Validated hydration model for slag-blended cement based on calorimetry measurements

Cement and Concrete Research 128 (2020) 105950

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Validated hydration model for slag-blended cement based on calorimetry measurements

T

Markus Königsberger*, Jérôme Carette BATir Department, ULB-Université libre de Bruxelles CP194/4, 87 Avenue A. Buyl, Brussels 1050, Belgium

ARTICLE INFO

ABSTRACT

Keywords: Hydration Granulated blast-furnace slag Blended cement Modeling Calcium-silicate-hydrate (C-S-H)

Modeling of the complex interlinked chemical reactions involved in the hydration process of slag-blended cement is rather challenging, in particular since accurate prediction of the hydration kinetics of clinker and slag hydration, respectively, is still out of reach. To overcome this challenge, we propose a hybrid modeling approach based on calorimetry measurements combined with state-of-the-art hydration models. The model features intrinsic C-(A)-S-H nanoparticles related to clinker and slag hydration, respectively, with precipitation spacedependent densities of the corresponding gel phases. Successful validation against published experimental data, obtained on 54 different mixes in 7 different laboratories, proves the model's applicability and corroborates that C-(A)-S-H gel densifies progressively during hydration, that portlandite consumption upon slag reaction is caused by the precipitation of calcium-aluminate hydrates and that the ultimate heat of slag depends significantly on its chemical composition.

1. Introduction Ground granulated blast-furnace slag (BFS), accompanied with mineral fillers like limestone or quartz, are widely used in blended cementitious materials as partial replacement of ordinary Portland cement (OPC) clinker. Their increased popularity stems from aspiration towards a more sustainable and environmentally-friendly construction sector, since the cement production accounts for approximately 8% of the anthropogenic global CO2 emissions [1], while slag is an industrial by-product. Slag-blended cementitious materials ultimately provide materials with comparable mechanical properties [2] and even improved chemical resistance [3, 4]. However, at early material ages, the hydration reaction is less advanced, accompanied with significantly higher porosity and with reduced strength and stiffness as compared to OPC systems [5-9]. The slow overall hydration process of slag-blended cements [10-12] results from the reduced reactivity of BFS as compared to OPC [2]. BFS particles mixed with OPC react only after activation due to the release of alkalis from the clinker reaction [3]. The hydraulic reactions of both cement clinker and slag occur simultaneously and under mutual influence [13, 14], yielding a very complex assemblage of different hydration products. Since slag contains typically less calcium than cement clinker [15], the calcium-silicate-hydrates (C-S-H), the most abundant hydration products, exhibit a smaller calcium-to-silicate ratio (C/S ratio) in slag-blended systems as compared to OPC systems [13]. C-S-H

∗

with low C/S, in turn, incorporates considerable amounts of alumina into the silicate chains [16, 15], facilitated by the relative high alumina contents of typical slags. As for the amount of water which is chemically bound inside the C-S-H nanoparticle or physically adsorbed in nanoscopic gel pores, experimental insight is still very limited [17]. Using small angle neutron scattering techniques, Thomas et al. [18] conclude that the C-S-H nanoparticle exhibits significantly lower water content and a slightly increased density, as compared to OPC pastes. Apart from C-S-H, nature and volumetric dosage of other hydration products does also change when using BFS-blended cements. Portlandite, produced from the hydration of cement clinker, is partly consumed during the hydration of BFS, as shown by the reduced portlandite content in mature slag-blended mixes [19, 20]. Moreover, talcite-like hydration products precipitate in slag-blended systems due to the high magnesia content of typical BFS [14, 15], but are absent in OPC systems. In order to better understand and predict the phase assemblage of hydration products, the development of their volume fractions, and their influence on the material properties of blended cement paste systems, in particular within the crucial period of early material ages, hydration models have been proven indispensable. They complement experimental investigations which typically require complex and time-consuming techniques and can never cover all possible mix composition and all material ages of interest. As for pure OPC systems, Powers and Brownyard [21] published already in the 1940s an experimentally validated set of equations for

Corresponding author. E-mail address: [email protected] (M. Königsberger).

https://doi.org/10.1016/j.cemconres.2019.105950 Received 12 April 2019; Received in revised form 14 November 2019; Accepted 21 November 2019 0008-8846/ © 2019 Elsevier Ltd. All rights reserved.

Cement and Concrete Research 128 (2020) 105950

M. Königsberger and J. Carette

estimating the phase volume evolutions as function of the hydration degrees. Even in recent modeling campaigns, it provides a sound basis for modeling activities designed for prediction of early age material properties of cementitious materials [22, 23]. As for slag-blended systems, Chen and Brouwers [14] proposed stoichiometric reaction models of slag-blended cement paste, which allow for predicting the chemical composition and volume balance of the hydration products at mature ages. Several multiphase hydration models for slag-blended systems have been developed during the last decade [24-27] which use similar or slightly modified stoichiometric equations in combination with kinetic models of clinker and slag. Meinhard and Lackner [24] successfully reproduce the heat of hydration of mixes with different contents of slag adopting the Avrami equation together with an exponential decay to describe the slag reaction kinetics. Wang et al. [25] divided the slag reaction into three kinetic stages (dormant period, boundary reaction, and diffusion) and showed that, after calibration, the model agrees very well with experimentally measured mass fraction evolutions of clinker phases, slag, and hydration products. An empirical law for the hydration kinetics was used by Merzouki et al. [27] to model the chemical shrinkage. Kolani et al. [26] incorporate the effects of the water content and temperature exchange on the hydration rate, and thereby, very successfully model the volume evolutions of portlandite and unreacted slag. Despite intensive efforts, validation of the kinetic models against independent experimental data, beyond the compositions the model was designed for, is still very challenging. Thermodynamics-based hydration models for blended cements [28, 15, 29] are a very interesting alternative to avoid the calibration of kinetic laws, but their predictive capabilities are still limited. In order to overcome the inherent difficulties related to the prediction of the slag hydration kinetics, we aim for developing a modeling approach which rests on experimental insights from calorimetry tests regarding the early-age kinetics. Isothermal calorimetry (IC) experiments are considered as the basis, given that this technique is accurate, robust and provides continuous measurement results up to material ages of several days [30]. To decouple the total heat release into the individual contribution of cement and slag, respectively, we follow De Schutter and Taerwe [31] and use a reference mix without slag as baseline. This allows for establishing the link between material age and hydration degree of both slag and clinker. From the days-long IC measurements, we extrapolate to mature ages of up to several years by using simple kinetic models for clinker and slag available in the literature as well as by considering an empirical relation for the ultimate hydration degree. This experimentally-supported kinetics model is complemented with hypotheses regarding the hydrates' chemical composition and their physical properties. We particularly account for recent insights into the chemo-physical structure of C-S-H based on nuclear magnetic

resonance relaxometry [32], and by considering that C-S-H progressively densifies during the hydration reaction. This way, we aim for predicting the volume evolutions of reactants (clinker and slag) and the main products involved in the reaction processes (e.g. C-S-H, portlandite, ettringite), as well as the extent of the limestone filler reactivity. The remainder of the paper is structured as follows. Section 2 refers to model development. First the main hydration mechanisms of slagblended pastes are discussed and stoichiometric equations are formulated based on the composition of reactants and products (Section 2.1). This is followed by the development of the hydration kinetics model which consists of a decoupling and an extrapolation procedure for calorimetry measurements (Section 2.2). Mass and volume balance considerations allow for quantifying temporal evolution of phase mass and volume fractions (Section 2.3). The model development is completed by discussing the chemical composition of C-(A)S-H and the experimentally supported C-S-H densification rule (Section 2.4). In Section 3, the model is challenged by a large set of experimental data available in the literature, consisting of 54 different mix compositions prepared with 15 different clinker compositions, 13 blast furnace slags, tested in a total of 7 laboratories. These experiments are first summarized (Section 3.1) and then compared to the model (Section 3.2). The comprehensive experimental validation further allows us to profoundly discuss several model assumptions (Section 4). Finally, the paper is closed by concluding remarks (Section 5). 2. Model development 2.1. Hydration mechanisms The development of a hydration model requires consideration of a specific reaction chemistry, for which we use the standard abbrevia¯ = CO2, F = Fe2O3,H = H2O,M = MgO,S tions: A = Al2O3,C = CaO, C = SiO2 and S¯ = SO3. The model developed herein considers the interlinked hydration equations of the reactions of the four clinker phases and the slag reaction, as shortly summarized next. Additional assumptions necessary for stoichiometric balance and full details on the molar coefficients of all phases are presented in Appendix A. The hydration of C3S and C2S with water yields portlandite (CH) and C-S-H. Aluminate is incorporated into C-S-H, resulting in clinkerrelated C − A − S − H products (denoted CASHc), as long as either of the aluminate clinker phase, C3A or C4AF, is available (see reactions 1a and 2a in Table 1). In case no aluminate reactants are left, further C3S and C2S reaction yields CSH without aluminum substitution as well as

Table 1 Hydration mechanisms. # …condition

reactants→ products

C3S

1a…C3A > 0 ∨ C4AF > 0 1b…C3A=C4AF=0

C3S, C3A, C4AF, C, M, H → CASHc, CH, FH3, MH C3S, C, M, H →CSH, CH, MH

C2S

2a …C3A > 0 ∨ C4AF > 0 2b…C3A=C4AF=0

C2S, C3A,C4AF, H →C − A − S − Hc, CH, FH3 C2S, H →CSH, CH

C3A

C4AF

Slag

3a…CS¯>0 3b…CS¯ =0 ∧ CC¯ =0 ∧ C6AS¯3 H32 > 0 3c…CS¯ =0 ∧ CC¯ =0 ∧ C6AS¯3 H32=0 3d…CS¯ =0 ∧ CC¯ > 0

C3A, CS¯ , H →C6AS¯3 H32 C3A, C6AS¯3 H32, H → C4AS¯ H4 C3A, CH, H → C4AH13 C3A, CC¯ , H → C4AC¯ H11

4a…CS¯ > 0 4b…CS¯ =0 ∧ CC¯ =0 ∧ C6AS¯3 H32 > 0 4c…CS¯ =0 ∧ CC¯ =0 ∧ C6AS¯3 H32=0 4d…CS¯ =0 ∧ CC¯ > 0

C4AF, CS¯ , H →C6AS¯3 H32,FH3,CH C4AF, C6AS¯3 H32, H → C4AS¯ H4, FH3 C4AF, CH, H → C4AH13, FH3 C4AF, CC¯ , H →C4AC¯ H11, FH3

5a…CS¯ > 0 5b…CS¯ =0

Slag, CS¯ , CH, H →C − A − S − Hs, M6AH13, C6AS¯3 H32, MH, S¯ Slag, CH, H →equal to 5a, but including C4AH13

2

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CH (reactions 1b and 2b). Potentially available free c or free M is considered to react to CH and brucite (MH). C3A and C4AF phases form ettringite (C6AS¯3 H32) in case sulfate—in form of anhydrite (CS¯)—is left in the mix (reactions 3a and 4a). Additionally, C4AF is considered to form iron hydroxide FH3, as suggested earlier [33, 12], and small amounts of portlandite. If all sulfate is consumed, the reactions switch to monosulfoaluminate (C4AS¯ H12) production at the expense of the previously formed ettringite (reactions 3b and 4b). If, in turn, all the ettringite is consumed, an hydroxy-AFm phase (tetracalcium aluminate13-hydrate, C4AH13) forms and portlandite is consumed (reactions 3c and 4c). Notably, we consider that potentially available calcite CC¯ , often present as limestone in the cement or added to blend the mix, is reacting with the aluminate clinker phases to form mono¯ H11) and thus stabilizing the ettringite (reactions carboaluminate (C4AC 3d and 4d). As for the slag reaction, we consider that the main five oxides of blast-furnace slag, namely C, S, A, M, and S¯ , react to C-A-S-H products (denoted CASHs) and potentially to the following products: hydrotalcite (M6AH13), ettringite (C6AS¯3 H32), hydroxy-AFm (C4AH13) or brucite (MH), with potentially free sulfate (S¯ ). Alumina from slag is partly incorporated into the C-(A)-S-H structure. If A is left, formation of hydrotalcite is preferred. Provided that sulfates (in form of anhydrite) are still present in the mix (reaction 5a), and that all magnesia from the slag has been consumed for the hydrotalcite formation, additional A is considered to form ettringite. If no anhydrite is available in the mix (reaction 5b), ettringite production is limited by the sulfate content of the slag, and potentially available excess aluminum reacts to hydroxyAFm. If extra M is available after all other hydrates are formed, it precipitates as MH. As commonly done in hydration modeling [14, 24], other phases which might be present in small quantities, such as strätlingite, are not considered herein.

Moreover, the water-to-solid ratio and the gypsum-to-cement ratio of slag-blended and reference mix must be identical. Notably, in case significant amounts of filler are included in the mix such that they induce a change in the hydration kinetics, the reference composition should therefore also contain this filler. The applicability of the superposition principle for slag-blended clinker was initially observed by means of isothermal calorimetry tests by De Schutter and Taerwe [31]. The approach has not only been successfully used in later works [24], but also verified by successive quantitative XRD by Kocaba et al. [12], despite slight differences in particle size, water-to-solid ratio, and/or gypsum content. The hydration degrees of clinker ξc and slag ξs can then be computed from the decoupled heat release as i (t )

We herein aim for adding a time scale to the reaction mechanisms presented in Table 1, i.e. we aim for quantification of the reaction kinetics. Therefore, we introduce the phase hydration degrees ξi(t), defined as the amount of already reacted phase i divided by its initial amount. Corresponding to the five hydration mechanisms 1–5 according to Table 1, the hydration degrees ξi are defined for the four clinker phases and for slag, i ∈{C3S,C2S,C3A,C4AF,s}. In addition, we define the clinker hydration degree ξc as

=

i

mi (t = 0) × mi (t = 0) i

i (t )

,

i

{C3 S, C2 S, C3 A, C4 AF }

.

Qi (t ) Qi,

i

{c , s }

t

tIC ,

(2)

whereby tIC is the duration of IC measurements but maximal 7 d, since at later ages, the extrapolation method described hereafter is considered to be more realistic than actual measurement of the heat flow by IC. Qi,∞ in Eq. (2) refers to the ultimate heat of hydration of the compound. For clinker, this is computed by adding the contribution of its four phases, considering values of ultimate heat of hydration of 517 J/g for C3S, 262 J/g for C2S, 1144 J/g for C3A, and 725 J/g for C4AF [34]. For slag, in turn, studies on the ultimate heat of hydration are rare. Interestingly, ultimate heats for magnesia-rich slags [35, 36] were reported to be considerably higher than ultimate heats for slags exhibiting small magnesia contents [37]. We estimate the ultimate heat of slag as linear function of the magnesia content: Qs, = A × mMs + B , whereby mMs denotes the mass fraction of magnesia in slag and A = 8526 J and B = −241 J/g are obtained from fitting the slag hydration degrees based on the gathered experimental data reported in Section 3. In order to (i) decouple clinker reactions into phase reaction degrees of C3S, C2S, C3A and C4AF, as well as to (ii) extrapolate beyond the time IC measurements are trustworthy and feasible, hydration kinetics models are required. The hydration degree of the four clinker phases is customarily estimated based on three successive chemo-physical processes: induction, nucleation and growth and diffusion [38]. As for the slag hydration degree, in turn, we adopt the dispersion model of Knudsen [39], as typically done for slag hydration modeling [27]. Full details on the corresponding mathematical expressions for both the clinker and the slag hydration models are given in Appendix 2.2. These kinetics models provide blind predictions of phase hydration degrees, labelled herein as i* (t ) . Enriching the blind predictions with IC measurements then provides access to IC-based predictions of phase hydration degrees ξi(t), as described next. For the early stage t ≤ tIC IC-based predictions of phase hydration degrees follow from enforcing that the total predicted hydration degree c* (t ), obtained from Eq. (1), matches the IC-based (total) hydration degree. For t > tIC, a linear extrapolation of i* up to ultimate degrees ξi,∞ is used, as illustrated in Fig. 1. The corresponding extrapolated phase hydration degrees read as

2.2. Hydration kinetics based on calorimetry measurements

c (t )

=

(1)

The quantification of ξc(t) and ξs(t) at early ages is based on isothermal calorimetry (IC) measurements and analytical formulas for hydration kinetics, as discussed next. Notably, all considerations refer to a constant temperature of 20 °C. IC experiments provide access to the temporal evolution of cumulative heat release Q(t). In order to separate Q into the contribution of cement (Qc) and slag (Qs), respectively, we use the superposition principle [31]. It implies that Q(t) = Qc(t) + Qs(t), whereby the clinkerrelated heat release Qc is determined based on a reference composition without slag. The measured heat release of this reference composition, Qref, results from the clinker hydration only, Qref (t ) = Qcref (t ) × mcref , with mcref denoting the mass fraction of clinker in the reference mix. The clinker-related heat release in the slag-blended mix is proportional to the heat release in the reference mix, Qc (t ) = Qcref (t ) × mc / mcref . The slag-related heat release then follows from Qs(t) = Q(t) − Qc(t). This approach rests on the hypotheses that hydrates precipitate (i) in the same fashion and (ii) at the same rate on either surface, being it the surface of unhydrated clinker or slag particles, other hydrates, or any other filler material; and that the surface area of all initially available particles is identical, i.e. they must be ground to the same size.

i,

i (t )=

1 i

i (tIC )

* i (tIC )

[ i* (t )

1] +

i,

{C3 S, C2 S, C3 A, C4 AF , s}

, t > tIC

.

(3)

The ultimate phase hydration degrees ξi,∞, in turn, follow from an empirical relation developed by Lin and Meyer [40], as detailed in Appendix 2.2. 2.3. Mass and volume balance Next, mass fractions of reactants and products are derived. The derivation is based on the phase hydration degrees ξi(t) from Eqs. (1)– (3) and on stoichiometric considerations presented in Section 2.1 and mathematized in Appendix A. The change in mass dmi of any phase i at 3

Cement and Concrete Research 128 (2020) 105950

M. Königsberger and J. Carette

Table 2 Mass densities and molar masses of reactants and products Phase name

Abbreviation

Mass density ρi [g/cm3]

Molar mass Mi [g/mol]

Alite Blite Celite Delite Anhydrite

C3S C2S C3A C4AF CS¯ CC¯

3.15 3.27 3.03 3.71 2.97

228.3 172.2 270.2 486.0 136.1

Cinker filler Slag filler Water#

cfill sfill H

2.73† 2.70–2.93‡ 1.00

18.01

Solid C-S-H Solid C-A-S-Hc° Solid C-A-S-Hs° Portlandite Ettringite Monosulfoaluminate Monocarboaluminate

C1.7SH1.875 C1.875A0.042SH1.8 C C / Ss A A/ Ss SH0.97 CH C6AS¯3 H32 C4AS¯ H12

2.60 2.60 2.73 2.25 1.78 2.01 2.18

193.4 195.10 vary 74.09 1255 622.5 584.4

Calcite (limestone) Quartz Free lime Free magnesia Slag*

Fig. 1. Extrapolation of phase hydration degrees between IC measurements and ultimate hydration degrees.

time t involved in the reaction can be written as

dm i (t ) dt

d

+ j

d

= Mi j

j

dt

(t )

mj (t = 0) Mj

dt

(t )

mj (t = 0) Mj

ni

ni j

j

{C3 S , C2 S, C3 A, C4 AF , s}

. (4)

whereby Mi denotes the molar mass of phase i, given in Table 2, and whereby ni j are the molar coefficients of phase i in reaction equations 1a–5b corresponding to the main reaction product j according to Appendix A. The current mass of a phase at any time t can then be computed by means of integration as

mi (t ) = mi (t = 0) +

t 0

d mi ( )d dt

2.71 [42] 2.65 [43] 3.35 [43] 3.58 [43] 2.70-2.93

2.04 1.95 2.37 3.00 1.92

[44] [44] [18] [42] [42] [42] [42] [42] [42] [42] [33] [43]

116.1 56.08 40.30 vary

560.5 577.9 58.31 213.7 80.06

* Slag properties vary, see Table 3 for details on the mass composition of each slag. † Considered identical to density of limestone. ‡ Considered identical to density of slag. # Water is further separated in capillary and and gel water, abbreviated cH and gH; moreover, all solid C-(A)-S-H and gel water is summarized to a single C-(A)S-H gel phase with varying density and composition. ° Changes in alumina incorporation into the C-(A)-S-H is assumed not to change its density [17].

i reactive

j

C4AC¯ H11 C4AH13 M6AH13 MH FH3 S¯

Hydroxy-AFm Hydrotalcite Brucite Iron hydroxide Free sulfate

i product j

Q C M C C / Ssl SA A/ Ssl M M / Ssl S¯ S¯ / Ssl

[41] [41] [42] [42] [42]

design nor with age. We note that the C/S and A/S ratios of the C-(A)-SH gel (which is typically assessed experimentally) are the mass average of the ratios of all three individual building blocks and therefore do change with mix design and with age, since the mass fractions change. CASHc as well as the part of CSH which results from the calcium silicate reaction of clinker with water (reactions 1a–2b in Table 1), are considered to exhibit a molar C/(A+S) ratio amounting to 1.8, following results from scanning electron microscope and energy dispersive spectrometer experiments on ordinary Portland cement paste [46]. Molar C/S ratios, in turn, are determined on this basis, as described next. The C/S ratio of aluminate-free CSH is equal to its C/(A+S) ratio and amounts to 1.8. To quantify the replacement of S by A in the CASHc, we refer to the electron-microscopic studies of Richardson and co-workers [16, 47]. They concluded that the molar A/S ratio of C − A − S − H does linearly decrease with increasing C/S ratio:

(5)

Translation of phase mass fractions mi(t) to phase volumes Vi(t) follows from Vi(t) = mi(t)/ρi(t), whereby ρi denotes the phase mass density. We assume that all reactants and all solid hydrate phases exhibit material-intrinsic, constant densities, see Table 2. Notably, the C(A)-S-H gel phases densify when hydration proceeds, as discussed in the next subsection. We follow the classical assumption of Powers and Brownyard [21] and consider that the total volume of the mix does not change with hydration, Vtot(t) = ∑ iVi(t = 0) is constant (the sum over i comprises all phases listed in Table 2). Shrinkage-induced air voids fill the remaining volume, Vair(t) = Vtot −∑ iVi(t). Phase volume fractions vi(t), finally, read as vi(t) = Vi(t)/Vtot. 2.4. Composition and density of C-(A)-S-H phases

A/ S = 0.2113

0.0904 × C /S

(6)

.

Rewriting the definition of the C/(A+S) ratio and specifying the A/S according to Richardson's Eq. (6) yield the sought C/S ratio of CASHc, denoted C/Sc, reading as

While the chemical composition and density of all crystalline hydration products are intrinsic and well documented in the literature, see Table 2, we herein discuss the properties of the amorphous C-(A)-S-H phases to complete the model development. Therefore, we clearly differentiate between solid C-(A)-S-H phases, referring to the nanoparticles with interlayer water, and C-(A)-S-H gel phases, referring to the solid C(A)-S-H and the surrounding gel water which is physically adsorbed to the nanoparticle [45]. In our model, we distinguish three solid C-(A)-SH building blocks introduced in Section 2.1: CASHc and CSH from the clinker reaction, and CASHs from the slag reaction. Each of these building blocks is considered to exhibit intrinsic molar C/S and A/S ratios, respectively, i.e. they are assumed to neither change with mix

C /(S + A) =

C /S 1 + A/ S

= 1.875

,

C / Sc =

1.2113 × C /(A + S )c 1 + 0.0904 × C /(A + S )c (7)

and the sought A/S of clinker-related CASHc which amounts to A/ Sc = 0.042. The C/S ratio of CASHs resulting from the slag hydration (reactions 5a and 5b), is significantly lower than the one related to clinker reaction [48, 20, 7]. We consider that the C/S ratio of slagrelated CASHs, denoted C/Ss, and the C/S ratio of the slag itself, 4

Cement and Concrete Research 128 (2020) 105950

M. Königsberger and J. Carette

denoted C/Ssl, are identical:

C /Ss = C / Ssl

(8)

.

By analogy to clinker-related CASHc, the A/Ss ratio of slag-related CASHs is considered to be a linear function of the C/Ss ratio, according to Eq. (6). To ensure stoichiometric balance of slag reactions 5a and 5b, we additionally assume that the CASHc -related A/Ss ratio cannot be larger than the slag-related A/Ssl ratio. These two assumptions lead to

A/ Ss = min {0.2113

0.0904 × C / Ssl; A/ Ssl}

(9)

.

Next, we discuss the amount of interlayer water in three solid C-(A)S-H phases, i.e. the H/S ratio, and their density. Combining different small angle scattering techniques, Allen et al. [45] quantified that the H/S ratio of C-(A)-S-H in plain Portland cement paste amounts to 1.8 and its density amounts to 2.60 g/cm3. By using similar experimental techniques, Thomas et al. [18] quantified that H/S=0.97 for CASHs in alkali-activated slag, and that its density amounts to 2.73 g/cm3. Herein, we apply these values for our blended cements and consider them to be intrinsic (composition- and age-independent). However, the amount of gel water which is physically adsorbed to a single solid C(A)-S-H nanoparticles, typically decreases during hydration [49, 50], resulting in an increase of the C-(A)-S-H gel density, as discussed next. Therefore, we first focus on plain cement paste without slag. NMR relaxometry measurements on white cement pastes at temperatures of 20°C, performed by Muller et al. [51, 49], have shown that the C-(A)-SH gel phases densify during hydration. The NMR-evidenced gel densification can be numerically realized by considering a single physical quantitity, the so-called specific precipitation space γ, defined as [50]

vH vsCASH + v H

=

,

0

1

,

Fig. 2. C-(A)-S-H gel density ρgel as function of the specific precipitation space γ: experimental points from NMR relaxometry of [32] for slag-blended cement paste exhibiting w/c = 0.40 (red circles) and pure white cement pastes (black crosses) exhibiting w/c ∈{0.32,0.40,0.48}; and modeled density evolution from Eq. (12) according to [50].

gel. Next, we discuss whether the observed densification law also applies to blended cement pastes. We therefore rely again on NMR relaxometry results of Muller [32], who studied cement-slag-quartz mixes at ages of 28 days. The studied pastes exhibit a water-to-solid ratio of 0.4 and 60% of the solid was cement clinker. Blast-furnace slag was added with contents of 0, 10, 20, 30, 40%, respectively; the rest was inert quartz. Again, the study was conducted at 20°C. The experimentally measured relaxation times were translated to C-(A)-S-H gel densities and specific precipitation spaces γ by analogy to the procedure described in [50]. For all five tested mixes, the inferred gel density agrees very well with the mathematical densification rule (12). This corroborates its validity for cement pastes blended with slag and quartz and provides strong motivation to use the densification rule in our novel hydration model. Finally, the sought volume fraction of the gel water, vgH, follows from combination of the numerical gel densification rule (12) and the gel density definition (11). Capillary water, in turn, comprises the remaining water: vcH = vH-vgH, whereby the total water volume fraction vH is known from stoichiometric equations.

(10)

whereby vH denotes the volumes occupied by gel and capillary water (vH = vgH+vcH) and vsCASH denotes the volume of all solid C-(A)-S-H (vsCASH = vC−A−S−Hc+vCSH+vC−A−S−Hs). The NMR-measured C-(A)-SH gel density ρgel, defined as gel

=

sCASH

vsCASH +

H

vg H

vsCASH + vg H

,

(11)

was found to be a universal function of the specific precipitation space and reads as [50]

gel sCASH

=

1 10.98 2 + 35.73 3.51 2 + 278.1 1

1

0.942 , 24.24 0.942 > > 0.426 268.3 H

sCASH

0.426

,

,

(12)

3. Model validation

with ρsCASH = 2.60, see Fig. 2 for an illustration. Very remarkably, the C-(A)-S-H gel density ρgel is independent of the paste's water-to-cement ratio, as experimental points in Fig. 2 refer to three different compositions exhibiting w/c ∈{0.32,0.4,0.48}. The densification rule comprises three characteristic precipitation regimes [50], see Fig. 2, starting from the right-hand side:

3.1. Experimental dataset For validation of the hydration model developed in Section 2, nine experimental studies [7-9, 11, 52-56] from seven different laboratories are considered. This way, the model will be challenged by in total 54 different mix compositions, see Table 3, exhibiting water-to-binder ratios w/b ranging from 0.35 to 0.58 (note that water within potentially added gypsum is included here), with slag-to-binder ratios s/b up to 82%, anhydrite-to-binder ratios CS¯ / b up to 8.5%, small amounts of free M and free C (expressed as mass ratios C/b and M/b), limestone-tobinder ratios CC¯ / b up to 41%, and inert-to-binder ratios up to 51% (whereby inert comprises quartz addition as well as non-reactive filler in cement and slag). The studies of Carette and co-workers [52, 57, 58] include two mixes of plain cement paste with w/b ∈{0.41,0.58} and three blended pastes (where cement is replaced by either only slag or only limestone, or by both), see compositions C1–C5 in Table 3. Three plain cements using three chemically different cements and six blended cement mixes using two slags (including a high-aluminum slag, and a C4AF-free cement) were studied by Kocaba and co-workers [53, 12],

• In regime I (1 ≥ γ ≥ 0.942), C-(A)-S-H appears in the form of compact solid precipitates which do not contain any (gel) porosity. • In regime II (0.942 > γ > 0.426), C-(A)-S-H precipitates as nano-

•

porous gel containing gel pores; the corresponding gel density of all gel formed in regime II increases linearly with decreasing precipitation space, see Königsberger et al. [50] for details. This process is accompanied by a progressive reduction of the satured (i.e. waterfilled) capillary porosity, as the latter provides water for the hydration process. Once all capillary water is consumed, hydration regime III (0.426 ≥ γ ≥ 0) starts. Further hydration occurs at the expense of the water in the gel pores. This leads to a further densification of the C-(A)-S-H 5

Cement and Concrete Research 128 (2020) 105950

M. Königsberger and J. Carette

Table 3 Mass fractions in percent (binder-related, clinker-related, and slag-related) for the compositions used for validation. Study

Binder-related mass fractions [%]

Clinker-related [%]

Slag-related [%]

Ref

#

w/b

cl/b

s/b

CS¯ /b

M/b

C/b

CC¯ /b

i/b

C3S

C2S

C3A

C4AF

C

S

A

M

S¯

[52]

C1 C2 C3 C4 C5

40.5 41.7 41.1 41.7 57.6

89.6 22.6 60.8 22.6 89.6

0 66.7 0 37.9 0

5.7 5.7 5.8 5.7 5.7

0.9 0.2 0.6 0.2 0.9

1.4 0.4 0.9 0.4 1.4

2.0 0.5 31.0 30.3 2

0.3 4.0 0.8 2.9 0.3

67.6 67.6 67.6 67.6 67.6

13.4 13.4 13.4 13.4 13.4

8.6 8.6 8.6 8.6 8.6

10.4 10.4 10.4 10.4 10.4

41.5 41.5 -

33.3 33.3 -

12.5 12.5 -

7.0 7.0 -

0.2 0.2 -

[53]

K1 K2 K3 K4 K5 K6 K7 K8 K9

40.0 41.4 41.4 40.3 41.6 42.2 40.3 41.6 42.2

96.3 57.8 57.8 91.1 54.6 54.6 95.1 57 57

0 39.1 37.9 0 39.2 38.0 0 39.2 38.0

3.4 2.5 3.4 5.6 3.8 4.7 4.1 2.9 3.8

0 0 0 1.8 1.1 1.1 0.7 0.4 0.4

0 0 0 1.5 0.9 0.9 0 0 0

0 0 0 0 0 0 0 0 0

0.3 0.7 0.9 0 0.5 0.7 0.1 0.5 0.8

71.7 71.7 71.7 54.1 54.1 54.1 65.3 65.3 65.3

24.3 24.3 24.3 26.1 26.1 26.1 17.8 17.8 17.8

4.0 4.0 4.0 6.0 6.0 6.0 7.1 7.1 7.1

0 0 0 13.7 13.7 13.7 9.8 9.8 9.8

41.1 31.1 41.1 31.1 41.1 31.1

36.6 34.6 36.6 34.6 36.6 34.6

12.2 20.0 12.2 20.0 12.2 20.0

7.8 9.2 7.8 9.2 7.8 9.2

0 0 0 0 0 0

[54]

B1 B2 B3 B4 B5 B6 B7 B8 B9

50.0 50.9 50.4 50.2 50.1 50.1 50.8 50.2 50.2

81.1 67.7 55.4 75.3 46.6 18.6 85.4 48.3 17.1

0 0 0 13.5 45.7 72.0 5.6 43.9 72.8

8.5 7.4 7.0 8.3 4.1 5.2 8.4 4.6 5.8

1.5 1.2 1.0 1.3 0.8 0.3 0.7 0.4 0.1

2.1 0.8 0.5 0.8 0.5 0 0 0 0

5.9 22.8 35.9 0 0 0 0 0 0

0.9 0.2 0.2 0.9 2.2 3.8 0 2.8 4.1

62.1 62.7 60.5 62.2 61.6 73.7 58.5 60.6 64.9

19.2 16.5 18.5 20.1 20.2 11.3 24 23 19.3

7.0 7.0 7.2 6.4 6.4 4.3 0 0 0

11.6 13.8 13.8 11.3 11.8 10.8 17.5 16.4 15.8

45.0 45.0 45.0 45.0 45.0 45.0

34.4 34.4 34.4 34.4 34.4 34.4

10.2 10.2 10.2 10.2 10.2 10.2

6.0 6.0 6.0 6.0 6.0 6.0

0 0 0 0 0 0

H1 H2 H3 H4

51.5 55.1 54.6 52.9

94.2 56.2 55.3 53.8

0 0 0 42.9

5.9 3.5 3.4 3.3

0 0 0 0

0 0 0 0

0 0 41.3 0

0 40.4 0 0

60.7 60.7 60.7 60.7

22.1 22.1 22.1 22.1

6.3 6.3 6.3 6.3

10.9 10.9 10.9 10.9

42.3

35.8

11.2

8.3

2.0

G1 G2 G3 G4 G5 G6 G7 G8 G9 G10

50.0 50.0 50.0 50.0 50.0 50.0 50.0 50.0 50.0 50.0

88.1 88.6 90 44 44.3 45 13.2 13.3 13.5 62

0 0 0 47.7 47.2 48.2 81.0 80.3 82.0 28.3

5.2 5.2 5.7 2.6 2.6 2.8 0.8 0.8 0.9 3.7

0.9 1.0 0.9 0.4 0.5 0.4 0.1 0.2 0.1 0.7

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

5.9 5.1 3.5 5.3 5.4 3.5 4.9 5.5 3.5 5.3

67.8 75.5 66.7 67.8 75.5 66.7 67.8 75.5 66.7 75.5

10.2 3.6 9.9 10.2 3.6 9.9 10.2 3.6 9.9 3.6

8.9 7.2 8.8 8.9 7.2 8.8 8.9 7.2 8.8 7.2

13.1 13.7 14.6 13.1 13.7 14.6 13.1 13.7 14.6 13.7

40.4 42.6 41.2 40.4 42.6 41.2 42.6

34.4 33.9 36.4 34.4 33.9 36.4 33.9

11.4 8.9 9.8 11.4 8.9 9.8 8.9

7.6 7.4 7.4 7.6 7.4 7.4 7.4

1.7 1.6 1.6 1.7 1.6 1.6 1.6

P1 P2 P3 P4

45.0 45.0 35.0 35.0

88.4 66.3 88.4 66.3

0 24.3 0 24.3

4.8 3.6 4.8 3.6

3.4 2.6 3.4 2.6

0 0 0 0

0 0 0 0

3.4 3.3 3.4 3.3

60.7 60.7 60.7 60.7

20.4 20.4 20.4 20.4

10.3 10.3 10.3 10.3

8.6 8.6 8.6 8.6

38.0 38.0

37.5 37.5

7.8 7.8

10.7 10.7

3.2 3.2

W1 W2 W3 W4

50.3 50.2 50.2 50.2

88.9 53.3 53.3 51.5

0 38.0 39.0 38.0

4.3 2.6 2.6 5.5

2.2 1.3 1.3 1.3

0 0 0 0

3.7 2.2 2.2 2.1

0.9 2.6 1.6 1.6

68.8 68.8 68.8 68.8

13.4 13.4 13.4 13.4

8.5 8.5 8.5 8.5

9.4 9.4 9.4 9.4

38.2 38.5 38.5

39.8 34.4 34.4

7.4 12.3 12.3

7.6 9.6 9.6

1.8 2.6 2.6

A1 A2 A3 A4 A5 A6

50.0 50.0 50.0 50.0 50.0 50.0

45.8 44.7 44.8 45.2 45.2 45.2

0 0 45.9 37.1 37.1 27.8

2.5 4.7 4.7 4.7 4.7 4.7

0.5 0.5 0.5 0.5 0.5 0.5

0 0 0 0 0 0

3.4 3.3 2.1 10.1 2.3 19.1

47.8 46.8 2.1 2.1 10.2 2.1

65.8 65.8 65.8 65.8 65.8 65.8

16.2 16.2 16.2 16.2 16.2 16.2

10.4 10.4 10.4 10.4 10.4 10.4

7.6 7.6 7.6 7.6 7.6 7.6

41.8 41.8 41.8 41.8

34.9 34.9 34.9 34.9

11.6 11.6 11.6 11.6

5.8 5.8 5.8 5.8

3.1 3.1 3.1 3.1

D1 D2 D3

41.2 40.7 40.8

90.5 49.9 49.7

0 0 43.7

6.1 3.4 3.7

0 0 0

0 0 0

1.8 1.0 1.0

1.6 45.7 1.9

72.9 72.9 72.9

9.1 9.1 9.1

9.6 9.6 9.6

8.5 8.5 8.5

38.9

36.7

11.6

7.8

2.8

[8]

[55]

[11]

[7]

[56]

[9]

denoted as K1–K9 herein. Bourchy [54] also studied nine mixes, three of which are limestone blends ( B1–B3), the other six are slag blends ( B4–B9), whereby the mass fraction of the limestone or slag is varied. Notably, the clinker used for B6–B9 does not contain C4AF. Three blended cement binders, obtained by replacing 45% of cement volume either by finely ground fillers (quartz or limestone, respectively) or by slag, and one reference plain paste were studied by Hlobil et al. [8] and

are denoted H1–H4 herein. From the work of Gruyaert and coworkers [55; 59], we include 10 mixes, G1–G10, whereby three are plain Portland cement pastes, and the other seven are blended by different amounts of two types of slag. Pane and Hansen [11] studied four compositions with w/b ∈{0.35,0.45}, two plain Portland pastes (P1,P3) and two slag-blended pastes (P2,P4). Whittaker and co-workers [7, 60] studied one plain Portland paste (W1) and three blended mixes ( 6

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M. Königsberger and J. Carette

Table 4 Overview of experimental dataset used for validation of model predictions: entries are composed of the technique used (XRD, BSE, TGA, MIP, ChS, EDS, TEM), the range of ages measured (with h,d,m denoting hours, days, and months, respectively), and the number (#) of tests conducted per composition; validation is grouped into five categories: A refers to decoupling of IC, B to extrapolation of IC, C to mass fractions, D to volume fractions, and E to molar ratios of C-S-H phases In Fig.

C1–C5 [52, 57, 58]

K1–K9 [53, 12]

B1–B9 [54]

H1–H4 [8]

G1–G10 [59, 55]

P1–P4 [11]

W1–W4 [60, 7]

A1–A6 [56]

D1–D3 [61, 9]

XRD+BSE 12h7d#5 ✓ ✓ XRD+BSE 14d24m #6 ✓ TGA 2h-24 m #12

XRD 6h-3d #4-8 ✓ XRD 28 #1

-

-

XRD+BSE 1d-7d #2-3 ✓ ✓ XRD+BSE 14d12m #4-6 ✓ TGA* 1d-12 m #9

-

-

-

XRD+P 12h7d #0-4 ✓ ✓ XRD+P 12h7d #0-4 ✓ TGA* 1d-6 m #0-6 XRD 12h-6 m #0-8

XRD+P XRD+BSE 1d-7d #2 ✓ ✓ XRD+P XRD+BSE 1d-7d #2 ✓ -

-

BSE 2d #0-1 ✓ BSE 7d-28m #0-4 ✓ TGA 1d-33 m #1-11 -

-

XRD 6h28d #5-9 ✓ ✓

XRD 1d-3d #1-2 ✓ XRD 7d3 m #3 XRD 7d-3m #3 ✓ ✓

-

-

-

-

-

-

ChS -28d EDS 1d-6 m #3

MIP† 1d-6 m #0-6 EDS 6 m #0-1

A

mC3 S ,…

3

-

B

mcl msl mcl

3 3 4

-

C

msl mCH

4 5

mCS¯ mCC¯

5 5

TGA 3h28d #7-10 ✓ ✓

mC6 AS¯3 H32

5

-

-

✓

✓

vcpor+vair

6,10

-

-

-

-

BSE 2d-28 m #0-5 ✓

vprod vair C/S, C/A C/(S+A)

6 7 8,9

-

EDS/TEM 7d24 m #10

-

-

✓ -

D

E

mamorph vanh

5 6

-

-

✓ -

✓ -

TGA 6h8 m #9 -

-

-

XRD 1d-12m#0-6

MIP† 1d-12 m #6 EDS 1m-12 m #0-2

* Not used for validation since different TGA temperature range is used. † MIP provides the sum of the volume fraction of capillary pores and air voids and a part of the gel pore volume [62], therefore these results are not included in the validation but discussed in Section 4.1.

W2–W4) with approximately 40% of two types of slag, whereby additional sulfate was added to the last mix. The study of Adu-Amankwah et al. [56] comprises a plain Portland cement paste (A1), a quartz-blend paste (A2), a quartz-blended paste with additional anhydrite (A3), and three ternary slag cements with either limestone or quartz ( A4–A6). From the study of Durdzińsky and co-workers [9, 61] we include a plain cement paste (D1), a quartz-blended cement (D2), and a slag-blended cement (D3). Gathered experimental data are obtained by several experimental techniques which are used at different material ages, as summarized in Table 4 and in the following paragraph. All nine experimental campaigns report heat flow evolution with respect to hydration time from isothermal calorimetry (IC) measurements, conducted at 20°C. Given that heat flow decreases and thus that experimental errors accumulate with hydration time, we consider measurements within the first week to be reliable. IC-based cumulative total heat flows are the basis of the model, as they allow for the quantification of the reaction degrees of cement and slag as described in Section 2.2. As for the decoupling, we carefully select the following reference mixes: C5/C3 for C2/C4, K1/ K4/K7 for Kocaba's mixes according to the cement composition, H2 for Hlobil's slag mix, G1/G2/G3 for Gruyaert's mixes according to the cement composition, P1/P3 for P2/P4 (given the different w/c ratios), W1 for Whittaker's mixes, A1 for the mixes of Adu-Amankwah, and D2 for Durdzińsky's mix. Thermogravimetric analysis (TGA) results from five of the nine experimental studies [11, 52, 53, 55] are used for validation. Thereby, by means of differential analysis of the mass change due to loss of water bound to the hydrates, mass fractions of portlandite (mCH), anhydrite (mCS¯ ), and calcite (mCC¯ ), with respect to the total solid mass msolid, can be determined accurately, and are therefore used for validation, see Table 4 for details on which experimental data is used from which source. X-ray diffraction (XRD) measurements coupled with Rietveld analysis of the diffraction patterns were conducted by campaigns [7-9, 53, 54, 56]. The inferred mass fraction of crystalline phases portlandite mCH, anhydrite mCS¯ , calcite mCC¯ , and ettringite m C6 S¯3 H32 , as well as the mass of clinker phases (m C3 S , m C2 S , m C3 A , and m C4 AF ) or the total clinker mass mc are used for validation. The remaining, unassigned

mass in XRD measurements, mainly C-S-H phases and slag, is typically referred to as amorphous phase and is also compared to the modeled counterpart. The amount of unreacted slag remaining in the mix is either quantified by backscattered scanning electron microscopy (BSE), as done in experimental campaigns [7, 9, 53, 55] or by means of the PONKCS simulation method based on XRD results [56, 9], herein abbreviated XRD+P. This way, mass fractions of unreacted slag msl are quantified in the experiments and can be used for model validation. Furthermore, BSE images provide access to area fractions (which are considered to be equal to volume fractions, given that the number of two-dimensional images is adequately high [59]) of cement clinker, portlandite, pores, and of the remaining matrix phase can be validated. Air volume fractions can be validated based on continuous chemical shrinkage measurements (ChS), conducted by Whittaker et al. [7]. By using energy dispersive X-ray spectroscopy (EDS) Kocaba [53] Whittaker et al. [7] Adu-Amankwah et al. [56] and Durdziński et al. [9] quantified the amounts of C, S and A in the C-(A)-S-H phases. These are used for validation of the three molar ratios C/(A+S), C/S, and A/S. 3.2. Results First, the IC-based decoupling of clinker and slag reactions is validated based on XRD (potentially coupled with PONKCS analysis) and/ or BSE experiments obtained within the time frame of IC tests, see Table 4. Model-predicted and experimentally measured mass fraction evolutions of unhydrated clinker mcl and unhydrated slag msl do agree very well, as quantified by correlation coefficients R2 amounting to 0.88 for clinker and 0.70 for slag, and further quantified by mean absolute errors δ amounting to less than 5%, see the correlation plots in Fig. 3 (a) and (b). This corroborates the conclusions from earlier studies [31, 12] that decoupling of total heat flows in slag-blended pastes based on a reference composition without slag does indeed provide very reliable evolutions of clinker and slag contents. Next, the decoupling of the clinker hydration into the contributions of its four phases is validated based on XRD experiments. The decoupling relies on the three-stage kinetics model of Bernard et al. [38] and on the therein fitted kinetic 7

Cement and Concrete Research 128 (2020) 105950

M. Königsberger and J. Carette

Fig. 3. Model validation of IC decoupling by means of (a) clinker, (b) slag, (c) C3S, (d) C2S, (e) C3A and (f) C4AF mass fractions based on XRD and BSE measurements of [7-9, 53, 54, 56, 59].

parameters, see Appendix B for details. Most notably, these parameters are therefore considered to be independent of the actual binder composition. Despite the simplicity of the approach, model-predicted evolutions of the clinker phase mass fractions and experimental counterparts agree reasonably well, see Fig. 3 (c) –(f), in particular the mass fraction evolution of C3S, mC3 S . Motivated by the model performance related to the decoupling, we now use experimental data from XRD and/or BSE on more mature pastes beyond the age tIC for which trustworthy IC results are available. This way, we aim for validation of the linear extrapolation of the clinker and slag hydration degrees given in Eq. (3). Very remarkably, the proposed extrapolation procedure of days-long IC measurements allows for nice reproduction of the XRD/BSE-measured mass fraction evolutions of clinker and slag even up to ages of two to three years, see Fig. 4. After having successfully validated the kinetics model based on clinker and slag mass fractions and corresponding hydration degrees, we now aim for validation of the mass fraction evolution of portlandite CH, anhydrite CS¯ , ettringite C6AS¯3 H32, calcite CC¯ , and amorphous phase, quantified by means of TGA and XRD experiments. Given that both XRD and TGA are typically presented as solid mass fractions, we also normalize the model predictions by means of the initial solid mass msolid = 1 − mH(t = 0). Notably, the mass of amorphous materials mamorph is considered as the sum of the masses of slag, of the remaining hydration products (mostly C-S-H) and of inert fillers. Model-predicted portlandite mass evolutions agree exceptionally well with experimental results, see Fig. 5 (a), as quantified by correlation coefficients R2 = 0.86. Interestingly, the mass fractions for the slag-blended mixes (depicted as filled circles in all plots) do agree as well as or even better than the slag-free cement pastes (depicted as crosses in all plots). The

error δ for the portlandite mass fraction is 1.3% for slag-blended mixes but 1.8% for OPC mixes. Given the large amount of measurements available, this corroborates the distribution of calcite in the hydration products. Thus, the proposed reaction model for the CH consumption of the slag, as well as the proposed C/S of the slag-related CASHs are indeed validated. For a detailed discussion on the latter aspects, we refer to Section 4.2. The model-predicted mass fractions of anhydrite and ettringite do also agree well with experimental data, see Fig. 5 (b) and (c). The observed deviations concern mostly slag free cement pastes. This shows that the presented extension of the hydration kinetics model towards slag-cement mixes yields a better performance than applying the same three-stage kinetics model [38] to plain cement systems. Moreover, we note that the accuracy of XRD measurements decreases as the phase mass fractions approach zero [63]. The pronounced differences for small experimental mass fractions, as e.g. for anhydrite in Fig. 5 (b), are therefore partly attributed to experimental errors. The mass fraction of the amorphous phase does agree remarkably well with the experimental data, for all compositions tested from Hlobil et al. [8] and Bourchy [54]. Not surprisingly, calcite mass fractions also compare very well with experimental results, given that the calcite reaction to monocarboaluminate, here considered to occur in parallel to the aluminate reactions (see cases 3d and 4d in Table 1), results in only a small calcite consumption and therefore only slightly decreasing calcite mass fractions. Nevertheless, it is important to consider the reactivity of calcite, as it stabilizes ettringite, see discussion Section 4.3 for more details. Additional validation can be performed based on BSE-measured phase volume fractions of anhydrous phases (cement and slag), portlandite, other hydration products, and large pores (air pores and 8

Cement and Concrete Research 128 (2020) 105950

M. Königsberger and J. Carette

Fig. 4. Model validation of IC extrapolation by means of (a) clinker and (b) slag mass fractions based on XRD and BSE measurements of [7; 9; 53; 56; 59].

capillary pores). The experimental results of Gruyaert [59] do agree remarkably well with the predicted volume fraction evolutions, see Fig. 6. The good agreement between the pore volume fraction vcpor+vair particularly corroborates the underlying C-(A)-S-H densification model, as model predictions considering a constant C-(A)-S-H density are significantly worse, see the discussion section for more details. Air pore volumes (normalized by the mass of clinker), as assessed by ChS measurements from Whittaker [60], are compared to model

predictions in Fig. 7 (d). The remarkably good agreement further validates our modeling approach. Finally, we compare model-predicted and experimentally assessed chemical composition of C-(A)-S-H by studying the evolution of the molar ratios (C/S, A/S, and C/(A+S)). Notably, model-predicted ratios are mass averages of all solid C-(A)-S-H phases (C-S-H, CASHc and CASHs). Only after averaging model results can be compared to experimental data obtained from electron microscopy studies, as the

Fig. 5. Model validation of mass fractions of (a) portlandite mCH, (b) anhydrite mCS¯ , (c) ettringite mC6 AS¯3 H32 , (d) amorphous mamorph and (e) calcite mCC¯ , normalized by the solid mass msolid, based on TGA [7, 53, 56, 57, 59] and XRD measurements [7-9, 54, 56]. 9

Cement and Concrete Research 128 (2020) 105950

M. Königsberger and J. Carette

G3

100

G6

100

G9

100

pores 75 BSE analysis

50 25 0 101

(a)

75 ot her hydrat es

50 Clinker 25

102

103 104 t ime [h]

v [%]

v [%]

v [%]

75

0 101

105

102

(b)

Slag

CH

103 104 t ime [h]

50 25 0 101

105

(c)

102

103 104 t ime [h]

105

Fig. 6. Model validation of volume fractions based on BSE measurements [55] for (a) mix G3, (b) Mix G6, and (c) mix G9.

Fig. 7. Model validation of hydration-induced air pore volume fractions based on chemical shrinkage measurements of [7].

resolution of the micrographs is typically more than 100 nm, and thereby at least one order of magnitude larger than the 5-nanometerlarge single C-(A)-S-H nanoparticle [45] whose composition is modeled herein. For the slag-blended mixes, the model-predicted average C/S and C/(A+S) ratios decrease with increasing hydration degree (see Fig. 8), given that (i) the clinker-related CASHc exhibits higher calcite contents than the slag-related CASHs and (ii) the slag hydration occurs later. The model-predicted A/§, in turn, increases upon hydration. Experimental results are obtained by EDS measurements from various studies [7, 56, 9]. We note that experimental values result from both outer and inner C-(A)-S-H, but that there difference is rather small and that model predictions typically fall in between the two limit cases, see Fig. 8. Moreover, we clarify that Kacoba [53] measured the molar ratios by means of EDS and transmission electron microscopy (TEM). TEM-based ratios, which are stated to be more precise but more challenging to obtain, are, on average, by a factor 0.88 smaller than EDS points. In order to use all measurements, in particular at different ages, we apply the correction factor for EDS-based ratios. Comparing all experiments to averaged model predictions indicates a good model performance, since all the points in the correlation plot form a relative narrow band, and since mean absolute errors are rather small (δ ≤ 0.06), as illustrated in Fig. 9.

Fig. 8. Model predicted molar C/(A+S) ratio evolution of C-(A)-S-H (solid line) and EDS/TEM results (points) of mix K9 measured by Kocaba [53]; EDS results were corrected based on TEM results, see text.

relaxometry, we assumed that the C-(A)-S-H gel density in slag-blended cement pastes is a function of the available precipitation space for C-SH according to Fig. 2. This is in contrast to predecessor hydration models for blended cement pastes [17, 27], where the C-S-H gel density is considered to be virtually constant, ρgel = 2.26 g/cm3. This motivates us to compare the model considering the C-(A)-S-H gel densification to the conventional assumption of a constant C-(A)-S-H gel density. Therefore, the model is evaluated for the mixes A1, A4, A6 and D1–D3, see Fig. 10. While the total amount of water in gel and capillary pores does remain unchanged, the densification approach yields gel water volumes associated to C-(A)-S-H gel which are considerably higher at early ages. The capillary pore space, in turn, is filled much more rapidly. The two modeling approaches are further compared to mercury intrusion porosimetry (MIP) performed from Adu-Amankwah et al. [56] and Durdziński et al. [9], as discussed next. Notably, the total pore volume measured by means of MIP comprises shrinkage-induced air voids and water-filled capillary pores, but additionally, an unknown part of the water-filled gel pores [62]. The amount of gel porosity accessed by mercury in MIP experiments might depend on the size distribution and the geometry of the pore space, and cannot be quantified further. Therefore, experimentally measured MIP porosities vMIP have to be larger than the sum of the model-predicted air and capillary pore volume fractions, but smaller than the model-predicted sum of air,

4. Discussions 4.1. Further evidence for C-(A)-S-H gel densification in slag-blended mixes based on MIP measurements Based on recent insight from nuclear magnetic resonance 10

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Fig. 9. Model validation of the molar ratios (a) C/S, (b) A/S, and (c) C/(A+S) based on EDS or TEM measurements from [7, 9, 53, 56].

capillary, and gel pore volume fractions: vair + vcH ≤ vMIP ≤ vair + vcH + vgH. This restriction on the model-predicted pore volumes is illustrated in Fig. 10, where MIP-based points must fall in the top region labelled as gel pores. Comparing the two model approaches, i.e. comparing the densification-based predictions given in Fig. 10 (a,b,e,f,i,j) to the predictions with constant C-(A)-S-H gel densities given in Fig. 10 (c,d,g,h,k,l), shows that the densification-based approach is clearly superior. MIP pore volumes contradict model predictions related to a constant C-(A)-S-H gel density, as most vividly seen in Fig. 10 (c) and (l). MIP suggest a relative rapid decrease of accessible pore volume for these mixes, which can only be predicted if we consider the C-(A)-S-H gel to densify during hydration. This finding is further supported by the

fact that volume fraction evolutions measured by means of BSE, shown in Fig. 6, are much better represented when C-(A)-S-H gel densification is considered. 4.2. Origin of portlandite consumption While clinker hydration results in progressive precipitation of portlandite crystals, slag, in turn, reacts by consuming some portlandite. Herein, we discuss how we quantify the amount of consumed portlandite, and compare our model to predecessors. We consider that the C/S ratio of C-(A)-S-H is equal to C/Ss, see Eq. (8), and thus intrinsic for a given chemical slag composition. While C and S are balanced between

Fig. 10. Model-predicted porosity evolution (broken down into the contribution of air voids, water-filled capillary pores, and water-filled gel pores) with (a,b,e,f,i,j) and without (c,d,g,h,k,l) C-(A)-S-H gel densification for different compositions; and comparison to MIP-measured total porosities from [9, 56]. 11

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reacting slag and produced C-(A)-S-H, the available A of the slag is released through solution and reacts with the CH to form calciumaluminate-hydrates (AFt and AFm phases), herein represented as C6AS¯3 H32 and C4AH13. We assume that the calcite demand of these hydrates alone allows for quantification of the CH consumption upon slag hydration. This way, our strategy is considerably different than the one employed by Chen and Brouwers [14]. The authors did not consider any slag reaction product other than C-(A)-S-H. To account for the experimentally observed CH consumption by slag hydration, they introduced a partial CH uptake by C-(A)-S-H, thus increasing the C/S ratio of C-(A)S-H beyond the C/S of the slag. This was further developed by Kolani et al. [26], who related this uptake to the amount of CH and to the calcium available in unhydrated slag grains at each computation step. Our approach with constant C/S ratio of C-(A)-S-H is supported by extensive experimental validation involving 14 different slags, with C/ Ss ranging from 0.96 (K3, K6, K9) to 1.40 ( B4–B9). Fig. 5 (a) shows that predictions of the CH contents in slag-blended mixes agree well with experimental data. Figs. 8 and 9, in turn, demonstrate that the considered C/S ratio of C-(A)-S-H agrees with the experimental data. If we considered an increasing C/S ratio of slag-related C-A-S-H due to C uptake from portlandite, the predicted overall C/S ratio of C-(A)-S-H would be significantly higher than experimental results suggest. These results support our hypothesis that the CH consumption by slag is not due to C uptake by CASHs products, but by the formation of the subsequent calcium-aluminate phases.

Considering the high molar mass of C4AC¯ H11, it is expected that its amount can reach surprisingly high mass fractions of up to 15 wt.% in cement-limestone blends without slags. 4.4. Ultimate heat of slag The ultimate heat of hydration of slag naturally depends on its chemical composition. While this is an essential parameter for estimating the hydration degree based on calorimetry measurements, there is currently no appropriate way to compute it. In this context, we refer to the well-developed hydraulic indexes of BFS [68], which might give insights. However, they typically estimate the long-term strength based on the slag composition, rather than the ultimate heat. The long-term strength depends on various parameters, among which slag heat release is not clearly predominant. We have proposed, as a first approach, to link the ultimate heat of hydration of BFS, Qs,∞, to its M content, as presented in Section 2.2. In order to fit the two involved parameters A and B, we minimized the mean absolute prediction error δ quantifying the differences between the model-predicted slag hydration degree and the experimental counterparts for all mixes for which the information is available: K2, K3, K8, K9, W2, W3, A3, A4, A5, A6, D3, G6 and G9 [53, 56, 59-61]. This results in δ = 2.8 wt.% for the optimum paramater set (A = 8526 J, B = −241 J/g), see Fig. 4 (b). We challenge this prediction error now by considering an intrinsic ultimate heat release of 461 J/g, which was experimentally determined by [37], and later used in several predecessor models [24, 26, 69-71]. The related prediction error is almost twice as high (δ = 4.0 wt. %). This demonstrates the benefits of considering the ultimate heat as function of the slag's M content. Notably, considering more dependencies regarding the C, A, S or S¯ contents does not improve the predictability. To further elaborate the preditive capabilities, we compare related blind model predictions of both the early age and long-term CH and C6AS¯3 H32 mass fractions to the experimental results from composition B6, as this mix contains 72% slag (slag hydration-related effects should therefore be very prominent) and since this mix has not been used for fitting the ultimate heat of slag. The magnesite contents of the slag used in mix B6 are very small, resulting, in turn, in small Qs,∞≈ 270 J/g. The (blind) model performance is significantly improved considering Qs,∞≈ 270 J/g, rather than the composition-independent 461 J/g, see Fig. 12. The lower Qs,∞ value induces a higher slag hydration degree, which accounts for the experimentally measured small portlandite contents (resulting from the CH consumption during slag hydration) and earlier ettringite production. Finally, we compare the predicted ultimate heat of the 13 slags included in our study, to other values reported in the literature. Interestingly, we obtain quite significant variations of Qs,∞ approximately between 270 J/g and 550 J/g. This is in line with the few results

4.3. Limestone filler reaction The partial reaction of CC¯ with C3A results in the formation of carboaluminate [64, 65, 66]. We follow Lothenbach et al. [67], and consider that monocarboaluminate (C4AC¯ H11) instead of monosulfoaluminate (C4AS¯ H12) is formed as long as calcite (CC¯ ) is present, see reaction 3d in Table 1. Both C4AC¯ H11 and C4AS¯ H12 are AFm phases and differ only by means of the anion incorporated into its structure (either carbonate or sulfate). Therefore, the main consequence of the calcite reaction process is the stabilization of ettringite, as the carbonate from CC¯ replaces the sulfate from ettringite to form the AFm phase. Fig. 11 illustrates that if CC¯ is not considered as a reactive, the amount of C6AS¯3 H32 is significantly underestimated, even though the CC¯ content is very low (between 2 and 3 wt.%). For all modeled compositions, we have observed that the total mass fraction of reacting CC¯ can go up to 3%. The amount of CC¯ reactivity is mostly dependent on the amounts of C3A and C4AF as well as on the initial amount of available gypsum. An a priory estimation of the r , reads as maximum amount of CC¯ mass that is expected to react, mCC ¯ r = 0.24 × (m mCC C3 A + mC4 AF ¯

mCS¯ ).

(13)

Fig. 11. Model-predicted temporal ettringite mass evolutions considering/neglecting limestone (CC¯ ) reaction and comparison to experimental data from [60] for (a) mix W3 and (b) mix W4. 12

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Fig. 12. Model-predicted temporal mass fraction evolutions of (a) CH and (b) C6AS¯3 H32 of mix B6 with intrinsic and composition-dependent ultimate slag heat release and experimental results from Bourchy [54].

available in the literature. For instance, Bensted [72] suggests values as low as 355 J/g while Gruyaert [59] obtains values between 400 J/g and 500 J/g. Luan et al. [73], Han et al. [36] and Goto [74] obtain values as high as 525 J/g, 530 J/g and 570 J/g respectively. This huge range calls for thorough studies on the exact reasons – our model only provides a first composition-based estimate.

show in Fig. 13 (b) that in the case of blind predictions, the prediction error on amorphous phases, ettringite and portlandite is increased by 20% to 40%, while the C/(A+S) ratio prediction error is doubled. This highlights the need to improve the currently available predictive kinetics models for both clinker and slag hydration, and therefore supports our approach of using experimental IC data as input for hydration modeling.

4.5. Model performance without isothermal calorimetry data

5. Conclusions

Finally, it is interesting to investigate whether the model performance would be significantly compromised if we neglect the isothermal calorimetry data. Therefore, we reevaluate the model whereby we either do not rely on calorimetry experiments at all (the duration of calorimetry data thus is tIC = 0), or we consider a shorter measurement duration tIC ∈{0.5,1,2,3,4,5} days rather than tIC = 7 days which was the basis of all previous developments. In other words, we extend the length of the extrapolation period, for which we rely on predictions of state-of-the-art kinetics models available in the literature. Resulting mean absolute prediction errors δ decrease significantly with increasing measurement duration tIC, see Fig. 13. Interestingly, for blind kinetics prediction (tIC = 0) the error related to slag mass fraction ms is by a factor of 3.6 larger than for the standard tIC = 7 days. This shows the inapplicability of the slag hydration model for the whole range of mixes we incorporated in our study, even though it has been successfully calibrated against experimental data of one particular slag-blended cement paste by Merzouki et al. [27]. The hydration model for cement does perform much better, even if we apply it in blind fashion, as the related prediction error for the clinker mass fraction mc is only by 25% larger than in case tIC = 7 days. However, this error of 25% for the clinker hydration degree is already significant considering the effect that it has on the phase volume fraction predictions. As a result, we

The hydration model presented here allows for quantification of evolutions of mass or volume fractions of reactants and hydration products in slag-blended cement paste systems, as demonstrated in Fig. 14. It is based on isothermal calorimetry measurements on the blended mix and on a carefully selected reference mix without slag, which allows for decoupling of the heat release into its contributions from cement and slag, respectively. Extrapolation of the early-age calorimetry data up to ages of several years is based on rather simple kinetics laws, available in the literature. Stoichiometric relations combined with hypotheses concerning the C-(A)-S-H composition and density evolution complete the model. The model is then evaluated for 54 mix compositions with different amounts of slag, cement, limestone, sulfate and fillers, for which experimental results have been reported. This way, the model is challenged by several experimental results from nine comprehensive studies. The comparison is performed (i) for mass/volume fractions of clinker, slag, calcite, portlandite, ettringite, and pores from combining XRD, BSE, TGA and MIP measurements, (ii) for air pore volumes from chemical shrinkage measurements and (iii) for calciumto-silica ratio of C-(A)-S-H products obtained from EDS or TEM measurements. The remarkably good agreement between model predictions

Fig. 13. Mean absolute prediction errors as function of the duration of the isothermal calorimetry test for (a) clinker and slag mass fractions and (b) portlandite, ettringite and amorphous mass fractions as well as the molar C/(A+S) ratio of C-(A)-S-H. 13

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Fig. 14. Volume fraction evolution for mix K5 from Kacoba [53] as a function of time and total degree of hydration ξ.

• The ultimate heat of hydration of slag is highly variable, and de-

and all experiments data does validate the presented modeling approach and its underlying hypothesis. This leads to the following major conclusions:

• Decoupling and extrapolation of slag and cement hydration based • • •

•

on calorimetry measurements result in trustworthy mass evolutions of clinker and slag, provided that the reference mix without slag does provide approximately the same surface area on particle surfaces for nucleation of new hydrates. C-(A)-S-H gel densifies during hydration. Considering the densification to be universal, i.e. independent of the chemical composition of C-(A)-S-H, allows for nicely reproducing the experimentally observed evolution of gel and capillary pore volumes. The experimentally observed decrease of the calcium-to-silica ratio of C-(A)-S-H upon hydration can be explained by considering three intrinsic solid C-(A)-S-H phases with constant chemical composition but varying volume dosage. The experimentally measured portlandite consumption by the slag reaction can be explained solely by considering the formation of calcium-aluminate hydrates other than CASHs. Calcium uptake by the slag-related C-(A)-S-H is not required.

pends on the slag's chemical composition. Considering a simple linear relation between ultimate heat of slag and the slag's magnesite content significantly improves the long-term predictions of the remaining slag mass fraction. Accounting for limestone reaction is important for explaining the stabilization of ettringite phases in ternary blended mixes.

Declaration of competing interest The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The authors gratefully acknowledge the financial support from the Belgian National Funds for Scientific Research--FNRS. Furthermore, the authors thank Michal Hlobil for sharing partly unpublished results of his PhD research.

Appendix A. Stoichiometric equations for hydration reactions Herein, the hydration mechanisms given in Table 1 are complemented with stoichiometric relations. In more detail, we aim for calculating the coefficients ni j which quantify the molar amount of reactant or product i involved in the reaction equation j, i.e. the reaction of one mol of the main reactant (C3S in reaction equations 1a and 1b; C2S in reaction equations 2a and 2b; C3A in reaction equations 3a-3d, C4AF in reaction equations 4a4d; Slag in reaction equations 5a and 5b). The following additional assumptions allow us to quantify all molar coefficients given in Tables A.5-A.7.

• We assume that both C A and C AF provide aluminate for CASH . C A and C AF in reactions 1a and 2a, are consumed proportionally to their 3

4

c

3

4

remaining molar content at any time t. Thus, we define the molar ratio RA as the ratio of molar C3A content to molar C4AF content, RA(t)=n Ccem 3A (t)/n Ccem (t), where nCcem (t) and n Ccem (t) denote the (time-dependent) molar contents of free C3A and of C4AF in the remaining unhydrated clinker. 3A 4 AF 4 AF This allows us to get a relation between the coefficients nC13aA and n1Ca4 AF , as well as between nC23aA and nC24aAF , reading as

nC1a3 A nC1a4 AF

(t ) =

nC2a3 A nC2a4 AF

(t ) = RA (t )

.

(A.1)

• We consider that potentially available free C and all free M in the clinker react proportionally to C S in reaction 1a and 1b, and therefore define 3

the molar ratio RM as

RM =

cem nM nCcem 3S

(A.2)

whereby and denote the initial molar contents of free M and of C3A in cement clinker, respectively. This way, the coefficient for M in 3a = RM . reaction Eq. 3a reads as nM The reaction products of the slag reactions (5a and 5b) depend on the availability of anhydrite and on the chemical composition of the slag. As for the latter, four regimes of aluminate contents in terms of the slag's A/Ssl ratio can be distinguished: cem nM

•

, nCcem 3S

14

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1. If the slag-related A/Ssl is smaller than the A/S predicted from Richardson's Eq. (6) based on the slag's C/S , the CASHc -related C/S ratio is reduced according to Eq. (9). This way, all available A is incorporated in CASHc and other aluminate hydrates cannot form. 2. If the A content in slag is large enough to allow for the desired A/Ss ratio of the CASHc , hydrotalcite (M6AH13) is considered to form preferably, since it is commonly found in slag-blended cement paste [56]. Its production is limited either by the amount of available M in the 5a slag (quantified by the M/Ssl ratio), or by the amount of available aluminum (quantified by the A/Ssl ratio), see the two conditions for n M 6 AH13 M / Ssl 5b and n M6 AH13 in Table A.7. Consequently, if A/Ss < A/Ssl < A/Ss+ , neither ettringite nor hydroxy-AFm form. 6 3. If the A content in slag is large enough to sustain the A/Ss ratio in CASHc as well as to allow for complete reaction of slag-related M to ¯ hydrotalcite, excess A is considered to form ettringite C6AS¯3 H32. If A/Ss+ M / Ssl < A/Ssl < A/Ss+ M / Ssl + S / S , there is enough sulfate in the mix 6 6 3 to sustain ettringite production. 4. Finally, if the A content in slag is large enough to (i) sustain the A/Ss ratio in CASHc and (ii) allow for complete reaction of slag-related M to hydrotalcite and of slag-related S to ettringite, excess A is considered to form further ettringite by consumption of anhydrite (reaction 5a) or to ¯ form hydroxy-AFm C4AH13 (if no anhydrite is available, reaction 5b). This regime is found in slags exhibiting A/Ssl > A/Ss+ M / Ssl + S / S . 6 3 5a 5b Remaining M after hydrotalcite production is always considered to form brucite MH (see coefficient nMH = nMH in Table A.7), remaining S¯

after ettringite production is considered to remain unhydrated (see coefficient n S5¯ a and n S5¯ b ). Portlandite consumption due to the slag reaction only occurs if A/Ssl > A/Ss+ M / Ssl (see coefficient nCH5a and nCH5b). The slag reaction is considered to stop as soon as the portlandite content 6 becomes zero. The water demand, in turn, is a consequence of all other formed hydrates (see coefficient nH5a and nH5b).

Table A.5

Stoichiometric coefficients ni j for silicate reactions (j ={1a,1b, 2a, 2b}). Reactants

Products

j

nCj3 S

nCj2 S

nCj3 A

1a

1

-

A/Sc/(1+1/RA)

1b

1

-

-

2a

-

1

A/Sc/(1+1/RA)

2b

-

1

-

nCj

nMj

nHj

nC−A−S−Hcj

nCSHj

nCHj

j nFH 3

A/Sc/(1+RA)

RC

RM

-

RC

RM

H/Sc+3nC1a4 AF +nCH1a+RM

1

-

H/Sc+nCH1b+RM

-

1

3+3nC1a3 A +4nC1a4 AF +RM-C/Sc

nC1a4 AF

A/Sc/(1+RA)

-

-

-

-

-

H/Sc+3nC24a AF +nCH2a

1

-

-

1

2+3nC23aA +4nC24a AF -C/Sc

nC24a AF

nCj4 AF

H/Sc+nCH2b

3+RM-C/Sc

-

2-C/Sc

-

nMHj RM RM -

Table A.6

Stoichiometric coefficients ni j for aluminate reactions (j ={3a,3b,3c,3d,4a,4b,4c,4d}). Reactants

Products

j

nCj3 A

nCj4 AF

j nCS ¯

nCj

nCH*

3a 3b 3c 3d

1 1 1 1

-

3 -

0.5 -

4a 4b 4c 4d

-

1 1 1 1

3 -

0.5 -

6 AS¯3 H32 *

j

nCj

nCj

nCj4 AH13

nCj

nCHj

j nFH 3

32 2 12 11

1 -

1.5 -

1.5 -

1

-

-

36 6 12 16

1 -

1.5 -

1.5 -

1

1 1 -

1 1 1

j nCC ¯

nH

1 -

1

1 -

-

j

6 AS¯3 H32

¯ 4 4 ASH

¯ 11 4 ACH

Table A.7

Stoichiometric coefficients ni j for slag reactions (j ={5a, 5b}). Reactants j

nslagj

j nCS ¯

5a

1

3nett5a-S¯ /Ssl

5b

1

-

Products

0

nCHj

nHj

nC−A−S−Hsj

6nett5a

5a nH *

1

min{

M / Ssl ; 6

A/ Ssl -A /Ss }

6nett5a+4ntca5a

5b nH *

1

min{

M / Ssl ; 6

A/ Ssl -A /Ss }

j n Mj 6 AH13 = ntal

nCj

6 AS¯3 H32

j = nett

A/Ssl-A/Ss-ntal5a ≥ 0 A/Ssl-A/Ss-ntal5b ≥ 0

j nCj4 AH13 = ntca

A/Ssl-A/Ss-ntal5b-nett5b 0

nMHj M/Ssl6ntal5a ≥ M/Ssl6ntal5b

nS¯j 5a -3n 5a S¯ /Ssl +nCS ett ¯

S¯ /Ssl -3nett5b

j * nHj =0.97+13ntalj+32nettj+ntca +nMHj-nCHj

Appendix B. Mathematical expressions of the hydration kinetics model The predicted hydration degree i* (t ) for any clinker phase i can be expressed as a function of time t according to a three-stage hydration model proposed by Bernard et al. [38] as

15

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M. Königsberger and J. Carette

0, i

t0 * (t ) =

0, i

i

1

+1

(1

t

t i cl

exp

(t

t0)

t0 < t

t0 te

0 1/3 e, i )

2Di

t

te R

i

1/2 3 i

t > te

,

0

(B.1)

{C3 S, C2 S , C3 A, C4 AF } 2

whereby R is the average clinker grain size, ϕc is the clinker fineness, ϕ0 = 360 m /kg, t0 = 1 h, and te is the time when ξi = ξe,i. Parameters ξe,i, ξ0,i and κi are dependent on the w/c ratio, and can be found in [38], except 0, C4 AF which is adopted to 0.2 on the basis of the gathered experimental data. The predicted slag hydration degree s* (t ) , in turn, is obtained from Knudsen's model [39] adopted by Merzouki et al. [27]

* (t ) =

s

k (t t 0 ) n 1 + k (t t0 )n

(B.2)

with parameters n = 0.7 (adopted herein to fit to the gathered experimental data) and k = k0 exp−Ea/R/T. Furthermore, herein T = 293 K, and k0 and Ea were overtaken from [27] as k0 = 10.4605 × ms(t = 0)/msolid − 1.8289 and Ea = 13934 × ms(t = 0)/msolid + 11264. We consider that the hydration stops at the ultimate hydration degree ξ∞. Its figure is obtained from an empirical relation taking into account the binder fineness and the water-to-reactive mass ratio as [40]

=

1( 2(

)m

)+

mH (t = 0) c (t = 0) + mH (t = 0) mH (t = 0) m c (t = 0) + mH (t = 0)

,1

1 (B.3)

whereby β1 and β2 are functions of the binder's Blaine fineness as 1(

)=

1 9.33( /100)

2.82

+ 0.38

,

2(

)=

220 147.78 + 1.656(

220)

,

(B.4) 2

and ϕ is the volume average of the Blaine fineness of clinker and slag, whereby ϕ ≥ 270 m /kg. Next, we discuss how this total ultimate hydration degree is used to obtain ultimate phase hydration degrees ξi,∞ of the four clinker phases and the slag, which are required to calculate actual phase hydration degrees according to Eq. (3). We define the total hydration degree ξ* as

* (t ) =

i

mi (t = 0) i (t ) i

mi (t = 0)

,

i

{C3 S , C2 S, C3 A, C4 AF , s}

(B.5)

The time t where ξ*(t) = ξ∞ is denoted the ultimate time t∞. The ultimate phase hydration degrees ξi,∞ then follow from evaluating the phase hydration degrees at the ultimate time, i.e. i, = i* (t ) .

reaction of slag in blended cement pastes, Cem. Concr. Res. 42 (2012) 511–525. [13] I.G. Richardson, G.W. Groves, Microstructure and microanalysis of hardened cement pastes involving ground granulated blast-furnace slag, J. Mater. Sci. 27 (1992) 6204–6212. [14] W. Chen, H.J. Brouwers, The hydration of slag, part 2: reaction models for blended cement, J. Mater. Sci. 42 (2007) 444–464. [15] B. Lothenbach, K. Scrivener, R.D. Hooton, Supplementary cementitious materials, Cem. Concr. Res. 41 (2011) 1244–1256. [16] I. Richardson, G. Groves, The incorporation of minor and trace elements into calcium silicate hydrate (C-S-H) gel in hardened cement pastes, Cem. Concr. Res. 23 (1993) 131–138. [17] W. Chen, H.J.H. Brouwers, The hydration of slag, part 1: reaction models for alkaliactivated slag, J. Mater. Sci. 42 (2007) 428–443. [18] J.J. Thomas, A.J. Allen, H.M. Jennings, Density and water content of nanoscale solid C-S-H formed in alkali-activated slag (AAS) paste and implications for chemical shrinkage, Cem. Concr. Res. 42 (2012) 377–383. [19] K. Luke, E. Lachowski, Internal composition of 20-year-old fly ash and slag-blended ordinary Portland cement pastes, J. Am. Ceram. Soc. 91 (2008) 4084–4092. [20] R. Taylor, I.G. Richardson, R.M. Brydson, Composition and microstructure of 20year-old ordinary Portland cement-ground granulated blast-furnace slag blends containing 0 to 100% slag, Cem. Concr. Res. 40 (2010) 971–983. [21] T.C. Powers, T.L. Brownyard, Studies of the physical properties of hardened {P} ortland cement paste, Am. Concr. Inst. J. Proc. 18 (1947) 101–992. [22] B. Pichler, C. Hellmich, Upscaling quasi-brittle strength of cement paste and mortar: a multi-scale engineering mechanics model, Cem. Concr. Res. 41 (2011) 467–476. [23] M. Königsberger, M. Hlobil, B. Delsaute, S. Staquet, C. Hellmich, B. Pichler, Hydrate failure in ITZ governs concrete strength: a micro-to-macro validated engineering mechanics model, Cem. Concr. Res. 103 (2018) 77–94. [24] K. Meinhard, R. Lackner, Multi-phase hydration model for prediction of hydrationheat release of blended cements, Cem. Concr. Res. 38 (2008) 794–802. [25] X.Y. Wang, H.S. Lee, K.B. Park, J.J. Kim, J.S. Golden, A multi-phase kinetic model to simulate hydration of slag-cement blends, Cem. Concr. Compos. 32 (2010) 468–477. [26] B. Kolani, L. Buffo-Lacarrière, A. Sellier, G. Escadeillas, L. Boutillon, L. Linger, Hydration of slag-blended cements, Cem. Concr. Compos. 34 (2012) 1009–1018. [27] T. Merzouki, M. Bouasker, N.E. Houda Khalifa, P. Mounanga, Contribution to the

References

[1] J.G.J. Olivier, G. Janssens-Maenhout, M. Muntean, J. Peters, Trends in global CO2 emissions, Technical Report, PBL Netherlands Environmental Assessment Agency; European Commission, Joint Research Centre (EC-JRC), 2015. [2] J.I. Escalante-Garcia, J.H. Sharp, The microstructure and mechanical properties of blended cements hydrated at various temperatures, Cem. Concr. Res. 31 (2001) 695–702. [3] D.M. Roy, G.M. Idorn, Hydration, structure, and properties of blast furnace slag cements, mortars, and concrete, ACI J. Proc. 79 (1982) 444–457. [4] F. Leng, N. Feng, X. Lu, An experimental study on the properties of resistance to diffusion of chloride ions of fly ash and blast furnace slag concrete, Cem. Concr. Res. 30 (2000) 989–992. [5] G. Menéndez, V. Bonavetti, E.F. Irassar, Strength development of ternary blended cement with limestone filler and blast-furnace slag, Cem. Concr. Compos. 25 (2003) 61–67. [6] S. Hoshino, K. Yamada, H. Hirao, XRD/Rietveld analysis of the hydration and strength development of slag and limestone blended cement, J. Adv. Concr. Technol. 4 (2006) 357–367. [7] M.J. Whittaker, M. Zajac, M. Ben Haha, F. Bullerjahn, L. Black, The role of the alumina content of slag, plus the presence of additional sulfate on the hydration and microstructure of Portland cement-slag blends, Cem. Concr. Res. 66 (2014) 91–101. [8] M. Hlobil, V. Šmilauer, G. Chanvillard, Micromechanical multiscale fracture model for compressive strength of blended cement pastes, Cem. Concr. Res. 83 (2016) 188–202. [9] P.T. Durdziński, M. Ben Haha, M. Zajac, K.L. Scrivener, Phase assemblage of composite cements, Cem. Concr. Res. 99 (2017) 172–182. [10] D.E. Macphee, M. Atkins, P.P. Glassar, Phase Development and Pore Solution Chemistry in Ageing Blast Furnace Slag-Portland Cement Blends, MRS Proc. 127 (1988) 475. [11] I. Pane, W. Hansen, Investigation of blended cement hydration by isothermal calorimetry and thermal analysis, Cem. Concr. Res. 35 (2005) 1155–1164. [12] V. Kocaba, E. Gallucci, K.L. Scrivener, Methods for determination of degree of

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M. Königsberger and J. Carette

[28] [29] [30]

[31] [32] [33] [34]

[35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50]

[51] A.C.A. Muller, K.L. Scrivener, A.M. Gajewicz, P.J. McDonald, Densification of C-S-H measured by 1H NMR relaxometry, J. Phys. Chem. C 117 (2012) 403–412. [52] J. Carette, Towards early age characterisation of eco-concrete containing blastfurnace slag and limestone filler, Ph.D. thesis, Université libre de Bruxelles, 2015. [53] V. Kocaba, Development and evaluation of methods to follow microstructural development of cementitious systems including slags, Ph.D. thesis, École Polytechnique Fédérale de Lausanne, 2009. [54] A. Bourchy, Relation chaleur d’hydratation du ciment - montée en température et contraintes générées au jeune âge du béton, Ph.D. thesis, Université Paris-Est, 2018. [55] E. Gruyaert, N. Robeyst, N. De Belie, Study of the hydration of Portland cement blended with blast-furnace slag by calorimetry and thermogravimetry, J. Therm. Anal. Calorim. 102 (2010) 941–951. [56] S. Adu-Amankwah, M. Zajac, C. Stabler, B. Lothenbach, L. Black, Influence of limestone on the hydration of ternary slag cements, Cem. Concr. Res. 100 (2017) 96–109. [57] J. Carette, S. Staquet, Monitoring and modelling the early age and hardening behaviour of eco-concrete through continuous non-destructive measurements: Part I. Hydration and apparent activation energy, Cem. Concr. Compos. 73 (2016) 10–18. [58] J. Carette, S. Joseph, Ö. Cizer, S. Staquet, Decoupling the autogenous swelling from the self-desiccation deformation in early age concrete with mineral additions: micro-macro observations and unified modelling, Cem. Concr. Compos. 85 (2018) 122–132. [59] E. Gruyaert, Effect of blast-furnace slag as cement replacement on hydration, microstructure, strength and durability of concrete, Ph.D. thesis, Universiteit Gent, 2010. [60] M.J. Whittaker, The impact of slag composition on the microstructure of composite slag cements exposed to sulfate attack, Ph.D. thesis, University of Leeds, 2014. [61] P.T. Durdziński, Hydration of multi-component cements containing clinker, slag, type-V fly ash and limestone, Ph.D. thesis, École Polytechnique Fédérale de Lausanne, 2016. [62] A.C. Muller, K.L. Scrivener, A reassessment of mercury intrusion porosimetry by comparison with 1H NMR relaxometry, Cem. Concr. Res. 100 (2017) 350–360. [63] K.L. Scrivener, T. Füllmann, E. Gallucci, G. Walenta, E. Bermejo, Quantitative study of Portland cement hydration by X-ray diffraction/Rietveld analysis and independent methods, Cem. Concr. Res. 34 (2004) 1541–1547. [64] R.F. Feldaman, V.S. Ramachandran, P.J. Sereda, Influence of CaCO3 on the hydration of 3CaO·Al2O3, J. Am. Ceram. Soc. 48 (1965) 25–30. [65] H.J. Kuzel, H. Pöllmann, Hydration of C3A in the presence of Ca(OH)2, CaSO4·2H2O and CaCO3, Cem. Concr. Res. 21 (1991) 885–895. [66] V.L. Bonavetti, V.F. Rahhal, E.F. Irassar, Studies on the carboaluminate formation in limestone filler-blended cements, Cem. Concr. Res. 31 (2001) 853–859. [67] B. Lothenbach, G. Le Saout, E. Gallucci, K. Scrivener, Influence of limestone on the hydration of Portland cements, Cem. Concr. Res. 38 (2008) 848–860. [68] A. Hadjsadok, S. Kenai, L. Courard, F. Michel, J. Khatib, Durability of mortar and concretes containing slag with low hydraulic activity, Cem. Concr. Compos. 34 (2012) 671–677. [69] A.K. Schindler, K.J. Folliard, Heat of hydration models for cementitious materials, ACI Mater. J. 102 (2005) 24–33. [70] Z. Tan, G. De Schutter, G. Ye, Y. Gao, L. Machiels, Influence of particle size on the early hydration of slag particle activated by Ca(OH)2 solution, Constr. Build. Mater. 52 (2014) 488–493. [71] A. Attari, C. McNally, M.G. Richardson, A combined SEMCalorimetric approach for assessing hydration and porosity development in GGBS concrete, Cem. Concr. Compos. 68 (2016) 46–56. [72] J. Bensted, Hydration of Portland cement, Adv. Cem. Technol. 1983, pp. 307–347. [73] Y. Luan, T. Ishida, T. Nawa, S. Takahiro, Enhanced model and simulation of hydration process of blast furnace slag in blended cement, J. Adv. Concr. Technol. (2012) 10–2012. [74] S. Goto, Hydration of hydraulic materials a discussion on heat liberation and strength development, Adv. Cem. Res. 21 (2009) 113–117.

modeling of hydration and chemical shrinkage of slag-blended cement at early age, Constr. Build. Mater. 44 (2013) 368–380. M. Atkins, D.G. Bennett, A.C. Dawes, F.P. Glasser, A. Kindness, D. Read, A thermodynamic model for blended cements, Cem. Concr. Res. 22 (1992) 497–502. Y. Elakneswaran, E. Owaki, S. Miyahara, M. Ogino, T. Maruya, T. Nawa, Hydration study of slag-blended cement based on thermodynamic considerations, Constr. Build. Mater. 124 (2016) 615–625. K. Scrivener, B. Lothenbach, N. De Belie, E. Gruyaert, J. Skibsted, R. Snellings, A. Vollpracht, TC 238-SCM: hydration and microstructure of concrete with SCMs: State of the art on methods to determine degree of reaction of SCMs, Mater. Struct. Constr. 48 (2015) 835–862. G. De Schutter, L. Taerwe, General hydration model for portland cement and blast furnace slag cement, Cem. Concr. Res. 25 (1995) 593–604. A.C.A. Muller, Characterization of porosity & CSH in cement pastes by 1H NMR, Ph.D. thesis École Polytechnique Fédérale de Lausanne, 2014. D.P. Bentz, CEMHYD3D: a three-dimensional cement hydration and microstructure development modelling package. Version 2.0, Natl. Inst. Stand. Technol. Interag. Rep. 7232 (2000). D.P. Bentz, A three-dimensional cement hydration and microstructure program. I. hydration rate, heat of hydration, and chemical shrinkage, Technical Report, US Department of Commerce, National Institute of Standards and Technology. NISTIR 5756, 1995. F. Han, R. Liu, D. Wang, P. Yan, Characteristics of the hydration heat evolution of composite binder at different hydrating temperature, Thermochim. Acta 586 (2014) 52–57. F. Han, X. He, Z. Zhang, J. Liu, Hydration heat of slag or fly ash in the composite binder at different temperatures, Thermochim. Acta 655 (2017) 202–210. T. Kishi, K. Maekawa, Thermal and mechanical modelling of young concrete based on hydration process of multi-component cement minerals, Proc. Int. RILEM Symp. Therm. Crack. Concr. Early Ages, 2014, pp. 11–18. O. Bernard, F.J.F.-J. Ulm, E. Lemarchand, A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials, Cem. Concr. Res. 33 (2003) 1293–1309. T. Knudsen, The dispersion model for hydration of portland cement I. General concepts, Cem. Concr. Res. 14 (1984) 622–630. F. Lin, C. Meyer, Hydration kinetics modeling of Portland cement considering the effects of curing temperature and applied pressure, Cem. Concr. Res. 39 (2009) 255–265. G.C. Bye, Portland Cement: Composition, Production and Properties, Thomas Telford, London, UK, 1999. M. Balonis, F.P. Glasser, The density of cement phases, Cem. Concr. Res. 39 (2009) 733–739. R.C. Weast, CRC Handbook of Chemistry and Physics, CRC Press, Cleveland, US, 1978. J.J. Thomas, H.M. Jennings, A colloidal interpretation of chemical aging of the C-SH gel and its effects on the properties of cement paste, Cem. Concr. Res. 36 (2006) 30–38. A.J. Allen, J.J. Thomas, H.M. Jennings, Composition and density of nanoscale calcium-silicate-hydrate in cement, Nat. Mater. 6 (2007) 311–316. E. Gallucci, X. Zhang, K.L. Scrivener, Effect of temperature on the microstructure of calcium silicate hydrate (C-S-H), Cem. Concr. Res. 53 (2013) 185–195. I.G. Richardson, The nature of CSH in hardened cements, Cem. Concr. Res. 29 (1999) 1131–1147. I.G. Richardson, The nature of the hydration products in hardened cement pastes, Cem. Concr. Compos. 22 (2000) 97–113. A.C.A. Muller, K.L. Scrivener, A.M. Gajewicz, P.J. McDonald, Use of bench-top NMR to measure the density, composition and desorption isotherm of C-S-H in cement paste, Microporous Mesoporous Mater. 178 (2013) 99–103. M. Königsberger, C. Hellmich, B. Pichler, Densification of C-S-H is mainly driven by available precipitation space, as quantified through an analytical cement hydration model based on NMR data, Cem. Concr. Res. 88 (2016) 170–183.

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