Effect of Reinforcement Corrosion on Flexural Strength of RC Beams
1. 1
Faculty of Engineering and Physical Sciences
Civil Engineering
Effect of Reinforcement Corrosion on Flexural Strength of
Reinforced Concrete Beams
Varun Poddar
A dissertation submitted in partial fulfilment of the requirements for the
Degree of Master of Science in MSc Bridge Engineering
2014-2015
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Declaration of Originality
I confirm that the dissertation entitled “Effect of Reinforcement Corrosion on Flexural
Strength of Reinforced Concrete Beams” for the partial fulfilment of the degree of
MSc in MSc Bridge Engineering, has been composed by myself and has not been
presented or accepted in any previous application for a degree. The work, of which
this is a record, has been carried out by myself unless otherwise stated and where
the work is mine, it reflects personal views and values. All quotations have been
distinguished by quotation marks and all sources of information have been
acknowledged by means of references including those of the internet.’
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Summary
This report deals with the effects the corrosion on flexural strength of reinforced
concrete beam. The report follows the logical order to first describe the corrosion
process i.e initiation and propagation of corrosion. The report also discusses
different mechanisms of corrosion possible in reinforced concrete beam. Different
techniques available for preventing corrosion in RC structures have also been
discussed in detail.
Once the basics of corrosion are dealt with, different deterioration models for flexural
beams have been discussed.
There are three ways to estimate the residual strength of corroded beams namely,
empirical, experimental and analytical by use of modelling softwares. Experimental
evaluation gives the most accurate results. However, because it is destructive in
nature, it cannot be used for structures that are already in use. Therefore, empirical
models and analytical models are important tools for carrying out the analysis of
damaged structure which are already in use.
This report deals only with empirical and analytical models. As a part of dissertation
project, corroded reinforced concrete beam has been modelled and analysed in
Ansys 14.5. Bar diameter has been varied from 32 mm to 27 mm. Flexural strengths
of the beam is analysed by first considering that there is no bond degradation at
concrete steel interface and then considering that there is bond degradation, which is
calculated using empirical models. The result of this analysis are then compared with
those obtained from empirical models.
It is observed that results from two models are similar when bond degradation is not
considered. However, there is significant divergence in results when bond
degradation is considered. This may be attributed to the absence of consideration of
spalling effects in Ansys model. However, to be certain, experimental studies will
need to be conducted to verify the results. Based on the experimental observations,
the analytical model can be further improved to better represent the real world
scenario.
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Acknowledgements
First of all, I am particularly grateful for the assistance given by Dr Stergios Mitoulis
for his valuable advice and supervision of this dissertation.
I am extremely grateful to my family and friends for their unconditional support and
understanding at all times. Thanks for always being there when I needed it.
Last, but not least, I would like to say thanks to all those living with me in Hamilton
Drive 13, for the improvised Zumba lessons and the laughs (and sometimes tears)
shared.
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Contents
Summary.................................................................................................................... 3
Acknowledgements .................................................................................................... 4
Abstract...................................................................................................................... 7
Introduction ................................................................................................................ 8
Research Gap and Objectives ................................................................................. 10
Research Gap....................................................................................................... 10
Objectives ............................................................................................................. 10
Literature Review ..................................................................................................... 11
Basics of Corrosion............................................................................................... 11
Corrosion of Steel in Concrete.............................................................................. 13
Approaches available for prevention of corrosion ................................................. 15
Fusion bonded epoxy coated reinforcement...................................................... 15
Waterproofing membranes ................................................................................ 16
Corrosion Inhibitors............................................................................................ 16
Cathodic Protection ........................................................................................... 17
Inspection.............................................................................................................. 21
Need for detection ............................................................................................. 21
Half Cell Potential Measurements...................................................................... 21
Chloride Content determination ......................................................................... 21
Polarization decay testing.................................................................................. 21
Case Study I ......................................................................................................... 22
Case Study II ........................................................................................................ 23
Abilities for maintaining RC structures .................................................................. 24
Effects of Corrosion .............................................................................................. 24
Loss of Bond Strength ....................................................................................... 25
Loss of Area....................................................................................................... 27
Effects of Reinforcement Corrosion on reinforced concrete.................................. 28
Cracking ............................................................................................................ 28
Spalling.............................................................................................................. 29
Mode of Failure of beam with Corroded Steel....................................................... 30
Empirical Models................................................................................................... 31
Sample Calculation............................................................................................ 33
Methodology............................................................................................................. 35
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Introduction ........................................................................................................... 35
Problem description .............................................................................................. 36
Preprocessing....................................................................................................... 36
Element type......................................................................................................... 36
Real constants ...................................................................................................... 39
Material Properties................................................................................................ 40
Modeling ............................................................................................................... 41
Meshing ................................................................................................................ 44
Solution................................................................................................................. 45
Analysis type...................................................................................................... 45
Boundary conditions .......................................................................................... 45
Post processing ................................................................................................. 46
Results and Discussions .......................................................................................... 47
First crack induced Load....................................................................................... 47
Results Contours .................................................................................................. 48
Conclusion ............................................................................................................... 56
Future Work ............................................................................................................. 57
Experimental Studies ............................................................................................ 57
Analysis of Prestressed Beams ............................................................................ 58
Determination of shear strength............................................................................ 58
References............................................................................................................... 59
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Abstract
Majority of infrastructure in developed countries like UK and USA was built before
1970. This has led to large number of structures needing maintenance to be able to
carry on with their intended purpose. Among many forms of deterioration, corrosion is
the largest contributor to the degradation of structures. According to the NACE
International which is a world’s leading professional organisation for the corrosion
control industry, corrosion amounts to 3.1% loss of GDP of developed countries
every year. There are different techniques available to counter corrosion in built
structures like use of waterproof membrane, corrosion inhibitors and electrochemical
repairs among many others. This report briefly describes the process of corrosion,
different techniques available to quantify the extent of deterioration and ways to
protect structures against corrosion. It further delves into mechanisms which leads to
loss in strength. As a part of dissertation project, a beam was modelled in Finite
Element Software with varying cross sections of reinforcement. Subsequently,
flexural strength variation with the varying cross section has been discussed. The
results from the software analysis have been compared to the ones derived from
empirical analysis.
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Introduction
At the time of construction of reinforced and prestressed structures, it was thought
that they would be maintenance free because the reinforcement and tendons were
embedded inside the concrete and therefore there was no risk of corrosion.
However, problems related to corrosion damage to structural components have
come to the fore in last few decades. One such example is the sudden collapse of
Ynys-y Gwas Bridge in 1985 and Malle Bridge in 1992. These collapses were
attributed to the corrosion of tendons inside the beams.
In case of Ynys-y-Gwas Bridge, ingress of chloride ions through segmental joints
was believed to lead to pitting corrosion of tendons which finally led to the collapse of
bridge (Woodward et al., 1988)
Due to no certain way to know the condition of tendons and further estimate the
remaining strength of the beams, bridge owners are left with very little choice other
than to replace the whole bridge, which is generally very expensive and budget is not
always available for the same.
One of the major reasons for degradation of reinforced concrete beams is due to the
corrosion of bars in the concrete. It is important to consider that however, loss in
strength and failure of the beam does not occur solely due to loss in strength of
steel, but there are many more contributing factors.
Whenever, the reinforcing bars corrode in the structure, this is accompanied by
expansion of corroded products, leading to cracking and eventual spalling of the
concrete cover. Also, there is loss of bond between concrete and bars and loss of
cross sectional area of reinforcement which contribute to the failure of the structure.
Initial bar rusting is not necessarily disadvantageous to the bond. Various studies
have shown that corrosion up to the extent of 1% loss in cross sectional area of bars
actually make the bond stronger.
The estimation of residual capacity of reinforced and prestressed structures can aid
in taking the right decisions regarding the repair/ rehabilitation of the structure.
Residual structural capacity estimation also helps in planning for the maintenance of
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structures and assigning priority to the structures which are in the urgent need of
repair or replacement.
The calculation of remaining flexural strength of such corroded beams can be either
carried out using finite element modelling software tools or using various empirical
models suggested by different researchers based on experimental studies. One such
empirical model proposed by Bhargava et al., 2008 has been used in this study to
model corroded beams. Alternatively, finite element software tool Ansys has been
used to model the corroded beams. Results obtained from both empirical and
software model have been discussed and compared in this report.
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Research Gap and Objectives
Research Gap
Corrosion is one of the major drags on developed economies in the modern world.
An estimated 3.1% of GDP is lost to the corrosion related issues every year.
Corrosion is a field of active research around the world. Most of the research is
directed towards understanding how corrosion works, on different ways to protect
structures against corrosion and quantifying the damage caused by the process.
Corrosion of steel structures is easy to understand and there are plenty of options
available for protecting such structures and quantifying the damage. However,
reinforced concrete structures are more complex to understand. As the steel bars
are embedded inside the concrete, there is no definitive way to ascertain the extent
of corrosion. It is even more difficult to protect such structures which were built
without any provision for protection against corrosion effects.
Other major issue with such structures is determination of residual strength available
in the structure. Many empirical models have been proposed to this affect, however
the results from such models vary to great extent depending on quality of concrete,
reinforcement position, type of corrosion etc. This report uses one of such proposed
empirical model to compare the results with finite element software analysis.
Objectives
1. Discussion on corrosion initiation and propagation in reinforced concrete
structures.
2. Brief description about different techniques for quantifying the extent of corrosion
in RC structures and different ways for mitigating corrosion.
3. Review of failure mechanism in corrosion damaged RC beams and different
deterioration models.
4. Modelling a corroded RC beam in finite element software package and
comparing the results with empirical models.
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Literature Review
Basics of Corrosion
Corrosion can be defined as a process by which any material reacts with its
environment and in the process deteriorates leading to changed physical and
chemical properties. It is an exothermic process and therefore most metals have a
tendency to return to their natural state and in the process release energy in the
environment (Broomfield, 2002)
Corrosion process can be effectively explained using the concept of electrochemical
cell. Therefore, proper understanding of this phenomenon can enable us to design
structures, which are more resistant to the effects of corrosion and thus increase the
life of the structure. Figure 1 is a representation of typical electrochemical cell.
Figure 1. Electrochemical cell (Holze, 2008)
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Corrosion is a chemical reaction and therefore, there has to be an exchange of ions
and electrons in the process. The corrosion mechanism can be described as an
electrochemical process. Just as in electrochemical process, there is an anode,
cathode, electron path and electrolyte in the corrosion (Jones, 1996).
Oxidation takes place at the anodic site, in the process releasing electrons which
then travel to cathodic site where reduction takes place. These components of the
corrosion cell are briefly described here.
Anode
Anode is the site where metal cations are formed and electrons are released.
The anode is the material which lies in the lower echelon of the galvanic series
meaning that it is less noble then the cathode. The mass loss occurs at the surface
of the metal in to the environment whereas electrons in the metal are free to move
based on the voltage gradients. In Figure 1 Zn acts as an anode.
Cathode
Reduction takes place at the cathodic site. Cathode is the material which is nobler
than the anode of corrosion cell. The electrons produced at the anode migrate to the
cathodic site where they are consumed to form by products. Therefore, no loss of
mass occurs here.
Electron Path
Electron path is required for the electrons to travel from the anode to cathode to
maintain the reaction equilibrium. This movement of electrons is governed by the
voltage difference between the cathodic and anodic site. This path has to be metallic
in nature for the electrons to travel as electrons cannot travel through the solution
medium. In case of corrosion of in steel bar, this path is generally the corroding
material itself.
Electrolyte
Electrolyte is a solution through which the movement of anions and cations takes
place. This is necessary to maintain the charge equilibrium and counter the
movement of electrons through the metallic path. As the anions and
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cations are unable to move through the metallic path, electrolyte solution is required.
Therefore, in an electrochemical cell, cations tend to move towards the cathodic site
whereas anions move towards the anodic site. In the case of corrosion of steel bar in
concrete, role of electrolyte is played by the pore solution in concrete (Broomfield,
2002).
Corrosion of Steel in Concrete
Corrosion of reinforcement in concrete structures is one of the most common
reasons for cause of deterioration of the structures in coastal areas. India has
extensive coastal region, which suffers from severe corrosion (Lahiri, 1970).
Because, the volume of corrosion byproduct is much higher in volume then the steel
bar itself, this may lead to cracks and eventual spalling of concrete cover (Alonso et
al., 1998).
Corrosion is a reason for large amount of economic cost associated with failure of
old structures. When the new structure is built, the alkaline nature of pore solution
keeps the steel reinforcement passivated. This prevents the corrosion of bars.
Initiation of the corrosion can occur either by the reduction in alkalinity from
carbonation or breakdown of passive layer by chloride attack (Hausmann, 1967).
Time taken to initiate corrosion in the structure is largely determined by the cover
provided to the reinforcement as well as the permeability of the concrete
(Rasheeduzzafar et al., 1992). Once the corrosion process has started, the rate of
propagation is largely decided by the anodic and cathodic reactions and electrolytic
properties of the concrete (Broomfield, 1997).
Corrosion process in the concrete can be described in terms of corrosion cell. Just
like the electrochemical cell, it contains anode, cathode, electrolyte and the electron
path. Both anodes and cathodes are formed on the steel bar whereby
electrochemical reactions take place. The steel bar itself acts as an electron path
and the pore solution in the concrete acts as an electrolyte for transporting different
anions and cations (Broomfield, 1997). In this way a complete corrosion cell is
formed. The mechanism of corrosion in concrete reinforcement is demonstrated in
Figure 2.
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Figure 2. Mechanism of corrosion (Ahmad, 2003)
Anodic and Cathodic Reactions
Separate reactions at anode and cathode are known as half-cell reactions. Oxidation
reactions take place at the anodic site whereas reduction takes place at the cathode.
These reactions are governed by the pH of pore solution in concrete, presence of
aggressive ions and prevailing electrochemical potential in different portions of steel
bar surface (Moreno et al., 2004). Different reactions taking place at anodic and
cathodic sites are listed below in Table 1 and 2 respectively.
Table 1 Anodic Reactions
Table 2 Cathodic Reactions
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Approaches available for prevention of corrosion
There are several measures available for prevention and protection of rebars against
corrosion such as use of epoxy coating, corrosion inhibitors, cathodic protection, etc.
Corrosion initiation can also be postponed by increasing cover depth over the rebar,
using high cement content, and use of admixtures for decreasing the permeability of
concrete. Few of the widely used measures are discussed briefly here.
Fusion bonded epoxy coated reinforcement
Epoxy coating can be applied to the rebars in a factory process. The bars are
properly cleaned and then heated in induction furnace and then coated with fine
epoxy powder by spraying. The powder fuses with the hot bar, after which the bar is
quenched. The epoxy thus obtained has a dielectric nature which is very important
for preventing charged ions like chloride from penetrating to the bar (Broomfield,
1997). Further, the epoxy coating also has a good adhesion to the steel.
Disadvantages
The epoxy coat insulates the steel bar from electrical current. This poses a major
hindrance during the maintenance work of the structure. Because of the electrical
insulation provided by the epoxy coating, electrical and electrochemical techniques
for determining the state of the bar as well as carrying out the repair work is difficult
(Broomfield, 1997). It is difficult to interpret the results of half-cell potential and linear
polarization technique. In case of extensive damage due to corrosion, it is more
difficult to carry out the repair works such as realkalization, chloride removal and
cathodic protection. Epoxy coating also presents increased risk of pitting corrosion if
the coating breaks down over the small portion of rebar (Vaca-Cortés et al., 1998).
Moreover, there are high chances of damage to coating during the transportation
and handling.
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Waterproofing membranes
Waterproof membranes are used to waterproof the concrete structure. In this way,
conditions necessary for the initiation of corrosion are prevented.
Membrane comes in two forms, in a liquid form that solidifies in its place and a sheet
which is glued to the concrete surface (Broomfield, 1997). These waterproof
membranes have a lifetime of around 15 years, after which they need to be replaced.
Disadvantages
For the membrane to be effective, it should be applied with minimum number of
defects. These defects can occur as blow holes, penetrations or mechanical damage
to the liquid applied types, or cuts, tears, bad joints or perforations in the sheets.
Further, the membrane may be damaged at the time of overlay of asphalt, either by
its heat or mechanical damage from aggregate particles. Other important
disadvantage of using the membrane is the inability to use the cathodic protection
system at later stage (Vassie, 1994). If the anode is used outside of the membrane,
it blocks the electrical path, thereby leaving the protection ineffective. Application of
anodes below the membrane creates the problem of accumulation of gases released
from the anode (Broomfield, 1997).
Corrosion Inhibitors
Corrosion inhibitors are chemical substances, which are capable of retarding or
preventing corrosion of steel in concrete. They are added in small quantities to the
concrete mix (Elsener et al., 1997). They should not have adverse effects on the
concrete properties like compressive strength. One of the major advantage of using
corrosion inhibitor is that unlike epoxy coating and waterproof membranes, they do
not hinder the application of electrical and electrochemical repair and measurement
techniques (Broomfield, 1997).
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Mechanism
There are various ways in which different corrosion inhibitors work to prevent and
retard the action of corrosion. Based on the mechanism of action, corrosion inhibitors
can be divided into following types (Trabanelli, 1987).
Adsorption inhibitors: These inhibitors prevents or retards either the anodic or
cathodic partial reaction or both reactions.
Film forming inhibitors: These inhibitors prevent corrosion by forming a film on the
surface of steel bar.
Passivators: They help in corrosion prevention by favouring the formation of
passivation layer on the steel bar.
Buffering: They act as a buffer to maintain high pH in the local pit environment.
Disadvantages
As the inhibitor is itself consumed during the mechanism of corrosion prevention, it is
very important to predict the right amount required based on the design life of
structure and environmental conditions around the structure
(Broomfield, 1997).
Cathodic Protection
Cathodic protection derives its name from the fact that it protects the metal from
corrosion by changing the role of corroding metal from anode to cathode.
Current flows between anode and cathode because of potential difference between
the two. In the corrosion cell, anode potential is more negative than the cathode,
which acts as a driving force for current flow and hence corrosion (Broomfield, 1997).
Cathodic protection helps in preventing corrosion by minimizing this potential
difference between the anode and cathode. This is done by supplying current from
outside source and when enough current is provided, the complete steel bar comes
at the same potential and starts acting as an anode. This source of current can either
be some sacrificial metal/alloy or battery supplying direct current. Based on the
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source of current, cathodic protection can be divided into two sub categories namely
Galvanic and Impressed Current Cathodic Protection (Broomfield, 1997).
Cathodic protection is an effective for both prevention as well as protection of
concrete from cathodic protection (Bertolini et al., 2009). It is effective against both
carbonate and chloride affected concrete. Further, it can be used for realkalization
and repassivation (Bertolini et al., 2008) of corrosion infected concrete.
Galvanic System
Galvanic method of cathodic protection uses galvanic series to decide on metal,
which has more negative potential than the metal which has to be protected. For
example, zinc can be used to protect the steel bar because zinc is more corrosive
than the steel bar and therefore act as an anode and in the process transforms the
steel bar in to cathode. This is done by either embedding the anode in the concrete
or superimposing it on the surface of concrete. Concrete acts as an electrolyte and
an outside wire connection is provided between the anode and the steel bar. In the
process of protection of steel bar, these galvanic anodes corrode themselves and
are therefore called sacrificial anodes. Galvanic anodes are usually made of
magnesium or zinc because of their higher potential compared to steel structures
(Broomfield, 1997).
Impressed Current Cathodic Protection Systems
Impressed Current Cathodic Protection (ICCP) systems are extremely accurate and
can be controlled to deliver optimal protective current to the structure. Anodes are
connected to a DC power supply to deliver low-voltage electric currents and are
controlled by strategically placed reference electrodes. These reference electrodes
are connected to a monitoring system that observes and verifies the system
performance.
The rectifier is used to transform alternating current (AC) to direct current (DC),
which is then passed through the structure using non sacrificial anode to provide
protection to the steel. The anode can be embedded in the concrete in the form of a
rod or can be superimposed on the concrete in the form of fabric. Common choices
for the anodes include mixed metal oxide, high silicon iron, platinized titanium/
niobium/ zirconium.
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Criteria for successful implementation of ICCP system include following
characteristics (Vukcevic, 2010).
Operating at all times (i.e. being continuously powered-on).
Functioning at all times (i.e. delivering CP by continuously operating within a
regulating loop).
Providing optimal protection (i.e. not over-protecting or under protecting after
initial steel polarization period).
Working autonomously (i.e. not needing operator attendance, also being self-
adjusting and self-regulating).
Reliable (i.e. being fault-tolerant, redundant, self-protecting, self-calibrating).
Incorporating alarm functions (i.e. reporting malfunctions, operation out of range,
independent watch-dog status).
Everlasting (i.e. having average operating lifetime equal to or longer than
projected infrastructure lifetime).
It is very important to determine the right amount of current needed to achieve the
desired prevention/protection. The current should be such that the structure is
neither under protected nor over protected. Over protection of the structure may lead
to hydrogen embrittlement on prestressed structures (Bertolini et al., 2002).
Table 3 mentions the current requirement for various real world conditions (Chess et
al, 1998)
Table 3 Current requirement for real word conditions (Chess et al., 1998)
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Figure 3 is a demonstrative figure of ICCP setup. Primary anodes here is an inert
material so that it does not decompose in a very short time. This primary anode can
be made of CFRP or titanium. As is clear from the figure, for protection to be
effective, the current has to pass through the concrete medium. However, due to
high resistivity values of concrete, there is non uniform distribution of current on the
steel bar. This necessitates the research into making concrete less resistive for
efficient use of cathodic protection system.
Figure 3 Impressed cathodic current protection setup (Bertolini et al., 98)
Rectifier and system component evaluation
It is important to check components of the system. The components include rectifier,
anode, and wiring. Rectifiers should be housed in a box and should not be
accessible to the public to avoid vandalism. Periodic inspection are necessary to
inspect the conditions of anodic systems. If sacrificial anode have been used, they
need to be replaced and replenished after certain period. Non sacrificial anodes
should also be checked for delamination.
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Inspection
Need for detection
Majority of the structures in second half of the century have been built with the use of
RC. At the time of their construction, it was thought that these structures are going to
be durable. It was only much later, that corrosion related problems became
widespread. However, unlike steel structures, where it is easier to ascertain the
health of the structure and maintain the structure, it is very difficult to do the same in
case of RC members. Therefore, innovative ways are needed for ascertaining the
level of corrosion in the reinforcement members as well as for maintenance of the
structure if so required.
Half Cell Potential Measurements
Half-cell potential measurements are very handy and fast way to ascertain the rate of
corrosion in the rebar. It measures the potential difference between the concrete and
rebar. However, for taking half-cell potential measurements, clear connection to
rebar on which corrosion has to be measured needs to be established.
Chloride Content determination
Chloride content can be found in the concrete to determine the risk of corrosion to
rebars. As chloride penetrates concrete and reaches rebars, passivation layer is
broken down which makes rebars susceptible to corrosion. Effective cathodic
protection is able to drive out chloride ions away from the rebar.
Polarization decay testing
Polarization decay testing takes longer time to do, however it is much more reliable
test for effectiveness of cathodic protection. Cathodic protection system is
disconnected and potential measurements between concrete and rebar are taken at
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the instant off and then again after 4 hours and 24 hours. As the time passes by, if
there is a potential decay, it establishes that cathodic protection was effective before
switching off and corrosion potential has again started to build up after the system
stopped working. Usually, potential decay of more than 100 mV implies that cathodic
protection is effective.
Case Study I
Strategic Highway Research Program (USA) had supported a study on cathodic
protection of bridge elements. This case study describes briefly the methodology
used and the performance of cathodic protection.
Location: Yaquina Bay, Oregon, USA
Anode Type and Location: Porter Paint and Coating on beams and soffit
Conductive coating was applied to the underside of the bridge deck. Structural
cracks has appeared on the underside of deck owing to the corrosion of
reinforcement in rebars due to highly corrosive marine environment.
Methodology: Cathodic protection system (Impressed Current Cathodic Protection)
was installed on the structure. Rectifier with specification of 8V, 2A was installed.
Porter Paint was applied on beams and soffit which acted both as the anode as well
as the conductive layer for uniform distribution of current through the concrete cover
to the rebars (cathode). Thus, forming the electrochemical cell and reversing the
function of rebar from anode to the cathode. The current density for the CP was set
to 0.5 to 0.6 mA/sqft.
Results:
The best way to check the efficiency of the Cathodic Protection system is to measure
the potential decay after 4 Hrs and 24 Hrs of switching off of the CP system. It was
observed that after 24 Hrs, potential has decayed from -387mV at the switch off
instant to -186mV after 4 Hrs and to -100mV after 24 Hrs of switching off.
This establishes that installed cathodic protection system is effective in controlling
corrosion of rebars in reinforced concrete. Further, concrete cores were taken from
the areas with active cathodic protection and control areas. On measuring the
chloride content in the samples, it was found that chloride content in the CP core
23. 23
was less than the control sample. This establishes that cathodic protection is also
effective in repelling of chloride ions from the rebar area. This further helps in
repassivation of rebars and thus preventing corrosion.
Case Study II
Location: East Camino under crossing, California State Highway System, USA
Anode type and location: Metallized Zn Anode on deck and soffit surface.
Protection type: Impressed current cathodic protection
Impressed current cathodic protection (ICCP) was applied to the bridge which is a 3
span (27 m long) reinforced concrete structure and was built in 1964. There were
large scale corrosion in reinforcements owing to chloride ingress due to deicing
operations during winter.
Methodology: Deck and soffit surface were coated with thermal sprayed Zn which
acts as an anode in the ICCP scheme. In addition to acting as anode, Zn layer also
helps in uniform distribution of current through the concrete. Sprayed layer of Zn was
0.6 mm thick. The system was energized in 1985 and current density was set to 0.43
mA/ft2.
Results:
The ICCP system was analysed after 10 years of service. It was observed that
driving voltage varied from 26 to 40 V. Further, it was observed that CP currents
were higher in winter when compared to summer months. This can be attributed to
change in conductivity of concrete. Due to higher moisture content in winter,
concrete becomes more conductive resulting in higher CP currents thereby making
the system more efficient.
On core examination, it was found that there were significant amount of corrosion
product of Zn deposited under the Zn coating. This lead to debonding of the anode
layer from the concrete surface and thus affecting the performance of the ICCP
system. This is one of the major drawback with using Zn as anode material. High
amount of chloride ions were also observed in the core owing to the extensive de-
icing operations during the winter months.
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Abilities for maintaining RC structures
For maintaining RC structure (mainly from the view point of corrosion), following
abilities are required.
1. To determine the level of corrosion in the structure. Which can be done using
many techniques such as half-cell, AC impedance, LPR etc. However, it should
be kept in mind that none of these techniques are definitive and that there are
high chances of error in the results from such techniques. Therefore, it is required
that more than one method is used to determine the level of corrosion in the
structure.
2. Once the level of corrosion in the reinforcement is determined, it is important to
find the residual strength of the member. However, it is necessary to remember
that strength of the member is not dependent solely on the cross section area of
the member. It also depends on the bond strength between concrete and steel.
Effects of Corrosion
As the reinforcement corrodes, it grows in volume and thus resulting in formation of
crack which eventually lead to spalling. However, even before the spalling happens,
the structure can fail due to reduction in the load carrying capacity of the structure or
beam. Corrosion also reduces the cross sectional area of the reinforcement and
reduces the bond strength between the concrete and steel, leading to reduction in
flexural strength of the beam (Mehta and Monterio 1997).
As the reinforcement corrodes, volume of the byproducts formed from corrosion is
substantially higher than the original bars. This results in exertion of expansive radial
pressure at the steel-concrete interface leading to hoop tensile stresses in the
surrounding concrete. Once, the maximum hoop tensile stress exceeds the tensile
strength of the concrete, cracking follows (Bhargava et al., 2008)
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Loss of Bond Strength
Many researchers have conducted research in the bond behavior of corroded steel.
A lot of research has been done to predict the loss in bond strength due to the loss
resulting from corrosion. While, some research papers have proposed empirical
formulas derived from experimental results (Cabrera 1996; Stanish et al., 1999; Lee
et al., 2002; Chung et al., 2004), others have proposed analytical models (Lundgren
2002; Coronelli 2002; Wang and Liu 2004).
However, despite a lot of research in this field, there exists considerable
discrepancies between the predicted and experimentally observed values. This may
be the result of difference in testing procedures, varying material strengths of
concrete and steel and variation in corrosion inducing conditions.
There are a number of tests available to estimate the bond strength in RC structures.
Some of the most commonly used ones are concentric pullout test, tension pullout
test, bond beam test, Bureau of Standards test, cantilever bond test and University
of Texas beam test. The results may vary depending on the type of test used for
calculating the bond strength value.
Bond between concrete and reinforcement bars play an important role in the
composite action of reinforced structure. With the reduction in the bond strength
between the bar and concrete, it is imperative that there will be reduction in flexural
strength of the concrete.
The bond strength increases slightly with the initial corrosion which can be attributed
to the expansive nature of iron oxides due to which roughness in the concrete
reinforcement interface increases leading to increased bond strength. However, with
increased corrosion, there is build-up of loose corrosion products at the interface
leading to loss in bond strength. The bond stress declines consistently until about
7.5% loss in the initial area of the rebars, after which it becomes negligible. This loss
in bond strength can be further attributed to loss of mechanical interlocking rebars
and concrete and lubrication effects produced by the flaky corroded materials (Naus
et al). Experimental bond values tend to increase up to 1-4% corrosion level (Al-
Sulaimani et al., 1990) after which it starts to decline again. As the corrosion
increases, accumulation of corrosion products exerts hoop tensile stress in the
26. 26
surrounding concrete leading to development of cracks and loss of adhesion and
friction between the concrete and reinforcement.
Figure 4. Variation in bond strength with corrosion (Bilcik et al., 2012)
Figure 5. Expansive pressure on steel concrete interface due to corrosion products
(Zhao et al., 2011)
Studies have shown that loss of bond strength for unconfined reinforcement is more
critical than the loss of reinforcement area. Therefore, it is recommended that the
27. 27
longitudinal and transverse reinforcement be provided with the confining bars to
counteract the bond less.
Bhargava et al 2008, has proposed empirical models to evaluate bond degradation
for concrete and steel reinforcement without stirrups.
The empirical formula has been proposed on two different experimental data of
Pullout testing and flexural testing.
Based on pullout testing experimental data
R = 1.0 for X ≤ 1.5 %; R = 1.192e-0.117X for X > 1.5%
Based on flexural testing experimental data
R = 1.0 for X ≤ 1.5 %; R = 1.346e-0.198X for X > 1.5%
Where R is nominal bond strength and X is the weight loss in percentage.
As the bond strength in the above formula has been normalized, this negates to
great extent the difference in material strengths of concrete and steel, testing
procedures and corrosion process used in different experiments.
Loss of Area
The loss in the area of the bars depends on the corrosion mechanism namely
chloride or carbonation induced corrosion. Carbonation induced corrosion
leads to a uniform corrosion throughout the bar length and therefore, reduction
in cross section area is limited. Whereas chloride induced mechanism leads to
severe pitting of bars and localized loss in steel cross section area. Cairns and
Millar, 1999 have shown that there is balance between the strength loss from
the loss in cross section and strength gained as a result of hardening of
undamaged material in the bar.
28. 28
Effects of Reinforcement Corrosion on reinforced concrete
Deterioration model
Deterioration of reinforced concrete can be subdivided into three stages, namely
initiation, propagation and finally serviceability/ ultimate failures.
Initiation and propagation of corrosion have already been explained in previous
sections. Different modes of failures have been described here briefly.
Figure 6. Deterioration model of service life due to reinforcement corrosion (Bilcik et
al., 2012)
Cracking
As the corrosion occurs, the resulting oxidation of iron leads to products formation
which has volume of up to 5 times or more the volume of the original iron. Therefore,
the reinforcement tends to expand and the resulting pressure on surrounding
concrete leads to cracking, spalling and delamination of the concrete. In addition to
the reduction in strength of the member, cracking also makes the structure
vulnerable to further ingress of chloride ions and therefore, accelerating the pace of
corrosion.
29. 29
Figure 7. Oxidation states of iron and representation of different forms of corrosion
(Naus et al., 2007)
Morinaga, using the laboratory data has suggested an empirical equation for
determining the time taken for cracking of concrete.
Where
Qcr = critical mass of corrosion products (10-4g/cm2)
c = concrete cover to the reinforcement
d = diameter of reinforcing bars
icorr = corrosion rate (g/day)
tcr = time to cracking
Spalling
(Du et al., 2013) has shown that bar clear distance is the determining factor when
the spalling of the concrete cover arising from corrosion is considered. Bar clear
distance can be described as ratio of distance between consecutive bars and
concrete cover (s/c). This terminology further becomes clear from the subsequent
Figure 8.
30. 30
Therefore, when value of s/c decreases, less amount of radial expansion from
corrosion is required to cause internal penetration and therefore, spalling occurs
more easily.
Therefore, it is important to take care of both concrete cover and internal spacing of
bars when designing RC structures.
Figure 8. Representation of cracking mechanism in corroded beam
It is preferable that bar clear distance is higher than 2.2 times the concrete cover.
This will help in identifying that corrosion is occurring in the early stage as the
corrosion cracks will appear on external surface before spalling begins. It is
recommended that for maintenenace of existing corroded structures, one should be
aware of internal penetration happening where ever the clear distance is less than
2.2 times the concrete cover. In such cases, exterior concrete surface might not give
any hints to the corrosion occurring inside the concrete.
Mode of Failure of beam with Corroded Steel
Mode of failure of RC beams with corroded is depended on the extent of corrosion
that has already occurred in the beam. However, the failure pattern in both corroded
and non-corroded beams before the cracking stage is quite similar (Almusallam et
al., 1996).
31. 31
The deflection increases gradually with the increasing load, after which there are
transverse flexural cracks in middle of the beam. This is accompanied by sudden
increase in deflection. With further increase in the loading, flexural cracks propagate
across the width and depth of the beam. The crack width increases with increasing
loads.
With further increase in the load, there is yielding of bars leading to huge deflection.
Once the bars have yielded, flexural cracks propagate upwards reducing the
compression zone, leading to secondary compression failure. With increasing load,
flexural cracks propagate and merge with the longitudinal cracks which originate
from the corrosion in the reinforcing steel leading to sudden longitudinal splitting of
the beam along with the reinforcing bar.
This failure is a result of the bond failure between the rebars and the concrete.
(Uomoto et al., 1984) observed that shear bond failure was the predominant mode of
deterioration in beams with corroded reinforcements.
Empirical Models
Bhargava et al 2008, has proposed empirical models to evaluate bond degradation
for concrete and steel reinforcement without stirrups. The empirical formula has been
proposed on two different experimental data of Pullout testing and flexural testing.
Based on pullout testing experimental data
R = 1.0 for X ≤ 1.5 %; R = 1.192e-0.117X for X > 1.5%
Based on flexural testing experimental data
R = 1.0 for X ≤ 1.5 %; R = 1.346e-0.198X for X > 1.5%
Where R is nominal bond strength and X is the weight loss in percentage.
Flexural strengths of corroded beams can be estimated using empirical models and
the procedure for the same is shown as below:
Tension in the bottom reinforcement can be given by:
Ftx = nst x π x Dstx x ld x τbux(Bhargava et al., 2008)
32. 32
Where
Ftx = Tensile force generated in the corroded tensile reinforcement at any stage of
corrosion
nst = number of bottom tensile steel rebars
Dstx = Diameter of bottom tensile steel bar
ld = Development length in tension
τbux = Bond strength at the corrosion level X
Development length in this expression is calculated as follows:
Ld = 0.025fy α β λ (db)/fc
0.5
Where
fy = specified yield strength of reinforcement bars in psi
α = 1.3 for top bars and 1.0 for all other bars
β = 1.0 for uncoated bars and 1.5 for epoxy coated bars
λ = 1.0 for nominal weight concrete
db = nominal diameter of the bars in inches
fc = specified compressive strength of concrete in psi
Calculation of bond strength at corrosion level X
Bond strength when there is no corrosion:
Ft = 0.3 (fc)0.6
Bond strength at corrosion level X can be calculated using nominal bond strength
Therefore,
τbux = 1.346e-0.198X x 0.3 (fc)0.6
Calculation of Design Flexural Strength for a beam
Depth of equivalent compressive block, a
a = Asfy/0.85fc.b
Where
Asfy = Ftx (Tensile force generated in the corroded tensile reinforcement at any stage
of corrosion)
33. 33
fc = compressive strength of concrete
b = width of the beam
Nominal moment is then given by the expression:
Mn = Ftx (d-a/2)
Where d = distance between the centroid of tensile steel and the edge of the
compression zone
Design Moment Strength
Md = 0.9 Mn
Critical point load when applied at the centre of the beam
w = 4Md/L
Where L is the length of the beam
Sample Calculation
Sample calculation of uncorroded beam using the above described empirical
method:
For uncorroded beam
Ld = 0.025fy α β λ (db)/fc
0.5
α = β = λ = 1
fy = 415 MPa
db = 32 mm
fc = 25 MPa
Therefore, Development length, Ld = 797 mm
Bond strength at the corrosion level X, τbux = 0.3 (fc)0.6 = 2 MPa
Tension in the bottom reinforcement,
Ftx = nst x π x Dstx x ld x τbux = 3 x 3.14 x 32 x 797 x 2
Ftx = 480 kN
34. 34
Depth of equivalent compressive block, a = Asfy/0.85fc.b
a = 482/(0.85 x 25 x 300) = 75 mm
Nominal Moment, Mn = 482 (250 – 37.5) = 102.425 kNm
Design Moment, Md = 92.205 kNm
Critical point load when applied at the centre of the beam
w = 73.6 kN
35. 35
Methodology
Reinforced concrete beam was modelled using Finite Element software Ansys. The
beam was taken to be of the dimensions 5m x 0.3m x 0.3m.
In this report, nonlinear finite element analysis for the reinforced beam has been
carried out. The beam is simply supported with pinned support at one end and roller
supports at the other end. The beam is placed on the pair of bearings.
Point load has been applied at the centre of the beam, the load was applied
increased until the beam failed in flexure. Ansys Workbench 14.5 has been used to
carry out the modelling and analysis of the beam.
Introduction
Structural concrete beams require the understanding of responses of flexural
strength and crack initiation and propagation subjected to a variety of loadings.
There are various available procedures for modelling concrete beams using both
empirical and numerical/analytical methods. Finite elemen analysis (FEA) is a
numerical method which is widely used to model concrete beams using non linear
elements available in different software tools. Ansys 14.5 is capable of simulating
and predicting the responses of reinforced and prestressed beam members. In
addition to Ansys, there are many other commercial tools for analysis reinforced
concrete members. I recent years, use of finite element analysis has grown because
of increase in processing power of computers and increased availability of software
option.
Since, each material has its own complicated stress-strain behaviour, nonlinear
modelling of structural members play an important role in carrying out a nonlinear
analysis.
ANSYS incorporates a 3D element SOLID65 with the nonlinear properties similar to
that of concrete. SOLID65 element hasa smeared crack analogy for cracking in
tension zones. It also has a plasticity algorithm to simulate crushing behaviour of
36. 36
concrete in compression zones. SOLID65 is a solid isoperimetric element with the
integration points for crushing as well cracking checks.
Problem description
Flexural strength analysis of reinforcement steel concrete beam study has been
carried out in this report. A rectangular cross section beam was used with three
reinforcement steel bars at equally spacing. Bearing surfaces were applied at both
ends as well as at centre. Roller support was applied at one end while pinned
support was applied at other end. A point load was applied at the centre bearing
surface. Beam dimension was 5m X 0.3m X 0.3m. Rebars radius was varied ranging
from 16 mm to 13.5 mm with step size of 0.25 mm.
Main concern of this study was to determine the load at which a first crack generates
and corresponding stresses at that point. Second, objective was to optimize the
diameters of steel reinforcements. Lastly, flexural strength of beam under analysis
was evaluated and the stresses at which beams fails to bear more load.
ANSYS APDL module was used to obtain all described goals. Deformations, von
mises stresses as well as cracks propagations has been evaluated here using FEA
(finite element analysis) techniques.
Preprocessing
For the Finite element model to run in Ansys, there are multiple tasks that need to be
taken care of. Finite element model can be either created using command prompt
line or with the use of Graphical use interface. For this report, graphical user
interface method has been used. The subsequent section describes different
parameters and entries used to model the reinforced concrete beam.
Element type
The element types for this model are shown in Table 4. The Solid65 element was used
to model the concrete and concrete bearing support. The element has eight different
37. 37
nodes in a shape of a cube. Each node has three degrees of freedom, i.e translation in
x, y and z directions. The element is able to deform plastically, crack in all the three
orthogonal directions, and crush as well.. A schematic of the element is shown in
Figure 9.
Material Type ANSYS Element
Concrete SOLID65
Reinforcement
Steel
LINK180
Concrete bearing SOLID65
Table 4. Element Type
Figure 9. Ansys SOLID65 Element
A Link180 element was used to model steel reinforcement. This element is a 3D spar
element and it has two nodes with three degrees of freedom – translations in the
38. 38
nodal x, y, and z directions. This element is also capable of plastic deformation. This
element is shown in Figure 10.
Figure 10. Ansys LINK180 Element
Additionally, COMBIN39 element was used to model the interface between the steel
and concrete.
COMBIN39 is a nonlinear unidirectional element. The element can be either used for
longitudinal or torsional capability. In this study, longitudinal option was used zwhich
has uniaxial tension – compression ability with three degrees of freedon at each
node. Each node is allowed to translate in nodal x, y and z directions. The element is
not allowed to bend.
Figure 11. COMBIN39 Element
39. 39
Real constants
The real constants for this model are shown in Table 5.
Table 5. Real Constants for calibration model
Real Constant Set 1 is used for the Solid65 element. Custom values can be input for
volume ratio. The material number in the table refers to the material type of
reinforcement bars and volume ratio refers to the volumetric ratio between concrete
and steel in the element.
Real Constant Sets 2, 3, 4, 5, 6, 7, 8,9,10 are defined for the Link180 element.
Values for cross-sectional area and initial strain have also been entered. Initial strain
value is set to zero as there is no initial or residual stress in the reinforcement bars.
Real constant set no Element Type Parameters Value
1
SOLID65
Material number 0
Volume ratio
0
2
LINK180
Initial strain 0
Cross sectional area(m2) 0.000803
3
LINK180
Initial strain 0
Cross sectional area(m2) 0.000754
4
LINK180
Initial strain 0
Cross sectional area(m2) 0.000706
5
LINK180
Initial strain 0
Cross sectional area(m2) 0.000660
6
LINK180
Initial strain 0
Cross sectional area(m2) 0.000615
7
LINK180
Initial strain 0
Cross sectional area(m2) 0.000572
8
LINK180
Initial strain 0
Cross sectional area(m2) 0.000530
9
LINK180
Initial strain 0
Cross sectional area(m2) 0.000490
10
LINK180
Initial strain 0
Cross sectional area(m2) 0.000452
11
LINK180
Initial strain 0
Cross sectional area(m2) 0.000415
40. 40
Material Properties
Parameters required to define concrete and rebars are shown in Table 6. There are
multiple parts of the material model for each element.
Material Number Element Type Material properties
1 SOLID Density(Kg/m3)
Density 2400
Linear Isotropic
EX 2.5e10 N/m2
PRXY 0.2
Concrete
Open shear transfer
coef
0.3
Closed shear
transfer coef
1
uniaxial cracking
stress
3.58MPa
Uniaxial crushing
stress
-1MPa
Multilinear elastic
Point Strain Stress(N/m2)
1 0.0003 7.5E+006
2 0.00054 1.268E+007
3 0.00124 2.239E+007
4 0.00184 2.491E+007
5 0.00237 2.5E+007
2 LINK180 Density
Density 7850(Kg/m3)
Linear Isotropic
EX 2e11(N/m2)
PRXY 0.3
Bilinear Isotropic
Yield Strength 4.15e8
Tang Mod 2e7
Table 6. Material Properties
41. 41
Material Model Number 1 in the above table refers to Solid65 element. The Solid65
element makes use of linear isotropic material properties to adequately model
concrete properties. The Multilinear isotropic material uses the von Mises failure
criterion to define the failure of the concrete. EX is the modulus of elasticity of the
concrete, and PRXY is the Poisson’s ratio (ν).
The Multilinear isotropic stress-strain implementation requires the first point of the
curve to be defined by the user and it also must satisfy the Hooke’s law.
Implementation of the material model in ANSYS requires that different constants be
defined. These constants are
1. Shear transfer coefficients (open crack)
2. Shear transfer coefficients (closed crack)
3. Uniaxial tensile cracking stress
4. Uniaxial crushing stress
5. Biaxial crushing stress
Material Model Number 2 in Table 6 refers to the Link180 element. The Link180
element has been assigned to all the steel reinforcement in the RC beam model.
Bilinear isotropic material is also based on the von Mises failure criteria. The
hardening modulus have been defined as 2e7 N/m2 and the yield stress for steel has
been used as 415 MPa.
Modeling
Beam and bearing supports were modelled as volume. Beam dimensions were 0.3m
x 0.3m x 5m and bearing supports size was 0.3m x 0.2m x 0.3m. Two bearing
supports were applied at beam ends while one was at the centre of top. Steel
reinforcement link was created from element attributes by just selecting the nodes
created from solid65 volumes so they do not need to be meshed again. The steel
bars were at same plane 50mm above the beam bottom surface and distance of 1st,
42. 42
2nd and 3rd bar from side surface of beam was 50mm, 150mm and 250mm.
Geometry of problem description has been shown in Figure 12.
Figure 12. Beam Geometry
Beam dimensions and bearing dimensions are shown in the Figure 13. Length of the
beam is 5m and the bearing dimensions are 0.3 m x 0.3 m x 0.2 m.
Figure 13. Beam dimensions
43. 43
The contact force between the steel and concrete was varied to stimulate reduction
in bond strength as a result of corrosion. This bond strength was calculated using
empirical models discussed in methodology section of the report.
Diameter
Bond Strength
(Mpa)
32 2.36
31.5 1.72
31 0.94
30.5 0.52
30 0.29
29.5 0.16
29 0.09
28.5 0.05
28 0.03
27.5 0.02
27 0.01
Table 7. Bond strength vs with diameter as a result of corrosion
Figure 14. Bond Strength vs Diameter
Strength of bond reduces exponentially as the diameter of the bar is decreased as a
result of the corrosion proces.
0
0.5
1
1.5
2
2.5
26 27 28 29 30 31 32 33
BondStrength
Diameter
44. 44
Meshing
The element type number, material number, and real constant set number for the
calibration model were set for each mesh as shown in Table 8.
Model Parts Element type Material
number
Real constant
set
Concrete SOLID65 1 1
Steel bars LINK180 2 2
Bearings SOLID65 1 1
Table 8. Meshing Attributes of the Model Beam
Rectangular mesh has been used for element SOLID65 to obtain simulate the
behaviour of concrete in real world. Meshing for bearing supports have been done
using volume sweep command in the Ansys toolbox. Use of volume sweep
command sets the width and length of elements in the bearing plates to be
consistent with the elements and nodes of the main beam. This is an important stp
avoid the problems related with convergence.The overall mesh of the concrete and
bearing support volumes is shown in Figure 15.
45. 45
Figure 15. Mapped meshing of model beam
Solution
Analysis type
Static analysis type was selected in new analysis tab of solution analysis type and in
the solution control automatic time stepping was kept on. The number of sub steps
was kept to 5 and maximum sub steps were selected as 10 while keeping the
minimum number of sub steps as 5.
Boundary conditions
Displacement boundary conditions are needed to constrain the model to get a
unique solution. Roller boundary conditions were applied at left end by keeping
displacement values in Y and Z directions zero and pinned support was applied right
end by keeping displacement in Y direction as zero. The load was applied at top
surface nodes of centre bearing as shown in Figure 16..
46. 46
Figure 16. Boundary conditions
Post processing
Convergence history of problem has been shown in Figure 17.
Figure 17. Convergence History
47. 47
Results and Discussions
First crack induced Load
Initially, beam with 16mm radius bar were used by selecting the real constant set
number 2 for that and a load of 75KN were applied at centre and it was observed
many number of cracks, then load was reduced until it was examined where the first
crack propagates and it was just above the 71.5 KN.
Similarly, first crack induced load were manipulated for different sizes of steel bar,
the safe load for this beam has been tabulated in given table.
S.No Bar
diamter(mm)
Bar cross sectional
area(mm2)
Load(KN)
1 32 803 88.4
2 31.5 778 64
3 31 754 44
4 30.5 730 36
5 30 706 25.6
6 29.5 683 20
48. 48
7 29 660 16
8 28.5 637 8
9 28 615 4
10 27.5 593 3.6
11 27 572 2.4
Table 9. First crack induced load
Results Contours
Stresses corresponding to first crack were also examined and it was noted that these
stresses range from 10 Mpa to 12 Mpa where concrete strength was considered as
35 Mpa. Contours of different parameters like stresses, deformation, steel bar stress
as well as deformation for a specific case has been shown in onward pictures.
50. 50
Figure 20. Total deformation beyond the first crack
Figure 21. Total deformation at steel reinforcement at safe load
51. 51
Figure 22. No crack just before first crack load
Figure 23. Cracks beyond the first crack load
52. 52
As is evident from the figure 24, loss in bond strength resulting from corrosion plays
an important role in the determination of the flexural strength. Flexural strength
varies linearly with the diameter of the reinforcement when the consideration is made
that there is no reduction in bond strength. However, the flexural strength starts to
decline exponentially when the bond degradation is considered along with the
reduction in the area of the reinforcement. The same phenomenon is demonstrated
in the Figure 25.
Figure 24 Variation of Flexural Strength vs Reinforcement Diameter (Empirical
Model)
The same relation between the flexural strength and reinforcement diameter is
observed in the Ansys results. However, the graph are not as streamlined as the one
derived from the empirical model. This may be the result of the method Ansys uses
to analyse the model and the elements used for modelling of different structural
elements.
Figure 25 Variation of Flexural Strength vs Diameter of Reinforcement (Ansys
Model)
When comparing the flexural strength from empirical and ansys model (no bond
degradation), the results are similar. This shows that empirical models are efficient in
predicting the flexural strengths.
0
20
40
60
80
100
120
140
26 27 28 29 30 31 32 33
FlexuralStrength(kNm)
Reinforcement Diameter (mm)
No Bond Degradation Bond Degradation
53. 53
Figure 25. Flexural strength vs diameter for Ansys model
Figure 26. Flexural Strength vs reinforcement diameter without bond degradation
However, the flexural strength reduction in empirical model is more radical when
bond degradation is considered. One reason for such discrepancy is the effect of
spalling. The empirical model takes into account the spalling of concrete as the
reinforcement corrodes and exerts outward pressure on the surrounding concrete.
However, this effect is not taken into account in the Ansys modelling.
0
20
40
60
80
100
120
26 27 28 29 30 31 32 33
FlexuralStrength(kNm)
Reinforcement Diameter (mm)
No Bond Degradation Bond Degradation
0
20
40
60
80
100
120
26 27 28 29 30 31 32 33
FlexuralStrength(kNm)
Reinforcement Diameter (mm)
Ansys Model Empirical Model
54. 54
Figure 27. Flexural Strength vs reinforcement diameter with bond degradation
The analysis carried out in the finite element software assumed that the corrosion is
uniform through the bar length which may not be the case in the reality. If the
corrosion is chloride induced, there might be pitting corrosion which will lead to
flexural strengths much less than predicted in this report.
Results for flexural strength from empirical and ansys model are tabulated here for
reference.
Diameter(mm)
Flexural Strength
(kNm) -No bond
degradation
Flexural Strength kNm -
Bond degradation
32 106.5541924 132.4162753
31.5 103.9603911 80.40663157
31 101.3630674 45.68772355
30.5 98.76433412 25.33560096
30 96.16627037 13.95032112
29.5 93.57092134 7.688105981
29 90.98029848 4.25728995
28.5 88.39637938 2.373477507
28 85.82110787 1.333576273
27.5 83.25639395 0.755546011
27 80.70411382 0.431749855
Table 10. Flexural strength results for empirical model
0
20
40
60
80
100
120
140
26 27 28 29 30 31 32 33
FlexuralStrength(kNm)
Reinforcement Diameter (mm)
Ansys Model Empirical Model
56. 56
Conclusion
Bending moment capacity of corroded reinforced beams has been calculated using
empirical model as well as Ansys model.
The flexural capacity of beam is affected by two major factors resulting from
corrosion namely mass loss of steel and loss in bond strength between concrete and
reinforcement. Other factors responsible for strength reduction are spalling and
cracking.
Both empirical and FE software model considers the effects of loss in bond strength
and mass loss, however they do no account for the effects of spalling.
It is observed that there is similarity in the strengths of both the models when no
bond degradation is considered. However, there is marked difference between the
flexural strengths of both models when bond degradation is taken into the account.
It is observed that loss in bond strength is the most critical factor effecting the
flexural strength of corroded beams and loss in steel area contributes negligibly to
the strength loss.
57. 57
Future Work
As is evident from the results, there is a considerable difference in flexural strength
of RC beams when the results from the finite element software and empirical
methods are compared. Few of the steps that can be taken to further the scope of
the study are described briefly here.
Experimental Studies
The beams can be cast in the lab and then allowed to corrode for some time. The
corrosion in such beams could be expedited by the use of salt contaminated water.
This is done by creating a small dam on top of the specimen beam.
Figure 28. Setup to expedite corrosion process
The above figure illustrates a mechanism to expedite the corrosion mechanism. The
dam is filled with varying level of chloride contaminated solution to effect the rate of
corrosion. Level of corrosion can be monitored by measuring Icorr and thus deducing
the extent of mass loss. Once the desired corrosion has happened, the beam can be
tested for flexural strength.
58. 58
These results can then be corroborated with the observations obtained from analysis
in finite element software and empirical models. With the use of these results, finite
element model can be further optimized and the formulas used in empirical models
can also be tweaked to get more consistent results with the experimental value.
Analysis of Prestressed Beams
Similar studies can be conducted for studying the effect of corroded prestressed
tendons on the flexural strength of prestressed beams. However, the major factor
affecting the corrosion of tendons is the process used for grouting and the quality of
the overall process. However, for modelling the beam with tendons without the
surrounding duct can be carried out on the similar lines as used in this report.
Another important consideration will be design and modelling of anchorage for such
beams.
Determination of shear strength
This report doesn’t cover the effects of corrosion on the shear strength of the beam.
This can be another area for further research in to the effects of corrosion.
59. 59
References
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GLAMORGAN. In ICE Proceedings (Vol. 84, No. 4, pp. 635-669). Thomas Telford.
2. Broomfield, J. P. (2002). Corrosion of steel in concrete: understanding, investigation and repair.
CRC Press.
3. Holze, R. (2008). PR Roberge (ed): Corrosion basics: an introduction. Journal of Solid State
Electrochemistry, 12(6), 771-772.
4. Jones, D. A. (1996). Principles and Prevention of Corrosion, Chapter 2,“Thermodynamics and
Electrode Potential,”. ISBN 0-13-359993-0, Prentice-Hall International.
5. Lahiri, A. K. (1970). Corrosion map of India. K. N. P. Rao (Ed.). Corrosion Advisory Bureau,
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