is widely accepted that the transport behavior of chloride ions in concrete is a more complex and complicated process than can be described by Fick’s law of diffusion. This approach, therefore, can be characterized as semi-empirical, resulting in the calculation of an apparent effective diffusivity. The binding of chloride ion by cementitious materials is very complicated, and is influenced by many factors including chloride concentration, cement composition, hydroxyl concentration, cation of chloride salt, temperature, supplementary cementing materials, carbonation, sulfate ions and electrical field etc. There is a generally good correlation between C3A content (or C4AF when there is lack of C3A phase) and chloride binding capacity. There is also evidence for the binding of chlorides in CeSeH gel, possibly in interlayer space. The Naþ ions can be bound in CeSeH gel lattice, especially when the C/S ratio is low [3]. Several secondary chlorideecalcium compounds have also been reported. In addition to the chemical binding, the effects of ionic interaction, lagging motion of cations, and formation of an electrical double layer on the solid surface all play an important role in the transport of chloride ions in concrete.
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Fig. 6. The comparison between experiment results [15] and simulation results of bound water.
The relationship between bound and free chlorides is nonlinear and may be expressed by the Langmuir equation, the Freundlich equation, or the modified Brunauer, Emmet and Teller (BET) equation. Of these, the Langmuir equation is both fundamental and easier to use in practical applications [6]. Pereira and Hegedus [20] were the first to identify and model chloride diffusion and reaction in fully saturated concrete as a Langmuirian equilibrium process coupled with Fickian diffusion. Furthermore, Papadakis et al. [21] generalized this pioneering model effort of Pereira and Hegedus and extended it to more general conditions, offering an alternative simpler, yet equally accurate, numerical and analytical solution. Papadakis proposed that the physicochemical processes of diffusion of Cl in the aqueous phase of pores, their adsorption and binding in the solid phase of concrete, and their desorption can be described by a nonlinear partial differential equation for the concentration of Cl in the aqueous phase [Cl(aq)] (kg m3 pore solution). The equations for calculating the Cl in the aqueous phase [Cl(aq)] and Cl bound in the solid phase [Cl(s)] (kg m3 concrete) are shown as follows:
2 De;Cl 1 þ Keq Cl aq v Cl aq v2 Cl aq ¼ 2 vt vx2 Keq Cl s þ 3 1 þ Keq Cl aq sat
(14a)
i h Keq Cl s sat Cl aq ¼ Cl s 1 þ Keq Cl aq
(14b)
With initial condition: [Cl(aq)] ¼ [Cl(aq)]in at t ¼ 0 (initial concentration); and boundary condition: [Cl(aq)] ¼ [Cl(aq)]0 at x ¼ 0 (concrete surface) and v[Cl(aq)]/vx ¼ 0 at x ¼ M (axis of symmetry). In Eqs. (14a) and (14b), x is the distance from the concrete surface (m); t is the time(s); D e,Cl is the intrinsic effective diffusivity of chloride ion in concrete (m2 s1); Keq is the equilibrium constant for chloride binding (m3 of pore solution/kg); and [Cl(s)]sat is the saturation concentration of chloride ion in the solid phase (kg m3 concrete). As observed from Eq. (14b), the chloride binding capacity depends both on [Cl(s)]sat (contents of sites that can bind chlorides) and Keq (ratio of adsorption to desorption rate constants). In a non-steady-state diffusion process, the gradient of the free chloride ions in the pore solution is the effective driving force; the diffusion coefficient derived from measured free chloride concentration profiles is the effective diffusion coefficient. The effective diffusion coefficients can also be derived from measured concentration profiles in existing structures and serve as a basis for estimates on the future progress of the chloride penetration. In this paper, by introducing a chlorideesolid phase interaction term, the effective diffusivity is named as an “intrinsic” effective diffusivity. The intrinsic effective diffusivity of chloride ion in concrete (m2 s1) can be estimated by the following semi-empirical equations:
Fig. 7. The comparison between experiment results [15] and simulation results of porosity.
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De;Cl ¼
2:4 1010 Ce0 þ kP
rc
3 eff
¼
w0
rw
þ
w0
2
3:5
3 eff
(14c)
rw
0:226 103 ðCe0 þ kPÞ a
(14d)
where rc is the density of cement; k is the efficiency factor of the low-calcium fly ash for chloride penetration (based on the fit of experimental results, Papadakis proposed that k ¼ 3 for lowcalcium fly ash); and 3 eff is the effective porosity for diffusion. In the original chloride diffusion model [3], Papadakis made an assumption that cement hydration and pozzolanic reaction have been completed, i.e. a ¼ 1. While in the extension model of this paper, the degree of hydration is obtained from the proposed hydration model. By using Eq. (14c) and Eq. (14d), it can be found that with the increasing of fly ash replacement, due to the pore restructuring from fly ash reaction and the finer gel pores of pozzolanic CeSeH, the chloride diffusivity will decrease and the chloride ingress will be retarded. Eq. (14b) shows the Langmuir chloride binding isotherm between the Cl in the aqueous phase [Cl(aq)] and Cl bound in the solid phase [Cl(s)]. In Eq. (14b), parameters [Cl(s)]sat and Keq can be determined from the slope and the intercept of straight lines fitted to test data on the steady-state values of the [Cl(aq)] and [Cl(s)] in concrete samples with known initial concentration. Papadakis determined parameters [Cl(s)]sat and Keq from chloride binding isotherms experiments [2,3]. The equilibrium constant for chloride binding was found fairly constant for all mixtures (Keq ¼ 0.1 m3 of pore volume/kg Cl). And the saturation concentration of chloride in the solid phase can be estimated by the following empirical equation:
h
i Cl s
sat
¼ 8:8 103 ðCe0 þ kPÞ
(14e)
As shown in Eqs. (14a)e(14e), the influences of fly ash on chloride ingress are considered through two aspects, the effect of fly ash on chloride effective diffusivity and the effect of fly ash on chloride binding capacity. With the increasing of fly ash replacement, due to the pore restructuring from fly ash reaction and the finer gel pores of pozzolanic CeSeH, the chloride diffusivity will decrease. Also with the increasing of fly ash replacement, the saturation concentration of chloride ion in the solid phase will increase, and the chloride binding capacity will increase. Consequently, the chloride ingress will be retarded due to the decreasing of chloride diffusivity and the increasing of chloride binding capacity. Eqs. (14a) and (14b), in space is a boundary-value problem and in time is an initial-value problem. In this paper, a one dimensional finite element method is adopted to solve this equation. For numerical time integration part, the Galerkin method is used to confirm the stability of numerical integration [22e24]. 5.2. Verification of the proposed model Papadkis made experimental investigations on chloride penetration in low-calcium fly ash blended concrete according to Nordtest method NT Build 443 [3]. The mixing proportions of specimens are shown in Table 2. The mortar specimens were cast in steel cylinders of 100-mm diameter and 200-mm height, vibrated for 30 s on a vibration table, and then hermetically sealed to minimize water evaporation. The molds were stripped after 24 h and the specimens were placed, separately for each mixture, underwater at 20 C for 1 year. This long-term curing period underwater ensures an advanced degree of both Portland cement hydration and pozzolanic activity. So the
925
specimens in the chloride penetration tests can be approximately regarded as hardened concrete. The slice specimen for chloride penetration tests, with 60 mm thick, was taken from the initially 200 mm specimens. Prior to immersion, the samples were coated with epoxy resin. And then the samples were immersed in a chloride solution (165 g NaCl/L) for 100 days. The temperature was kept constant at 20 C throughout the entire test period. At the end of the immersion period, the exposed surface was ground using a dry process by removing thin successive layers from different depths. The total chloride content of the powders was determined by the Volhard titration method in accordance with the method NT Build code. By using Eqs. (14a) and (14b), we predicted the total chloride concentration (3 ½Cl ðaqÞ þ ½Cl ðsÞ), as a function of the distance from the outer concrete surface. As shown in Fig. 8, both my extension model and Papadakis’ original model can generally reproduce the experimental results. It should be noticed that the calculation results from Papadakis’ original model are slightly lower than my extension model. This is because Papadakis’ original model assumed that cement hydration and pozzolanic reaction have been completed, and consequently the porosity and chloride diffusivity used in Papadakis’ original model is a little lower than my extension model. In addition, the analysis results show that the specimens incorporating fly ash, whether it substitutes aggregate of cement, exhibit significantly lower total chloride content for all depths from the surface than the control specimen. Given a certain water to binder ratio, with the increasing of fly ash amount, the ingress depth of chloride ions decreases significantly. Oh and Jang [25] made an experimental research on the effects of materials and environmental factors on chloride penetration profiles in concrete structures. The Type I (ordinary Portland cement) and Type V (sulphate resisting cement) were used and the content of fly ash in the mixture was 20% of total cementitious materials, respectively. The water to binder ratio of specimens was 0.38. The concrete specimens (phi10 20 cm) were continuously immersed in 3.5% chloride solutions for 15 weeks after 28-days water curing at 23 C. It should be noticed that the 28 days curing period can not ensure the advanced degree of cement hydration and fly ash reaction. Especially, in the case of fly ash blended concrete, the pozzolanic reaction of fly ash can proceed continuously until one year. So the densification of microstructure of specimens will occur during the following chloride penetration test. In the chloride penetration test, all surfaces of the concrete specimens except top and bottom sides were sealed by epoxy resin so that the chloride penetration can occur only in one-direction. The solution was replenished every week to maintain uniform concentration, even though the reservoir is large enough. After immersion period, the total (acid-soluble) chloride profiles were measured. By using the proposed model, the total chloride concentrations are predicted as a function of the distance from the outer concrete surface. As shown in Fig. 9, because of the consideration the dependence of chloride diffusivity and porosity on the age, my extension model can generally reproduce the experimental results. Contrastively, the analysis results from Papadakis’ original model are much lower than the experimental results. This is because of the ignorance of densification of microstructure of specimens during the chloride diffusion test. On the other hand, it should be noticed that the deviation degrees between Papadakis’ model results and experimental results vary with mixing proportions of concrete. In the case of fly ash blended concrete (Fig. 9b and c), the deviation degrees are much larger than that of Portland cement concrete (Fig. 9a). This is because the pozzolanic reaction of fly ash mainly occurs after 28 days, and the decreasing of chloride diffusivity and porosity of fly ash blended concrete is much larger than that of Portland cement concrete. Summarily, the original model is only valid for chloride diffusion in hardened concrete, while due to the combination of hydration model, the proposed extension model is valid for chloride diffusion in both hardened concrete and
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Fig. 8. The comparison between experimental results [3] and simulated results of chloride penetration profiles.
hardening concrete. Similarly with Papadakis’ report [2,3], the specimens incorporating fly ash exhibit lower total chloride content than the control specimen. The difference between experimental results and prediction results maybe come from the difference of reactivity of fly ash between Papadakis’ experiment [3] and Oh’s experiment [25]. The depassivation of steel bars takes place when molar concentration of dissolved Cl, [Cl(aq)], in their vicinity drops below
a certain percentage of the molar concentration of hydroxyls in the pore water, [OH]. The critical value of the [Cl(aq)]/OH] ratio which signals depassivation seems to be 0.3 [21]. The molar concentration of [OH] depends on the cation type and on whether concrete is carbonated or not. By using the proposed model, we can predict the chloride penetration/binding profiles and estimate the time required for the chloride concentration surrounding the reinforcement to increase over the threshold of depassivation of
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Fig. 9. The comparison between experimental results [25] and simulated results of chloride penetration profiles.
reinforcing bars. The protection measures against chloride induced depassivation of steel in concrete also can be achieved. The intrinsic contributions of this paper are shown as follows: First, Papadakis [2,3] proposed a series of models on the chemical reactions of fly ash blended concrete and chloride ingress into blended concrete. Papadakis’ model can be used to determine the stoichiometric ratio in the chemical reactions of fly ash blended concrete, such as the stoichiometric ratio of hydration of cement and the pozzolanic reaction of fly ash. However, until now Papadakis’ model does not consider the influences of water to binder ratio and fly ash replacement on the reactivity of fly ash. Comparatively, in this paper, the proposed hydration model can describe the increasing of reactivity of fly ash with an increase of water to binder ratio or with a reduction of the replacement level of mineral admixture. So the first intrinsic contribution of this paper is the improvement on the modeling of reactions of fly ash blended concrete. By using the hydration model, the evolution of properties of low-calcium fly ash blended concrete is predicted as a function of curing age and these properties are adopted as input parameters for the chloride penetration model. Second, this paper contributes on modeling the chloride diffusion and reaction in a hydrating concrete in presence of fly ash. Especially the case of modeling of chloride penetration in a concrete that simultaneously is being hydrated offers originality. Yoon [5], Han [6], Ishida’s [8] work can be used to model the simultaneous chloride diffusion & reaction in a hydrating Portland cement concrete. In the case of fly ash blended concrete, Yoon [5], Han [6],
Ishida’s [8] work is not valid currently. On the other hand, Song’s [7] work can model the chloride diffusion in hardened silica fume blended concrete. When chloride diffusion and reaction happen together, Song’s [7] work is not valid currently. So the second intrinsic contribution of this paper is on the modeling the chloride diffusion and reaction in a hydrating concrete in presence of fly ash. Third, the proposed model in this paper can be used to evaluate the evolution of degree of hydration of cement and degree of reaction of fly ash as a function of curing age. Based on the degree of hydration of cement and degree of reaction of fly ash, the contents of evaporable water, calcium hydroxide, and porosity of hardening fly ash blended concrete can be determined. Our former work has evaluated the mechanical properties material chemical properties and thermal factors of hardening fly ash blended concrete [26]. This paper focuses on the modeling chloride ingress into fly ash blended concrete. So the third intrinsic contribution of this paper is that we proposed an integrated model for evaluation both early-age properties and durability aspects for fly ash blended concrete. On the other hand, compared with low-calcium fly ash, highcalcium fly ash has higher free CaO and sulfur contents. It should be noticed that the proposed hydration model in this paper is only valid for low-calcium fly ash blended concrete. For high-calcium fly ash blended concrete, because of the coexistence of cement hydration, rapid free CaO reaction and the reaction of glass phase in high-calcium fly ash, the hydration of FH-cement blends is more complicated than that of FL-cement blends. The investigation of interaction mechanisms
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among cement hydration, rapid free CaO reaction and high-calcium fly ash glass phase reaction will be carried out in the further research. In addition, Papadakis’ previous research on the stoichiometry of highcalcium fly ash reaction is very valuable for the development of kinetic reaction model of FH-cement blends [27]. The chemical and volumetric compositions of FH concrete obtained from Papadakis’ model can be used for the evaluation of durability aspects of FH blended concrete, such as carbonation and chloride ingress [3]. 6. Conclusions In this paper, we proposed a numerical procedure to evaluate the chloride diffusion in low-calcium fly ash blended concrete. This numerical procedure consists of two sub models, i.e. a hydration model and a chloride diffusion model. First, based on the combination of Papadakis’ chemical-based steady-state model and the kinetic reaction mechanisms involved in cement hydration and the pozzolanic reaction, a kinetic model is proposed to describe the hydration process of FL-concrete. By considering the production of calcium hydroxide in cement hydration and its consumption in pozzolanic reaction, the pozzolanic reaction of FL is separated from cement hydration. The proposed model considers the dependence of pozzolanic activity on the mass of calcium hydroxide and the influence of FL on the hydration of Portland cement. The contents of evaporable water, calcium hydroxide, and porosity were obtained as companied results of the hydration model and were used as input parameters for evaluation of the penetration of chloride ion. Second, in the chloride diffusion model, the physicochemical processes of diffusion of chloride ion in the aqueous phase of pores, the adsorption and binding in the solid phase of concrete, and the desorption are described by a nonlinear partial differential equation. The prediction results on chloride penetration profiles generally agree with experimental results. Acknowledgment This study was supported by 2012 Research Grant from Kangwon National University. Nomenclature
aji
hydration degree of the mineral component in a given cement particle i mineral component of cement j number of cement particles t time stoichiometric ratio by the mass of water to mineral vi component physically bound water wag ri density of the anhydrate cement mineral component reaction coefficient in a dormant period kd radius of anhydrate cement particles r0j effective diffusion coefficient of water in the cement Dei hydration product coefficient of reaction rate for each mineral component kri rw density of water B and C reaction coefficients in a dormant period initial diffusion coefficient Dei0 mass fraction in mineral components gi mass fraction of individual particle in cement gj n total number of cement particles in a cell space a degree of hydration of cement freesurface/totalsurface ratio between the free surface area and the total surface area water mass in a mixing proportion w0
Ce0 cement mass in a mixing proportion fS,P and fA,P mass fraction of S and A in fly ash gS and gA active (glass) part of S and A aglass reacted degree of active (glass) part of fly ash P fly ash mass in a mixing proportion chemically bound water of fly ash. mH2O mCH(t) calcium hydroxide mass in the hydrating cement-fly ash blends stoichiometry ratio by mass of CH to low-calcium fly ash vFL radius of low-calcium fly ash particle rFL0 rFL density of fly ash reaction rate coefficients of fly ash in a dormant period kdFL BFL and CFL reaction coefficients of fly ash in a dormant period initial diffusion coefficient of fly ash DeFL0 reaction rate coefficient of fly ash krFL aflyash reacted ratio of the fly ash mass of capillary water wcap D3 h porosity reduction due to hydration of Portland cement D3 p porosity reduction due to the pozzolanic activity 3 porosity [Cle(aq)] Cl concentration in the aqueous phase [Cle(s)] Cl bound in the solid phase x distance from the concrete surface intrinsic effective diffusivity of chloride ion in concrete D e,Cl equilibrium constant for chloride binding Keq [Cl(s)]satsaturation concentration of chloride ion in the solid phase rc density of cement k efficiency factor of the low-calcium fly ash for chloride penetration 3 eff effective porosity for diffusion References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
[19]
[20] [21]
[22] [23] [24] [25] [26] [27]
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