vetite mekanike te fibrave ne betone

8/13/2019 Vetite Mekanike Te Fibrave Ne Betone

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FIBER REINFORCED CONCRETE FOR LIFE TIME ENGINEERING

OF CIVIL INFRASTRUCTURE

N. Banthia

University of British Columbia, Canada

ABSTRACT: The usefulness of fiber reinforced concrete (FRC) in various civil engineering applications isindisputable. Fiber reinforced concrete has so far been successfully used in slabs on grade, shotcrete,architectural panels, precast products, offshore structures, structures in seismic regions, thin and thick repairs,

crash barriers, footings, hydraulic structures and many other applications. With the insurmountable durability

concerns for our current transportation infrastructure and especially bridge decks, the use of high performancefiber reinforced concrete for both new infrastructure and for rehabilitation of older infrastructure appears highly

promising. Fibers control shrinkage cracking, abate micro-cracks from widening and provide concrete with high

ductility, toughness, impact resistance and fatigue endurance. Fibers also reduce permeability of stressed

concrete and can be made to undergo multiple cracking such that the resulting material is significantly more

damage tolerant while maintaining its stress carrying capability. This paper presents a brief state-of-the-artreport on mechanical properties and durability of fiber reinforced concrete and identifies the numerous

advantages that may be potentially derived from use of such high performance materials.

KEYWORDS:FRC, fiber reinforced concrete, toughness, fatigue, shrinkage, durability, permeability, bond,repair

1. INTRODUCTION

Compared to other building materials such as metals and polymers, concrete is significantly more brittle andexhibits a poor tensile strength. Concrete carries flaws and micro-cracks both in the material and at the interfaces

even before an external load is applied. These defects and micro-cracks emanate from excess water, bleeding, plastic

settlement, thermal and shrinkage strains and stress concentrations imposed by external restraints. Under an appliedload, distributed micro-cracks propagate, coalesce and align themselves to produce macro-cracks. When loads are

further increased, conditions of critical crack growth are attained at tips of the macro-cracks and unstable and

catastrophic failure is precipitated. Under fatigue loads, concrete cracks easily, and cracks create easy access

routes for deleterious agents leading to early saturation, freeze-thaw damage, scaling, discoloration and steel

corrosion.

The micro and macro-fracturing processes described above can be favourably modified by adding short, randomlydistributed fibers of various suitable materials. Fibers not only suppress the formation of cracks, but also abate their

propagation and growth. The resulting material termed fiber reinforced concrete (FRC) is rapidly becoming a

well-accepted mainstream construction material. There are currently 200,000 metric tons of fibers used for

concrete reinforcement. Table 1 shows the existing commercial fibers and their properties. This paper discusses the

use of fiber reinforced concrete in transportation infrastructure especially bridge decks.

2. FIBER REINFORCEMENT MECHANISMS

In the hardened state, when fibers are properly bonded, they interact with the matrix at the level of micro-cracks and

effectively bridge these cracks thereby providing stress transfer media that delays their coalescence and unstable

growth (Figure 1). If the fiber volume fraction is sufficiently high, this may result in an increase in the tensilestrength of the matrix beyond the Bend Over Point, BOP. Indeed, for some high volume fraction fiber composite [1],

a notable increase in the tensile/flexural strength over and above the plain matrix has been reported (Figure 2). Once

the tensile capacity of the composite is reached, and coalescence and conversion of micro-cracks to macro-crackshas occurred, fibers, depending on their length and bonding characteristics continue to restrain crack opening and

crack growth by effectively bridging across macro-cracks. This post-peak macro-crack bridging is the primary

reinforcement mechanisms in the majority of commercial fiber reinforced concrete composites.


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Figure 1. Fiber Reinforcement Before and After the Creation of a Macro-Crack (Left)

and Crack Bridging by Fibers (Right)

Table 1. Properties of Fibers used as Reinforcement in Concrete

Fiber type Tensile

strength

(MPa)

Tensile

modulus

(GPa)

Tensile

strain ( %)

(max-min)

Fiber

diameter

(m)

Alkali

stability,

(relative)

Asbestos 600-3600 69-150 0.3-0.1 0.02-30 excellent

Carbon 590-4800 28-520 2-1 7-18 excellent

Aramid 2700 62-130 4-3 11-12 good

Polypropylene 200-700 0.5-9.8 15-10 10-150 excellent

Polyamide 700-1000 3.9-6.0 15-10 10-50 -

Polyester 800-1300 up to 15 20-8 10-50 -

Rayon 450-1100 up to 11 15-7 10-50 fairPolyvinyl

Alcohol800-1500 29-40 10-6 14-600 good

Polyacrylonitrile 850-1000 17-18 9 19 good

Polyethylene 400 2-4 400-100 40 excellent

High Density

Polyethylene2585 117 2.2 38 excellent

Carbon steel 3000 200 2-1 50-85 excellent

Stainless steel 3000 200 2-1 50-85 excellent

AR- Glass 1700 72 2 12-20 good

3. CRITICAL FIBER VOLUME, STRAIN HARDENING AND MULTIPLE CRACKING

It emerges therefore that fiber-reinforced cementitious composites can be classified into two broad categories:

normal performance (or conventional) fiber-reinforced cementitious composites and high-performance fiber-

reinforced cementitious composites. In normal performance FRCs with low to medium volume fraction of fibers,fibers do not enhance the tensile/flexural strength of the composite and benefits of fiber reinforcement are limited to

either a reduction in the plastic shrinkage crack control or to enhancement of energy absorption (toughness) in the

post-cracking regime only. For high performance fiber reinforced composites, on the other hand, with high fiberdosages, benefits of fiber reinforcement are noted in an increased tensile strength, strain-ha.rdening response before

localization and enhanced toughness beyond crack localization. Fiber volume fraction at which fibers can be

expected to produce an increase in the tensile/flexural strength is given by [2]:

Micro crackFormation

Macro crackFormation

peak

BOP

Pre-BOP Post-BOP


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)(1

1)(

21321

+

=

f

f

mu

fucriticalff

d

lVV (1)

where, fuis the average interfacial bond strength at the interface, muis the tensile strength of the matrix, lf is the

fiber length and df is the fiber diameter.

1,

2,

3are efficiency factors related to length, orientation and grouping,

respectively, and 1 and 2are constants pertaining to uncracked state of the composite. For a given FRC, Equation1 guarantees that if the critical volume fraction is exceeded, composite will depict strain hardening and show

multiple cracking. Some such curves for carbon fiber reinforced concrete in tension are given in Figure 2. Note thepresence of strain hardening in the composite beyond 2% by volume.

Figure 2. (Left) A CFRC Composite in Tension and (Right) Stress-Strain Curves

Showing Strain-Hardening and Multiple Cracking at High Fiber Volume Fractions

In FRCs with volume fractions higher than the critical, after the bend-over point, BOP, (Figure 2), multiple crackingis expected to occur and the composite is expected to crack in segments of lengths betweenx and 2x(wherexis the

transfer length) given by:

=

42

f

fu

mu

f

md

V

Vx

(2)

4. FRACTURE MECHANICS BASED REPRESENTATION

Equation (1) is a rather simplistic approach to FRC. It assumes that the composite goes from an uncracked state toa cracked state (albeit showing multiple cracking at Vf > Vfcritical). In reality, concrete is a micro-fracturing,

strain-softening material, and in the case of fiber reinforced concrete, in addition to crack closing pressure due to

aggregate interlocking, fiber bridging occurs behind the tip of a propagating crack where fibers undergo bond-slip processes and provide additional closing pressures. The fracture processes in fiber reinforced cement

composites are therefore complex and advanced models are needed to simulate these processes. Attempts have

been made to model fracture in FRC using the cohesive crack model [3] as well as the J-integral [4]. However,strictly speaking, these are only crack initiation criteria and fail to define conditions for continued crack growth.

To define both crack initiation and growth, there is now general agreement that a continuous curve of fracture

conditions at the crack tip is needed as done in an R-curve [5]. An R-curve (Figure 3) is a significantly more


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suitable representation of fracture in FRCs, as one can monitor variations in the stress intensity as the crack

grows and derive a multi-parameter fracture criterion. Some R-Curves are shown in Figure 4 [6].

Figure 3. R-Curve Representation of

Fracture in FRC

Figure 4. R-Curves Generated from

A Crack Growth Test

5. FIBER-MATRIX INTERFACIAL BOND

As in any fiber reinforced composite, fiber-matrix bond in FRC is of critical importance. However, unlike fiberreinforced polymers (FRPs) with continuous fibers used by the aerospace and automobile industries, short fibers in

FRC mean that the bond in most cases is not fully developed. For a fiber embedded in a cementitious matrix and

subjected to a pull-out load (Figure 5), shear-lag will occur and interfacial debonding will commence at the point of

fiber entry which will slowly propagate towards the free end of the fiber. Thus, some energy absorption will occur atthe fiber-matrix interface while the bond is being mobilized and the fiber prepares to slip. Tensile stress in the fiber

[f (x)]and shear stress at the interface [(x)] can be given by:

(3)

whereR= Radius of matrix around the fiber taking part in transfer, r = radius of the fiber, lf= length of the

fiber,Ef= modulus of elasticity of the fiber, Gm= Shear modulus of the matrix at the interface,R/rdepends

upon the fiber packing and fiber volume fraction. For 2-D packing: ln R/r = (1/2) ln (p/Vf) and for 3-D packing:

ln R/r = (1/2) ln [2p/(3Vf)].

( ) mff

f

f El

xl

x

=

2cosh

)2

cosh1

1

1

2/1

2

1

ln

2

=

r

RrE

G

f

m

( )

2cosh

2

1sinh

ln21

1

)2/1(

f

f

m

mff l

x

r

RE

GEx

=


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One can show that the ratio of the maximum interfacial bond stress [(max)] to the tensile stress [f(max)] is given

by:

4coth

)/ln(2(max)

(max) 12

1

f

ff

l

rRE

G

= (4)

For 2% fiber volume, with a max= 15 MPa one gets a max= 200 MPa which is much lower than the yield strengthof steel. Consequently, a steel fiber for normal lengths of 25-60 mm cannot ever develop stresses close to its capacity

and hence most fibers in practice are deformed. However, even here there is a limit. If deformed excessively, fibersmay develop stresses that exceed their strength and fracture in the process (Figure 6). The energy absorption in such

cases is limited, and although some fiber slippage may precede fracture, poor toughening ensues. For maximized

fiber efficiency, a pull-out mode of fiber failure where pull-out occurs at a fiber stress close to its tensile strength is

preferred. It is important to mention that fiber failure mode is highly dependent on the angle at which fiber is

inclined with respect to the direction of the pull-out force. In FRC, inelastic bond failure mechanisms such as

interfacial crack growth, crack tortuousity and fiber slip are of greater relevance.

Figure 5. Shear-Lag in a Bonded Fiber

with Inelastic Mechanisms

Figure 6. Bond-Slip Pull-Out Curves for Various Deformed

Fibers. Notice Fiber Fracture in an Excessively Deformed Fiber

6. SOFTENING AND TOUGHNESS

In the softening regime, where the load starts to drop, the response of the composite is completely dependent uponthe bond-slip behaviour of the fibers under an applied pull-out load. The response in the softening regime can

therefore be assembled by first expressing the bond-slip behavior of a given fiber and then integrating the

contribution of all fibers across a crack. In the case of pure tension, the stress vs crack separation, tension(w), curvecan be expressed as [7]:

dzdzppwfd

Vw

fL

zf

f

tension )()(),(4/

)(0

cos)2/(

02 = == (5)

where,f(, w) is the bond-slip response of a single fiber at a crack opening (w)and inclination angle , p() andp(z)are probability density functions of the orientation of fiber w.r.t. the tensile loading direction and centroidal distance

of the fiber from the crack plane, respectively.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 5 10 15Slip (mm)

Load(kN)

Undeformed

Deformed Fiber (Pull-Out)

Excessively Deformed Fiber (Fracture)a) Intact interface.

b) Partially debonded interface.


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Figure 7. Modeling FRC in Flexure

In the case of flexure, which is more pertinent to FRC, Armelin and Banthia [8] proposed a stochastic model

(Figure 7). The compressive strain, o,at the top-most fiber of the specimen leads to an axial shortening, o,asshown. This in turn leads to stress, c,in the uncracked concrete. On the other hand, it results in fiber slippage,wi, below the neutral axis and corresponding forces, fi, as the fibers pull-out. Thus, the flexural load carried

during the post-crack phase is obtained by satisfying the equilibrium of moments:

l

MP e

2= (6)

The equilibrating moment,Me, may be calculated by summing the moments generated by concrete stresses and

the individual moments generated by theNindividual fibers bridging the crack below the neutral axis. It follows

from Figure 7, that

( ) =+'

0 10.

c N

ic fdyb (equilibrating forces) (7)

( ) ( ) +=N

ii

c

ce yfydybM10

.

'

(equilibrating moments) (8)

The model expresses the pull-out force in each fiber (fi) as a function of the crack width, wi, according to theaverage pull-out force versus slip (or crack width) relationship obtained experimentally at the full embedment

length, le=l/2.

( )

( )[ ]

+

+=

CC

i

ipiii

Bw

AAwEwf

1

1

1, (9)

where the constantsA,B, CandEp, are obtained for each orientation through the Ramberg-Osgood formulation.

Recognizing that the average force in the fibers at a layer which is at a distance y from the neutral axis is

averaged over the entire range of embedment and inclination that is possible, the value of fi to be substituted inEquations 7 and 8 may be computed as:

( )( ) ( ) ( )

( )( )

+

++++= wf

wfwfwfwf

wff geometryi

4

1

222

1 905.67455.22

0 (10)

CMOD

0

0

displacements

i..

3

2

1

i = f(wi i li

c

uncracked

section

wi

1

2

3i

strains

C


7/17

Some predictions of the above model are compared with experimental findings in Figure 8. Note an excellent match.

Figure 8. Model Predictions for FRC Flexural Toughness

7. DYNAMIC PROPERTIES

Due to the excellent ability of fibers to control crack growth and provide crack-tip toughening, the fatigue

performance of concrete is significantly enhanced due to fiber reinforcement (Figure 9) [9].

Drop Weight Impact Tests [10] are generally performed to measure the resistance of fiber reinforced concrete to

impact loads. For fiber reinforced concrete, while an improvement in impact properties is widely reported, on aworrisome note, steel fibers are reported [11] to fracture across cracks at high rates of loading and thus produce

a brittle response at very high strain-rates. As seen in Figures 10 and 11, SFRC may show increased brittleness

under very high strain rates. Polypropylene fibers, on the other hand, do not show onset of brittleness at highrates of loading. The exact reasons of the observed brittleness of some FRC materials under impact have been

investigated via fundamental testing of bond-slip mechanisms, fracture studies and modeling [12].

Figure 9 Fatigue Response of FRC


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Figure 10. Impact Resistance of Steel FRC and Polypropylene FRC. Note the

increased brittleness in SFRC at high rates of loading.

Figure 11. Impact Response of SFRC Beams. Notice Brittleness at

High Strain-Rates

8. SHRINKAGE

Soon after placement, evaporation of the mix water and the autogenous process of concrete hydration causeshrinkage strains in concrete. With their large surface areas, fibers engage water in the mix and reduce bleeding and

segregation. The result is that there is less water available for evaporation and less overall free shrinkage (Figure

12a; Ref. 13). Further, when the concrete is restrained, as will be the case in a bridge deck, fibers bridge cracks and

reduce crack widths and crack areas (Figure12 b, c and d). Indeed, a number of attempts have been made in the pastto provide shrinkage and thermal reinfor cement in bridge decks using fiber reinforcement as in the steel free deck

systems [14, 15, 16].

0

10

20

30

40

50

60

70

80

90

200 500 750 1000Drop Height (mm)

Tou

ghness(Nm) Steel Fiber

Polypropylene

Fiber

0

50

100

150

200

250

300

350

0 0.2 0.4 0.6 0.8 1

Deflection (mm)

Load(kN)

Low Strain-Rate Impact

High Strain-Rate Impact

Quasi-Static


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0.0

0.5

1.0

1.5

2.0

2.5

0.0% 0.1% 0.2% 0.3% 0.4%Volume Fraction (%)

AverageCrackWidth(mm)

F1 F2

F3 F4

F5 F6

F7

0

50

100

150

200

250

300

350

0.0% 0.1% 0.2% 0.3% 0.4%

Volume Fraction (%)

AverageCrackArea(mm

2)

F1 F2

F3 F4

F5 F6

F7

Figure 12 a. Free Shrinkage Strains in

FRC and Plain Concrete.

Figure 12 b. Control of Shrinkage

Cracking in Restrained Overlay (Top:

Plain; Middle: 0.1% Fiber; Bottom:

0.2% Fiber

Figure 12 c. Plastic Shrinkage Crack Control

Efficiency of Various Fibers (F1-F7): Average

Crack Area

Figure 12 d. Plastic Shrinkage Crack

Control Efficiency of Various Fibers

(F1-F7): Average Crack Width

9. PERMEABILITY, CRACKING AND SERVICE LIFE PREDICTIONS

Permeability and Cracking: The long term performance of bridge decks is becoming an issue of greater

significance in modern bridge engineering. In this context, corrosion of the reinforcing steel is the biggest

concern. Chloride penetration and carbonation are the primary reasons for such corrosion and any measures

aimed at mitigating the ingress of chlorides or CO2 into the body of concrete are expected to significantly

enhance the durability of bridge decks. These deleterious agents enter the body of concrete through one of thethree transport mechanisms: diffusion, capillary sorption and permeability, of these, the permeability is

considered as the dominant mode. Any measures adopted to reduce permeability of concrete will therefore helpin preserving the durability of a concrete deck. Results have indicated that permeability, in turn, is highly

dependent upon cracking in concrete and an increase in the crack width will not only produce a highly

permeable concrete (Figure 13) but also enhance the possibility of rebar corrosion (Figure 14) [17].


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Figure 13: Effect of Crack Width on Permeability [17]

Figure 14. Effect of Crack Width on Corrosion Potential. A potential below 280mV indicates

corrosion initiation, and below 400mV indicates active corrosion [17]

Bentur et al [17] also considered the potential of fibers and other technologies in controlling crack widths in a

typical bridge deck and their results are given in Table 2. It was found that the use of shrinkage reducing

admixture and fibers could be as effective as doubling of the steel reinforcement.

Table 2: Effect of the Type of Reinforcement on Cracking in a 30m Long Bridge Deck

(w/cm = 0.38; FEMASSE Software)

Crack width, mmReinforcement

Average Minimum Maximum

Number of

cracks

Rebar 0.40 0.25 0.60 15

Doubling of rebar 0.21 0.11 0.25 22

Rebar + SRA1 0.22 0.18 0.28 8

Rebar + fiber2 0.29 0.20 0.36 23

1Shrinkage Reducing Admixture2Equivalent flexural strength of 1.8 MPa (JCI-SF4)


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0

0.5

1

1.5

2

2.5

0 0.1 0.2 0.3 0.4 0.5

Stress Level (fu )

NormalizedPermeabilityCoefficientx10-10

(m/s)

0.0% Fiber

0.1% Fiber

0.3% Fiber

0.5% Fiber

The influence of an externally applied stress on the permeability of concrete remains poorly understood. Banthia

and co-workers [18, 19] developed a novel technique of measuring the permeability of concrete under anapplied stress and investigated the benefits of fiber reinforcement. The permeability cell was mounted directly in

a 200 kN hydraulic Universal Testing Machine (UTM) such that a uniform compressive stress could be applied

directly on the concrete specimen housed in the cell. The water collected was related to the coefficient of water

permeability (Kw) by applying Darcys law:

hAQLKw

= (11)

Kw =Coefficient of water permeability (m/s), Q= Rate of Water Flow (m3/s),L = Thickness of specimen wall

(m),A= Permeation area (m2) and h= Pressure head (m)

Their data are plotted in Figure 15. Notice that under conditions of no-stress, fibers reduce the permeability ofconcrete, and the reduction appears to be proportional to the fiber volume fraction. Data further indicates that

stress has a significant influence on the permeability of concrete. When stress was first increased to 0.3fu, both

plain and FRC showed a decrease in the permeability. However, when the stress was increased to 0.5fu, plainand FRC showed very different trends. At 0.5fu, the permeability of plain concrete increased substantially over

that of the unstressed specimen, but for FRC, while there was an increase in the permeability over 0.3fu, the

permeability still stayed below that of the unstressed specimen.

Figure 15. Normalized Permeability Coefficients

The above observations can be related to cracking. At 0.3fu, it is conceivable that in both plain and FRC, there is

no discernible cracking that can affect the flow of water. However, at 0.3fu, the stress-strain response for both

plain and FRC would become non-linear indicating the presence of cracking. As given by the Poiseuille Law[20], the flow of water through cracks is proportional to the cube of the crack width. In the case of FRC, one can

expect the fibers to suppress cracking and hence maintain the rate of flow similar to an unstressed specimen.

When combined with the phenomenon of pore compression, this implies that the permeability of FRC understress can in fact be lower than that of an unstressed specimen.

Service Life Prediction:Bhargava and Banthia [19] extended the permeability data described above towards

service life prediction. Most service life prediction models for concrete involve the use of diffusion coefficients[21]. Unfortunately, studies relating different transport coefficients are rare. In particular, experimental data

relating permeability and diffusion coefficient is lacking, and only a theoretical correlation can be established

between these two coefficients via a correlation constant, as follows:

Empirical equations for the permeability coefficient were proposed by Hedegaard et al.[22] and for diffusion

coefficient were proposed by Hansen et al.[23] as follows:


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+

+= 0.431.0

3.4expw

fcKw (12)

+

+

=0.7

3.0

107.1 w

fc

xD (13)

where,

Kw= water permeability coefficient (m/s)

D= Chloride ion diffusion coefficient, in cm2/s

c= cement content of concrete, in kg/m3

w= water content of concrete, in kg/m3

f= fly-ash content of concrete, in kg/m3

By substituting the values of c, wandf for the concrete mixture used in the permeability tests in Equations 12and 13, one obtains Kw=1.07x10

-10(m/s) andD = 7.89x10

-13(m

2/s).

Further, the permeability K(m2) of a single straight pore with effective pore radius

effr embedded in a medium

of cross-sectional area A can be related to effective pore radius by assumingHagen-Poiseuilleslaw to be validfor small pores.

A

rK

eff

8

4

= (14)

where effr is the effective pore radius defined as the radius of the effective pores which take part in the

transport. Also, the diffusion coefficient can be related to the area fraction of effective pores as,

A

rDaDD

eff

oeffo

2== (15)

whereeffa = is the area fraction of effective pores

oD = is the diffusion coefficient in a bulk fluid

Assuming that the effective pore radius in Equations 14 and 15 is the same, a general relationship betweenpermeability K(m

2) and diffusion coefficients D (m

2/s) emerges,

DD

rK

o

eff

8

2

= (16)

Further, it is to be noted that an interconnected pore system is necessary for a continuous network of flow paths

to be available for various transporting media. In saturated conditions, the steady state flow coefficient can be

related to the water permeability coefficient as the two processes occur simultaneously,

g

KKw

= (17)

Using Equations 16 and 17, the water permeability coefficient wK (m/s) and the diffusion coefficient D (m2/s)

can be related as,


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DD

grK

o

effw

8

2

= (18)

Where Kwas before is the water permeability coefficient (m/s),

Dis the diffusion coefficient (m

2

/s),reffis the effective pore radius,

is the viscosity of water (Ns/m2),

is the density of water (kg/m3) and,

g is the gravity (m/s2)

This equation corresponds to Katz-Thompson Equation [24], and is based on the assumption that the effectiveradius affecting the permeability and the diffusion coefficient is the same. Equation 18 can be further modified

to consider the effect of stress and the fibers on concrete. Since the permeability coefficient is proportional to

the fourth power of effective pore radius (Equation 14) and since the normalized permeability coefficient is

related to the water permeability coefficient of unstressed plain concrete through the previously defined factorsFand S, describing, respectively, the influence of fiber reinforcement and stress [see Ref. 19 for details], theeffective pore radius can be modified to:

effnormalized rSFr25.025.0* = (19)

where, r* normalizedis the effective pore radius corresponding to normalized permeability values and effr in this

case is the effective pore radius of plain concrete under zero stress condition.

Substituting Eqn 19 into Eqn. 18, we get a modified equation which relates normalized water permeability to

diffusion coefficient as,

DSCFKnormalized5.05.0= (20)

where C =

oeffD

gr

8

2

is a constant proportional to second power of the effective pore radius of plain concrete

under zero stress condition.

For plain concrete and zero stress condition F=S=1 and for this case:

CxDKKunstressedplainwnormalized

== (21)

Substituting the empirical values of the water permeability coefficient Kw=1.07x10-10

m/s and the chloride iondiffusion coefficient D= 7.89x10

-13m

2/s, as obtained previously, the value of constant C for the concrete in

question can be calculated:

C = 135.62 m

-1

(22)

The constant C computed above takes into consideration the effective pore radius of plain concrete under zerostress condition and properties of the chloride ion diffusion coefficient. The calculated chloride ion diffusion

coefficients are given in Table 3.


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Table 3. Computed Values of Chloride ion Diffusion Coefficient

Fiber Volume

Fraction

Vf

Applied Stress

Level

Normalized water

permeability

coefficientKnormalizedx10

-10(m/s)

F S

Chloride ion

diffusion

coefficientDx10

-13(m

2/s)

0.0fu 1.66 1 1 12.24

0.3fu 103 1 0.62 9.640.0%

0.5fu 2.30 1 1.38 14.43

0.0fu 0.95 0.57 1 9.27

0.3fu 0.53 0.57 0.57 6.850.1%

0.5fu 0.71 0.57 0.76 7.95

0.0fu 0.60 0.36 1 7.37

0.3fu 0.32 0.36 0.53 5.400.3%

0.5fu 0.45 0.36 0.75 6.38

0.0fu 0.30 0.18 1 5.21

0.3fu 0.10 0.18 0.33 3.020.5%

0.5fu 0.18 0.18 0.62 3.97

In this study, the Durability Factor, D, for a given concrete under a given stress level was defined as the ratio ofits expected service life to that of companion plain concrete under zero stress. Using Tuuttis model [21], ingressof chlorides is estimated by a one-dimensional diffusion process using the Ficks Second Law of diffusion. For

non-steady state condition, the chloride concentration Cat a locationxand at a time tis given by [25].

=x

CD

xt

C

(23)

Here, the diffusion coefficient D may be a constant or a function of other variables such as chloride

concentration, location, time, temperature, etc.For a simple case with known geometry and boundary conditions where the diffusion coefficient D can be

assumed to be a constant, solution to Eq. 23 is given by [26]:

= Dt

x

erfCtxC s 21),( (24)

=

zt

dtezerf0

22)(

(25)

where,erfis a standard error function,

xis effective concrete cover depth,

sC is the concentration of the chloride ions at the outside surface of the concrete and is assumed to be constant

with time. That is, sCC= forx = 0and for any t

iC is the concentration at the depth of the reinforcement; assumed to be zero at t =0.

tC is the threshold concentration required to initiate steel reinforcement corrosion. The initiation period is

accomplished when ti CC = and,t= time

Eq.24 can be solved by using a normal standard distribution [27]:

1)2(2)( = zNzerf (26)

dtezNz

t

=2

2

2

2

1)2(

(27)


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0

0.5

1

1.52

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6

Stress Level (fu )

DurabilityFactor,

D 0.0% Fiber

0.1% Fiber

0.3% Fiber

0.5% Fiber

The initiation time can thus be calculated by assuming a constant diffusion coefficient for concrete, a known

surface chloride content (dictated by the environment), the thickness of the concrete cover and critical chlorideion content at which onset of corrosion is expected.

Solving the above equation for tC = threshold concentration of chloride ions = 0.50 % (based on the mass of

cement), sC =chloride ions concentration at the surface of concrete = 0.70 % (based on the mass of cement), x

= 25 mm, and diffusion coefficients,D, from Table 3:

D

xtt i

2678.0

2

= (28)

Figure 16. Durability Factors: Notice Durability Enhancements

with Fiber Reinforcement

Notice that a lower value of 0.50% threshold concentration of chloride ions was chosen due to the presence of

fly-ash in concrete which is known to increase the rate of corrosion. The above equation predicts that service life

of any concrete is proportional to x2, and holds an inverse relationship with the chloride ion diffusioncoefficient. Therefore doubling the concrete cover increases service life of concrete by a factor of 4, whereas a

10-fold reduction in diffusion coefficient will result in a 10-fold increase in the predicted service life.

Substituting the values of diffusion coefficient from Table 3 into Eq. 28 for different concrete types and stressconditions, the Durability Factors were computed and are plotted in Fig. 16. Notice in Figure 16 that as per the

model, fiber reinforcement can be effective in enhancing the durability of concrete under both stressed and

unstressed conditions.

10. FRC IN REPAIR: BOND WITH OLD CONCRETE

A thin bonded concrete overlay provides an increase in the structural capacity, and rehabilitation of old bridge decks

with FRC has become a common practice around the world. Any repair performed on a structure must meet fourmajor requirements. First, it should be able to arrest further deterioration and particularly the corrosion of the

reinforcing steel if present. This requires that the material used for repair be adequately impermeable to

aggressive liquids and gases. The second requirement is that the repair material should be able to bond properlywith the old concrete and restore structural integrity. Third, the repair should be durable and be able to withstand

the severe climatic conditions imposed upon it. Finally, the repair material should have chemical,

electrochemical, permeability and dimensional compatibility with the substrate.

Based on the above, it is clear that fiber reinforced concrete has all of the attributes needed for a durable repair

of bridge decks [28]. Indeed closed-loop repair bond tests with plain and fiber reinforced concrete [29] have

indicated that there is both an increase in the bond strength and bond toughness as quantified by interfacial Gfvalues (Table 4) due to fiber reinforcement. Some typical bond strength curves are given in Figure 17.


16/17

Figure 17. Closed-Loop Repair Bond Strength Test (Left) and Results (Right).

Notice the Beneficial Effect of Fibers

Table 4. Bond Strength of FRC with Old Concrete

Surface

Condition

Polymer Fiber Type of

Failure

Interfacial

Bond

Strength

Interfacial

Gf

Type Volume

Fraction

(MPa) (N-mm/mm2)

x102

0 % A * 0.74 0.019

Steel 1 % C ** 1.33 0.051

0 % 2 % A & C 0.97 0.020

Smooth carbon 1 % A & C 0.83 0.041

2 % C 1.13 0.063

0 % A 0.98 0.037

10 % Steel 1 % C 1.24 0.0542 % C 1.49 0.078

0 % C 1.31 0.047

Steel 1 % C 1.75 0.085

Rough 0 % 2 % C 2.02 0.126

carbon 1 % A 1.03 0.055

2 % C 1.21 0.078

* Adhesive failure

** Cohesive failure

11. CONCLUDING REMARKS

With the current durability concerns for our transportation infrastructure (and especially the bridge decks), theuse of high performance fiber reinforced concrete for both new construction and repair appears highly

promising. Fibers control shrinkage cracking, abate micro-cracks from coalescing and enhance ductility,

toughness, impact resistance and fatigue endurance. With their high resistance to crack nucleation and growth,fibers reduce the permeability of concrete and prevent the ingress of deleterious agents thereby delaying both

material degradation and steel corrosion.


17/17

12. REFERENCES

[1] Banthia, N. and Sheng, J., Cement and Concr. Composites., 18: pp. 251-269; 1996.[2] Naaman, A.E., Proceedings HPFRCC-4, RILEM Proc. 30, Paris, pp. 95-116.[3] Hillerborg, A., Cement and Concrete Composites, 2, pp. 177-84; 1980.[4] Mindess, S. et al, Cement and Concrete Research, 7, 731-742; 1977.[5] Mobasher, B., Ouyang, C. and Shah, S.P.,Int. J. of Fracture, 50, pp. 199-219; 1991.

[6] Banthia, N., and Genois, I., ACI, Special Publication: Application and Testing of Fracture MechanicsConcepts(Ed. C. Vipulanandan), SP-201, pp. 55-74; 2000.

[7] Li, V., , Kluwer Academic Publishers, The Netherlands, 1991, pp. 447-466.[8] Armelin, H. and Banthia, N.,ACI Mat. J., 94(1): pp. 18-31; 1997.[9] Ramakrishnan, V., Proceedings of the Sixth International Purdue Conference on Concrete Pavement:

Design and Materials for High Performance, Indianapolis, Indiana, Nov., 18-21, 1997, pp. 119-130.[10] Banthia, N., Mindess, S., Bentur, A. and Pigeon, M.,Expt. Mech. 29 (2): pp. 63-69; 1989.[11] Bindiganavile, V and Banthia, N.,American Concrete Institute, Materials Journal, Vol. 98(1): pp. 17-24;

2001.

[12] Kaadi, G.W., MS Thesis, The University of Illinois, Chicago, (1983).[13] Zollo, R. F.; Ilter, J. A.; and Bouchacourt, G. B., 1986, Third International Symposium on Developments

in Fibre Reinforced Cement and Concrete, RILEM Symposium FRC 86, V. 1, RILEM Technical

Committee 49-TFR, July.

[14] Newhook, J. P., and Mufti, A.A., Concrete International, V. 18, No. 6, 1996.

[15] Mufti, A., Banthia, N. and Bakht, B., Banthia, N., Sakai, K. and Gj rv, O.E, Proc., 3rd InternationalConference on Concrete Under Severe Conditions of Environment and Loading,. (Eds.) Vancouver, June2001, The University of BC, 2001, pp. 1032-1041.

[16] Banthia, N., Yan, C., Mufti, A., and Bakht, B., (Eds.: Peled, Shah and Banthia) ACI, Special TechnicalPublication, SP-190,American Concrete Institute, Detroit, USA, pp. 21-39.

[17] Bentur, A., et al, N.S. Berke, L. Li, K.A. Rieder, ConMat05 Mindess Symposium Proc., University ofBritish Columbia (Ed. Banthia, Bentur and Shah), 2005.

[18] Banthia, N. and Bhargava, A., American Concrete Institute, Materials Journal,104(1), Jan-Feb, 2007,pp. 303-309.

[19] Bhargava, A. and Banthia, N.,RILEM, Materials and Structures, 41, Jan 2008, pp. 363-372.[20] Edvardsen, C., ACI Materials Journal,V. 96, No. 4, July-August 1999, pp. 448-454.[21] Tuutti, K., Swedish Cement and Concrete Research Institute, Stockholm, Sweden (1982).[22] Hedegaard, S.E., Hansen, T.C.,Materials and Structures, 25 (1992) 381-387.[23] Hansen, T.C., Jensen, J., Johannesson, T., Cement and Concrete Research, 16 (5) (1986) 782-784.

[24] Garboczi, J., Cement and Concrete Research, 20 (4) (1990) 590-601.[25] Crank J., Mathematics of diffusion,Oxford: Clarendon Press,1956.[26] Newman, A.B., ,American Institute of Chemical Engineers, Vol. 27 (1970).[27] Bertolini, L., Elsener, B., Pedeferri, P., and Polder, R., , WILEY-VCH Verlag GmbH and Co. kGaA,

Weinheim (2004).[28] Carter, P., et al., Concrete International, July 2002 , pp. 51-58.[29] Banthia, N. and Yan, C.,ACI Special Publication on High Performance Materials for Repairs(edited by

Krstulovic-Opara et al), ACI SP-185, pp. 69-80.

vetite mekanike te fibrave ne betone

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