Consistent models for estimating chloride ingress parameters in fly ash concrete

Author’s Accepted Manuscript Consistent Models for estimating chloride ingress Parameters in fly ash concrete S. Muthulingam, B.N. Rao

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To appear in: Journal of Building Engineering Received date: 10 November 2014 Revised date: 15 April 2015 Accepted date: 24 April 2015 Cite this article as: S. Muthulingam and B.N. Rao, Consistent Models for estimating chloride ingress Parameters in fly ash concrete, Journal of Building Engineering, http://dx.doi.org/10.1016/j.jobe.2015.04.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Revised & Resubmitted to Journal of Building Engineering, April 2015

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Consistent Models for Estimating Chloride Ingress Parameters in Fly Ash Concrete by

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S. Muthulingam Department of Civil Engineering SSN College of Engineering Kalavakkam 603 110, INDIA B. N. Rao* Structural Engineering Division Department of Civil Engineering Indian Institute of Technology Madras Chennai 600 036, INDIA Tel No: +914422574285 Fax No: +914422574252

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Email: [email protected]

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*Author to whom all correspondence should be addressed

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ABSTRACT

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The addition of fly ash in cement or concrete is widely acknowledged to reduce

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chloride penetration and to enhance chloride binding capacity of cement paste fraction. This

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study proposes three parameter prediction models (submodels) of a chloride ingress model

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for fly ash concrete: time-variant surface chloride content; Langmuir and Freundlich

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isotherms constants; and reference chloride diffusion coefficient. The reliable evaluation of

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these submodels is essential to achieve more accurate estimation of the service life of

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concrete structures. Additionally, these submodels are required for physical modeling of

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coupled chloride-moisture transport in concrete. The comparison of chloride values between

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that estimated by incorporating submodels into the chloride ingress model with that from

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laboratory and field data show good agreement. The effects of submodel coefficients on the

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chloride ingress model are investigated through sensitivity analyses.

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KEYWORDS

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Binding Isotherm; Chloride Diffusion Coefficient; Chloride Ingress; Finite Element

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Modeling; Fly Ash Concrete; Surface Chloride; Sensitivity Analysis;

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1.

Introduction

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Concrete is the most consumed material in the world next to water, with three tonnes

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per year used for every person in the world. It is very likely that concrete will remain in use

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as a primary construction material for infrastructure in the future. Despite the availability of

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higher levels of know-how and equipment for quality concrete construction, in the recent past

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many concrete structures under chloride environments have undergone premature

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deterioration resulting in early reconstruction or major repairs involving a substantial

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investment.

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deterioration in concrete structures exposed to chloride environments.

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environments can be attributed to the presence of seawater, de-icing salt, sea-salt spray or

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even industrial effluents [1, 2].

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undergo not only earlier deterioration due to rebar corrosion but also severe degradation of

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concrete properties due to reactions of hydration products [3].

Chloride-induced rebar corrosion is one of the most common causes of Chloride

Concrete structures exposed to chloride environments

1

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Chloride-induced rebar corrosion adversely affects the safety and serviceability of

57

concrete structures, thus shortening their service lives. To avoid these, there are two main

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approaches; producing durable concrete that is capable of either stopping or slowing down

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the ingress of chloride ions [4, 5], or applying appropriate maintenance plans [6]. Addition of

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supplementary cementitious materials, such as blastfurnace slag and fly ash, has been widely

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accepted to assist in producing both durable and sustainable concrete (e.g. Refs. [5, 7]).

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When fly ash is added to either cement or concrete, calcium hydroxide liberated during

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hydration process reacts slowly with pozzolanic compounds present in fly ash. This reaction

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changes the pore structure of concrete thereby making it more dense, which not only reduces

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chloride and cation penetrations but also increases chloride binding capacity of the cement

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paste fraction [8, 9]. It is highly desirable to quantitatively assess such characteristics of fly

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ash as it can assist in effective service life modeling of concrete structures under chloride

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environments.

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This study proposes three submodels for estimating the parameters involved in a

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chloride ingress model of fly ash concrete, namely, time-variant surface chloride content,

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Langmuir and Freundlich isotherms constants, and reference chloride diffusion coefficient.

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Reliable and careful evaluation of these submodels is essential to achieve more accurate and

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realistic estimation of the service life of concrete structures. Additionally, these submodels

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are required for physical modeling of coupled chloride-moisture transport in concrete

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(e.g. Ref. [10]). This work is presented in three main parts. The first part discusses relevant

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background, appropriate experimental data and procedure used to develop each of the three

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submodels.

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developed submodels based on the variety of real field and laboratory data while the third

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part presents a sensitivity analysis of submodel coefficients.

The second part provides experimental validation and comparison of the

2

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2.

Time-variant surface chloride content

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2.1. Background

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In analytical and numerical models for the prediction of chloride ingress into concrete,

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surface chloride content  Cs  is one of the primary input parameters. Cs may depend on

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various parameters, such as the structure location, surface orientation, and chloride content in

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the environment. Table 1 lists various time-variant Cs models reported in literature for

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concrete specimens exposed to chloride environments. In Table 1, w b represents water-to-

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binder ratio (a ratio by mass) and t represents exposure time in years. Table 1 indicates that,

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in the past, linear [11], power law [11, 12], and natural logarithmic [13–15] functions or their

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combinations (e.g. Ref. [16]) have been adopted to find the trend of a given Cs data. Fig. 1

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shows the plot of various Cs models listed in Table 1 along with a set of real field data

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reported in the literature [15, 17]. Note that w b ratios of 0.48, 0.50, 0.45, and 0.50 are

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adopted in Fig. 1 for Cs models reported in Refs. [11], [12], [15], and [16], respectively. The

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real field data shown in Fig. 1 reveals that chloride ions build-up progressively on the

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exposed surfaces of concrete under chloride environments. Additionally, Fig. 1 shows that

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such chloride build-up is faster during initial exposure period and becomes progressively

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slower with time and may even attain a constant value. The effects of binding induce

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progressive build-up of chloride on the surface of concrete, wetting-drying cycles also play a

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role, specifically when concrete is exposed to splash or tidal conditions [13]. Fig. 2 shows

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the plot of two of the natural logarithmic function based Cs models reported in the literature

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[13, 14]. The following critical observations are drawn from Table 1, Figs. 1 and 2: 3

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1. The values of Cs are time-variant and are considerably affected by w b ratio.

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Moreover, two models of Cs (i.e. Refs. [14, 16]), which although are based on

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experiments conducted on fly ash concrete, are considered to be independent of the

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level of fly ash replacement (0–50%). This could mean that Cs values are not

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significantly affected by the level of fly ash replacement.

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2. Trend lines predicted by the linear [11], power law [11, 12], and combination of

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natural logarithm and power law [16] functions are inconsistent with real field data

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reported in the literature [15, 17].

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functions significantly under- or over-estimate the values of Cs at different exposure

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periods.

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Instead of making reliable predictions, these

3. Among various functions used to represent the trend of Cs data, natural logarithmic

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function provides best fit estimates under chloride environments.

The natural

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logarithmic function most effectively represents the progressive build-up of chlorides

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occurring at the surfaces of concrete during the period of initial exposure.

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4. Although two models reported in Refs. [13, 14] (see Fig. 2) are based on natural

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logarithmic function, they predict negative values of Cs during initial exposure period

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(say 0–0.6 years). This implies that the surface chloride ions are moving out rather

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than penetrating into concrete, which is inapplicable in the problem of chloride

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ingress into concrete.

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Perhaps, it needs to be added here that few studies in the past (e.g. Refs. [18, 19]) have

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modeled chloride ingress into concrete by considering constant values of Cs , thereby

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ignoring the time-variant nature of Cs . This was primarily done based on the hypothesis that 4

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chloride ions at the surfaces of concrete remain in chemical equilibrium in the form of

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di-electric layer [18, 19]. Moreover, among the Cs models listed in Table 1, the model

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proposed by Pack et al. [15] is relatively promising mainly because it predicts positive values

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at all times and is based on natural logarithmic function. Nevertheless, the model reported in

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Ref. [15] fails to account explicitly for the dependency of Cs on w b ratio. Therefore, it is

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highly desirable that this model is improved by incorporating the dependency of Cs on w b

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ratio.

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2.2. Developed model

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In the current study, a model for time-variant surface chloride content Cs  t  , having a form of natural logarithmic function is developed as given below:

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Cs  t   1 ln 2 t  1  3  w b  [% wt. of binder]

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where 1 ,  2 , and  3 are coefficients to be obtained from regression analysis of an

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experimental or a numerical data and t is exposure time in years. The developed model

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(i.e. Eq. (1)) is very promising as it fulfills all the requirements of a complete model for

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estimating the values of Cs in concrete exposed to chloride environments, namely, time-

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dependency, natural logarithmic trend, prediction of positive value at all time, dependency on

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w b ratio and independent of fly ash replacement level. Note that the developed model

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considers Cs to be independent of the level of fly ash replacement. Although increase in the

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level of fly ash replacement reduces the quantity of active material in paste, which delays the

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hydration process of cement paste, it has only a slight influence on Cs [20].

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2.3. Model demonstration 5

(1)

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To demonstrate better prediction capabilities of the developed model (i.e. Eq. (1)), it is

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compared with two other models reported in Refs. [14, 16] (see Table 1), but for the same

147

experimental data [14]. In order to evaluate the coefficients of the developed Cs model, a

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regression analysis is performed over the Cs model of Chalee et al. [14] and the values of

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coefficients 1 ,  2 , and  3 are estimated as 2.0, 1.912, and 2.365 respectively, with a

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corresponding R-Square value of 0.99.

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analysis could have been conducted on both models (i.e. Refs. [14, 16]), the former is

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preferred as its estimates are consistent with real field data, whereas the latter is not

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considered due to the presence of a square root term that could potentially lead to

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overestimation of Cs values.

It may be noted here that, although regression

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Fig. 3 shows the comparison between Cs models reported in Refs. [14, 16] with that of

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the developed model. It is seen that the developed model, when compared with the model of

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Chalee et al. [14], predicts not only consistent but also non-negative values of Cs during the

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entire period of exposure. Additionally, Fig. 3 also shows that the Cs model proposed in

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Ref. [16], which contains a combination of logarithmic and square root functions,

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significantly overestimates the values of Cs at higher exposure period (say > 5 years). Such

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inflated estimates of Cs values at the exposed surfaces of concrete, apart from indicating

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increased ingress of chlorides into concrete leading to much shorter time to corrosion

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initiation of rebars also reduce estimated service life of concrete structures and foresee earlier

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maintenance applications. Further, Fig. 3 shows comparison between the developed model

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and Pack et al. [15] model. In this case, by performing regression analysis, 1 ,  2 , and  3

6

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are estimated as 0.26, 3.77, and 3.06 respectively, with a corresponding R-Square value of

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0.99. Note the comparison shows very good agreement between the two models.

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3.

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3.1. Background

Langmuir and Freundlich isotherms constant

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Chloride binding involves the processes through which chloride ions in the pore

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solution of concrete are fixed to different extent on certain cement hydrates [21, 22]. In

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general, chloride binding isotherm (CBI) relates free chloride C f

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at equilibrium and is characteristic of each cementitious system. The two types of commonly

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used CBIs for cementitious materials are [21, 23]:

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(1) Langmuir isotherm: CbL 

  and bound chloride  C 

 Cf 1   C f L

b

(2)

L

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

 L CbL  C f 1   L C f





(2) Freundlich isotherm: CbF    F C f





2

F

 1 CbF   F  F C f F C f

(3)

(4)

(5)

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where  L (mL pore solution/g sample),  L (mL pore solution/mg Cl),  F (mL pore

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solution/g sample), and  F represent CBIs constants as a function of fly ash replacement

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level. The term Cb C f represents binding capacity of the cementitious system, which is

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the slope of CBI. Langmuir and Freundlich isotherms predict the relation between bound and

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free chlorides better at lower and higher free chloride concentrations, respectively [23]. 7

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In general, CBIs constants are determined by conducting tests on cement or fly ash

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pastes and not on concrete, mainly because; (1) the presence of aggregates in concrete does

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not influence CBIs; and (2) the void size range, where moisture equilibrium processes

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described by CBIs take place, is much smaller than paste-aggregate interface heterogeneities

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and typical voids present in this zone [24]. Recently, Ishida et al. [25] proposed a CBI model

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given by Eq. (6) for fly ash concrete and expressed the relation between CBI constant  ,

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and level of fly ash replacement f , using Eq. (7):

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Cb 

 Cf 1  4.0C f

  15.5 f 2  1.8 f  11.8

(6)

(7)

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In Eqs. (6) and (7), Cb and C f are expressed in percentage mass of binder, f takes

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values between 0 and 0.4. Based on Eqs. (6) and (7), Fig. 4 shows the distribution of bound

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chloride and binding capacity of fly ash concrete at various fly ash replacement levels.

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Fig. 4 demonstrates that both bound chloride and binding capacity values decrease with

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increasing levels of fly ash replacement. However, the contribution of fly ash in either

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cement or concrete enhances chloride binding capacity of the cementitious matrix [26–31].

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This can be attributed to the following three reasons [26, 32, 33]: (1) increased formation of

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less porous Friedel’s salt after the pozzolanic reaction; (2) higher surface area and

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adsorptivity of fly ash cement; and (3) relatively lower chloride ion diffusion coefficient.

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Hence, Eqs. (6) and (7) predictions contradict past research findings. Additionally, when

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incorporated into a coupled chloride-moisture transport model, Eqs. (6) and (7) are very

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likely to estimate faster transport of chlorides with increasing levels of fly ash replacement

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(0–40%), which effectively reduces the service life of concrete structures. Therefore, a more 8

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consistent model is required for estimating CBIs constants in fly ash concrete. Further, it

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needs to be added here that in the absence of direct experimental data for CBI constants,

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numerical inverse analysis is a potential alternative for evaluating their values. The inverse

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analysis approach aims to best fit the experimentally measured chloride profile with

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that computed through a chloride transport model by treating CBI constants as

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unknowns [22, 28, 34].

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3.2. Model development

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In the present study, an attempt is made to develop a simple yet consistent model for

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estimating Langmuir and Freundlich isotherms constants in terms of fly ash replacement

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level. This model is based on data from the experimental work of Zibara [22]. Fig. 5 shows

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experimental data reported in Ref. [22] for cement pastes with 0% and 25% levels of fly ash

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replacement having a w b ratio of 0.5. The experimental data shown in Fig. 5 represent

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binding properties of pastes having specific w b ratio and mix compositions in the form of a

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binding relation, with the amount of bound chlorides expressed as a function of the amount of

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free chlorides. It is noticed from Fig. 5 that bound chlorides increase with increasing levels

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of fly ash replacement. Moreover, Fig. 5 also shows the trend lines drawn through the data

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points using a standard smooth curve fitting technique (non-linear regression) employing

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CBIs (i.e. Eqs. (2) and (4)). Table 2 presents estimated values of curve fitting coefficients,

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which are none other than CBIs constants.

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3.3. Developed model

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In the current work, relation between Langmuir and Freundlich isotherms constants and fly ash replacement level is approximated using a linear function given below:

9

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

L

,  L , F ,  F

 1  2 f

(8)

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where f represents fly ash replacement level expressed in percentage, 1 and  2 are

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coefficients to be obtained from regression analysis of an experimental or a numerical data.

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The developed model (i.e. Eq. (8)), in addition to considering the relation between CBIs

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constants and fly ash replacement level to be linear for simplicity, assumes the effects of w b

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ratio on chloride binding capacity to be negligible. The validity of these considerations could

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be justified on the basis of outcomes from a long-term experimental study [4], which

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reported; (1) fairly linear increase in chloride binding capacity, expressed in percentage of

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total chloride content (TCC), with increasing levels of fly ash replacement (050%); and (2)

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the effects of w b ratio on chloride binding capacity as small.

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Table 3 lists estimated values of the developed model coefficients 1 and  2 for each

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CBIs constants  L ,  L ,  F , and  F obtained by fitting the model to data shown in

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Table 2. Table 3 indicates increasing trends (i.e. positive slope) for CBIs constants  L ,  L

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, and  F and decreasing trend (i.e. negative slope) for CBI constant  F . These trends,

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though estimated for fly ash replacement levels between 0% and 25%, are very likely to

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continue between 25% and 50%. A similar observation demonstrating a steady increase of

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bound chloride in concrete with increasing levels of fly ash replacement between 0% and

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50% is also reported in Ref. [29]. Hence, in the current study, for simplicity, the linear trends

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of CBIs constants for fly ash replacement levels between 0% and 25% are assumed to

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continue with the same slope even between 25% and 50%. It needs to be acknowledged here

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that, such extrapolation though assists in estimating the constants of CBIs at higher levels of

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fly ash replacement (i.e. 2550%), may not follow linear trends. Fig. 6 shows relation 10

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between CBIs constants and fly ash replacement level; solid lines for 025% (estimated) and

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dotted lines for 2550% (extrapolated).

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3.4. Model demonstration

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Figs. 7a and b show the profiles of Langmuir and Freundlich isotherms (i.e. Eqs. (2)

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and (4)), respectively, for various fly ash replacement levels based on the developed model

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(i.e. Eq. (8)). It is seen that profiles are very consistent with past research findings [26–31]

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(i.e. bound chloride increases with increasing levels of fly ash replacement). However, it

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needs to be noted here that chloride binding may vary; (1) with different types of fly ash (i.e.

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fly ash having different chemical compositions) [30]; (2) when fly ash is used with different

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types of Portland cement (I and V) [27].

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Although, the developed model linearly approximates the relation between CBIs constants

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and fly ash replacement level, nevertheless promising due to its simplicity and consistency.

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4.

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4.1. Background

Hence, this is an area for further research.

Reference chloride diffusion coefficient

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Numerous factors, such as the type of cementitious material, w b ratio, curing time,

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concrete age, and other physical factors, govern chloride ingress profiles in concrete.

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Moreover, chloride ingress profiles based on long-term exposure in an actual chloride

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environment could very well reveal the behavior of chloride ingress into concrete [14].

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In 2009, Chalee et al. [14] reported chloride data of fly ash concrete measured over a period

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of five years under tidal exposure condition. In brief, Chalee et al. [14]; (1) casted concrete

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cube specimens of size 0.2 × 0.2 × 0.2 m with various combinations of w b ratio (i.e. 0.45,

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0.55, and 0.65) and fly ash replacement level (i.e. 0%, 15%, 25%, 35%, and 50%); (2) 11

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transferred the specimens, after 27 days of curing, to a tidal in Chonburi Province, in the Gulf

273

of Thailand; (3) exposed the specimens to seawater wetting-drying cycles for five years; and

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(4) dry-cored the specimens, after 2, 3, 4, and 5 years, to obtain a core sample of 50 mm

275

diameter for determining TCC of concrete in accordance with ASTM C1152 [35].

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addition, Chalee et al. [14] proposed a chloride ingress model and validated the model with

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the measured experimental data. The chloride ingress model proposed in Ref. [14] is based

278

on a simplified analytical solution to Fick’s second law of diffusion:     x Ct  x, t  CS 1  erf    t1  2  1 

279

     

In

(9)

280

where x is distance from concrete surface (mm), t is exposure time (s), Cs is surface

281

chloride content (see Table 1), and  represents a coefficient obtained from data analysis

282

[14]:

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   0.0015  w b   0.0034 f   0.175  w b   0.840

(10)

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However, Petcherdchoo [16] analysed Eq. (9) and reported that the chloride profiles

285

obtained from Eq. (9) are inconsistent with those obtained from the finite difference method.

286

To overcome such inconsistencies, Petcherdchoo [16] perfomed regression analysis over

287

Eq. (9) with an alternate chloride ingress model (i.e. Eq. (11)), which is also based on a

288

simplfied solution to Fick’s second law of diffusion:

  x  x    x  Ct  x, t   C1  erfc   C t e 4Da t    2 D t   2  2 D t  a  a     2

289

12

  x   erfc    t 2 D a    

(11)

290

where C1 represents initial surface chloride (% wt. of binder), C2 is a constant, t is exposure

291

time (years), and Da is apparent chloride diffusion coefficient (mm2/year).

292

formulation, Petcherdchoo [16] employed a time-variant Da , which is based on the study of

293

Tang and Gulkiers [36]:

For model

294

Dc ,ref  tex 1m  tex 1m   tref  Da   1         1  m  t   t    t 

295

where Dc ,ref reference chloride diffusion coefficient corresponding to time tref (=28 days),

296

m normally being referred to as the age factor, and tex is exposure time in years. It is worth

297

to note here that, Dc ,ref is one of the important parameters because it acts as a base value for

298

estimating the diffusivity of chloride in concrete. By directly substituting Eq. (12) in Eq. (11)

299

and performing regression analysis with Eq. (9), Petcherdchoo [16] proposed an expression,

300

as a function of f , for determining the values of Dc ,ref :

301

m

Dc,ref  101.776 1.364  w b   5.806  18.69  w b   f [mm2/year]

(12)

(13)

302

As an alternative to numerical deduction from experimental data, mortar or concrete

303

specimens are also used to measure the values of Dc ,ref under laboratory conditions at

304

28 days [33]. Based on a large database of bulk diffusion tests, Life-365 program [37]

305

proposed the following equation for evaluating Dc ,ref :

306

Dc,ref  1012.06  2.4  w b [m2/s]

(14)

307

It is important to note that, Eq. (14) considers Dc ,ref as a function of w b ratio only

308

based on the assumption that neither fly ash nor slag affects early chloride diffusion coefficient. 13

309

Fig. 8a shows comparison between two Dc ,ref models Eqs. (13) and (14) for various

310

w b ratios by presetting the value of f in Eq. (13) equal to zero while Fig. 8b examines

311

Dc ,ref

312

Figs. 8a and b:

predictions based on Eq. (13).

The following inferences are drawn from

313

1. For a given w b ratio (see Fig. 8a), the values of Dc ,ref estimated by the program of

314

Life365 [37] (i.e. Eq. (14)) are higher than that estimated by the model of

315

Petcherdchoo [16] (i.e. Eq. (13)).

316

incorporated with Eq. (14) would predict relatively higher chloride diffusivity in

317

concrete, which leads to faster corrosion of rebars and earlier times of maintenance

318

applications.

This implies that a chloride ingress model

319

2. Eq. (13) is inconsistent (see Fig. 8b) in estimating the values of Dc ,ref at various w b

320

ratios and fly ash replacement levels. For example, at w b ratio of 0.3, the model

321

predicts increasing values of Dc ,ref with increasing levels of fly ash replacement.

322

Moreover, inconsistent predictions by the model contradict widely held view

323

(e.g. Refs. [4, 14, 26, 38]) that concrete becomes less porous and hence less diffusive

324

to ingress of chloride ions with increasing levels of fly ash replacement (0–50%).

325

The inconsistencies illustrated in Fig. 8b could be due to; (1) inappropriate choice of

326

the mathematical function to determine the trend of Dc ,ref values; and (2) the model

327

constructed from a simplified analytical solution to Fick’s second law of diffusion. For

328

instance, while deriving analytical solutions, surface chloride content needs to be enforced as

329

a boundary condition. However, when realistic surface chloride content profile such as

330

natural logarithmic function is encountered, the underlying analytical solution procedure is 14

331

extremely complex [15]. Hence, using constant and simplified forms of surface chloride

332

content, so as to obtain an analytical solution to Fick’s second law of diffusion, could lead to

333

potential inaccuracies in the estimated values of Dc ,ref and consequently in its function.

334

From these discussions, it is understood that a consistent model for Dc ,ref , which is

335

developed from a comprehensive chloride ingress model, is highly desired.

336

4.2. Fundamentals of chloride ingress model

337

The process of chloride ingress into concrete is very complex due to; (1) interaction

338

between many physical and chemical phenomena; (2) dependency on many internal

339

parameters (level of hydration in concrete, porosity, binder type, etc.); and (3) external

340

environmental conditions (temperature, relative humidity, chloride, etc.). An effective way to

341

study the problem of chloride ingress into concrete is to consider it as an interaction between

342

three phenomena, namely, heat transport, moisture transport, and chloride transport. A field

343

equation represents each of these phenomena, and subsequent simultaneous solution

344

considers their interaction.

345

equations representing the process of chloride ingress into concrete:

346

The following general form expresses the governing field

               0 diffusion

(15)

convection

347

The correspondence between  ,  ,  ,  ,  and the terms for the transport quantity

348

is presented in Table 4. For chloride transport, C f is the free chlorides content dissolved in

349

the pore solution (kg/m3), Dca and Dha represent apparent chloride and humidity diffusion

350

coefficients (m2/s), respectively:

15

351

Dca 

352

Dha 

Dc ,ref f c T  f c  t  f c  h  1   Cb 1  we   C f

  

Dh ,ref f h T  f h  h  f h  te  1   Cb 1  we   C f

  

[m2/s]

(16)

[m2/s]

(17)

353

where Dc ,ref and Dh,ref are reference chloride and humidity diffusion coefficients (m2/s)

354

measured under standard conditions, we is evaporable water content (m3 of water/m3 of

355

concrete), f c and f h are modification factors to account for the effects of temperature T ,

356

relative humidity h (a ratio between water vapor pressure and saturated vapor pressure),

357

ageing, and the level of hydration in concrete. These factors are detailed in Ref. [39]. If the

358

chemically bound and physically sorbed chlorides are grouped as bound chlorides Cb

359

(kg/m3), then TCC Ct , can be expressed as [40]:

Ct  Cb  weC f [kg/m3]

360

(18)

361

For moisture transport, Dh represents humidity diffusion coefficient (m2/s) and the

362

derivative of water content with respect to pore relative humidity (i.e. we h ) is defined as

363

moisture capacity.

364

evaporable water content and pore relative humidity. Based on thermodynamic principle of

365

adsorption, Braunauer-Skalny-Bodor model considers this relation to depend on temperature,

366

w b ratio, and level of hydration in concrete, te (days) [41]:

367

At standard temperature and pressure, adsorption isotherm relates

we 

C k Vm h 1  k h  1   C  1 k h 

16

(19)

368

where C is a constant that takes into account the influence of change in temperature on the

369

adsorption isotherm, k is a constant resulted from the assumption that the number of

370

adsorbed layers is a finite small number and Vm represents the monolayer capacity (equal to

371

the mass of adsorbate required to cover the adsorbent with a single molecular layer). These

372

parameters are detailed in Ref. [39]. From the adsorption isotherm, moisture capacity can be

373

obtained by taking its derivative with respect to h : 2 2 2 2 we CkVm  Ch k  h k  1  2 2 h  hk  1  Chk  hk  1

374

(20)

375

For heat transport, T is temperature (K),  is the density of concrete (kg/m3), c p is

376

the specific heat capacity of concrete (J/kg K), and DT is the thermal conductivity of concrete

377

(W/m K). An analytical solution is very difficult to obtain for the field equations (i.e. Table

378

4) due to the dependence of the various material properties and boundary conditions on the

379

physical parameters of the concrete and the time level of exposure. Hence, a combined finite

380

element (FE) and finite difference scheme is widely adopted to numerically solve the field

381

equations (e.g. Ref. [10]). FE formulation and solution procedure of governing PDEs are

382

well documented in the literature [10, 42, 43] and will not be dealt here. The pertinent

383

boundary conditions are employed to enforce mean monthly variations in temperature and

384

relative humidity at the exposed boundaries as fluxes. The following general form represents

385

the boundary conditions:

386

X    b        b    diffusion

387 388

(21)

convection

The correspondence between X ,  ,  ,  and the different boundary conditions associated with the diffusion and convection terms of the transport quantity is presented in 17

b

389

Table 5. In Table 5, X cb (kg/m2 s), X h (m/s), and X Tb (W/m2) represent chloride, relative

390

humidity, and heat fluxes at the exposed boundaries, respectively. Moreover, Bc (m/s),

391

Bh (m/s), and BT (W/m2 K) are chloride, relative humidity, and heat transfer coefficients,

392

respectively. In addition, C b (kg/m3), hb , and T b (K) are chloride, relative humidity, and

393

temperature values at the exposed boundaries, respectively. Furthermore, Cenv (kg/m3), henv ,

394

Tenv (K) represent, chloride, relative humidity, and temperature values in the surrounding

395

environment, respectively.

396

397

398

4.3. Model development

399

In the current study, an attempt is made to propose a Dc,ref model based on the

400

comprehensive chloride ingress model described in the preceding subsection. Adopting such

401

a comprehensive chloride ingress model is highly promising to reduce the serious gap

402

between simulated and real environments by accounting for; (1) time-variant ambient effects

403

such as temperature and relative humidity in the environment; (2) concrete age and chloride

404

binding; (3) realistic yet complex variations in surface chloride content; and (4) moisture flux

405

due to wetting-drying cycles. However, the chloride ingress model requires an adsorption

406

isotherm model for fly ash concrete. Since the experimental work done on this area is very

407

limited, in the current model development, the adsorption isotherm in Eq. (19) is assumed to

408

be valid for fly ash concrete. Moreover, developing a proper adsorption isotherm model for

409

fly ash concrete is beyond the scope of this research. Furthermore, CBIs constants estimated

410

for pastes using Eq. (8) needs to be idealized for concrete. This is accomplished by following 18

411

a simple procedure reported in the literature [22, 28]. In brief, this procedure follows the

412

numerical inverse analysis approach discussed in subsection 3.1 by assuming we values of

413

8%, 10%, 11%, 13%, and 14% and effective diffusion coefficient values of 3 × 10-12, 2.5 ×

414

10-12, 2.0 × 10-12, 1.5 × 10-12, and 1.0 × 10-12 for fly ash replacement levels of 0%, 15%, 25%,

415

35%, and 50%, respectively [22, 34, 44]. By adopting this procedure, constants of CBIs

416

determined using Eq. (8) are idealized for concrete, and their values are listed in Table 6.

417

The experimental work of Chalee et al. [14] is used for developing Dc,ref model. The

418

procedure of developing the Dc,ref model involves numerical simulation of the experimental

419

work reported in Ref. [14] using the chloride ingress model by enforcing appropriate

420

boundary and initial conditions. Firstly, the concrete cross-section (i.e. 0.2 × 0.2 m) is

421

discretized into four-noded quadrilateral isoparametric elements of size 5 × 5 mm. Secondly,

422

pertinent boundary and initial conditions are enforced on the exposed boundaries of FE

423

model. The essential boundary conditions are surface chloride content profile, ambient

424

temperature and relative humidity in the environment. The surface chloride content model

425

reported in [14] (see Table 1) is considered in numerical analyses by recasting it into the form

426

of the developed Cs model for reasons described in subsection 2.1.

427

To enforce boundary conditions to the numerical model, the ambient temperature and

428

relative humidity data needs be gathered within the specific region where concrete

429

component is located.

430

Meteorological Department, TMD [45], Thailand, and assuming a sinusoidal variation similar

431

to that reported in Ref. [46], the monthly variations of temperature is obtained by a simple

432

curve fitting technique as a function of time ( t in years) as follows:

Using the mean monthly temperature obtained from Thai

19

Tenv  t   300.60  7.05sin (2  t )

433

(22)

434

Moreover, concretes in tidal zones experience rising and falling tides every day, which

435

results in frequent moisture flux shuttling from the external environment to the concrete

436

surface. To account for this phenomenon, Cheung et al. [47] suggested that the effective

437

monthly moisture condition on the concrete surface is estimated by an increase of the local

438

average relative humidity. Using the mean monthly relative humidity data obtained from

439

Thai Meteorological Department, TMD [45], Thailand, and considering the expression

440

suggested in Ref. [47], the monthly variations of relative humidity is expressed as a function

441

of time ( t in months):

442

  henv  t   0.89  0.05sin  t  0.78  6 

(23)

443

All the input values used in FE analysis are listed in Table 7 [40, 48–50]. In addition,

444

Dh,ref values of 1 × 10-12, 5 × 10-12, and 2.5 × 10-11 m2/s [40] are considered for the w b ratios

445

of 0.45, 0.55, and 0.65, respectively. To determine Dc,ref values, the sum of the squared

446

differences between the TCC values from; (1) the experimental data reported in Refs. [14, 51]

447

for w b ratios of 0.45 and 0.65 with 0%, 15%, 25%, 35%, and 50% fly ash replacement

448

levels, and for the w b ratio of 0.55 with 0%, 25%, and 50% fly ash replacement levels; and

449

(2) the regression analysis of Chalee et al. [14] (i.e. Eq. (9)) for the w b ratio of 0.55 with

450

15% and 35% fly ash replacement levels and that obtained from numerical analyses by

451

adopting the chloride ingress model are minimized by adjusting Dc,ref values. Perhaps it

452

needs to be clarified here that while conducting numerical analyses, Eq. (9) is considered for

453

the w b ratio of 0.55 with 15% and 35% fly ash replacement levels instead of corresponding 20

454

experimental data because the researchers have not reported these data. In addition, it may

455

also be noted that while performing numerical analyses, models developed for surface

456

chloride content (i.e. Eq. (1)) and CBIs constants (i.e. Eq. (8)) are incorporated into the

457

chloride ingress model. The determined values of Dc,ref for various w b ratios and fly ash

458

replacement levels along with root of mean square errors (RMSE) are listed in Table 8.

459

4.4. Developed model

460 461

462

In the present work, mathematical function of the form given by Eq. (24) is chosen as a first approximation to determine the trend for Dc,ref values listed in Table 8: Log10 Dc,ref  1  w b   2  w b   3 f   4 [mm2/day] 2

(24)

463

where 1 ,  2 ,  3 , and  4 are coefficients to be obtained from regression analysis of an

464

experimental or a numerical data. In Eq. (24), Dc, ref values are logarithmically related to a

465

quadratic form of w b ratio and a linear form of fly ash replacement level.

466

mathematical functions are also reported in Refs. [52, 53]; however, these functions do not

467

explicitly consider the effects of fly ash on the diffusivity of chloride in concrete.

468

4.5. Model demonstration

Similar

469

Fig. 9 shows values of Dc,ref averaged over the exposure period of 2–5 years (see

470

Table 8, a factor of 106/24×60×60 could be adopted for changing the unit from mm2/day to

471

m2/s) as data points for various combinations of fly ash replacement level and w b ratio. By

472

adding trend lines using Eq. (24) for each w b ratio (i.e. 0.45, 0.55, and 0.65) to these data

473

points, three distinct equations (see Fig. 9) representing the relations between Dc,ref and fly

21

474

ash replacement level are obtained. It is seen in Fig. 9 that all the trend lines added to Dc,ref

475

data have an R-Square value of 0.99 indicating that the developed model (i.e. Eq. (24)) better

476

represents the trend of Dc,ref values listed in Table 8. The developed model needs to be

477

examined further for its capability to predict the trend of other Dc,ref data. The estimates of

478

Dc,ref based on regression analysis as reported in Ref. [16] are used for this purpose. Fig. 10

479

shows Dc,ref estimates obtained from Ref. [16] as data points along with two trend lines, one

480

based on Eq. (13) and other based on developed model. Fig. 10 reveals that, for Dc,ref

481

estimates reported in Ref. [16], trend lines based on Eq. (13) have R-Square values of 0.61,

482

0.74, and 0.56, whereas those based on developed model have R-Square values of 0.70, 0.82,

483

and 0.76. These relatively higher R-Square values distinctively indicate that the developed

484

model better characterizes the trend of Dc,ref values, specifically in fly ash concrete.

485

Furthermore, by conducting non-linear regression analysis using Eq. (24) with all the

486

values of Dc,ref averaged over the period of 2–5 years (see Table 8), the values of coefficients

487

1 ,  2 ,  3 , and  4 are determined as 0.4821, 0.2127, 0.0136, and 0.2824, respectively.

488

This regression analysis yielded a RMSE of 0.479 and an R-Square value of 0.9847

489

indicating that the developed model fits very well with the values of Dc,ref listed in Table 8.

490

Fig. 11 shows the relation between Dc,ref and fly ash replacement level for various w b ratios

491

(0.3–0.7) based on the developed model. Fig. 11 demonstrates that the values of Dc,ref

492

estimated based on the developed model are very consistent, that is, for a given w b ratio, the

493

model predicts decreasing values of Dc,ref with increasing levels of fly ash replacement.

22

The ratio between Dc,ref

494 495

in the developed model to that in the model of

Petcherdchoo [16] can be written as: Dc ,ref , Developed

496

Dc ,ref , Petcherdchoo [16]



10

100.4821 w b 

1.776 1.364  w b 

2

 0.2127  w b   0.0136 f  0.2824

 5.806  18.69  w b   f

 365

(25)

497

The factor (i.e. 365) is used to convert the unit of Dc,ref reported in Ref. [16] from

498

mm2/year to mm2/day. Fig. 12 shows the plot of ratio between Dc,ref in the developed model

499

to that in Petcherdchoo [16] model with fly ash replacement level in addition to varying w b

500

ratio. It is estimated from Fig. 12 that this ratio ranges from 0.31.6 for various combinations

501

of w b ratio and fly ash replacement level. In addition, Fig. 12 also indicates instances of

502

inconsistencies in these ratios that are due to discrepancies in Dc,ref predictions by

503

Petcherdchoo [16] model (see Fig. 8b).

504

5.

Model validation

505

The chloride profiles obtained by incorporating the three developed models, namely,

506

time-variant surface chloride content (i.e. Eq. (1)), CBIs constants (i.e. Eq. (8)), and reference

507

chloride diffusion coefficient (i.e. Eq. (24)) into the chloride ingress model (i.e. Section 4.2)

508

are compared with variety of field and laboratory experiments. The experimental data of

509

Chalee et al. [14] is again considered here, but to compare the values of TCC estimated by

510

chloride ingress model with that predicted by two simplified analytical models, one based on

511

Eq. (9) and the other based on Eq. (11). Figs. 13a–c show comparison between experimental

512

data reported in Ref. [14] with TCC profiles estimated by the chloride ingress model and two

513

analytical models after five years of exposure for concrete having various w b ratios and fly

514

ash replacement levels. When comparing TCC profiles in Figs. 13a–c, it is observed that 23

515

those estimated by the chloride ingress model show better agreement with the experimental

516

data than those estimated by the two analytical models. The better comparisons provided by

517

the chloride ingress model are due to its promising attributes as discussed earlier in

518

subsection 4.3.

519

Furthermore, values of TCC estimated by the chloride ingress model are also compared

520

with real field data of Costa and Appleton [12], Pack et al. [15], and Thomas and

521

Matthews [54] along with the laboratory data of McPolin et al. [55]. In the field study of

522

Pack et al. [15], a chloride profile of normal concrete with w b of 0.45 under 22.54 year

523

exposure in the West Sea side of Korea exposed to the tidal zone, is reported. For Costa and

524

Appleton [12], an experiment using concrete ( w b = 0.5) exposed for 3 years, is chosen for

525

comparison. In addition, from the work of Thomas and Matthews [54], an experiment using

526

30% fly ash replaced concrete ( w b = 0.45) exposed for 10 years under an English tidal zone

527

BRE marine site, is selected for validation. Among the four experiments listed above,

528

McPolin [55] experiment was performed under laboratory conditions where concrete

529

specimens (with 0.55M NaCl) were exposed to alternate wetting-drying cycles for a period of

530

48 weeks. It needs to be emphasized here that, while validating these experiments, variations

531

in temperature, relative humidity and surface chloride content as reported by the above-listed

532

researchers are taken into account (see Table 9). During numerical analysis, the equation for

533

surface chloride content (i.e. Cs ) proposed by Costa and Appleton [12] (see Table 1) is recast

534

into the form of the developed model (i.e. Eq. (1)) for various reasons discussed in subsection

535

2.1 (see Table 9). Further, Cs equation for Thomas and Matthews [54] (see Table 9) is

536

determined by performing regression analysis using Eq. (1) on Cs data obtained from curve

537

fitting (with traditional analytical solution to Fick’s law) the reported experimental data (i.e. 24

538

w b = 0.45, f = 30%). Fig. 14 shows the comparison of TCC values between field and

539

laboratory data with that predicted by the chloride ingress model. From comparison in Fig.

540

14, it is found that most of the results fall within the error line of 30% indicating that the

541

values of TCC estimated by incorporating the three submodels into the chloride ingress

542

model shows good agreement with that reported by various experiments (both field and

543

laboratory).

544

6.

Sensitivity analysis

545

To observe the effects of three developed submodel coefficients ( 1 ,  2 ,  3 , 1 ,  2 ,

546

1 ,  2 ,  3 , and  4 ) on the chloride ingress model, sensitivity analysis is conducted by

547

considering these coefficients as sensitivity parameters. Sensitivity analysis is conducted by

548

comparing the TCC values estimated for the actual values of these parameters with that

549

obtained by perturbing each parameter value by ± 10%. Moreover, for comparison purpose

550

the TCC values are estimated at 10–100 mm from the concrete surface and 2–, 3–, 4–, 5–, 7–,

551

10–, 15–, and 20–year exposure. It needs to be noted that the exposure time is limited to 20

552

years, because it is very likely that the maintenance applications would occur by 20 years,

553

which leads to change in the amount of chloride ions [16].

554

The results of sensitivity study for three parameters of the surface chloride content

555

model (i.e. 1 –  3 in Eq. (1)) are shown in Fig. 15. It is observed from Fig. 15 that the TCC

556

values have the margin of errors of about ±1015%, ±25%, and ±25% for the sensitivity

557

parameters 1 ,  2 , and  3 , respectively.

558

parameters, the values of TCC are more sensitive to 1 than  2 and  3 , it can be safely

559

concluded that the margin of error is within acceptable limits.

Even though among the three sensitivity

25

560

The results of sensitivity study for two parameters of the chloride binding isotherms

561

constants model (i.e. 1 and  2 in Eq. (8)) are shown in Fig. 16 for Langmuir isotherm and

562

in Fig. 17 for Freundlich isotherm. It is found from Figs. 16 and 17 that the TCC values have

563

the margin of errors of ±23% only for the sensitivity parameters 1 and  2 . Hence, it can

564

be concluded that the TCC values are not very sensitive to 1 and  2 .

565

Finally, the results of sensitivity study for four parameters of the reference chloride

566

diffusion coefficient model (i.e. 1   4 in Eq. (24)) are shown in Fig. 18. It is observed

567

from Fig. 18 that the TCC values have the margin of errors of about ± 25%, ± 25%,

568

± 515%, and ± 25% for the sensitivity parameters 1 ,  2 ,  3 , and  4 , respectively. Even

569

though among the four sensitivity parameters, the values of TCC are more sensitive to  3

570

than 1 ,  2 , and  4 , it can be safely concluded that the margin of error is within acceptable

571

limits.

572

7.

Summary and conclusions

573

In this study, three submodels for predicting the parameters involved in the chloride

574

ingress model, namely, time-variant surface chloride content, Langmuir and Freundlich

575

isotherms constants, and reference chloride diffusion coefficient are developed for fly ash

576

concrete. The values of TCC estimated by incorporating the three developed submodels into

577

the chloride ingress model are compared with variety of field and laboratory data. The

578

effects of three developed submodel coefficients on the chloride ingress model are examined

579

by performing sensitivity analyses. The conclusions that can be drawn up from present

580

results and from the analysis made are:

26

581

1. The developed surface chloride content model fulfills all the requirements of a

582

complete model for estimating its values in concrete exposed to chloride

583

environments, namely, time-dependency, natural logarithmic trend, prediction of

584

positive value at all time, dependency on w b ratio, and independent of fly ash

585

replacement level. From the sensitivity study on the three model parameters, it is

586

observed that the TCC values are relatively more sensitive to 1 than 2 and 3 .

587

2. A consistent yet simple model for estimating chloride binding constants of Langmuir

588

and Freundlich isotherms is developed for fly ash concrete. The developed model

589

profiles are very consistent with the past research findings (i.e. bound chloride

590

increases with increasing levels of fly ash replacement).

591

3. A reliable model for evaluating reference chloride diffusion coefficient for fly ash

592

concrete is developed. From the sensitivity study on the four model parameters, it is

593

observed that TCC values are relatively more sensitive to 3 than 1 ,  2 , and  4 .

594

Since this is a reference model, it can be used for any exposure conditions in either

595

field or laboratory.

596

4. The values of TCC estimated by incorporating the three developed submodels into the

597

chloride ingress model are compared with variety of field and laboratory data and are

598

found to show good agreement.

599

5. The performance of the developed models needs to be investigated more rigorously

600

by considering more real field data for practical prediction of chloride profiles in fly

601

ash concrete exposed to different chloride environments. This topic is recommended

602

for further study. 27

603

References

604

[1] J.M. Costa, M. Vilarrasa, Effect of air pollution on atmospheric corrosion of zinc, British

605

Corrosion Journal, 28 (1993) 117–120.

606

[2] G.R. Meira, C. Andrade, C. Alonso, I.J. Padaratz, J.C. Borba, Modelling sea-salt transport

607

and deposition in marine atmosphere zone – A tool for corrosion studies, Corrosion

608

Science, 50 (2008) 2724–2731.

609

[3] T.U. Mohammed, T. Yamaji, H. Hamada, Chloride diffusion, microstructure, and

610

mineralogy of concrete after 15 years of exposure in tidal environment, ACI Materials

611

Journal, 99 (2002) 256–263.

612

[4] T. Cheewaketa, C. Jaturapitakkul, W. Chalee, Long term performance of chloride binding

613

capacity in fly ash concrete in a marine environment, Construction and Building

614

Materials, 24 (2010) 1352–1357.

615 616

[5] M. Uysal, V. Akyuncu, Durability performance of concrete incorporating Class F and Class C fly ashes, Construction and Building Materials, 34 (2012) 170–178.

617

[6] N.M. Okasha, D.M. Frangopol, Novel approach for multicriteria optimization of life-

618

cycle preventive and essential maintenance of deteriorating structures, ASCE Journal of

619

structural engineering, 136 (2010) 1009–1022.

620

[7] M. Otieno, H. Beushausen, M. Alexander, Effect of chemical composition of slag on

621

chloride penetration resistance of concrete, Cement and Concrete Composites, 46 (2014)

622

56–64.

623 624

[8] M.A. Ward, Hardened mortar and concrete with fly ash, in: K. Wesche (Ed.) Fly ash in concrete: Properties and performance, CRC Press, 2004.

625

[9] R. Siddique, M.I. Khan, Supplementary cementing materials, Springer, 2011.

626

[10] B. Martin-Perez, S.J. Pantazopoulou, M.D.A. Thomas, Numerical solution of mass

627

transport equations in concrete structures, Computers & Structures, 79 (2001) 1251–

628

1264.

629

[11] S.L. Amey, D.A. Johnson, M.A. Miltenberger, H. Farzam, Predicting the service life of

630

concrete marine structures: An environmental methodology, ACI Structural Journal, 95

631

(1998) 205–214.

28

632

[12] A. Costa, J. Appleton, Chloride penetration into concrete in marine environment - Part I:

633

Main parameters affecting chloride penetration, Materials and Structures, 32 (1999) 252–

634

259.

635

[13] H.W. Song, C.H. Lee, K.Y. Ann, Factors influencing chloride transport in concrete

636

structures exposed to marine environments, Cement & Concrete Composites, 30 (2008)

637

113–121.

638 639

[14] W. Chalee, C. Jaturapitakkul, P. Chindaprasirt, Predicting the chloride penetration of fly ash concrete in seawater, Marine Structures, 22 (2009) 341–353.

640

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641

chloride transport in concrete structures exposed to a marine environment, Cement and

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643

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644

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645

38 (2013) 497–507.

646

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647

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650 651 652 653

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654

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655

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Concrete Structures, West Lafayette, USA, 2014.

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29

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664

materials - Part I: Essential tool for analysis of hygral behaviour and its relation to pore

665

structure, Cement and Concrete Research, 37 (2007) 414–437.

666

[25] T. Ishida, S. Miyahara, T. Maruya, Chloride binding capacity of mortars made with

667

various Portland cements and mineral admixtures, Journal of Advanced Concrete

668

Technology, 6 (2008) 287–301.

669 670

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capacity in fly ash concrete in a marine environment, Construction and Building

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Materials, 24 (2010) 1352–1357.

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675

chloride binding on service life predictions, Cement and Concrete Research, 30 (2000)

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1215–1223.

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682 683

[31] C. Arya, N.R. Buenfeld, J.B. Newman, Factors influencing chloride-binding in concrete, Cement and Concrete Research, 20 (1990) 291–300.

684

[32] K. Byfors, C.M. Hansson, J. Tritthart, Pore solution expression as a method to determine

685

the influence of mineral additives on chloride binding, Cement and Concrete Research,

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16 (1986) 760–770.

687 688

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689

[34] V. Baroghel-Bouny, X. Wang, M. Thiery, M. Saillio, F. Barberon, Prediction of chloride

690

binding isotherms of cementitious materials by analytical model or numerical inverse

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analysis, Cement and Concrete Research, 42 (2012) 1207–1224.

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30

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[36] T. Luping, J. Gulikers, On the mathematics of time-dependent apparent chloride

695

diffusion coefficient in concrete, Cement and Concrete Research, 37 (2007) 589–595.

696

[37] M.D.A. Thomas, E.C. Bentz, Life-365 manual released with program by Master

697 698 699 700 701 702 703 704 705

Builders, 2000. [38] M.D.A. Thomas, P.B. Bamforth, Modelling chloride diffusion in concrete - Effect of fly ash and slag, Cement and Concrete Research, 29 (1999) 487–495. [39] S. Muthulingam, B.N. Rao, Non-uniform time-to-corrosion initiation in steel reinforced concrete under chloride environment, Corrosion Science, 82 (2014) 304–315. [40] A.V. Saetta, R.V. Scotta, R.V. Vitaliani, Analysis of chloride diffusion into partially saturated concrete, ACI Structural Journal, 90 (1993) 441–451. [41] Y.P. Xi, Z.P. Bazant, H.M. Jennings, Moisture diffusion in cementitious materials – Adsorption-isotherms, Advanced Cement Based Materials, 1 (1994) 248–257.

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[42] O.B. Isgor, A.G. Razaqpur, Advanced modelling of concrete deterioration due to

707

reinforcement corrosion, Canadian Journal of Civil Engineering, 33 (2006) 707–718.

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[43] S. Muthulingam, B.N. Rao, Non-uniform corrosion states of rebar in concrete under

709

chloride environment, Corrosion Science, 93 (2015) 267–282.

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[44] B. Shafei, A. Alipour, M. Shinozuka, Prediction of corrosion initiation in reinforced

711

concrete members subjected to environmental stressors: A finite‐element framework,

712

Cement and Concrete Research, 42 (2012) 365–376.

713 714

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715

[46] E. Bastidas-Arteaga, A. Chateauneuf, M. Sanchez-Silva, P. Bressolette, F. Schoefs, A

716

comprehensive probabilistic model of chloride ingress in unsaturated concrete,

717

Engineering Structures, 33 (2011) 720–730.

718

[47] M.M.S. Cheung, J. Zhao, Y.B. Chan, Service Life Prediction of RC Bridge Structures

719

Exposed to Chloride Environments, ASCE Journal of Bridge Engineering, 14 (2009)

720

164–178.

721

[48] A.A. Khan, W.D. Cook, D. Mitchell, Thermal properties and transient thermal analysis

722

of structural members during hydration, ACI Materials Journal, 95 (1998) 293–303.

723

[49] Z.P. Bažant, L.J. Najjar, Drying of concrete as a nonlinear diffusion problem, Cement

724

and Concrete Research, 1 (1971) 461–473.

31

725

[50] H. Akita, T. Fujiwara, Y. Ozaka, A practical procedure for the analysis of moisture

726

transfer within concrete due to drying, Magazine of Concrete Research, 49 (1997) 129–

727

137.

728

[51] W. Chalee, C. Jaturapitakkul, Effects of W/B ratios and fly ash finenesses on chloride

729

diffusion coefficient of concrete in marine environment, Materials and Structures, 42

730

(2008) 505–514.

731 732 733 734 735 736

[52] M. Boulfiza, K. Sakai, N. Banthia, H. Yoshida, Prediction of chloride ions ingress in uncracked and cracked concrete, ACI Materials Journal, 100 (2003) 38–48. [53] JSCE, Standard specification for concrete structures (Maintenance), Society of Civil Engineers, Tokyo, Japan, 2007. [54] M.D.A. Thomas, J.D. Matthews, Performance of pfa concrete in a marine environment– –10-year results, Cement and Concrete Composites, 26 (2004) 5–20.

737

[55] D. McPolin, P.A.M. Basheer, A.E. Long, K.T.V. Grattan, T. Sun, Obtaining progressive

738

chloride profiles in cementitious materials, Construction and Building Materials, 19

739

(2005) 666–673.

740 741

742

32

743 744

Fig. 1. Trend lines of various C s models listed in Table 1 along with the field data of and Bentz et al. [17].

745 746 747 748

749 750

Fig. 2. C s estimates based on Song et al. [13] and Chalee et al. [14] models.

751

33

Pack et al. [15]

752 753

Fig. 3. Comparison between surface chloride content models of Chalee et al. [14], and Petcherdchoo [16] with the developed model.

754 755 756 757

758 759

Fig. 4. Non-linear bound chloride and binding capacity based on Ishida et al. [24].

760

34

Pack et al. [15],

761 762 763

Fig. 5. “Best-fit” isotherms to the experimental data of Zibara [22] (w/b=0.5, f=0%, and f=25%).

764 765

766

767

768

769

770

771

772

Fig. 6. CBIs constants Vs fly ash replacement level based on the developed model.

35

773 774 775

Fig. 7. CBIs based on the developed model: (a) Langmuir; (b) Freundlich.

776 777 778 779 780 781 782

783 784 785

Fig. 8. Plots showing: (a) Ratio of

Dc ,ref in Life-365 program [37] to that in Petcherdchoo [16] model; (b)

Dc ,ref estimates based on Petcherdchoo [16] model.

786 787

36

788 789 790

Fig. 9. Trend lines for

Dc ,ref estimates based on the developed model.

791 792 793

794 795 796

Fig. 10. Trend lines for the regression data of Petcherdchoo [16] based on developed and Petcherdchoo [16] models.

37

797 798

Fig. 11.

Dc ,ref estimates based on the developed model.

799 800 801 802

803 804

Fig. 12. Ratio of

Dc ,ref in developed model to that in Petcherdchoo [16] model. 38

805

806 807 808

Fig. 13. TCC profiles based on Chalee et al [14], Petcherdchoo [16] and chloride ingress model along with the experimental data of Chalee et al. [14]: (a) f=0%; (b) f=25%; (c) f=50%.

809

39

810 811

Fig. 14. Comparison of the predicted and experimental result of TCC based on data from Costa and Appleton [12], Pack et al. [15], Thomas and Mathews [54], and McPolin et al. [55].

812 813 814

Fig. 15. Sensitivity of TCC to

1 –  3

for concrete with w/b=0.45–0.65 and f=0–50% at

distance from the surface at 2–, 3–, 4–, 5–, 7–, 10–, 15–, and 20–year exposure.

815 816 817 818 819 820 821 822 823 824 825

40

10–100 mm

826

827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844

Fig. 16. Sensitivity of TCC to



L

and



L

for concrete with w/b=0.45–0.65 and

mm distance from the surface at 2–, 3–, 4–, 5–, 7–, 10–, 15–, and 20–year.

41

f=0–50% at 10–100

845 846 847 848

Fig. 17. Sensitivity of TCC to  F and  F for concrete with w/b=0.45–0.65 and

f=0–50% at 10–100 mm

distance from the surface at 2–, 3–, 4–, 5–, 7–, 10–, 15–, and 20–year exposure.

42

849

850 851

Fig. 18. Sensitivity of TCC to 1   4 for concrete with w/b=0.45–0.65 and f=0–50% at distance from the surface at 2–, 3–, 4–, 5–, 7–, 10–, 15–, and 20–year exposure.

852 853

Table 1. Published time-variant surface chloride content models. Cs (t)

Source Amey et al. [11]

2t , 2 t (kg/m3) 0.38 t

Costa and Appleton

0.37

(% wt. of concrete) [12]

3.0431 + 0.6856

ln  t  (% wt. of binder)

Song et al. [13]

 0.379  w/b   2.064 ln  t   4.078  w/b  1.011 Chalee et al. [14]

43

10–100 mm

(% wt. of binder)

0.26 ln  3.77 t 1 1.38 (% wt. of binder) [0.841 w/b   0.213]

10

Pack et al. [15]

 2.11 t (% wt. of binder)

Petcherdchoo [16]

854 855

Table 2. Curve fitting constants for 0% and 25 % fly ash replacement level.

ψα

f 0%

ψβ

L

34. 27

25%

2 .83

37. 17

L

ψα 8

2

ψβ

F

0

.20

.24

F

.32 1

0

0.12

.38

856

Table 3. Values of 1 and  2 for CBIs constants.

857



2

859

34.27 L

15



858

1

Binding isotherm constant

0.1161 2.834

L

9



37

860 0.02 861 862

8.205 F

1

0.0767 863



0.323 F

7

0.0022 864 865

866

867

Table 4. Correspondence between Eq. (15) and the governing field equations.

Transp

Diffusion terms

Convection terms

ort

44

y e

quantit Chlorid

Φ Cf

Moistur

h

Heat

T



e







1

D

D

h

we h  cp

Dh





DT





a c

a h

868

869

870

Table 5. Correspondence between Eq. (21) and the imposed boundary conditions.

Transport quantity

Diffusion terms X

Convection terms

b





b









Chloride

X cb

C bf

Bc

Cenv

hb

Bh

henv Cenv

Moisture

X hb

hb

Bh

henv









Heat

X Tb

Tb

BT

Tenv









871

872

Table 6. Idealized values of CBIs constants for concrete.

873

Binding isotherm constant f (

ψα

ψβ

L

3

3

(m of pore solution/m of concrete)

%) 0

0.4621

3

(m solution/kg)

ψα

L

of

pore

0.0799

ψβ

F

3

(m of pore solution/m3 of concrete)

1.2354

0.3 237

1

0.4855

0.0699

1.2486

5

0.3 573

2

0.5012

0.0632

1.2483

5

0.3 796

3

0.5169

0.0565

1.2408

5

0.4 021

5

0.5404

0.0465

1.2158

0

0.4 357

874

45

F

875

Table 7. Values used for numerical analysis.

876

Heat transport

Moisture transport

Chloride transport

concrete = 2400 kg/m3

 o = 0.05 [49]

tref = 28 days

c p, concrete

hc = 0.75 [49]

Bc = 1 m/s [40]

n = 10 [49]

R = 8.314 J/mol.°K

te = 28 days

Cini = 0.0

=

1000

J/kg.°K

DT,concrete

=

2

W/m.°K

Tini = 300.60 °K BT =

7.75 W/m2.°K

[48]

Bh =

3 × 10-7 m/s

[50]

hini = 0.89 877

Table 8. Values of Dc ,ref obtained from numerical analysis.

878

/b

w (%)

f year

Reference chloride diffusion coefficient (mm2/day)

2

R MSE year

0

0

.792

.45

0

1

5

.425 2

5

3 5

5 0

.100

0 .873

0 .1035

0

0

.250 0

.2549 0

0

0 .0307

.100

0

0 .2242

0

.210

0884

.100

46

1052

0 .274

0 .0563

0 .100

.425

.2319

.210

0

0

0

0.

.851

.1286

.252

0

0

0

0.

0

.1656

.425

1423

5 0

0

0.

0

0 .0348

0913

.252

0

0.

verage

MSE

.871

A

R year

0.

0

0

year

5

4

1387

.425

.1320

.230

0

0

0

MSE

.873

.1008

R year

0

0

0

year

4

3

.0678

.425

.0763

.240

year

0

0

R MSE

2

.0829

.342

year

3

0 .223

0 .0859

0 .100

0

0

.942 † 0 .55

5

1 .580

0

0

3 5

.276

0

.150 † 0

.65

0

1

5

.750 2

5

3 5

0 879 880

.235

0

0

0

1

0

0

0

0

0

.530

.0992

1624

.405

1249 0

.230

0749

.524

.1019 0 .2405

Table 9. Exposure conditions used for experimental validation. Exposure conditions

Tenv  t   293.65  21.5sin  2  t  0.5   henv  t   0.86  0.11sin  2 t  Cs  t   0.23Ln 1.07 t  1  0.07  % wt. of concrete 

Pack et al. [15] West coast side of Korea

Tenv  t   287.05  12.1sin  2  t  0.5     henv  t   0.76  0.07 sin  t  0.73  6  Cs  t   0.26 Ln  3.77t  1  1.38  % wt .of binder 

47

0 .416

† Numerical analysis performed using Eq. (9)

Source and Site Costa and Appleton [12] Setenave

0

0

0 .232

.754

.1166

.420

0

0

0

0.

.130

.3933

.520

1

0

0

0.

.151

.2923

.752

0

0

0

0.

0

0 .0909

2303

.276

.3413

.110

0

0

1

0.

0

0

0 .235

.763

.0975

.420

3200

.392

.0010

.154

0

0

0

0.

0

0

0

0 .2229

0

0

0.

1

.580

.2094 †

0

0

0 .276

0010

.128

.1383

.520

.1239

0

0

0

0

0

0

0.

0 .941

.0010

.396

0010

.151 †

.1403

.752

.1058

0

.580

0010

†

0 †

0.

0 .275

.0010

.150

.0866

0

.2039

0.

0

0

0 .943

0010

.391 †

.0010

.153 †

.3409

.418 5

0

1

.525

†

0 .581

.0010

0. 0010

†

0

0 .274

.0010

.130

0

0 .0010

0 .0010

.393 †

0 .941 †

.0010

†

0

0

0

0 .582

.0010

†

5 0

0 .0010

.390 †

0 .941 †

.0010

†

2 5

0

0 .233

Thomas

and

[54] Shoeburyness

Mathews

Tenv  t   284.82  6.66sin  2  t  0.5     henv  t   0.78  0.05sin  t  0.74  6  Cs  t   2.18 Ln  0.21t  1  0.94  % wt. of binder 

881 882 883

HIGHLIGHTS



Inconsistencies in surface chloride, isotherm constant, and diffusion coefficient models are shown.



Consistent parameter prediction models for chloride ingress into fly ash concrete are developed.



Experimental validation for the developed models is performed with field and laboratory data.



A sensitivity analysis of the developed model coefficients is conducted.

884 885

48