nasrin 2013 - nonlinear fem analysis of rc columns confined by cfrp.pdf
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NONLINEAR FINITE ELEMENT ANALYSIS OF CONCRETE COLUMNS
CONFINED BY FIBRE- REINFORCED POLYMERS
SABREENA NASRIN
STUDENT NO: 1009042348
MASTER OF SCIENCE IN CIVIL ENGINEERING (STRUCTURAL)
DEPARTMENT OF CIVIL ENGINEERING
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY
DHAKA-1000, BANGLADESH
JULY, 2013
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NONLINEAR FINITE ELEMENT ANALYSIS OF CONCRETE COLUMNS
CONFINED BY FIBRE- REINFORCED POLYMERS
SUBMITTED BY
SABREENA NASRIN
STUDENT NO: 1009042348
A Thesis submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in Civil Engineering (Structural)
DEPARTMENT OF CIVIL ENGINEERING
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY
DHAKA-1000, BANGLADESH
JULY, 2013
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DEDICATED
TO
My Beloved Parents
Late Dr. Nazrul Islam Miah
Mrs. Meherunnesa Khan
Engr. Humayun Kabir
&
Mrs. Nurunnahar Begum
CERTIFICATE OF APPROVAL
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The thesis titled Nonlinear Finite Element Analysis of Concrete Columns Confined by Fibre-Reinforced Polymers submitted by Sabreena Nasrin, Student Number 1009042348F, Session: October, 2009 has been accepted as satisfactory in partial fulfillment of the requirement for the degree of Master of Science in Civil Engineering (Structural) on 29th July, 2013.
BOARD OF EXAMINERS
1. Dr. Mahbuba Begum Chairman Associate Professor (Supervisor) Department of Civil Engineering BUET, Dhaka-1000
2. Dr. Md. Mujibur Rahman Member Professor and Head (Ex-Officio) Department of Civil Engineering BUET, Dhaka-1000
3. Dr. Sk. Sekender Ali Member Professor Department of Civil Engineering BUET, Dhaka-1000
4. Dr. A. M. M. Taufiqul Anwar Member Professor Department of Civil Engineering BUET, Dhaka-1000
5. Dr. Md. Mozammel Hoque Member Associate Professor (External) Department of Civil Engineering
DUET, Gazipur
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CHAPTER 1
INTRODUCTION 1.1 General In recent years, considerable attention has been focused on the use of fibre-reinforced
polymer (FRP) composite materials for structural rehabilitation and strengthening purpose.
Highly aggressive environmental conditions have a significant effect on the durability and
structural integrity of steel reinforced concrete piles, piers and columns. Corrosion of steel
rods is a potential cause for the structural damage of these reinforced concrete columns.
Dealing with the problem of steel reinforcement corrosion has usually meant improving the
quality of the concrete itself, but this approach has had only limited success. A traditional
way of repair of damaged concrete columns is wrapping a sheet of steel around the column.
While the strength of repaired columns can be increased for a short-term, the steel wrapping
suffers from the same problem as the steel rebar, corrosion and poor durability. It also suffers
from labor-intensive construction problem due to its weight.
In a new approach, FRPs are now being used as alternatives for steel wrappings in repair,
rehabilitation and strengthening of reinforced concrete columns. If correctly applied, the use
of FRP composites for strengthening reinforced concrete (RC) structures can result in
significant enhancements to durability, and decreased maintenance costs, as well as in
improved serviceability, ultimate strength, and ductility. Moreover, the FRP composites can
generally be applied while the structure is in use, with negligible changes in the member
dimensions. Other advantages include high strength and stiffness-to-weight ratios, a high
degree of chemical inertness, controllable thermal expansion, damping characteristics, and
electromagnetic neutrality. In addition to repair, FRP confined concrete columns have been
developed in new construction and rebuilding of concrete piers/piles in engineering
structures.
Extensive experimental studies have been conducted by several research groups on the
behavior of confined concrete columns (Benmokrane and Rahman, 1998; Saadatmanesh and
Ehsani, 1998; Meir and Betti 1997; El-Badry 1996). However, most of these studies are
confined to circular shaped columns. Experimental studies related to rectangular and square
columns are limited (Bousias et.al. 2004). Despite of the availability of a large amount of
experimental data for predicting the behavior of FRP confined concrete circular columns, a
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complete 3-D finite element model for understanding the influence of geometric shapes,
aspect ratios and FRP stiffness is somewhat lacking. As a contribution to fill this need an
attempt has been taken to develop a complete 3-D finite element model to investigate the
effect of aspect ratios, corner radius and thickness of FRP wrap on the behavior of FRP
wrapped concrete columns. This study also aims to evaluate the effect of FRP-concrete
interface on the behavior of FRP confined concrete.
1.2 Objectives of the Study The objectives of the study are
1 To perform a nonlinear 3D finite element analysis on concrete columns of different
shapes confined with FRP wrap.
2 To validate the numerical model with respect to the experimental database available in
the literature.
3 To study the effect of selected parameters such as aspect ratio (a/b), the corner radius (R)
and the thickness of FRP wrap (tf) on the strength and ductility of FRP confined concrete
columns under concentric axial loading only.
1.3 Scope
The numerical simulation of concentrically loaded FRP confined concrete column has been
performed using ABAQUS, a finite element software package. A 3D finite element model
incorporating the nonlinear material behavior of concrete has been developed. The interface
between concrete and FRP has been modeled using contact pair algorithm in ABAQUS. A
perfect bond and a cohesion based surface interaction model have been assumed to define the
contact behavior of the concrete-FRP interface. The nonlinear load displacement response up
to failure of the confined columns has been traced using Riks solution strategy.
The performance of the developed model has been studied by simulating test columns
confined with FRP available in the published literature. These columns had various geometric
shapes as well as various FRP configurations. Finally the effect of the selected parameters
like cross-section shape factor, corner radius and the thickness of the FRP wrap on the
strength and ductility of FRP confined concrete columns have been investigated.
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1.4 Organization of the Study The thesis has been organized in six chapters. Chapter 1 includes the background of the
work along with the objectives and scope of current study. A brief review on the available
literatures regarding the characteristics and available types of composites as well as different
rehabilitation schemed for various structural components has been reported in chapter 2.
Moreover, this chapter presents various analytical models proposed by different research
groups for predicting the behavior of concrete rectangular and square columns confined with
Fibre reinforced polymers
.
Chapter 3 includes the properties of reference columns and the characteristics of the finite
element. The performance of the FE model has been studied in chapter 4 by comparing the
numerically obtained graphs with available experimental graphs.
Chapter 5 incorporates the parametric study which includes the effects of aspect ratio, corner
sharpness and confinement effectiveness of FRP-strengthened concrete columns. Finally, the
summary and conclusions of the work along with the recommendations for future research
have been included in chapter 6.
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CHAPTER 2
LITERATURE REVIEW
2.1 General Recent evaluation of civil engineering infrastructure has demonstrated that most of it will
need major repairs in the near future. The strength and stability of these structural members,
bridges, water retaining structures, sewerage treatment plants, wharfs, etc. are provided by
concrete. Therefore it is very important to protect concrete and any deterioration or damage
to concrete must be repaired promptly in order not to compromise the integrity of structures
built with concrete. Concrete rehabilitation particularly in critical infrastructures is as
important as any other maintenance activity and must be carried out in a timely manner.
Repairs performed at early stage would save extremely expensive remediation that may
become necessary at latter stages. Concrete can be deteriorated for many reasons such as-
Accidental Loadings Chemical Reactions Construction Errors Corrosion of Embedded Metals Design Errors Abrasion and Cavitations Freezing and Thawing Settlement and Movement Shrinkage Temperature Changes Weathering etc.
The strengthening and retrofitting of existing concrete structures to resist higher design loads,
correct deterioration-related damage or increased ductility has traditionally been
accomplished using conventional materials and construction techniques. Externally bonded
steel plates, steel or concrete jackets and external post tensioning are just some of the many
techniques available. However, to repair and extend the life of damaged structures externally
bonded fibre reinforced polymers (FRP) have been proved to be the most effective alternative
to the conventional ones. Despite a high material cost, some advantages like high strength to
weight ratio, high corrosion resistance, easy handling and installation processes are
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establishing them as the most convenient option over the traditional strengthening materials
for rehabilitation of corroded RC structures, seismic damaged structures and so on. (Nasrin et
al., 2010). The composition and the type of this new composite material are presented in this
chapter. The materials mechanical behavior is also included here. This chapter mainly
focuses on the repairing techniques by FRP laminates for shear and flexural strengthening of
corroded RC structures, strengthening of concrete beam-column joints and strengthening of
rectangular concrete columns in accordance with the numerical and experimental
investigations. The behavior of FRP confined concrete columns along with the design
guidelines are also reported in the literatures.
2.2 Fibre-Reinforced Polymers Fibre-reinforced polymer (FRP) composites consist of continuous carbon (C), glass (G) or
aramid (A) fibres bonded together in a matrix of epoxy, vinylester or polyester. The fibres are
the basic load carrying component in FRP whereas the plastic, the matrix material, transfers
shear. FRP products commonly used for structural rehabilitation can take the form of strips,
sheets and laminates as shown in Figure 2.1.
Figure 2.1 FRP products for structural rehabilitation, (a) FRP strips and (b) FRP sheets (Rizkalla et al. 2003).
Use of FRP has now become a common alternative over steel to repair, retrofit and strengthen buildings and bridges. FRP materials may offer a number of advantages over steel plates which include,
1. High specific stiffness (E/).
2. High specific strength (ult /)
3. High corrosion resistance
4. Ease of handling and installation
Moreover, its resistance to high temperature and extreme mechanical and environmental
conditions has made it a material of choice for seismic rehabilitation. Some of the
(a) (b)
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disadvantages of using FRP materials include their high cost, low impact resistance and high
electric conductivity.
2.3 Properties and Behavior of FRP
2.3.1 Tensile Behavior
The tensile strength and stiffness of FRP material is dependent on several factors. As the
fibres of FRP are the main load-carrying constituents, so the type of fibres, the orientation of
fibres and the quantity of fibres govern the tensile behavior mostly. When this FRP is loaded
under direct tension it does not exhibit any plastic behavior (yielding) before rupture. Most of
the time, FRP shows a linearly elastic stress-strain relationship until failure. Table 2.1 present
the tensile properties of commercially available FRP system.
Table 2.1 The tensile properties of some of the commercially available FRP systems
Fibre type Elastic modulus Ultimate Strength Rupture
strain, min
103 ksi GPa ksi MPa %
Carbon
General Purpose 32-34 220-240 300-550 2050-3790 1.2
High Strength 32-34 220-240 550-700 3790-4820 1.4
Ultra- High Strength 32-34 220-240 700-900 4820-6200 1.5
High modulus 50-75 340-520 250-450 1720-3100 0.5
Ultra- High modulus 75-100 520-690 200-350 1380-2400 0.2
Glass
E-glass 10-10.5 69-72 270-390 1860-2680 4.5
S-glass 12.5-13 86-90 500-700 3440-4140 5.4
Aramid
General Purpose 10-12 69-83 500-600 3440-4140 2.5
High performance 16-18 110-124 500-600 3440-4140 1.6
(Italian National Research Council, 2004)
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2.4 Applications of FRP in Structural Rehabilitation In the last ten to fifteen years, FRP materials have emerged as promising alternative repair
materials for reinforced concrete structures and they are rapidly becoming materials of choice
for strengthening and rehabilitation of concrete infrastructure. There are currently three main
applications for the use of FRPs as external reinforcement of reinforced concrete structures
such as
Flexural strengthening (FRP materials are bonded to the tension face of a beam) Shear strengthening (FRP materials are bonded to the side faces of a beam) and Confining reinforcement (columns are wrapped in the circumferential direction with
FRP sheets)
2.4.1 Beam Strengthening with FRP Laminates
Flexural strengthening of reinforced concrete beams using FRP composites is generally done
by bonding of FRP sheets at the tension side of the beam. The bonded sheets work as tension
reinforcement and in turn increase the flexural capacity of the beam considerably.Bonding of
FRP plates and laminates to RC beams has now become a popular strengthening technique
which was first introduced by Meiers group (Meier 1997) at the Swiss Federal Laboratories
for Materials Testing and Research. Since then, extensive experimental and analytical studies
(Colalillo and Sheikh 2009; Saxena et al. 2008; Choi et al. 2008; Nitereka and Neal 1999;
Brena et al. 2003; Bonacci and Maalej 2000) have been carried out all over the world on
flexural strengthening of concrete beams. These studies have concluded that introduction of
FRP can significantly enhance the flexural strength of a reinforced concrete beam.
Considerable research has been conducted to establish a better understanding of these
laminated system behavior .Several types premature failure modes such as tensile failure of
the bonded plate, concrete failure in the compressive zone, and sudden or continuous peeling
off of the laminate have also been observed. According to ACI code 2005 the following
failure modes should be investigated for an FRP strengthened section
Yielding of the steel in tension followed by rupture of the FRP laminate. Yielding of the steel in tension followed by concrete crushing. Debonding of the FRP from the concrete substrate. Shear / tension delamination of the concrete cover (cover delamination);and Crushing of the concrete in compressive before yielding of the reinforcing steel.
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Some factors like the composite ratio Ac/As, the percentage of conventional tensile steel
reinforcement ; and the bond achieved between the FRP and the concrete influence the
degree of strength enhancement attained. It is reported that bonding very thin FRP plates to
the tension face of the beams can introduce a significant amount of enhancement in the
flexural strength of lightly reinforced beam, while more heavily reinforced beams requires an
increased amount of FRP, or a comparable composite ratio to achieve comparable strength
enhancement (Ross et.al., 1999). High composite ratio plays an important part in the
strengthening effect of light to moderately reinforced beams. By CFRP application,
approximately 10 to 35% higher load carrying capacity can be obtained along with a 10 to
32% decrease in the beam deflections at ultimate failure (Bonnaci et al.,2000) .
In addition to the strength enhancement, the FRP strengthening scheme with anchoring
system improves the ductility of the retrofitted beam by confining the concrete. Various
analytical models (Saadatmanesh et al. 1996, Niterika and Neale, 1999) have been proposed
to predict the ultimate moment capacities of reinforced concrete beams strengthened with
externally bonded composite laminates. In general, these models ignore the nonlinear stress
strain behavior of the concrete and the contribution of tension concrete. Applications based
on such models are limited to structures with fairly simple geometries and loading conditions.
In addition to flexural strengthening, many experiments are now being carried out on shear
strengthening with FRP composites. The results show that significant increases in shear
capacity are possible with this FRP repair technique. The failure modes and degree of
strength enhancement, however, are strongly dependent on the details of the bonding scheme
and anchorage method. Shear strengthening using external FRP may be provided at locations
of expected plastic hinges or stress reversal and for enhancing post yield flexural behavior of
members in moment frames resisting seismic loads only by completely wrapping the section.
However, since the FRP materials behave differently than steel, the contribution of FRP
materials need to be included carefully in the design equations on the basis of detailed
experimental evaluation.
The bond behavior and load transfer behavior between concrete beam and FRP laminates is
an important tool to predict the failure behavior and stress distribution of retrofitted beams.
Experimental studies (Brena et al. 2003; Hamad et al. 2004; Saxena et al. 2008; and Choi
et al. 2008) indicated that debonding of the bottom strip from the concrete surface is the most
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common mode of failure for concrete beams strengthened by externally bonded FRP sheets.
The debonding results in the loss of the composite action between the concrete and FRP
laminates. The effective stress transfer between FRP and concrete is essential to develop the
composite action. The local debonding initiates when high interfacial shear and normal
stresses exceed the concrete strength (Kotynia et al. 2008). Additional U-jacket strips or
sheets can be provided in the debonding initiation region to delay the FRP debonding
resulting in increased efficiency of the FRP retrofitting scheme. More experimental and
analytical studies should be carried out to find a more reliable relation between bond behavior
of FRP laminates and concrete to make sure that the FRP fitted structure does not fail
prematurely.
2.4.2 Column Strengthening
Reinforced concrete columns are considered to be the most important part of a typical
reinforced concrete structure as they are the major load carrying element of the building.
Minimum cross section size and lack of steel reinforcement in under designed columns leads
to a weak columnstrong beam construction. To avoid a soft story collapse of a building due
to seismic action, columns should be adequately designed.
During an earthquake, plastic hinges are most likely to form in columns in weak column
strong beam construction which may result in a sudden story collapse of the whole structure.
So it is very necessary to strengthen the columns so that plastic hinges are formed in the
beams since it allows more effective energy dissipation. It is reported that, closely spaced
transverse reinforcement used in the plastic hinge zone of concrete bridge columns will help
in increasing the compressive strength as well as increase the ultimate compressive strain in
the core concrete (Mirmiran and Shahawy 1997). Therefore, a significant amount of increase
in compressive strain will result in increasing the ductility of concrete columns. Researchers
have shown that an increase in the thickness of CFRP and AFRP jacket proportionally
increases the shear strength of the upgraded column or pier (Fujisaki et al. 1997; Masukawa
et al. 1997).
2.4.2.1 Experimental investigations
Unidirectional FRP sheets can be wrapped around the concrete columns as an external
reinforcement and confinement. Several investigations (Benzoni et al., 1996; Masukawa
et al., 1997; Seible et al., 1997; Lavergne and Labossiere, 1997; Saadatmanesh et al., 1997;
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Seible et al., 1999; Mirmiran and Shahawy 1997; Fukuyama et al., 1999; Pantelides et al.
2000b; Bousias et al. 2004 and Harajli et al. 2006) have been conducted to study the
effectiveness of FRP in restrengthening of circular, square and rectangular reinforced
concrete columns. Most of the research works were done for identifying the behavior of FRP
confined concrete circular columns.
Saafi et.al. (1999) confirmed that for circular columns external confinement of concrete by
FRP tubes can significantly enhance the strength, ductility, and energy absorption capacity of
concrete.
Experiments regarding behavior of rectangular columns confined with FRP laminates are
limited. Haralji et al. (2006) reported that for square column sections without longitudinal
reinforcement (plain concrete) the increase in axial strength was found to be 154%, 213%,
and 230% for one, two, or three layers of CFRP wraps, respectively.
Rochette and Labossie`re (2000) performed experimental research for identifying the
influence of FRP thickness and corner radius of rectangular columns. They reported that for a
given number of wraps around a section (or a given transverse reinforcement ratio), the
confinement effect is directly related to the shape of the section and the section corners
should always be rounded off sufficiently to prevent premature failure by punching of the
fibres in the wrap. To investigate the influence of aspect ratio Chaallal, O. et al. (2003)
performed an experiment having different cross sectional properties and material properties
of rectangular columns. The gain in performance of axial strength and ductility due to the
wrapping was found greater for the 3 ksi concrete wrapped columns than for the
corresponding 6 ksi concrete columns. The maximum gain achieved for the 3 ksi concrete
wrapped columns was approximately 90% as compared to only 30% for the 6 ksi columns.
Figure 2.3 shows a picture of FRP applications on concrete column for retrofitting.
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13
the concrete shortly after the concrete has reached its ultimate compressive strength. To better
understand the FRP confinement of the concrete a proper stress-strain model has to be
developed. Exclusive work has been done in understanding this behavior.
2.5.1. Circular Columns
The confinement action exerted by the FRP on the concrete core is of the passive type, that is,
it arises as a result of the lateral expansion of concrete under axial load. As the axial stress
increases, the corresponding lateral strain increases and the confining device develops a
tensile hoop stress balanced by a uniform radial pressure which reacts against the concrete
lateral expansion (De Lorenzis & Tepfers, 2003.). When an FRP confined cylinder is subject
to axial compression, the concrete expands laterally and this expansion is restrained by the
FRP. The confining action of the FRP composite for circular concrete columns is shown in
Figure 2.4.
For circular columns, the concrete is subject to uniform confinement, and the maximum
confining pressure provided by FRP composite is related to the amount and strength of FRP
and the diameter of the confined concrete core. The maximum value of the confinement
pressure that the FRP can exert is attained when the circumferential strain in the FRP reaches
its ultimate strain and the fibres rupture leading to brittle failure of the cylinder. This
confining pressure is given by Equation 2.1:
(2.1)
Figure 2.4 Confinement action of FRP composite in circular sections
(Benzaid and Mesbah, 2013)
ffrp ffrp tfrp tfrp
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Where fl is the lateral confining pressure, Efrp is the elastic modulus of the FRP composite, fu is the ultimate FRP tensile strain, ffrp is the ultimate tensile strength of the FRP composite, tfrp
is the total thickness of the FRP, d is the diameter of the concrete cylinder, and frp is the FRP
volumetric ratio given by the following Equation 2.2 for fully wrapped circular cross section:
= /
(2.2)
2.5.2. Rectangular Columns
A square column with rounded corners is shown in Figure 2.4. To improve the effectiveness
of FRP confinement, corner rounding is generally recommended. Due to the presence of
internal steel reinforcement, the corner radius R is generally limited to small values. Existing
studies on steel confined concrete (Park and Paulay, 1975; Mander, et al.1988; Cusson and
Paultre, 1995). have led to the simple proposition that the concrete in a square section is
confined by the transverse reinforcement through arching actions, and only the concrete
contained by the four second-degree parabolas as shown in Figure 2.5 (b) is fully confined
while the confinement to the rest is negligible. These parabolas intersect the edges at 45.
While there are differences between steel and FRP in providing confinement, the observation
that only part of the section is well confined is obviously also valid in the case of FRP
confinement. Youssef et al. (2007) showed that confining square concrete members with FRP
materials tends to produce confining stress concentrated around the corners of such members,
as shown in Figure 2.5(a). The reduced effectiveness of an FRP jacket for a square section
than for a circular section has been confirmed by experimental results (Rochette &
Labossire, 2000). Despite this reduced effectiveness, an FRP-confined square concrete
column generally also fails by FRP rupture (Benzaid et. al., 2008). For finding the confining
pressure for rectangular columns in Equation (2.1), d is replaced by the diagonal length of the
square section. For a square section with rounded corners, d can be written as:
2 22 1 (2.3)
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tion of FRP Mesba
15
ete specimen
height of th
d catastroph
ncrete core
ing and wav
failure of the
o failed by f
gh the stress
ncrete prism
e of the com
hstand the l
nement thus
ng various
e and shiftin
ean and per
wo external
dius, the brea
ure 2.6. The
first. It was,
(b)with
composite inah, 2013)
ns is general
he specimen
hic, accomp
in the form
ving of the t
e FRP tube a
fracture of th
s-strain curv
s occurred w
mposite wrap
oad, which
triggers a su
stages of l
ng of the ag
rpendicular t
plies of the
akage line ap
e ultimate co
of course, h
) Effectivelyin a square
n square sec
lly marked b
n However,
anied by a
m of a cone,
tubes were
as reported b
he CFRP co
ves indicate a
without adva
p. When the
correspond
udden failure
loading. The
ggregates (C
to the fibre
e specimens
ppears at a c
omposite str
higher for sp
y confined ce column
ctions (Benza
by fracture o
in the carbo
simultaneou
as shown i
observed, th
by Saafi et a
omposite at o
an increase i
ance warnin
e confinemen
ds to a stres
e mechanism
e sounds ar
Chaallal et al
es. On a fe
s occurred. I
orner, exactl
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pecimens wit
oncrete
aid and
of
on
us
in
he
al.
or
in
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nt
ss
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re
l.,
w
In
ly
ed
th
-
larger rou
with only
For stron
specimen
2.7 DesiThe Ame
of FRP a
The axia
calculate
factored
Vertical
also limi
jacket. Th
the load
calculate
ACI 318
If the me
FRP jack
Figure
unded off co
y a few com
ngly confined
ns (Rochette
ign Guidelierican Concr
as confining r
al compressi
d using the
confined con
displacemen
it the amoun
he axial dem
factors requ
d using the
(2002).
ember is sub
ket should be
e 2.6 Typical
(a
orners. For c
mposite plies
d columns, w
& Labossi
ines rete Institute
reinforceme
ive strength
e convention
ncrete streng
nt, section di
nt of additio
mand on an F
uired by AC
strength-red
bjected to c
e limited bas
l failed spec
a)
columns conf
s), the break
wrap breaka
re, 2000).
e (ACI 2002
ent for streng
of a non-sl
nal expressio
gth f fcc. Th
ilation, crack
nal compres
FRP-strength
CI 318 (2002
duction fact
combined co
sed on the cr
imens (a) cir(Chaallal
16
fined weakly
kage in the w
age was obse
2) published
gthening circ
lender mem
ons of ACI
he additiona
king, and str
ssion strengt
hened concre
2) and the a
tors, , for
ompression a
riteria given
rcular (Saafiet al., 2003)
(b
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wrap was on
erved on alm
design reco
cular concret
mber confine
318 (2002)
l reduction f
rain limitatio
th that can b
ete member
axial compre
spiral and ti
and shear, t
by
i et al., 1999
b)
no rounded
nly 50150 m
most the full
ommendation
te columns.
ed with an F
) substitutin
factor is set t
ons in the FR
be achieved
should be co
ession streng
ied element
the effective
9) and (b) rec
off corners o
mm in length
l height of th
ns for the us
FRP jacket
ng for fc th
to f = 0.95.
RP jacket ca
with an FR
omputed wit
gth should b
s required b
e strain in th
ctangular
or
h.
he
se
is
he
an
RP
th
be
by
he
-
17
0.004 0.75 (2.4)
At load levels near ultimate, damage to the concrete in the form of significant cracking in the
radial direction occurs. The FRP jacket contains the damage and maintains the structural
integrity of the column. At service load levels, this type of damage should be avoided. In this
way, the FRP jacket will only act during overloads that are temporary in nature. To ensure
that radial cracking will not occur under service loads, the stress in the concrete is limited to
0.65f c. In addition, the stress in the steel should remain below 0.60fy to avoid plastic
deformation under sustained or cyclic loads. By maintaining the specified stress in the
concrete at service, the stress in the FRP jacket will be negligible. (Nanni, A. 2001). These
guidelines are only for the circular FRP-wrapped columns under concentric axial load
because test data on square and rectangular, slender, and eccentrically-loaded columns are
comparatively scarce.
Guidelines in Canada (CSA and ISIS) and Europe (FIB) provide design equations for
strengthening rectangular columns retrofitted with externally-bonded confining composite
wrap. The enhancement of confined concrete strength depends on the passive confinement
due to the lateral pressure generated by the lateral FRP fibres. The design and construction
guide for strengthening concrete structures with externally bonded FRP systems reported by
the ACI Committee 440 (2002) is aware of the enhanced concrete strength reported by
researchers, but it still considers it as marginal and no recommendations have yet been
provided, given the many unknowns related to this type of application. It should be
mentioned that most of the research on confinement of rectangular concrete columns was
presented after the ACI 440.2R guidelines were published.
2.7.1 CSA-S806-022 (2002)
According to the Canadian Standards CSA-S806-02 the load carrying capacity of a confined
column can be calculated as follows
(2.5)
where ke is a resistance factor (= 0.80 for columns with transverse steel ties), c and s are the
resistance factors for concrete and steel (c = 0.6 and s = 0.85), 1 is the ratio of average
-
18
compression stress to the concrete strength, that is, 1 = (0.85 0.0015f c ) 0.67, Ag and Ast are the gross concrete area and the area of steel bars respectively.
The CSA guidelines limit the applicability of the design equations to columns with small
aspect ratios and rounded corners. The maximum aspect ratio is limited to 1.5 (that is, b/h
1.5). Also, the corner radius is to be greater than or equal to 20 mm (0.8 in.) (r 20 mm [0.8
in.]). For rectangular columns meeting these conditions, the confined concrete strength f cc
can be calculated using Equation (2.6) to (2.8).
0.85 (2.6)
6.7 -0.17 (2.7)
(2.8)
Where, kc is a confinement coefficient equal to 0.25 for rectangular columns, D is the
diameter of an equivalent circular column; tj is the thickness of the FRP jacket, fFj is the
stress in the FRP jacket (= minimum [0.004Ej, F fFu]), F is the resistance reduction factor for FRP and fFu is the ultimate FRP tensile strength.
2.7.2 ISIS Canada (2001)
According to the design guidelines provided by ISIS Canada the confined concrete strength
can be calculatedusing Equation (2.9) ,
1 (2.9)
where pr is a performance coefficient (=1); Ww is the volumetric strength ratio. To ensure an
effective confinement, the ISIS guidelines limit the applicability of the design equations to
quasi-square columns with rounded corners because the maximum aspect ratio is limited to
1.1 (b/h 1.1). Also, the corner radius should be greater than or equal to b/6 and not less than
35 mm (1.4 in.) [(r b/6] and [r 35 mm (1.4 in.)]. The guidelines, however, do not specify
any limiting values on the confining pressure as was the case for circular columns.
-
19
2.7.3 FIB Guidelines (2001)
In its technical report Externally Bonded FRP Reinforcement for RC Structures, the
International Federation of Structural Concrete (FIB) provides equations for the design of
rectangular columns confined with FRP wrap. The ultimate confined concrete strength is
calculated using Equation (2.10) to (2.13).
0.2 3 (2.10)
Where can be calculated from Equation 2.11
(2.11)
(2.12)
(2.13)
where ke is the effectiveness coefficient representing the ratio of the effectively confined area
of the cross section to the total cross-sectional area and ju is the effective ultimate
circumferential strain of the FRP jacket. The guidelines state that in view of the limited
proper values of ju, the value chosen should be justified by experimental evidence.
2.8 Summary From the review of literature presented in this chapter it is clear that extensive experimental
investigations have been performed on strengthening of concrete circular columns using fibre
reinforced polymers. The performance of FRP confined concrete circular columns is now
relatively well understood from the experimental point of view. But information about
behavior of confined rectangular columns is limited. Since laboratory experiments are
expensive and time-consuming, reliable analytical procedures should be developed for
predicting the structural response of concrete columns confined by fibre-reinforced polymers.
To fully simulate their behavior up to failure, numerical models which are capable of
predicting the complexities of material nonlinearity, concrete post cracking tension softening,
as well as interaction between the concrete and FRP surface, is required. Therefore, an
attempt has been made in current study to address these issues and thereby to develop a full
scale 3D finite element model for FRP confined concrete columns under axial loading.
-
20
CHAPTER 3
FINITE ELEMENT MODELING
3.1 General
Due to relatively high cost of large-scale experimental research, a means of modeling FRP-
confined concrete columns using computer aided program is needed to broaden the current
knowledge about the complete behavior and influence of the geometric properties. In this
study an attempt has been made to develop a complete Finite Element model that can be
applied for a variety of geometries of FRP confined concrete columns subjected to uniaxial
loading and provide accurate simulations of the compressive behavior. The model therefore is
to be capable of simulating numerically the compressive behavior of concrete columns
confined by Fibre-Reinforced Polymers. The model is developed using the
ABAQUS/Standard finite element software code.
A concrete damage plasticity model which is capable of predicting both compressive and
tensile failures is used to model the concrete material behavior. The FRPconcrete interface
in the confined concrete column is modeled using the contact pair algorithm in ABAQUS.
Both cohesion and perfect bond formulation having simple masterslave contact are used at
the interface of the FRP laminate and concrete infill. Nonlinear material behavior as well as
the geometric nonlinearities is accounted for in the numerical model. A static Riks solution
strategy is used to trace a stable post-peak response of the composite system up to failure.
Experimental results of 11 specimens, representing FRP-confined concrete columns are used
to validate the numerical results. To validate the model, simulations are conducted for axially
loaded rectangular test specimens reported in the literature, varying in cross section from
152152 mm to 108165 mm, including a variety of corner radius and concrete compressive
strength (25 MPa to 42 MPa). For circular columns the diameter of the columns are 152 mm.
The thickness of the FRP sheets is also varied here.
Detailed descriptions of the test specimens are provided in the following section. This is
followed by a description of the finite element model geometry used to simulate the various
tests, the material model parameters, as well as the loading program.
-
21
3.2 Properties of Reference Test Specimens 3.2.1 Geometric and Material Properties of Square Columns The column sets tested by Rochette and Labossie`re (2003) includes five square specimens
named S5C5, S25C3, S25C4, S25C5 and S38C3 are modeled for finite element analysis. The
lists of these specimens, along with their geometric properties, are given in Table 3.1 and
shown in Figure 3.1. These specimens had square cross sections of 152 mm X 152 mm with a
height of 500 mm. The corner radiuses of the specimens were varied from 5 mm to 38 mm
where 5 mm represented the sharpest square column. The material properties of these test
specimens are presented in Table 3.2. These specimens were wrapped with two to five plies
of carbon fibre. In all cases, the principal fibres were oriented perpendicular to the column
axis, in a so-called 0 orientation. The mechanical properties of these test specimens are
presented in Table 3.2. To provide confinement, composite sheets were wrapped around the
column models in a continuous manner. Once the appropriate number of laps had been
placed, the outermost confining sheet was extended by an additional overlapping length, in
order to provide a sufficient anchorage and prevent slip between layers. An overlap length of
100 mm was applied and was found to be sufficient. After placement of the external 0 layer,
a 25 mm wide strip was added at each end of the specimens. This additional local
confinement prevents local damages and ensures that compressive failure occurs in the
central portion of the model. The specimens were subjected to a monotonic uniaxial
compression loading up to failure. The load was applied at a strain rate of 10 /s with a
hydraulic press. Prior to the test, a thin sulfide layer was put on both ends of the column to
ensure that contact areas were flat and parallel. These specimens were modeled to investigate
the confinement efficiency and influence of the corner radius for a constant FRP laminate
thickness.
3.2.2 Geometric and Material Properties of Rectangular Columns
Four rectangular columns SC-1L3-0.7, SC-2L3-0.7, SC-3L3-0.7 and SC-4L3-0.7 constitute
the column set of Chaallal et al.(1999) having different aspect ratio (a/b=0.7) are also
modeled to validate the numerical results. These specimens had rectangular cross sections of
165 mm X 108 mm with a height of 305 mm which is shown in Figure 3.1. The compressive
strength of concrete was around 21 MPa. For the specimens receiving carbon lamination, the
required layers of the standard CFRP system were applied. The standard system consists of a
-
22
bidirectional weave with an average of 6.7 yarns per inch in each direction and per layer.
Details of the material properties of the CFRP are presented in Table 3.2. For each specimen,
the corners were rounded with a corner radius equal to 25.4 mm to improve their behavior
and to avoid premature failure of CFRP material due to shearing at sharp corners. All
specimens were tested using a 550 kip (2,446 kN) MTS compression machine and an
automatic data acquisition system. Specimens were tested to failure under a monotonically
increased concentric load and a displacement control mode. Failure was usually caused by
sudden rupture of the composite wrap. After failure, the confined concrete was found to be
disintegrated in about one third of the total volume of the specimen. Experimental
observations suggest that the micro-cracking occurs in a more diffuse manner than in
unconfined concrete. Despite all measures, it was impossible to precisely identify the exact
location where failure initiated in the confining laminate (Chaallal et al., 2003)
3.2.3 Geometric and Material Properties of Circular Columns
To test the performance of circular concrete columns confined with FRP tubes, two circular
columns named C1 and C2 of Saafi et.al. (1999) with different thickness of FRP laminates
are also modeled under compression. All specimens consisted of short columns with a length-
to-diameter ratio of 2.85. Each specimen measured 152.4 mm in diameter and 435 mm in
length. The geometric properties are summarized in Table 3.3. The mechanical properties of
the FRP tubes are summarized in Table 3.4. The FRP tubes used in that study were made of
carbon-fibre filament winding-reinforced polymers, all consisting of 60 percent fibre and 40
percent polyester resin. The fibres oriented in the circumferential direction of the cylinders.
The concrete consisted of ASTM Type I Portland cement, river sand aggregate with a
fineness modulus of 2.6 and a crushed limestone aggregate with a maximum size of 10 mm.
The water-cement ratio (w/c) was 0.5 by mass. The average 28-day compressive strength of
the concrete was 38 MPa, and the modulus of elasticity was 30 GPa. Concrete encased with
carbon FRP tubes of thicknesses of 0.11 and 0.23 mm were designated as C1 and C2. The
confined cylinders, as well as unconfined samples, were tested using a 300-kip testing
machine. The load was applied to the specimen through a pad having the same area as the
concrete core. Failure of the composite specimens was initiated by fracture of the fibre tube.
-
23
Figure 3.1 Geometric properties of square, rectangular and circular columns
b = 152 mm
R
a=152 mm
500 mm
R
b =165.10 mm
108 mm
305 mm 435 mm
D=152.4
-
24
Table 3.1 Geometric properties of square and rectangular columns
Reference
Column
Designation
Columns Dimensions (mm) Fibre-Reinforced
Polymers
(CFRP)
a (shorter
side)
b(longer
side)
H
Corner
Radius (R)
No. of
Layers
Thickness
(mm) (mm) (mm) (mm) (mm)
Rochette and
Labossie`re(2000)
S25C3 152 152 500 25 3 0.9
S25C4 4 1.2
S25C5 5 1.5
S38C3 38 3 0.9
S5C5 5 5 1.5
Chaallal, O. et
al.(2003)
SC-1L6-0.7 108.00 165.1 305 25.4 1 0.5
SC-2L6-0.7 2 1.0
SC-3L6-0.7
SC-4L6-0.7
3
4
1.5
2.0
Table 3.2 Material properties of square and rectangular columns
Reference
Column
Designation
Concrete Properties Fibre-Reinforced Polymers
(CFRP)
(%)
fc (MPa)
w
(g/cm3)
ult %
Ej (GPa)
ffu (MPa)
Rochette, and
Labossie`re,(2000)
S25C3 2.26 42.00 1.80 1.5 82.7 1265
S25C4 3.02 43.90
S25C5 3.79 43.90
S38C3 2.25 42.00
S5C5 3.93 43.90
Chaallal, O. et al.(2003) SC-1L6-0.7 0.37 25.10 - 0.28 231 3650
SC-2L6-0.7 0.75 0.50
SC-3L6-0.7
SC-4L6-0.7
1.12
1.5
0.60
0.50
-
25
Table 3.3 Geometric properties of circular columns
Reference
Column
Designation
Columns Dimensions
Fibre-Reinforced
Polymers
(CFRP)
D
H
No. of
Layers
Thickness
(mm) (mm) (mm)
Saafi et.al. (1999) C1 152.4 435 1 0.11
C2 2 0.23
Table 3.4 Material properties of circular columns
Reference
Column
Designation
Concrete properties Fibre-Reinforced
Polymers
(CFRP)
fc
Ej
ffu
(MPa) (GPa) (MPa)
Saafi et.al. (1999) C1 35 367 3300
C2 390 3550
-
3.3 Cha3.3.1 Geo
In this st
like cross
stiffness
The mod
section is
3.3.1.1 E
As report
the simu
capture t
whereas
used to s
Typically
brick ele
translatio
Figure
L
X
racteristicsometric Pro
tudy FRP co
s-sectional s
factor on
del used in th
s shown.
Element selec
ted in chapte
ultaneous oc
this behavio
eight-node
simulate the
y, the numb
ement is ca
onal degrees
e 3.2 (a) 3-D
Y
Z
s of the Finoperties and
onfined conc
shape factor
n confineme
he analysis i
ction
er 2, the FR
ccurrence of
or eight node
finite strain
FRP sheets
er of nodes
alled C3D8
of freedom
D view of the
(a)
nite Elemend Finite Elem
crete column
(a/b), the co
ent efficien
is shown in
RP-confined c
f rupture of
e brick elem
n reduced in
s and lamina
in an eleme
8R and the
are consider
e column me
26
nt Model ment Model
ns are mode
orner sharpn
ncy of exp
Figure 3.2(a
concrete col
f FRP lamin
ments (C3D8
ntegration co
ates, Details
ent is clearl
8-node she
red in each n
sh and (b) C
a
ls
eled to study
ness factor (a
perimental
a) and in the
lumns reach
nates and c
8R) are use
ontinuum sh
s are shown
y identified
ell element
node for both
Cross section
(b)
y the effect o
a/R) and the
FRP confin
e Figure 3.2
their ultima
crushing of
d to model
hell element
in Figure 3
in its name
is called S
h elements.
n (with CFRP
b
of paramete
e confinemen
ned column
2 (b) the cros
ate capacity
concrete. T
the concret
s (SC8R) ar
.3(a) and (b
e. The 8-nod
SC8R. Thre
For modelin
P laminate)
R
rs
nt
n.
ss
at
To
te,
re
b).
de
ee
ng
)
-
the circu
provide f
A body
symmetry
3.3(c) sh
point on
coordinat
Figur
ular columns
for the mode
of revolutio
y axis) and
ows a typica
this cross-se
tes coincide
re 3.3 Finite
(a)
s axisymmet
eling of bodi
on is genera
is readily d
al reference
ection are de
with the glo
elements us
(c
tric element
ies of revolu
ated by revo
described in
cross-sectio
enoted by r a
obal Cartesia
sed in the mo
c) Axisymme
(c)
27
ts (CAX4R)
ution under a
olving a pla
cylindrical
on at =0. T
and z, respec
an X- and Y-c
odel, (a) 8-no
etric solid el
) were used.
axially symm
ane cross-se
polar coord
The radial a
ctively. At
coordinates.
ode solid (b
lement
(b)
. Axisymme
metric loadin
ection about
dinates r, z, a
and axial coo
=0. , the ra
b) 8- shell el
etric elemen
ng condition
t an axis (th
and . Figur
ordinates of
adial and axi
lement and
nts
ns.
he
re
f a
al
-
28
3.3.1.2 Mesh description
The mesh configuration for the full FRP confined concrete column model is shown in Figure
3.2. A sensitivity analysis was performed using 555 mm, 252525 mm and 505050
mm rectangular block to optimize the mesh in order to produce proper representation of the
rupture of FRP sheets. Since, the rupture of the FRP sheets always started at the corners
(Rochette and Labossie`re, 2000) a finer mesh was defined at the corners of the rectangular
and square columns. The mesh size of other portions didnt have any significant influence on
the compressive behavior of confined columns. The element sizes of the concrete and FRP
are selected to be approximately 505050 mm rectangular block as it can properly simulate
the behavior and minimize the computational time.
3.3.1.3 Modeling of concrete-FRP interface
One of the most challenging aspects of this study was to model successfully the concrete
FRP interaction at their interfaces with a contact algorithm. Contact conditions are a special
class of discontinuous constraint in numerical analysis. They allow forces to be transmitted
from one surface to another only when they are in contact. When the surfaces separate, no
constraint is applied. ABAQUS provides two algorithms for modeling contact: a general
contact algorithm and a contact-pair algorithm. The general contact algorithm is more
powerful and allows in simpler cases where as a contact pair algorithm is needed for
specialized contact features such as in the current problem.
Two different models were used to represent the interface between concrete and CFRP. In the
first model the interface was modeled as a perfect bond while in the second it was modeled
using a cohesive zone model. In perfect bond model contact pair algorithm is used between
concrete FRP interface. First, two surfaces were defined geometrically. The surface of the
FRP laminates was defined as slave surface whereas the concrete surface was defined as
master surface. As long as the two surfaces were in contact, they transmitted shear and
normal force across the interface.
In cohesive based interface model simple traction-separation law is used in between master
slave interfaces. Figure 3.4 shows a graphic interpretation of a simple bilinear traction
separation law written in terms of the effective traction and effective opening displacement
.
-
29
Figure 3.4 Bilinear traction separation constitutive law
The interface is modeled as a rich zone of small thickness and the initial stiffness K0 is
defined as:
1
3.1
where, ti is the resin thickness, tc is the concrete thickness, and Gi and Gc are the shear
modulus of resin and concrete respectively.
The values used for this study were ti = 1 mm, tc = 5 mm, Gi = 0.665 GPa, and Gc = 10.8 GPa.
From Figure 3.4, it is obvious that the relationship between the traction stress and effective
opening displacement is defined by the stiffness, K0, the local strength of the material, max, a
characteristic opening displacement at fracture, f, and the energy needed for opening the
crack, Gcr, which is equal to the area under the traction displacement curve. Equati` on.
3.2 provides an upper limit for the maximum shear stress, max, giving max = 3 MPa in this
case:
1.5 (3.2)
where
2.25
/ 1.25
3.3
and bf is CFRP plate width, bc is concrete width and fct is concrete tensile strength.
Gcr
max
f 0
K0
Effe
ctiv
e tr
actio
n,
Effective opening displacement,
-
30
The initiation of damage was assumed to occur when a quadratic traction function involving
the nominal stress ratios reached the value one. This criterion can be represented by
1 3.4
where n is the cohesive tensile and s and t are shear stresses of the interface, and n, s, and t
refer to the direction of the stress components.
Interface damage evolution was expressed in terms of energy release. The description of this
model is available in the Abaqus material library. The dependence of the fracture energy was
defined based on the BenzaggahKenane fracture criterion. BenzaggahKenane fracture
criterion is particularly useful when the critical fracture energies during deformation purely
along the first and the second shear directions are the same;
i.e., Gsc= Gtc. It is given by:
3.5
where G = GS + Gt , G= Gn + Gs and are the material parameter. Gn, Gs and Gt refer to
the work done by the traction and its conjugate separation in the normal, the first and the
second shear directions, respectively. (Obaidat et.al, 2009)
Axial stress vs. axial strain responses of confined columns found from both models ensured
same ultimate capacity. Actually the failure of the FRP-confined concrete columns is
governed by the rupture of the FRP laminates at corners. Debonding of FRP sheets is not an
important criterion of failure in FRP confined concrete columns. So, the cohesion model
didnt affect the ultimate capacity at all. Figure 3.5 (a) and (b) clearly illustrates that for
concentric loading there is no significant influence of cohesion model. However, it may
affect the ultimate capacity for eccentric loading condition. Hence perfect bond model is used
for further numerical modeling as it minimizes the computational time.
-
31
(a) (b)
Figure 3.5 Axial stress vs. axial strain responses of column S25C5 (a) using cohesive zone model (b) using perfect bond model.
3.3.1.4. Load application & boundary condition
In the experiments the specimens were subjected to a monotonic uniaxial compression
loading up to failure. The load was applied with a hydraulic press. Prior to the test, a thin
sulfide layer was put on both ends of the column to ensure that contact areas were flat and
parallel. Uniaxial compressive load is applied in the model just like the experimental way
shown in Figure 3.6. As full cylinders and prisms have been modeled so fixed support is
applied at bottom end and displacement controlled loading is applied on the top. The top
surface is made rigid to ensure uniform transfer of the applied loading to the adjacent
concrete and FRP nodes.
Figure 3.6 Load application and boundary condition
FEM FEM
TEST TEST
Axial Strain % Axial Strain %
Axi
al S
tress
(MPa
)
Displacement control loading
Fixed Support
0
20
40
60
80
0 0.5 1 1.5
0
10
20
30
40
50
60
70
0 0.5 1 1.5
-
32
3.3.2 Material Properties
3.3.2.1 Concrete
Concrete is modeled using concrete damaged plasticity model provided by ABAQUS
software. The concrete damaged plasticity model is primarily intended to provide a general
capability for the analysis of concrete structures under cyclic and/or dynamic loading. The
model is also suitable for the analysis of other quasi-brittle materials, such as rock, mortar
and ceramics; but it is the behavior of concrete that is used in the remainder of this section to
motivate different aspects of the constitutive theory. Under low confining pressures, concrete
behaves in a brittle manner; the main failure mechanisms are cracking in tension and crushing
in compression. The brittle behavior of concrete disappears when the confining pressure is
sufficiently large to prevent crack propagation. In these circumstances failure is driven by the
consolidation and collapse of the concrete micro porous microstructure, leading to a
macroscopic response that resembles that of a ductile material with work hardening.
The model is capable of taking into consideration the degradation of elastic stiffness (or
damage) induced by reversible cycles as well as high temperatures both in tension and
compression. The concrete damage plasticity model uses a non-associated plastic flow rule in
combination with isotropic damage elasticity. The DruckerPrager hyperbolic function is
used to define the plastic flow potential. The dilation angle defines the plastic strain direction
with respect to the deviatoric stress axis in the meridian plane. The volumetric expansion of
concrete can be controlled by varying the dilation angle.
The model uses the yield function of Lubliner et al. (1989), with modifications to account for
a different evolution of strength under tension and compression using multiple hardening
variables. The two hardening variables used to trace the evolution of the yield surface are the
effective plastic strains in compression and in tension, c~pl and t~pl, respectively. The start of
compressive yield in a numerical analysis using this model occurs when c~pl > 0, whereas
when t~pl > 0 and the principal plastic strain is positive, it indicates the onset of tensile
cracking.
Uniaxial tension and compression stress behavior The uniaxial tensile and compressive responses (Figures 3.3(a) and 3.3(b), respectively) of
concrete used in this model are somewhat simplified to capture the main features of the
response. Under uniaxial compression, the stressstrain response (as shown in Figure 3.7(b))
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33
is assumed to be linear up to the initial yield stress, which is assumed to be 0.30fcu in the
current study. The plastic region is characterized by stress hardening, followed by strain
softening after reaching the ultimate strength, fcu. The uniaxial compression hardening curve
is defined in terms of the inelastic strain, c~in, which is calculated using Equation (3.6). The
damage plasticity model automatically calculates the compressive plastic strains, c~pl,
Equation (3.7), using a damage parameter, dc, that represents the degradation of the elastic
stiffness of the material in compression.
~
3.6
~ ~
1
3.7
Figure 3.7(a) shows the uniaxial tensile behavior of concrete used in the damage plasticity
model. The stressstrain curve in tension is assumed to be linearly elastic until the failure
stress, ftu , is reached. After this point strain softening represents the response of the cracked
concrete that is expressed by a stress versus cracking displacement curve. The values of the
plastic displacements calculated by the damage model are equal to the cracking
displacements since the tensile damage parame ter, dt , is zero for current study.
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34
Figure 3.7 Response of concrete to uniaxial loading in (a) tension and (b)compression.
A general form of serpentine curve, as given by the following equations (Carriera and Chu,
1985) is used to represent the complete stress-strain relationship of unconfined concrete
1
3.8
1
1
3.9
(a)
(b)
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35
Where, is a material parameter which depends on the shape of the stress- strain diagram.
The value of = 3 is used in this thesis which is proposed by Tulin and Grestle (1964).A
stress-strain relationship curve of concrete for different values of c is plotted using the
above equations and this curve is shown in Figure 3.8 (a). Figure 3.8 (b) shows axial stress
versus plastic strain curve for compression hardening of concrete.
Figure 3.8 Stress-strain relationship curve of concrete for compression hardening
(a) stress versus total strain (b) stress versus plastic strain
(a)
(b)
0
5
10
15
20
25
30
35
40
45
0 1000 2000 3000 4000 5000 6000
Stre
ss, M
Pa
Strain ,
0
5
10
15
20
25
30
35
40
45
50
0 1000 2000 3000 4000 5000
Stre
ss, M
Pa
Plastic Strain ()
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36
A same form of serpentine curve is used shown in Figure 3.9 (a) and (b) for the average
stress-strain diagram and stress- inelastic strain diagram of reinforced concrete in tension.
Figure 3.9 Stress-strain relationship curve of concrete for tension stiffening
(a) stress versus total strain (b) stress versus inelastic strain
3.3.2.2 FRP laminate
The FRP laminate is modeled as an isotropic homogeneous material as shown in Figure 3.10
using a linear elastic stress-strain curve with a poisons ratio of 0.30. The density used in
modeling is 1.8 g/cc (Rochette and Labossie`re, 2000).
Stre
ss, M
Pa
(a)
(b)
Stre
ss, M
Pa
0
0.5
1
1.5
2
2.5
3
0 0.0001 0.0002 0.0003 0.0004 0.0005
Strain,
0
0.5
1
1.5
2
2.5
3
0 0.0001 0.0002 0.0003 0.0004 0.0005Inelastic strain
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37
Figure.3.10 Typical Elastic stress-strain curve of CFRP
Most of the FRP confined rectangular columns failed due to rupture of the FRP laminate at
the corners when the FRP sheets reached their hoop strength (Chaallal et al., 2003; Rochette
and Labossire, 2000). Hoop strength of carbon sheet generally ranges from 0.41 to 0.61 of
the tensile ultimate strength as reported by Rousakis et al. To simulate the failure behavior
hoop stress is provided 0.5 of the tensile strength.
3.3.3 Solution Strategy
The solution strategy is based on the Riks method. In simple cases linear eigenvalue analysis
may be sufficient for design evaluation; but if there is concern about material nonlinearity,
geometric nonlinearity prior to buckling, or unstable postbuckling response, a load-deflection
(Riks) analysis must be performed to investigate the problem further. The Riks method:
Generally is used to predict unstable, geometrically nonlinear collapse of a structure. Can include nonlinear materials and boundary conditions. Often follows an eigenvalue buckling analysis to provide complete information about
a structure's collapse and
Can be used to speed convergence of ill-conditioned or snap-through problems that do not exhibit instability.
The Riks method uses the load magnitude as an additional unknown; it solves simultaneously
for loads and displacements. Therefore, another quantity must be used to measure the
progress of the solution; Abaqus/Standard uses the arc length, s, along the static
equilibrium path in load-displacement space. This approach provides solutions regardless of
whether the response is stable or unstable shown in Figure 3.11.
Tens
ile
Stre
ss, M
Pa
Strain, %
ult= 1.5%
ftf=1265 MPa
-
If the Rik
the step
whose m
prescribe
specified
The load
defined b
Where,
proportio
Abaqus/S
incremen
The Riks
initial inc
step, the
ks step is a c
and are not
magnitude is
ed loads are
d.
ding during a
by
P0 is the
onality facto
Standard pri
nt.
s procedure u
crement in a
initial load p
continuation
redefined a
s defined in
e ramped fr
a Riks step i
dead load,
or. The loa
ints out the
uses only a
arc length a
proportional
Figure 3.1
of a previou
are treated a
n the Riks
rom the ini
s always pro
, Pref is th
ad proportio
e current va
1% extrapol
long the sta
ity factor,
38
11 Riks meth
us history, an
s dead loa
step is refe
itial (dead l
oportional. T
he reference
onality facto
alue of the
lation of the
atic equilibri
, is comp
hod.
ny loads tha
ads with con
erred to as
load) value
The current l
e load vec
or is found
load propo
e strain incre
um path,
puted as
t exist at the
nstant magn
a referenc
to the refe
load magnitu
tor, and
as part of
ortionality fa
ement. After
and after
e beginning o
nitude. A loa
ce load. A
erence value
ude, ,
(3.10
is the loa
the solution
actor at eac
r providing a
r defining th
(3.11
of
ad
All
es
is
0)
ad
n.
ch
an
he
1)
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39
Where lperiod is a user-specified total arc length scale factor (typically set equal to 1). This
value of is used during the first iteration of a Riks step. For subsequent iterations and
increments the value of is computed automatically, so there is no control over the load
magnitude. The value of is part of the solution. Minimum and maximum arc length
increments, and , can be used to control the automatic incrementation.
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40
CHAPTER 4
PERFORMANCE OF FINITE ELEMENT MODELS
4.1 General
The finite element models developed in chapter 3 are validated using simulations of 11 FRP-
confined concrete columns reported in literature (Chaallal et al.,2003 ; Rochette and
Labossire, 2000 and Shaafi et al., 1999). The tests were performed on a wide variety of
concrete columns confined with fibre-reinforced polymers with different geometric properties
and material properties. The descriptions of the geometric and material properties of these
columns have been reported in chapter 3. From the finite element analysis of each of these
test columns, the predicted axial stress versus axial strain and transverse strain response are
obtained and compared with the corresponding experimental results. Moreover the finite
element model is also used to study the effect of corner radius, confinement effectiveness and
shape factor on the strength of confined concrete columns.
4.2 Performance of FEM Models 4.2.1 Ultimate Capacity and Strain
A finite element model with FRP wrapping was developed to predict the compressive
behavior of confined column under uniaxial loading. The ultimate capacities obtained from
numerical models are compared with those obtained from the experiments in Table 4.1. The
maximum axial stresses are found to be very close to those observed in the experiments. The
mean value of the experimental-to-numerical stress ratio is 1.01 with a standard deviation of
0.03.
The axial strain values at the ultimate strain for numerical models, along with the ratios of the
experimental-to-numerical failure strains are shown in Table 4.1. The numerically predicted
ultimate axial strains are found to be higher compared to the experimental values with an
average experimental-to-numerical ratio of 0.96 with a standard deviation of 0.09.
Table 4.1 contains all the results for concrete columns confined with carbon sheets. As
expected, the ratio increases with the confinement effectiveness. It also confirms that each
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41
additional layer for a given section shape provides a significant increase in compressive
strength and for any constant number of confining layers, an increase of the corner radius has
positive consequences on the axial strength.
Table 4.1 Performance of Numerical Models
Specimen
Designation
Axial Stresses fexp./fnum Axial strain at ultimate
point
exp/num
Experimental Numerical
Experimental
Numerical
fz,max fz,max max max
(MPa) (MPa)
% %
SC-1L3-0.7 29.2 29.0 1.01 0.38 0.35 1.09
SC-2L3-0.7 34.3 33.7 1.01 0.50 0.49 1.01
SC-3L3-0.7 41.2 40.5 1.01 0.60 0.62 0.97
SC-4L3-0.7 47.6 46.8 1.02 0.60 0.71 0.85
S5C5 43.9 46.8 0.94 1.02 1.58 0.65
S25C3 41.6 43.1 0.97 0.94 0.94 1.00
S25C4 50.9 47.5 1.07 1.35 1.25 1.08
S25C5 47.9 47.9 1.00 0.90 1.1 0.82
S38C3 47.5 45.5 1.04 1.08 1.13 0.96
C1 55.0 56.9 0.97 1.00 1.13 0.88
C2 68.0 69.4 0.98 1.25 0.93 1.34
Mean* 1.01 0.96
Standard deviation* 0.03 0.09
*Excluding the value of S5C5 as it was not confined properly during experiment.
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42
4.2.2 Axial stress versus Axial Strain Response
Figures 4.1 to 4.11 show the numerically and experimentally obtained axial strains plotted
against average longitudinal strain of the concentrically loaded five square specimens, four
rectangular specimens and two circular specimens. In all graphs shown in the figures, the
axial stress was calculated by dividing the axial load by the concrete cross sections, assuming
that the composite wrapping has a negligible stiffness in the longitudinal direction.
4.2.2.1 Rectangular columns
Figures 4.1 to 4.4 show the comparison of axial stress versus axial strain response of
rectangular columns having 25mm corner radius and different confinement effectiveness. In
the initial stages of loading, up to a value close to the concrete fc, the relationship follows a
curve typical of unconfined concrete specimens in compression. It is then followed by a
plastic zone in which maximum measured strains are much more important than for the
unconfined concrete.
In general, the initial portions of the numerical stress versus strain curves match very well
with the experimental ones, though a slight underestimation of axial stiffness is observed in
the initial curves for specimens SC-3L3-0.7 and SC-4L3-0.7. The axial stress versus axial
strain responses of the SC-1L3-0.7 and SC-2L3-0.7 specimens are in good agreement with
the experiment in both peak and post peak region.
It can be observed that the number of layers had little effect on the initial slope. However, as
the number of layers increased, the inflection point moved up to a higher stress level. The
slope of the second branch of the stress-strain curves increased with the number of CFRP
layers, while the first branch was generally not affected.
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43
Figure 4.1 Numerical and experimental axial stress versus axial strain response for column SC-1L3-0.7
Figure 4.2 Numerical and experimental axial stress versus axial strain response for column SC-2L3-0.7
Axial Strain (%)
Axi
al S
tres
s (M
Pa)
Axi
al S
tres
s (M
Pa)
Axial Strain (%)
0
5
10
15
20
25
30
35
0 0.1 0.2 0.3 0.4
TEST
FEM
EXPERIMENT
0
5
10
15
20
25
30
35
40
0 0.1 0.2 0.3 0.4 0.5 0.6
TEST
FEM
EXPERIMENT
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44
Figure 4.3 Numerical and experimental axial stress versus axial strain response for column SC-3L3-0.7
Figure 4.4 Numerical and experimental axial stress versus axial strain response for column SC-4L3-0.7
Axi
al S
tres
s (M
Pa)
Axi
al S
tres
s (M
Pa)
Axial Strain (%)
Axial Strain (%)
0
5
10
15
20
25
30
35
40
45
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
TEST
FEM
EXPERIMENT
0
10
20
30
40
50
60
0 0.2 0.4 0.6 0.8
TEST
FEM
EXPERIMENT
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45
4.2.2.2 Square columns
In square columns the maximum axial strain has reached an average value of 1.2%. For square
specimens, at low strain levels in the wraps, a small strength increase is initially produced, but
at higher strains the concrete decay in the center of the prism faces is too rapid and the strain
increase in the wraps is not sufficient to compensate for it, resulting in strain softening. It
occurs when the confining material has higher strength and higher deformation capability. In
experiment each concrete column had an overlap length of 100 mm and 25 mm wide CFRP
strip was added at each end of the specimens which prevented local damages and ensured
compressive failure at the centre of the concrete core. This local confinement is not modeled
in the FE model. May be for this reason a softening branch is found in the post peak region.
Experimental prism data reported by some researchers exhibit this same strain softening after
the first peak Figure 6 of Mirmiran et al. (2000). So the maximum axial strength was
measured at first peak. For high degree of confinement this softening branch seems to
disappear.
For models S25C3, S25C4 and S25C5 the maximum strength were found 43.1 MPa, 47.5 MPa
and 47.9 MPa respectively. It confirms that additional layer of FRP laminate increase the
capacity of the columns. The ultimate strength were measured 43.1 MPa and 45.5 MPa for
columns S25C3 and S38C3 which indicate that for a constant thickness of FRP more rounding
off of corners increase the capacity of square columns.
Figure 4.5 Numerical and experimental axial stress versus axial strain response for column S5C5.
Axi
al S
tres
s (M
Pa)
Axial Strain (%)
0
10
20
30
40
50
60
0 0.5 1 1.5
FEM
TESTEXPERIMENT
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46
Figure 4.6 Numerical and experimental axial stress versus axial strain response for column S25C3.
Figure 4.7 Numerical and experimental axial stress versus axial strain response for column S25C4
Axi
al S
tres
s (M
Pa)
Axial Strain (%)
Axi
al S
tres
s (M
Pa)
Axial Strain (%)
0
10
20
30
40
50
60
0 0.2 0.4 0.6 0.8 1 1.2
FEM
TESTEXPERIMENT
0
10
20
30
40
50
60
70
0 0.5 1 1.5
FEM
TESTEXPERIMENT
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47
Figure 4.8 Numerical and experimental axial stress versus axial strain response for column S25C5
Figure 4.9 Numerical and experimental axial stress versus axial strain response for column S38C3
Axi
al S
tres
s (M
Pa)
Axial Strain (%)
Axial Strain (%)