Activation Energy of Chloride Induced
Corrosion of Steel Reinforcement in Concrete
Anker Henriksen and Burak Demirci
December 2010
Activation Energy of Chloride Induced
Corrosion of Steel Reinforcement in Concrete
We confirm that this is our own work and that we have not plagiarised any part of it. All work cited
in the present study is referenced.
Authors:
Anker Henriksen (s072006)
Burak Demirci (s071979)
Supervisors:
Mette Geiker
Alexander Michel
Project type:
Bachelor Project
Date:
2010-12-16
Department of Civil Engineering
Technical University of Denmark
Preface
This is a 20 ECTS points bachelor project made by Anker Henriksen and Burak Demirci at the
Technical University of Denmark, Department of Civil Engineering. The duration of the project
was three months from October to December 2010.
Lyngby the 16th of December 2010,
Anker Henriksen and Burak Demirci
I
Acknowledgements
We are grateful for the support of our supervisors, Professor Mette Geiker and Ph.D. student
Alexander Michel, Department of Civil Engineering, Technical University of Denmark.
Furthermore we would like to thank Peter Vagn Nygaard and Henrik Marnø for their support and
help with the experimental setup.
II
Abstract
This project consisted of an investigation of the short-term influence of climatic conditions on the
corrosion rate of steel reinforcement in concrete. The studied concrete specimens, with and without
mixed-in chlorides, were exposed to varying temperatures and relative humidity. The following
parameters were investigated; free corrosion potential, corrosion current density and activation
energy.
The reinforced concrete specimens were placed in climate chambers with three different initial
) and cycled through five temperatures (
).
relative humidity (
Each climate chamber contained three concrete specimens subjected to passive, general active and
localized active corrosion, respectively. The moisture content in the concrete specimens was
assumed constant during the experiments due to the short periods of exposure, approximately three
days, to different temperatures.
Measurements of the corrosion related parameters were performed using the galvanostatic pulse
method and the linear polarization resistance (LPR) method. The activation energy was calculated
using the Arrhenius equation.
Results indicated no clear short-term influence of temperature and moisture on the passive
reinforcement bars. The free corrosion potentials and corrosion current densities for the areas of the
actively corroding reinforcement increased with increasing relative humidity. No clear trend was
observed for the short-term influence of temperature on the free corrosion potential and corrosion
current density. The activation energies were higher for corrosion in concrete with mixed-in
chloride than for concrete without chlorides.
III
Resumé
Projektet indeholdte en undersøgelse af den kortvarige indflydelse af klimatiske forhold på
korrosionen af stålarmeringen i beton. Betonprøverne med og uden kloridindhold var i dette projekt
udsat for varierende temperaturer og luftfugtigheder. De følgende korrosionsrelaterede parametre
blev undersøgt; korrosionspotentiale, korrosionshastighed og aktiveringsenergi.
De armerede betonprøver blev anbragt i klimakamre med tre forskellige initial luftfugtigheder
(
) og udsat for fem forskellige temperaturer (
). Hvert
klimakammer indeholdt tre betonprøver, som blev udsat for henholdsvis passiv, generelt aktiv og
lokalt aktiv korrosion. Fugtindholdet i betonprøverne antoges konstant under eksperimenterne på
grund af den kortvarige udsættelse for forskellige temperaturer i omtrent tre dage.
De korrosionsrelaterede parametre blev målt ved brug af metoderne galvanostatic pulse og linear
polarization resistance (LPR). Aktiveringsenergien blev beregnet med Arrhenius-ligningen.
Resultaterne i rapporten indikerede ingen klar korttidsindflydelse af hverken temperatur eller fugt
på de passive armeringsstænger. Korrosionspotentialerne og korrosionshastighederne for de aktivt
korroderende armeringsstænger forøgedes, når den relative fugtighed steg. Ingen klar sammenhæng
for korttidsindflydelsen af temperatur på korrosionspotentialet og korrosionshastigheden blev
observeret. Aktiveringsenergierne blev højere for beton med kloridindhold end for beton uden
klorider.
IV
Table of Contents
1 Introduction
1
1.1 Background
1
1.2 Objective
1
1.3 Approach
1
2 Corrosion Mechanisms of Steel in Concrete
3
2.1 Electrochemical Reactions
3
2.2 Passive and Active Corrosion
4
2.3 Breakdown of Passive Layers
5
2.3.1 Carbonation and Chloride Ingress
5
2.3.2 Pitting
6
2.4 Electrode Potential
8
2.4.1 Pourbaix Diagram
10
2.5 Polarization
11
2.5.1 Activation Polarization
12
2.5.2 Concentration Polarization
12
2.5.3 Resistance Polarization
13
2.6 Corrosion Rate
14
2.6.1 Influence of Temperature
16
2.6.2 Influence of Moisture Content
17
2.7 Activation Energy
18
2.8 Moisture Storage
20
2.8.1 Prediction of Adsorption Isotherms
21
3 Experimental Work
23
3.1 Test Specimens
23
3.2 Equilibrium State
26
3.3 Test Methods
28
V
3.3.1 Galvanostatic Pulse Method
28
3.3.2 Potentiodynamic Linear Polarization Resistance
29
3.4 Calculation of Activation Energy
31
4 Experimental Results
32
4.1 Corrosion Potential
32
4.2 Polarization Resistance
35
4.3 Corrosion Current Density
37
4.4 Activation Energy
39
5 Discussion
43
5.1 Sources of Error
43
5.2 Temperature
44
5.3 Relative Humidity
46
6 Conclusion
49
Bibliography
50
List of Figures
52
List of Tables
55
Appendix A: Time to Reach Temperature Equilibrium
56
Appendix B: Prediction of Adsorption Isotherms
57
Appendix C: Matlab Function pulse
58
Appendix D: Matlab Function lpr
60
Appendix E: Matlab Function energy
62
Appendix F: Matlab Program Code for Series I
63
Appendix G: Matlab Program Code for Series II
66
Appendix H: Matlab Program Code for Series III
69
Appendix I: Mean Values and Standard Deviations
72
VI
1.1 Background
1 Introduction
1 Introduction
1.1
Background
Concrete is a widely used building material and is often reinforced with steel to improve the tensile
strength. The condition of the reinforced steel is therefore very important to maintain a strong and
durable concrete. The reinforcement is typically well protected by a passive film formed in the
alkaline environment of the concrete. If the passive film is destroyed, corrosion of the steel can
initiate given the availability of sufficient amounts of oxygen and moisture at the surface of the steel
reinforcement. The passive layer can break down due to chlorides, if they are able to penetrate the
concrete cover, or due to carbonation. The deciding factors that influence the breakdown of the
passive layer are temperature, moisture and chloride (Tuutti, 1982).
The corrosion current density is defined as the amount of current per area and relates to the
thickness of the steel being reduced over time, that is, the corrosion rate. The corrosion current
density is related to the activation energy needed for the electrochemical reactions to occur. The
activation energy is dependent on temperature and the content of moisture and chloride present in
the electrolyte, that is, the concrete. These intervening factors are investigated separately under
controlled laboratory conditions.
The effect of temperature on the corrosion rate was among others investigated by Pour-Ghaz (2008)
and Tuutti (1982) and lately a Ph.D. project by Nygaard (2009) was carried out, in which the longterm influence of the temperature and moisture content is described.
1.2
Objective
The objective of this work is to investigate the short-term influence of temperature and moisture on
corrosion of steel in concrete. The activation energy is investigated by monitoring the corrosion
current density and the corrosion potential on concrete specimens with and without mixed-in
chlorides.
1.3
Approach
Measurements were performed on concrete specimens each with ten reinforcement bars. In this
project experimental investigations were performed on five reinforcement bars that were assumed to
be representative for the experimental studies. Three different types of specimens each with the
same geometry have been prepared by Nygaard (2009) in states with passive, active general and
active localized corrosion, respectively. The measurements were made using the experimental setup
prepared and used by Nygaard (2009).
Concrete specimens were placed in climate chambers each with initial relative humidity
(
) and each of the chambers were exposed to five different temperatures
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1 Introduction
1.3 Approach
(
). Due to the short-term exposure to temperature the moisture content of the
concrete was assumed not to vary. The different climatic conditions were obtained by using freezers
as temperature chambers and saturated salt solutions to control the relative humidity.
Results from measurements of polarization resistance were used to calculate the corrosion current
density and the activation energy was found using the Arrhenius equation:
(
)
(1)
where is the corrosion current density at temperature
and
is the activation energy. The
corrosion current density was determined using the polarization resistance, which was found by the
linear polarization resistance (LPR) method. For each temperature the following parameters were
determined:



The free corrosion potential,
The ohmic resistance,
The polarization resistance,
For each reinforcement bar the free corrosion potential was monitored and measurements of the
ohmic resistance were performed using the galvanostatic pulse method. The polarization resistance,
Eq. (2), was determined by polarizing the reinforcement bar
versus the free corrosion
potential in cathodic and anodic direction, respectively, and was corrected by the ohmic resistance:
(2)
The experiments were performed in a controlled environment allowing for an investigation of each
parameter; temperature and moisture content on specimens with and without mixed-in chloride.
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2.1 Electrochemical Reactions
2 Corrosion Mechanisms of Steel in Concrete
2 Corrosion Mechanisms of Steel in Concrete
2.1
Electrochemical Reactions
Corrosion of steel involves electrochemical reactions. Such reactions are based on the principle of
donating or receiving electrons. Generally these are called oxidation (emission of electrons) and
reduction (consumption of electrons) reactions and are principally presented below:
(3)
In the reaction
is an oxidizing agent (electron receiver),
is a reducing agent (electron
donor) and z is the number of electrons transferred in the reaction. Oxygen is one of many oxidizing
agents and is in particular important when dealing with corrosion of steel in concrete (Mattsson,
1996). The fundamental mechanism for corrosion of steel in concrete is shown in Figure 1. The
figure illustrates the anodic and cathodic processes as well as the stable products, which are
thermodynamically feasible. The corrosion process is influenced by environmental conditions such
as temperature and moisture content. This influences the pH and corrosion rate and thereby the
reactions that occur. The figure also includes chloride and carbonation attacks as environmental
conditions impacting the process (Küter, 2009).
Figure 1: Fundamental mechanism for corrosion (Küter, 2009).
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2 Corrosion Mechanisms of Steel in Concrete
2.2 Passive and Active Corrosion
It is important to know that electrons cannot exist freely. Therefore a reduction reaction must
consume the electrons emitted from the oxidation reaction. This fact is decisive in corrosion theory.
As mentioned earlier the corrosion process involves an anodic (oxidation) and a cathodic
(reduction) reaction, which take place on the steel surface. Initially the anodic process occurs and
the emitted electrons then react at the cathodic area. An example of possible reactions for active
corrosion is shown below (Mattsson, 1996):
The anodic reaction:
(4)
The cathodic reaction:
(5)
A more detailed overview of possible reaction mechanisms for corrosion of steel in concrete can be
found in Küter (2009). For the given example the cathodic reaction can only take place if a
sufficient amount of oxygen and moisture is available. Furthermore, moisture is required for
transport of ions in concrete.
2.2
Passive and Active Corrosion
Steel in concrete is generally in a passive state because concrete is alkaline, since it contains high
concentrations of soluble calcium, sodium and potassium ions. The presence of these ions results in
a basic environment with a pH around - (Broomfield, 1997). Given a high pH value and the
availability of oxygen at the steel surface the corrosion products form a dense oxide film on the
metal. The oxide film prevents the transport of metal ions from the metal resulting in a very low
corrosion rate. The corrosion is then said to be under anodic control and referred to as passivation.
Passive film can be broken down by lack of oxygen, carbonation of the concrete or the presence of
aggressive ions such as chloride (Bardal, 2004).
The active corrosion process depends on the availability of oxygen and moisture and is in natural
environments considered to happen due to carbonation and chloride attack. A limited supply of
oxygen curbs the active corrosion rate and the corrosion is said to be under cathodic control
(Broomfield, 1997; Bardal, 2004).
The corrosion of steel can be seen as the formation of rust on the steel surface. Rust is one of many
possible corrosion products, which might be formed (Küter, 2009). Below the formation of red rust,
which can be observed as red/brown brittle flakes on the steel bar, is presented. The cathodic
reaction (3) produces hydroxyl ions,
, which increase the alkalinity and preserve the passive
oxide layer on the steel locally. Rust is formed in several more stages based on the anodic and
cathodic reactions:
(
4
(
)
(
)
)
(
)
Ferrous hydroxide
(6)
Ferric hydroxide
(7)
Hydrated ferric oxide
(8)
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2.3 Breakdown of Passive Layers
2 Corrosion Mechanisms of Steel in Concrete
The unhydrated ferric oxide,
, has a volume about twice the volume of the replaced steel.
When hydrated it swells and the total volume increase is two to ten times at the interface between
steel and concrete. The volume increase can result in cracking and spalling of the concrete. If the
supply of oxygen to the anode is limited, but the supply to the cathode is sufficient, corrosion may
propagate with no visible signs. The reaction products formed under these circumstances are
referred to as green or black rust based on the colour of the liquid seen on reinforcement when
exposed to air (Broomfield, 1997).
2.3
Breakdown of Passive Layers
Dissolution of the passive layer can occur because of the solubility of the oxide in the passive state,
which by change of pH, increase of temperature or concentration of aggressive ions can become
higher.
2.3.1 Carbonation and Chloride Ingress
Corrosion of steel in concrete is mainly initiated by two causes; carbonation and chloride attack
(Mattson, 1996). Carbonation is the reaction of
in the atmosphere and water content in the
concrete. The reactants form carbonic acid, which neutralizes the alkalis in the concrete and reduces
the pH. Carbonation follows the chemical reactions below:
(9)
(
)
(10)
( ) , in the pore solution and
The carbonic acid,
, reacts with the calcium hydroxide,
reduces the pH. There is, however, more calcium hydroxide present in the concrete pores that can
be dissolved in the pore water and the high pH level of
is maintained until the calcium
hydroxide is consumed. When all the locally available calcium hydroxide reacts the pH value will
drop. Carbonation initiated corrosion is severe when the concrete cover thickness is small, the pore
structure is open and well-connected allowing
to penetrate rapidly or when alkaline reserves in
the pores are low. These problems occur when the cement content is low, there is a high water-tocement ratio or the concrete is poorly cured (Mattson, 1996).
Contrary to carbonation the attack of chlorides do not result in a decreased pH level, but the
penetration of chloride ions and its accumulation to beyond a certain concentration in the vicinity of
the steel surface can result in the destruction of the protecting passive film initiating corrosion. The
chloride threshold is introduced as the concentration level which results in a breakdown of the
passive film. The threshold depends on the ratio between chloride and hydroxyl. Figure 2 shows the
chloride threshold by weight of cement as a function of water saturation for different concrete
qualities and degrees of carbonation. Typically the threshold for carbon-steel in uncarbonated
concrete is in the range of
to
chloride by weight of the cement (Küter, 2009).
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2 Corrosion Mechanisms of Steel in Concrete
2.3 Breakdown of Passive Layers
Figure 2: Dependence of chloride threshold on concrete properties and exposure conditions (Küter,
2009).
2.3.2 Pitting
Pitting is a localized attack with a different corrosion rate in certain areas of the metal than others.
The corrosion is resulting in a formation of pits at the metal surface and is generally initiated due to
a local breakdown of the passive layer in environments containing chloride, bromide, iodide or
perchlorate ions. Different theories for the complex breakdown of passive layers can be found in
Küter (2009) and literature cited therein. One theory, described in Wranglén (1985), is that the
pitting is initiated at weak points of the passive oxide layer due to irregularities in the oxide
structure or inclusions in the metal. After formation, the pit starts to grow creating an anodic area
situated in the pit and a cathodic area usually on the surrounding surface. The solution in the pit
becomes acidic and metal ions diffuse towards the mouth of the pit where they react with hydroxide
ions forming a crust, see Figure 3.
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2.3 Breakdown of Passive Layers
2 Corrosion Mechanisms of Steel in Concrete
Figure 3: Sketch of a corrosion pit in iron. Potential referred to a standard hydrogen electrode
(SHE) (Bardal, 2004).
The corrosion products covering the pit prevent an exchange of electrolyte between inside and
outside of the pit resulting in further corrosion as well as a difference in pH and potential. Pitting
can only occur if the pitting potential is attained. This potential is increased with increasing pH and
decreasing chloride concentration. Increasing temperature usually decreases the pitting potential.
Figure 4 shows the pitting potential for three different chloride concentrations drawn in a Pourbaix
diagram. The pitting potential decreases with decreasing pH (Bardal, 2004).
Corrosion fatigue can occur in concrete exposed to chloride attack and precracks are often seen as
pits caused by the attacking chloride ions, see Figure 5 (Bardal, 2004).
Figure 4: Pitting potential curves for different chloride concentrations: Clpit,ia=10-2 mol/L,
Clpit,ia=10-1 mol/L and Clpit,ia=1 mol/L. Index ia stands for ion activity (Küter, 2009).
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2 Corrosion Mechanisms of Steel in Concrete
2.4 Electrode Potential
Figure 5: Left: Reinforcing steel after corrosion fatigue test. Right: Pitting induced corrosionfatigue in chloride-containing concrete (Nürnberger, 1997).
2.4
Electrode Potential
Electrode potential is a way to measure the activity of a metal in an electrolyte and a possibility to
predict whether corrosion occurs or not. The relationship between the redox potential, , and the
activity of the reaction components, , is given by Nernst’s equation:
(
)
(11)
where
is the standard electrode potential,
(
) is the gas constant, is the
absolute temperature and
is Faraday’s constant. The Nernst equation applies to
the following structural electrode reaction:
(12)
If the reaction is in the equilibrium state the redox potential is equal to the corrosion potential
referred to as
. The driving force of the electrochemical reaction is the potential difference
between the anodic and cathodic reaction (Bardal, 2004). When corrosion takes place the corrosion
potential,
, is measured as a mixed value between the equilibrium potential for the anode and
cathode reactions, see Figure 6 (Küter, 2009).
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2.4 Electrode Potential
2 Corrosion Mechanisms of Steel in Concrete
Figure 6: Corrosion potential, Ecorr, as a mixed value between E0,a (anodic potential) and E0,c
(cathodic potential). icorr is the exchange current density (Küter, 2009).
It is difficult to determine the electrode potential experimentally and therefore a relative value is
used in general. This value is determined by connecting a test electrode, whose electrode potential
is to be measured, to a reference electrode via an electrolyte (liquid junction). The electrode
potential of the test electrode, referred to as working electrode, is measured against the reference
electrode. The relationship between the working electrode and the reference electrode is given by:
(13)
The value of the electrode potential of the working electrode depends on the type of reference
electrode used, see Table 1 (Mattsson, 1996).
The standard hydrogen electrode consists of a platinum wire platinised by electrolysis in a solution
with an activity of the
-ion equal to 1 and bathed in hydrogen gas at
pressure. The
advantage of using a standard hydrogen electrode is that the electrode potential,
, is given the
value zero on the hydrogen scale which means a measurement of
corresponds to
(Mattsson, 1996).
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2.4 Electrode Potential
Table 1: Electrode potentials for reference electrodes on the hydrogen scale at 25 °C.
Reference electrode
( )
Designation
(
Standard hydrogen electrode (SHE)
)
(
(
Calomel electrode, saturated (SCE)
Silver/silver chloride electrode (
Manganese dioxide electrode
)
)
(
)
)
(
)
2.4.1 Pourbaix Diagram
The Pourbaix diagram sums up the thermodynamic data which relate to the electrochemical and
corrosion behaviour of metals in an electrolyte. A graphical relation between electrode potentials
and pH for steel is given in the Pourbaix diagrams shown in Figure 7. The equilibrium electrode
potentials in Figure 7 are determined from Nernst’s equation, see Eq. (11). An analytical
background for the Pourbaix diagram can be found in Küter (2009). The diagram shows different
regions for corrosion, passivity and immunity where the metal does not react.
Generally
is known to form a passive oxide layer on the metal (Bardal, 2004). pH in the
diagram refers to the values close to the metal surface and might differ from the pH of the solution.
Figure 7: Pourbaix diagram of iron in water at 25 °C. [A]: Immune, passive and corrosive
domains. [B]: Dominant species in their stability domains (Küter, 2009).
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2.5 Polarization
2.5
2 Corrosion Mechanisms of Steel in Concrete
Polarization
In most cases the electrode reactions deviate from equilibrium and lead to a difference in potential.
This difference is called polarization and the steel surface is said to be polarized. The polarization is
determined by the overpotential which is the difference between the measured potential and the
corrosion potential,
, see Figure 8:
{
where
}
(14)
symbolizes the overpotential (Bardal, 2004).
It is possible to relate the overpotential, , to the reaction rate. At equilibrium stage the reaction
rates of the oxidation and reduction reactions are identical. The reaction rate is often expressed by
exchange current, , and exchange current density, . When a reaction deviates from equilibrium, a
net current flow is obtained in one of the directions. This leads to a resistance acting against the
current flow and depending on the type of resistance mainly three types of polarization can occur
simultaneously or separately from each other; activation, concentration and resistance (ohmic)
polarization, see Figure 9 (Bardal, 2004). The equations describing the polarization types, , ,
and , in the figure are introduced in Section 2.5.1-2.5.3.
Figure 8: Anodic and cathodic activation overpotential (Küter, 2009).
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2 Corrosion Mechanisms of Steel in Concrete
2.5 Polarization
Figure 9: The three types of polarization (Møller, 2009).
2.5.1 Activation Polarization
Activation polarization is a result of a resistance against the reaction itself at the interface between
metal and electrolyte. In this particular case the relationship between the overpotential, , and the
exchange current density,
, is given by the Tafel equation:
(15)
where is the exchange current density for the anode and cathode reactions respectively. The Tafel
constant is given by
(16)
where
is determined by the shape of the energy barrier that must be overcome (Bardal, 2004).
2.5.2 Concentration Polarization
Concentration polarization is caused by a difference in concentration on the electrode surface and
that of the solution (Wranglén, 1985). In this case the diffusion of ions or molecules within the
solution controls the corrosion rate (Bardal, 2004). Regarding steel in concrete concentration
polarization is often seen as a lack of oxygen.
Considering the reduction of oxygen, see Eq. (5), and a metal in an aerated solution the
concentration depends on the distance from the electrode to the surface. The overpotential is related
to the exchange current density as seen below:
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2.5 Polarization
2 Corrosion Mechanisms of Steel in Concrete
(
where
)
(17)
is given by
(18)
where is a diffusion coefficient of oxyge, the thickness of the diffusion boundary layer and
the concentration of oxygen at the boundary (Bardal, 2004).
2.5.3 Resistance Polarization
Ohmic resistance is caused by the resistivity of the electrolyte. In the case of concrete there is a
resistance when the current is transferred from the cathode to the anode via the pore solution.
Furthermore, ohmic resistance may occur on the surface layer of the metals. This phenomenon is
known for the case of oxide films on stainless steel in passive state. When the current is flowing
through the oxide film an ohmic drop is obtained and the resistance is given by Ohm’s law:
(19)
where
( ) and (
) are the resistances (Bardal, 2004).
Figure 10 shows a hypothetical cathodic and anodic polarization curve for a metal in a passive state.
The anodic polarization curve visualizes the passivation behaviour of metals and Tafel lines are
illustrated by dashed lines.
When
is increased slightly in anodic direction the polarization curve is controlled by
activation polarization. After the linear part the high corrosion rate,
, results in a high
concentration of metal ions. Here the curve is controlled by concentration polarization raising the
potential to
. In the passive region with early constant current density the curve is controlled by
the ohmic resistance. Further potential increment leads to the transpassive region, the secondary
passivity and oxygen evolution at high potentials (Küter, 2009).
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2 Corrosion Mechanisms of Steel in Concrete
2.6 Corrosion Rate
Figure 10: Hypothetical cathodic and anodic polarization curve of passive metal (Küter, 2009).
2.6
Corrosion Rate
One way of determining the corrosion rate is to use the measured potential and the corrosion
current. The relationship between these parameters is given by the Stern-Geary equation:
(
where
and
(20)
)
are the anodic and cathodic Tafel constants respectively and
the slope of the
polarization curve (Bardal, 2004; Uhlig, 1985). The slope of the polarization curve is often called
polarization resistance,
, and this notation will be used here forth. By using the Stern-Geary
equation an approximation of the exchange current is obtained. This approximation is most accurate
in a limited potential range near the corrosion potential, because a linear relationship between the
potential and the corrosion exchange current can be assumed, see Figure 11 (Bardal, 2004).
The Stern-Geary equation is often compared to the corrosion current density,
as below:
14
, and is presented
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2.6 Corrosion Rate
2 Corrosion Mechanisms of Steel in Concrete
(21)
where
is the polarized steel area and
(
is a constant containing the Tafel constants:
(22)
)
When the Tafel constants are known
is determined by using the measured polarization
resistance, . The corrosion current density expresses the amount of current per area and is related
to the thickness reduction per time which is equal to the corrosion rate. This relationship is given by
Faraday’s law:
or
(23)
where
is given in
,
is the molar mass of the metal and is the density of the metal
(Nygaard, 2009). Using the molar mass of iron,
, a metal density of
and
the relation
is obtained.
The dominating factors influencing the rate of corrosion are temperature around the corroding areas,
moisture content, given as relative humidity in the pore system, the chemical composition of the
pore solution, the porosity and the thickness of the concrete cover (Tuutti, 1982).
Figure 11: Relation between polarization and exchange current (Bardal, 2004).
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2 Corrosion Mechanisms of Steel in Concrete
2.6 Corrosion Rate
2.6.1 Influence of Temperature
The influence of temperature is important when dealing with corrosion of steel in concrete. The
effect of temperature is a complex phenomenon, which is partly due to the kinetic parameters of
corrosion, equilibrium potentials, exchange current densities and Tafel slopes, and partly due to
changes in the concrete property (Pour-Ghaz, 2008). The effect of temperature on the corrosion rate
was among others investigated by Tuutti (1982), who found that the corrosion current density,
,
changed with a factor
in the interval of
to
, see Figure 12. The figure is based on
a single carbonated concrete with a high water-to-cement ratio. Samples were conditioned at only
relative humidity. Data points in Figure 12 have been obtained by measuring different
specimens stored at a certain temperature. In the present study measurements are performed under
controlled conditions and the specimens used have been exposed to changing temperatures.
Figure 13 shows a relation between macro-cell current and temperature for steel in mortar. A
macro-cell is a form of corrosion with a net distinction between the corroding (anode) and the noncorroding (cathode) areas. Local chloride induced corrosion is a well-defined macro-cell
(Broomfield, 1997). The figure shows correlation between results obtained by Jäggi et al. (2001)
and data presented in the literature. It is seen that cell current increases with increasing temperature
similarly to Figure 12. However, the linear relationship between temperature and current observed
in Figure 12 is not reflected in Figure 13 that shows an exponential relation.
Figure 12: Measured corrosion current density, icorr, as a function of the temperature (Tuutti,
1982).
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2.6 Corrosion Rate
2 Corrosion Mechanisms of Steel in Concrete
Figure 13: Macro-cell current as a function of the temperature for steel in mortar. The macro-cell
current is given in
of the current recorded at 20 °C. Results obtained by Schiessl and Raupach
(1990), Arya and Vassie (1995), Raupach (1997b), Liu and Weyers (1998) and Jäggi et al. (2001)
are shown together (Jäggi., 2001).
2.6.2 Influence of Moisture Content
The concrete resistivity as well as the oxygen diffusion is dependent on the moisture content. The
two factors have an opposite effect on the corrosion rate. The oxygen permeability decreases with
increased moisture content curbing the corrosion rate and the resistivity of the concrete also
decreases with increased moisture content stimulating the corrosion process (Nygaard, 2009).
A relation between relative humidity and corrosion rate is presented in the work of Tuutti (1982),
see Figure 14. The figure is based on a single carbonated concrete with a high water-to-cement ratio
and shows a maximum value of corrosion current density at approximately
relative humidity.
Department of Civil Engineering - Technical University of Denmark
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2 Corrosion Mechanisms of Steel in Concrete
2.7 Activation Energy
Figure 14: Corrosion current density, icorr, as a function of the internal relative humidity (Tuutti,
1982).
2.7
Activation Energy
Any molecule in motion contains kinetic energy and the faster it moves, the greater the energy.
When molecules collide and the initial kinetic energies are large, the colliding molecules will
vibrate in such a way that some of the chemical bonds will break down. This phenomenon is the
first step toward product formation and is governed by the activation energy,
, which is the
minimum amount of energy required to initiate a chemical reaction, see figure 13. When the
activation energy is not obtained, the molecules will remain intact and product formation will not
occur due to the collision (Chang, 2008).
Figure 15: Change of potential energy as reactants, A and B, are formed to products, C and D
(Chang, 2008).
The short time effect of temperature on the corrosion current density,
Arrhenius equation:
18
, can be described by the
Department of Civil Engineering - Technical University of Denmark
2.7 Activation Energy
2 Corrosion Mechanisms of Steel in Concrete
(24)
where
is the rate constant,
the frequency constant and
the activation energy. In most cases
it is preferable to use another version of the Arrhenius equation:
(
(25)
)
where is the corrosion current density at temperature
and the corrosion current density at
temperature . The rearranged version of the Arrhenius equation, Eq. (25), describes the relative
effect of the temperature shift, i.e. the actual corrosion current density as a function of the previous
value of the corrosion current density and the temperatures (Raupach, 1997a).
The effect of resistivity is said to be one of the most important factors affecting the corrosion rate of
steel in concrete (Pour-Ghaz, 2008). The temperature effect on the resistivity can be described by
the Arrhenius equation:
(
where
2009).
)
(26)
is the resistivity at temperature
and
the resistivity at temperature
(Nygaard,
Activation energies from studies on macro-cells with chloride induced corrosion are presented in
Table 2. Raupach (1997a) stored a test specimen with water-to-cement ratio of
in a climatic
chamber at constant relative humidity and increased the temperature as seen in the table. This was
done for
and
relative humidity each for a test period of approximately
days. The
table shows that the activation energy increases with increasing relative humidity in the temperature
interval
to approximately
.
Table 2: Activation energy, , dependant on temperature and relative humidity. The result from
Bertolini and Polder (1997) is cited in Raupach (1997a).
Study
Temperature
RH
Raupach (1997a)
Bertolini and Polder (1997) 1)
1) Found for steel in concrete
Department of Civil Engineering - Technical University of Denmark
19
2 Corrosion Mechanisms of Steel in Concrete
2.8
2.8 Moisture Storage
Moisture Storage
Concrete is a porous material as illustrated in Figure 16 and due to the microstructure of the
material water is able to diffuse into the capillary cavities (Pihlajavaara, 1965). The water content in
the concrete is dependent on climatic exposure, that is, among others temperature and relative
humidity. The relation between moisture content in the concrete and relative humidity is described
by the sorption isotherms. Two different sorption curves are considered; adsorption, when the
material takes up water, and desorption, when the material releases water to the surroundings. In
Figure 17 examples of sorption isotherms are displayed at three different temperatures. With
increasing temperatures the distance between the adsorption and desorption curves seems to be
reduced.
In this project the sorption isotherms are used to estimate the change of relative humidity in the
concrete due to temperature changes. An empirical model, see Section 2.8.1, is used to estimate the
adsorption curve for different temperatures. The desorption curve is approximated using Figure 17.
Figure 16: Microstructure of a concrete paste. Areas marked with C indicate capillary cavities able
to contain air and water (Pihlajavaara, 1965).
Figure 17: Sorption isotherms at different temperatures plotted as relative humidity versus water
content in concrete (Pihlajavaara, 1965).
20
Department of Civil Engineering - Technical University of Denmark
2.8 Moisture Storage
2 Corrosion Mechanisms of Steel in Concrete
2.8.1 Prediction of Adsorption Isotherms
In a case study by Bažant et al. (1994) a prediction formula based on the famous Brunauer-EmmetTeller (BET) model has been improved. While the BET-model often only covers the relative
humidity from
to
, a BSB-model has been used to improve the prediction formulas.
Results obtained from this study are applicable in the range from
to
relative humidity.
The relation between the quantity of vapour adsorbed at pressure p in grams of water per grams of
cement paste, , and the actual pore relative humidity, , is found as:
(
where the parameter
)(
(
)
(27)
)
and monolayer capacity,
(
, are constants used in the BET-model given by:
)
(
(28)
)(
)
(29)
where is the temperature, is the age of the specimen in days and
is the water-to-cement
ratio. The parameter k is described by the BSB-model and depends on the number of adsorbed
layers at saturation state, n:
(
(
)
(30)
)(
)
The expressions for
and are only useable while
cement ratio is between
and
. The quantity of
(31)
is greater than five days and the water-toand
depends on the cement type.
The empirical formulas presented in the article predict the parameters quite accurately and can be
used to predict the adsorption isotherms for various cement pastes. Figure 18 shows a calculated
adsorption isotherm plotted with measured data for one concrete block.
Desorption isotherms are considered in Section 3.2.
Department of Civil Engineering - Technical University of Denmark
21
2 Corrosion Mechanisms of Steel in Concrete
2.8 Moisture Storage
Figure 18: Comparison of predicted curve with isotherms measured for one concrete block (Bažant
et al., 1995).
22
Department of Civil Engineering - Technical University of Denmark
3.1 Test Specimens
3 Experimental Work
3 Experimental Work
3.1
Test Specimens
The experimental work was carried out using three different types of concrete specimens (series IIII), see Table 3. The specimens were manufactured and conditioned by Nygaard (2009). The nickel
coating on series III acts as a barrier to corrosion and only the uncoated part of the reinforcement
bar,
wide, was actively corroding, see Figure 19.
Each specimen had a rectangular geometry (
) and contained ten reinforcement
bars with a diameter of
and a length of
of which
was embedded in the
concrete. Five reinforcement bars, that were assumed to be representative for the experimental
studies, were used in this project. A
-reference electrode, a mmo-titanium mesh counter
electrode (
) and two pairs of resistivity sensors were embedded in each specimen.
The counter electrode was used to supply a uniform current distribution during the measurements.
The reference electrode was placed centrally in the specimen and the counter electrode was placed
at a depth of approximately
below the concrete surface, see Figure 20.
Table 3: Properties of the test specimens (Nygaard, 2009).
Corrosion state/type
Chloride content
Reinforcement bars
Series I
Passive
Uncoated
Series II
Active/general
Uncoated
Series III
Active/localized
coated
Figure 19: Reinforcement bars used in the experiment. The part left to the vertical line was
embedded in concrete. Lower: Cleaned and uncoated bar used in series I and II. Upper: Partly
nickel coated bar used in series III. (Nygaard, 2009).
Department of Civil Engineering - Technical University of Denmark
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3 Experimental Work
3.1 Test Specimens
Figure 20: Geometry of one test specimen (Nygaard, 2009).
Each of the three climate chambers, with different initial relative humidity (
),
contained one concrete specimen from each series, see Figure 21. For each initial relative humidity
five different temperatures (
) were applied in order to measure the influence of
both temperature and moisture content on the activation energy. Freezers with installed light bulbs
were used as climate chambers controlling the temperature and saturated salt solutions were used to
control the relative humidity. For each value of the initial relative humidity two climate chambers
were used; one for the cold temperatures (
and
) and one for the warm temperatures
(
,
and
) (Nygaard, 2009).
The composition of the carbon steel used for the reinforcement bars is given in Table 4.
24
Department of Civil Engineering - Technical University of Denmark
3.1 Test Specimens
3 Experimental Work
The mix design of the concrete with a water-to-cement ratio of
is shown in Table 5. For further
details on the casting of the test specimens and the preparation of the reinforcement bars see
Nygaard (2009).
The measurements for each initial relative humidity were carried out according to the plan in Table
6. After the first measurements were performed the temperature was changed and the next
measurement took place approximately days later. Measurement number 6 was used to investigate
whether changing the temperature for the specimens in the boxes have had any influence after the
specimens have been returned to their original environments.
Figure 21: A test specimen from each series is placed in a freezer.
Table 4: Composition of the carbon steel [mass%]. The value marked with * is calculated as
remainder (Nygaard, 2009).
Department of Civil Engineering - Technical University of Denmark
25
3 Experimental Work
3.2 Equilibrium State
Table 5: Mix design of concrete (Nygaard, 2009).
Property
Unit
Amount
Cement
Water
Series I
Chloride
Series II
mass% of binder
Series III
Aggregate
Table 6: Plan of measurements.
Initial RH
3.2
Measurement
75
Temperature
85
Temperature
96
Temperature
1
2
3
4
5
6
Equilibrium State
The specimens have been cured for approximately four years and have been corroding during this
time, but it assumed not to have had any influence on the experimental work in this project due to
the low corrosion rates reported by Nygaard (2009). Changes of environmental exposure were
studied and the state of the reinforcement bars does not restrict such a study.
The time to reach temperature equilibrium in the concrete after a temperature change has been
estimated to approximately two hours as seen in Appendix A. The three days between each
measurement ensure that the conditions of a stable system have been met.
It is assumed that the moisture content in the concrete did not vary during the experiments and was
not influenced by temperature changes. This assumption is based on the fact that the exposure time
at each temperature was approximately three days.
The initial relative humidity in the concrete varied because of temperature changes resulting in a
relative humidity range for each initial value that is estimated using the sorption isotherms.
Adsorption isotherms are predicted using the BET-model, see Section 2.8.1. The moisture content
at the initial temperature and relative humidity for each series were calculated, see Appendix B. The
26
Department of Civil Engineering - Technical University of Denmark
3.2 Equilibrium State
3 Experimental Work
calculated moisture content is then kept constant in the determination of the adsorption isotherms
for the different temperatures. In this way the relative humidity in the pores can be calculated at
each temperature. In the model a concrete type of 1 is used in accordance with the concrete type
used by Nygaard (2009). The model is used to estimate the change of relative humidity with
increase of temperature.
The desorption curves in Figure 17 are used to estimate the change of relative humidity with
decrease of temperature.
Considering measurement 1 in Table 6 with a temperature of
and an initial relative humidity
of
the temperature shift to
results in a relative humidity of
, see Appendix B. An
example of using the desorption curve is shown in Figure 22 for a relative humidity of
at
. The temperature is decreased to
resulting in a relative humidity of
. Based on this
the change of relative humidity from
to
is estimated to
.
Estimations of relative humidity for all measurements are seen in Table 7.
Figure 22: Example of estimating the relative humidity due to decrease of temperature from
to
using desorption isotherms.
Table 7: Actual estimated values of relative humidity.
Initial RH
Measurement
75
RH
85
RH
96
RH
1
2
Department of Civil Engineering - Technical University of Denmark
3
4
5
27
3 Experimental Work
3.3
3.3 Test Methods
Test Methods
The galvanostatic pulse method was used to determine the free corrosion potential and the ohmic
resistance. The potentiodynamic linear polarization resistance method was used to obtain the
polarization resistance.
All measurements were performed on a single reinforcement bar acting as working electrode with
the mmo-titanium mesh as counter electrode and the
-electrode as reference. The following
measurements were carried out for each temperature:



The free corrosion potential,
The ohmic resistance,
The polarization resistance,
The test specimens were placed in climate chambers with a certain relative humidity and
temperature, see Section 3.1.
3.3.1 Galvanostatic Pulse Method
The free corrosion potential,
, was measured for the reinforcement bar versus the reference
electrode. Equilibrium was assumed when the change in potential was smaller than
over a
period of three seconds. At this point
was recorded over the next two seconds (Nygaard,
2009).
The ohmic resistance, , was measured using the galvanostatic pulse method by applying a current
pulse of
from the counter electrode for four seconds. The potential was recorded at a
frequency of
during the pulse (Nygaard, 2009).
When the current, , was applied at the time the resistance over the double layer would be zero
due to the double layer capacitance,
. At this time the potential response, , would correspond
to the ohmic resistance, , which can be calculated by fitting the measurements to the equation:
(
where
(
))
(32)
is the potential corresponding to the time, (Nygaard, 2009).
As the double layer capacitance charges, the potential response will increase exponentially, see
Figure 23. The galvanostatic pulse method assumes that the ohmic resistance,
, was constant
during measurement of the polarization resistance,
(Nygaard, 2009).
Typical results obtained using the galvanostatic pulse method on one of the actively corroding
reinforcement bars are illustrated in Figure 24. The figure shows that the free corrosion potential,
, was measured during the initial seconds and Eq. (32) is fitted in the time range
to
seconds as proposed by Nygaard (2009).
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Department of Civil Engineering - Technical University of Denmark
3.3 Test Methods
3 Experimental Work
Figure 23: Schematic illustration of the galvanostatic pulse method (Nyggard, 2008).
Figure 24: Typical short pulse data for the actively corroding reinforcement bars.
3.3.2 Potentiodynamic Linear Polarization Resistance
The potentiodynamic linear polarization resistance (LPR) method was used to determine the
polarization resistance,
. By polarizing the reinforcement bar
versus the free corrosion
potential in cathodic and anodic direction, respectively, a polarization curve can be obtained, see
Figure 25. The linear part of the polarization curve is then controlled by the polarization resistance.
The horizontal line is the free corrosion potential and the figure clearly shows how the actual
potentials differ from the equilibrium state. The measurements were performed with a target sweep
rate of
per minute corresponding to a total measurement time of
seconds (Nygaard,
2009).
Department of Civil Engineering - Technical University of Denmark
29
3 Experimental Work
3.3 Test Methods
Figure 25: Typical polarization curve as a function of time. The decreasing part of the curve is the
cathodic polarization and the increasing part is the anodic polarization.
In order to determine the polarization resistance, the cathodic curve from the LPR-measurement is
fitted to a straight line:
(33)
The cathodic and anodic curves are assumed to result in the same polarization resistance in
accordance with Figure 11.
Using Eq. (33) the slope defines the reciprocal polarization resistance and is corrected for ohmic
resistance using Eq. (32):
(34)
The polarization resistance is used when calculating the corrosion current density,
. It should
be mentioned that the ohmic drop is assumed to be negligible for the passive corroding
reinforcement bars since
(Nygaard, 2009).
The treatment of data has been performed in Matlab using the programs in Appendix C-H. Each
specimen has its own program code where the data is loaded and treated using three functions,
pulse, lpr and energy, which have been established. The function pulse returns the mean value of
the free corrosion potentials for all the reinforcement bars as well as the ohmic resistance in
accordance with Section 3.3.1. The function lpr returns the polarization resistance using the
cathodic part of the polarization curve, see Figure 25. Calculations are made in accordance with
Section 3.3.2. The function energy returns the activation energy and a fitted curve used for plotting.
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Department of Civil Engineering - Technical University of Denmark
3.4 Calculation of Activation Energy
3.4
3 Experimental Work
Calculation of Activation Energy
The corrosion current density,
, is calculated using Eq. (21). The proportionality factor, , is
set to
for the passive bars in series I and
for the actively corroding bars in series II
and III. The values of have been proposed by Andrade and Gonzalez (1978) and used in a number
of studies on corrosion of steel in concrete (Alonso et al., 1988; Glass et al., 1997; Andrade et al.,
2004; Nygaard 2009). The steel area, , of a reinforcement bar is
. Due to the low
corrosion rates reported by Nygaard (2009) the reduction of the diameter of the reinforcement bars
is approximately
after years. The LPR-method is used to determine the polarization
resistance, , as the slope of the polarization curve, see Section 0. Using the Arrhenius equation it
is possible to plot the reciprocal value of the temperature, , versus the rate constant,
, in a
logarithmic scale resulting in a correlation between the two with
is the
as the slope, where
gas constant, see Figure 26. The correlation is found using the following rearrangement of Eq. (24):
(
)
(
)
(
)
(35)
The rate constant is equal to the corrosion current density, see Eq. (25). The calculations are made
for each value of the relative humidity to investigate the influence of moisture on the activation
energy.
Figure 26: Schematic illustration of determination of activation energy.
Department of Civil Engineering - Technical University of Denmark
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4 Experimental Results
4.1 Corrosion Potential
4 Experimental Results
In Section 3.2 it was found that the initial relative humidity changed with temperature during the
experiments. The estimated ranges are seen in Table 7. In the following the relative humidity is
referred to as the initial value, that is,
relative humidity represents the range from
to
relative humidity.
4.1
Corrosion Potential
The free corrosion potentials measured for each series of specimens are shown in Figure 27-29. The
potentials are calculated as mean values for the five reinforcement bars considered for each
specimen using the galvanostatic pulse method, see Section 0. The values of
have been
excluded if they are not within one standard deviation when all five bars are considered. The
standard deviations can be seen in Appendix I. The corrosion potentials have been measured using
the embedded
-reference electrode and have been converted from
versus
to
versus
according to Table 1. The figures show the change of the free corrosion potential
as a function of temperature and include measured values for the different values of the relative
humidity;
,
and
.
Figure 27 shows that there is no distinct correlation between the potentials for the passive
reinforcement bars and temperature or relative humidity. The potentials range from
to
versus
.
Figure 27: Corrosion potentials,
reinforcement bars exposed to
(
humidity.
32
, as a function of temperature for the passive corroding
) ,
(
) and
(
) relative
Department of Civil Engineering - Technical University of Denmark
4.1 Corrosion Potential
4 Experimental Results
The potentials for the generally actively corroding reinforcement bars show a major influence of
relative humidity. In general the measured potentials are lower for higher relative humidity at each
temperature with exceptions at
and
. The potentials are highest at
for all values of
the relative humidity though at
for
relative humidity the potential is slightly higher.
Lower potentials are observed for
relative humidity. The potentials range from
to
versus
.
The potentials for the actively corroding nickel coated reinforcement bars are mixed values because
they represent both the non-corroding nickel coated parts of the reinforcement bars and the actively
corroding uncoated carbon steel band which is
wide. There seem to be no distinct relations
between measured potentials and neither temperature nor relative humidity overall. The potentials
at
and
relative humidity are quite similar with the largest difference being
at
. At
relative humidity the potentials are higher with higher temperature except from
to
. The lowest potentials are observed at
except for
relative humidity where the
potentials are much lower for all temperatures, which deviate from the appearance of the two other
curves. The potentials range from
to
versus
.
Figure 28: Corrosion potentials,
, as a function of temperature for the generally active
corroding reinforcement bars exposed to
(
) ,
(
) and
(
)
relative humidity.
Department of Civil Engineering - Technical University of Denmark
33
4 Experimental Results
4.1 Corrosion Potential
Figure 29: Corrosion potentials,
, as a function of temperature for the generally active
corroding reinforcement bars exposed
(
) ,
(
) and
(
)
relative humidity.
Generally the potentials for series II are much lower than for series I and III while the highest
potentials are observed for series I when excluding
relative humidity for series III.
Table 8 contains the corrosion potentials for each series at the first and last day of measuring. It is
seen that there are some differences in the measured corrosion potentials. For series I the largest
numerically difference is
versus
and for series II and III it is
and
versus
, respectively.
Table 8: Corrosion potentials for the first and last measurement.
Initial RH
34
Series
I
II
III
Measurement
Department of Civil Engineering - Technical University of Denmark
4.2 Polarization Resistance
4.2
4 Experimental Results
Polarization Resistance
The polarization resistance,
, is calculated using the LPR-method, see Section 3.3.2, and is
corrected with the ohmic resistance, , found with the galvanostatic pulse method, see Eq. (32).
For the passive reinforcement bars in series I there seems to be no distinct correlation between the
polarization resistance and temperature or relative humidity, though for
relative humidity it is
decreasing with increasing temperature except at
, see Figure 30. The values range from
to
.
For the generally active corroding reinforcement bars in series II the polarization resistance is
higher for low temperatures, see Figure 31. For
relative humidity the values are decreasing
with increasing temperature and for
relative humidity the values are only changing slightly
from
to
. This is also true for
relative humidity from
to
. For lower
relative humidity the temperature seems to have a more pronounced effect and the differences
between the lowest and the highest values observed are smaller. The values range from
to
.
Figure 32 shows that the polarization resistances for the actively corroding nickel coated
reinforcement bars for
and
relative humidity are very similar, which was also the case
for the corrosion potentials, see Figure 29. For
relative humidity at
and
the values
of the polarization resistance are exceptionally high. The values range from
to
.
In general observed polarization resistances for series II and III are much lower than for series I.
Figure 30: Polarization resistance, , as a function of temperature for the passive reinforcement
bars exposed to
(
) ,
(
) and
(
) relative humidity.
Department of Civil Engineering - Technical University of Denmark
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4 Experimental Results
4.2 Polarization Resistance
Figure 31: Polarization resistance, , as a function of temperature for the generally active
corroding reinforcement bars exposed to
(
) ,
(
) and
(
relative humidity.
)
Figure 32: Polarization resistance, , as a function of temperature for the actively corroding
nickel coated reinforcement bars exposed to
(
) ,
(
) and
(
) relative humidity.
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Department of Civil Engineering - Technical University of Denmark
4.3 Corrosion Current Density
4.3
4 Experimental Results
Corrosion Current Density
The corrosion current densities,
, are calculated using the polarization resistances from Section
4.2 and Eq. (34). For the passive reinforcement bars the proportionality factor, , is set to
and for the actively corroding bars it is
. The quantities of corrosion current densities directly
reflect the polarization resistances for each series. It is seen that the values are generally higher for
specimens exposed to
relative humidity. The curve representing
relative humidity
generally decreases with increasing temperatures and deviates from the appearance of the two other
curves. The values range from
to
.
The corrosion current densities for series II generally increases with increasing relative humidity
with the exception of
relative humidity, see Figure 34.The influence of temperature generally
results in higher corrosion current densities with increased temperature and is more evident for
than for
relative humidity. For
there is only a slight change in the values from
to
and for
relative humidity the same is true from
to
. The values
range from
to
.
The corrosion current densities for series III generally increase with increasing temperature, see
Figure 35. From
to
for
relative humidity there is a slight decrease in the corrosion
current densities. For
relative humidity at
or
there is a deviation from the overall
correlation between corrosion current density and temperature. The influence of the relative
humidity is not clear as the corrosion current densities are lower at
relative humidity than
and the highest values are seen for
relative humidity. The values range from
to
.
Figure 33: Corrosion current density,
reinforcement bars exposed to
(
humidity.
, as a function of temperature for the passive
) ,
(
) and
(
) relative
Department of Civil Engineering - Technical University of Denmark
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4 Experimental Results
4.3 Corrosion Current Density
Figure 34: Corrosion current density,
reinforcement bars exposed to
(
humidity.
, as a function of temperature for the generally active
) ,
(
) and
(
) relative
Figure 35: Corrosion current density,
, as a function of temperature for the actively corroding
nickel coated reinforcement bars exposed to
(
) ,
(
) and
(
) relative humidity.
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Department of Civil Engineering - Technical University of Denmark
4.4 Activation Energy
4.4
4 Experimental Results
Activation Energy
The activation energy is calculated as described in Section 2.6.1 and Section 3.4. Using the
corrosion current density as rate constant it is plotted in a logarithmic scale versus the reciprocal
value of temperature. In this way the activation energy can be found as the slope of the fitted line,
see Figure 36-38. The calculated values of the activation energy can be seen in Table 9.
There seems to be no distinctive relation between activation energy and relative humidity. It is seen
from the table that the activation energy for series I is highest for
relative humidity. For series
II the highest value is obtained for
relative humidity. For series III the maximum value of the
activation energy is seen for
relative humidity.
Overall series II shows the highest value for
relative humidity while the values for series III
are highest for the other two values of relative humidity. For series I for
relative humidity the
slope is negative and deviates from all other results. The fitted lines are best for series II, with the
exception of
relative humidity, and series III, with the exception of
relative humidity,
see Figure 36-38.
Table 9: Calculated values of the activation energy,
Initial RH
Series
I
II
.
III
Figure 36: Rate constant versus the reciprocal value of temperature for the passive reinforcement
bars exposed to
(
) ,
(
) and
(
) relative humidity.
Activation energy, , is defined as the slope of the fitted curves.
Department of Civil Engineering - Technical University of Denmark
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4 Experimental Results
4.4 Activation Energy
Figure 37: Rate constant versus the reciprocal value of temperature for the generally active
reinforcement bars exposed to
(
) ,
(
) and
(
) relative
humidity. Activation energy, , is defined as the slope of the fitted curves.
Figure 38: Rate constant versus the reciprocal value of temperature for the actively corroding
nickel coated reinforcement bars exposed to
(
) ,
(
) and
(
) relative humidity. Activation energy, , is defined as the slope of the fitted curves.
Due to the changes of temperature the relative humidity changed in the pores during the experiment.
The values of relative humidity were estimated in Table 7 and in order to investigate the activation
energy for a rather constant relative humidity only some of the measurements are considered.
40
Department of Civil Engineering - Technical University of Denmark
4.4 Activation Energy
4 Experimental Results
The target relative humidity of
is represented by measurements , , and for initial
relative humidity of
and also measurement for initial relative humidity of
. This results
in five data points for temperatures
,
,
,
and
and a relative humidity
range of
.
The target relative humidity
points for temperatures
,
is represented by measurements , and resulting in three data
and
and a relative humidity range of
.
All measurements are used for target relative humidity
due to the more or less constant
relative humidity and the activation energies are seen in Table 9.
This selection of data results in activation energies shown in Table 10 and Figure 39-41.
Table 10: Calculated values of the activation energy for rather constant relative humidity.
Range of RH
Series
I
II
Figure 39: Activation energy for series I when considering the ranges
relative humidity.
Department of Civil Engineering - Technical University of Denmark
III
and
41
4 Experimental Results
4.4 Activation Energy
Figure 40: Activation energy for series II when considering the ranges
relative humidity.
Figure 41: Activation energy for series III when considering the ranges
relative humidity.
42
and
and
Department of Civil Engineering - Technical University of Denmark
5.1 Sources of Error
5 Discussion
5 Discussion
In this section the impact of the temperature and relative humidity on the various corrosion specific
parameters is discussed based on the experimental results presented in Section 4. Furthermore, the
influence of both temperature and relative humidity on activation energy is discussed.
5.1
Sources of Error
Data was measured with an uncertainty of measurements within
and
due to the salt
solutions dependency on temperature (Nygaard, 2009; Bates et al., 1960). This could have caused
larger ranges of relative humidity than the estimated values in Table 7.
In order to evaluate deviations in the experimental results, mean values and standard deviations for
the free corrosion potential, the ohmic resistance and the polarization resistance have been
calculated and are seen in Appendix I in Table I1 to Table I3.
Considering the free corrosion potential for series I for
relative humidity measurement 4 and
5, temperatures
and
, have rather large standard deviations and might cause error. For
and
relative humidity the deviations are smaller.
For series II at
relative humidity measurement 2, temperature
, shows a large standard
deviation. The same is true for measurement 4 and 5 for
relative humidity, temperatures
and
. The values measured for series III at
relative humidity show clear deviations for
measurement 3, 4 and 5, temperatures
,
and
. For
relative humidity the values
of the corrosion potential show high standard deviations and should not be considered. For
relative humidity all measured values show low standard deviations except measurement number 1
and 2, temperatures
and
.
It is clearly seen from the tables in Appendix I that the polarization resistance for series I is higher
than for series II and series III, which corresponds to the fact that series I is the passive
reinforcement bars. There is, however, a large deviation in measured polarization resistance values
suggesting the difficulty in determining the correct values for passive steel bars. It should also be
noted, that for series I the ohmic resistance is much smaller than the polarization resistance.
For series II the polarization resistance values deviates much less than for series I. Measurement
number 2 and 4, temperatures
and
, for series III at
relative humidity have large
deviations of both the ohmic drop and the polarization resistance.
When determining the ohmic resistance in Section 3.3.1 from the measured short pulse data a time
range from to
seconds were fitted to Eq. (32). This range has been chosen as suggested by
Nygaard (2009) and the calculated values would change with use of another time range.
Department of Civil Engineering - Technical University of Denmark
43
5 Discussion
5.2
5.2 Temperature
Temperature
For the passive corroding reinforcement bars, series I, no distinct effect of the temperature on the
free corrosion potential and corrosion current densities were observed, see Figure 27 and Figure 33.
The passive oxide layer on the reinforcement bars in series I, which requires a high pH value and
sufficient amount of oxygen, seems to have been maintained in spite of the environmental changes.
Specimens from series II and III contain chloride, which have resulted in a breakdown of the
passive oxide layer.
The corrosion potentials for the generally actively corroding reinforcement bars, series II, for
and
relative humidity are increasing from
to
and decreasing from
to
.
The curve for
relative humidity shows no clear correlation with the appearance of the other
curves. No clear influence of temperature is seen. Considering the curve for
relative humidity
for series II the free corrosion potentials are relatively constant with temperature while the corrosion
rates are increasing. The mechanisms controlling the corrosion process can be evaluated using the
Evans diagrams in Figure 42. The corrosion is seen to be controlled by resistance polarization. For
relative humidity the corrosion current densities are more or less constant from
to
contrary to results by Nygaard (2009) and Tuutti (1982), see Figure 14, the corrosion current
densities are lower than for
relative humidity. The constant values can be explained by the
corrosion process being under a combination of anodic and resistance control (Nygaard, 2009). In
the temperature range from
to
for
relative humidity the corrosion potentials are
decreasing, when considering numerical values, and corresponding corrosion current densities are
increasing. Considering Figure 42 the corrosion process is under anodic control. Similar results
have been reported by Glass et al. (1991) on a polarization resistance probe exposed to a carbonated
mortar containing
chloride. In the present work, however, it is found when only three
different temperatures are considered. From
to
there is a slight decrease in the free
corrosion potentials, when considering numerical values, while the corrosion current densities are
also slightly decreasing. Therefore when considering the whole temperature range for
relative
humidity no clear conclusion can be made.
The potentials for the actively corroding nickel coated reinforcement bars, series III, show no clear
influence of temperature for
relative humidity and it is relatively constant in the temperature
range
to
while the corrosion current densities are increasing slightly suggesting that the
corrosion process is under resistance control. The potentials are increasing, when considering
numerical values, with increasing temperature for
relative humidity while there is no clear
correlation between the corrosion current densities and temperature. The curve for
relative
humidity is not considered due to major deviations, see Table H3 in Appendix I.
44
Department of Civil Engineering - Technical University of Denmark
5.2 Temperature
5 Discussion
Figure 42: Evans diagrams showing the increase in corrosion rate from
to
and
corresponding changes in corrosion potential from
to
resulting from (a) a process
under anodic control, (b) a process under cathodic control and (c) a process under resistance
control (Glass et al., 1991).
Figure 43: Relationship between corrosion potential and corrosion rate obtained on a polarization
resistance probe exposed to a carbonated mortar containing
chloride (Glass et al., 1991).
Department of Civil Engineering - Technical University of Denmark
45
5 Discussion
5.3
5.3 Relative Humidity
Relative Humidity
Moisture is required for transport of ions and therefore the corrosion rate is expected to be
influenced by relative humidity. The impact of relative humidity on the corrosion potentials is
different for each of the series of concrete elements. For series I there is no clear impact of the
relative humidity on neither the free corrosion potential,
, nor the corrosion current density,
, which corresponds to the fact that the reinforcement bars are passive and under anodic
control. This is seen from the low corrosion rates, Figure 33. There is no influence from
concentration polarization on the corrosion process since the decreased oxygen permeability as a
result of increased moisture content is not resulting in decreased corrosion rates. The corrosion is
then controlled by activation and resistance polarization. The unit of the corrosion current densities
are converted from
to
and the values obtained in the present work are
,
and
for
,
and
relative humidity,
respectively.
Omitting the curve for
relative humidity there is a clear correlation between the corrosion
potential and the relative humidity for series II with the general corroding reinforcement bars.
Increased relative humidity results in decreased potentials. The corrosion current density increases
with increased relative humidity in general. This is in correspondence with the results obtained by
Tuutti (1982), see Figure 14. For
the corrosion current densities are
,
and
for
,
and
relative humidity, respectively. The values
obtained at
are used for comparison with the results reported by Tuutti (1982) in Figure 44.
The results are a product of a long-term study and have been obtained at
for concrete with a
water-to-cement ratio of
. Tuutti (1982) reported higher corrosion rates than those measured in
the present work and differences in water-to-cement ratio, temperature and chloride content are
causing the deviations. Comparing the corrosion rates to those obtained at a higher water-to-cement
ratio Figure 44 suggests slightly lower values for
relative humidity. The corrosion rates for
series I and II can be seen in Figure 45 and it is clear that the values are much higher for chloride
induced corrosion.
For series III the area used, when calculating the corrosion current density, is the full steel area
including the nickel coated parts and not only the corroding part of the reinforcement bars. This is
done due to the non-uniform current distribution when performing the LPR measurements
(Nygaard, 2009). The obtained values of the polarisation resistance,
, should be considered
apparent values, which is also the case for
. This, however, still allows for an internal
comparison of the data measured for series III for different temperatures and relative humidity. The
curve for
relative humidity deviates a lot and should be disregarded. In general the corrosion
potentials are slightly lower and the corrosion current densities are slightly larger for
than for
relative humidity.
Compared to the work of Nygaard (2009) the same tendencies for all series can be observed
regarding the influence of relative humidity.
46
Department of Civil Engineering - Technical University of Denmark
5.3 Relative Humidity
5 Discussion
Figure 44: Measured rate of corrosion (
) on the total metal area as a
function of relative humidity for carbonated mortar and concrete with
. Dotted lines
correspond to maximum and minimum values at data points with major variations (Tuutti, 1982).
Figure 45: Measured rate of corrosion (
(
) ,
(
) and
(
)
) for series I and II for
relative humidity.
Influence of relative humidity on the activation energy is considered by comparing the measured
data to the values in Table 2, which contains activation energies from other studies. In order to do
this the activation energies are shown in the temperature interval from
to
, see Table 11.
The results show no clear relation to the studies of Raupach (1997a) regarding increased activation
energy with increased relative humidity. For
relative humidity the values for the chloride
induced corrosion, series II and III, are
and
, respectively. These results are
similar to the activation energy of
for
relative humidity as presented by
Raupach (1997a). The measured values for
relative humidity are disregarded due to negative
Department of Civil Engineering - Technical University of Denmark
47
5 Discussion
5.3 Relative Humidity
activation energies. There are some large standard deviations at this relative humidity for series III
and measurement 4 and 5 clearly deviates from the rest, see Table I3 in Appendix I, suggesting a
very low corrosion current density at
and
. Series III, however, is nickel coated and only
apparent values are obtained due to this. Therefore the basis for comparison is rather week.
If a temperature interval of
to
and a relative humidity of
is used, in order to
simulate the temperature range used by Bertolini and Polder (1997), series II has an activation
energy of
. The reported value in the study is
and is similar, see Table 2.
The activation energies for the relative humidity ranges given in Table 10 do not show a clear
influence of the relative humidity. The relative humidity range of
is based on only three
data points and can not be compared with those of
due to different temperature
intervals.
Table 11: Calculated values of the activation energy,
for chloride induced corrosion.
Initial RH
48
Series
, in the temperature range
II
to
III
Department of Civil Engineering - Technical University of Denmark
6 Conclusion
6 Conclusion
The following conclusions can be drawn from the results presented in this report:

No short-term influence of temperature and moisture was seen on the passive reinforcement
bars and low corrosion rates were observed.

The polarization resistance in concrete with passive reinforcement showed large deviations.

For the actively corroding reinforcement bars in specimens containing chloride higher
corrosion rates were observed and increase in relative humidity resulted in an increase of the
corrosion potentials and corrosion current densities in general.

Temperature affects both the free corrosion potential as well as corrosion current density for
the actively corroding reinforcement bars, however, no clear trend was observed.

The highest values of activation energies of corrosion of steel in concrete were observed for
specimens with mixed-in chloride, but no clear effect of relative humidity was seen.
Department of Civil Engineering - Technical University of Denmark
49
Bibliography
Bibliography
Arya, C. and Vassie, P. R. W. “Influence of Cathode-to-anode Area Ration and Separation
Distance on Galvanic Corrosion Currents of Steel in Concrete Containing Chlorides”. Cement and
Concrete Research (1995).
Bardal, E. “Corrosion and Protection”. Engineering Materials and Processes London, UK:
Springer, 1st edition, (2004).
Bates, D., Winston, P. “Saturated Solutions For the Control of Humidity in Biological
Research”. Ecological Society of America, (1960).
Bažant, Z., Jennings, H., Xi, Y. “Moisture Diffusion in Cementitious Materials: Adsorption
Isotherms”. Department of Civil Engineering, Northwestern University, Evanston, Illinois, (1994).
Broomfield, J. P. “Corrosion of Steel in Concrete”. E & FN Spon, (1997).
Chang, R. “General Chemistry: The Essential Concepts”. McGraw Hill International Edition,
5th edition, (2008).
Glass, G., Page, C., Short, N. “Factors Affecting the Corrosion Rate of Steel in Carbonated
Mortars”. Department of Civil Engineering, Aston University, Birmingham, U.K., (1991).
Jäggi, S. “Experimentelle und numerische Mudellerung der lokalen Korrosion von Stahl in
Beton”. Ph.D. Thesis. ETh Zürich (2001).
Jäggi, S., Böhni, H., and Elsener, B. “Macrocell Corrosion of Steel in Concrete - Experiments
and Numerical Modelling”. European Federation of Corrosion, (2001).
Küter, A. “Management of Reinforcement Corrosion. A Thermodynamical Approach”. Ph.D.
Thesis. Department of Civil Engineering. Technical University of Denmark, (2009).
Liu, T. and Weyers, R. W. “Modeling the Dynamic Corrosion Process in Chloride
Contaminated Structures”. Cement and Concrete Research, (1998).
Mattsson, E. “Basic Corrosion Technology for Scientists and Engineers”. The Institute of
Materials, (1996).
Møller, P. “Lecture Notes”, Course: Corrosion (Theory and Engineering), Technical
University of Denmark, (2009).
Nürnberger, U. “Corrosion Induced Cracking of Reinforcing Steel”. In Mietz, J., Elsener, B.,
and Polder, R., editors, Corrosion of Reinforcement in Concrete - Monitoring, Prevention and
Rehabilitation. IOM Communications, (1997).
Nygaard, P. V. “Non-destructive Electrochemical Monitoring of Reinforcement Corrosion”.
Ph.D. Thesis. Department of Civil Engineering. Technical University of Denmark, (2009).
Pihlajavaara, S. “On the Main Features and Methods of Investigation of Drying and Related
Phenomena in Concrete”. University of Helsinki, Philosophical Faculty, Division for Mathematics
and Natural Sciences, (1965).
Pour-Ghaz, M., Isgor, O. Burkan, Ghods, P. “The Effect of Temperature on the Corrosion of
Steel in Concrete”. Journal of Corrosion Science 51, (2008).
Raupach, M. “Effect of Temperature on Chloride Induced Steel Corrosion in Concrete”. In
Bardal, E., editor, EUROCORR 97, The European Corrosion Congress, Event No. 208, European
Federation of Corrosion, Tapir, (1997a).
50
Department of Civil Engineering - Technical University of Denmark
Bibliography
Raupach, M. “Results from Laboratory Tests and Evaluation of Literature on the Influence of
Temperature on Reinforcement Corrosion”. In Mietz, J., Elsener, B., and Polder, R., editors,
Corrosion of Reinforcement in Concrete - Monitoring, Prevention and Rehabilitation. IOM
Communications, (1997b).
Schiessl, P. and Raupach, M. “Influence of Concrete Composition and Microclimate on the
Critical Chloride Content in Concrete”. In Page, C. L., Treadaway, K. W. J., and Bamforth, P. B.
editors, Corrosion of Reinforcement in Concrete. Society of Chemical Industry. Elsevier Applied
Science, (1990).
Tuutti, K. “Corrosion of Steel in Concrete”. CBI forskning/research, Swedish Cement and
Concrete Research Institute, (1982).
Uhlig, H. H., Revie, R. W. “Corrosion and Corrosion Control”. John Wiley & Sons, Inc,
(1985).
Wranglen, G. “An Introduction to Corrosion and Protection of Metals”. Chapman and Hall,
(1985).
Department of Civil Engineering - Technical University of Denmark
51
List of Figures
List of Figures
Figure 1: Fundamental mechanism for corrosion (Küter, 2009). ........................................................ 3
Figure 2: Dependence of chloride threshold on concrete properties and exposure conditions (Küter,
2009). ................................................................................................................................................... 6
Figure 3: Sketch of a corrosion pit in iron. Potential referred to a standard hydrogen electrode
(SHE) (Bardal, 2004). .......................................................................................................................... 7
Figure 4: Pitting potential curves for different chloride concentrations: Clpit,ia=10-2 mol/L, Clpit,ia=101
mol/L and Clpit,ia=1 mol/L. Index ia stands for ion activity (Küter, 2009). ....................................... 7
Figure 5: Left: Reinforcing steel after corrosion fatigue test. Right: Pitting induced corrosionfatigue in chloride-containing concrete (Nürnberger, 1997). .............................................................. 8
Figure 6: Corrosion potential, Ecorr, as a mixed value between E0,a (anodic potential) and E0,c
(cathodic potential). icorr is the exchange current density (Küter, 2009). ............................................. 9
Figure 7: Pourbaix diagram of iron in water at 25 °C. [A]: Immune, passive and corrosive domains.
[B]: Dominant species in their stability domains (Küter, 2009). ....................................................... 10
Figure 8: Anodic and cathodic activation overpotential (Küter, 2009). ............................................ 11
Figure 9: The three types of polarization (Møller, 2009). ................................................................. 12
Figure 10: Hypothetical cathodic and anodic polarization curve of passive metal (Küter, 2009). .... 14
Figure 11: Relation between polarization and exchange current (Bardal, 2004)............................... 15
Figure 12: Measured corrosion current density, icorr, as a function of the temperature (Tuutti, 1982).
............................................................................................................................................................ 16
Figure 13: Macro-cell current as a function of the temperature for steel in mortar. The macro-cell
current is given in of the current recorded at 20 °C. Results obtained by Schiessl and Raupach
(1990), Arya and Vassie (1995), Raupach (1997b), Liu and Weyers (1998) and Jäggi et al. (2001)
are shown together (Jäggi., 2001). ..................................................................................................... 17
Figure 14: Corrosion current density, icorr, as a function of the internal relative humidity (Tuutti,
1982). ................................................................................................................................................. 18
Figure 15: Change of potential energy as reactants, A and B, are formed to products, C and D
(Chang, 2008)..................................................................................................................................... 18
Figure 16: Microstructure of a concrete paste. Areas marked with C indicate capillary cavities able
to contain air and water (Pihlajavaara, 1965). ................................................................................... 20
Figure 17: Sorption isotherms at different temperatures plotted as relative humidity versus water
content in concrete (Pihlajavaara, 1965). ........................................................................................... 20
Figure 18: Comparison of predicted curve with isotherms measured for one concrete block (Bažant
et al., 1995)......................................................................................................................................... 22
52
Department of Civil Engineering - Technical University of Denmark
List of Figures
Figure 19: Reinforcement bars used in the experiment. The part left to the vertical line was
embedded in concrete. Lower: Cleaned and uncoated bar used in series I and II. Upper: Partly
nickel coated bar used in series III. (Nygaard, 2009). ....................................................................... 23
Figure 20: Geometry of one test specimen (Nygaard, 2009). ............................................................ 24
Figure 21: A test specimen from each series is placed in a freezer. .................................................. 25
Figure 22: Example of estimating the relative humidity due to decrease of temperature from
to
using desorption isotherms. .................................................................................................... 27
Figure 23: Schematic illustration of the galvanostatic pulse method (Nyggard, 2008). .................... 29
Figure 24: Typical short pulse data for the actively corroding reinforcement bars. .......................... 29
Figure 25: Typical polarization curve as a function of time. The decreasing part of the curve is the
cathodic polarization and the increasing part is the anodic polarization. .......................................... 30
Figure 26: Schematic illustration of determination of activation energy........................................... 31
Figure 27: Corrosion potentials,
, as a function of temperature for the passive corroding
reinforcement bars exposed to
(
) ,
(
) and
(
) relative
humidity. ............................................................................................................................................ 32
Figure 28: Corrosion potentials,
, as a function of temperature for the generally active
corroding reinforcement bars exposed to
(
) ,
(
) and
(
)
relative humidity. ............................................................................................................................... 33
Figure 29: Corrosion potentials,
, as a function of temperature for the generally active
corroding reinforcement bars exposed
(
) ,
(
) and
(
)
relative humidity. ............................................................................................................................... 34
Figure 30: Polarization resistance,
bars exposed to
(
) ,
, as a function of temperature for the passive reinforcement
(
) and
(
) relative humidity. .......... 35
Figure 31: Polarization resistance, , as a function of temperature for the generally active
corroding reinforcement bars exposed to
(
) ,
(
) and
(
)
relative humidity. ............................................................................................................................... 36
Figure 32: Polarization resistance, , as a function of temperature for the actively corroding nickel
coated reinforcement bars exposed to
(
) ,
(
) and
(
)
relative humidity. ............................................................................................................................... 36
Figure 33: Corrosion current density,
, as a function of temperature for the passive
reinforcement bars exposed to
(
) ,
(
) and
(
) relative
humidity. ............................................................................................................................................ 37
Figure 34: Corrosion current density,
, as a function of temperature for the generally active
reinforcement bars exposed to
(
) ,
(
) and
(
) relative
humidity. ............................................................................................................................................ 38
Department of Civil Engineering - Technical University of Denmark
53
List of Figures
Figure 35: Corrosion current density,
, as a function of temperature for the actively corroding
nickel coated reinforcement bars exposed to
(
) ,
(
) and
(
) relative humidity. .................................................................................................................... 38
Figure 36: Rate constant versus the reciprocal value of temperature for the passive reinforcement
bars exposed to
(
) ,
(
) and
(
) relative humidity.
Activation energy, , is defined as the slope of the fitted curves. ................................................... 39
Figure 37: Rate constant versus the reciprocal value of temperature for the generally active
reinforcement bars exposed to
(
) ,
(
) and
(
) relative
humidity. Activation energy, , is defined as the slope of the fitted curves. .................................. 40
Figure 38: Rate constant versus the reciprocal value of temperature for the actively corroding nickel
coated reinforcement bars exposed to
(
) ,
(
) and
(
)
relative humidity. Activation energy, , is defined as the slope of the fitted curves. ..................... 40
Figure 39: Activation energy for series I when considering the ranges
and
relative humidity. ............................................................................................................................... 41
Figure 40: Activation energy for series II when considering the ranges
and
relative humidity. ............................................................................................................................... 42
Figure 41: Activation energy for series III when considering the ranges
and
relative humidity. ............................................................................................................................... 42
Figure 42: Evans diagrams showing the increase in corrosion rate from
to
and
corresponding changes in corrosion potential from
to
resulting from (a) a process
under anodic control, (b) a process under cathodic control and (c) a process under resistance control
(Glass et al., 1991). ............................................................................................................................ 45
Figure 43: Relationship between corrosion potential and corrosion rate obtained on a polarization
resistance probe exposed to a carbonated mortar containing
chloride (Glass et al., 1991)..... 45
Figure 44: Measured rate of corrosion (
) on the total metal area as a
function of relative humidity for carbonated mortar and concrete with
. Dotted lines
correspond to maximum and minimum values at data points with major variations (Tuutti, 1982). 47
Figure 45: Measured rate of corrosion (
(
) ,
(
) and
54
(
)
) for series I and II for
relative humidity. .................................... 47
Department of Civil Engineering - Technical University of Denmark
List of Tables
List of Tables
Table 1: Electrode potentials for reference electrodes on the hydrogen scale at 25 °C. .................... 10
Table 2: Activation energy, , dependant on temperature and relative humidity. The result from
Bertolini and Polder (1997) is cited in Raupach (1997a)................................................................... 19
Table 3: Properties of the test specimens (Nygaard, 2009). .............................................................. 23
Table 4: Composition of the carbon steel [mass%]. The value marked with * is calculated as
remainder (Nygaard, 2009). ............................................................................................................... 25
Table 5: Mix design of concrete (Nygaard, 2009). ............................................................................ 26
Table 6: Plan of measurements. ......................................................................................................... 26
Table 7: Actual estimated values of relative humidity. ..................................................................... 27
Table 8: Corrosion potentials for the first and last measurement. ..................................................... 34
Table 9: Calculated values of the activation energy,
. .................................................................. 39
Table 10: Calculated values of the activation energy for rather constant relative humidity. ............ 41
Table 11: Calculated values of the activation energy, , in the temperature range
to
for chloride induced corrosion. .......................................................................................................... 48
Department of Civil Engineering - Technical University of Denmark
55
Appendix A
Appendix A: Time to Reach Temperature Equilibrium
In this appendix the results obtained for the time to reach temperature equilibrium inside the
concrete are shown. The calculations have been performed using a Finite Element Method with the
parameters
,
and
. Results are seen in Figure A1.
330
Temperature [K]
320
310
T 0-50
T 0-40
300
T 0-30
290
T 0-20
T 0-10
280
270
0
0,5
1
1,5
2
2,5
3
Time [h]
Figure A1: Time to reach temperature equilibrium in concrete.
56
Department of Civil Engineering - Technical University of Denmark
Appendix B
Appendix B: Prediction of Adsorption Isotherms
In this appendix the results obtained using the empircal BET-model are shown. The calculations
have been performed in Excel.
Constants
w/c
C0
Vct
Nct
t
Equations
Vm
n
0.5
855
0.9
1
730
0.06550
3.6044
type 1
type 1
days
RH [%] T [° C]
75
25
35
50
1
15
T [° K]
298
308
323
274
288
C
17.62
16.05
14.11
22.66
19.47
k
0.7059
0.7041
0.7014
0.7097
0.7075
w [g/g]
0.132
0.132
0.132
0.132
0.132
H [%]
75.00
75.47
76.19
73.92
74.54
RH [%] T [° C]
85
35
25
50
1
15
T [° K]
308
298
323
274
288
C
16.05
17.62
14.11
22.66
19.47
k
0.7041
0.7059
0.7014
0.7097
0.7075
w [g/g]
0.157
0.157
0.157
0.157
0.157
H [%]
85.00
84.60
85.62
83.69
84.21
RH [%] T [° C]
96
15
1
50
35
25
T [° K]
288
274
323
308
298
C
19.47
22.66
14.11
16.05
17.62
k
0.7075
0.7097
0.7014
0.7041
0.7059
w [g/g]
0.199
0.199
0.199
0.199
0.199
H [%]
96.00
95.55
97.23
96.68
96.34
Department of Civil Engineering - Technical University of Denmark
57
Appendix C
Appendix C: Matlab Function pulse
In this appendix the Matlab function pulse is shown. It uses the short pulse data as input and returns
the mean of the free corrosion potentials and the mean of the ohmic resistance for a single specimen
as output.
% Input: Short pulse data.
% Output: Free corrosion potential, Ecorr, and ohmic resistance, Rohm.
function output = pulse(data)
area = 2*pi*0.005*0.200;
xdata = [4.1:0.1:5.5];
start = [50 100 0.3];
lb = [10,1,0.01];
ub = [10e6 10e6 5];
%
%
%
%
%
Steel surface area [m^2]
Time range [s]
Start values
Lower boundary
Upper boundary
% Loop through all available reinforcement bars.
for i = 1:size(data,1)
% The free corrosion potential is calculated as a mean of the first 2
% seconds of the data. The potential range corresponding to xdata is
% stored in ydata.
Ecorr(i) = -mean(data(i,5:24))*1e-3;
% Potential [mV]
ydata = -(data(i,47:61)*1e-3+Ecorr(i)); % Potential [mV]
% The data is fitted to Eq. (32).
f=fittype('-25*1e-3*Rohm-25*1e-3*Rp*(1-exp(-x/(Rp*Cdl)))');
f1=fit(xdata',ydata',f,'StartPoint',start,'MaxFunEvals',5000,'Lower',lb,'Upper',
ub);
values(i,:)=coeffvalues(f1);
calc(i,:)=[Ecorr(i) values(i,:)];
end
MEcorr = mean(calc(:,1));
SEcorr = std(calc(:,1));
k=1;
% Mean, Ecorr [mV]
% Standard deviation, Ecorr [mV]
% Values of Ecorr deviating more than one standard deviation from the mean
% are excluded. The remaining values are stored in REcorr.
for i = 1:size(calc(:,1))
if calc(i,1)>MEcorr-SEcorr && calc(i,1)<MEcorr+SEcorr
REcorr(k,:) = calc(i,1);
k=k+1;
end
end
MRohm = mean(calc(:,3));
SRohm = std(calc(:,3));
k=1;
% Mean, Rohm [Ohm]
% Standard deviation, Rohm [Ohm]
% Values of Rohm deviating more than one standard deviation from the mean
% are excluded. The remaining values are stored in RRohm.
58
Department of Civil Engineering - Technical University of Denmark
Appendix C
for i = 1:size(calc(:,3))
if calc(i,3)>MRohm-SRohm && calc(i,3)<MRohm+SRohm
RRohm(k,:) = calc(i,3);
k=k+1;
end
end
% Mean of REcorr in mV vs. MnO2 is converted to mV vs. Ag/AgCl. Mean of
% RRohm is converted to kOhm and multiplied by the steel surface area.
Ecorr = mean(REcorr)+197;
% Potential [mV]
Rohm = mean(RRohm)*area*1e1;
% Ohmic resistance [kOhm*cm^2]
output = [Ecorr Rohm];
end
Department of Civil Engineering - Technical University of Denmark
59
Appendix D
Appendix D: Matlab Function lpr
In this appendix the Matlab function lpr is shown. It uses the linear polarization resistance (LPR)
data as input and returns the mean of the polarization resistance for a single specimen as output.
% Input: Linear polarization resistance (LPR) data.
% Output: Polarization resistance, Rp.
function output = lpr(data)
area = 2*pi*0.005*0.200;
% Steel surface area [m^2]
% Loop through all available reinforcement bars.
for i = 1:10
% Data for the actual reinforcement bar is located.
L(i) = length(find(data(:,4) == i));
% Data is only used if more than 5 data points exist.
if L(i)>5
for j = find(data(:,4) == i)
xdata(j) = data(j,6);
% Potential [mV]
ydata(j) = data(j,7);
% Current [1/50 nA]
end
% Start (n) and end (m) index in located data (xdata, ydata).
m = sum(L(1:i));
n = 1+m-L(i);
% Maximum potential is located.
if i == 1
top0 = 0;
else
top0 = n-1;
end
top = top0+find((data(n:m,6)) == max(data(n:m,6)));
% The LPR-data is fitted to Eq. (33) and the reciprocal value of
% the slope is Rp.
f = fit(xdata(n+1:top)',ydata(n+1:top)',fittype('a*x+b'),'StartPoint',[1
1]);
coeff = coeffvalues(f);
Rp(i) = 1/coeff(1);
end
end
SRp = std(Rp);
MRp = mean(Rp);
k=1;
% Mean, Rp [50 MOhm]
% Standard deviation, Rp [50 MOhm]
% Values of Rp deviating more than one standard deviation from the mean
% are excluded. The remaining values are stored in RRp.
for i = 1:length(Rp)
if Rp(i)>MRp-SRp && Rp(i)<MRp+SRp
RRp(k) = Rp(i);
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Appendix D
k=k+1;
end
end
% Mean of RRp is converted to kOhm and multiplied by the steel surface area.
output = mean(RRp)/50*1e6*area*1e1;
% Polarization resistance
[kOhm*cm^2]
end
Department of Civil Engineering - Technical University of Denmark
61
Appendix E
Appendix E: Matlab Function energy
In this appendix the Matlab function energy is shown. It uses the corrosion current densities as input
and returns the activation energy and a fitted line as output.
% Input: Corrosion current densities, icorr.
% Output: Activation energy, Ea, and fitted line.
function output = energy(data)
T = 1./(273+[1 15 25 35 50]);
R = 8.314;
% Temperature [1/K]
% Gas constant [J/(mol*K)]
% The data is fitted to Eq. (35). In Matlab ln(x) is denoted log(x).
f = fit(T',log(data)',fittype('a*x+b'),'StartPoint',[1 1]);
coeff = coeffvalues(f);
yfit = coeff(2)+coeff(1)*T;
% Activation energy is found from the slope of the fitted line.
Ea = -coeff(1)*R;
% Activation energy [J/mol]
output = [Ea yfit];
62
Department of Civil Engineering - Technical University of Denmark
Appendix F
Appendix F: Matlab Program Code for Series I
In this appendix the Matlab program code for series I is shown. The functions in Appendix C-E are
used for the calculations of the corrosion parameters.
clear all
close all
clc
format short e
B = 52;
T = [1 15 25 35 50];
% Proportionality factor [mV]
% Temperature [degree C]
% ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: %
% Ecorr and Rohm are calculated using the function pulse. Load of data.
% Letters A-F contain measurements 1-6. Values of relative humidity are 75, 85
and 96.
A75 = pulse(textread('../RH75/S1/25_D1E10.TXT_short_pulse_data.txt'));
B75 = pulse(textread('../RH75/S1/35_D2E10.TXT_short_pulse_data.txt'));
C75 = pulse(textread('../RH75/S1/50_D3E10.TXT_short_pulse_data.txt'));
D75 = pulse(textread('../RH75/S1/1_D4E01.TXT_short_pulse_data.txt'));
E75 = pulse(textread('../RH75/S1/15_D5E01.TXT_short_pulse_data.txt'));
F75 = pulse(textread('../RH75/S1/25_D6E10.TXT_short_pulse_data.txt'));
A85
B85
C85
D85
E85
F85
=
=
=
=
=
=
pulse(textread('../RH85/S1/35_D1E14.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S1/25_D2E14.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S1/50_D3E14.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S1/1_D4E05.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S1/15_D5E05.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S1/35_D6E14.TXT_short_pulse_data.txt'));
A96
B96
C96
D96
E96
F96
=
=
=
=
=
=
pulse(textread('../RH96/S1/15_D1E09.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S1/1_D2E09.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S1/50_D3E12.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S1/35_D4E12.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S1/25_D5E12.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S1/15_D6E09.TXT_short_pulse_data.txt'));
% Free corrosion potentials, Ecorr [mV].
Ecorr75 = [D75(1) E75(1) A75(1) B75(1) C75(1)];
Ecorr85 = [D85(1) E85(1) B85(1) A85(1) C85(1)];
Ecorr96 = [B96(1) A96(1) E96(1) D96(1) C96(1)];
% Ohmic resistance, Rohm [kOhm*cm^2].
Rohm75 = [D75(2) E75(2) A75(2) B75(2) C75(2)];
Rohm85 = [D85(2) E85(2) B85(2) A85(2) C85(2)];
Rohm96 = [B96(2) A96(2) E96(2) D96(2) C96(2)];
% Plot of Ecorr vs. temperature (F is not used).
scrsz = get(0,'ScreenSize');
figure('Position',[scrsz(3)/2-305 scrsz(4)/2-150 610 300])
plot(T,Ecorr75,'-ro',T,Ecorr85,'-gs',T,Ecorr96,'-bv')
title('Series I - Plain Steel, 0% Cl^-');
xlabel('T [\circC]');
ylabel('E_{corr} [mV vs. Ag/AgCl]');
legend('75% RH','85% RH','96% RH','Location','NorthEastOutside');
Department of Civil Engineering - Technical University of Denmark
63
Appendix F
grid on
% ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: %
% Rp is calculated using the function lpr. Load of data. Letters A-F
% contain measurements 1-6. Values of the relative humidity are 75, 85 and 96.
A75 = lpr(textread('../RH75/S1/25_D1E10.TXT_lpr_data.txt'));
B75 = lpr(textread('../RH75/S1/35_D2E10.TXT_lpr_data.txt'));
C75 = lpr(textread('../RH75/S1/50_D3E10.TXT_lpr_data.txt'));
D75 = lpr(textread('../RH75/S1/1_D4E01.TXT_lpr_data.txt'));
E75 = lpr(textread('../RH75/S1/15_D5E01.TXT_lpr_data.txt'));
F75 = lpr(textread('../RH75/S1/25_D6E10.TXT_lpr_data.txt'));
A85
B85
C85
D85
E85
F85
=
=
=
=
=
=
lpr(textread('../RH85/S1/35_D1E14.TXT_lpr_data.txt'));
lpr(textread('../RH85/S1/25_D2E14.TXT_lpr_data.txt'));
lpr(textread('../RH85/S1/50_D3E14.TXT_lpr_data.txt'));
lpr(textread('../RH85/S1/1_D4E05.TXT_lpr_data.txt'));
lpr(textread('../RH85/S1/15_D5E05.TXT_lpr_data.txt'));
lpr(textread('../RH85/S1/35_D6E14.TXT_lpr_data.txt'));
A96
B96
C96
D96
E96
F96
=
=
=
=
=
=
lpr(textread('../RH96/S1/15_D1E09.TXT_lpr_data.txt'));
lpr(textread('../RH96/S1/1_D2E09.TXT_lpr_data.txt'));
lpr(textread('../RH96/S1/50_D3E12.TXT_lpr_data.txt'));
lpr(textread('../RH96/S1/35_D4E12.TXT_lpr_data.txt'));
lpr(textread('../RH96/S1/25_D5E12.TXT_lpr_data.txt'));
lpr(textread('../RH96/S1/15_D6E09.TXT_lpr_data.txt'));
% Polarization resistance, Rp [kOhm*cm^2]. Rohm is neglected since
% Rp >> Rohm.
Rohm75 = 0;
Rohm85 = 0;
Rohm96 = 0;
Rp75 = [D75 E75 A75 B75 C75]-Rohm75;
Rp85 = [D85 E85 B85 A85 C85]-Rohm85;
Rp96 = [B96 A96 E96 D96 C96]-Rohm96;
% Plot of Rp vs. temperature (F is not used).
scrsz = get(0,'ScreenSize');
figure('Position',[scrsz(3)/2-305 scrsz(4)/2-150 610 300])
plot(T,Rp75,'-ro',T,Rp85,'-gs',T,Rp96,'-bv')
title('Series I - Plain Steel, 0% Cl^-');
xlabel('T [\circC]');
ylabel('R_p [kOhm \itx \rmcm^2]');
legend('75% RH','85% RH','96% RH','Location','NorthEastOutside');
grid on
% ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: %
% icorr and Ea are calculated based on the results obtained using the lpr
% function.
% Corrosion current density, icorr [uA/cm^2].
icorr75 = B./Rp75;
icorr85 = B./Rp85;
icorr96 = B./Rp96;
% Plot of icorr vs. temperature (F is not used).
scrsz = get(0,'ScreenSize');
figure('Position',[scrsz(3)/2-305 scrsz(4)/2-150 610 300])
plot(T,icorr75,'-ro',T,icorr85,'-gs',T,icorr96,'-bv')
title('Series I - Plain Steel, 0% Cl^-');
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Department of Civil Engineering - Technical University of Denmark
Appendix F
xlabel('T [\circC]');
ylabel('i_{corr} [\muA/cm^2]');
legend('75% RH','85% RH','96% RH','Location','NorthEastOutside');
grid on
% Activation energy, Ea [J/mol].
Ea75 = energy(icorr75);
Ea85 = energy(icorr85);
Ea96 = energy(icorr96);
Ea = [Ea75(1) Ea85(1) Ea96(1)]
% Plot of rate constant vs. reciprocal temperature and a fitted curve for
% activation energy (F is not used).
T = 1./(273+[1 15 25 35 50]);
scrsz = get(0,'ScreenSize');
figure('Position',[scrsz(3)/2-305 scrsz(4)/2-150 610 300])
plot(T,log(icorr75),'-ro',T,Ea75(2:end),'--r',T,log(icorr85),'gs',T,Ea85(2:end),'--g',T,log(icorr96),'-bv',T,Ea96(2:end),'--b')
title('Series I - Plain Steel, 0% Cl^-');
xlabel('1/T [1/\circK]');
ylabel('ln(i_{corr}) [\muA/cm^2]')
legend('75% RH','fit','85% RH','fit','96%
RH','fit','Location','NorthEastOutside');
grid on
Department of Civil Engineering - Technical University of Denmark
65
Appendix G
Appendix G: Matlab Program Code for Series II
In this appendix the Matlab program code for series II is shown. The functions in Appendix C-E are
used for the calculations of the corrosion parameters.
clear all
close all
clc
format short e
B = 26;
T = [1 15 25 35 50];
% Proportionality factor [mV]
% Temperature [degree C]
% ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: %
% Ecorr and Rohm are calculated using the function pulse. Load of data.
% Letters A-F contain measurements 1-6. Values of the relative humidity are 75,
85 and 96.
A75 = pulse(textread('../RH75/S2/25_D1E25.TXT_short_pulse_data.txt'));
B75 = pulse(textread('../RH75/S2/35_D2E25.TXT_short_pulse_data.txt'));
C75 = pulse(textread('../RH75/S2/50_D3E25.TXT_short_pulse_data.txt'));
D75 = pulse(textread('../RH75/S2/1_D4E16.TXT_short_pulse_data.txt'));
E75 = pulse(textread('../RH75/S2/15_D5E16.TXT_short_pulse_data.txt'));
F75 = pulse(textread('../RH75/S2/25_D6E25.TXT_short_pulse_data.txt'));
A85
B85
C85
D85
E85
F85
=
=
=
=
=
=
pulse(textread('../RH85/S2/35_D1E29.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S2/25_D2E29.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S2/50_D3E29.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S2/1_D4E17.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S2/15_D5E17.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S2/35_D6E29.TXT_short_pulse_data.txt'));
A96
B96
C96
D96
E96
F96
=
=
=
=
=
=
pulse(textread('../RH96/S2/15_D1E24.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S2/1_D2E24.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S2/50_D3E27.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S2/35_D4E27.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S2/25_D5E27.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S2/15_D6E24.TXT_short_pulse_data.txt'));
% Free corrosion potentials, Ecorr [mV].
Ecorr75 = [D75(1) E75(1) A75(1) B75(1) C75(1)];
Ecorr85 = [D85(1) E85(1) B85(1) A85(1) C85(1)];
Ecorr96 = [B96(1) A96(1) E96(1) D96(1) C96(1)];
% Ohmic resistance, Rohm [kOhm*cm^2].
Rohm75 = [D75(2) E75(2) A75(2) B75(2) C75(2)];
Rohm85 = [D85(2) E85(2) B85(2) A85(2) C85(2)];
Rohm96 = [B96(2) A96(2) E96(2) D96(2) C96(2)];
% Plot of Ecorr vs. temperature (F is not used).
scrsz = get(0,'ScreenSize');
figure('Position',[scrsz(3)/2-305 scrsz(4)/2-150 610 300])
plot(T,Ecorr75,'-ro',T,Ecorr85,'-gs',T,Ecorr96,'-bv')
title('Series II - Plain Steel, 4% Cl^-');
xlabel('T [\circC]');
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Department of Civil Engineering - Technical University of Denmark
Appendix G
ylabel('E_{corr} [mV vs. Ag/AgCl]');
legend('75% RH','85% RH','96% RH','Location','NorthEastOutside');
grid on
% ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: %
% Rp is calculated using the function lpr. Load of data. Letters A-F
% contain measurements 1-6. Values of the relative humidity are 75, 85 and 96.
A75 = lpr(textread('../RH75/S2/25_D1E25.TXT_lpr_data.txt'));
B75 = lpr(textread('../RH75/S2/35_D2E25.TXT_lpr_data.txt'));
C75 = lpr(textread('../RH75/S2/50_D3E25.TXT_lpr_data.txt'));
D75 = lpr(textread('../RH75/S2/1_D4E16.TXT_lpr_data.txt'));
E75 = lpr(textread('../RH75/S2/15_D5E16.TXT_lpr_data.txt'));
F75 = lpr(textread('../RH75/S2/25_D6E25.TXT_lpr_data.txt'));
A85
B85
C85
D85
E85
F85
=
=
=
=
=
=
lpr(textread('../RH85/S2/35_D1E29.TXT_lpr_data.txt'));
lpr(textread('../RH85/S2/25_D2E29.TXT_lpr_data.txt'));
lpr(textread('../RH85/S2/50_D3E29.TXT_lpr_data.txt'));
lpr(textread('../RH85/S2/1_D4E17.TXT_lpr_data.txt'));
lpr(textread('../RH85/S2/15_D5E17.TXT_lpr_data.txt'));
lpr(textread('../RH85/S2/35_D6E29.TXT_lpr_data.txt'));
A96
B96
C96
D96
E96
F96
=
=
=
=
=
=
lpr(textread('../RH96/S2/15_D1E24.TXT_lpr_data.txt'));
lpr(textread('../RH96/S2/1_D2E24.TXT_lpr_data.txt'));
lpr(textread('../RH96/S2/50_D3E27.TXT_lpr_data.txt'));
lpr(textread('../RH96/S2/35_D4E27.TXT_lpr_data.txt'));
lpr(textread('../RH96/S2/25_D5E27.TXT_lpr_data.txt'));
lpr(textread('../RH96/S2/15_D6E24.TXT_lpr_data.txt'));
% Polarization resistance, Rp [kOhm*cm^2].
Rp75 = [D75 E75 A75 B75 C75]-Rohm75;
Rp85 = [D85 E85 B85 A85 C85]-Rohm85;
Rp96 = [B96 A96 E96 D96 C96]-Rohm96;
% Plot of Rp vs. temperature (F is not used).
scrsz = get(0,'ScreenSize');
figure('Position',[scrsz(3)/2-305 scrsz(4)/2-150 610 300])
plot(T,Rp75,'-ro',T,Rp85,'-gs',T,Rp96,'-bv')
title('Series II - Plain Steel, 4% Cl^-');
xlabel('T [\circC]');
ylabel('R_p [kOhm \itx \rmcm^2]');
legend('75% RH','85% RH','96% RH','Location','NorthEastOutside');
grid on
% ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: %
% icorr and Ea are calculated based on the results obtained using the lpr
% function.
% Corrosion current density, icorr [uA/cm^2].
icorr75 = B./Rp75;
icorr85 = B./Rp85;
icorr96 = B./Rp96;
% Plot of icorr vs. temperature (F is not used).
scrsz = get(0,'ScreenSize');
figure('Position',[scrsz(3)/2-305 scrsz(4)/2-150 610 300])
plot(T,icorr75,'-ro',T,icorr85,'-gs',T,icorr96,'-bv')
title('Series II - Plain Steel, 4% Cl^-');
Department of Civil Engineering - Technical University of Denmark
67
Appendix G
xlabel('T [\circC]');
ylabel('i_{corr} [\muA/cm^2]');
legend('75% RH','85% RH','96% RH','Location','NorthEastOutside');
grid on
% Activation energy, Ea [J/mol].
Ea75 = energy(icorr75);
Ea85 = energy(icorr85);
Ea96 = energy(icorr96);
Ea = [Ea75(1) Ea85(1) Ea96(1)];
% Plot of rate constant vs. reciprocal temperature and a fitted curve for
% activation energy (F is not used).
T = 1./(273+[1 15 25 35 50]);
scrsz = get(0,'ScreenSize');
figure('Position',[scrsz(3)/2-305 scrsz(4)/2-150 610 300])
plot(T,log(icorr75),'-ro',T,Ea75(2:end),'--r',T,log(icorr85),'gs',T,Ea85(2:end),'--g',T,log(icorr96),'-bv',T,Ea96(2:end),'--b')
title('Series II - Plain Steel, 4% Cl^-');
xlabel('1/T [1/\circK]');
ylabel('ln(i_{corr}) [\muA/cm^2]')
legend('75% RH','fit','85% RH','fit','96%
RH','fit','Location','NorthEastOutside');
grid on
68
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Appendix H
Appendix H: Matlab Program Code for Series III
In this appendix the Matlab program code for series III is shown. The functions in Appendix C-E
are used for the calculations of the corrosion parameters.
clear all
close all
clc
format short e
B = 26;
T = [1 15 25 35 50];
% Proportionality factor [mV]
% Temperature [degree C]
% ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: %
% Ecorr and Rohm are calculated using the function pulse. Load of data.
% Letters A-F contain measurements 1-6. Values of the relative humidity are 75,
85 and 96.
A75 = pulse(textread('../RH75/S3/25_D1E40.TXT_short_pulse_data.txt'));
B75 = pulse(textread('../RH75/S3/35_D2E40.TXT_short_pulse_data.txt'));
C75 = pulse(textread('../RH75/S3/50_D3E40.TXT_short_pulse_data.txt'));
D75 = pulse(textread('../RH75/S3/1_D4E31.TXT_short_pulse_data.txt'));
E75 = pulse(textread('../RH75/S3/15_D5E31.TXT_short_pulse_data.txt'));
F75 = pulse(textread('../RH75/S3/25_D6E40.TXT_short_pulse_data.txt'));
A85
B85
C85
D85
E85
F85
=
=
=
=
=
=
pulse(textread('../RH85/S3/35_D1E44.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S3/25_D2E44.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S3/50_D3E44.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S3/1_D4E32.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S3/15_D5E32.TXT_short_pulse_data.txt'));
pulse(textread('../RH85/S3/35_D6E44.TXT_short_pulse_data.txt'));
A96
B96
C96
D96
E96
F96
=
=
=
=
=
=
pulse(textread('../RH96/S3/15_D1E39.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S3/1_D2E39.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S3/50_D3E42.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S3/35_D4E42.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S3/25_D5E42.TXT_short_pulse_data.txt'));
pulse(textread('../RH96/S3/15_D6E39.TXT_short_pulse_data.txt'));
% Free corrosion potentials, Ecorr [mV].
Ecorr75 = [D75(1) E75(1) A75(1) B75(1) C75(1)];
Ecorr85 = [D85(1) E85(1) B85(1) A85(1) C85(1)];
Ecorr96 = [B96(1) A96(1) E96(1) D96(1) C96(1)];
% Ohmic resistance, Rohm [kOhm*cm^2].
Rohm75 = [D75(2) E75(2) A75(2) B75(2) C75(2)];
Rohm85 = [D85(2) E85(2) B85(2) A85(2) C85(2)];
Rohm96 = [B96(2) A96(2) E96(2) D96(2) C96(2)];
% Plot of Ecorr vs. temperature (F is not used).
scrsz = get(0,'ScreenSize');
figure('Position',[scrsz(3)/2-305 scrsz(4)/2-150 610 300])
plot(T,Ecorr75,'-ro',T,Ecorr85,'-gs',T,Ecorr96,'-bv')
title('Series III - Ni Coated Steel, 4% Cl^-');
xlabel('T [\circC]');
Department of Civil Engineering - Technical University of Denmark
69
Appendix H
ylabel('E_{corr} [mV vs. Ag/AgCl]');
legend('75% RH','85% RH','96% RH','Location','NorthEastOutside');
grid on
% ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: %
% Rp is calculated using the function lpr. Load of data. Letters A-F
% contain measurements 1-6. Values of the relative humidity are 75, 85 and 96.
A75 = lpr(textread('../RH75/S3/25_D1E40.TXT_lpr_data.txt'));
B75 = lpr(textread('../RH75/S3/35_D2E40.TXT_lpr_data.txt'));
C75 = lpr(textread('../RH75/S3/50_D3E40.TXT_lpr_data.txt'));
D75 = lpr(textread('../RH75/S3/1_D4E31.TXT_lpr_data.txt'));
E75 = lpr(textread('../RH75/S3/15_D5E31.TXT_lpr_data.txt'));
F75 = lpr(textread('../RH75/S3/25_D6E40.TXT_lpr_data.txt'));
A85
B85
C85
D85
E85
F85
=
=
=
=
=
=
lpr(textread('../RH85/S3/35_D1E44.TXT_lpr_data.txt'));
lpr(textread('../RH85/S3/25_D2E44.TXT_lpr_data.txt'));
lpr(textread('../RH85/S3/50_D3E44.TXT_lpr_data.txt'));
lpr(textread('../RH85/S3/1_D4E32.TXT_lpr_data.txt'));
lpr(textread('../RH85/S3/15_D5E32.TXT_lpr_data.txt'));
lpr(textread('../RH85/S3/35_D6E44.TXT_lpr_data.txt'));
A96
B96
C96
D96
E96
F96
=
=
=
=
=
=
lpr(textread('../RH96/S3/15_D1E39.TXT_lpr_data.txt'));
lpr(textread('../RH96/S3/1_D2E39.TXT_lpr_data.txt'));
lpr(textread('../RH96/S3/50_D3E42.TXT_lpr_data.txt'));
lpr(textread('../RH96/S3/35_D4E42.TXT_lpr_data.txt'));
lpr(textread('../RH96/S3/25_D5E42.TXT_lpr_data.txt'));
lpr(textread('../RH96/S3/15_D6E39.TXT_lpr_data.txt'));
% Polarization resistance, Rp [kOhm*cm^2].
Rp75 = [D75 E75 A75 B75 C75]-Rohm75;
Rp85 = [D85 E85 B85 A85 C85]-Rohm85;
Rp96 = [B96 A96 E96 D96 C96]-Rohm96;
% Plot of Rp vs. temperature (F is not used).
scrsz = get(0,'ScreenSize');
figure('Position',[scrsz(3)/2-305 scrsz(4)/2-150 610 300])
plot(T,Rp75,'-ro',T,Rp85,'-gs',T,Rp96,'-bv')
title('Series III - Ni Coated Steel, 4% Cl^-');
xlabel('T [\circC]');
ylabel('R_p [kOhm \itx \rmcm^2]');
legend('75% RH','85% RH','96% RH','Location','NorthEastOutside');
grid on
% ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: %
% icorr and Ea are calculated based on the results obtained using the lpr
% function.
% Corrosion current density, icorr [uA/cm^2].
icorr75 = B./Rp75;
icorr85 = B./Rp85;
icorr96 = B./Rp96;
% Plot of icorr vs. temperature (F is not used).
scrsz = get(0,'ScreenSize');
figure('Position',[scrsz(3)/2-305 scrsz(4)/2-150 610 300])
plot(T,icorr75,'-ro',T,icorr85,'-gs',T,icorr96,'-bv')
title('Series III - Ni Coated Steel, 4% Cl^-');
70
Department of Civil Engineering - Technical University of Denmark
Appendix H
xlabel('T [\circC]');
ylabel('i_{corr} [\muA/cm^2]');
legend('75% RH','85% RH','96% RH','Location','NorthEastOutside');
grid on
% Activation energy, Ea [J/mol].
Ea75 = energy(icorr75);
Ea85 = energy(icorr85);
Ea96 = energy(icorr96);
Ea = [Ea75(1) Ea85(1) Ea96(1)];
% Plot of rate constant vs. reciprocal temperature and a fitted curve for
% activation energy (F is not used).
T = 1./(273+[1 15 25 35 50]);
scrsz = get(0,'ScreenSize');
figure('Position',[scrsz(3)/2-305 scrsz(4)/2-150 610 300])
plot(T,log(icorr75),'-ro',T,Ea75(2:end),'--r',T,log(icorr85),'gs',T,Ea85(2:end),'--g',T,log(icorr96),'-bv',T,Ea96(2:end),'--b')
title('Series III - Ni Coated Steel, 4% Cl^-');
xlabel('1/T [1/\circK]');
ylabel('ln(i_{corr}) [\muA/cm^2]')
legend('75% RH','fit','85% RH','fit','96%
RH','fit','Location','NorthEastOutside');
grid on
Department of Civil Engineering - Technical University of Denmark
71
Appendix I
Appendix I: Mean Values and Standard Deviations
In this appendix the mean values and standard deviations for the free corrosion potential,
ohmic resistance, , and the polarization resistance, , are seen in tables.
, the
Table I1: Mean values and standard deviations for
, , and
for the passive corroding
reinforcement bars. The values for
are not corrected with the ohmic resistance.
Series I,
Measurement
Mean
Std.
Mean
Std.
Mean Std.
Series I,
Measurement
Mean
Std.
Mean
Std.
Mean Std.
Series I,
Measurement
Mean
Std.
Mean
Std.
Mean
72
Std.
Department of Civil Engineering - Technical University of Denmark
Appendix I
Table I2: Mean values and standard deviations for
, , and
for the active generally
corroding reinforcement bars. The values for
are not corrected with the ohmic resistance.
Series II,
Measurement
Mean
Std.
Mean
Std.
Mean Std.
Series II,
Measurement
Mean
Std.
Mean
Std.
Mean Std.
Series II,
Measurement
Mean
Std.
Mean
Std.
Mean Std.
Department of Civil Engineering - Technical University of Denmark
73
Appendix I
Table I3: Mean values and standard deviations for
, , and
for the actively corroding
nickel coated reinforcement bars. The values for
are not corrected with the ohmic resistance.
Series III,
Measurement
Mean
Std.
Mean
Std.
Mean Std.
Series III,
Measurement
Mean
Std.
Mean
Std.
Mean Std.
Series III,
Measurement
Mean
Std.
Mean
Std.
Mean Std.
74
Department of Civil Engineering - Technical University of Denmark