## Laurie Aldridge

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This is an AZo Open Access Rewards System (AZo-OARS) article distributed under the terms of the AZo–OARS https://www.azom.com/oars.asp which permits unrestricted use provided the original work is properly cited but is limited to non-commercial distribution and reproduction.

Submitted: 23^{rd} November 2011

Volume 8 January 2012

## Topics Covered

AbstractKeywords

Background

Using Fick’s Laws to Model Chloride Diffusion

Interpretation of Penetration Profiles of Cl in Concrete from Literature Data

Fitting Chloride Penetration Profiles of Concrete Cured at Different Times

References

Contact Details

## Abstract

Billions of dollars are spent annually to replace defective infrastructure that needs replacement only because of concrete failing to attain its expected service life. Much of this cost is due to the effects of chloride ingress into the concrete removing protective sheaths from steel reinforcement leading to destructive corrosion of the infra structure. Thus accurate prediction of the rate of chloride ingress into concrete would lead to the establishment of specification of an adequate concrete cover to give defined service life.

There have been a number of studies in which the chloride penetration profile of concretes exposed to a chloride solution for different defined periods of time. In this series of papers these data sets were fitted to a consistent simple semi- empirical Fick’s law equations using an excel spreadsheet. The method of fitting appeared to be robust enough so that time dependant chloride profiles could be fit. Such fits can be used to estimate a service life of concrete that is limited by chloride corrosion of the reinforcement steel placed at a defined depth from the surface of the structure.

In this part – the second of a three part series the fits of literature data sets to the semi –empirical model is shown.

## Keywords

Concrete, Durability, Chloride Diffusion, Reinforcement Corrosion, Service life

## Background

In Part 1 of this series a simplified version of the Fick’s law equation was used to compute the chloride profile from the equation

C(x) = S (1-erf[x/(2*sqrt{t*D}]) (1)

Where C(x) is the amount of chloride expressed as % of binder x (mm) is the distance from the surface and S the surface concentration of chloride, t the time (years) and D is the diffusion coefficient (mm^{2}/years). Note this can be converted to the SI definition of D (m^{2}/sec) by dividing by ~ 31.5*10^{-12}.

This relationship relied on the assumption that S and D was constant which was not the case. It was found [15] that both S and D varied with time and that this variation could be predicted by a power law where

D(t) = D_{0}(t/t_{0})^{-n} (2)

S(t) = S_{0}(t/t_{0})^{m} (3)

Where t_{0} is a reference time (generally 28 days or 0.07 years)

The values n and m are powers lying between 0 and 1. Note the difference in signs in equations 2& 3 due to the fact that S increased with time while D decreased with time. In fact it as will be discussed later it is only because of the significant decrease of D with time that concrete can be used in marine waters.

Combining Equations 1, 2, & 3 gives the Fick’s law equation (4) that will be used in the remainder of this report.

C(x) = S_{0}(t/t_{0})^{m} (1 – erf(x/ {2 sqrt(t D_{0}(t/t_{0})^{-n})}) (4)

It was emphasised that equation (4) was only semi-empirical and should be regarded as tool for fitting rather than a physical equation that can be used to predict exact long term solutions. In this part of the series the focus of the work is fitting the data taken from a number of authors who measured Chloride penetration profiles taken at different times. These are fitted to equation (4) as a function of time, the power series exponents, D_{0} & S_{0} generally taken at 28 days.

## Using Fick’s Laws to Model Chloride Diffusion

The calculation of chloride diffusivity by Fick’s laws use many approximations which must be understood if one want to estimate a real design life from chloride ingress. Page et al [36] measured chloride diffusion for what can be considered fully reacted cement pastes and found significant variation in chloride diffusivity depending on the water binder w/b ratios and temperature of the pastes. Evidently there are considerable differences between the different cements with blended cement having PFA or GGBFS being considerably more resistant to chloride ingress than OPC. Their results [36] are commonly used to extrapolate for expected temperatures of marine exposure.

**Table 1.** Diffusion coefficients of fully cured cement pastes (w/b 0.5) made from Ordinary Portland Cement (OPC), Sulphate Resistant Portland Cement (SRPC) and cement blended with Pulverized Fly Ash (PFA) or Ground Granulated Blast Furnace Slag (GGBFS). Results [36] determined by through diffusion.

Pastes | D * 10^{-12} m^{2}/sec |
D mm^{2}/year |
---|---|---|

OPC | 4.5 | 140 |

SRPC | 10.0 | 320 |

OPC 30% PFA | 1.5 | 47 |

OPC / 65%GGBFS | 0.4 | 12 |

OPC | 4.5 | 140 |

The effect of cement type on the diffusivity of chloride in cement pastes was determined by Hansson et al [37]. They found that different cements gave an order of magnitude difference in chloride diffusion. Hansson et al [38] subsequently found that much of the difference was due to the fineness of the cement paste.

**Table 2.** Comparison of diffusion coefficients (mm^{2}/yr) from different pastes cured for 28 or 90 days with w/b ratios 0.4 or 0.6 & measured at 30°C [37].

Effect of time | 28 days | 90 days | |
---|---|---|---|

Effect of w/b | 0.4 0.6 | 0.4 0.6 | |

Type of Cement | |||

OPC | 85 337 | 10 82 | |

Rapid Hardening OPC | 139 576 | 110 677 | |

Sulphate Resiting Cement SRPC | 239 668 | 302 901 |

Ashbridge et al [39] were able to show that when mortar comprised of cement paste (with diffusion coefficient D_{i}) mixed with sand with the volume fraction of paste Φ has an effective diffusion coefficient D_{eff} that can be approximated by the formula:

D_{eff} = 2 D_{i}(1- Φ)/(2+ Φ) (6)

From this formula it is to be expected that concrete would be more resistant to chloride than the corresponding cement paste.

## Interpretation of Penetration Profiles of Cl in Concrete from Literature Data

Bai et al [32] made eleven mixes concrete mixes with a binder either Ordinary Portland Cement, or Pulverised Fly Ash or Meta-Kaolin (OPC–PFA–MK) content of 390 kg/m^{3}, w/b ratio of 0.5 and a wide range of MK–PFA combinations. After de -moulding the samples were water cured for 28 days, coated with a sea water resistant coating material and then left exposed for the resultant time to a synthetic sea water made from 30 g/l NaCl, 6 g/l MgCl_{2}, 5 g/l MgSO_{4}, 1.5 g/l CaSO_{4}-2H_{2}O and 0.2 g/l KHCO_{3}. The samples where sliced and chloride penetration profiles were measured as a function of depth. The profiles representing OPC or where 30% of the OPC was replaced by PFA were digitized and then converted so that the Cl content was expressed as %wt binder.

Using an excel spreadsheet and the excel solver routine it was possible to evaluate the values of D and S at t_{0} (defined to be at 28 days) using equation 4. For the OPC concrete D(t_{0}) and S(t_{0}) were 33mm^{2}/yrs and 1.8% respectively with m=0.22 and n was set to 0 while for the OPC/PFA concrete D(t_{0}) and S(t_{0}) were 20 mm^{2}/yrs and 0.31% respectively with m=-0.87 and n=0.67.

**Figure 6.** Comparing Bai et al’s [32] data to the fits for both 100% OPC concrete and 70%OPC-30%OPC concrete.

**Table 3.** Comparing Bai et al’s data [32] for both 100% OPC concrete and 70%OPC-30%OPC concrete when the Cl profile was fit by equation 4. The data and the quality of the fits are shown in Figure 5.

Effect of time | 100% OPC | 70%OPC 30% PFA |
---|---|---|

Months | D (mm^{2}/yrs) S |
D (mm^{2}/yrs) S |

2 | 33 2.1 | 12.1 0.6 |

4 | 33 | 8.0 1.1 |

10 | 33 3.0 | 4.6 2.5 |

18 | 33 3.4 | 3.2 4.2 |

Graphs of the data and the resulting fits are shown in the next two figures. The quality of the fit is very much better than expected. However there is a problem in the OPC concrete where fits were made allowing the D values to vary as equation 2 as the D increased with time suggesting that D was constant with respect to time. Hence the value of n was fixed at 0 to give the published fit.

It should be noted that although the 100% OPC is better fit to equation 4 by the data in figure 5 this must be due to errors in the data as the fits do not make physical sense. Hence it is concluded that for the OPC concrete the diffusion does not vary significantly with time. In contrast for the 70%OPC-30%OPC concrete diffusion significantly varies with time. There is a surprising difference between the relationship between S and time for the concretes made from 100% OPC and from 70%OPC- 30%OPC. This is shown in Figure 6. For concrete made from 100% OPC it would appear that after 2 years there was little significant increase in S but for 70%OPC-30%OPC there is no such pattern. In fact the fitted pattern implies that after 100 years more that 100% of the binder will in fact be chloride. This is most unlikely and illustrates the folly of extrapolation experimental data of this type beyond the experimental data when the physical causes of the behavior are not understood.

Tang [40] has reported on a number of concretes exposed to the sea water for periods of 10 years. The data included concretes placed in the submerged zone and had been made with three different OPC at water binder ratios of 0.35, 0.40 & 0.50. The cements were designated Anl - a Swedish sulphate resistant cement, Deg400 - a Danish sulphate resistant cement, and Slite - a Swedish OPC. The published chloride ingress profiles of these cements were digitized and the results together with the fits to equation 4 are shown in Figure 7.

**Table 4.** Parameters of equation 4 needed to fit chloride profiles (Tang[40]) of concretes made from Portland Cement at different water to binder ratios. D_{0} (mm^{2}/s) & S_{0} (wt % Cl with respect to binder) were fitted at 28 days. (In the data shown w/b varied from 0.35- 0.50). Three different cements were used; Dec a Danish Cement and Swedish cements Slite & Anl. Fits (as lines) and data as scatter plots) are shown in Figure 7.

w/b | D_{0} |
n | S_{0} |
m | D_{0} |
n | S_{0} |
m | ||
---|---|---|---|---|---|---|---|---|---|---|

0.35 | Dec | 189 | 0.46 | 1.20 | 0.12 | |||||

0.35 | Anl | 334 | 0.43 | 1.16 | 0.18 | Slite | 71 | 0.15 | 4.63 | 0^{+} |

0.40 | Anl | 126 | 0^{+} |
2.11 | 0.15 | Slite | 84 | 0.02 | 1.86 | 0.14 |

0.50 | Anl^{+} |
197* | 0^{+} |
1.17 | 0.32 | Slite | 319^{0} |
0^{+} |
0.91 | 0.27 |

^{+}This parameter was set to 0 during fitting^{*}Note that two data sets were omitted in this fit^{0}Note that the middle data set was omitted in this fit

Although the fits shown in Figure 6 have impressive agreement between the data and the lines fitted to equation 4 some care had to be exercised in the fitting procedure. Firstly for the W/B ratio of 0.50 the middle profiles had to be ignored. Tang suggested that some of these results might be due to analysis errors or casting segregation. The shape of the profiles suggests that it would be difficult if not impossible to fit the profiles to Fick’s law and yet the regularity of the profiles suggest that simple errors will not explain the profile shapes. It is tempting to “explain the results” by suggesting that sea water was finding pathways not confined by diffusion and that casting flaws were in fact responsible for the rejected results. Secondly some fits could only be carried out if some parameters were set to zero and not fitted. These cases are indicated in Table 5.

It should be noted that Tang has reported diffusion estimates obtained using NT Build 492 from samples cured in the laboratory for about 6 months. Surprisingly the NT Build 492 results (after 6 months cure) was reported by Tang to have a similar magnitude to D measured that he estimated from the samples exposed in sea water for years. Such a result was very surprising as it would be expected (1) that the time dependence of the diffusivity would ensure that the latter estimates would have significantly less diffusivity, (2) the sea water would inhibit diffusion more than NaCl solution and (3) that the Cl concentration which was greater in the salt solution than seawater would enhance the Cl diffusivity. Perhaps the explanation of these observations lie in a combination of the following factors (i) different temperatures of exposure, (ii) mechanical damage by the sea exposure open micro-cracks that enhanced Cl transport (iii) casting flaws in the samples introduced sampling errors because of differences in the cast samples. Whatever the explanation these phenomena should be further investigated.

**Figure 7.** Tang's data [40]. Fitted and plotted Chloride profiles of Concrete made from Portland Cement - OPC (Slite) and Sulphate Resistant (Anl & Dec400) at different times and water binder ratios.

Collins and Grace [41] measured chloride penetration in a jetty structure in Hong Kong. This jetty was constructed in 1986 from normal Portland Cement concrete (W/B 0.4) with a cement content of 450 kg/m^{3}. The chemical analysis was taken from core samples on beam soffits exposed to periodic seawater splash conditions. Their averaged data (Figure 4 in [41]) was digitised and fitted to equation 4. The Cl concentrations were corrected from % concrete to % binder by the factor 2400/450 (Derived by assuming the mix density was 2400 kg/m^{3} and the binder in the concrete 400 kg/m^{3}). This data was fit by equation 4 to give D=85 mm^{2}/year S= 0.77, n=0.0 and m=0.27. The results are shown in Figure 8.

**Figure 8.** Fit of Penetration profiles given by Collins and Grace [41] assuming D=85 mm^{2}/year S= 0.77, n=0.0 and m=0.27.The profiles were taken at varying times from concrete exposed to periodic seawater splash.

Another data set comes from a study of McCarter et al [42] who used the construction of a road bridge in 1991 to arrange 9 pier stems placed on the causeway leading to the bridge. The piers had minimum cover of 65 mm and were exposed to the tidal and other zones. The piers were cored at 1.17, 2.67, 4.84 and 6.67 years and the chloride profiles obtained for three concretes; (1) Plain concrete (460 kg OPC/ m^{3} concrete – W/B 0.40) (2) Similar concrete but with 30 l/ m^{3} of Caltite added into the mix (3) identical concrete to (1) but treated with silane. After 6 years all of the cover had greater than 0.6% of Cl % Wt of Binder. However both the Caltite and Silane samples had unusual penetration profiles that could not be fitted by equation 4. It was as if there was another phenomenon to diffusion was acting. Perhaps the sealant inhibited curing and when breached allowed the ingress of salt water by hydration suction as suggested by Volkwein [22-23].

**Figure 9.** McCarter et al [42] data comparing Chloride profiles in OPC concrete to that treated with Calcite and Silane. The treated concrete profiles could not be fit by equation 4 suggesting that a process other than diffusion governed the chloride ingress.

The final fit of a data set comes from data supplied by a recent New Zealand study where a number of production concretes were made [43]. In the study a number of concretes were exposed under different conditions and the chloride profiles measured. The concretes selected for fitting by equation 4 were exposed just above the high tide level to sea water for 0.5, 1.0, 1.5, 2.5 & 5.0 years. At these times the concrete was cored and the duplicate chloride profiles determined. These concretes were made from New Zealand General Purpose (GP) OPC cement and Durcem Cement (DC) where 65% GGBFS acted as a cement replacement (The GGBFS or Ground Granulated Blast Furnace Slag was imported from Port Kembla NSW, Australia). Two different cement contents were used at target loadings of 325 kg/m^{3} or 400 kg/m^{3} binder/concrete.

These results and the fitted profiles are shown in figure 8. With the exception of the results taken from the surface layers the chloride concentrations can be seen to lie within the expected experimental errors of the fitted results. As discussed the actual surface chloride would be expected to vary due to surface alterations occurring with time during the exposure the concrete to seawater. It should be noted that for two concretes S(t) appeared to be constant (m=0) while in the other two concretes S varied with time.

Details of the mix composition and the fitted parameters are given in Table 5.

**Figure 10.** Chloride Profiles from Lee and Chisholm [43] fitted by the equation 4 for concretes GP325 GP400 DC325 & DC400. Concretes are made from OPC (or General Purpose) or GGBFS/OPC (DC Cement) at loadings or either 325 or 400 kg/m^{3}.

**Table 5.** Fitted Parameters (From fits in Figure 8) and data from Lee and Chisholm [43]. D_{0} (mm^{2}/s) & S_{0} (wt % Cl with respect to binder) were fitted at 28 days. The water binder (w/b) Density (ρ) (kg/m^{3}) & Compressive strength (MPa) at 28 days f_{c} values were all taken from Lee and Chisholm [43].

D0 | n | S0 | m | w/b | ρ | fc | |
---|---|---|---|---|---|---|---|

GP325 | 266 | 0.28 | 1.92 | 0.00 | 0.49 | 2403 | 54 |

GP400 | 159 | 0.28 | 1.77 | 0.06 | 0.40 | 2421 | 60 |

DC325 | 165 | 0.58 | 4.63 | 0.00 | 0.49 | 2442 | 39 |

DC400 | 158 | 0.61 | 2.37 | 0.18 | 0.44 | 2442 | 42 |

## Fitting Chloride Penetration Profiles of Concrete Cured at Different Times

In this part of the review a number of different concretes have been found in the literature where penetration profiles have been published after being exposed to chlorides at different times. All of these profiles have been converted into common units and fitted by equation 4. With the signal exception of three datasets all of these profiles could be adequately fitted by the equations. The three exceptions were from McCarter et al [42] where the two samples were sealed from the water and the Anl (W/C=0.5) from Tang[40] where the concentration of the chloride in an earlier time was greater then that of a latter time. This Anl sample must be regarded as flawed and was discarded from further analysis. In contrast the McCarter samples point to the fact that in this case diffusion did not control the chloride penetration. It is suggested that this was caused by hydration suction.

It is suggested that it is the cure time that is one of the key factors in controlling and limiting the chloride diffusion. However in most of the samples the curing was taking place while the sample was exposed to the chloride and it was one of the surprise results in this review that this complex problem could be so well fit by the semi-empirical function defined in equation 4.

Also it should be noted that there are many different exposure factors including; chloride concentrations, temperature of the chlorides, the presence or absence of sea water the ability of the cements to bind chlorides, and different techniques (and exposure conditions) used in measuring penetration profiles. Each of these factors could significantly alter the chloride penetration profile. Furthermore most of the samples were exposed under water. In contrast the samples of Lee and Chisholm [43] were exposed just above the high tide zone. It is not clear what the conditions of water saturation and wetting and drying have on the chloride transport. Despite these concerns it is suggested that to a first approximation the chloride transport can be modeled by equation 4.

## References

These are given in Part 3 of the paper

## Contact Details

**L.P. Aldridge**

Company:

Monitoring Applications of Durability,

24 Balmer Cres Woonona,

NSW 2517

E-mail: [email protected]