NASRIN 2013 - Nonlinear FEM analysis of RC columns confined by CFRP.pdf

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

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

DEDICATED

TO

My Beloved Parents

Late Dr. Nazrul Islam Miah

Mrs. Meherunnesa Khan

Engr. Humayun Kabir

&

Mrs. Nurunnahar Begum

CERTIFICATE OF APPROVAL

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

1

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

2

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.

3

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.

4

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

5

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)

6

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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8

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.

9

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

10

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;

11

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

14

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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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

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n square sec

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n However,

anied by a

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tubes were

as reported b

he CFRP co

ves indicate a

without adva

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correspond

udden failure

loading. The

ggregates (C

to the fibre

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ppears at a c

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ctions (Benza

by fracture o

in the carbo

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as shown i

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by Saafi et a

omposite at o

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Chaallal et al

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For stron

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2.7 DesiThe Ame

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calculate

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the load

calculate

ACI 318

If the me

FRP jack

Figure

unded off co

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ns (Rochette

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as confining r

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(2002).

ember is sub

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e (ACI 2002

ent for streng

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FRP-strength

CI 318 (2002

duction fact

combined co

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16

fined weakly

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l reduction f

rain limitatio

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spiral and ti

and shear, t

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i et al., 1999

b)

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nly 50150 m

most the full

ommendation

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ed with an F

) substitutin

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be achieved

should be co

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the effective

9) and (b) rec

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mm in length

l height of th

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FRP jacket

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RP jacket ca

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omputed wit

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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))

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.

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)

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 ()

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

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)

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.

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

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.

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.

43

Figure 4.1 Numerical and experimental axial stress versus axial strain response for column SC-1L3-0.7


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

44



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

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

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

47



Axi

al S

tres

s (M

Pa)

Axial Strain (%)

Axial Strain (%)

Documents

NASRIN 2013 - Nonlinear FEM analysis of RC columns confined by CFRP.pdf