Experimental and modelling research of the accelerated calcium leaching of cement paste in ammonium nitrate solution

Construction and Building Materials 40 (2013) 832–846

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Experimental and modelling research of the accelerated calcium leaching of cement paste in ammonium nitrate solution Keshu Wan a,b,⇑, Yan Li b, Wei Sun a,b a b

Jiangsu Key Laboratory of Construction Materials, Nanjing 211189, People’s Republic of China School of Materials Science and Engineering, Southeast University, Nanjing 211189, People’s Republic of China

h i g h l i g h t s " An accelerated calcium leaching model of pure cement paste in 6 mol/L ammonium nitrate leaching solution was built up. " The model was verified using elemental distributions and leaching fronts. " An accelerated factor of about 130 was calculated.

a r t i c l e

i n f o

Article history: Received 17 August 2012 Received in revised form 12 October 2012 Accepted 21 November 2012 Available online 28 December 2012 Keywords: Calcium leaching Modeling Cement paste Characterization

a b s t r a c t Calcium leaching of cement-based materials is of concern for scientific and application significance. Considering the altered solid–liquid equilibrium curve, an accelerated calcium leaching model of pure cement paste in 6 mol/L ammonium nitrate leaching solution was built up in this research. The model was numerically solved using finite difference method, and the influences of w/c ratio and initial cement composition on leaching were addressed. The accelerated model was further verified using elemental distributions and leaching fronts. Besides, through comparing the accelerated model in 6 mol/L ammonium nitrate solution and the un-accelerated model in deionized water, an accelerated factor of about 130 was found, which was slightly influenced by the initial material compositions. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Cement-based materials are widely used. However, leaching of calcium from the matrix will result in deterioration. Calcium leaching is of concern in the structures used for radioactive waste disposal containers, underground pipes, dams, and water tanks that are constantly composed to the low pH environment. Generally speaking, the calcium leaching is mainly controlled by two processes [1–7]. One is namely the calcium dissolution from the skeleton and the other is the transport of the calcium ions in the pore solution. The concentration gradients between the pore solution and the environment water lead to diffusion of calcium ions from the pore solution to the surrounding water. Once the concentration of pore solution is reduced, the solid calcium in skeleton, mainly the calcium hydroxide (CH) and calcium–silicate–hydrate (C–S– H), will dissolve gradually. These processes will increase the ⇑ Corresponding author at: School of Materials Science and Engineering, Southeast University, Nanjing 211189, People’s Republic of China. Tel.: +86 25 52090670; fax: +86 25 52090667. E-mail address: [email protected] (K. Wan). 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.11.066

porosity, consequently increase the permeability and decrease the strength of the cement matrix [5–8]. For modeling research of calcium leaching, Adenot and Buil [1], Buil [2], Berner [3], Carde et al. [4,5], Gerard et al. [6] and Pichler et al. [7] considered diffusion as the transport mechanism of leached constituents in their chemical leaching models, and modeled alteration due to the leaching and diffusion of calcium from hardened cement paste to analyze the distribution of solid calcium concentration in the cement paste with time. Ulm et al. [9] and Nguyen et al. [10] further extended the chemical leaching model to the mechanical model for predicting the strength and modulus of the leached materials. It needs to note that most of these modeling researches considered only calcium leaching in pure water/ deionized water. Gerard et al. proposed an acceleration model considering ammonium nitrate attack [6]. The liquid calcium concentration in their model was still in the range of 0–20 mmol/L. The main accelerating effect was controlled by the magnifying factor of 60 on the effective diffusion coefficient [6]. Experimentally, it was reported that the leaching front of concrete submerged in still field water for 100 years was about 5– 10 mm [11,12]. Considering the time consuming of the field water,

K. Wan et al. / Construction and Building Materials 40 (2013) 832–846

most of the laboratory tests applied accelerating leaching protocols with different accelerated methods, mainly ammonium nitrate solution [7,8,10,13–17], ammonium chloride solution [18], deionized water [13,19–21], and electrochemical method [22,23]. Among these methods, 6 mol/L ammonium nitrate solution, which can accelerate the leaching speed up to 100 times while still get the same end products [24], was intensively used to experimentally investigate calcium leaching behavior. Several accelerated factors ranging from 60 to 300 between deionized water and 6 mol/L ammonium nitrate solution were experimentally obtained by different researchers [6,8,13]. Calcium leaching is a gradual process and causes composition, structure and property gradient. It is a challenge to experimentally characterize these spatial distributions. X-ray elemental analysis, also known as EDS or EPMA is an effective method to give elemental spatial distribution and has been applied for calcium leaching research [6,20,21,25]. X-ray Computer Tomography (CT) is an effective method for microstructure analysis and has been applied for calcium leaching research [14,26,27]. In a recent investigation, X-ray CT method was further developed for characterizing the composition distribution of calcium leached specimens, which will also be applied in this research [28]. For the final applications of calcium leaching models on field water, there are two gaps needed to be bridged. The first gap is the accelerated influence between the field water and deionized water, which is case dependent because of the different ion concentrations of different field water. The other gap is the accelerated influence between deionized water and 6 mol/L ammonium nitrate solution, which is universal. Once this accelerated influence is clarified, huge experimental data on 6 mol/L ammonium nitrate solution can be used to verify the model on pure water. The verified model on pure water can be further used for engineering applications based on the experimentally determined field accelerated factor. This research focuses primarily on evaluating the accelerated influence between 6 mol/L ammonium nitrate solution and deionized water. An accelerated calcium leaching model was built and a series of laboratory tests were carried out to verify the model. Besides the leaching front information, the model was further verified using the spatial distributed elemental composition obtained from the X-ray CT method. 2. Modelling The leaching degradation of cement paste is simulated using mass conservation and thermodynamic equilibrium laws. Several assumptions or approximations are applied in this model: (i) silicon does not leach at all, and the rehydration and leaching of the unhydrated cement particles are ignored either, so only CH and C–S–H are considered in the leaching process; (ii) the time required to dissolve a given phase is much shorter compared to the diffusion time, and a thermodynamic equilibrium state is kept, so that solid-liquid equilibrium curve can be used to relate the calcium content in solid skeleton and the calcium ion concentration in pore solution [6,19]; (iii) for any local point, only after all CH is leached out, C–S–H begin to leach; (iv) CH leaching generates capillary pores and C–S–H leaching generates gel pores; (v) only room temperature is considered; (vi) only one dimensional (1D) leaching is considered in this model.

833

leaching experiments, generally, the specimens have been cured for a long time (ten months in this research). So the maximum hydration degree of the cement paste, a was applied in this model, which can be calculated by the following equation [29]:

a ¼ 0:239 þ 0:745 tan h½3:62ðw=c  0:095Þ

ð1Þ

where tan h is the hyperbolic tangent function. For more precise modeling, true hydration degrees need to be experimentally determined. 2.2. Initial compositions Suppose the volume of the cement paste is a simple addition of the volume of cement and water [30], the density of the cement paste q can be given by the density of the cement qC (taken as 3.15 g/cm3), the density of water qH2 O (taken as 1 g/cm3), and w/ c as following:

q¼

1 þ w=c 1

qC

þ qw=c

ð2Þ

H2 O

Using Bogue calculation of cement mineral composition, the mineral phase compositions of any cement can be calculated from the elemental compositions. For simplification, only the two main clinker phases of cement, i.e., tricalcium silicate (C3S), dicalcium silicate (C2S) are considered using the following stoichiometric reactions [31]:

C3 S þ 5:3H ¼ 1:3CH þ C1:7 SH4 C2 S þ 4:3H ¼ 0:3CH þ C1:7 SH4

ð3Þ

And from the stoichiometric hydration reactions, the concentration of hydration products CH and C–S–H can be calculated from the initial cement composition, w/c ratio, and the hydration degree, so the initial leachable calcium concentration in C–S–H and CH form, can be calculated:

CCSH ¼ ð1:7  fC3 S =228 þ 1:7  fC2 S =172Þ  q=ð1 þ w=cÞ  a  106 ðmmol=LÞCCH ¼ ð1:3  fC3 S =228 þ 0:3  fC2 S =172Þ  q=ð1 þ w=cÞ  a  106 ðmmol=LÞ

ð4Þ

where fC3 S is the volume fraction of C3S in the cement; fC2 S is the volume fraction of C2S in the cement. The initial leachable calcium concentration in solid before leaching can be expressed by the sum of CCSH and CCH, so the unleachable calcium contents Dus including un-hydration cement, ettringite etc. can be calculated accordingly:

Dus ¼

fCaO q  a  106   CCSH þ CCH 56 1 þ w=c

ð5Þ

where fCaO is the volume fraction of CaO in the cement. 2.3. Initial porosity and porosity evolution Before leaching, the porosity is assumed to be the same at any spatial position x, then the initial capillary porosity /cap(x, 0), the initial gel porosity /gel(x, 0), and the initial total porosity /(x, 0) can be determined using follow equations [31]:

ðw=cÞ  0:36a ðw=cÞ þ 0:32 0:19a /gel ðx; 0Þ ¼ ðw=cÞ þ 0:32 /ðx; 0Þ ¼ /cap ðx; 0Þ þ /gel ðx; 0Þ

/cap ðx; 0Þ ¼ 2.1. Hydration degree Hydration degree of a cement paste mainly depends on the water cement (w/c) ratio, curing conditions, and curing time. For

ð6Þ

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K. Wan et al. / Construction and Building Materials 40 (2013) 832–846

Both CH and C–S–H are leached out in the form of CH, so additional porosity caused by leaching can be described as follows:

MCH

/ðx; tÞ ¼ /ðx; 0Þ þ

qCH

½usðx; 0Þ  usðx; tÞ

ð7Þ

where MCH is the molar mass of CH (74 g/mol); qCH is the density of CH (2210 g/cm3); us(x, 0) is the initial leachable calcium concentration in solid before leaching (mmol/L); us(x, t) is the leachable calcium concentration in solid after leaching time t (mmol/L). According to the assumption that CH leaching generates capillary pores and C–S–H leaching generates gel pores, then: 8 < /cap ðx; 0Þ þ MCH ½usðx; 0Þ  usðx; tÞ usðx; tÞ > CCSH qCH /cap ðx; tÞ ¼ : /cap ðx; 0Þ þ MCH CCH usðx; tÞ 6 CCSH qCH ð8Þ ( usðx; tÞ > CCSH /gel ðx; 0Þ /gel ðx; tÞ ¼ /gel ðx; 0Þ þ Mq CH ½usðx; 0Þ  usðx; tÞ  CCH  usðx; tÞ 6 CCSH CH

2.4. Diffusivity evolution Diffusivity of calcium ions through cement-based materials is one of the most important factors that determine the calcium leaching processes. Several diffusivity equations and models were proposed on the relation between diffusivity and pore structure [10,20,32–34]. The diffusivity model proposed by Garboczi and Bentz based on image analysis was applied in this research [32]:

h i d ¼ 0:001 þ 0:07/2cap þ 1:8Hð/cap  /c Þð/cap  /2c d0

ð9Þ

where uc is the threshold limit value taken as 18% [32], and H(x) is the Heaviside function:

HðxÞ ¼



1; x > 0

ð10Þ

0; x 6 0

However, when the leaching is underway, the equation of (9) does not stand. Because the diffusivity increases more quickly in the process of leaching than the diffusivity decreased in the process of hydration, the threshold limit value can be revised as 16% [35]. According to Synder and Clifton, the equation can be written as [35]:

dðx; tÞ ¼0:001  0:07/cap ðx; 0Þ2  1:8Hð/cap ðx; 0Þ  0:18Þð/cap ðx; 0Þ d0  0:182 þ 0:14/cap ðx; tÞ2 þ 3:6Hð/cap ðx; tÞ  0:16Þð/cap ðx; tÞ  0:16Þ2

ð11Þ

Nevertheless, after a certain time of leaching, all the CH has dissolved, and the cement-based material only has C–S–H gel. At this time, a new revised value 0.0025 instead of 0.001 was introduced [36]. dðx; tÞ ¼0:0025  0:07/cap ðx; 0Þ2  1:8Hð/cap ðx; 0Þ  0:18Þð/cap ðx; 0Þ  0:18Þ2 d0 þ 0:14/cap ðx; tÞ2 þ 3:6Hð/cap ðx; tÞ  0:16Þð/cap ðx; tÞ  0:16Þ2

2.5. Solid–liquid equilibrium curves To describe the solubility of cement hydration product in water, solid-liquid equilibrium curve of calcium has been experimentally established for a long time [37]. In recent years, solid-liquid equilibrium curve was intensively applied to build calcium leaching models, such as in Refs. [6,19]. In calcium leaching models, the equilibrium curve was used to relate the leachable solid calcium content in solid skeleton and the calcium ion concentration u in pore solution. Eq. (13) is the solid liquid equilibrium curve applied in this research:

8   1=3  > 2 3 3 2 u > u þ u C CSH usatu > x3 x21 > 1 > > >   <  1=3 u us ¼ CCSH usatu > > > >  1=3  > > > : CCSH u u þ ðu CCH ðu  x2 Þ3 satu x Þ3 satu

x 1 < u 6 x2 x2 < u

The dissolution of CH in ammonium nitrate solution can be written according to the following reaction equation:

12000

(b) 9000

us (mmol/L)

9000

6000

3000

3000

acceler.-model

un-acceler.-model 0

0 0

5

10

u (mmol/L)

15

20

ð13Þ

2.6. Acceleration considerations

(a) us (mmol/L)

2

0 6 u 6 x1

where x1 is the calcium concentration in pore solution when C– S–H dissolved quickly (mmol/L); x2 is the calcium concentration in pore solution when CH had completed dissolved, and C–S–H began to dissolve (mmol/L); usatu is the calcium ions’ saturation concentration in deionized water under normal temperature (mmol/L). The model is built at room temperature in this research, so x1 is taken as 2 mmol/L, x2 taken as (usatu  3) mmol/L, and usatu taken as 20 mmol/L [6,19]. Once the initial cement composition and w/c ratio is known, CCH and CCSH can be calculated from Eq. (4), and then solid–liquid equilibrium curve can be drawn using Eq. (13).

12000

6000

ð12Þ

0

400

800

1200

1600

2000

2400

u (mmol/L)

Fig. 1. The solid–liquid equaialium curves (a) in deionized water and (b) in 6 mol/L ammonium nitrate solution.

2800

K. Wan et al. / Construction and Building Materials 40 (2013) 832–846

835

CaðOHÞ2 þ 2NH4 NO3 ¢ Ca2þ þ 2OH þ 2Hþ þ 2NH3 þ 2NO3 ¢ CaðNO3 Þ2 þ 2NH3 þ 2H2 O

ð14Þ

For the dissolution of CSH, a similar reaction equation is followed. The gaseous reaction product NH3 and the high solubility of reaction product calcium nitrate favor the reaction process greatly. For modeling influence, main the high solubility of calcium nitrate is considered. At room temperature, the saturated calcium concentration in CH solution is only about 20 mmol/L, while it changes to 2730 mmol/L in calcium nitrate solution [6,33]. Besides, x1 and x2 are supposed to change proportionally, and x1 is taken as 273 mmol/L and x2 taken as 2320 mmol/L in this model. Finally, the solid–liquid equilibrium curve changes accordingly, and the differences between solid–liquid equilibrium curves in deionized water and in 6 mol/L ammonium nitrate solution are drawn and compared in Fig. 1. 2.7. General conservation equations Fig. 2. Illustration of the principle and apparatus of X-ray CT.

The calcium ions’ concentration in pore solution is taken as a variable in the leaching process. The calcium ions in pore solution and the solid calcium in matrix observe the mass conservation equation with the calcium ions flux J, which is a function of the porosity, diffusivity, and calcium ion concentration. Then based on the Fick’s law, the following equation can be applied [6]:

@ð/  uÞ @us þ  div J ¼ 0 @t @t div J ¼ f ð/; d0 ; uÞ

ð15Þ

And the basic mass conservation formula for one-dimensional conditions is shown in the following equation:

  @½/ðx; tÞ  uðx; tÞ @ @uðx; tÞ @usðx; tÞ ¼ /ðx; tÞ  dðx; tÞ  @t @x @x @t

ð16Þ

The first term on the right side of Eq. (16) represents the diffusion of calcium ions in the pore solution, which is assumed to increase with the increased porosity associated with dissolution in the model, so the porosity and diffusivity cannot be removed from the partial differential equation. The second term on the right side represents the dissolution of calcium ions into the pore solution from the solid skeleton. For calcium leaching in deionized water, the boundary condition of the model is described as:

uðx; 0Þ ¼ 20 mmol=L

scheme was used to improve the stability. The spatial and temporal distributions of calcium ion concentration in pore solution, solid calcium concentration in matrix, porosity, diffusion coefficient can be numerically calculated, and then the leaching front can be determined accordingly. 3. Experimental 3.1. Sample preparations and calcium leaching experiments The specimens were prepared with PI 52.5 Portland cement from Wuhan Huaxin factory, which were produced by the pure cement clinker mixed with 5 wt% gypsum. The chemical composition of the cement is listed in Table 1. Three kinds of cement pastes with w/c ratios of 0.53, 0.35 and 0.23 were used in this research. Polycarboxylicacid superlasticizer from Jiangsu Construction Science Research Institute was applied to w/c ratio 0.35 and 0.23 samples with cement superplasticizeer ratio of 0.008 and 0.016 respectively, whose water reducing ratio is over 25%. All the specimens were cured in a standard curing room (temperature 20 ± 3 °C, relative humidity over 95%) for 10 months before further calcium leaching experiments.

ð17Þ

uð0; tÞ ¼ uðL; tÞ ¼ 0 mmol=L

where L is the length of the sample along the leaching direction (mm). For calcium leaching in 6 mol/L ammonium nitrate solution, the boundary condition is described as:

uðx; 0Þ ¼ 2730 mmol=L

ð18Þ

uð0; tÞ ¼ uðL; tÞ ¼ 0 mmol=L 2.8. Numerical solutions

Finite difference method was applied to numerically solve the differential equations, and a three layer Crank-Nicolson differential

Table 1 Chemical composition of the cement/wt%. CaO

SiO2

Al2O3

Fe2O3

MgO

SO3

K2O/Na2O

62.6

21.35

4.64

3.31

3.08

2.25

0.75

Fig. 3. One typical CT slice of a partly leached specimen showing the CT method for leaching front.

836

K. Wan et al. / Construction and Building Materials 40 (2013) 832–846 The transmitted X-ray beams have a modulated intensity dependent on the overall linear attenuation characteristics of the intervening material. This varying intensity image is referred to as a projection, and the projection information is then manipulated to produce a reconstructed image of a slice of the sample, CT image. The resulting CT image is a spatial distribution of the linear attenuation coefficients, which is expressed by grayscale values, with brighter regions corresponding to higher values of the coefficient and darker regions to lower ones. When calcium element is leached out from the cement matrix, the X-ray attenuation coefficient will decrease, so grayscale values will decrease in the CT image accordingly. One typical CT slice of a partly leached specimen is shown in Fig. 3, from which the sharp leaching front can be observed directly from grayscale value differences in the CT image. Besides the leaching front, the spatial distribution of the solid calcium is one of the main parameters of the different leaching degrees. Using the method developed in the recent research, the spatial distributions of the solid calcium caused by calcium leaching can be characterized by CT method as well [28]. All CT scans were performed at the YXLON micro-focus X-ray CT system (Y.CT Precision S, YXLON). The X-ray source is 225 kV twin head micro-focus source (Y.FXE 225.99), with direct beam head and transmission beam head. For the direct beam head applied in this research, the focus spot size is capable of less than 3 lm. The detector is a flat panel detector (Y.XRD 0820) with a pixel number of 1024  1024 and pixel size of 200 lm. Because of the cone beam magnification of 10 times, the effective pixel size is 20 lm. All scans were performed with X-ray peak energy at 195 kV and current at 0.16 mA. Each scan consisted of 1080 projections, with an acquisition time of 8 s per projection.

Fig. 4. Photographs of a partly leached specimen showing the phenolphthalein method.

3.3. Phenolphthalein experiments

Table 2 List of the main modeling parameters. L (mm)

n

dt (s)

d0 (m2/s)

usatu (mmol/L)

20

201

864

4.5  1010

2730

Leaching front is one of the main indicators of the leaching degrees. Besides the CT method, an independent phenolphthalein method was used to characterize the leaching front. Phenolphthalein is a pH-indicator which becomes pink on the sound area of the sample, where the pH value is larger than 9. The leached specimens were cut freshly for phenolphthalein test, and typical photographs of partly leached specimens are shown in Fig. 4, from which the leaching front can be clearly observed and measured.

1D calcium leaching experiment was applied in this research, and the tested specimens were prisms of 40 mm  40 mm  20 mm. In order to allow the calcium leaching process to take place only from the two 40 mm  40 mm faces, the 40 mm  20 mm faces were sealed with epoxy resin. An accelerated leaching experiment using 6 mol/L ammonium nitrate solution was used and the pH was periodically measured to keep the solution concentration. In order to avoid carbonation, nitrogen bubbling protection was applied. After a certain leaching time (1, 4, 9, 16 days), the specimens were taken out for further characterizations.

3.4. X-ray elemental analysis To verify the solid calcium distributions, an independent X-ray elemental analysis was used to characterize the Ca/Si ratios of several specimens. X-ray elemental analysis was performed on an SEM-EDS system (XL-30) using the point mode. A hundred points with step of 0.1 mm were measured along the leaching direction, with the accelerating voltage of 20 kV, the current of 60–70 lA, the probe diameter of 1 lm, and the duration time of 50 s for one point. The small samples for X-ray elemental analysis were cut from a large calcium leaching specimen, and then they were stopped hydration and exchanged water using alcohols for one week. After that, they were dried at 50 °C for 48 h and vacuum impregnated using epoxy. To obtain a flat sectional surface, they were polished using 600, 1200 grit SiC abrasive papers, and 0.25 lm diamond suspicions. Finally, the samples were further dried at 50 °C for 24 h before SEM-EDS analysis.

3.2. X-ray CT experiments The principle of X-ray CT imaging has been discussed extensively elsewhere [38,39]. Basically, as illustrated in Fig. 2, X-ray imaging measurements taken around an object from different directions produce cross-sectional images of an object. Lambert–Beer’s law is used to relate the intensity of transmitted radiation I and the intensity of incident radiation I0 to the object described by its linear attenuation coefficient l, and the distance traveled through the object t:

I ¼ I0 elt

ð19Þ

sd3

Part1

sd2

Part2

sd1

Part3

Part4

CSH and CH

CH totally leached

CH partly

totally leached

and C-S-H partly

leached and

leached

C-S-H intact

Sound part

Fig. 5. Illustration of the arbitrarily divided parts and different leaching fronts in a partly leached specimen.

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K. Wan et al. / Construction and Building Materials 40 (2013) 832–846

(a)

10

w/c=0.35

(b)

8

8

6

6

sd (mm)

sd (mm)

10

sd1 sd2 sd3

4

2

w/c=0.35

4

sd1 sd2 sd3

2

0

0 0

10

20

30

40

0

1

2

3

4

5

6

7

t0.5 (day0.5)

t (day)

Fig. 6. Different leaching fronts as a function of (a) the leaching time and (b) square of leaching time.

(a)

3000

4-day

4-day

(b) 12000

1800 1200

w/c=0.53 w/c=0.35 w/c=0.23

600

9000

us (mmol/L)

u (mmol/L)

2400

6000

w/c=0.53 w/c=0.35 w/c=0.23

3000

0

0 0

2

4

6

8

0

10

2

4

0.8

(c)

6

8

10

x (mm)

x (mm)

4-day 16

φ

d*1011 (m2 /s)

w/c=0.53 w/c=0.35 w/c=0.23

0.6

20

(d)

4-day

0.4

w/c=0.53 w/c=0.35 w/c=0.23

12 8 4

0.2

0 0

2

4

6

8

10

0

2

4

x (mm)

(e) 24000

6

8

10

x (mm) 3.6

(f)

4-day

4-day

18000 2.4

Ca/Si

us+Δ us (mmol/L))

3.0

12000

w/c=0.53 w/c=0.35 w/c=0.23

6000

0

2

4

6

x (mm)

8

1.8

w/c=0.53 w/c=0.35 w/c=0.23

1.2 0.6 10

0

2

4

6

8

10

x (mm)

Fig. 7. The spatial distributions of the main leaching parameters of the specimens with different w/c ratios (0.53, 0.35, 0.23) after 4 days leaching: (a) liquid calcium concentration, (b)leachable solid calcium concentration, (c) porosity, (d) effective diffusion coefficient, (e) the total solid calcium concentration, and (f) the Ca/Si ratio.

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K. Wan et al. / Construction and Building Materials 40 (2013) 832–846

4. Modelling results The cement composition was shown in Table 1, and the other main modeling parameters are presented in Table 2, where n is the number of space points, and dt is the time interval. 4.1. Leaching front Leaching front is one of the most important and direct results showing the leaching degrees. As introduced in the experimental part, different methods including CT method and phenolphthalein method were used to characterize the leaching fronts. In the modeling view, how to define the leaching front needs to be considered carefully, which is defined and discussed here. As is illustrated in Fig. 5, a partly calcium leached specimen can be divided into 4 parts: both CH and C–S–H are totally leached out in part 1; all CH and part C–S–H are leached out in part 2; CH is partly leached and C–S–H is intact in part 3; and the sound part 4. Then three different leaching fronts can be defined accordingly in the leaching model: the first leaching front sd1 is defined by us < CCSH + CCH, where CH begins leaching; the second leaching front sd2 is defined by us > CCSH, where CH is totally leached and C–S–H begins leaching; and the third leaching front sd3 is defined by us = 0, so principally, sd1 > sd2 > sd3. According to the definitions, the leaching fronts can be calculated, which are shown in Fig. 6 using a w/c ratio of 0.35. From Fig. 6, it is found that sd3 is always very small in the leaching period, so sd3 is not further considered. It is reasonable considering the difficulty of totally detachment of CSH. Besides,

(a) 3000

sd1 is always close with sd2 in any leaching period, which means the part 3 in Fig. 5 is small and CH leaches quickly. It is reasonable either considering the solid-liquid equilibrium curve. Because sd1 is close to sd2, and the leaching front is very sharp, it does not need care too much whether the experimentally measured leaching front is sd1, sd2, or between them. For the sake of consistency, sd2 is used as the leaching front in the following research. 4.2. Influence of w/c ratio w/c Ratio has great influence on calcium leaching, which has been experimentally observed [13,20]. From modeling view, w/c ratio controls the porosity and hydration degree, consequently controls the initial composition and microstructure. For the accelerated calcium leaching model, the mechanism of w/c ratio influencing on calcium leaching does not change. The dependences on the w/c ratio of main leaching parameters including liquid calcium concentration, solid calcium concentration, porosity, effective diffusion coefficient, and leaching front were calculated and shown in Figs. 7–9. From Figs. 7–9, the influence of w/c ratio is clearly distinguished, and as expected, the lower w/c ratio leaches much slower. At a certain leaching time (4 days in Fig. 7), the main leaching parameters are spatially distributed. The liquid calcium concentration is saturated at 2730 mmol/L on the sound part, and decreases gradually from the sound part of the leaching surface in Fig. 7a; then the solid calcium concentration decreases gradually from the sound part either in Fig. 7b; and then porosity and effective

(b)

x=5mm

x=5mm

12000

us (mmol/L)

u (mmol/L)

2400

1800

1200

6000

w/c=0.53 w/c=0.35 w/c=0.23

600

w/c=0.53 w/c=0.35 w/c=0.23

9000

3000

0 0

10

20

30

0

40

10

t (day)

(c)

0.75

20

30

40

t (day)

(d)

x=5mm

12

x=5mm 9

φ

d*1011 (m2/s)

0.60

0.45

w/c=0.53 w/c=0.35 w/c=0.23

6

w/c=0.53 w/c=0.35 w/c=0.23

3

0.30 0 0

10

20

t (day)

30

40

0

10

20

30

40

t (day)

Fig. 8. The temporal distributions of the main leaching parameters of the specimens with different w/c ratios (0.53, 0.35, 0.23) at 5 mm from the leaching surface: (a) liquid calcium concentration, (b) leachable solid calcium concentration, (c) porosity, and (d) effective diffusion coefficient.

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(a) 10

(b)

10

8

sd2 (mm)

sd2 (mm)

8

6

4

6

4

w/c=0.53 w/c=0.35 w/c=0.23

2

w/c=0.53 w/c=0.35 w/c=0.23

2

0

0 0

10

20

30

0

40

2

4

6

t0.5 (day0.5)

t (day)

Fig. 9. Progress of the CH leaching front of the specimens with different w/c ratios (0.53, 0.35, 0.23) in function of (a) time and (b) the square of time.

diffusion coefficient increase accordingly from the sound part of the leaching surface in Fig. 7c and d. Besides the leachable solid calcium us, the un-leachable solid calcium Dus is considered either. The spatial distributions of the total solid calcium content are calculated and showed in Fig. 7e and f, which is convenient for experimental comparison. At a certain depth (5 mm from the leaching surface, in Fig. 8), the main leaching parameters are time-varying. At the beginning, the leaching front does not reach 5 mm, so the liquid calcium

(a) 3000

concentration is saturated at 2730 mmol/L, then decreased with the leaching time in Fig. 8a; then the solid calcium concentration decreased gradually in Fig. 8b; and then the porosity and effective diffusion coefficient increased accordingly in Fig. 8c and d. For a w/ c ratio of 0.23 specimens, the leaching front does not reach 5 mm even after 40 days leaching, so that all the parameters are constant during this period. The evolutions of the leaching fronts (sd2) for different w/c ratios are shown in Fig. 9. As expected, high w/c ratio cement paste

(b)

w/c=0.53,4-day

w/c=0.53,4-day

12000

9000

us (mmol/L)

u (mmol/L)

2400

1800

1200

6000

Ca/Si=2.14 Ca/Si=3.14 Ca/Si=4.14

600

Ca/Si=2.14 Ca/Si=3.14 Ca/Si=4.14

3000

0

0 0

2

4

6

8

10

0

2

4

x (mm)

(c)

(d)

0.8

w/c=0.53,4-day

8

10

20

w/c=0.53,4-day

16

d*1011 (m2/s)

0.7

φ

6

x (mm)

0.6

Ca/Si=2.14 Ca/Si=3.14 Ca/Si=4.14

0.5

12

Ca/Si=2.14 Ca/Si=3.14 Ca/Si=4.14

8

4

0.4

0 0

2

4

6

x (mm)

8

10

0

2

4

6

8

10

x (mm)

Fig. 10. The spatial distributions of the main leaching parameters of the specimens with same w/c ratio of 0.53 but different cements with different Ca/Si ratios (2.14, 3.14, and 4.14) after 4 days leaching: (a) liquid calcium concentration, (b) leachable solid calcium concentration, (c) porosity, and (d) effective diffusion coefficient.

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(a) 3000

(b)

w/c=0.53,x=5mm

w/c=0.53,x=5mm

12000

Ca/Si=2.14 Ca/Si=3.14 Ca/Si=4.14

1800

1200

Ca/Si=2.14 Ca/Si=3.14 Ca/Si=4.14

9000

us (mmol/L)

u (mmol/L)

2400

6000

600

3000

0 0

10

20

30

40

0

10

t (day)

(c)

0.75

20

30

40

t (day)

(d)

w/c=0.53,x=5mm

16

w/c=0.53,x=5mm

d*1011 (m2/s)

12

φ

0.60

Ca/Si=2.14 Ca/Si=3.14 Ca/Si=4.14

0.45

8

Ca/Si=2.14 Ca/Si=3.14 Ca/Si=4.14

4

0 0

10

20

30

40

0

10

20

30

40

t (day)

t (day)

Fig. 11. The temporal distribution of the main leaching parameters of the specimens with same w/c ratio of 0.53 but different cements with different Ca/Si ratios (2.14, 3.14, and 4.14) at a 5 mm from the leaching surface: (a) liquid calcium concentration, (b)leachable solid calcium concentration, (c) porosity, and (d) effective diffusion coefficient.

corresponds to high leaching speed, and the influence of w/c ratios is significant.

4.3. Influence of Ca/Si ratio of the initial cement composition Besides the w/c ratios, the initial cement composition has also an influence on calcium leaching either. From the modeling point of view, cement composition influences calcium leaching through controlling the concentration of CH and CSH. Here, we fix the other elements in Table 1 besides calcium and silicon, and change the Ca/ Si ratios as 2.14, 3.14, and 4.14 respectively. The dependences on the Ca/Si ratios of the main leaching parameters are evaluated in Figs. 10–13. From the spatial distributions of the main leaching parameters on a certain leaching period (4 days in Fig. 10) and the temporal distributions on a certain depth from leaching surface (5 mm in Fig. 11), the influence of the Ca/Si ratios can be clearly distinguished. It is found that the specimen with larger Ca/Si ratio leaches more quickly. Because the w/c ratio is fixed at 0.53 in these calculations, the main difference is the initial content of CH and CSH, and larger Ca/Si ratio means more C3S, and consequently more CH content and few C–S–H content calculated from the Eq. (4). Because CH is much more soluble than C–S–H from the solid-liquid curve, the specimen with larger Ca/Si ratio leaches more quickly. As is verified from Fig. 12, the CH content decreases more quickly for large Ca/Si cement specimen. From Fig. 12a and c, it can be clearly seen that even with more CH content for large Ca/Si

cement specimen, the CH content is exhausted firstly after some leaching time. Besides, it is very interesting to find that the leaching speed of C–S–H is becoming quicker after the CH is totally leached out from the circle part in Fig. 12b. The evolution of the CH leaching front (sd2) on time is shown in Fig. 13, from which the influence of initial cement Ca/Si ratio is clearly distinguished either. Besides, it is found that the influence of initial cement Ca/Si ratio on CH leaching front is not so significant from Fig. 13.

4.4. Accelerated factors To evaluate the accelerated leaching effect of 6 mol/L ammonium nitrate solution, an accelerated factor was defined based on the leaching front, which is defined by the ratio of leaching time in deionized water and in 6 mol/L ammonium nitrate solution when they reach the same leaching front. According to this definition, the accelerated factor of different conditions can be obtained using the modeling results showed in Figs. 14 and 15. Fig. 14 describes the leaching front evolution of different w/c ratios, from which the accelerated factors of 142, 133, and 125 for w/ c ratio of 0.53, 0.35, and 0.23 were obtained. Fig. 15 describe the leaching front evolution of different cement Ca/Si ratios, from which the accelerated factor of 134, 132, and 126 for cement Ca/ Si ratio of 2.14, 3.14, and 4.14 were obtained. These results show that accelerated factor is only slightly influenced by the initial cement compositions and the w/c ratios.

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(a)

w/c=0.53

Ca/Si=2.14 Ca/Si=3.14 Ca/Si=4.14

8000

CSH (mmol/L)

CH (mmol/L)

(b)

w/c=0.53

6000

4500

Ca/Si=2.14 Ca/Si=3.14 Ca/Si=4.14

3000

6000

4000

1500 2000 0 0

10

20

30

0

40

10

20

t (day)

(c) 1200

CH (mmol/L)

30

40

t (day)

w/c=0.53

800

Ca/Si=2.14 Ca/Si=3.14 Ca/Si=4.14

400

0 16

20

24

28

t (day) Fig. 12. The temporal distribution of (a) the averaged CH content and (b) the averaged C–S–H content of the specimens with same w/c ratio of 0.53 but different cements with different Ca/Si ratios (2.14, 3.14, and 4.14); and (c) is the enlarged part of the circle in (a).

(a) 10

(b) 10

w/c=0.53

8

sd2 (mm)

sd2 (mm)

8

w/c=0.53

6

4

Ca/Si=2.14 Ca/Si=3.14 Ca/Si=4.14

2

6

4

Ca/Si=2.14 Ca/Si=3.14 Ca/Si=4.14

2

0

0 0

10

20

30

t (day)

0.0

0.9

1.8

2.7

3.6

4.5

t0.5 (day0.5)

Fig. 13. Progress of the CH leaching front (sd2) of the specimens with same w/c ratio of 0.53 but different cements with different Ca/Si ratios (2.14, 3.14, and 4.14) in function of (a) time and (b) the square root of time.

5. Comparisons and verifications The modeling results in Section 4 will be further compared with experimental results. Three typical leaching parameters: leaching front, solid calcium distribution, and accelerated factor, were applied for comparisons and verifications. 5.1. Leaching fronts 5.1.1. Leaching front of our experiments From the grayscale variations of the X-ray CT images showed in Fig. 16, the leaching front can be clearly observed. As has been

illustrated in Fig. 4, the leaching front can be easily measured using the phenolphthalein method either. The leaching front results from both experimental methods were compared with the modeling leaching front, which are shown in Fig. 17. Both experimental methods give similar leaching front results. It is found that some deviations of the theoretical curve from the experimental values from the 9th day onward for w/c 0.53 and 0.35 specimen (Fig. 17a and b). The problem might arise from the reduced solution concentration after longer leaching time (9, 16 days), although the pH was controlled to be acidic, the concentration would be less than 6 mol/L. Then the leaching speed would be reduced, so our experimental results are less than the theoretical results. Because

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(a) 6.0

(b) 6.0

w/c=0.53

4.5

sd (mm)

sd (mm)

4.5

w/c=0.35

3.0

1.5

3.0

1.5

acc. unacc.

acc unacc

0.0

0.0 0

10

20

30

40

0

50

10

20

30

40

50

t0.5 (day0.5)

t0.5 (day0.5)

(c) 6.0

w/c=0.23

sd (mm)

4.5

3.0

1.5

acc unacc 0.0 0

10

20

30

40

50

t0.5 (day0.5) Fig. 14. Influence of w/c ratios on the progress of the leaching front and the accelerated factor.

the leaching degree of w/c 0.23 specimen is much smaller, so this trend is not obvious (Fig. 17c). The deviation for 1 day and 4 day leaching in Fig. 17c should be experimental error, which was inevitable in measuring small leaching fronts (12 mm). In brief, although the experimental results deviate a little from the modeling results, acceptable agreements are obtained for three different w/c ratios. 5.1.2. Leaching front of references Besides our experimental leaching front results, several leaching front results from open published references were applied to verify the model either [13,24]. The initial material parameters and the leaching conditions of Ref. [24] are listed in Table 3. The calculated leaching fronts using our model and the reference’s leaching fronts determined by phenolphthalein method [24] are compared in Fig. 18. A satisfactory consistency between the modeling results and reference’s experimental results is obtained. Fig. 19 shows another verification using Ref. [13], and the initial cement composition and the leaching conditions are listed in Table 4. A satisfactory leaching front consistency between the modeling results and reference’s experimental results is obtained either. 5.2. Spatial distributions of the Ca/Si ratios In this section, the model will be further verified using the spatial distributions of solid calcium characterized by the X-ray CT method [28]. Because silicon does not leach, so the Ca/Si ratio is applied to express the solid calcium distribution caused by leaching. To verify the CT method, an independent X-ray elemental analysis

was applied to characterize the Ca/Si ratios of the specimen with w/c of 0.35 and leached for 16 days in Fig. 20a. Both experimental methods give similar solid calcium distribution, which means the X-ray CT method is acceptable in determining the Ca/Si ratios of the calcium leaching specimen. Considering the simplicity of the CT method, the spatial distributions of the Ca/Si ratios of all the specimens were experimentally determined using this method. Three w/c ratios of 0.53, 0.35, 0.23 and four leaching periods of 1, 4, 9, 16 days were considered, and the spatial distributions were further compared with the modeling results. For the w/c ratios of 0.53 and 0.35 specimens shown in Fig. 20b and c, satisfactory agreements between the modeling Ca/ Si ratio distributions and the experimental results are obtained. While for the w/c ratios of 0.23 specimens shown in Fig. 20d, the experimental leaching fronts are faster than the modeling results, which might be caused by the error of the grayscale values on the leaching surface. 5.3. Accelerated factors In Section 4.4, the accelerated factors is calculated by means of the proposed numerical model, to be about 130, which is slightly influenced by the initial specimen composition. In this section, this value will be further compared with the references’ results. Moranville et al. [40] got an accelerated factor of 121 based on the leaching front of the cement paste with a w/c ratio of 0.4 in 6 mol/L ammonium nitrate solution and in deionized water, which is very similar to the value obtained in this research. Kamali et al. [13] got an accelerated factor of 207 through experimentally comparing the

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12

(b) 12

w/c=0.53;casib=2.14 10

10

8

8

sd (mm)

sd (mm)

(a)

6 4

w/c=0.53;casib=3.14

6 4

acc. unacc.

2

acc. unacc.

2

0

0 0

10

20

30

40

50

0

10

20

30

40

50

t0.5 (day0.5)

t0.5 (day0.5)

(c) 12

w/c=0.53;casib=4.14

10

sd (mm)

8 6 4

acc. unacc.

2 0 0

10

20

30

40

50

t0.5 (day0.5) Fig. 15. Influence of cement Ca/Si ratios on the progress of the leaching front and the accelerated factor.

w/c 0.53

w/c 0.35

w/c 0.23

1 day

3mm

3mm

3mm

4 days

3mm

3mm

3mm

3mm

3mm

3mm

3mm

3mm

3mm

9 days

16 days

Fig. 16. Typical 2D topographic slices of specimens with different compositions and different leaching period.

leaching fronts in deionized water and in 6 mol/L ammonium nitrate solution. But the leaching fronts were returned from different specimen and under different temperatures. Heukamp et al. [8] got

an accelerated factor of 300 through comparing their leaching fronts in 6 mol/L ammonium nitrate solution and the reference’s results [1] in deionized water. This value was just one kind of

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(a) 10

(b)

w/c=0.53

w/c=0.35

6

sd (mm)

sd (mm)

8

8

6 4

4

Exp.phenol.

Exp.phenol. 2

Exp.CT Sim.

2

Exp.CT Sim.

0

0 0

6

12

18

24

0

30

6

12

18

24

30

t (day)

t (day)

(c) 4

w/c=0.23

sd (mm)

3

2

Exp.phenol. Exp.CT Sim.

1

0 0

4

8

12

16

20

t (day) Fig. 17. Comparison of the leaching fronts using different experimental methods and modeling results: (a) w/c 0.53, (b) w/c 0.35, and (c) w/c 0.23.

Table 3 The initial composition and leaching conditions according to Ref. [24].

w/c=0.25

SiO2 CaO Fe2O3 Al2O3 SO3 20.2% 63.4% 3% 4.9% 3.2% w/c = 0.3, 437 g/L ammonium nitrate and room temperature

8

sd (mm)

Composition wt% Conditions

10

6 4

Exp. 8

0

6

sd (mm)

sd

2

w/c=0.3

0

20

40

60

80

t (day) 4

Fig. 19. Comparison between our modeling leaching front and the experimental results from Ref. [13].

Exp. 2

sd Table 4 The initial cement composition and the leaching conditions according to Ref. [13].

0 0

7

14

21

28

t (day)

Composition wt% Conditions

SiO2 CaO Fe2O3 Al2O3 SO3 Free CaO 22.75% 67.1% 1.9% 2.7% 2.1% 0.55% w/c = 0.25, 480 g/l ammonium nitrate and room temperature

Fig. 18. Comparison between our modeling leaching front and the experimental results from Ref. [24].

estimation using the results from different specimens with different composition and curing conditions. Gerard et al. [6] got an accelerated factor of 60 through comparing an accelerated model’s leaching front and experimental results. All in all, the accelerated

factors of 6 mol/L ammonium nitrate solution in references are still scattered and open for researching. A value of about 130 is found in this research using pure modeling methods, and it is very interesting to find that the accelerate factor is only slightly influenced by

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K. Wan et al. / Construction and Building Materials 40 (2013) 832–846

(a) 4.0

(b)

w/c=0.35,16-day

w/c=0.53

2.8

2.4

Ca/Si

Ca/Si

3.2

3.5

2.1

1.6 1.4

CT EDS

0.8

Sim.-1-day Sim.-4-day Sim.-9-day Sim.-16-day

0.7

CT-1-day CT-4-day CT-9-day CT-16-day

0.0 0

2

4

6

8

10

0

2

4

6

x (mm)

(c) 3.5

(d)

w/c=0.35

2.8

10

12

3.5

w/c=0.23

2.8

Ca/Si

Ca/Si

8

x (mm)

2.1

2.1

Sim.-1-day Sim.-4-day Sim.-9-day Sim.-16-day

1.4

CT-1-day CT-4-day CT-9-day CT-16-day

Sim.-1-day Sim.-4-day Sim.-9-day Sim.-16-day

1.4

CT-1-day CT-4-day CT-9-day CT-16-day

0.7

0

2

4

6

8

10

0

2

4

6

8

10

x (mm)

x(mm)

Fig. 20. (a) Ca/Si ratio distributions of w/c 0.35 leached for 16 days using the proposed CT method and the X-ray elemental analysis, and the Ca/Si distributions of w/c of (b) 0.53, (c) 0.35, and (d) 0.23 using the X-ray CT method and modeling method.

the w/c ratios and the cement compositions. Strict experimental investigations on more specimens with different compositions are required to obtain a more precise experimental accelerated factor. 6. Conclusions Considering the increased calcium ion concentration in the pore solution and the different contributions of CH and C–S–H on leaching, an accelerated calcium leaching model of pure cement paste in 6 mol/L ammonium nitrate leaching solution was built up in this research, from which the liquid calcium in pore solution, the solid calcium in skeleton, the porosity, the diffusivity, and the leaching front can be numerically solved using finite difference method. It was found that low w/c ratio and low Ca/Si ratio in initial cement composition can effectively reduce calcium leaching. The model was verified using the solid calcium distribution and the leaching front characterized by the X-ray CT method, the X-ray elemental analysis, and the phenolphthalein method. And the model was further verified by the different references’ results. Besides, through comparing the leaching front evolutions of the accelerated model in 6 mol/L ammonium nitrate solution and the un-accelerated model in deionized water, an accelerated factor of about 130 was found, and it was interesting to find that the accelerated factor was only slightly influenced by the initial specimen compositions, such as the w/c ratios or the Ca/Si ratios in cement. Acknowledgments This research was sponsored by the foundation of the National Basic Research Program of China (No. 2009CB623203) and the National Natural Science Foundation of China (No. 51008072).

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