1

Strengthening of Concrete Columns using Hybrid FRP Jacketing

Sérgio Carneiro Henriques

April 2015

_________________________________________________________________________________

Abstract

Presently, fibre reinforced polymers (FRP) are commonly used in the structural rehabilitation of the built environment,

due to their major advantages, when compared to alternative methods, mainly: easy and fast application procedure, and

insignificant geometry change of the original elements, combined with high increase of both strength and ductility of the

original concrete members. In the case of concrete columns, a considerable enhancement is reached using external

confinement with FRP jackets. However, although structural designers can define the number of FRP layers, they are

limited to adopt one single fibre type: glass (G), aramid (A), or carbon (C), the latter being available with different values

of stiffness and cost.

The research study herein described was developed aiming at defining the cost/benefit ratio of hybrid FRP jackets,

considering three layers and only two different types of fibres. Twenty-seven experimental tests (monotonic centred

compression) were carried out on cylindrical concrete specimens strengthened using this innovative hybrid approach.

Models were defined starting with three layers of high Young’s modulus (640GPa) CFRP sheets, and successively

replacing each one of these by one sheet of low Young’s modulus (240GPa) CFRP sheets, then by AFRP sheets, and

finally ending with three layers of GFRP sheets. Experimental results were compared to predictions obtained from

models proposed by several authors. A design expression, specifically developed to address the hybrid FRP jacketing,

and calibrated based on the study undertaken, is also presented. Lastly, the cost/benefit analysis is conducted and major

conclusions are drawn.

Keywords: hybrid systems, FRP, strengthening, jacketing, concrete columns, circular cross-section, confinement.

1 Introduction

The structures are designed to withstand a prescribed lifespan. After this lifespan, they must be evaluate and repair or

strengthening works must be applied, when necessary. In other hand, there are several situations during the lifespan

structures where its rehabilitation interventions are requested, due to: seismic retrofit to satisfy current code

requirements, upgraded loading requirements, damage caused by accidents and environmental conditions and change

of usage. The confinement is generally applied to members in compression, with the aim of enhancing their load capacity

or, in case of seismic upgrading, to increase their ductility in the potential plastic hinge region. Confinement may be

beneficial in non-seismic zones too, where the axial load capacity of a column must be increased to support higher

vertical loads. Confinement with FRP may be provided by wrapping concrete columns with prefabricated jackets or in situ

cured sheets [1]. The main advantages of FRP applications are related to its high tensile strength, reduced volume

weight, corrosion and fatigue resistance, diversity and versatility in the commercialized systems and easy application

[2, 3]. By contrast, the disadvantages of FRP are the need of qualified labour, high sensibility to fire, required protection

against ultraviolet rays and elastic behaviour up to failure. The effectiveness of confinement is known to be greater for

specimens of circular cross-section than for those of rectangular section, due to the singularity and stress concentration

introduced at the edges, and the reduced confinement on the flat sides. The mitigation of this shape effect may be

achieved by rounding the corners of rectangular sections with the effectiveness of the procedure increasing with

rounding radius, until a certain threshold is reached [4].

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2 Confined concrete with FRP systems

This study concerns only concrete circular cross sections confined by FRP subjected to axial monotonic compression. An

unconfined concrete column subjected to compression is characterized by uniaxial state of stress, in FRP confined

column, FRP jacket contrasts expansion with a passive action, in this case the concrete core is under triaxial

compression during loading [5]. Maximum principal stress (σ1) is parallel to column axis. The other two principal stresses,

(σ2 and σ3) are equal and parallel to the plane of cross section. In the case of circular section the stresses σ2 and σ3 are

equal to the confinement pressure fl, and is uniform across the perimeter section (Figure 1). The confinement pressure,

at the ultimate condition, is expressed by the expression (1).

(1)

where fju is the ultimate tensile strength of the jacket; Ej is the Young’s modulus of the jacket; εju is the effective strain at

failure of the jacket; tj is the total structural thickness of the layers of the jacket; D is the diameter of the concrete

cross-section; and flu is the ultimate lateral confinement pressure provided by the jacket.

Figure 1 - Ultimate FRP jacket confinement pressure on circular column.

3 FRP analytical confinement models

The strength models for FRP-confined concrete could be divided into two categories [6]: the design-oriented models and

the analysis-oriented models. In the first category, the models are based primarily on empirical relationships resulting

from statistical elaboration of experimental results, and they can be used directly in the design. In the second category,

the models are based primarily on constitutive relationships or on empirical approaches. Stress–strain curves of

FRP-confined concrete are generated using an incremental numerical procedure. In this second approach, an active

confinement model for concrete is used to evaluate the axial stress and strain of passively confined concrete at a given

confining pressure, and the interaction between the concrete and the confining material is explicitly accounted by the

equilibrium between axial and lateral strain of concrete.

Most of the design-oriented models for circular sections are based on the expressions developed by Richart et al [7],

expressed by the expressions (2) and (3). They differ in the expressions of coefficient k1 and k2. Some are characterized

by a linear dependence on confinement pressure (Fardis and Khalili-Richart [8], Lam and Teng [9], Nisticò and

Monti [10]), others nonlinear (Fardis and Khalili-Newman [8], Karbhari and Gao I [11], Samaan et al [12], Toutanji [13],

Saafi et al [14], Spoelstra and Monti approximate [15], CNR-DT 200/2004 [16], Wei e Wu [17]).

(2)

(3)

where fcc is confined concrete strength and fc0 is the unconfined concrete strength; k1 and k2 are the confinement

effectiveness coefficient; and fl is the lateral confinement pressure.

Other authors propose different approaches to evaluate the ultimate conditions of confined concrete by FRP, as

Teng et al [18] and Rousakis et al [19]. The ultimate strain and compressive strength equations proposed by

Teng et al [18] first defines the confinement stiffness ratio ρk and the strain ratio ρε. Then, they take them into account in

their strength model separately, instead of using their product, which is the confinement ratio fl/fco.

The approach by Rousakis et al [19] considers that the effective strain at failure of the confining material (εju) and the

confinement effectiveness coefficient (k1) are both varying. Yet, their product has been found strongly dependent on the

elastic modulus of the fibers of FRP confinement. Thus, the strength prediction does not require the lateral confinement

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pressure (fl) and therefore the identification of the suitable k1 and εju values. It is only dependent on the FRP confinement

volumetric ratio ρj, the modulus of elasticity of the jacket (Ej), and the unconfined concrete strength fc0.

4 Experimental study of confined concrete with FRP hybrid systems

4.1 Experimental program

In order to study the behavior of reinforced concrete columns confined with FRP composites, a research program was

developed at Instituto Superior Técnico (IST), which included 27 monotonic tests on short columns (Φ 0.15m for 0.75m

of height) subjected to axial compression in order to evaluate the influence of the following parameters: (i) fiber type

(CFRP, HM CFRP, AFRP and GFRP); (ii) hybrid confinement systems; (iii) layers arrangement in hybrid confinement

systems.

4.2 Materials

Two series of columns were produced. The average cylindrical compressive strength at the time of the concrete column

tests, was fc0 = 34,4MPa, for concrete B1, and fc0 = 31,8MPa for concrete B2. The external jacketing was performed by

unidirectional fiber layers: carbon (S&P C-Sheet 240 - 300g/m2) denominated in the present study as C1, high modulus

carbon (S&P C-Sheet 640) designated in the present study as C2, aramid (S&P A-Sheet 120 - 290g/m2) referred in the

present study as A and bidirectional glass, (S&P G-Sheet AR 90/10 type B) identified in the present study as G.

Mechanical properties of the fibres were supplied by the manufacturer. Table 1 summarizes the fibre mechanical

properties.

Table 1 – Manufacturer fiber mechanical properties [21].

Properties C1 C2 A G

Elastic modulus [GPa] 240 640 120 65

Tensile strength [MPa] 3800 2650 2900 3000

Elongation at rupture [%] 15.5 4.0 25.0 43.0

Design thickness [mm] 0.176 0.190 0.200 0.299

Density [g/cm3] 1.70 2.10 1.45 2.68

All composite systems, besides the mentioned fibre types, also contained epoxy resin, Resin S&P 55, composed by two

components (resin and hardener).

4.3 Axial monotonic compression tests

4.3.1 Concrete specimens characterization

The experimental results of twenty seven tests of this research program will be presented in this paper. These tests were

carried out for monotonic axial compression concrete columns (Φ 0.15m for 0.60m of height). All specimens, except

reference ones, were reinforced with FRP layers. The specimens were confined with four different types of composites:

C1FRP, C2FRP, AFRP and GFRP. All specimens were strengthened with three FRP layers. Some specimens were

strengthened with two different fiber types, leading to hybrid confinement systems (Figure 2).

Figure 2 – Hybrid confinement system with CFRP and AFRP.

The adopted nomenclature to specimen’s identification begins with the code “PB” followed by “1” or “2”, according to the

first or second series of concrete mixtures. Then the identification of the fibers, which indicates the order in which the

several layers were applied, starting with the inner layer. At fibers were assigned "C1" codes (CFRP), "C2" (HM CFRP),

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"G" (GFRP) and "A" (AFRP). Thus PB1.C1.2A nomenclature refers to a specimen of concrete type 1 reinforced with low

modulus carbon fiber layer on the inside and two aramid fiber layers on the outside. The reference specimens, not

reinforced, received the designation of PB1.000 and PB2.000, depending on the adopted concrete. Table 2 presents the

used confinement systems.

Table 2 – FRP layers arrangement of confinement systems.

Group Series FRP arrangement

inner middle outsider

1

PB1.000 Not reinforced specimen (reference)

PB1.3C1 Carbon C1 (Ej=240MPa) Carbon C1 (Ej=240MPa) Carbon C1 (Ej=240MPa)

PB1.3C2 Carbon C2 (Ej=640MPa) Carbon C2 (Ej=640MPa) Carbon C2 (Ej=640MPa)

PB1.C1.2C2 Carbon C1 (Ej=240MPa) Carbon C2 (Ej=640MPa) Carbon C2 (Ej=640MPa)

PB1.2C1.C2 Carbon C1 (Ej=240MPa) Carbon C1 (Ej=240MPa) Carbon C2 (Ej=640MPa)

PB1.C1.2A Carbon C1 (Ej=240MPa) Aramid (Ej=120MPa) Aramid (Ej=120MPa)

PB1.2C1.A Carbon C1 (Ej=240MPa) Carbon C1 (Ej=240MPa) Aramid (Ej=120MPa)

PB1.A.C1.A Aramid (Ej=120MPa) Carbon C1 (Ej=240MPa) Aramid (Ej=120MPa)

PB1.2A.C1 Aramid (Ej=120MPa) Aramid (Ej=120MPa) Carbon C1 (Ej=240MPa)

2

PB2.000 Not reinforced specimen (reference)

PB2.3A Aramid (Ej=120MPa) Aramid (Ej=120MPa) Aramid (Ej=120MPa)

PB2.3G Glass (Ej=65MPa) Glass (Ej=65MPa) Glass (Ej=65MPa)

PB2.2A.G Aramid (Ej=120MPa) Aramid (Ej=120MPa) Glass (Ej=65MPa)

PB2.A.2G Aramid (Ej=120MPa) Glass (Ej=65MPa) Glass (Ej=65MPa)

4.3.2 FRP wrapping

The concrete surface was roughened by careful abrasion with an angle grinder, then it was cleaned and completely dried

before wrapping. A primary was then applied, to ensure a correct bonding between concrete and FRP. The epoxy

system consisted of two parts, resin and hardener, mixed in the ratio of 2:1, applied to the concrete surface using a

brush. The sheets were wrapped around the perimeter of the specimens. Special attention was taken to insure that there

were no voids between the sheet and concrete surface. An overlap of 150mm was set to insure the development of full

composite strength. After the application of the first layer of the FRP sheet, a second layer of epoxy was applied on the

surface of the first layer to allow impregnation of the second layer. This process was repeated, until the desired layer

thickness was achieved. Finally, a thin layer of epoxy was applied to the FRP sheet surface to protect it from

environmental conditions.

4.3.3 Instrumentation and loading conditions

Tests were conducted with a 3000 kN press. All specimens were subjected to monotonic increasing axial load until

failure. Axial and transverse strains of concrete and FRP were recorded by two axial and transversal strain gauges (TML

PFL-10-11), bonded on the two opposite faces. The vertical displacements were measured with two linear-variable

differential transducers (LVDTs) TML-CDP100. A load cell was used to record the axial force. Load, strain and

displacements values were collected by means of a high-speed acquisition data system Datalogger HBM Quantum

MX840 with HBM software.

5 Tests results and discussion

5.1 General remarks

In general, the compressive behaviour of two specimens of each series was similar with regard to the main aspects that

characterize it, in particular in the obtained stress-strain diagrams and failure modes. Except the C2FRP series, all the

others presented bilinear stress-strain diagrams (Figure 3a and b). The first zone is similar to the curve of reference

specimens (thick black curve) and the circumferential FRP strain (εj) it’s reduced. When stresses reaches near

unconfined concrete strength, lateral expansion of concrete occurs, mobilizing the confining FRP jacket, occurring a

change in the slope of the curve, which is dependent of the confinement system stiffness. All bilinear stress-strain

diagrams observed, presented an increasing type behaviour (Figure 3). Both the compressive strength and the ultimate

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strain are reached at the same point and are significantly enhanced. In the present study peak compressive strength fcc,

is equal to ultimate compressive strength fcu, and peak strain εcc, is equal to ultimate strain εcu. Table 3 resumes all

experimental results.

Table 3 – Experimental results.

Série fcc [MPa] fcc /fc0 εcc

[%] εcc/ɛc0 εju

[%]

PB1.000 34.4 1.00 0.210 1.00 -

PB1.3C1 54.5 1.58 0.82 3.92 0.43

PB1.3C2 46.9 1.36 0.23 1.10 0.07

PB1.C1.2C2 51.5 1.49 0.48 2.28 0.09

PB1.2C1.C2 67.9 1.97 0.70 3.35 0.19

PB1.C1.2A 67.5 1.96 1.26 6.00 0.53

PB1.2C1.A 75.0 2.18 1.37 6.50 0.64

PB1.A.C1.A 75.5 2.19 1.08 5.14 0.79

PB1.2A.C1 74.8 2.17 1.12 5.34 0.95

PB2.000 31.8 1.00 0.205 1.00 -

PB2.3A 87.4 2.75 2.15 10.46 1.53

PB2.3G 70.3 2.21 1.04 5.07 0.67

PB2.A.2G 78.1 2.45 1.47 7.15 1.15

PB2.2A.G 86.5 2.72 1.98 9.64 1.11

Figure 3 – Stress-strain diagrams: a) Series of concrete B1; b) Series of concrete B2.

Typical failure of specimens was marked by sudden FRP failure, sometimes explosive (Figure 4). Near failure, most

specimens emitted a clicking sound associated with fiber reorientation, very localized failures of fibers and crushing of

the concrete. After removing the jacket, shear cones were observed in the FRP failure region. The Tables, diagrams and

figures in this section represent values taken from the mean result of the repeated specimens of which series.

Figure 4 – Failure modes examples: a) PB1.3C1 series; b) PB1.2A.C1 series.

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

-1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50

f c [

MP

a]

εl [%] εc [%]

PB1.3C1

PB1.3C2

PB1.C1.2C2

PB1.2C1.C2

PB1.2C1.A

PB1.C1.2A

PB1.A.C1.A

PB1.2A.C1

PB1.000 0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

-2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50

f c [

MP

a]

εl [%] εc [%]

PB2.3A

PB2.3G

PB2.A.2G

PB2.2A.G

PB2.000

a) b)

a) b)

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5.2 Fibre type influence

Figure 5 presents the axial normalized strength at failure and respective strain (divided by unconfined concrete axial

strength fc0, and respective strain εc0), for the confinement systems with a single fibre type. The AFRP reinforcement led

to maximum increased strength, 175%, followed by GFRP reinforcement (121%), and finally reinforcement with CFRP

and HM CFRP, with strength increases of 58% and 36%, respectively (Figure 5a). Higher ductility increase is obtained

for AFRP reinforced series, 946% (Figure 5b), followed by GFRP reinforced series (407%). The ductility improvement of

CFRP reinforced series ductility, corresponds to 292%, finally HM CFRP reinforced series presents a low ductility

improvement, of 10% (Figure 5b).

Figure 5 – Experimental results for wrapped series with a single fibre type: a) Normalized ultimate strength; b) Normalized ultimate strain.

5.3 Hybrid confinement systems influence

Figure 6 shows the normalized ultimate compressive strength and the corresponding axial strain to hybrid confinement

systems. The introduction of low modulus carbon fibers (C1) in the jacketing with a high modulus carbon (C2) leads to

increased strength and ductility (Figure 6a): PB1.3C2 and PB1.C1.2C2 series, with high modulus carbon fibers

predominance, have a strength increase below 50%, series containing more than one layer of low modulus carbon fibers,

have higher strength increases, registering increases of 58% (PB1.3C1) and 97% (PB1.2C1.C2). The reinforced series

with low modulus carbon (C1) and aramid (A) also indicate a trend (Figure 6a), the introduction of the aramid layers in the

wrapping with low modulus carbon, led to an improvement in the strength and ductility capacity: the wrapped

carbon C1-aramid series presents a strength improvement between 96% (PB1.C1.2A series) to 119% (PB1.A.C1.A series)

greater than the series PB1.3C1 increase (58%). Figure 6b illustrates the performance of hybrid reinforcement containing

aramid (A) and glass (G) fibers. It is noted that, as aramid is replaced by glass fibers, the mechanical strength decreases

progressively: PB2.2A.G solution has a 172% increase strength, very close to PB2.3A solution (175%), but the strength

decreases with PB2.A.2G (149%) until PB2.3G (124%). With respect to the axial strains, analyzing Figure 6b, it appears

that smaller axial strains are associated to systems with carbon fibers, although with very different values, with axial

strains increases between 10% (PB1.3C2 series) and 292% (PB1.3C1 series). There was a ductility increase with the

addition of aramid fibers to carbon fibers in the confinement hybrid systems, which have recorded axial strains increases

between 414% (PB1.A.C1.A series) and 550% (PB1.2C1.A series) up to a maximum increase of 946%, to the series

confined with aramid fibers. In the confinement hybrid systems with aramid and glass fibres, as aramid layers are

replaced by glass, the ductility decreases. The PB2.2A.G solution has an axial strain increased of 864%, nearer to

PB2.3A solution (946%), but the axial deformation decreases with PB2.A.2G (615%) until PB2.3G (407%). The

introduction of AFRP in hybrid confinement systems with CFRP and GFRP leads to strength and ductility capacity

improvement.

1.00

1.58 1.36

1.00

2.75

2.21

0.00

0.50

1.00

1.50

2.00

2.50

3.00

f cc

/ f c

0

Series

1.00

3.92

1.10 1.00

10.46

5.07

0.00

2.00

4.00

6.00

8.00

10.00

12.00

εc

c / ε

c0

Series

a) b)

7

Figure 6 – Normalized experimental results for hybrid confinement systems influence analysis: a) Normalized ultimate strength for hybrid confinement systems with carbon and/or aramid; b) Normalized ultimate strength for hybrid confinement systems with glass and/or aramid; c) Normalized ultimate axial strain for hybrid confinement systems with carbon and/or aramid; d) Normalized ultimate axial strain for hybrid confinement systems with glass and/or aramid.

5.4 Layers arrangement in hybrid systems

A set of series series confined with carbon-aramid hybrid systems was tested, to analyze the influence of the relative

position of the different layers: PB1.C1.2A, PB1.A.C1.A and PB1.2A.C1. The arrangement consists in considering an inner

layer of carbon, in the first specimen, an intermediate layer, in the second specimen, and an outer layer, in the third

specimen. The tree series presents a similar strength and ductility capacity. PB1.2A.C1 and PB1.A.C1.A series present a

strength increase of 117% and 119%, respectively, while PB1.C1.2A series presents a 96% increase (Figure 6a). The

ductility increase was similar to tree series to (Figure 6c). The results show that the layer arrangement in hybrid

confinement systems does not present a significant influence in the final strength and ductility capacity.

5.5 FRP strain

Experimental results showed that the FRP ultimate strain was not reached at the failure of FRP in FRP confined

concrete. This can be due to the curvature of the jacket, shearing action between the jacket and the cracked concrete

and localized jacket punching damage. Table 4 provides the average ratios between the measured circumferential strain

at FRP rupture (εju) and the FRP material ultimate tensile strain (εfu).

1.00 1.00

1.36 1.49

1.97

1.58

1.96 2.17 2.18 2.19

2.75

0.00

0.50

1.00

1.50

2.00

2.50

3.00

f cc/f

c0

Séries

1.00

2.21 2.45

2.72 2.75

0.00

0.50

1.00

1.50

2.00

2.50

3.00

f cc/f

c0

Séries

1.00 1.00 1.10 2.28

3.35 3.92

6.00 5.34

6.50 5.14

10.46

0.00

2.00

4.00

6.00

8.00

10.00

12.00

εc

c /ε

c0

Séries

1.00

5.07

7.15

9.64 10.46

0.00

2.00

4.00

6.00

8.00

10.00

12.00

εc

c /ε

c0

Séries

a)

c)

b)

d)

8

Table 4 – Experimental circumferential strain failure.

Series εju [%] εju

/ εfu [%]

PB1.3C1 0.43 28.1

PB1.3C2 0.07 16.3

PB1.C1.2C2 0.09 22.4

PB1.2C1.C2 0.19 48.4

PB1.C1.2A 0.53 34.1

PB1.2C1.A 0.64 41.3

PB1.A.C1.A 0.79 51.3

PB1.2A.C1 0.95 61.3

PB2.3A 1.53 61.1

PB2.3G 0.67 15.6

PB2.A.2G 1.15 45.9

PB2.2A.G 1.11 44.5

FRP ultimate strain: C1FRP-εfu=1.55%; C2FRP-εfu=0.40%; AFRP-εfu=2.50%; GFRP-εfu=4.30%

In the hybrid confinement systems (two types of FRP), it was observed that the circumferential strain associated to the

specimens failures was lower than the FRP confinement strain with lesser ultimate tensile strain. Jacketing reinforcement

with GFRP and C2FRP presents a lower ratio between the measured circumferential strain at FRP rupture (εju) and the

FRP material ultimate tensile strain (εfu), 15.6% and 16.3%, respectively, followed by the jacket with C1FRP (28.1%) and

the hybrid jacketing with C1FRP and C2FRP of the PB1.C1.2C2 series (22.4%). In general, confinement systems

containing AFRP have a greater ratio between εju and εfu, verifying the maximum value of 61.3% for the jacketing of

PB1.2A.C1 series, similar to the PB2.3A series (61.1%). The aramid fibre has a high impact resistance, and for example in

the formula 1 is used in the construction of fuel tanks in order to avoid their puncturing by protruding objects in case of

accident. Thus, the increased mobilization of the ultimate capacity of the aramid fiber compared to the carbon and glass

fibers may be related to its greater abrasion resistance [22, 23]. At the moment of concrete cracking, the concrete

aggregates, which may have protruding edges, start to degrade and abrade the reinforcement layer. Since the aramid is

a material with high abrasion resistance compared to the reduced abrasion resistance of carbon and glass fibers, the

increased mobilization of its ultimate capacity may be related to its inherent characteristic. This can explain the better

performance of the series wherein the confinement system contains aramid, compared to other series in which aramid

was not used in confinement system.

5.6 Confinement level

Compressive strength and axial strain, is directly connected to the confinement pressure generated by the composite

jacket. Indeed, the strength gain at failure linearly increases with the confinement ratio (Figure 7), parameter defined as

the ratio between ultimate confinement pressure (flu) and the unconfined compressive strength (fc0). The ultimate

confinement pressure is determined by expression (1). The elastic modulus of jacket Ej, for systems with a single type of

fiber is assumed as the elastic modulus provided by the manufacturer. In the hybrid systems, the elastic modulus was

defined by expression (4). Since the sheets cure, was made in situ, in fl calculation, just the fibre properties shall be

considered, as recommended in Bulletin 14 [5]. The elastic modulus of FRP Ej, takes the value of the equivalent elastic

modulus of the fibers, E'fib defined by expression (4):

(4)

where E'fib is the equivalent fibre elastic modulus ; ρfib,i is the density of i fibre sheets and E

'fib,i is the elastic modulus of i

fibre sheet.

9

Figure 7 - Relationship between strength gain and confinement ratio.

5.7 Volumetric strain

Another way to look at FRP jacket behavior is to trace curves for volumetric response versus normalized axial stress.

Volumetric strain, change of volume per unit volume, is calculated by expression (5):

(5)

where εv is the volumetric strain; εc is the axial strain; εl is the lateral strain. Assuming negative the tensile stresses and

positive the compressive stresses, a positive volumetric strain indicates a volume reduction (contraction) and a negative

volumetric strain represents a volume increase (dilation). In Figure 8 distinct behaviours are observed for tested series.

Figure 8 – Volumetric strain for: a) Confinement systems with carbon C1 and/or carbon C2 and systems with carbon C1 and/or aramid; b) Confinement systems with aramid and/or glass.

Except PB1.3C2, PB1.C1.2C2 and PB1.2C1.C2 series, for stresses up to unconfined strength, dilation occurs for all

specimens. As concrete reaches its unconfined strength, the dilation of concrete increases with the growth of micro

cracks. In some series, for higher stresses, contraction occurs again. Aramid and glass confined series exhibit a

significant dilatation until failure, and consequently, a higher passive confinement action, as compared to series confined

with low and high modulus carbon (Figure 8). The higher activation of passive confinement in series with aramid and

glass fibers, allowed a greater increase in load capacity models. The hybrid confinement systems, carbon C1-aramid and

aramid-glass exhibit a greater volumetric dilation, comparatively to hybrid confinement systems with carbon C1 and

carbon C2, generating a greater effect of passive confinement. Although the higher stiffness of the confinement system

with high modulus carbon, they are less efficient due to its reduced ultimate tensile strain. The series that exhibited a

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

f cc / f

c0

fl u / fc0

PB1.3C1

PB1.3C2

PB1.C1.2C2

PB1.2C1.C2

PB1.C1.2A

PB1.2C1.A

PB1.A.C1.A

PB1.2A.C1

PB2.3A

PB2.3G

PB2.A.2G

PB2.2A.G

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75

f c /f

c0

εv [%]

PB1.3C1

PB1.3C2

PB1.C1.2C2

PB1.2C1.C2

PB1.C1.2A

PB1.2C1.A

PB1.A.C1.A

PB1.2A.C1

PB2.3A 0.0

0.5

1.0

1.5

2.0

2.5

3.0

-1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20

f c /f

c0

εv [%]

PB2.3A

PB2.3G

PB2.A.2G

PB2.2A.G

a) b)

10

higher volumetric expansion, suffered a major action of the passive confinement, increasing significantly the strength

capacity, as was the case of the series confined only with aramid, glass, and hybrid systems with aramid. The carbon

confined series exhibits a lower volumetric expansion, so a minor confinement effect was verified, resulting in a lower

increase of strength capacity. The lower efficiency of carbon strengthened series may be associated with the fibre

reduced ultimate tensile strain. However, the higher stiffness of carbon confinement systems, and consequent minor

dilation, may be appropriate in the confinement of lower strength concrete, or concrete exhibiting already some cracking,

as it may mobilize faster the passive confinement, before the occurrence of higher cracking and expansion levels in

concrete, as can happen for less stiffness confinement systems.

5.8 Cost / benefit analysis

Figure 9 shows the ratio between the strengthening cost and strength increase. Series in which predominate layers of

high modulus carbon fibers have a high ratio, with values of 152.1€/ΔR and 273.0€/ΔR, resulted from higher cost of this

FRP sheets and reduced increase of strength experimentally verified (white bars). PB1.C1.2A series, and PB1.3C1

PB1.2C1.C2 (light gray bars) have a cost increase strength, ranging from 43.5€/ΔR and 52.7€/ΔR. Finally, there is a range

of costs that has seven of the twelve tested series (dark gray bars), in which the cost increase strength ranges from

24.9€/ΔR and 35.4€/ΔR, being the lowest cost associated to PB2.A.2G series. The confined series with less stiffer

materials (aramid and glass) have a lower cost / increase strength ratio since, as experimentally demonstrated, they

provide a greater strength increase when compared to the series using stiffer confining materials (carbon C1 and C2),

where the confinement action is lower. The series that presents the best cost / benefit ratio, corresponds to PB2.A.2G

series.

Figure 9 – Cost / benefit ratio.

6 Comparison of analytical models and experimental results

In existing models for FRP-confined concrete, it is commonly assumed that the FRP fails when the circumferential strain

(εj) in the FRP jacket reaches its ultimate tensile strain (εfu) from either flat coupon tests. This assumption is the basis for

calculating the ultimate confinement pressure flu using the expression (6):

(6)

where εfu is the ultimate tensile strain. However, experimental results show that, in most cases, the ultimate tensile strain

was not reached at the rupture of FRP in FRP confined concrete, thus the ultimate confining pressure can be estimated

with expression (1). Figure 10 presents the comparison between experimental results and analytical models to predict

confined strength (thirteen models) and respective axial strain (twelve models) based on ultimate confinement pressure

flu(εju), determined by expression (1), using ultimate rupture circumferential strain experimentally verified (εju). In general

the predicted strength based on flu(εju), provides conservative values (Figure 10a). The predicted axial strains present a

large scatter of values (Figure 10b).

24.9 27.0 27.2 27.5 29.1 34.8 35.4 43.5 49.6 52.7

152.1

273.0

0.0

50.0

100.0

150.0

200.0

250.0

300.0

€/Δ

Rc

Series

11

Figure 10 – Comparison between experimental results and analytical models based on rupture circumferential strain experimentally verified (εju): a) Confined concrete strength (fcc); b) Ultimate axial strain (εcc).

Figure 11 is similar to Figure 10, presenting the comparison between experimental results and analytical models to

predict confined concrete strength and respective axial strain based on ultimate confinement pressure flu(εfu), determined

by expression (6), using ultimate tensile strain (εfu). Since it was experimentally observed that in the hybrid confinement

systems the circumferential strain associated to the specimens failures was lower than the FRP confinement strain with

lesser ultimate tensile strain, the ultimate confinement pressure flu(εfu) was calculated with the lesser strain εfu of the

hybrid system indicated by the supplier. Various analytical models to predict FRP confined concrete strength based on

flu(εfu) overestimate strength values when compared to the theoretical values obtained by flu(εju) (Figure 11a). Except the

models proposed by Lam and Teng [9], CNR-DT 200/2004 [16] and Teng et al [18], which requires the reduction of the

ultimate tensile strain of the FRP, in the other models the FRP ultimate tensile strain provided by the manufacturer is

used to predict the confined concrete strength and respective axial strain. The proposed model by Lam and Teng [9] and

Teng et al [18] have a efficiency coefficient (kε) to reduce the ultimate tensile strain of FRP, which depends on the fiber

type, particularly carbon-0.586, glass-0.624 and aramid-0.851. CNR-DT 200/2004 [16] presents a single coefficient kε, of

0.60. In the model proposed by Rousakis et al [19], the strength prediction does not require the flu and therefore the

identification of the suitable kε and εju values. It is only dependent on the FRP confinement volumetric ratio, the elastic

modulus of fibers and the unconfined concrete strength. The most recent expressions proposed by Lam and Teng [9],

CNR-DT 200/2004 [16], Teng et al [18], Rousakis et al [19], Wei e Wu [17] and Nisticò e Monti [10] are also the more

suitable for the assessment of fcc. Theoretical axial strain values based on FRP ultimate tensile strain presents a large

scatter of values. In addition to large scatter of values results, there are some models that can lead to higher

overestimation of the ultimate strain of FRP confined concrete, as in the case of the approximate formula of Spoelstra

and Monti [15] and Toutanji [13] and Saafi et al [14] models. The older expression proposed by Karbhari e Gao I [11] and

the most recent models proposed by De Lorenzis e Tepfers [20] Lam and Teng [9] and CNR-DT 200/2004 [16] are the

more suitable for the assessment of εcc. Rousakis et al [19] also provides good results, with the exception of PB1.3C2 and

PB1.C1.2C2 series associated to higher jacket elastic modulus.

0

1

2

3

4

0 1 2 3 4

f cc

an

aly

. /fc

0-ε

ju

fccexp./fc0

Fardis and Khalili (1982)-Richart Fardis and Khalili (1982)-Newman

Karbhari and Gao I (19997) Samaan et al (1998)

Approximate Spoelstra and Monti (1999) Toutanji (1999)

Saafi et al (1999) Lam e Teng (2003)

CNR-DT 200/2004 (2004) Teng et al (2009)

Wei and Wu (2012) Rousakis et al (2012)

Nistico and Monti (2013)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

εc

ca

na

ly. /ε

c0-ε

ju

εccexp./εc0

Fardis and Khalili (1982) Karbhari and Gao I (19997)

Samaan et al (1998) Approximate Spoelstra e Monti (1999)

Toutanji (1999) Saafi et al (1999)

Lam and Teng (2003) De Lorenzis and Tepfers (2003)

CNR-DT 200/2004 (2004) Teng et al (2009)

Wei and Wu (2012) Rousakis et al (2012)

a) b)

12

Figure 11 – Comparison between experimental results and analytical models based on ultimate tensile strain (εfu): a) Confined concrete strength (fcc); b) Ultimate axial strain (εcc).

6.1 Proposed model

In this section two modes to predict the FRP confined concrete strength are proposed. The first model is developed

based on Richart et al [7] expression (expression (2)), and the second one is based on Rousakis et al [19] model.

6.1.1 Analytical model 1

The confinement pressure is a function of the lateral strain and the stiffness of confinement system, and is calculated

with expression (1). The values of the coefficient k1 were plotted as a function of the ratio between the confinement

pressure and the unconfined concrete strength (flu/fc0) (Figure 12). Using a regression analysis, an equation for k1 is

obtained and is expressed by expression (7).

(7)

Figure 12 - Confinement coefficient k1 as function of ratio between confinement pressure and unconfined concrete strength (flu/fc0).

The FRP confined concrete strength is defined by the expression (2) of Richart et al [7], substituting expression (7) into

expression (2), the expression (8) to predict the confined concrete strength of FRP confined concrete is obtained:

(8)

0

1

2

3

4

5

0 1 2 3 4 5

f cc

an

aly

. /fc

0-ε

fu

fccexp./fc0

Fardis and Khalili (1982)-Richart Fardis and Khalili (1982)-Newman

Karbhari and Gao I (19997) Samaan et al (1998)

Approximate Spoelstra e Monti (1999) Toutanji (1999)

Saafi et al (1999) Lam and Teng (2003)

CNR-DT 200/2004 (2004) Teng et al (2009)

Wei and Wu (2012) Rousakis et al (2012)

Nistico and Monti (2013)

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

εc

ca

na

ly. /ε

c0-ε

fu

εccexp./εc0

Fardis and Khalili (1982) Karbhari and Gao I (19997)

Samaan et al (1998) Approximate Spoelstra e Monti (1999)

Toutanji (1999) Saafi et al (1999)

Lam and Teng (2003) De Lorenzis and Tepfers (2003)

CNR-DT 200/2004 (2004) Teng et al (2009)

Wei and Wu (2012) Rousakis et al (2012)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

k1

flu / fc0

Experimental results

a) b)

R2 = -0.9324

k1=2.37(flu /fc0)-0.55

13

In the determination of confinement pressure flu, the ultimate tensile strain of the FRP provided by the manufacturer,

must be reduced by a efficiency factor kε. The ultimate strain is defined by expressions (9) and (10):

(9)

(10)

Figure 13 shows the comparison between the theoretical and experimental results for the strength of FRP confined

concrete.

Figure 13 – Comparison between experimental results and analytical model 1 results.

6.1.2 Analytical model 2

The analytical model 2, is based on expression (11) proposed by Rousakis et al [19]. The analytical model 2 proposed,

consists in changing the parameters α and β indicated by Rousakis et al [19]

(11)

Figure 14 shows the relation between the coefficient A which corresponds to the product 0,5k1εju and the elastic modulus

of the FRP confinement. Thus, for the series contained only carbon fibers or hybrid systems with high and low modulus

carbon fibers, the parameters α and β take the values, 0.1468 and 0.0105, respectively. In the case of hybrid

confinement systems with low modulus carbon C1 and aramid fibers, α and β parameters take the values, -1.053 and

0.0323, respectively. Finally, for aramid and glass confinement systems, and for hybrid systems with aramid and glass,

parameters α and β take the values, 0.6061 and 0.0230, respectively.

Figure 14 – Relation of A parameter with fiber elastic modulus of wrapping materials: a) High or/and low modulus carbon fibers; b) Low modulus carbon and aramid fibers; c) Aramid and/or glass fibers.

Figure 15 shows the comparison between the theoretical and experimental results for the strength of FRP confined

concrete.

0

1

2

3

4

0 1 2 3 4

f cc

an

aly

. /fc

0

fccexp./fc0

Analytical model 1

y = -0.1468x + 0,0105 R² = 0.8419

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.000 0.020 0.040 0.060 0.080

A

Ejx 10-6/Ejμ

Experimental results

y = -1.0153x + 0.0323

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.000 0.005 0.010 0.015 0.020 0.025

A

Ejx 10-6/Ejμ

Experimental results

y = 0.6061x + 0.023 R² = 0.362

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.000 0.005 0.010 0.015

A

Ejx 10-6/Ej

Experimental results

R2 = 0.2398

a) b) c)

14

Figure 15 – Comparison between experimental results and analytical model 2 results.

7 Conclusions

The FRP confinement provides a gain of strength and ductility.

Different single-type of fiber confining materials systems present different increase strength values: AFRP led to a

greater increase in load capacity, exhibiting a relationship fcc/fc0 of 2.8 times, followed by strengthening systems with

glass fibers, with an increased strength of 2.2 times and finally the strengthening systems using HM CFRP and CFRP

composites, with strength increases of 1.6 times.

In hybrid confinement systems, higher strength increases were found for systems with aramid and glass fibers showing

ratios of fcc/fc0 between 2.5 and 2.7 times. Systems with carbon and aramid fibers also show high load capacity increases

(2.0 to 2.2 times), while systems composed by high and low elastic modulus carbon fibers lead to lower values (1.5 to 2.0

times). Aramid fibers combined with low modulus carbon fibers or glass fibers, lead to an improvement in strength and

ductility capacity. The ultimate circumferential strain of the FRP jacket has always occurred to a lower value than ultimate

tensile strain provided by the manufacturer. It has been found experimentally that the higher elastic modulus, associated

with a lower fibers ultimate tensile strain can lead to a lower capacity mobilization of these, thus generating a lesser

effect of passive confinement. This may explain the lower performance of high and low modulus carbon fibers, especially

high modulus, when compared, for example, with aramid fibers. The low elastic modulus, the higher ultimate tensile

strain and higher abrasion resistance of aramid, allow a greater actuation of passive confinement.

The layers arrangement of confinement hybrid systems showed no significant influence on the increase of strength and

ductility capacity.

With the present study it was found it is possible to obtain hybrid confinement solutions with similar strength capacity at

lower costs. The tested series that presented the best cost / benefit ratio, corresponded to PB2.A.2G series.

Comparison between experimental and theoretical values was made. In general the predicted strength based on jacket

circumferential strain experimentally verified εju, provides conservative values in the prediction of strength values. The

predicted axial strains presents a large scatter of values. Analytical models to predict confined concrete strength and

respective axial strain based on ultimate tensile strain εfu, overestimate strength values when compared to the theoretical

values obtained by εju. The most recent expressions proposed by Lam and Teng [9], CNR-DT 200/2004 [16], Teng et al

[18], Rousakis et al [19], Wei e Wu [17] and Nisticò e Monti [10] are also the more suitable for the assessment of fcc.

Theoretical axial strain values based on FRP ultimate tensile strain presents a large scatter of values and can lead to

overestimation of the ultimate strain of FRP confined concrete, as in the case of the approximate formula of Spoelstra

and Monti [15] and Toutanji [13] and Saafi et al [14] models. The older expression proposed by Karbhari e Gao I [11] and

the most recent models proposed by De Lorenzis e Tepfers [20], Lam and Teng [9] and CNR-DT 200/2004 [16] are the

more suitable for the assessment of εcc. Rousakis et al [19] also provides good results. The errors related to confined

concrete strength are lower than that of ultimate strain.

0

1

2

3

4

0 1 2 3 4

f cc

an

aly

. /fc

0

fccexp./fc0

Analytical model 2

15

In this work two analytical models for predicting the confined concrete strength are proposed. Except for the hybrid

confinement systems with low and high elastic modulus carbon fibres, the analytical results for the other hybrid systems

compare well the experimental data.

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16

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[21] Interprise S&P Clever Reinforcement Ibérica Lda.

[22] www.christinedemerchant.com, visitada em 24/04/2015.

[23] www.aviacao.org, visitada em 24/04/2015.