Chloride binding and time-dependent surface chloride content models for fly ash concrete

Abstract

Corrosion of embedded rebars is a classical deterioration mechanism of reinforced concrete structures exposed to chloride environments. Such environments can be attributed to the presence of seawater, deicing or sea-salts, which have high concentrations of chloride ion. Chloride ingress into concrete, essential for inducing rebar corrosion, is a complex interaction between many physical and chemical processes. The current study proposes two chloride ingress parameter models for fly ash concrete, namely: 1) surface chloride content under tidal exposure condition; and 2) chloride binding. First, inconsistencies in surface chloride content and chloride binding models reported in literature, due to them not being in line with past research studies, are pointed out. Secondly, to avoid such inconsistencies, surface chloride content and chloride binding models for fly ash concrete are proposed based upon the experimental work done by other researchers. It is observed that, proposed models are simple, consistent and in line with past research studies reported in literature.

Keywords

binding isotherms / chloride ingress / concrete / fly ash / surface chloride content

Introduction

Corrosion of rebars in reinforced concrete (RC) structures is a common degrading mechanism that affects both load and serviceability limit states. RC structures at close proximity to marine environment are highly vulnerable to corrosion induced by chloride ingress. The concrete atmosphere characterized mainly by temperature and relative humidity catalyzes intrusion of chloride ions into RC. The rebar embedded in the concrete is: 1) chemically protected by the highly alkaline (pH ~ 13−14) passive layer; and 2) physically protected by the concrete cover acting as a barrier to the intrusion of aggressive species. However, chloride-induced corrosion begins when the concentration of chloride at the steel bar level reaches critical chloride content or chloride threshold value thereby destroying the protective layer. Critical chloride content or chloride threshold value of rebar in concrete, can be defined as the concentration of chloride at the depth of the rebar that is necessary to sustain localized breakdown of its passive film and hence initiate its active corrosion [ 1, 2].

To sustain a chloride-induced corrosion free structure for a given service life, two approaches are reported in literature: 1) increasing the minimum cover thickness [ 3]; and 2) increasing chloride binding capacity and/or decreasing porosity of concrete by using supplementary cementitious materials like fly ash, slag, etc. Increase in cover thickness increases the distance between concrete surface and rebar level, whereas increase in fly ash content increases chloride binding capacity in concrete by causing reduction of rebar corrosion related free chloride ions [ 4, 5].

The most important principle in modeling chloride ingress into concrete are diffusion process and the nature of chloride binding [ 6]. Fick’s second law of diffusion empirically represents chloride ingress into the concrete, for which the solution is sought either analytically or numerically. The analytical solution of the diffusion equation based on the error function is valid only when: 1) RC structures are saturated and subjected to a constant concentration of chlorides on their exposed surfaces; 2) material is homogeneous; and 3) chloride diffusion coefficient is constant in time and space [ 7− 9]. Alternatively, two approaches have been proposed for better prediction of chloride ingress into RC components. Some models are based on a single-ion approach that considers only chloride ions transport, but also incorporate nonlinear chloride binding relationships, humidity and temperature variations [ 6, 10, 11]. More recently, multi-ionic approaches were also developed that take into account the intricate interaction between different ions and the hydrated cement paste during chloride ingress into concrete [ 12, 13]. Chloride binding was also reported to have significant effect on service life prediction of RC structures [ 14].

When a concrete member is exposed to tidal or splash zone, there is an initial build-up of chlorides on their surfaces which increases with time before reaching a steady-state condition [ 7, 15]. The influence of surface chloride build-up on the exposed surfaces of concrete members was evaluated by considering linear, square root and refine model of a surface chloride build-up at a given diffusion coefficient [ 15]. More recently, a surface chloride content model was proposed and validated [ 16] with experiment conducted on concrete with and without fly ash under tidal exposure conditions. However, the surface chloride content model proposed in literature [ 7, 16] predicts negative values during initial exposure periods, indicating surface chloride ions movement out of concrete, which is inapplicable in the problem of chloride penetration through concrete [ 17].

Chloride binding in concrete has significant effect on service life predictions of RC structures, because: 1) less free chloride near rebar delays corrosion; 2) slows down chloride movement into concrete due to the formation of less porous Friedel’s salt [ 14, 18]. Addition of supplementary cementitious materials like GGBS, fly ash was reported to increase chloride binding capacity of concrete [ 4, 5, 19]. More recently, a binding isotherm model was proposed [ 20] for cement with different supplementary cementitious materials like fly ash and slag. However, the proposed [ 20] model, predicts decreasing binding capacity with increasing fly ash content. Time-dependent apparent chloride diffusion coefficient models were proposed in literature [ 21, 22], so that they could be used as inputs into the closed-form solution of Fick’s second law of diffusion. More recently, a reference chloride diffusion coefficient model was reported in the literature [ 17] for fly ash concrete based on the proposed [ 22] time-dependent apparent chloride diffusion coefficient model.

Within this context, the current study proposes two chloride ingress parameter models for fly ash concrete: 1) surface chloride content model under tidal exposure condition; and 2) chloride binding, based on the experimental works reported in the literature [ 16, 23]. Section 2 and 3 present surface chloride content model under tidal condition and chloride binding model, for fly ash concrete, respectively.

Time-dependent surface chloride content model

The quantity of surface chloride ( C_s ) on the exposed surface of a concrete member depends on the type of exposure condition. C_s obtained under seawater submerged condition was higher than that obtained under tidal/splash condition, and concrete structures exposed to airborne chlorides have lowest C_s . In addition, C_s for concrete under submerged condition was observed to be time-invariant due to chemical equilibrium, whereas C_s was reported to be time-dependent under tidal condition due to wet and dry cycles [ 7]. Under tidal exposure condition, the chlorides initially build up over exposed surfaces of concrete components with time, before reaching a steady-state condition [ 7, 15]. There are twofold factors that may govern such initial chlorides build up: 1) chloride binding capacity of the cement matrix, as increase in binding capacity increases free chlorides accumulation on the concrete surface, thereby increasing the total chloride content [ 24]; and 2) exposure conditions (e.g., temperature and relative humidity), and seawater salt concentration or chloride anion type [ 15]. Table 1 lists time-dependent C_s models reported in literature for tidal exposure condition ( w/b represents water/binder ratio).

It can be observed from Table 1 that linear [ 25], power [ 25, 26] and natural logarithmic [ 7, 16, 27] type of functions of time or their combination [ 17] are reported in the literature to model C_s under tidal exposure condition. However, nature logarithmic function is reported [ 7, 16] to best model C_s under tidal conditions, as this function can effectively capture the initial chloride build-up along the exposed concrete surface. In addition, linear [ 25] and power [ 17, 25, 26] functions would overestimate C_s over time under tidal exposure conditions.

Although logarithmic function is accepted to best represent time-dependent C_s under tidal condition, few proposed forms [ 7, 16] predict negative values of C_s during initial exposure periods, as shown in Fig. 1. Negative values of C_s would theoretically mean that the surface chloride ions are moving out of concrete during initial exposure periods, which is contrary to chloride ingress into the concrete [ 17]. Hence, the proposed forms are inapplicable to model time-dependent C_s under tidal exposure condition. It can also be observed from Table 1 and Fig. 1, two proposed forms of time-dependent C_s [ 16, 17] also indicate that C_s is also dependent on w/b ratio.

From the preceding discussion it is understood that, a time-dependent C_s logarithmic function form that can predict not only positive values at all times but also that accounts for initial build-up of C_s under tidal exposure condition is required. Therefore, a logarithmic function form that is similar to the one reported in the literature [ 27] is proposed (Eq. (1)).

(1) C_s(t)={\xi }_{\mathrm{1}}\ln ({\xi }_{\mathrm{2}}t+\mathrm{1})+{\xi }_{\mathrm{3}}\left({\displaystyle \frac{w}{b}}\right)(\%\mathrm{wt}\mathrm{.}\mathrm{of}\mathrm{binder}),

where {\xi }_{\mathrm{1}} , {\xi }_{\mathrm{2}} and {\xi }_{\mathrm{3}} are constants to be obtained by performing regression analysis on particular experimental/numerical data, t is time period in years, and w/b is water/binder ratio. Note that due to the chemistry between cement matrix and chloride ions, immediately after being exposed to a chloride environment, the concrete surface is surrounded by chloride ions leading to a certain amount of chloride ions [ 7, 15, 17]. Therefore, it is necessary to have a nonzero term (at t = 0) in C_s model to represent the initial surface chloride content, as done in this study.

To demonstrate that the developed C_s model can predict the trend of C_s better, the trend lines of all C_s models listed in Table 1 as well as the developed C_s model are drawn (see Fig. 2) through the long-term real data reported in the literature [ 28] by using a standard smooth curve fitting technique (nonlinear regression). Note that the trend line equations along with their R-Square values are also shown in Fig. 2. Figure 2 shows that 1) trend lines based on the C_s models reported in the literature [ 7, 16] predict negative values of C_s during initial exposure periods, 2) trend lines based on the C_s models reported in the literature [ 25, 26] does not account for the immediate accumulation of chloride ions as soon as the concrete surface is exposed to a chloride environment, and 3) trend lines based on the C_s models having power terms (e.g., [ 17, 25, 26]) has the potential to overestimate C_s values over time. However, the trend line based on the developed C_s model is very promising as it fulfills all the requirements of a complete model for estimating the values of C_s in concrete exposed to chloride environments, namely, time-dependency, natural logarithmic trend, prediction of positive value at all time, dependency on w/b ratio and independent of fly ash replacement level.

Chloride binding model

Chloride binding is the process of chloride ions in the pore solution of concrete getting bound to different extent on certain cement hydrates [ 23, 24]. Two types of chloride ions can be present in the concrete: 1) chemically bound to the hydration products of the cement and physically sorbed on the surfaces of the gel pores (bound chlorides); and 2) dissolved in the pore solution (free chlorides) [ 29, 30]. Addition of supplementary cementitious materials like GGBS, fly ash was observed to increase chloride binding capacity of concrete [ 4, 5, 19, 31].

Binding isotherm relates the free ( C_f ) and bound ( C_b^{ } ) chloride concentrations at equilibrium and is characteristic of each cementitious system. There are two types of commonly used binding isotherms for cementitious materials and they are given as [ 24, 29]:

1) Langmuir isotherm:

(2) C_b^L={\displaystyle \frac{{\psi }_{{\alpha }_L}{C}_f}{\mathrm{1}+{\psi }_{{\beta }_L}{C}_f}},

(3) {\displaystyle \frac{\partial C_b^L}{\partial C_f}}={\displaystyle \frac{{\psi }_{{\alpha }_L}}{{(\mathrm{1}+{\psi }_{{\beta }_L}{C}_f)}^{\mathrm{2}}}}.

2) Freundlich isotherm:

(4) C_b^F={\psi }_{{\alpha }_F}{C}_f^{{\psi }_{{\beta }_{\mathrm{F}}}},

(5) {\displaystyle \frac{\partial C_b^F}{\partial C_f}}={\psi }_{{\alpha }_F}{\psi }_{{\beta }_F}{C}_f^{{\psi }_{{\beta }_{\mathrm{F}}}^{-}}.

where {\psi }_{{\alpha }_L} (mL pore solution/g sample), {\psi }_{{\beta }_L} (mL pore solution/mg Cl), {\psi }_{{\alpha }_F} (mL pore solution/g sample) and {\psi }_{{\beta }_F} represent binding as a function of fly ash replacement level. The term \partial C_b/\partial C_f represents binding capacity of the cementitious system, which is the slope of chloride binding isotherm. Langmuir isotherm predict the relationship between bound and free chloride better for lower free chloride concentration (<1.773 kg/m³), whereas Freundlich isotherm predict better for higher free chloride concentration (>0.355 kg/m³). It is important to note that, the binding capacity is mainly dependent on CSH gel content and is independent of w/b ratio. This is because chloride binding occurs only through the interface between the pore solution and hydrated products of concrete [ 29, 32].

Binding isotherms constants need to be evaluated experimentally for a given concrete mix proportions. More recently, Langmuir isotherm binding model (Eq. (6)) for cement with different supplementary cementitious materials like fly ash and slag, based on experiment was reported in the literature [ 20]:

(6) C_b={\displaystyle \frac{\alpha C_{\mathrm{f}}}{\mathrm{1}+\mathrm{4.0}{C}_{\mathrm{f}}}},

where C_{\mathrm{b}}^{ } and C_{\mathrm{f}} represent bound and free chlorides (% mass of binder), and \alpha for different fly ash ( f_{\mathrm{a}} ) replacement (0 − 0.4) is given by Eq. (7).

(7) \alpha =-\mathrm{15.5}{f}_{\mathrm{a}}^{\mathrm{2}}+\mathrm{1.8}{f}_{\mathrm{a}}+\mathrm{11.8.}

Figure 3 shows the plot of binding and binding capacity predictions based on Ishida et al. [ 20] model (i.e., Eq. (6)) for various percentage of fly ash replacements (0 to 40 %). It can be observed from Fig. 3, that both bound chloride (% mass of binder) and binding capacity decreases with increase in fly ash content. However, according to past studies [ 4, 5, 14, 31, 33, 34], increase in fly ash content was reported to increase chloride binding and binding capacity. The ability of fly ash to increase the chloride binding capacity of the hardened cement matrix can be attributed to threefold reasons: 1) increased formation of less porous Friedel’s salt after the pozzolanic reaction [ 4]; 2) higher surface area and adsorptivity of fly ash cement [ 35]; and 3) relatively lower chloride ion diffusion coefficient [ 36]. Therefore, Ishida et al. [ 20] binding model (i.e., Eq. (6)) with fly ash binder is not in line with research findings of past studies as indicated above.

Most recently, a numerical inverse analysis approach was also proposed in the literature [ 37] for estimating chloride binding isotherm. Such numerical inverse analysis methods for estimating chloride binding isotherms are classified into two groups: 1) based on fitting computed profile, obtained through a one-dimensional numerical multispecies transport model developed in saturated and isothermal conditions, on the measure data which may be total chloride content profile and chloride diffusion coefficient or solely total chloride content profile; and 2) based on the composition of the material at a given age [ 37]. However, such inverse numerical methods although can predict specific chloride binding isotherm pertaining to a particular experimental data, nevertheless are indirect. Hence, a consistent and direct chloride binding isotherm model is required. In the current study, chloride binding models (both Langmuir and Freundlich types) are proposed based on the extensive experimental research work reported in the literature [ 23].

Zibara [ 23] experimental work

The experiment investigated the effects of binder type and w/b ratio on chloride binding by examining different supplementary cementitious materials (silica fume, metakaolin, blast furnace slag and fly ash) at two w/b ratios (0.30 and 0.50). All mixes used in the experiment were prepared as pastes containing cementitious materials and distilled water, with a superplasticiser being used for the mixes at w/b ratio of 0.30. The paste was then cast into 50 × 100 mm cylindrical molds. After curing the paste samples for a period of two months, the central portion was cut into 3 mm thick discs. The 3 mm discs broken into 25 g fragments, were placed in 125 mL plastic bottles which were then filled with NaCl solution having seven different concentrations (0.1, 0.3, 0.5, 0.7, 1.0, 2.0, and 3.0 M). Then 0.30 and 0.50 w/b ratio samples were sealed and stored for six months, and, between five and sixweeks, respectively. The host solutions were then analyzed for chloride concentration by means of potentiometric titration using 0.01 M AgNO₃. In the equilibrium method, it is assumed that after equilibrium is reached between the external solution and the pore solution of the sample, the reduction in the concentration of the host solution is attributed to chloride being bound by the cement. Then, knowing the initial and final concentration, the volume of the external solution and the dry mass of the sample, the amount of bound chloride can be determined from:

(8) C_{\mathrm{b}}={\displaystyle \frac{\mathrm{35.453}{V}_{\mathrm{e}}(C_{\mathrm{i}}-C_{\mathrm{f}})}{W_{\mathrm{d}}}}

where, C_{\mathrm{b}} is the amount of bound chloride in mg Cl/g of the sample, V_{\mathrm{e}} is the volume of the external solution in mL, C_{\mathrm{i}} is the initial chloride concentration of the external solution in mol/l, C_{\mathrm{f}} is the free chloride concentration at equilibrium of the external solution in mol/l, and W_{\mathrm{d}} is the dry mass of the sample in g.

Estimation of binding isotherm constants

Figure 4 shows the effect of fly ash at a replacement level of 25%, on the relationship between bound and free chlorides. In addition, Fig. 4 shows the experimental data based on Zibara [ 23] and the “best-fit” binding isotherms (using Eqs. (2) and (4)) for fly ash pastes with 0 and 25% replacement level having 0.50 w/b ratio. It can be observed from Fig. 4 that bound chloride increases with increase in fly ash content. The binding constants, {\psi }_{{\alpha }_{\mathrm{L}}} and {\psi }_{{\beta }_{\mathrm{L}}} for Langmuir isotherm (i.e., Eq. (2)), {\psi }_{{\alpha }_{\mathrm{F}}} and {\psi }_{{\beta }_{\mathrm{F}}} for Freundlich isotherm (i.e., Eq. (4)) fitted to the experimental data for 0 and 25% fly ash replacement level are presented in Table 2.

Higher proportions of active alumina in fly ash when compared to that of Portland cement is capable of binding and immobilizing chloride ions in solution. In addition, bound chloride content in concrete was reported to peak at about 50% fly ash replacement. Moreover, bound chloride was also found to increase with chloride exposure concentration, and at the optimum replacement level (50 %) was not affected by the w/b ratio [ 33]. More recently, chloride binding capacity of chloride ions in fly ash concrete under marine exposure was investigated [ 5]. The study observed: 1) Chloride binding capacity (% of total chloride) values at 7 years exposure of 14.4%, 17.4%, 19.4%, 21.0%, and 23.8% for the concretes containing fly ash 0%, 15%, 25%, 35%, and 50% by weight of binder, respectively, with a w/b ratio of 0.45; 2) Chloride binding capacity is not correlated with w/b ratio, hence w/b ratio does not affect the ratio of bound chloride compared to total chloride ingress in concrete; and 3) fairly linear relationship between chloride binding capacity and fly ash replacement level (0 to 50 %).

Based on the preceding discussion, relation between Langmuir and Freundlich isotherms constants and fly ash replacement level is approximated using a linear function given below:

(9) {\psi }_{{\alpha }_{\mathrm{L}},{\beta }_{\mathrm{L}},{\alpha }_{\mathrm{F}},{\beta }_{\mathrm{F}}}={\eta }_{\mathrm{1}}+{\eta }_{\mathrm{2}}f,

where f represents fly ash replacement level expressed in percentage, and, {\eta }_{\mathrm{1}} and {\eta }_{\mathrm{2}} represent linear regression constants that are to be obtained by performing regression analysis on a given experimental/numerical data. By performing linear curve fitting using Eq. (9) on binding isotherm constants values listed in Table 2, {\eta }_{\mathrm{1}} and {\eta }_{\mathrm{2}} are obtained and same is listed in Table 3.

It can be observed from Table 3 that, binding isotherm constants {\mathit{\psi }}_{{\mathit{\alpha }}_{\mathrm{L}}} , {\mathit{\psi }}_{{\mathit{\alpha }}_{\mathrm{F}}} and {\mathit{\psi }}_{{\mathit{\beta }}_{\mathrm{F}}} , and, {\mathit{\psi }}_{{\mathit{\beta }}_{\mathrm{L}}} show increasing, and decreasing trends, respectively, with fly ash replacement level. By assuming binding isotherms constants linear trends to continue, their values are extrapolated (shown dotted) for other (i.e.,>25 and<= 50 %) fly ash replacement level, and the same is plotted in Fig. 5. Based on the proposed linear model (i.e., Eq. (9)) and binding isotherm constants values from Fig. 7, Langmuir and Freundlich isotherms for different fly ash replacement level are shown in Figs. 6(a) and (b).

It can be observed from Figs. 6(a) and (b), that Langmuir and Freundlich isotherms predicted by the proposed model (i.e., Eq. (9)) are consistent with past experimental observations (i.e., increase in bound chloride and binding capacity with increase in fly ash content). Note the binding isotherms constants estimated for fly ash pastes using Eq. (9) needs to be idealized for concrete. This can be accomplished through a numerical inverse analysis procedure reported in the literature [ 14, 23]. The inverse analysis approach aims to best fit the experimentally measured chloride profile with that computed through a chloride transport model by treating binding isotherms constants as unknowns. Fick’s second law governing the mechanism of chloride diffusion in concrete is given by:

(10) {\displaystyle \frac{\partial C_{\mathrm{t}}}{\partial t}}={\displaystyle \frac{\partial }{\partial x}}\left(D_{\mathrm{e}}{w}_{\mathrm{e}}{\displaystyle \frac{\partial C_{\mathrm{f}}}{\partial x}}\right),

where C_{\mathrm{t}} is the total chloride content (kg/m³). C_{\mathrm{f}} is the free chloride content dissolved in the pore solution (kg/m³), D_{\mathrm{e}} is the effective chloride diffusion coefficient (m²/s) and w_{\mathrm{e}} is evaporable water content (m³ of water/m³ of concrete). By taking chloride binding into account, expressed by the following equation [ 6]:

(11) C_{\mathrm{t}}=C_{\mathrm{b}}+w_{\mathrm{e}}{C}_{\mathrm{f}}.

Further by substituting Eq. (11) into Eq. (10), Fick’s second law can be modified as:

(12) {\displaystyle \frac{\partial C_{\mathrm{f}}}{\partial t}}={\displaystyle \frac{\partial }{\partial x}}\left(D_{\mathrm{a}}{\displaystyle \frac{\partial C_{\mathrm{f}}}{\partial x}}\right),

where D_{\mathrm{a}} is the apparent chloride diffusion coefficient (m²/s) given as:

(13) D_{\mathrm{a}}={\displaystyle \frac{D_{\mathrm{e}}}{\mathrm{1}+{\displaystyle \frac{\mathrm{1}}{w_{\mathrm{e}}}}{\displaystyle \frac{\partial C_{\mathrm{b}}}{\partial C_{\mathrm{f}}}}}}.

By assuming w_{\mathrm{e}} values of 8%, 10%, 11%, 13%, and 14% and D_{\mathrm{e}} values of 3 × 10⁻¹², 2.5 × 10⁻¹², 2.0 × 10⁻¹², 1.5 × 10⁻¹² and 1.0 × 10⁻¹² m²/s for fly ash replacement levels of 0%, 15%, 25%, 35% and 50%, respectively [ 23, 37, 38], binding isotherms constants determined using Eq. (9) are idealized for concrete, and their values are listed in Table 4. It may be noted here that chloride binding may 1) vary with different types of fly ash (i.e., fly ash having different chemical compositions) [ 31] and 2) vary when fly ash is used with different types of Portland cement (I and V) [ 5]. Although, the proposed model for binding isotherm constants is simple and consistent, nevertheless, further research is required for better estimation.

Model validation

The chloride profiles obtained by incorporating the two developed models, namely, time-variant surface chloride content (i.e., Eq. (1)) and binding isotherms constants (i.e., Eq. (9)), into the chloride ingress model (i.e., Eq. (10)) are compared with variety of field and laboratory experiments. Note that Eq. (10) cannot be solved without using numerical methods because of the dependency of D_{\mathrm{a}} on C_{\mathrm{f}} . It is solved numerically in space as a boundary-value problem and in time as an initial-value problem using one-dimensional finite difference (Crank-Nicolson scheme). The initial and boundary conditions used for the numerical analyses are: 1) For t=\mathrm{0} , C_{\mathrm{f}}=\mathrm{0} at x>\mathrm{0} and 2) for t>\mathrm{0} , C_{\mathrm{f}}=C_{\mathrm{s}} at x=\mathrm{0} .

Chloride content estimated by the chloride ingress model are compared with real field data of Chalee et al. [ 16], Costa and Appleton [ 26], Pack et al. [ 27], and Thomas and Matthews [ 39] along with the laboratory data of McPolin et al. [ 40]. For Chalee et al. [ 16] chloride profiles of fly ash concrete with w/b ratios of 0.45, 0.55 and 0.65 with fly ash replacement levels of 0%, 25% and 50% are selected. In the field study of Pack et al. [ 27], a chloride profile of normal concrete with w/b of 0.45 under 22.54 year exposure in the West Sea side of Korea exposed to the tidal zone, is reported. For Costa and Appleton [ 26], an experiment using concrete ( w/b = 0.5) exposed for 3 years, is chosen for comparison. In addition, from the work of Thomas and Matthews [ 39], an experiment using 30% fly ash replaced concrete ( w/b = 0.45) exposed for 10 years under an English tidal zone BRE marine site, is selected for validation. Among the four experiments listed above, McPolin [ 40] experiment was performed under laboratory conditions where concrete specimens (with 0.55M NaCl) were exposed to alternate wetting-drying cycles for a period of 48 weeks. During numerical analysis, the equation for surface chloride content (i.e., C_{\mathrm{s}} ) proposed by Costa and Appleton [ 26] (see Table 1) is recast into the form of the developed model (i.e., Eq. (1)) leading to C_{\mathrm{s}}(t)=\mathrm{0.23}\mathrm{Ln}(\mathrm{1.07}t+\mathrm{1})+\mathrm{0.07}(\%\mathit{w}\mathit{t}. of\mathrm{concrete}) . Further, C_{\mathrm{s}} equation for Thomas and Matthews [ 39] is determined as C_{\mathrm{s}}(t) =\mathrm{2.18} \mathrm{Ln}(\mathrm{0.21} t+\mathrm{1})+\mathrm{0.94} (\%\mathrm{wt}. of binder) , by performing regression analysis using Eq. (1) on C_{\mathrm{s}} data obtained from curve fitting (with traditional analytical solution to Fick’s law) the reported experimental data (i.e., w/b = 0.45, f = 30%). Figure 7 shows the comparison of chloride content values between field and laboratory data with that predicted by the chloride ingress model. From comparison in Fig. 7, it is found that most of the results fall within the error line of±30% indicating that the values of chloride content estimated by incorporating the two developed models into the chloride ingress model shows good agreement with that reported by various experiments (both field and laboratory). However, the performance of the developed models needs to be investigated more rigorously by considering more real field data for practical prediction of chloride profiles in fly ash concrete exposed to different chloride environments. This topic is recommended for further study.

Summary and conclusions

Chloride binding and time-dependent surface chloride content models, which are very important for service life estimation of RC structures exposed to chloride ingress with and without fly ash, are proposed in this study based on the experimental observations of other researchers. The proposed surface chloride content model in the form of logarithmic function is very consistent with experimental observation as it predicts positive values at all time. Any surface chloride content data under tidal or splash cycle can be very well estimated using the proposed model form. An effective yet simple linear model for evaluating Langmuir and Freundlich binding isotherm constants for concrete with and without fly ash replacement up to 50% is proposed. The proposed chloride binding constants estimation model agreed well with other research findings that confirm increase in chloride binding with increase in fly ash replacement level (up to 50%).

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