insi.51.3.151.pdf

Insight Vol 51 No 3 March 2009 151

GROUND PENETRATING RADAR

Ground penetrating radar (GPR) is a valuable non-

destructive method for detecting steel bars in reinforced

concrete structures. Measuring the diameter of the steel

bars is difficult and few previous experiments have been

successful. We compare the difference of discrete wavelet

transform (DWT) and stationary wavelet transform (SWT)

and make the contour map of SWT detail coefficients, then

find that SWT is an effective method to measure the diameter

of steel bar. We also discuss our choice of the wavelet basis

that best interprets the raw GPR data.

Keywords: Ground penetrating radar (GPR), Concrete, Steel bar,

Diameter, Stationary wavelet transform.

1. Introduction

The safety of reinforced concrete structures greatly depends on

whether the actual position and diameter of steel reinforcement

match the design requirements. Ground penetrating radar (GPR)

is a non-destructive testing technique that uses a radio wave source

to send a pulse of electromagnetic energy into the test medium.

Sensors detect any reflected energy and record it for analysis. A widely used application of GPR has been detecting the location

of steel bars in concrete structures. However, the GPR scan image

itself gives no information on the diameter of the steel bars. Since

both steel bar position and diameter affect the structure’s safety, a

supplemental method is required to determine the diameter. Stolte

and Nick (1994)[1]

proposed an eccentricity migration method

to improve GPR images with hyperbolic response and possibly

determine the diameter of buried pipes from the geometry of a

hyperbola in a GPR section. Nevertheless, the method yielded no

successful results and remains just a possibility. Molyneaux et al

(1995)[2]

attempted to use neural networks to determine the diameter

of steel reinforcement but the results were not successful. They

concluded that their approach failed because they used a solitary

signal at the centre of each bar. As a promising alternative, they propose using an orthogonal antenna orientation to determine both

the size and depth of the bar. Newnham and Goodier (2000)[3]

also

used a neural network approach to measure the size of a reinforcing

bar but they too had difficulty in determining the bar’s diameter. Quek et al described polynomial-based separation algorithms in

radar image processing, which are precursors to analysis that allows

measurement of the diameters, orientations and depths of the bars[4]

.

They also used curvilinear models applied to orthogonal line scans

taken by an inductive sensor and the method allows estimates to be

made with accuracies of ± 1 bar size and ± 10% cover depth when

neither the depth nor the size is available[5]

.

This paper introduces an approach that uses a stationary wavelet

transform to determine the diameters of steel bars. The method also

accurately obtains the horizontal position and depth of the steel

reinforcement and uses the data to produce a 3D image.

2. Data acquisition

A pulseEKKO1000 system provided the GPR data using the reflection method. The system’s antenna had a centre frequency of 1200 MHz, a step size of 0.01 m. Figure 1 shows the location of

the steel bars and scan lines in the 850×245×150 mm reinforced

concrete slab test specimen. Figure 2, a typical GPR image, shows

six hyperbolas, of which hyperbolas 1, 2 and 3 indicate the position

of the steel reinforcement bars.

GPR measurement of the diameter of steel bars

in concrete specimens based on the stationary

wavelet transform

Runtao Zhan and Huicai Xie

Runtao Zhan is in the Department of Civil Engineering, Xinyang Normal

University. His research interests include non-destructive evaluation and

test techniques application in civil engineering.

Professor Huicai Xie is in the Department of Civil Engineering, Shantou

University. Email: [email protected]

Corresponding author: Runtao Zhan, Department of Civil Engineering,

Xinyang Normal University, Xinyang, Henan Province, 464000, China. Tel:

+00 (0)376 6391770; Email: [email protected]

Figure 1. Photo of the reinforced concrete slab specimen

Figure 2. GPR image of scan line

Submitted 22 Jun 2008 Accepted 15 Dec 2008

DOI: 10.1784/insi.2009.51.3.151

3. Analysis of the GPR scan image

3.1 Limitations of the GPR scan imageFigure 2 clearly illustrates the limitations of the GPR scan image.

First, the scan image cannot indicate the diameters of the steel bars.

Second, the scan image sometimes shows two or more hyperbolas

stacked on top of each other. If the top hyperbolas (hyperbolas 1,

2, 3 of Figure 2) indicate the position of the steel bars, it is difficult to explain what the lower hyperbolas (hyperbolas 4, 5, 6 of Figure

2) represent.

3.2 Velocity of the GPR waveThe velocity of the radar wave plays an important role in the

proposed method of measuring the diameter of the steel bars.

Placing two small concrete cubes below the specimen creates a

clear interface between the concrete block and the surrounding air

on the GPR image, as shown in Figure 2. This interface provides

a benchmark used in obtaining the accurate velocity of the radar

wave.

According to Figures 2 and 3, the reflection time from the top of the concrete slab is 1.6 ns and that from the bottom of the

concrete slab is 4.6 ns. Since the height of the concrete slab is 0.15

m, according to the formula:

v = 2 ! d / t ...................................... (1)

the radar wave’s velocity is 0.15/(4.6-1.6)×2 = 0.1 m/ns. Additional trials yield reflection times of 1.6 ns or 1.7 ns from the top of the slab and 4.6 ns or 4.7 ns from the bottom. These times produce similar velocities, so the calculated velocity of 0.1 m/ns is accurate.

4. DWT and SWT

If a signal, such as the GPR wave, has a time varying frequency, it

is non-stationary. To know the detailed information at a certain time

in a GPR wave, it is necessary to find a suitable signal processing method to handle the non-stationary signal. The wavelet transform is

a superior approach to other time-frequency analysis tools because its

time scale width of the window can be stretched to match the original

signal[6][7]

. This makes it particularly useful for non-stationary signal

analysis, such as noises and transients. For a discrete signal, a fast

algorithm of discrete wavelet transform (DWT) is multi-resolution

analysis, which is a non-redundant decomposition[8]

. However, the

non-redundant decomposition introduces an artifact-shift variance.

The artifacts will affect the precise alignments between the features

of the signal. Misalignments between wavelet coefficients lead to errors in locating the rebar’s position and, consequently, measuring

the rebar’s diameter. Several people have independently discovered

the stationary wavelet transform for different purposes[9-13]. Each

inventor gave the transform a different name, including the shift/

translation invariant wavelet transform, the undecimated discrete

wavelet transform, and the redundant wavelet transform. As these various names illustrate, the key aspects of the SWT is that

it is redundant, shift invariant and a denser approximation to the

continuous wavelet transform than that of the orthonormal discrete

wavelet transform (DWT). Lang et al provide a discussion of the

algorithm and its history[10]

.

The SWT method can be described as follows. At each level, when the high-pass and low-pass filters are applied to the data, the

two new sequences have the same length as the original sequences.

To do this, the original data is not decimated. However, the filters at

each level are modified by padding them out with zeros.

Supposing a function f(x) is projected at each step j on the subset

Vj(!! V

1! V

0) , this projection is defined by the scalar product

of cj,k

of f(x) with the scaling function φ(x) which is dilated and

translated:

cj ,k = f (x),! j ,k (x) = f (x)" ! j ,k (x)dx ............... (2)

! j ,k (x) = 2" j!(2" j

x " k) ........................ (3)

where φ(x) is a real scaling function, which is a low-pass filter. cj,k

is also called a discrete approximation at the resolution 2 j.

If ϕ(x) is a real wavelet function, the wavelet coefficients are

obtained by:

! j ,k = f (x),2" j#(2" j

x " k) .................... (4)

ωj,k

is called the discrete detail signal at the resolution 2 j.

The scaling function φ(x) and wavelet function ϕ(x) has the

following property:

1

2!(x

2) = h(n)!(x " n)

n

# ...................... (5a)

1

2!(x

2) = g(n)"(x # n)

n

$ ...................... (5b)

cj+1,k

and ωj+1,k

can be obtained by direct computation from cj,k

:

cj+1,k = h(n ! 2k)cj ,nn

" ....................... (6a)

! j+1,k = g(n " 2k)n

# cj ,n ........................ (6b)

Equations (6a) and (6b) are the multi-resolution algorithm of the traditional DWT. In this transform, a downsampling algorithm

is used to perform the transformation. That is, one point out of

two is kept during transformation. Therefore, the whole length of

the function f(x) will reduce by half after the transformation. This

process continues until the length of the function becomes one.

However, for stationary or redundant transform, instead of

downsampling, an upsampling procedure is carried out before

performing filter convolution at each scale. The distance between

samples increasing by a factor of two from scale to the next cj+1,k

is obtained by:

cj+1,k = h(l)l

! cj ,k+2 j l ........................... (7a)

and the discrete wavelet coefficients:

! j+1,k = g(l)l

" cj ,k+2 j l .......................... (7b)

The redundancy of this transform facilitates the identification of

salient features in a signal.

5. Measuring of the steel bars

There are many different types of wavelet families. Section 6 will

discuss how to choose the wavelet basis that best interprets the

raw GPR data. The desire to measure the diameter of steel bars

dictated choosing the Sym3 wavelet. Symlet wavelets are the

Figure 3. GPR wave at scan point 14

152 Insight Vol 51 No 3 March 2009


compactly supported wavelets with the least degree of asymmetry

and the highest number of vanishing moments for a given support

width. The associated scaling filters are near linear-phase filters. Figure 4(a)-(b) shows the wavelet and scale functions of the Sym3

wavelet.

Figure 5 is DWT detail coefficients (DWT cD1~5) and SWT

detail coefficients (SWT cD1~5) of GPR wave. As Figure 5 shows, the number of DWT coefficients decreases as the scale increases

while the number of SWT coefficients remains the same for every

signal scale. After normalising five scales of SWT detail coefficients to create the contour map of normalised SWT cD5 coefficients

shown in Figure 6, the image of the three steel bars becomes clear.

5.1 Measuring the diameter of the steel barsIn Figure 6, the clear image of the three steel bars is a result of

the ability of the higher scales to show slowly changing details.

The boundary between positive and negative cD5 coefficients clearly demarcates the bottom of the concrete slab. The position

of the steel bar in Figure 6 is unique, unlike that of Figure 2 where

one steel bar caused two hyperbolas that tend to confuse those

inexperienced with GPR evaluation. Unfortunately, Figure 9 does

not clearly show the positions of either zero time or the top of the

concrete slab.

Knowing the velocity of the GPR wave through the concrete

slab allows for the calculation of the distance using formula (1).

Therefore, 0.5 ns represents a distance of 0.1×0.5/2 = 0.025 m =

25 mm.

The next step is to load the images into AutoCAD 2004 and label the correlation size. There are two methods to determine the

diameter of the rebar:

1) Measure the maximum diameter of the circles contained in the

rebar pattern.

2) Measure the maximum distance of the rebar pattern in the time

dimension.

We measure the distance of 0.5 ns and get 117, then measure the maximum diameter of the circles contained in the rebar pattern of

Rebar 1 and get 60. When we measure the maximum distance of

the Rebar 1 pattern in the time dimension, we get 93.

Method 1: 25×60/117 = 12.8 mmMethod 2: 25×93/117 = 19.9 mmAverage: (12.8+19.9)/2 = 16.4 mm ≈ 16 mm

Similar calculations yield the diameter of Rebar 2 and Rebar 3.

5.2 Measuring the depth and horizontal position of the rebarThe distance between the top of the concrete slab and the centre of

the circles in Figure 6 is measured directly. The depth of Rebar 1 is:

25×242/117 = 52 mm. The system’s antenna has a step size of 0.01m and thus the distance from scan point 1 to scan point 68 is 680 mm.

According to Figure 1 and Figure 6, we measure the distance of 10 scan points from scan point 45 to scan point 55 and get 172, and the distance from the centre of Rebar 1 to the specimen’s side is:

215/172×100+80 = 205 mm. Similar calculations yield the depth and horizontal position of Rebar 2 and Rebar 3.

Using Autocad objectARX, post-processing programs are being developed. By inputting the steel bar and concrete specimen

parameters as shown Table 1 into the programs, the 3D image

shown in Figure 7 is obtained.

Specimen 2 was tested in order to justify the proposed methods.

Table 2 shows the results for the second specimen.

Figure 4. (a) Wavelet function of Sym3; (b) Scale function of

Sym3

Figure� 5.� Detail� coefficients� of� DWT� and� SWT� of� GPR� wave� at� scan point 14

Figure� 6.� Contour� map� of� normalised� SWT� cD5� coefficients

Figure 7. 3D image of specimen 1

Table 1. Parameters of steel bars of specimen 1 (Unit: mm)

Rebar 1 Rebar 2 Rebar 3

Diameter

(Method 1)

12.8 9.8 21.4

Diameter

(Method 2)

19.9 14.1 26.0

Diameter

(Average)16 12 24

Actual diameter 18 10 22

Depth 52 53 45

Actual depth 51 53 47

Distance 205 224 221 199

Actual distance 209 224 217 200

Table 2. Parameters of steel bars of specimen 2 (Unit: mm)

Rebar 1 Rebar 2

Diameter 10 18

Actual diameter 14 20

Depth 54 49

Actual depth 55 51

Distance 216 224

Actual distance 215 225

Distance 216 224 119

Actual distance 215 225 120

6. Choosing the wavelet basis

Choosing the wavelet basis is vitally important in determining

the diameter of the steel bars. There are many different wavelet

families and each has different properties. Three main properties

distinguish the wavelet families. Table 3 lists five main wavelet bases and their properties. Figure 8(a)-(c), Figure 9(a)-(c) and

Figure 10(a)-(c) show the SWT cD5 coefficients contour map for the wavelet families.

Table 3. Five wavelet bases and their properties

property symN dbN biorNr.Nd coifN meyer

Compact

support

l l l l

Orthogonal l l l l

Symmetry near l l

According the Figures: a) The support length of ϕ(x) is the speed of convergence to

zero of the wavelet functions that quantify both the time and

frequency localisations. Creating three maps of specimen 1

using symN wavelets that have a 2N-1 support width allowed

for the comparison of the effect of the compact length of the

wavelet bases on the method’s ability to measure rebar diameter.

As Figure 8(a)-(c) shows, the shorter the support width of the wavelet bases is, the closer the steel pattern is to actual size.

This is a result of the shorter width support giving more precise

time localisations.

b) Orthogonality of ϕ(x)

The symN, dbN, and coif1 wavelet functions are all orthogonal

wavelets and their coefficient maps clearly image the steel bar patterns, as seen in Figure 8(a)-(c), Figure 9(a)-(c) and Figure

10(c). However, as Figure 10(a) shows, the bior1.1 wavelet

function is not orthogonal and thus the steel bar pattern does not

appear on the image even though bior1.1 has a short 2-width

support. Therefore, the orthogonality of the wavelet basis is

important in the measurement of steel bars using GPR.

c) The symmetry of ϕ(x)

Except for the Haar basis, all real orthonormal wavelet bases with compact support are asymmetric

[5]. Symmetry is useful in

avoiding dephasing in image processing. Both the bior1.1 and

meyer wavelet functions are symmetric. Figure 10(a), made

using bior1.1 cD5 coefficients, does not clearly image the steel pattern. Likewise, Figure 10(b), made using meyer cD5

coefficients, is not sufficiently clear to determine the diameter of the steel bars, despite its orthogonality, because the Meyer

function’s support width is infinite. Therefore, the symmetry of wavelets is less important in measuring the diameters of steel

bars than are the other two main properties.

In summary, when measuring the diameter of steel bars, having

a short support width and being orthogonal are the most important

properties for a wavelet basis.

7. Conclusions

n The SWT wavelet transform is useful in measuring precisely

the diameter of steel bars in a concrete structure. Knowing the

velocity of the GPR wave is vitally important in measuring the

diameters and positions of the steel bars. The SWT coefficients contour map clearly images the steel reinforcement pattern,

thereby overcoming the drawback of GPR images that one steel

bar may cause two or more hyperbolas.

n Having a short support width and being orthogonal are the most

important properties to consider when choosing the wavelet

basis.

Acknowledgements

The authors wish to acknowledge the financial support of the Natural Science Foundation of the Guangdong province of China,

No. 032023, and the Science Foundation of Xinyang Normal University for young teacher, No. 20070211.

Figure� 8(a)-(c).� Contour� map� of� normalised� SWT� cD5� coefficients� of symN

Figure� 9(a)-(c).� Contour� map� of� normalised� SWT� cD5� coefficients� of dbN

Figure 10(a)-(c). Contour map of normalised SWT cD5

coefficients� of� bior1.1,� meyer,� coif1

154 Insight Vol 51 No 3 March 2009


References

1. C Stolte and K P Nick, ‘A method to improve the imaging of pipes in radar reflection data’, Proc 5th International Conference on GPR, Univ. of Waterloo, pp 723-731, 1994.

2. T C K Molyneaux, S G Millard, J H Bungey and J Q Zhou,

‘Radar assessment of structural concrete using neural

networks’, NDT&E International, Vol 28, No 5, pp 281-288, 1995.

3. L Newnham and A Goodier, ‘Using neural networks to interpret sub-surface radar imagery of reinforced concrete’, Proceedings

of SPIE – The International Society for Optical Engineering, Vol 4084, pp 434-440, May 2000.

4. S Quek, P Gaydecki, B Fernandes and G Miller, ‘Multiple

layer separation and visualisation of inductively scanned

images of reinforcing bars in concrete using a polynomial-

based separation algorithm’, NDT&E International, Vol 35, No 4, pp 233-240, 2002.

5. S Quek, P Gaydecki, M A M Zaid, G Miller and B Fernandes, ‘Three-dimensional image rendering of steel reinforcing bars

using Curvilinear models applied to orthogonal line scans

taken by an inductive sensor’, NDT&E International,Vol 36, No 1, pp 7-18, 2003.

6. S Mallat, ‘A wavelet tour of signal processing’, Academic Press, San Diego, 1998.

7. I Daubechies, ‘Ten lecture on wavelets’, Philadelphia, PA: SIAM, 1992.

8. S Mallat, ‘A theory for multiresolution signal decomposition: The wavelet representation’, IEEE Trans. Pattern Anal. Machine Intell, Vol 11, pp 674-693, July 1989.

9. G Beylkin, ‘On the representation of operators in bases of compactly supported wavelets’, SIAM J. Numer. Anal. 29(6):1716-1740, 1992.

10. M Lang, H Guo, J E Odegard, C S Burrus and R O Wells Jr, ‘Nonlinear processing of a shift-invariant DWT for noise

reduction’, SPIE conference on wavelet applications, Vol 2491, Orlando, FL, April 1995, Tech. report CML TR95-03, Rice University, Houston, TX.

11. M J Shensa, ‘The discrete wavelet transform: Wedding the à

trous and Mallat Algorithms’, IEEE Trans. Inform. Theory, 40:2464-2482, 1992.

12. S Mallat, ‘Zero-crossings of a wavelet transform’, IEEE Trans. Inform Theory, 37(4), July 1991.

13. R R Coifman and D L Donoho, ‘Translation invariant

de-noising’, Lecture Notes in Statistics, 103, pp 125-150,

1995.

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1 [CORROSION OF STEEL/BM]

THE CORROSION OF STEEL, AND ITS MONITORING, IN CONCRETE

INTRODUCTION This Guide describes: (a) the circumstances in which steel reinforcement in concrete can corrode, and (b) methods of revealing whether corrosion is occurring and, if so, at what rate.

WHY STEEL IN USED CONCRETE Concrete is a complex material of construction that enables the high compressive strength of natural stone to be used in any configuration. This is accomplished by breaking natural stone to suitable sizes and mixing the aggregates so formed with suitable proportions of water and cement. This mixture can then be moulded into any required shape while still fluid. The water and cement react chemically, forming a “glue” that bonds the pieces of stone aggregate together into a structural member, which becomes rigid and strong in compression when the chemical reaction is completed (i.e. the concrete is “cured”). In tension, however, concrete can be no stronger than the bond between the cured cement and the surfaces of the aggregate. This is generally much lower than the compressive strength of the concrete. Most structures are subjected to loadings that create bending moments, producing both compression and tension stresses within the structure. Since concrete is comparatively weak in tension, arrangements have to be made for the tensile stresses in the structure to be transferred to another material that is strong in tension. Concrete is therefore frequently reinforced, usually with steel, but occasionally with glass fibres or polymer filaments. Steel can be used for such reinforcement in one of two ways. When a system of steel bars or a steel mesh is incorporated in the concrete structure in such a way that the steel can support most of the tensile stresses and leave the immediately surrounding concrete comparatively free of tensile stress, then the complex is known as “reinforced concrete”. When the steel introduced is initially tensioned in such a manner that it applies a compressive stress to the surrounding hardened concrete such that no subsequent loading applied to the structure puts that concrete into tension, then the complex is known as “prestressed concrete”. The steel introduced into concrete can occasionally serve both of these functions.

CONCRETE AS AN ENVIRONMENT FOR STEEL The role of alkalinity

It is well known that if bright steel is left unprotected in the atmosphere a brown oxide rust quickly forms and will continue to grow until a scale flakes from the surface. This corrosion process will continue unless some external means is provided to prevent it. One method is to surround the steel with an alkaline environment having a pH value within the range 9.5 to 13.


Hydrated cement provides such an environment, the normal pH value being 12.6, at which steel is protected in the absence of aggressive anions. At this pH value a passive film forms on the steel that reduces the rate of corrosion to a very low and harmless value. Thus, concrete cover provides chemical as well as physical protection to the steel. However, circumstances do arise in which corrosion of reinforcement occurs. Since rust has a larger volume than the steel from which it is formed, the result can be cracking, rust-staining, or even spalling of the concrete cover. Such occurrences usually arise from loss of alkalinity in the immediate vicinity of the steel or from the presence of excessive quantities of aggressive anions in the concrete (normally chloride), or from a combination of both of these factors. Loss of alkalinity by carbonation

Alkalinity can be lost as a result of: (a) Reaction with acidic gases (such as carbon dioxide) in the atmosphere. The effects of sulphur dioxide are also included in the term “carbonation”. Or – (b) Leaching by water from the surface. In practice both of these factors contribute to the reduction of alkalinity in the concrete. Concrete is permeable and allows the slow ingress of the atmosphere; the acidic gases react with the alkalis (usually calcium, sodium and potassium hydroxides), neutralising them by forming carbonates and sulphates, and at the same time reducing the pH value. If the carbonated front penetrates sufficiently deeply into the concrete to intersect with the concrete reinforcement interface, protection is lost and, since both oxygen and moisture are available, the steel is likely to corrode. The extent of the advance of the carbonation front depends, to a considerable extent, on the porosity and permeability of the concrete and on the conditions of the exposure. For dense concretes, permeability and porosity are related to cement content, water/cement ratio, aggregate grading, degree of compaction, and adequacy of curing. Likewise, the permeability of lightweight concrete is determined mainly by the above factors and, to a lesser extent, by aggregate permeability where lightweight concretes are used. For aerated concretes, permeability is a function of the amount of air entrainment and the type of bubble formation; interconnecting bubbles allow easier ingress of the atmosphere than do discrete bubbles. (Methods of air entrainment for dense concrete should not permit the formation of other than discrete bubbles.) The extent of carbonation is likely to be greater in lightweight concretes than in dense concretes, and the depth of cover should be increased accordingly. Indeed, where carbonation of loss of alkalinity (in, for example, autoclaved aerated concrete) is expected to extend to the steel, additional protection to the reinforcement, or the use of a more corrosion-resistant material such as stainless steel, is necessary. It is normal to accept, in the long term, a degree of carbonation in the concrete according to the above factors of porosity, permeability and degree of exposure. To provide the steel with an effectively permanent protective alkaline environment, the designer therefore ensures that the depth of cover to the reinforcement nearest the surface is sufficiently greater than the depth of carbonation penetration.


Cracks in concrete formed as a result of tensile loading, shrinkage or other factors can also allow the ingress of the atmosphere and provide a zone from which the carbonation front can develop. If the crack penetrates to the steel, protection can be lost. This is especially so under tensile loading, for debonding of steel and concrete occurs to some extent on each side of the crack, thus removing the alkaline environment and so destroying the protection in the vicinity of the debonding. The extent of subsequent corrosion will be determined by a number of factors, including width of crack, loading conditions, degree of exposure and atmospheric pollution. In some circumstances the cracks will be closed by the product of carbonation reactions, ingress of dust or other solid airborne matter, or combinations of both of these influences, so restricting further oxygen and moisture access and minimising further corrosion. Where, however, cracks are not closed in this manner (especially cracks subject to movement resulting from fluctuating load conditions), oxygen and moisture still have access to the unprotected steel surface and corrosion is likely to progress. Effect of chloride in the concrete

The passivity provided by the alkaline conditions can also be destroyed by the presence of chloride ions, even though a high level of alkalinity remains in the concrete. The chloride ion can locally de-passivate the metal and promote active metal dissolution. Chlorides react with the calcium aluminate and calcium aluminoferrite in the concrete to form insoluble calcium chloroaluminates and calcium chloroferrites in which the chloride is bound in non-active form; however, the reaction is never complete and some active soluble chloride always remains in equilibrium in the aqueous phase in the concrete. It is this chloride in solution that is free to promote corrosion of the steel. At low levels of chloride in the aqueous phase, the rate of corrosion is very small, but higher concentration increases the risks of corrosion. Thus the amount of chloride in the concrete and, in turn, the amount of free chloride in the aqueous phase (which is partly a function of cement content and also of the cement type) will influence the risk of corrosion. While the concrete remains in an uncarbonated state the level of free chloride in the aqueous phase remains low (perhaps 10% of the total Cl). However, the influence of severe carbonation is to break down the hydrated cement phases and, in the case of chloroaluminates, the effect is to release chloride. Thus more free chloride is available in carbonated concrete than in uncarbonated materials. The properties of the concrete (controlled by water/cement ratio, cement content, aggregate grading and degree of compaction) have two influences on the effect of chloride in stimulating the corrosion of reinforcement. As the cement content of the concrete increases (for a fixed amount of chloride in the concrete), more chloride reacts to form solid phases, so reducing the amount in solution (and the risk of corrosion), and as the physical properties improve, the extent of carbonation declines, so preventing further liberation of chloride from the solid phase. When corrosion is a hazard

The great majority of reinforced concrete structures are built to guidelines given in British Standard Codes of Practice and are in situations where they given very long maintenance-free lives. There are, however, certain circumstances in which the concrete cannot be expected to give the desired, almost indefinite, protection to the steel reinforcement. These circumstances are:


(a) Where, because of error of construction, the full thickness of concrete cover was not given to the reinforcement.

(b) Where the concrete contains damaging amounts of chloride, either present in high concentration in the materials from which the concrete is made or added deliberately to accelerate setting.

(c) Where the concrete is exposed to sea water, to de-icing salts or to acid. In these circumstances it is very desirable to know whether or not the steel may be corroding.

METHODS OF DETECTING AND MONITORING CORROSION General

Detection methods reveal whether corrosion is taking place, but not the rate of corrosion or how much has already occurred. Monitoring methods tell either the rate of corrosion or the total amount of corrosion that has already taken place. Method A – Detection by electrode potential

The electrode potential of steel in concrete is an indicator of corrosion activity; the value reveals whether the steel is in a thermodynamically active or passive state. The half-cell shown is that usually used as a reference electrode, i.e. the saturated copper/ copper sulphate electrode (CSE). The following values of potential of reinforcement are generally accepted as revealing the active and passive conditions CSE potential : volts Condition 0.20 Passive 0.20 to 0.35 Active or passive 0.35 Active This method can be applied to existing structures provided that electrical connection can be made to the reinforcement. Method B – Detection by the constant anodic current polarisation method

The corrosive or inhibitive character of alkaline media such as concrete can be predicted by anodic polarisation measurements. This involves the application to the reinforcement of a small fixed anodic (oxidising) current in the range 5-20 PA cm-2 and observing how the electrode potential of the steel changes with time. If the concrete environment is inhibitive the passive film formed on the steel will be stable and, on application of the constant anodic current, the electrode potential will rise to a steady value in the region of 0.6 V SCE (standard calomel electrode), representing the evolution of oxygen from the passivated steel surface. If the concrete environment is corrosive to steel the passive film will be unstable; rusting can occur and the potential will not attain the oxygen-evolution value of 0.6 V SCE.


This method is used in laboratory tests on the corrosion of steel in concrete. It could be adapted for use on structures, in which case electrical connection to the reinforcement or to probes would be required. Method C – Monitoring by the electrical resistance probe

In this method the loss of section of a probe by corrosion is determined by measuring its electrical resistance. The resistance of the probe is given by:

tK

t1

wl

AlR ¸

¹·

¨©§U

U

where R denotes the resistance of the specimen U denotes the resistivity of the specimen l denotes the length of the specimen w denotes the width of the specimen A denotes the cross-sectional area of the specimen t denotes the thickness of the specimen K is a constant. In order to use this phenomenon to measure corrosion rates two conditions must be satisfied: 1. The probe must be made from the same metal of alloy as the reinforcement and must be sufficiently thin for corrosion to cause a significant loss of metal thickness in a convenient time interval. 2. Compensation for the variation of resistance with temperature is essential because resistance changes resulting from changes in temperature can swamp those caused by loss of section through corrosion. This compensation can be achieved by incorporating in the resistance probe a reference element, which experiences the same temperature variation as the test element and is protected from corrosion by a suitable coating. The reference and test elements of the probe are incorporated as two arms of an AC bridge network, which enables the resistance ratio of the reference and test elements of the probe to be measured. Schematic diagrams of the probe and electrical circuit are shown in.

TRR

TT

R

T

tK

t/Kt/K

RR

where RT denotes the resistance of the test element RR denotes the resistance of the reference element tT denotes the thickness of the test element tR denotes the thickness of the reference element K, KT, KR are constants. The main advantages of this method are that measurements can be made continuously and at a position remote from the probe location, and that the measurements are not affected by the conductivity of the concrete. Each reading shows the total corrosion to date; rates of corrosion can be readily calculated.


Method D – Monitoring by the polarisation resistance probe

In this method instantaneous corrosion rates are determined from measurements of small currents and potentials between two probe electrodes made of the same metal as the reinforcement and set in the concrete or between two pieces of isolated reinforcement. The results take into account all the corrosion processes that are taking place. In electrochemical terms the method gives a semi-logarithmic plot of potential versus log. current for any polarisation that is linear. The polarisation resistance relates the slope of the polarisation curve in the vicinity of the corrosion potential to the corrosion current by the following equation:

cacorr

aa

0E bb(i3.2bb

iE

� ¸

¹·

¨©§''

o'

where ba denotes the Tafel slope of the anodic reaction bc denotes the Tafel slope of the cathodic reaction icorr denotes the corrosion current

0Ei

E

o'¸¹·

¨©§'' is the polarisation resistance.

In order to measure precise corrosion rates it is necessary to know the values of the Tafel slopes ba and bc, but it has been shown that an estimate of the corrosion rate within a factor of two can be obtained even if the Tafel slopes are not known. The above equation is valid provided that E lies in the range 5-20 mV. Experimentally the simplest circuit for measuring polarisation resistance involves a two-electrode probe. A limitation of this method is that it can be applied only in a conducting medium (maximum resistivity 105 ohm cm). Somewhat higher resistivities can be tolerated if a three-electrode probe is used. This can be a problem in concrete that has dried out to a very low moisture content, because dry concrete has a high resistivity. Monitoring by AC impedance measurement

This method is being developed in the laboratory. It shows promise for use on steel in concrete and has the advantage that it is independent of the resistivity of the concrete. Application to in situ measurement

All four methods can be applied in situ, but methods B and C require wired probes to be cast in suitable positions in the concrete. This is preferable also for method D. Method A can be applied to existing structures provided that electrical connection can be made to the reinforcement. For future designs of structures that may be at hazard (for reasons given under the heading “When corrosion is a hazard”), full consideration should be given to casting-in suitably wired


probes on which measurements can be made. Owners of existing structures should consider using method A to find out if corrosion is occurring.

PROTECTION OF REINFORCEMENT AND REPAIR Designers of structures that may be at hazard are urged to consider protecting the reinforcement or using a corrosion-resistant reinforcement, such as austenitic stainless steel.

Publisher:

Publication Place:

Publication Date: Start Page: End Page: Language:

Assigned Organisational Unit(s):

Kalicka, Malgorzata

Acoustic Emission in Structural Health Monitoring - corrosion detecting in post-tensioned girders

Technical University of Denmark, Dept. of Civil Engineering

Fisher, Gregor; Geiker, Mette; Hededal, Ole; Ottosen, Lisbeth; Stang, Henrik

8th International PhD Symposium in Civil Engineering

8th International PhD Symposium in Civil Engineering

Kgs. Lyngby, Denmark

Kgs. Lyngby, Denmark

June 20-23, 2010

03353

2010 611 616 English

Editor(s)

Book Title:

Event Name:

Event Location:

Event Date:

8th fib PhD Symposium in Kgs. Lyngby, Denmark June 20 – 23, 2010

1

Acoustic Emission in Structural Health Monitoring - corrosion detecting

in post-tensioned girders M$à*25=$7$�KALICKA AND THOMAS VOGEL

Institute of Structural Engineering, ETH Zurich 8093 Zurich, Switzerland [email protected]

Abstract The aim of this work was applying the acoustic emission monitoring technique for evaluation of corrosion processes of steel tendons in post-tensioned concrete girders. Deteriorations and especially wire breaks, caused by corrosion of tendons, may result in disintegration of a whole structure. Detection and evaluation of corrosion processes in concrete girders is technically difficult and appropriate methods are still under development.

1. Introduction Corrosion of reinforcement is a serious problem in engineering structures and is most difficult to discover in its early stage of development, especially because early initiation and development appear inside of a structure, out of visibility. We are not aware of consequences, when it is not possible to discover products of corrosion. Corrosion causes the deterioration of concrete and reduction of steel reinforcement’s cross section As a result a collapse of a structure may occur. Detection and evaluation of an early stage corrosion processes is complicated and mostly destructive.

The experiments presented in this paper were executed at University Paul Sabatier in Toulouse, France during a master project. These tests were carried out to determine a more sufficient detection technique for recognition and evaluation of corrosion initiation processes. Acoustic Emission (AE) has been applied as a main monitoring method. AE is the elastic energy spontaneously released by materials when they undergo deformation [1]. AE signals are generated during deterioration initiation and development. This non-destructive method has been chosen due to many advantages like damage/deterioration localization, global monitoring covering the whole structure, only active damage/deterioration registration, monitoring under service conditions and finally damage/deterioration development intensity evaluation. AE monitoring was performed to detect the acoustic signals corresponding to accelerated corrosion processes.

In this study the corrosion processes of reinforcement of post tensioned tendons in concrete beams were examined. The laboratory tests have been performed on two post tensioned girders, which were of the same geometry. In one of beams, the tendon was treated with an acid attack for two weeks prior to the bending tests, while the second served as a reference without an acid treatment. Both of the beams were loaded in cycles up to failure in four point bending. The recorded data has been analysed with NOESIS Pattern Recognition Analysis. The results gained from this analysis provide some information considering sources of AE, which are the destructive processes.


2

1.1 Testing samples For the purpose of this research, two 3 m long post tensioned concrete beams (see Figure 1a) were constructed. The rectangular cross section of the beams measures 15x28 cm. Both tendons were tensioned with the same force of 75 kN. In each girder, a plastic hollow box (90x80x30 mm) had been encased on tendons to aggravate the corrosion process (see Figure 1b). Only one of the girders was treated with an acid (NH4

Figure 1: (a) Post tensioned 3 m long beams after 28 days of maturing; (b) The P2 beam

with the exposed tendon before applying the acid, during acid treatment.

SCN) for two weeks. Bending tests were undertaken on both girders i.e. P1 without acid treatment and P2 with the corroding tendon. During all of the experiment’ stages, AE monitoring was carried out.

1.2 Monitoring equipment As the main monitoring system the µSAMOS was used, which is a sensor based acoustic multichannel operation system containing a PCI-8 card [2].

For the monitoring, two types of AE piezoelectric sensors were used. On concrete surface, the Vallen Systems GmbH [3] VS30-V sensors with the mean frequency value of 55 kHz, high sensitivity low frequency were applied. This type of AE sensors are optimized for testing tank floors and other engineering structures as well as for leak detection. At the surface of the tendons, WD low sensitivity high frequency PAC Ltd. [2] AE sensors were positioned.

For the parametric measurements, a displacement sensor and a load cell were connected to the µSAMOS system.

For data acquisition, the AEWin, fully compatible with PACs standard (DTA) data files, Data Acquisition and Replay program was utilized [2].

The bending tests were performed on a testing stand SINTCO with a loading capacity up to 600 kN.

1.3 Experiments stages The experiment of two geometrically similar beams was performed to discover the influence of an aggressive chemical environment on the development of acoustic signals. The experiments were carried out in three main stages i.e. bending test of beam P1, corrosion monitoring of beam P2 followed by bending test. Both beams were loaded in cycles up to failure in four point bending. 1.3.1 Corrosion monitoring (P2) This part of the experiment was undertaken to discover initiation and development of corrosion processes on post-tensioned tendon by AE monitoring. The moment of corrosion initiation is very difficult to recognize.


3

During the corrosion monitoring, the tendon of beam P2 was treated with an acid with two different chemical solutions: NH4SCN (200 g/800 ml) i.e. solution 1, during the first week and NH4

1.3.2 Bending tests (P1, P2)

SCN (400 g/800 ml) i.e. solution 2, during the second week of the monitoring. During the test, AE was acquired and no load was applied.

The beams P1, P2 were loaded up to failure in seven cycles (see Figure 2): x Cycle 1: 0 – 35 kN x Cycle 2: 0 – 40 kN x Cycle 3: 0 – 40 kN x Cycle 4: 0 – 50 kN x Cycle 5: 0 – 50 kN x Cycle 6: 0 – 60 kN x Cycle 7: 0 – 105 kN.

Figure 2: Bending test: Loading cycles vs. Time.

The loading levels 40 kN and 50 kN were repeated to study the Kaiser Effect i.e.

2. Analysis of the acoustic signals

an effect, in which acoustic emissions are not observed during the reloading of a material until the stress exceeds its previous high value.

The following analysis focuses on the AE signals’ classification to recognize destructive processes in post-tensioned concrete girders. For the AE signal analysis, the NOESIS Unsupervised Pattern Recognition (UPR) analysis was used. Signals, collected during the mechanical and chemical parts of the experiments, were filtered i.e. removing correlated parameters, and classified by the unsupervised k-Means statistic with a different purposed number of classes.

In the presented signal patterns, results with an assumed number of classes (see Figure 3 - 4), which represent different destructive processes taking place during the bending tests and corrosion monitoring, are revealed. The results from the tests of the two post tensioned concrete beams, which were loaded up to failure under neutral environmental conditions (laboratory conditions), are presented in the next diagrams i.e. signal strength vs. time. It should be noted, that in the higher load cycles, the activity of acoustic emission was registered during both loading and unloading. High activity during unloading proves the presence of concrete cracking i.e. opening and closure of cracks. In regular service of structures, this defect allows corrosive agents to penetrate a structure.

105

020406080

100120

0 2000 4000 6000 8000 10000

Loa

d [k

N]

Time [sec]

Loading cycles


4

The failure of beam P1 revealed plastic deformations and tendon break and is represented by AE signals in the last loading cycle 7. The development of destructive processes in the concrete took place during prior loading cycles (see corresponding signals to the loading cycle 4, cycle 5 and cycle 6 on the Figure 3, 4). Beam P2, which was treated previously with a corrosive component, was loaded up to failure in the same loading cycles as beam P1. The results, which are shown on Figure 4, do not show any larger variation (compared to beam P1 bending tests’ results), which could clearly indicate the degradation of the tendon’s state due to corrosion.

Beam P2 reached its ultimate load

Figure 3: Beam P1 - AE classified signals during the loading cycles 1 to 7. AE signal

classification by the UPR method with 8 classes. AE signals not normalized.

by transfer cracking of the concrete and yielding of the tendon. These events produced high signal energy.

Figure 4: Beam P2 - AE classified signals during the loading cycles 1 to 7. AE signal

classification by UPR method with 8 classes. AE signals not normalized.

The tendon of beam P2 was treated with an aggressive corrosive component prior to the bending test. During the corrosion monitoring, acoustic signals were registered. The results from Day 8 are presented on Figure 5. The stronger AE activity appeared periodically, approximately every 50 000 sec. Between bursting events, registered signals appeared to have a regular and weak emission above the established threshold. The level of signal strength during bursts of corrosion products is nearly two times lower than the signals registered during the bending tests.


5

Figure 5: Beam P2, Day 8 – Corrosion monitoring. AE signals strength vs. time; data not

classified.

3. Conclusions

After seven days of monitoring, the corrosive solution was increased. The monitoring was continued during the following week. The energy of signals has not increased significantly, which means that raising the intensity of corrosive component did not result in an increase of the signals’ energy. Periodical emission’s activity may be caused by two main processes: bursting of corrosion products, which was previously observed during monitoring of steel tanks by Kielce University of Technology (KUT) in Poland, and/or caused by displacement of tendon due to loss of steel bar cross section in the corroded area.

Signals registered during initiation and development of corrosion processes show an intermitted nature. The corrosion intensity variation is detectable based on the AE activity. However, the signal strength of the registered data during corrosion monitoring is at least twice lower than the signal strength produced by the destructive processes during the bending tests. Due to a short term of an acid treatment of the tendon, the aggressive environment did not clearly influence the beam’s strength in this experiment.

As assumed at the beginning, AE has clearly detected signals coming from corrosion initiation and development, which produces weak signals, compared to processes like concrete cracking or wire breaking. However, this phenomenon has been detected in controlled laboratory conditions without any external loading. It would be very difficult to separate corrosion signals from so called noise signals in regular field monitoring conditions. Due to this fact, further AE is not preferred for corrosion in-situ monitoring.

4. Future research These experiments have been performed as a part of a research on structural health condition monitoring by acoustic emission. The main aim is to discover and recognize the acoustic signals leading to failure/collapse of a structure. This research has been studied previously at KUT, where laboratory tests on samples, beams, full scale girders and field monitoring on prestressed concrete bridges have been performed [4, 5].

The next step of the research would be developing an overall structural health monitoring for prestressed and post-tensioned concrete bridges. The monitoring should also concern an influence of loading/traffic variation, and environmental conditions on acoustic signals activity.


6

Acknowledgements ,�ZRXOG� OLNH� WR� WKDQN� 3URIHVVRU� /HV]HN�*RáDVNL� IURP�.LHOFH�8QLYHUVLW\� RI� 7HFKQRORJ\� IRU�great support and fruitful discussion. I would also like to thank Professor Jean-Paul Balayssac from University Paul Sabatier, Toulouse, who as my advisor supported this research at the Laboratory LMDC Toulouse.

References [1] American Society for Non-destructive Testing, “Acoustic Emission Testing”,

Nondestructive Testing Handbook, Third Edition, vol. 6.

[2] Physical Acoustic Ltd., home page: http://www.pacndt.com.

[3] Vallen Systeme GmbH, home page: http://www.vallen.de.

[4] /��*RáDVNL��*��ĝZLW��0��.DOLFND��.��2QR��³Acoustic Emission Behavior of Prestressed Concrete Girders during Proof Loading”

[5] M. Kalicka, “

, Journal of Acoustic Emission, vol. 24, 2007, pp. 187-195.

Health Assessment of Prestressed Girder by Deterioration Processes Evaluation”

, ICT for Bridges and Construction Practice, extended abstract, IABSE conference, Helsinki, June 2008, pp. 144-145.

PHILIPPINE ENGINEERING JOURNAL PEJ 2007; Vol. 28, No. 2:29-44 �

Received: November 13, 2009 Copyright © 2007 Philippine Engineering Journal Revised: November 27, 2009

Accepted: December 17, 2009

HISTORY AND DEVELOPMENT OF PREDICTION MODELS OF TIME-TO-INITIATE-CORROSION IN REINFORCED

CONCRETE STRUCTURES IN MARINE ENVIRONMENT

Norbert S. Que1

Institute of Civil Engineering, University of the Philippines Diliman

ABSTRACT

This paper presents the history and development of mathematical models for the prediction of time to initiate corrosion of reinforced concrete exposed to chlorides in marine environment. Emphasis is given to prediction models (empirical and mathematical) that consider Fick’s 2nd law of diffusion as the theoretical basis. Since repair and rehabilitation of corroded reinforced concrete marine structures draw significant portion of the budget for infrastructures, the capability to accurately predict deterioration levels due to chloride attack, especially the time-to-initiate corrosion, in reinforced concrete structures exposed to chloride-induced corrosion can translate to major economic savings and possible extension of service life of a member or a structure. Keywords : Chloride, Marine Environment, Fick’s 2nd Law, Reinforced Concrete, Corrosion

1. INTRODUCTION

A reinforced concrete structure exposed to water containing soluble salt (e.g. NaCl) imposes high risk of penetration of ions (in this case chloride Cl- and Sodium Na+) into concrete (HETEK, 1997a). Chloride ion penetration is a major concern on durability issues and service life design of reinforced concrete structures in the marine environment. Among structures vulnerable to chloride attack include ports, bridges and other marine infrastructures. The economic importance played by these structures demands careful attention in the study of chloride ion penetration phenomena so as to minimize its damaging effects and extend the service life of these important structures.

The penetration of chloride ions into the concrete material is through a system of capillary pores dominated mainly by diffusion and capillary absorption. When the amount of chloride deposited onto the surface of the reinforcing bar reaches a critical value between 0.2% and 0.6% by weight of cement, corrosion process is assumed to start. The time elapse from the construction of the structure up to this point is referred to as the time to initiate corrosion. _____________________ *Correspondence to: Institute of Civil Engineering, University of the Philippines Diliman, Quezon City 1101 PHILIPPINES. email:[email protected]

N.S.QUE

Copyright © 2007 Philippine Engineering Journal Phil. Engg. J. 2007; 28:29-44

30 �

Corrosion of steel reinforcing bars is generally accepted as electrochemical in nature.

The naturally occurring alkaline environment in concrete forms a thin passive film around the surface of reinforcing steel bars which serves as a barrier against carbonation induced corrosion and chloride induced corrosion. For marine exposed structures, the gradual penetration of chloride ions into the concrete structure will eventually lead to the weakening of the passive film where depassivation process starts. Figure 1 illustrates a chloride induced corrosion process.�

�

�

��

�

Fig. 1. Chloride induced corrosion process (Keller 2004)

A notch-like shape corrosion that affects rebar locally is formed after the passive film is destroyed by the penetration of chloride ions. The expansion of rust around the reinforcing bar will cause cracking and spalling of concrete. Service life of a structure is often equated when cracking due to corrosion occurs.

A conceptual model for service life prediction of corroded reinforced concrete structure as developed by Tuutti (1980) is shown in Figure 2. As the figure shows, there are two distinct stages in the evolution of deterioration caused by chloride corrosion. The first is the initiation period at which the chloride threshold value is reached at the concrete-steel interface to activate corrosion. The second is the propagation period which represents the period between corrosion initiation and cracking of concrete. �

�

Fig 2. Tuutti (1980) service life model of corroded structures

Time initiation period propagation

Degr

ee

of C

i

service life

HISTORY OF PREDICTION MODELS OF TIME

Copyright © 2007 Philippine Engineering Journal Phil. Engg. J. 2007; 28: 29-44 �

31

When cracking occurs, formation of rust oxide accelerates growing to a sufficient size affecting the stress-strain property of the steel on the corroding site and the near vicinity (HETEK, 1997a). Based on corrosion theories, when only 8% of the approximate area has corroded, the steel can no longer be treated as linear-elastic, ideal plastic material.

Progressing corrosion will continue to consume the affected steel area reducing the area of the steel section until it reaches a critical level where it may no longer be able to resist loads as required by design. This may cause the structure or a structural member to act in ductile manner since the steel strength capacity has been significantly reduced. It may even be more threatening if the affected area is a critical section of a structural member.

Inspection of reinforced concrete structures in marine environment is important. The use of NDT techniques in combination with coring may enable one to detect the early onset of corrosion where appropriate steps may be taken to slow down the corrosion process. Such inspection procedures, however, are quite costly as they require experts to conduct the tests and interpret the results.

To wait for the appearance of visible signs of corrosion in a structure such as rust stains and/or cracks before repair will be conducted is not cost effective. The presence of such visible signs is indicative of an advanced stage of corrosion which may require a thorough investigation of the entire structure in order to properly assess the type of repair or rehabilitation needed for the corroded structure.

The use of prediction models, specifically, the time to initiate corrosion can provide useful information regarding the early onset of corrosion which allows one to appropriately schedule the required maintenance.

2. PREDICTION MODELS

2.1 Fick’s 2nd Law of Diffusion Most of the existing mathematical models on the diffusion of chloride into concrete that predict chloride concentration as functions of time and depth, and time to initiate corrosion are based on Fick’s 2nd law of diffusion. The differential equation is expressed as

2

2

*xCD

tC

ww

ww (1)

In this expression, only four parameters are involved, namely, C for chloride concentration, D for diffusion coefficient, x for depth referred from the concrete surface, and time t.

Solution to this one-dimensional diffusion problem depends on boundary conditions and certain simplifying assumptions. Those who first attempted to create a model based on equation (1), to simplify an inherently difficult problem, assumed that the diffusion parameter and the surface chloride content Cs are constants. The following boundary and initial conditions are specified as:

N.S.QUE


32 �

�

2.2 Constant Chloride Diffusivity Case Many authors came up with the general solution below considering constant diffusivity. With Csa & D treated as constants, Fick’s 2nd law described by (1) leads to the following solution:

¸¸¹

·¨¨©

§

��

aexisai Dtt

xerfcCCCtxC)(4

)(),( (2a)

where: C (x,t) = chloride concentration at any time t and depth x Ci = initial chloride concentration (constant thru depth). Csa = chloride concentration at concrete surface (constant) Da = apparent diffusion coefficient (constant) x = depth referred from surface t = time of inspection / time in consideration If the initial surface chloride concentration is zero, then Equation (2a) can be rewritten as:

»¼

º«¬

ª¸̧¹

·¨̈©

§�

DtxerfCtxC s 2

1),( (2b)

»¼

º«¬

ª¸̧¹

·¨̈©

§

DtxerfcCtxC s 2

),( (2c)

Equation (2b) (Zhang, J.Y. and Lounis, Z., 2006) is famously known as the error function solution and is widely referred to by journals and books. Equation (2c) is just another form of equation (2b) using the error-function complement.

From this solution, considering constant diffusivity, the depth of chloride ingress and time to initiate corrosion can be evaluated or derived. Authors who have proposed prediction models of this case are Collepardi, et. al. (1972), Tuutti (1982), Browne (1980), and Poulsen (1990).

It had been shown, however, that models based on the assumption that chloride diffusivity is constant had exhibited gross errors. Experts found that this concept’s applicability is limited to old structures and concrete samples with very long exposure time. This is due to the fact that at significantly longer chloride exposure, concrete’s chloride diffusivity exhibits a constant behavior. 2.3 Time-Dependent Chloride Diffusivity Laboratory tests & field experiments had established that chloride ingress into concrete is time dependent. Diffusion of chloride into concrete decreases with time and this behavior can be mathematically captured using a power function equation. Since the amount of



33

chloride at any depth x of the structure depends on the diffusion rate, the concentration of chloride also varies with time. It was found out that chloride concentration increases with the increased exposure of a reinforced concrete member to a chloride-rich environment. In light of the observations from laboratory tests and field experiments, a more realistic model to predict chloride ingress into concrete was formulated which takes into account the time dependence of chloride diffusivity. Poulsen (1993) derived an expression for a time-dependent diffusion coefficient (Da) as,

WW dDt

Dt

a ³ 0

)(1 (3)

It should be noted the Da is not the true diffusion coefficient. Through the years, researchers had come to formulate varying expressions for the apparent diffusion coefficient. A power function for Da, however, became widely used and expressed generically as:

a

ooa t

tDD ¸

¸¹

·¨¨©

§ (4)

Where Do is the diffusion coefficient at time to and a is an aging factor. Mangat and Molloy (1994) proposed an expression in the form of equation (4) given by:

ma tDD � 1 (5)

where Da is the diffusion coefficient after exposure time t, D1 is the diffusion coefficient at one year, if t is expressed in year, and m is a material constant. The material constant m may be estimated as a function of the the water-cement ratio as:

6.05.2 �cw (6) Takewaka and Mastumoto (1988) and Maage, et. al. (1993) used a variation of the equation presented in (4) to model to the time dependence of the diffusion coefficient expressed as:

D

¸̧¹

·¨̈©

§

exaexa t

tDD (7)

where Daex is the apparent diffusion coefficient at the time of first exposure, tex is the time of first exposure and Į is an aging factor. For ordinary concrete with 0.25 � w/c < 0.60, one may use Poulsen’s (HETEK, 1997b) proposed expression for Į given by:

N.S.QUE


34 �

� �»»¼

º

««¬

ª¸¹·

¨©§�u�

»»¼

º

««¬

ª¸¸¹

·¨¨©

§�

5.22

/1.0exp1.0

19.0/exp

cwcwD (8)

The time dependency of chloride diffusion coefficient is considered to be the effect of

a complex physical phenomenon during chloride ingress and the varying intensity of chloride exposure environment (HETEK, 1996; HETEK, 1997b).

It is not only the diffusion coefficient that varies with time. Surface chloride concentration is also claimed to vary with time. Uji et al. (1990), among other researchers suggested that the surface chloride concentration should be proportional to the square root of time expressed as:

5.0

1)( tStCsa (9)

where: S1 = surface chloride concentration after year 1 of exposure t = time of exposure (years) To satisfy the boundary conditions, equation (9) was re-written as:

isa CC for 0 d t d tex (10)

exini ttSC �� 1 for t t tex

where: Ci = equally distributed initial concentration of chloride tex = time of exposure tin = time of inspection

It was highlighted in HETEK (1996) and HETEK (1997b) that in cases where Csa is a

function of time, the error function erf is not the solution of Fick’s 2nd law. However, the error function is still widely used in practice to find Csa & Da from chloride profiles using regression analysis.

For special cases, a solution for Fick’s 2nd law with chloride diffusivity as a function of time was presented in HETEK (1996). A solution was presented given that Dao is constant, Da is a function of time, and the chloride concentration, C(x,t) is of the form �

psa tStC 1)( (11)

)(),( 1 ztStxC p

p < (12)

aotD

xz4

(13)



35

For p = 0, Equation (11) reduces to the basic and well-known error function solution, equation (2b). In general, with Csa obeying the form of equation (9), Equation (11) can be expressed as:

)()(exp(),( 21 zerfczzttSCtxC exi S�� (14)

The Mejlbro function, �p, is defined as: �

¦ ¦f

f

�

��

�*�*

�

<

0 0

122

)!12()2()5.0(

)5.0()1(

)!2()2(

)(

n n

nnnn

p

nzp

pp

nzp

z

(15)

A number of models for the prediction of time to initiate corrosion is summarized in Table 1. Time dependent diffusivity models are discussed in the following section.

3. TIME DEPENDENT DIFFUSIVITY MODELS TO PREDICT THE TIME-TO-INITIATE CORROSION

3.1 Anacta Model Anacta (2009) proposed a model that computes for time-to-initiate corrosion. The model takes into account environmental factors such as temperature, rainfall and humidity. It also takes into account the influence of duration of exposure.

A model to compute for depth of chloride ingress was also formulated which was utilized in computing for the time-to-initiate corrosion. The expression to compute for the depth of chloride ingress model is:

tDSx cc 2 (16)

N.S.QUE


36 �

Table 1. Time-to-initiate corrosion prediction models

Model� Equation� Basis Remarks

A.�Constant�Diffusivity�Models�

Bazant��(1979)�

2

0

12

14

�

�»¼

º«¬

ª¸̧¹

·¨̈©

§�

CC

erfD

x

t

cr

c

c

ic

Fick’s� 2nd��law�

One�of�the�first�model�created.�

Yamamoto�(1995)�

� �

2

01 /12

1»¼

º«¬

ª

�

� CCerfx

D

t

cr

c

c

ic


�

Clear��(1976)� � � > @ 42.0

22.1

/129

s

cic Ccw

xt

�

� Empirical� �

B.�TimeͲDependent��Diffusivity�Models�

Anacta��(2009)�

2

2 »¼º

«¬ª

Sx

Df

t c

c

sic Fick’s� 2nd��

law�Considers�local�envi�and�

mat’l�impact.�

PoulsenͲMejlbro�(2006)�

D

D

�

�

¸¸¹

·¨¨©

§

/u

¸¸¹

·¨¨©

§

u

12

12

)(1

5.0

crp

aexex

c

exic

yinv

Dtx

tt


Hetek.�

TangͲNilsson�(1992)�

)()(

)(

,

1,

,

diffQtotalQ

totalQ

ji

ji

ji

'

�

� Numerical�� ClinConc�/�submerged�

is a shape factor for depth of chloride ingress and Į is an exponential constant obtained from curve fitting. The chloride diffusion coefficient, which is function of material and environmental parameters is given as: �

)()()()( 4321, RfRHfTftfDD rmtcc uuuu (18) �

where Dc,rmt is the reference chloride diffusion coefficient taken from the rapid migration test. The different factors fi are defined as follows: �



37

n

ref

tt

ktf ¸̧¹

·¨̈©

§ )(1 (19)�

»»¼

º

««¬

ª¸¸¹

·¨¨©

§�

TTGETf

ref

11exp)(2 (20)

»»¼

º

««¬

ª

��

� 4

4

3 )1()1(1)(

refRHRHRHf (21)

5.1

4 50001)( ¸

¹·

¨©§�

RRf (22)

where f1(t), f2(t), f3(t), and f4(t) are factors representing the influence of duration of exposure, influence of temperature, influence of relative humidity, and influence of rainfall, respectively.

To determine the time at which chloride ions will reach the depth of the reinforcing bars, equation (16) is used where the depth of chloride ingress is set equal to the concrete cover depth. The computed time, t, will be used to calculate the shape factor (S) and the diffusion coefficient (Dc) which is one of the parameters in computing for the time-to-initiate corrosion. �

2

2 »¼º

«¬ª

Sx

Df

t c

c

sic (23)

refics tf ,316.0 [ (24)

where: tic = time to initiate corrosion (years) tic, ref = reference time-to-initiate corrosion derived from laboratory experiments (days) xc = concrete cover thickness (mm) fs = reinforcement factor [ = curve-fitting parameter due to effect of corrosion

The advantage of using Anacta’s prediction model is the applicability of local data available for validation purposes which considers the influence of local environmental factors and materials.

The influences of local materials were indirectly considered in some of the parameters included in the model. The parameter D, which is used in computing for the shape factor S, is derived by curve-fitting the chloride ingress v.s. time curve. The chloride ingress v.s. time curve has been performed on materials of varying w/c ratio & fly ash content. Other parameters like k & n, used in calculating f1 (age factor), were determined by curve fitting, thus, it reflects the influence of local materials on chloride ingress into concrete indirectly.

N.S.QUE


38 �

The procedure in predicting the time to initiate corrosion using this model basically involves 3 steps: (1) Equate equation (16) to a given concrete cover depth, xc, and solve for t, (2) The computed t will then be used to calculate for the shape factor, S, and diffusion

coefficient using equations (17) & (18), respectively, (3) Once Dc is known, the time to initiate corrosion can then be computed using equation

(23) To be able to use this model, one must have the data for the following: (1) Rapid migration test (reference diffusion coefficient is obtained from this), (2) Plot of chloride ingress v.s. time (for determination of values of D), and (3) Environmental Data (rainfall & relative humidity can be taken from PAG-ASA)

However, this model has been limited to marine concrete or concrete samples

exposed under the tidal zone environment. Study has yet to be done if the same model can be applied for marine concrete & concrete samples exposed under different exposure conditions. This could be a topic of research for future development of the model.

Since the Anacta model to predict the time-to-initiate corrosion is dependent on material and environmental factors, massive verification studies have to be carried out using both laboratory and field tests to validate the model. The prediction equations, due to the presence of curve fitting parameters such as Į, k, and n are not expected to change in form as more tests will be conducted for validation. �

3.2 Mejlbro-Poulsen (Hetek) Model Mejlbro-Poulsen model is based on the assumption that the flow of chloride into concrete is proportional to the gradient of chloride concentration in the concrete, or basically the Fick’s law. Its applicability assumes that the following conditions are met:

x Da (apparent diffusion coefficient) is time-dependent x Csa (chloride concentration of the exposed surface) is time-dependent x Ci initial chloride concentration is constant (independent of time & distance from

surface) The apparent diffusion coefficient considered for this model is assumed to have taken the form of a power function (7):

D

¸¹·

¨©§

tt

DtD exaexa )(

Mejlbro has mathematically derived that the surface chloride concentration takes the following form:

� �> @paexisa tDttSCC )(*)�� (25)

With these two relationships, and the assumptions mentioned above, Mejlbro and Poulsen came up with the following prediction of chloride concentration at any time t and at any depth from the surface of concrete, expressed as:

� � ¸¸¹

·¨¨©

§

�<��

)(4*)(),(

tDttxCCCtxC

aexpisai (26)



39

where: C(x,t) = chloride concentration at any depth and time Ci = initial chloride concentration Csa = achieved surface chloride concentration Da (t) = achieved diffusion coefficient (function of time) tex = time of first exposure to chlorides t = time of inspection <p = Mejlbro function, as described by equation (15)

Vast studies conducted by Hetek Group enabled them to come up with tables and factors to determine the decisive parameters used in the prediction model. These include the parameters Daex, D, Sp, p which are expressed in terms of diffusion coefficient at year 1 & year 100, and chloride concentrations at year 1 & year 100. The procedure in using the Mejlbro-Poulsen’s model (Hetek, 1997b) involves: (1) The determination of year 1 & year 100 diffusion coefficients and chloride

concentrations (2) D1 & D100 parameters are then used to solve for the decisive parameters (3) Once the decisive parameters are known, Da & Csa can be determined (4) Da & Csa will then be substituted to equation (26) to predict chloride concentration at

any time & depth To predict the time to initiate corrosion, when the decisive parameters are known,

equation (26) has to be re-written as follows;

)(5.0),(2

zDtxSCtxC p

p

aexexpi /¸

¸¹

·¨¨©

§u� (27)

)(),( 2 zzSCtxC pp

pi /uu� (28)

where:

pp

p zz

z 2

)()(

< / (29)

aexex Dtxz

u

W5.0 (30)

�

Equating x = xc (i.e. making the depth equal to the cover depth), the initiation time can then be solved by the following steps: �

)(5.0

2

crp

p

aexex

cpicr z

Dtx

SCC /¸¸¹

·¨¨©

§u� (31)

N.S.QUE


40 �

aexexcrcr Dt

czu

W

5.0 (32)

DDD

W��

¸̧¹

·¨̈©

§#¸̧

¹

·¨̈©

§�¸̧

¹

·¨̈©

§

11

ex

cr

cr

ex

ex

crcr t

ttt

tt

(33)

)( crpcr yinvz / (34)

p

aexex

p

ircr c

DtS

CCy

2

5.0 ¸¸¹

·¨¨©

§u

� (35)

D�

¸¸

¹

·

¨¨

©

§

/uu

12

)(5.0

crpaexexexic yinvDt

ctt (36)

Equation (36) is the time to initiate corrosion equation and is measured from the time

of mixing. Note that the above derivation has been shown in Hetek Report No. 83 (Hetek, 1997b).

The highlight of Hetek Model is its applicability for three different exposure types, namely, submerged, splash & atmospheric. Calculation of time-to-initiate corrosion can also be performed using a diagram method Hetek (1996) since tables and graphs obtained from studies are available. However, these tables, graphs, and even, the tabulated efficiency factors (used in computing for D1 & D100 parameters) were localized and highly dependent on the experiment performed by Hetek. Its application here in the Philippines has yet to be verified. 3.3 Tang/ ClinConc Model This corrosion prediction model has been developed by Tang (1996, 2007, 2008) utilizing the concept of finite-difference numerical method. Among the highlights of this prediction model is its use of experimental data as input thus, limiting the reliance of prediction to various curve-fitting procedures employed by other models.

However, the model is hampered by its limitation to be applicable only for structures exposed to chloride under submerged setting (it models only the pure diffusion of chloride transport into concrete). �

Basically, the prediction equation is expressed as:

)()()( ,1,, diffQtotalQtotalQ jijiji '� � (37)�



41

jjijiji

ji

jiji

tx

cccD

diffAdiffQ

'»¼

º«¬

ª'

��

'

��2

1,11,1,1,

,,

2

*)()(

(38)�

¦ �� airncapillary WmdiffA HU

H 75.01)( (39)�

)()()()(@)(, ijjDooji xftgTfTDClD (40)�

¸̧¹

·¨̈©

§�

Hgel

boCTHoo

WKTDTD 1)(@)(@ (41)

¸̧¹

·¨̈©

§�

TTRE

oo

oD

o

D

eTD

DTf

11

)(@)( (42)

t

tt

tg oE

¸¹·

¨©§ )( if t�<�to�� (43)

1 if t�t�to

� �x

sxxxf

E

MM ¸̧¹

·¨̈©

§�� 1)( if x�<�xs� (44)�

1 if x�t�xs�

As we can see from above set of expressions, the required parameters for equations

(37) and (38) are all given and can be obtained mathematically (or experimentally). Only the expressions for ci,j are not provided. Similar to other finite difference calculations, this has to be computed progressively with the initial values obtained from initial & boundary conditions.

The computed total chloride concentration above based on ClinConc model can also be decomposed into “free” and “bound” chlorides part. Tang & Nilsson (1992) utilized the concept of mass-balance equation to decompose total chlorides into parts. ��

4. CONCLUSION

As we can see from above set of expressions, the required parameters for equations (37) and (38) are all given and can be obtained mathematically (or experimentally). Only the expressions for ci,j are not provided. Similar to other finite difference calculations, this has to be computed progressively with the initial values obtained from initial & boundary conditions.

N.S.QUE


42 �

The computed total chloride concentration above based on ClinConc model can also be decomposed into “free” and “bound” chlorides part. Tang & Nilsson (1992) utilized the concept of mass-balance equation to decompose total chlorides into parts. �

ACKNOWLEDGMENT

The author would like to acknowledge the Engineering Research and Development for Technology - Department of Science and Technology (ERDT-DOST) for funding the research under the Environment and Infrastructure Track of the ERDT program. He would also like to acknowledge his research assistants, namely, Mr. Richard de Jesus and Mr. Rogers Perdiguerra.

APPENDIX Definition of Terms

ɲ� = exponential constant determined from curve-fitting C(x,t) = chloride concentration at any depth and time Ccr = critical chloride concentration (chloride threshold value) Ci = initial chloride concentration (assumed to be equally distributed thru depth) Co = initial chloride concentration Cs = surface chloride concentration Csa = achieved surface chloride concentration Da (t) = achieved diffusion coefficient (function of time) Daex = apparent diffusion coefficient at time of 1st exposure to chlorides Dc = diffusion coefficient D c,rmt = reference cl diffusion coefficient (from migration test) Di = effective diffusion coefficient at t = 1 sec E = activation energy of cl diffusion process (kJ/mol) (~10 to 50 kJ/mol) = curve-fitting parameter due to effect of corrosion fs = corrosion factor / reinforcement factor G = universal gas constant (8.314 J/mol · K) m = material constant, equal to 2.5 w/c – 0.6 (Mangat) n = empirical exponent depending on mat’l properties (from curve-fitting) p = Mejlbro factor (p0 = 1, p1 = p, p2 = p x (p-1),.., pn = p (p-1) .. (p-n+1)) = 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, … Q i,j = Chloride concentration at point i, j-1 (Tang & Nilsson) Q i,j-1 = Chloride concentration at point i, j (Tang & Nilsson) ǻQ i,j = increase in Chloride concentration (Tang & Nilsson) R = rainfall intensity (mm) RH = actual relative humidity in concrete (%) RHref = reference relative humidity in concrete (%) S = shape factor S1 = surface chloride concentration after year 1 of exposure t = duration of exposure (years) tic = time to initiate corrosion tic, ref = reference time-to-initiate corrosion derived from lab expt (days) tex = time of 1st exposure to chloride tref = time when Dref was computed (28days) T = actual absolute temperature in concrete (K) Tref = reference temperature at which D c,rmt is determined (296K) w/c = water to cement ratio



43

xc = concrete cover thickness xc = depth of chloride penetration (mm) <p = Mejlbro function, as described by Equation (12) �

REFERENCES 1. Anacta, E. (2009), “Modelling the Depth of Chloride Ingress and Time-to-Initiate

Corrosion of RC exposed to Marine Environment”, Ph.D. Dissertation, Institute of Civil Engineering, University of the Philippines, Diliman, Quezon City.

1. Bazant, Z.P. (1979). Physica model for steel corrosion in sea structures – theory, Journal of the Structural Division, ASCE, Vol. 105, pp. 1137-1153.

2. Browne, R.D. (1980). “Mechanisms of corrosion of steel in concrete in relation to design, inspection, and repair of offshore and coastal structures”, Proceedings of the International Conference on Performance of Concrete in Marine Environment, ACI SP-65, pp. 169-203.

3. Clear, K.C. (1976). “Time-to-corrosion of reinforcing steel in concrete slabs”, FHWA-RD-76-70, Washington, DC.

4. Collepordi, M., Marcialis, A. and Tuniziani, R. (1972). Penetration of chloride ions into cement pastes and concretes, Journal of American Ceramic Society, Vol. 55, pp. 534-535.

5. Hetek (1996), “Chloride Penetration into Concrete”, State of the Art, Report No. 53, Road Directorate, Denmark.

6. Hetek (1997a). “Chloride Penetration into Concrete Manual.” Report No. 123, Road Directorate, Denmark.

7. Hetek (1997b). “A system for Estimation of Chloride Ingress into Concrete” Theoretical Background Report no. 83, Road Directorate, Denmark.

8. Keller, W. J. (2004). Effect of Environmental Conditions and Structural Design on Linear Cracking in Virginia Bridge Decks, MS Thesis, Civil and Environmental Engineering, Virginia Polytechnic Institute and State University.

9. Maage, M., Helland, S. and Carlsen, J.E. (1993). “Chloride penetration in high performance concrete exposed to marine environment”, in: Symposium on Utilization of High Strength Concrete, Lillehammer, Norway, p. 838.

10. Mangat, P.S., and Molloy, B.T. (1994). Predicting of long term chloride concentration in concrete, Materials and Structures, Vol. 27, pp. 338-346.

11. Poulsen, E. (1990). The chloride diffusion characteristics of concrete: approximate determination by linear regression analysis, Nordic Concrete Research No. 1, Nordic Concrete Federation.

12. Poulsen, E. (1993). “On a model of chloride ingress into concrete having time-dependent diffusion coefficient”, in: Chloride Penetration into Concrete Structure, Nordic Miniseminar, Sweden, pp. 298-309.

13. Poulsen, E., and Mejlbro, L. (2006). Diffusion of chloride in concrete – theory and application, Taylor and Francis, New York, New York.

�

14. Takewaka, K. and Mastumoto, S. (1988). “Quality and cover thickness of concrete based on the estimation of chloride penetration in marine environments”, in: Second International Conference on Concrete in Marine Environment, ACI SP 109, pp. 381-400.

15. Tang, L. (1996). Chloride transport in concrete-measurement and prediction, Ph.D. Thesis, Department of Building Materials, Chalmes University of Technology, Gothenburg, Sweden.

16. Tang, L. (2008). Engineering expression of the ClinConc model for prediction of free

N.S.QUE


44 �

and total chloride ingress in submerged marine concrete, Cement and Concrete Research 2008, Vol. 38, pp. 1092-1097.

17. Tang L, Gulikers J. (2007), On the Mathematics of Time-Dependent Achieve Diffusion Coefficient in Concrete, Cement and Concrete Research, Vol. 37, pp. 589-595.

18. Tang, L.P., and Nilsson, L.O. (1992). Rapid determination of chloride diffusivity in concrete by applying an electrical field, ACI Materials Journal, Vol. 89(1), pp. 49-53.

19. Tuutti, K. (1980). “Service life of structures with regard to corrosion of embedded steel”, Proceedings of the International Conference on Performance of Concrete in Marine Environment, ACI SP-65, pp. 223-236.

20. Tuutti, K. (1982). “Corrosion of steel in concrete”, Report 4-82, Swedish Cement and Concrete Research Institute, Stockholm, Sweden.

21. Uji, K., Matsuoka, Y., and Maruya, T. (1990). “Formulation of an equation for surface chloride content due to permeation of chloride”, in: Proceedings of the Third International Symposium on Corrosion of Reinforcement in Concrete Construction, Elsevier Applied Science, London, U.K., pp. 258-267.

�

�

insi.51.3.151.pdf

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