life prediction concrete

AP-T07

SERVICE LIFE PREDICTION OF REINFORCED CONCRETE STRUCTURES

AUSTROADS

Service Life Prediction of Reinforced Concrete Structures

First Published 2000

Austroads Inc. 2000

This work is copyright. Apart from any use as permitted under the Copyright Act 1968, no part may be reproduced by any process without the prior written permission of Austroads.

National Library of Australia Cataloguing-in-Publication data:

Service Life Prediction of Reinforced Concrete Structures ISBN 0 85588 576 9

Austroads Project No. N.T&E.9813

Austroads Publication No. APT07/00

Project Manager Rod McGee, Department of Infrastructure, Energy and Resources, Tasmania

Prepared by Guangling Song, ARRB Transport Research Ahmad Shayan, ARRB Transport Research

Published by Austroads Incorporated Level 9, Robell House 287 Elizabeth Street

Sydney NSW 2000 Australia Phone: +61 2 9264 7088

Fax: +61 2 9264 1657 Email: [email protected]

www.austroads.com.au

Austroads believes this publication to be correct at the time of printing and does not accept responsibility for any consequences arising from the use of information herein. Readers should rely on their own skill and judgement to apply information to particular issues.

SERVICE LIFE PREDICTION OF REINFORCED

CONCRETE STRUCTURES

Sydney 2000

Austroads Incorporated Austroads is the association of Australian and New Zealand road transport and traffic authorities whose mission is to contribute to development and delivery of the Australasian transport vision by: supporting safe and effective management and use of the road system developing and promoting national practices providing professional advice to member organisations and national and international

bodies.

Within this ambit, Austroads aims to provide strategic direction for the integrated development, management and operation of the Australian and New Zealand road system through the promotion of national uniformity and harmony, elimination of unnecessary duplication, and the identification and application of world best practice. Austroads is governed by a council consisting of the chief executive (or an alternative senior executive officer) of each of its eleven member organisations.

Member organisations

! Roads and Traffic Authority New South Wales ! Roads Corporation Victoria ! Department of Main Roads Queensland ! Main Roads Western Australia ! Transport South Australia ! Department of Infrastructure, Energy and Resources Tasmania ! Department of Transport and Works Northern Territory ! Department of Urban Services Australian Capital Territory ! Commonwealth Department of Transport and Regional Services ! Australian Local Government Association ! Transit New Zealand

Executive Summary

Service life prediction based on corrosion deterioration of reinforcement is critical to the safety of a reinforced concrete structure. Although considerable work in this area has been done, the prediction theory has not been well established. This report reviews and discusses the existing models, aiming at providing a background knowledge for future work in this area. The contents of this report can be summarised as follows:

The deterioration processes of reinforced concrete structures due to corrosion damage are mostly caused by the ingress of chloride ions and carbonation of the cover concrete. The processes can generally be classified into three stages: initiation, stable propagation and unpredictable propagation. The service life prediction mainly refers to the first two stages.

In the carbonation initiation stage, the diffusion mechanism plays a basic role in the carbonation process, based on which theoretical and empirical modifications and other more complicated formulation have been proposed and used when more complicated transport mechanisms other than diffusion are taken into account in the carbonation process. The pH threshold associated with the neutralisation of the pore solution by carbonation is discussed. The normal prediction procedures are also briefly addressed.

The initiation of chloride induced corrosion is closely related to the ingress of chloride. The binding effect of the concrete matrix with free chloride ions makes a significant contribution to the chloride penetration process. Diffusion and binding are always the basic transport mechanism for chloride ions in concrete. However, in some cases when immigration and other transport mechanisms are also responsible for the ingress of chloride ions, multi-transport, more complicated and even empirical models have to be introduced to characterise the initiation process of the chloride induced corrosion. The chloride threshold is a critical parameter. Estimating relevant parameters from measured chloride profiles according to a selected model is usually involved in a prediction technique at this stage.

Critical corrosion amount (corrosion depth, or thickness of corrosion product layer) is an important parameter in the stable propagation stage, which is addressed in most prediction models, including simple extrapolation, diffusion controlled corrosion modelling, laboratory simulation, and empirical formulation, etc. The prediction of this stage still requires the corrosion rate to be measured and the present corrosion state (amount) determined. Relatively less work has been done in association with this stage than the first stage.

The final chapter of the report briefly summarises a methodology of service life prediction and identifies current problems with the existing prediction techniques.

Contents

1. INTRODUCTION.............................................................................................................1

2. DETERIORATION OF REINFORCED CONCRETE STRUCTURES....................2

2.1 Causes of corrosion damage.........................................................................................2 2.2 Deterioration due to corrosion of reinforcement.........................................................2 2.3 End of service life .........................................................................................................4

3. SERVICE LIFE PREDICTION APPROACHES.........................................................6

4. INITIATION OF CARBONATION INDUCED CORROSION ..................................8

4.1 Carbonation mechanisms and processes.....................................................................8 4.1.1 Diffusion of carbon-dioxide....................................................................................8 4.1.2 Carbonation reactions ...........................................................................................8

4.2 Mathematical models ...................................................................................................9 4.2.1 General diffusion model ........................................................................................9 4.2.2 Simple diffusion model ........................................................................................13 4.2.3 Empirically modified models...............................................................................14 4.2.4 Theoretically modified models ............................................................................14 4.2.5 Other complicated mechanisms ..........................................................................16

4.3 Carbonation situation ................................................................................................17 4.3.1 Carbonation depth ...............................................................................................17 4.3.2 pH threshold for corrosion...................................................................................17

4.4 Prediction procedures.................................................................................................20 4.4.1 Determination of extent of carbonation..............................................................20 4.4.2 Selection of prediction models.............................................................................21 4.4.3 Obtaining model parameters...............................................................................21

5. INITIATION OF CHLORIDE INDUCED CORROSION........................................ 23

5.1 Ingress processes and mechanisms ...........................................................................23 5.1.1 Ingress and transport of chloride in concrete.....................................................23 5.1.2 Binding of chloride in concrete............................................................................24

5.2 Mathematical models .................................................................................................26 5.2.1 Simple diffusion model ........................................................................................26 5.2.2 Diffusion-binding model ......................................................................................29 5.2.3 Multi-transport-mechanism models ...................................................................31 5.2.4 Complicated models .............................................................................................32 5.2.5 Empirical models .................................................................................................37

5.3 Threshold concentration of chloride ..........................................................................38 5.4 Prediction techniques.................................................................................................40

5.4.1 Chloride profile ....................................................................................................40 5.4.2 Selection of models...............................................................................................40 5.4.3 Relevant parameters ...........................................................................................41

Contents (continued)

6. CORROSION PROPAGATION OF REINFORCING STEEL.............................. 43

6.1 Corrosion processes and mechanisms .................................................................... 43 6.2 Critical corrosion amount ....................................................................................... 45 6.3 Prediction models .................................................................................................... 46

6.3.1 Simple extrapolation......................................................................................... 46 6.3.2 Diffusion controlled model................................................................................ 47 6.3.3 Laboratory simulation models ......................................................................... 48 6.3.4 Empirical prediction models............................................................................. 49

6.4 Prediction procedures.............................................................................................. 50 6.4.1 Reconfirmation of deterioration stage ............................................................. 50 6.4.2 Estimation of corrosion rate............................................................................. 50 6.4.3 Determination of the present corrosion state.................................................. 51 6.4.4 Selection of prediction models.......................................................................... 51

7. CONCLUDING REMARKS....................................................................................... 52

7.1 Methodology of service life prediction .................................................................... 52 7.2 Problems to be solved.............................................................................................. 53

8. REFERENCES ............................................................................................................ 55

Service life prediction of reinforced concrete structures

1

1. Introduction

Each structure has its own design service life according to certain codes, but such a parameter set for the sake of safety is often an estimate. Concrete is usually designed to be resistant to corrosion, and corrosion induced damage is not a main factor considered in the design. In some cases, the design service life could be too conservative; while, in some other occasions, it could be too risky. Therefore, reasonable and reliable prediction of service life of a structure based on corrosion induced premature damage is always an important issue to be addressed.

A reliable prediction of service life based on corrosion state of the reinforcement is critical to the safety of reinforced concrete. It can also greatly affect the asset owners budget. A reasonable and accurate service life prediction can allow taking of necessary precautions in time, avoid unnecessary cost due to conservative design, and reduce risk of potential disaster due to the delay in taking precautionary measures.

However, such service life prediction is always complicated and difficult due to two basic facts:

A) service life is influenced by many unpredictable factors, such as the environmental parameters;

B) the mechanisms dominating service life could vary from time to time.

These difficulties are even more significant for reinforced concrete structures in the field because their deterioration could have various causes, such as a low grade of concrete used in severe environments, bad casting practices or design, chemical attacks from the environment, detrimental reactions in concrete (e.g. alkali aggregate reaction), corrosion of reinforcement, etc.

Even though most of these deterioration processes have been widely investigated, the potential for deterioration to be induced by corrosion of reinforcement was not recognised for many years. This was because there was a misunderstanding that the reinforcement was non-corrodable due to the high alkalinity of the pore solution in the concrete and to the barrier provided by the cover concrete against aggressive agents from outside. Now it is generally accepted that corrosion of reinforcement can critically determine the service life of a reinforced concrete structure.

Nevertheless, the history of investigations of corrosion of reinforcement is still relatively short, and the understanding of mechanisms involved is far from comprehensive. Therefore, service life predictions based on the corrosion mechanisms are still in their initial stages.

The aim of this project is to provide an overview of available models for service life prediction of reinforced concrete structures.


2

2. Deterioration of reinforced concrete structures

Signs of distress and deterioration can sometimes be found on concrete bridges in the form of cracking, delamination and spalling of concrete by rust, etc. However, more commonly, some reinforced concrete bridges may appear to be in good shape, but could actually be suffering from very serious corrosion attack on the reinforcement. The different manifestations of damage indicate different deterioration processes (mechanisms) the structures have undergone or are undergoing and different stages of deterioration.

2.1 Causes of corrosion damage

Many factors can induce deterioration in a reinforced concrete structure, such as early-age defects of the concrete itself, freeze/thaw, abrasion, acid dissolution, alkali-aggregate reaction, sulphate attack, carbonation, chloride contamination, etc. Most of these processes are directly responsible for deterioration of the cover concrete, the discussion of which is outside the scope of this report. However, damage of the cover concrete leading to corrosion of reinforcement is the main issue to be addressed in this report.

In addition to the factors that accelerate concrete deterioration accelerators, there are two processes which do not detrimentally affect the integrity and quality of the cover concrete to a great extent, but can directly trigger corrosion of reinforcement: 1) carbonation and 2) chloride contamination of concrete.

It should be stressed that when corrosion induced damage becomes visible, deterioration is usually at a late stage and it may be too late to take any prevention or protection measures. Therefore, the service life prediction based on corrosion damage of reinforcement is particularly important.

Carbonation induced corrosion most commonly occurs in relatively dry environments in which there is sufficient carbon oxide to diffuse into the cover concrete. However, in chloride containing environments, the ingress of chloride is usually faster than the carbonation process, and it is more likely to cause premature end of service of a structure.

2.2 Deterioration due to corrosion of reinforcement

Generally, deterioration of reinforced concrete starts with carbonation or ingress of chloride in the cover concrete. After the carbonation front or the chloride contamination reaches the vicinity of the reinforcement, the corrosion of reinforcement is initiated and damage commences.


3

Fagerlund (1985) has schematically presented the different stages of the general deterioration process due to corrosion of reinforcement. Tuutti (1982) presented a curve of the development of corrosion damage with time. Purvis et al (1994) proposed an empirical equation to approximate this process:

(1)

where a and b are empirical constants; index S (in %) is a function determined by the percentages of delamination, spalling and bars with chloride above the corrosion threshold (Cl).

Many investigators [Tuutti (1977, 1982), Cady et al (1984), Schiessl (1987), Broomfield (1995), Blankvoll (1997), Amey et al (1998)] have accepted the concept that deterioration experiences two stages: initiation (ti) and propagation (tp).

In the first stage (ti), the main processes would be the ingress of chloride or CO2 into the cover concrete, and the transport of chloride ions or the progress of carbonation to the vicinity of steel reinforcement. In this stage, the corrosion rate of reinforcement is still very low, as the content of chloride is still far below the corrosion threshold and the pH value of the pore solution still high enough in the vicinity of the reinforcement to maintain the passivity of the reinforcement. The duration of the first stage (ti) could vary widely, depending on the aggressiveness of the environments and the quality of the cover concrete. Nevertheless, mechanisms which dominate this stage are the transportation of chloride or CO2 through the cover concrete. These mechanisms will not change significantly throughout this stage.

In the second stage (tp), corrosion of steel in concrete is activated, and from then on the corrosion will develop further with time, which may finally lead to cracking and spalling of the cover concrete, if corrosion products are built up on the surface of steel. In this stage, the most important mechanisms are the corrosion reactions on the reinforcement.

The corrosion rate of reinforcement involved in the second stage can change with time, particularly when cracking or spalling of the cover concrete occurs as a result of the corrosion of reinforcement. When the corrosion of reinforcement is activated, the deterioration of reinforced concrete (e.g. reduction of cross section, the propagation of pitting depth, or the increase in the thickness of the rust layer) will be governed by certain corrosion mechanisms, such as transportation of Fe2+ across the rust layer or O2, in the cover concrete.

bteaS +

=1100


4

However, as corrosion damage of the reinforcement becomes more severe with time, the cover concrete would further deteriorate in respect of its corrosion protection effectiveness, through further cracking and spalling. As a result, the deterioration of the cover concrete can greatly worsen the corrosion conditions of the reinforcement by dramatically increasing the ease of ingress of chloride and CO2, the supply of corrosion depolarisation reagent O2, or removal of the rust layer which has a protection effect. Development of corrosion at this stage hasa different mechanism from that before the cover concrete is affected. After severe cracking or spalling of the cover concrete, the reinforcement may become directly exposed to the environmental agents, so that unpredictable changes of environmental parameters, such as wetting/drying, heating/cooling, etc. would directly impact on the corrosion of reinforcement with short response times.

Therefore, the deterioration of reinforced concrete caused by the corrosion of reinforcement might better be classified into three stages: initiation (ti), stable propagation (tsp), unpredictable propagation (tup) (see Figure 1). They are dominated by different processes: transportation of chloride or CO2 in the concrete; corrosion of reinforcement under relatively stable conditions in uncracked cover concrete, and corrosion of reinforcement in cracked concrete, respectively.

Figure 1. Deterioration stages of reinforced concrete due to corrosion of reinforcement

dete

rior

atio

n de

gree

(cor

rosi

on d

amag

e)

time

initiation (ti )

stablepropagation

(tsp)

unpredictablepropagation

(tup)

after crackingof the coverconcrete

com pletelydamaged


5

2.3 End of service life

The above-mentioned stages (ti, tsp, and tup) are the basis for service life prediction. If all the stages, i.e. ti , tsp and tup , could be known, then the service life will be reasonably predicted.

The service life of a structure may be different from the natural life or designed life. It seems that different researchers have different understandings of what should be defined as the service life for prediction purposes.

Basically, service life can be defined as the period until repair becomes necessary [Geiker et al (1993)]. Visible changes such as large cracking, spalling and delamination are usually considered as severe damage. When the extent of these types of damage rise to a certain percentage of structural elements, repair or rehabilitation work may become necessary [Purvis et al (1994)]. For instance, Weyers, et al, (1994) found that bridge decks had reached the end of their functional service life when 5 to 14% of the deck area was spalled, delaminated or patched with temporary asphalt patches, and 4% cracking, spalling and delamination represented the end of functional service life of the substructures. Chamberlin et al (1993) reported an estimation of service life of an overlay on a concrete bridge deck by extrapolating its historical performance data. The overlay performance was also assessed by the percentage of deck area damaged by delamination or spalling (associated with either bond failures or reinforcement corrosion).

The practical service life can also be defined as the duration before certain critical values of measurable properties are reached. This is a more widely adopted definition. In many cases, the definition of the service life is dependent on the deterioration mechanisms. For example, the time for the initiation of steel corrosion by ingress of chloride through cover concrete [Tuutti (1982)] or carbonation of cover concrete [Morinaga et al (1994)], has been taken as an important measure of concrete service life.

In practice, there may be a risk to continue the service of a structure in its unpredictable propagation stage when damage, such as spalling and cracking, already exists. For the sake of safety, the service of such a structure should be limited or stopped as soon as the structure gets into its unpredictable propagation stage.

On the other hand, it may also be too conservative to cease service at the onset of the stable corrosion stage, because the corrosion damage to the reinforcement may be still insignificant at that moment. It may be safe and economical to continue the service of a structure at this stage until certain amount of corrosion damage has occurred (reasonable prevention measures should be taken in this stage). Therefore, the service life (ts) could be defined as:


6

(2)

where ti is the initiation time and tsp the stable propagation time. The rationale for such a definition is as follows:

1) At the end of the stable propagation stage, the reinforcement in concrete has been corroded to some extent, which has started to detrimentally affect the cover concrete. Therefore, it could be the right moment that some repair or protection actions should be taken. Or the service of the structure should be stopped for the sake of safety.

2) The deterioration processes in the initiation and stable propagation stages dominated by certain predictable mechanisms, so the deterioration processes are relatively easy to predict compared with that in the unpredictable propagation stage which are affected by too many varying environmental factors.

In this report, service life prediction will be based on the initiation and stable propagation stages.

ts ti + tsp


7

3. Service life prediction approaches

To predict service life, the following facts must be known:

A) the mechanisms governing the initiation and stable propagation stages,

B) the relevant parameters involved in the mechanisms, and

C) the present state of the reinforced concrete.

Currently, prediction approaches have been classified into the following different categories [Clifton (1993)]:

1) estimations based on experience,

2) deductions from performance of similar materials,

3) estimations based on accelerated testing,

4) mathematical modeling based on the degradation and corrosion processes, and

5) application of some other new concepts, such as reliability and stochastic methods, etc.

For the first approach, the prediction is usually based on in-situ inspection. The performance of a concrete structure evaluated at certain time intervals can be extrapolated to the future [Sayward (1984)]. In the prediction, the mechanisms, the relevant parameters, and the stage that the structure is at, all need to be estimated, so this approach is not very reliable. However, it is very simple compared with other methods.

The second approach is also mainly based on experience. However, before the prediction is made, a sufficient database of the performance of similar materials must be available. In some cases, empirical expressions are proposed for the progress of deterioration with time [Purvis et al (1992)]. As the relevant information is provided by the database (which should be much more accurate than that estimated according to experience), this approach is more reliable than the first method. However, the mechanisms dominating the deterioration process, and the stage that the structure is at, are still not accurately determined.

Prediction based on laboratory tests uses accelerated or non-accelerated techniques to simulate the deterioration process of reinforced concrete in the field. Due to the fact that the deterioration of concrete under laboratory conditions may be different from the natural deterioration process in the field, it is essential to examine the correlation between laboratory results and field damage. As the mechanisms dominating the deterioration processes can be investigated under laboratory conditions, and the relevant parameters involved in the mechanisms could also be obtained by laboratory tests, the third approach is more reliable than the first two. This kind of test has been commonly employed as a standard method of assessing reinforced concrete durability [Vesikari (1986), Kalousek et al (1972)].


8

Recently, with the development of computer techniques and the accumulation of data, mathematical simulation and modelling has been widely proposed for more reliable service life prediction. This kind of prediction requires knowledge of the dominating mechanisms, relevant parameters and current deterioration stage. One of the typical models currently widely used is the modelling of transportation of chloride in the cover concrete based on Ficks diffusion law. In this case, the transportation of chloride in concrete is believed to be mainly governed by the diffusion mechanism, which provides a detailed mathematical expression for the model. The relevant parameters critical to prediction, such as diffusion coefficient of chloride in concrete, surface concentration of chloride and chloride content depth profile in the concrete, etc., are usually experimentally determined. Based on the chloride profile, the corrosion stage of the structure can easily be identified. Therefore, this kind of approach is theoretically much more reliable than the previous three, and should have a promising future. However, some difficulties have been encountered in the application of this kind of approach, e.g. the contribution of mechanisms other than the diffusion, the variation of the relevant parameters with time and from part to part in the same structure, etc. These difficulties can greatly affect the reliability of this kind of prediction.

In theory, if all the mechanisms affecting the deterioration processes and the corresponding parameters can be identified, then a prediction model can be accurately established and service life reasonably predicted. In practice, this is very difficult in many cases due to the complexity of the concretes and real-world environments, as well as a large number of unknown factors. To cope with these difficulties, some new concepts, such as reliability and stochastic methods [Clifton (1993)], have been proposed. However, these trials need further verification and more evidence from the field.

In summary, the fourth approach is currently the most reasonable and reliable, and hence the most promising in the future. Therefore, in this report, only the fourth approach will be reviewed.


9

4. Initiation of carbonation induced corrosion

Carbonation is an ongoing chemical reaction between carbon-dioxide in the atmosphere and some calceous components in the cementitious matrix, leading to the formation of calcium carbonate. It is one of the main causes of corrosion of reinforcement in concrete structures, and is a common phenomenon in old or badly built structures. In a concrete structure exposed to the atmosphere, a carbonation front develops and gradually advances inward from the surface of the concrete structure. After the front reaches the reinforcement, corrosion of the reinforcement is initiated, then the deterioration moves into the next stage, the corrosion propagation stage.

4.1 Carbonation mechanisms and processes

The carbonation phenomena have been widely investigated and well summarised [Aschan (1963), Hamada (1968), Smolczyk (1968), Kondo et al (1968), Wittmann et al (1986), Parrott (1987), Reardon et al (1990)]. Carbonation is regarded as being governed by a CO2-transport process accompanied by the chemical reactions that form calcium carbonate.

4.1.1 Diffusion of carbon-dioxide

Even though convection effects and the diffusion of other ions could contribute to the CO2 transport process, the diffusion of CO2 in concrete pores is generally believed to be the main mechanism responsible for the process, and can be theoretically expressed by Ficks diffusion law in a similar manner as that for chloride ingress [Li et al (1987)]. The difference in concentration of free carbon-dioxide within the cavities and pores is the driving force for the diffusion. The carbonation can progress throughout the concrete provided sufficient CO2 is available in the surrounding environment and the exposure time is long enough.

4.1.2 Carbonation reactions

After CO2 transports into concrete, it causes carbonation reactions in the concrete. Although the reactions involved in the carbonation process are very complicated [Richardsson (1988), Papadakis et al (1991a,1991b)], they are usually briefly expressed as:


10

(3)

(4)

These reactions mainly occur in the pore solution.

The pore solution of plain concrete mainly consists of sodium, potassium, and much less calcium ions in equilibrium with hydroxide ions at a pH value between 12 to 14. The production of the CaCO3 precipitate during carbonation consumes the Ca(OH)2 in the concrete (reaction (4)) and lowers the pH value of the pore solution.

In addition to the above principal carbonation reactions, CO2 in the concrete could still participate in some other reactions. For example, CO2 can directly react with the hydrated cement products, such as the calcium silicate hydrate and calcium aluminosulfates and cause their disintegration. Usually, the latter is significant only in badly deteriorated concrete.

The lowered pH level of the pore solution in concrete provides an aggressive medium environment for the steel, because the passive film on the reinforcing steel, which protects the steel from corrosion, becomes unstable when pH is lower than 11 [RILEM (1976)], thereby steel can be readily corroded in carbonated concrete.

4.2 Mathematical models

It should be stressed that the transport of CO2 and carbonation reactions occur simultaneously in the concrete. The former is usually much slower than the latter [Klopfer(1978)], hence the overall carbonation process, in most cases, is dominated by CO2 transport mechanisms.

4.2.1 General diffusion model

If only the diffusion of CO2 in the pores and its consumption by carbonation of concrete are considered in the carbonation process, then this process can be mathematically expressed by the following equation, which has been proposed in similar format by several authors [Fukushima (1991), Papadakis et al (1991b), Mauda et al (1993), Xu (1995)]:

CO2 + H2O (pore solution) H2CO3

H2CO3 + Ca(OH)2 CaCO3 + 2H2O


11

(5)

where, CCO2 is concentration of free CO2 in concrete, x is the space coordinate, t is the time coordinate, DCO2 is the diffusion coefficient of the CO2 in the concrete, fCO2 is the overall CO2 consumption rate of the carbonation reactions, a concentration of free CO2 dependent function.

This is a generalised model, which is based on a basic assumption:

I) Diffusion and consumption of CO2 by carbonation reactions are the main mechanisms dominating the carbonation process.

In addition, three assumptions or approximations are also widely used to simplify the above equation:

II) The concrete matrix through which the CO2 diffusion occurs is uniform in microstructure and properties;

III) The microstructure and properties of the concrete do not change significantly with time; and

IV) The microstructure and properties of the concrete do not change significantly with the concentration of the diffusing CO2.

Under these three assumptions, the diffusion coefficient DCO2, will be constant, independent of time (t), space (x), and CO2 concentration (CCO2). In this case, equation (5) can be further simplified into:

(6)

where De,CO2 is effective diffusion coefficient:

(7)

which represents the transport rate of free CO2 under the carbonation effect.

If V) The free CO2 consumption function fCO2 is simply assumed to be

linearly dependent on the concentration of free CO2, i.e. kCO2 = fCO2/CCO2 = constant,

22

22 )( COCOCOCO fx

CD

xtC

=

22

2

2,2

xC

Dt

C COCOe

CO

=

2

2

22,

1CO

CO

COCOe

Cf

DD

+=


12

Then, the effective diffusion coefficient would become a constant too:

(8)

In this case, Equation (6) is a typical Ficks second diffusion equation, which has an analytical solution under semi-infinite boundary condition and zero initial condition:

VI) The concentration (Cs,CO2) of CO2 on the concrete surface is constant, and the interior of the concrete far from the carbonation front has zero concentration of CO2, i.e.

(9)

VII) The concentration (Ci ) of CO2 in the concrete before carbonation is zero, i.e.

(10)

Conditions VI) and VII) are actually another two approximations, as for a field structure the concentration of carbondioxide in the surrounding air could change with time, and also the structure could be carbonated to some degree during its construction process, so semi-infinite and initial concentrations of CO2 could not be zero.

Based on the above assumptions I) to VII), the following analytical solution to equation (6) can be obtained:

(11)

which will give a distribution of concentration of CO2 from the concrete surface to the interior at a given time, as shown in Figure 2.

==

0

22)(1)( dzeerfcerf z

2

22, 1 CO

COCOe k

DD

+=

CCO2|x=0 =Cs,CO2 =const; CCO2|x= = C,CO2 = 0

CCO2|t=0 = Ci,CO2, = 0

CCO2 = Cs,CO2 {1-erf [x/(De,CO2 t)1/2]}


13

Figure 2. Typical distribution of CO2 concentration in concrete

Correspondingly, the change of the concentration of CO2 in a given position (depth) in the concrete can be schematically illustrated as Figure 3.

Figure 3. Change of CO2 concentration with time at a given depth in concrete

0

1

0 400000t, carbonation time

C CO

2, c

once

ntra

tion

of C

O 2 a

t dep

th x

=xt

Cs,CO2

tx

0

1

0 60x, depth from concrete surface

C CO

2, c

once

ntra

tion

of C

O

2 at t

ime

t=tx

Cs,CO2

xt


14

A very important conclusion from the above solution (11) is that any given concentration (C0,CO2) of CO2 at a given depth x0 in the concrete and at a given moment t0 will advance inward to the interior of the concrete with time in a parabolic manner:

(12)

(13)

where, XCO2 is the new position of the constant concentration (C0,CO2) of CO2 at carbonation time t (Figure 4).

Figure 4. Progress of CO2 of a given concentration with carbonation time in concrete

Theoretically, CCO2 will not decrease to 0 unless at an infinite distance from the concrete surface. However, it is more practical to choose a depth Xc as carbonation depth or carbonation front, at which the concentration CC is low enough, and beyond which the concentration of CO2 and the carbonation process can be neglected. As Xc is actually a particular point of X, it also follows the above parabolic equation (12), so:

(14)

implying that the carbonation depth also advances with time in a steadily reducing rate.

It is obvious that the assumptions I) to VII) are not reasonable in any cases. Only when all these assumptions are satisfactorily met, the solutions and conclusions about the distribution, change, and progress of the concentration of CO2 in concrete can reliably reflect the realistic situation of field concrete structures.

XCO2 = A0,CO2 1/2

A0,CO2= x0 /t01/2; t>t0, XCO2>x0

Xc = Ac t1/2 ; (Ac = constant)

0

18

0 1500000t, carbonation time

XCO

2 , de

pth

of a

sel

ecte

d co

ncen

tratio

n (C

0,C

O2 )

of C

O2

t0

x0


15

4.2.2 Simple diffusion model

The above general model can be further simplified by assuming that the flow of carbon-dioxide through the carbonated zone is subject only to the concentration of carbon-dioxide at the concrete surface and the distribution of CO2 concentration is linear along the depth of the concrete [Kondo et al (1968), Hamada (1968)]. This can be mathematically expressed by

(15)

Based on this assumption, the general model equation (5) becomes much simpler, having a solution for the progress of carbonation depth with time:

(16)

where K and Ac are constants.

This solution is similar to equation (14) which is based on the general model. However, the theoretical base of this solution (16) is not as solid. Moreover, the concentration distribution of CO2 does not follow a straight line along the depth of concrete, as assumed for the derivation of Eq(16).

4.2.3 Empirically modified models

In practice, the measured results are sometimes similar to the theoretical predictions made by general or simple diffusion models, but cannot be satisfactorily simulated by them. For simplicity, some empirical modifications could be made to equations (12) and (15) to simulate or curve-fit the measured results in the field. The general format of the modified equations of carbonation depth is:

(17)

where A and B are constants, and n could have a range of values around .

It has been noted that the linearity of Xc vs. t1/2 does not always start from time t=0, i.e. there appears to exist an initial depth (B) of carbonation in some cases [Nagataki et al (1986)]. The initial depth could be ascribed to the drying of the concrete surface that allows easy carbonation at early ages. In addition, a non-parabolic (square root) function of carbonation time was also proposed by Parrot et al (1991) for wet conditions. In that case, the power differs from and depends on the relative humidity of the environment.

CCO2/x = Cs,CO2 /Xc= const.

Xc = (2De,CO2 Cs,CO2 K)1/2 t1/2 =Ac t1/2

Xc = A tn + B


16

Generally, the empirically modified models do not have a solid theoretical base. Even though practical results could be better simulated by them, the reasonability of the predictions still need to be carefully analysed.

4.2.4 Theoretically modified models

As mentioned earlier, the conclusions based on the general and simple diffusion models are only applicable under certain conditions where those assumptions are completely met. However, in practice, all these assumptions do not always hold, because the carbonation process can be affected by many factors.

Concrete parameters can significantly affect CO2 transport and carbonation processes. The carbonation rate can be dependent on porosity, pore size, cement content, w/c ratio, aggregate/cement ratio, etc. [Papadakis et al (1991a,1991b)]. This makes the prediction much more complicated. For example, in some cases, the influence of heterogeneity of concrete is very significant in the carbonation process, so space-dependent parameters would be involved in the model. In other cases, the porosity, pore size and other concrete parameters can still be modified by the deposition of the carbonation product, CaCO3, [Broomfield(1997)], which means that some parameters involved in the model could be time-dependent.

Research work has been conducted on this issue to further improve understanding of the influence of concrete parameters on carbonation. In a theoretical and experimental study, Li et al (1987) found that pores with radii over 320 are most responsible for CO2 transport in concrete which is ascribed to the fact that this pore size is larger than the free-path of CO2 gas molecules for atmospheric carbon dioxide.

Papadakis et al (1991A) calculated the possible amounts of Ca(OH)2 and other hydration products produced by each cement component, and their (empirical) contribution to reducing the effective path for CO2 diffusion. They proposed empirical formulae to estimate the effect of total porosity and relative humidity on the diffusion coefficient of CO2 in concretes measured in their tests. Hamada (1968) concluded that concrete with lesser proportions of Ca(OH)2 in the matrix would carbonate faster than those with higher proportions of this substance. However, Smolczyk (1968) believed that a high content of free Ca(OH)2 cannot protect any concrete against carbonation.

Houst (1991) simultaneously determined the diffusion coefficients of oxygen and carbon-dioxide through hydrated cement paste as a function of relative humidity, and found that the coefficients increased with increasing w/c ratio and decreasing relative humidity. Similar trends for CO2 diffusion coefficients have also be reported by other authors [Masuda et al (1993), Cahydi et al (1993)].

In making predictions, the influences of the above factors are usually reflected in the parameters involved in equation (19). For example, some researchers have expressed A as a function of w/c [Hamada (1968), Zhang et al (1998)] whilst others [Smolczyk (1968), Nagataki et al (1986), Schubert (1987), Gebauer (1982), Scholz et al (1984), Costa et al (1992)] related A to the concrete strength. Parrot et al (1991) used a carbonation depth function which had concrete permeability (to gas) and relative humidity as relevant parameters.


17

Environmental factors also have a significant influences on CO2 transport and carbonation processes. Temperature can increase the diffusion coefficient of CO2, hence the carbonation process is usually speeded up at high temperature. Atmospheric concentration of CO2 directly affects Cs,CO2, so the carbonation is normally more severe if a structure is exposed in an environment with a high atmospheric concentration of CO2. Rain and wind can also influence humidity, Cs,CO2, and transport mechanisms of CO2 in concrete, so the effects on the carbonation process can be complicated.

It was reported [Klopfer (1978)] that the greatest carbonation rate occurs when concrete is exposed to relative humidities of between 50% and 70%. An atmosphere with 100% relative humidity can prevent carbonation of concrete, as the water in the pores close to the surface of the concrete impedes the penetration of carbon dioxide. If the relative humidity is lower than 30%, the carbonation of concrete would not be significant, since the carbonation reaction requires water. The higher the strength class of the concrete and the cement content, the more slowly the concrete is carbonated. A higher content of calcium hydroxide in the concrete, i.e. higher cement content could also lead to smaller depth of carbonation in the concrete.

Unfortunately, all these factors including concrete parameters and environmental influences could vary with time (t), space (x), and concentration of CO2, etc. in the field. This means that the relevant parameters of those diffusion based models, such as De,CO2 and Cs,CO2, etc. (which are closely associated with concrete and environment parameters) are not constants.

For example, in some cases, the Cs,CO2 could change seasonally, or De,CO2 may not longer be constant, but depend on time, space, CO2 concentration, etc. If these practical factors are taken into account in the model, then the equation describing the carbonation process would become very complicated and may have no analytical solutions. Some authors [e.g. Fukushima (1987), Fukushima (1991),] have made some considerable effort in clarifying these issues.

Fukushima (1991) introduced a function that described the long term as well as periodical variations in the atmospheric carbon-dioxide concentration, and assumed that the CO2 consumption rate during the carbonation process is linearly dependent on the CO2 concentration. Therefore, the boundary condition Cs,CO2 is no long constant, and also the term describing CO2 consumption in equation (5) becomes a function of CCO2. In this case, they obtained a complicated solution to the modified equation, which may be hard to apply in practice.

Masuda et al (1993) proposed a non-linear reaction term in replacement of the carbonation consumption term in equation (5). In their models, the carbonation consumption rate is not only determined by CO2 concentration, but also by concentration of Ca(OH)2 in the concrete. They gave an approximate solution to this equation.

Similar attempts have been made by Cahyadi et al (1993) who considered the carbon-dioxide consumption term as a function of time, and took the internal transport of water within the pore system into account.


18

All these modified models may be more reasonable than the general one, and could theoretically provide more reliable prediction of carbonation process, as some realistic factors influencing the carbonation process have been considered in these models. However, the complicated models usually would not have solutions as simple as the general or simple diffusion models, and could even have no analytical solutions in some cases. Therefore, the simple expression (equation (14) or (16)) for the progress of carbonation depth could not be obtained from these models. Obviously, they would make the prediction of carbonation depth difficult in practice.

4.2.5 Other complicated mechanisms

Some other mechanisms could also be responsible for the transport of CO2 in concrete, for example:

1) Convection effect: internal movements of the pore solution as a result of wetting and drying. This would not only speed up the transport of carbondioxide, but also eventually accelerate the movements of carbonate ions, alkali ions, etc., from place to place.

2) Diffusion of ions in the pore solution: the ions involved in the carbonation reactions diffuse away or into the carbonating zones. This could also increase or decrease the carbonation process.

If these mechanisms dominate the carbonation process, then the models mentioned earlier would be invalid, and significant error would be introduced in service life prediction if it was only based on the diffusion models.

4.3 Carbonation situation

Carbonation situation refers to the extent and intensity of carbonation in concrete.

4.3.1 Carbonation depth

As mentioned earlier, carbonation depth Xc is the distance from the concrete surface where carbonation originally starts to where carbonation starts to become insignificant. Within this zone, the properties of concrete change from its original uncarbonated condition, particular the pH value of the pore solution is decreased.

Based on the simple or general diffusion model, the carbonation depth is a parabolic (square root) function of carbonation time, and can generally be expressed as:

(18) Xc = Ac t1/2


19

where constant Ac is closely related to the concrete properties, particularly the permeability, amounts of calcium hydroxide and moisture in the concrete, and the concentration of CO2 in the environment. Theoretically this function may be less accurate than those derived from other modified models which take more realistic factors into account. However, its simplicity and capability of fitting field results has made this equation overwhelmingly popular as a base for carbonation prediction. In research, in spite of the arguments on how to archive this simple equation, the general conclusion that there existed a square root relationship between the depth of carbonation and the carbonation time has been supported by various investigators [Smolczyk (1968), Parrott (1968), Goodgrake (1978), Tuutti (1982), Richardsson (1988), Papadakis et al (1991a,1991b)].

4.3.2 pH threshold for corrosion

The carbonation degree could be indicated by various parameters, including the ratio of CaCO3 (carbonation product) over calcium containing components of cement matrix; the ratio of bound CO2 over maximum capacity to bind CO2, etc [Power (1962),]. However, as far as corrosion of reinforcement is concerned, the parameter of principal interest would be the pH value of the pore solution, as this parameter indicates the corrosivity of the concrete and is closely related to the stability of reinforcement in the concrete. The higher the CO2 concentration in the concrete, the higher the consumption of OH-, and the lower pH value of the concrete.

If carbonation is governed by the diffusion of CO2 in concrete, and the other carbonation reactions can be approximately regarded as steady or meta-steady processes, then an inverse proportional relationship could easily be obtained between the concentration of CO2 and concentration of OH- in concrete. In fact, experiments have demonstrated a clear decrease in the pH level as the carbonation degree (characterised by CaCO3/Ca(OH)2 ratio) increases (Figure 5) [Ohgishi et al (1983), Parrott (1987)].


20

Figure 5. relationship between pH level and CaCO3/Ca(OH)2 ratio determined by X-ray in a concrete wall [Ohgishi et al (1983), Parrott (1987)]

Since the concentration of CO2, as well as the carbonation degree, decreases with the depth of concrete (Figure 2), the typical pH profile in concrete would tend to increase from the concrete surface to the interior (Figure 6) [Forrester (1976), Broomfield (1997)].

Figure 6. Typical pH depth profile [Broomfield (1997)]


21

As shown in Figure 6 by Broomfield (1997), the threshold of pH for initiation of corrosion of reinforcement is about 11. In fact, some degree of carbonation would not necessarily cause corrosion of reinforcement. Hence, the carbonation depth (Xc) described by equation (18) is not closely related to the depth where corrosion of reinforcement could occur. In this sense, the carbonation depth Xc characterising the real carbonation extent cannot be used for accurate prediction of carbonation induced corrosion of reinforcement.

The reasonable depth corresponding to the initiation of corrosion of reinforcement should be the depth where the pH value of the pore solution is lower than the pH threshold. This depth, XpH, should have a corresponding concentration of CO2 (CpH), which is a particular point on the CO2 concentration depth profile (Figure 2), and can also be formulated by:

(19)

where ApH is still a constant.

The depth XpH as a function of carbonation time corresponds to the position where corrosion of reinforcement could occur. In other words, if the depth of pH threshold (XpH) reaches the reinforcement in concrete, then the reinforcement could be corroded. Therefore, from equation (19), when the corrosion of reinforcement will take place can be predicted, provided that current depth of pH threshold and the constant ApH involved in equation (19) are known.

4.4 Prediction procedures

In order to predict the carbonation progress, the current carbonation situation should be determined, then a reasonable mathematical model should be selected, and finally the necessary parameters required should be measured, estimated or calculated.

4.4.1 Determination of extent of carbonation

Normally, concrete samples should be taken from structures for the purpose of the determination of the extent of carbonation (either in the field directly or in the laboratory).

A number of methods are available for either qualitative or quantitative measurement of carbonation, such as X-ray diffraction [Richardsson (1988)], infra-red absorption spectroscopy [Slegers et al (1976)], thermal analysis [Kroone et al (1959)], mineralogical analysis [Meyer (1969)], and chemical analysis [Hamada (1968), Tuutti (1979), Litvan et al (1986), Kondo et al (1968), Conway (1957)].

XpH = ApH t1/2


22

In practice, carbonation of a concrete specimen is determined simply by means of spraying it with phenolphthalein, a pH indicator which is pink at pH values greater than 9.0-9.5 and colourless at pH values below 9.0. This is the most popular method for field testing. As far as corrosion of reinforcement is concerned, it demonstrates the extent of the pH drop in concrete due to carbonation, which is directly responsible for the corrosion damage of reinforcement in concrete.

The phenolphthalein indicator method of monitoring the depth of carbonation has been recommended by RILEM (1984). The indicator is prepared as a solution of 1% phenolphthalein in 70% ethyl alcohol. The samples should be broken rather than sawn to open fresh surfaces for application of the indicator. A solution of 3% phenolphalein and 95% denaturised ethyl alcohol is also suggested in the Swedish standard SS13 72 42. In fact, various researchers have used different types of acid/base indicators and different procedures of using phenolphthalein [Meyer (1969), Hobbs (1988)]. For example, the concentration of the phenolphthalein could vary from 1 % to 3% and that of the ethyl alcohol from 95% to 30%; other indicator types that have been tried include thymolphthalein and Alizarin R Yellow [Meyer (1969)].

The phenolphthalein indicator method of monitoring the depth of carbonation has proven convenient and yields reproducible results. The main limitation of the method is that it only indicates the depth at which the pH level is below 9.0-9.5. This does not necessarily correspond to either carbonation depth or pH threshold depth. In other words, the depth of colour change of the specimen (Xi) is different from the carbonation depth (Xc) and the pH threshold depth (XpH) (Figure 6). Therefore, it is generally concluded that the phenolphthalein indicator provides an approximate and incomplete picture of carbonation [Parrott (1987)].

If Xi is regarded as Xc or XpH, then a few mm error in the predicted carbonation depth and corrosion depth could occur, which could correspond to a few years of error in the predicted service life. Nagataki et al (1986) found that initiation of corrosion of reinforcement occurred earlier than the carbonation front, determined by the phenolphthalein indicator, reached the steel.

4.4.2 Selection of prediction models

In most cases, equation (18) or (19) is sufficiently reliable to model carbonation progress, based on which the initiation of carbonation induced corrosion of reinforcement can reasonably be predicted.

However, in some cases, the measured results significantly differ from the prediction of equation (18) or (19), for which the general and simple diffusion models appear to be unsuitable for service life prediction. In these situations, the theoretically modified models and/or the empirically modified equations should be considered.

It is relatively easy to use the empirically modified equation (17) to fit practical results. However, the meanings of the parameters involved need to be carefully analysed, as they lack theoretical foundation.

On the other hand, the theoretically modified models could more realistically describe the actual carbonation process, but their complicated solutions (sometime even no analytical solutions), could be meaningless to practical service life prediction.


23

4.4.3 Obtaining model parameters

To predict service life according to certain models, the parameters involved in the models should be known. There are several basic methods to obtain the parameters, including field testing and laboratory analysis, simple measurement and artificial acceleration. The selection of these methods depends on the models chosen for prediction.

If equation (18) or (19) is used, then the simplest way to obtain parameter Ac or ApH should be the phenolphthalein spraying method. As mentioned earlier, even though Xi is unequal to Xc and XpH, they follow the same form of equation. For a simple and approximate prediction, phenolphthalein indicator can be used to estimate XpH with acceptable errors. For example, based on equation (19), the relevant parameter ApH can be obtained as follows:

First, the carbonation time t is easily known at that moment, provided that carbonation started right after the construction of the structure. Then use the measured Xi as XpH and t to calculate ApH according to ApH = Xi/t1/2. The most attractive advantage of this method is its easy operation and suitability for field use. However, the accuracy of the parameter relies on one measurement, so the reliability of the calculated parameter could not be high, and consequently the prediction based on the parameter has low credibility. Measurements at different times are recommended, even though this would make the prediction more time consuming. Once ApH is known, determine how long it would take the carbonation depth to be equal to the depth of reinforcing steel in concrete. This would indicate the time for the initiation of corrosion.

If empirically modified model (17) is used for prediction, then the simple phenolphthalein method can still be used in the field. However, more than three different times of measurements are essential, and the time intervals between the different measurements should be specially selected to simplify the calculation of parameters A, B and n. Therefore, it is more time consuming, but still very simple and flexible and is particularly suitable for field use.

If the prediction is based on the general diffusion model (equation (11)), then parameters Cs,CO2 and De,CO2 need to be estimated. Cs,CO2 could be directly measured in the field, i.e., the atmospheric CO2 concentration, and De,CO2 can be measured by specially designed experiments in the laboratory. Another way to obtain these parameters is to measure the carbonation degree (or concentration of CO2) depth profile, through which the above parameters can also be calculated using equation (11). The methods that can be used to obtain the depth profile have been mentioned earlier in section 4.4.1.

If theoretically modified models are selected, then more parameters need to be estimated. The commonly used methods for determining De,CO2, Cs,CO2 and CCO2 depth profile would still be similar to those used to obtain the parameters for equation (11). Other parameters involved may need special measurement. Usually, these models have more complicated equations and solutions. To obtain relevant parameters based on these models, numerical solutions based on computation techniques could be preferable.


24

5. Initiation of chloride induced corrosion

The ingress and accumulation of chloride into the cover concrete is the first stage of chloride induced corrosion of reinforced concrete. Browne (1982) assumed that the corrosion-free life of a structure was the time for chloride ions to reach a critical concentration at the surface of reinforcement. Chloride ingress is more complicated than the carbonation process. It is less uniform across the cover concrete, and there is no such clear chloride front as in the case of carbonation. The chloride-induced corrosion is relatively fast and localised, and difficult to remedy after initiation [Blankvoll (1997)]. Corrosion of reinforcement is highly dependent on the process of ingress of chloride ions into concrete and transportation to the reinforcement steel. Understanding of these process is important in dealing with the corrosion problem.

5.1 Ingress processes and mechanisms

Chloride ions originate from different sources, such as 1) deliberate addition of chloride salts to concrete as accelerators; 2) use of water containing Cl-; 3) contaminated aggregates; 4) sea salt spray and direct sea water wetting; 5) deicing salts; and 6) use of chemicals. Etc.

Normally, chloride ions exist in concrete in two forms: 1) dissolved in the pore solution as free chloride; and 2) adsorbed on cement gel or combined with hydrated cement phases and aggregates as bound chloride. Only free chloride can accelerate the corrosion of steel in concrete. The bound chloride is inert to steel before it is dissolved into solution and becomes free chloride. Typically about 40~50% of the total chloride in concrete is bound [Gaynor (1985)]. Dhir et al (1990) estimated that the ratio between soluble and insoluble chloride in concrete was roughly 3 to 1. Stoltzner et al (1997) found that the ratio of free to total chloride contents in concrete with low-alkali, sulfate-resistant cement was about 50~70%, and for portland cement concrete 35~60%.

5.1.1 Ingress and transport of chloride in concrete

Ingress and transport always refers to the free chloride ions. After the free chloride ions are bound (adsorbed or chemically reacted), they would not travel in concrete until they become free (desorbed or dissolved) under certain conditions.

Chloride can travel in concrete and reach the reinforcing steel through diffusion, capillary movement or electrical migration, etc. Chloride transport in concrete can be greatly affected by mechanisms other than diffusion. Mechanisms such as hydroxide leaching, osmotic pressure, hydraulic flow, suction and filtering [Volkwein (1993)], and other membrane effects may all affect the transport of chloride through the concrete pores.


25

The penetration of chloride into a few centimeters of the outer cover concrete is initially dependent upon capillary suction, but the ingress of chloride ion into a greater depth would mainly be governed by long term diffusion [Bamforth et al (1990), Bamforth et al (1994)]. On a dry surface the uptake of chloride ion is mainly due to absorption; the chloride containing solution is absorbed into empty micro-cracks and pore spaces, and then penetrates further by capillary suction [Goto (1981a)]. If the surface is wet, the initial entry is likely to be by permeation or diffusion.

In a field concrete structure the ingress of chloride is very complicated and might be governed by a combination of several mechanisms. Figure 7 is a schematic illustration of some possible transport processes in a sea wall [Concrete Society Discussion Document(1996)]. Because of the combined contributions of different transport mechanisms in the sea wall, the deepest penetration of Cl- was found at about 1~2 metres above sea level, and the highest Cl- concentration was detected at the surface layer in the wall about 8 metres above the sea level.

Figure 7. Schematic diagram of the transport process of chloride in a sea wall [Concrete Society Discussion Document (1996)]


26

5.1.2 Binding of chloride in concrete

Binding of chloride refers to the adsorption of free chloride ions by cement gel and/or their chemical reactions with hydrated cement. When free chloride ions from the environment penetrate into concrete, some can be captured by the hydrated products through physical adsorption (physical binding) or chemical adsorption or reactions (chemical binding). The huge surface area of hydrate gel supplies plenty of active sites for the physical binding, while the chemical binding could be realised through reaction with the aluminate phases and formation of Friedels salt.

Even though detailed mechanisms for the binding of chloride in concrete are still unclear, it is generally believed that there is an equilibrium between the adsorption of free chloride from pore solution, and the desorption of bound chloride from cement gel. Some researchers [Tuutti (1982a), Arya et al (1990a), Fishcher et al (1984)] have assumed that the equilibrium relationship was only a simple linear adsorption isotherm. However, it was also suggested [Dhir et al (1990)] that the relationship between bound chloride and free chloride was much more complicated, and could be non-linear [Blunk et al (1986), Byfors (1990), Sandberg et al (1993a), Akita et al (1995)]. Pereira et al (1984) suggested a Langmuir isotherm to describe the chloride binding behaviour. However, the Langmuir isotherm equation could only give a good expression for the chloride binding behaviour at low concentration. In order to fit the experimental data at intermediate concentration ranges, a Freundlich adsorption isotherm [Tang (1993)] and a modified BET [Xu (1990)] model were proposed.

The relationship between free chloride and bound chloride is affected by binder type, degree of hydration, amount of pore solution, and other ions in the pore solution. Many researchers [Arya et al (1990), Tritthart (1989), Tritthart (1989a), Page et al (1986a)] have proposed a correlation between the tricalcium aluminate (C3A) content and the capacity of binding chloride ions through the formation of insoluble calcium chloroaluminates. Higher C3A contents bind more chloride ions, resulting in lower chloride ion level in the pore solution. Tang et al (1992) reported that the total amount of alumina and iron oxide in cement determined the chemical binding capacity; fly ash/cement binder contained higher amounts of alumina and iron oxide, so had a higher chemical binding capacity; slag cement formed finer hydrated products, and had higher physical binding capacity too. This is in addition to their beneficial effects on concrete microstructure and permeability.

The hydroxide concentration in pore solution has a significant influence on chloride binding [Tuutti (1982), Tritthart (1989a), Byfors (1990), Page et al (1991)]. The higher the hydroxide concentration, the less chloride will be found in the pore solution, probably as a result of change balance.

Temperature can also alter the chloride binding capacity. The amount of bound chloride decreased as temperature increased [Larsson (1995)]. Both physical and chemical desorption reaction tend to increase at higher temperature, decreasing the chloride binding capacity. This could also be because hydrated cement is more crystalline at higher temperature, with reduced adsorption capacity.


27

Some other factors such as curing temperature, curing age, original alkalinity also affect the chloride binding capacity of concrete [Arya et al (1995), Byfors et al (1986)]. It has been suggested that the presence of superplasticiser in concrete could lower the chloride binding capacity [Haque et al (1995)]. Larsen (1997) found that the chloride uptake and the pore solution composition in concrete were affected by wetting/drying and temperature, but the effects were influenced by chloride concentration. Carbonation strongly decreased the chloride uptake and reduced the chloride concentration of concrete. Page et al (1991) pointed out that cement hydrates could bind a substantial portion of chloride in an insoluble form below a total chloride content of 1%, and that beyond this point the binding capacity is largely exhausted.

The concentration of sulfate ions has also been reported to significantly influence the chloride binding capacity of a given binder [Yonezawa (1988), Tritthart (1989a), Byfors (1990), Sandberg et al (1993)]. Xu (1997) reported that calcium sulphate and sodium sulphate had different effects on chloride binding and pore solution chemistry; at the same sulphate content, cement pastes containing calcium sulphate had a higher chloride binding capacity than those containing sodium sulphate; this might be due to their different effects on OH- ion concentration in the pore solution; sodium sulphate increased the alkalinity of pore solution whereas calcium sulphate decreased it; so sodium sulphate had little effect on the ratio of Cl-/OH- while calcium sulphate significantly increased the ratio.

5.2 Mathematical models

A number of models have been put forward to describe the ingress and transport of chloride [Helffereich et al (1970), Frantz et al (1976), Crank (1979)] in concrete. However, the basis for those models is still the diffusion equation, based on which some other mechanisms and influencing factors are taken into consideration.

5.2.1 Simple diffusion model

Provided that the following assumptions hold:

I) Diffusion of chloride is the principal mechanism dominating the chloride transport process in concrete, no other mechanisms are taken into account.

II) The concrete matrix through which the diffusion occurs is uniform in microstructure or properties;

III) The microstructure and properties of the concrete do not change significantly with time; and

IV) The microstructure and properties of the concrete do not change significantly with the concentration of the diffusing chloride.

V) The concentration (Cs,Cl) of chloride on the concrete surface is constant;

VI) The initial concentration (CI,Cl) of chloride throughout the concrete is uniform,


28

then the general expression for the diffusion of Chloride in concrete can be expressed by:

(20)

where CCl is concentration of free chloride in concrete, and DCl is the diffusion coefficient of free chloride. So the concentration of chloride at depth x and at time t can be expressed as:

(21)

where Cs,Cl is concentration of the free chloride in the surface layer of cover concrete; Ci,Cl is the background concentration of the free chloride (which is equal to the concentration of free chloride in the concrete interior, unaffected by the ingress of chloride).

The above solution has a typical concentration distribution of free chloride as illustrated in Figure 8. Correspondingly, the change of free chloride concentration with time at a given depth in concrete can be schematically presented by Figure 9. They are quite similar to those of the carbonation profile and carbon-dioxide change with time in concrete (Figure 2 and Figure 3).

Figure 8. Distribution of the concentration of free chloride ions in concrete at a given time

2

2

xC

Dt

C ClCl

Cl

=

CCl = Cs,Cl - (Cs,Cl Ci,Cl) erf [x/(4DCl t)1/2]

0.00E+00

1.20E+00

0 60x, depth from concrete surface

C Cl,

con

cent

ratio

n of

Cl-

at ti

me

t=t x Cs,Cl

Ci,Cl

xt


29

Figure 9. Change of the concentration of free chloride ions with time at a give depth in concrete

Based on equation (21), the ingress of chloride ions in concrete with time can also be formulated by:

(22)

where XCl is the depth of a selected concentration of chloride ions, A0,Cl is a constant which is equal to x0 /t01/2, and xo and t0 are the initial position of the selected chloride concentration and the corresponding initial time; as the chloride ions always ingress deeper into concrete with time, so t>t0, X>x0. Equation (22) is also similar to equation (12), and can give a similar progress diagram (Figure 10).

Figure 10. Ingress of a given chloride concentration in concrete with time

XCl = A0,Cl t1/2

0

1.2

0 3000000000t, chloride ingress time

C Cl,

con

cent

ratio

n of

Cl- a

t dep

th x

=xt

Cs,Cl

Ci,Cl

tx

0

18

0 1500000t, chloride ingress time

XCl ,

dept

h of

a s

elec

ted

conc

entra

tion

(C0,

Cl )

of C

l-

t0

x0


30

Equations (20), (21) and (22) only describe the one dimensional diffusion process of chloride in concrete. The diffusion equation and the solution for the two-dimension model are much more complicated [Berke et al(1997)].

Theoretically, the above equations can only describe the diffusion of free chloride in concrete, rather than the distribution of bound chloride, as free chloride ions are travelling through the concrete [Sagues et al (1996)]. To deal with the total chloride distribution in concrete, the equation should be further modified and the meanings of some parameters involved could need redefining, leading to the following diffusion-binding model.

5.2.2 Diffusion-binding model

In the above simple diffusion model, the ingress and transport of chloride in concrete is ascribed to the diffusion of free chloride alone. However, in reality the binding of chloride in concrete is unavoidable, which would consume the free chloride ions during its diffusion. So, the diffusion equation for the free chloride should be expressed as:

(23)

where fCl is a function dependent on the concentration of free chloride ions dependent function, representing the rate for the binding and consumption of free chloride ions.

This equation can be converted into:

(24)

where, De,Cl is the effective diffusion coefficient of the free chloride ions in concrete, which has combined the binding effects into the diffusion process:

(25)

In the case of the binding rate being assumed to be linearly dependent on the concentration of free chloride ions, i.e., kCl=constant=fCl/CCl, the effective diffusion coefficient would become a constant:

(26)

ClCl

ClCl f

xC

Dt

C

=

2

2

2

2

, xCD

tC Cl

CleCl

=

Cl

Cl

ClCle

Cf

DD

+=1

,

consta1,

=+

=Cl

ClCle k

DD


31

Under this condition, the diffusion-binding model (24) has the same diffusion equation format as the simple diffusion model, except for the different physical meanings of their diffusion coefficients.

In some cases, if a linear relationship is assumed between the concentrations of bound (Cb) and free chloride ions:

(27)

then the concentration (Ct,Cl) of total chloride ions in concrete would be:

(28)

and equation (24) could be transformed into:

(29)

This means that the total chloride distribution in concrete could also obey the diffusion equation, provided that linear equilibrium is established between the bonded and free chloride ions [Sagues et al (1996), Fishcher et al (1984)]. Therefore, the diffusion equation (with an effective diffusion coefficient) sometimes can be directly used to describe the total chloride profile in concrete, as demonstrated by Nilsson (1992), Tang et al (1995a), and Xu et al (1995a).

As it is more convenient to measure a total chloride profile, rather than a free chloride profile, Eq (29) is very useful in practice. Therefore, equation (29) is more practical, as long as its precondition of linear relation between bound and free chloride can hold.

It should be stressed that equation (24) has the same solutions as equations (21), and (22) except that the DCl is replaced by De,Cl. However, due to the difference between the values of De,Cl and DCl, the depth profiles of free chloride and total chloride could be different. Also, the biding effect can change the chloride profile in concrete. For example, if the binding capacity is high, i.e. De,Cl is small, then the profile would be steep.

Cb,Cl = CCl + ; and are constants

Ct,Cl = (1+) CCl +

2,

2

,

,

xC

Dt

C CltCle

Clt

=


32

5.2.3 Multi-transport-mechanism models

The above models about ingress and transport of chloride are limited to a stationary pore solution system. In reality, concrete structures may be exposed in different environments with a gradient of water pressure or vapour pressure. Therefore, the ingress and transport of chloride in concrete could occur by mechanisms other than diffusion, such as hydraulic flow of chloride solution due to a gradient of water pressure [Edwardsen (1995)], capillary suction of chloride-bearing solution in an unsaturated pore system due to the surface tension of pore walls [Collepardi et al (1989), Akita et al (1995) ], convection of chloride solution due to wick action [Buenfeld et al (1995)], moisture flow and evaporation due to a gradient of vapour pressure [Tuutti (1982), Ohama et al (1995)], etc. However, all these mechanisms operating in the field are too complicated to be formulated by mathematical equations.

It is difficult or even impossible to quantify the influences of these combined processes on chloride ingress and transport [Nilsson et al (1996)].

In addition to the mechanisms, migration under electric field may be another important process for free chloride ions that carry negative charges in the pore solution. The migration effect is particularly significant for the reinforced concrete structures that are subjected to stray current interference, galvanic corrosion effect, or are under cathodic protection in the field. Furthermore, the non-uniform distribution of ions in concrete due to the heterogeneity of concrete could build up statistic charge, which generates electric fields in the concrete, and affects the transport of negatively charged chloride ions.

If the migration is combined in the transport model of free chloride ions, then the model can be mathematically expressed as:

(30)

where F is Faraday constant, E electric field strength in concrete, R gas constant, and T absolute temperature.

Equation (30) has an analytical solution [Tang et al (1992a, 1993, 1996a)]:

(31)

where =FE/(RT). This solution gives a steeper chloride profile than the simple diffusion and diffusion-binding models.

It should be stressed that the above solution is theoretically obtained under the condition that De,Cl is a constant independent of t, x, and CCl. In practice, the microstructure of concrete, its chloride binding capacity, the influence of other ions on chloride mobility, etc, can all affect the chloride profile. Therefore, the measured chloride profile may not be as sharp as that predicted by equation (31) [Tang et al (1995)].

)(2

2

, xC

RTFE

xC

Dt

C ClClCle

Cl

=

)]2

()2

([2

,

,

,

,,

tD

tDxerfc

tD

tDxerfce

CC

Cle

Cle

Cle

ClexClsCl

++

=


33

5.2.4 Complicated models

In the laboratory, the above diffusion based models for the ingress and transport of chloride may be considered valid, as diffusion, permeability, and absorption of chloride can be measured under controlled conditions. However, even under strictly controlled conditions, the measured data could still deviate significantly from theoretical predictions due to some unexpected factors not incorporated into the predictive models.

The application of equation (21) in analysing chloride profiles in concretes sampled from structures has been shown to be only partly successful. Swamy et al (1994) summarised the results obtained from more than 1000 sets of data on chloride content in concretes exposed to various marine conditions, including submerge, tidal, splash, atmosphere, etc. They showed that the estimated CS,Cl and De,Cl changed with time, and varied with depth and exposure conditions. Specifically, the Cl- diffusion coefficient of inner concrete (larger than 30 - 50 mm) was found to be quite different from that of the surface concrete. Weyers et al (1994) showed that the increase in chloride content in the concrete surface (0-0.5 in) approached that estimated by the square root of time function, however it was nearly constant after about 5 years. The above indicates that the assumptions based on which the diffusion based models are established are not reasonable in some cases.

For example, in practice, there are at least two basic facts that violate the above assumptions:

1) the surface concentration of chloride is not constant and varies with season and environmental factors (temperature and wetness, etc); and

2) the diffusion coefficient is not constant and varies with age and depth in concrete.

The variable surface concentration of chloride is the first main source of error in the prediction model. The change of environmental temperature and the wetting/drying of cover concrete can accelerate chloride uptake or wash away the accumulated chloride on the concrete surface, making the surface concentration change with time. Sometimes due to some reported condensation effects, the surface concentration of chloride in a saturated concrete can reach a level which is two to four times higher than that of the surrounding saline solution, even though diffusion is still the principal transport process in this case [Nagataki et al (1993)]. For example, the surface chloride concentration may increase in concrete in the tidal and splash zones of bridges and areas where de-icing salt is used in winter and where drying of the surface takes place, whereas rain may cause it to leach out [Saetta et al (1993), Fluge (1997), Andersen et al (1997)]. The variation in CS can also be caused by the chemical reaction of cement paste with the environment, e.g. carbonation and leaching [Larsen (1997)] can reduce the capacity of cement paste to adsorb chloride ions. The diffusion coefficient of chloride can be greatly enhanced by sulfate attack [Jones et al (1994)].

Because of these influences, in most practical cases, the chloride concentration profiles are anomalous in the surface layer [West et al (1985a)].


34

The most common practice to deal with the variation of surface concentration is to discard the first few millimeters of the concrete surface and take the concentration of chloride at about 10 mm depth as a constant pseudo surface concentration [Broomfield (1997)]. It is expected that the concentration of chloride at this depth would be constant. Obviously this is an approximation, and could introduce significant errors.

Establishment of a mathematical relationship between the surface concentration of chloride and time is another attempt to cope with the difficulty arising from the non-constant surface concentration.

Uji et al (1990) reported that the surface concentration of chloride was a function of the square root of time. Such an expression was regarded as the best estimate for surface concentration of chloride in practical application [Uji et al (1990), Purvis et al (1994), Amey et al (1996)]. Lin (1990) proposed another expression for the surface

Date post:	26-Nov-2015
Category:	Documents
Upload:	100liv
View:	51 times
Download:	3 times

life prediction concrete

Documents