Debonding failure mechani
sm in RC beam strengthening with CFRP
Energy and Hydro Technology/
Vol:1
/2008/No.1
1 INTRODUCTION
The pathological stu
dy of concrete stru
c
tures shows the
damage of these structures because of the deterioration
of materials, design errors or accidents. In relation to
di
f
ferent cases of disorder the maintenance of these
structures consists in protecting them to insure a goo
d
tightness and to limit corr
o
sion, in repairing them to
offset the loss of stiffness and strength, and in
strengthening them to improve the performance and the
durability of the structures. The strengthe
n
ing of
concrete structures in site with an e
x
ternal
ly bonded
composite plate (FRP) using epoxy resin a
p
pears to be
a feasible way of increasing the capacity and stiffness
of existing structures (An et al. 1991: Meier et al.
1991). Composite materials, because of their high
strength and stiffness, resistanc
e to corrosion and low
weight, can be of great interest in structures in order to
minimize the weight and increase the structural
performance. To analyze the behavior in fle
x
ion of
concrete beams strengthened by composite plates and
determine ultimate load
we present relationships
between e
x
ternal load and shear stress distribution at
concrete / plate interface. In this p
a
per also we
introduce different premature failure mode and the
method to determine average of shear stress at
i
n
terface.
2 PREMATURE FA
ILURE CRITERIA OF
RC BEAM
Different failure modes exist for a beam strengthened
by FRP plate. First
the
class
i
cal
rupture of
the beam
should be me
n
tioned: either by the plate tensile failure
(mode I), or by the concrete crush in the compressi
on
zone (mode II). However in this method of
strengthening, possibility of premature failure exists at
the interface b
e
cause of the separation of plate (fig 1).
2.1 Failure due to debonding of plate at the
interface
The interface could be cracked in a dir
e
c
tion parallel to
the glue line under combined shear and normal stresses.
However, when debonding, the failure is governed by
the Mohr

Coulomb law, which may be e
x
pressed in the
form:
c
tg
n
int
(1)
Where
INT
i
s the i
n
terface shear stress,
c
is the
cohesion,
n
is the normal stress to the glue line and
is the angle of the i
n
ternal friction. The ranges of
c
and
are attributed to variations in the
surface
prepar
a
tion and the properties of the adhesive and the
concrete. For the simplified case in which interface
bond stresses are constant in the anchorage zone,
replacing the force sy
s
tem with an equivalent
single
force and couple acting through the centroid of the plate
leads to (Fig. 2):
Debonding failure mechanism in RC beam
strengthening with CFRP
H. Varastehpour
Institute for Energy and Hydro Technology (IEHT)
,
Mashhad, IRAN
ABSTRACT
Carbon Fiber Reinforced plastic (CFRP) can be bonded to the tension face of r
e
inforced concrete
beams to
increase the flexural capacity. In this type of beams, high interface shear stress may
result in debonding of plate
and premature failure in concrete beam. To design of these beams failure mechanism and relationships
between external load
and shear stress distribution at concrete / plate interface must be considered. In this
paper we present different pr
e
mature failure mode and introduce
the method to determine average of shear
stress at interface.
Debonding failure mechanism in RC beam strengthening with CFRP
Energy and Hydro Technology/
Vol:1
/2008/No.1
2
int
).
2
/
.(
p
a
p
xy
T
T
b
M
(2)
Where
xy
M
is the peeling moment,
a
T
is the glue
thickness and
p
T
is
the FRP plate thickness. The
normal stress at the end of plate because of the peeling
moment could be calculated by:
int
.
K
n
(3)
Figure1. Different failure modes in Rc beam
strengthened with FRP plate
.
In this
equation K is a parameter relating the shear
stress and the normal stress at the end of the plate; it
depends on the physical and mechanical properties of
the plate and the adhesive (Roberts 1989)
4
1
)
.
.
(
31
.
1
p
a
a
p
E
T
E
T
K
(4)
stress.
Figure 2. Calculation of interfacial shear
Where
a
E
and
p
E
are adhesive and plate elastic
modulus. To determine of
C
and
we carried o
ut two
different tests. First to determine the cohesion
parameter
C
, we have used the e
x
perimental shear test
set up and in the second part, to determine the friction
angle
, different small beams strengthened wi
th FRP
were used (V
a
rastehpour et al. 1995) Using the average
results of different specimens which failed by
debonding, the cohesion parameter was equal to 5.4
Mpa and the average friction angle was o
b
tained equal
to 33°. Beginning with the Mohr

Coulomb eq
uation
that takes into account the failure criterion of the
i
n
terface, with
and
C
the admissible shear stress at
the interface can be calc
u
lated by:
)
33
1
(
4
.
5
Ktg
adm
(5)
This equation explains
the failure criteria due to the
debonding of plate at the inte
r
face and failure can
appear when the max
i
mum shear stress value at the
interface reaches
adm
.
2.2 Failure of concrete layer between the plate
and steel
The analysis of di
fferent beams showed, the crack
pattern when the failure occurs could be d
e
fined by
figure
(
3
)
(Zhang et al. 1995). The cracks propagate in
tensile zone of the beam in the concrete layer between
FRP plate and the reinforced steel. A part of co
n
crete
betwee
n two co
n
secutive cracks work similarly as a
cantilever beam. These ind
i
vidual uncracked portions
of concrete tend to bend under the infl
u
ence of shear
stresses at their end during the loading. When the
concrete tensile stress at the section in co
n
tact wit
h
steel (point A) is higher than the concrete tensile
strength (
t
f
'
)
, debonding can appear su
d
denly.
The above observations suggest a poss
i
ble failure
mode which is controlled by the characteristics of the
individual teeth between two
consecutively cracks in
the concrete cover. If we neglect interaction b
e
tween
each teeth supposing an elastic behaviour for each
cantilever beam, the te
n
sile stress in the point A can be
calculated as:
t
c
A
A
I
l
M
/
)
2
/
.(
(
6)
where
t
I
is the se
c
ond moment of area of the
section, equal to and:
12
/
.
3
c
t
l
b
I
d
b
l
M
p
c
A
.
.
.
int
(7)
Where
int
is the a
v
erage interface shear stress
which is re
a
sonably assumed t
o be uniformly
distributed and
c
l
is the height of the section in
cantilever beam equal to the flexural crack spacing in
the beam and finally
d
is the concrete layer thickness
b
e
tween the FRP plate and the reinfor
ced steel. With
the substitution of equation
(
7
)
by equation 6 and by
using
t
A
f
(ultimate resi
s
tance of concrete in
traction), the admissible shear stress at the interface is
o
b
tained:
)
/
/(
)
6
/
.
(
p
c
t
adm
b
b
d
l
f
(8
)
CL
CL
CL
CL
(a)
(c)
(b)
(d)
C
.
L
x
P
/
2
fi
fj
int
a
bp
yp
h
b
N
.
A
Ta
Tp
Mxy
x
int
(
pi
pj
)
.
p
E
.
p
A
/
p
b
.
x
Debonding failure mechani
sm in RC beam strengthening with CFRP
Energy and Hydro Technology/
Vol:1
/2008/No.1
1,5
2,0
2,5
3,0
1,5
3,5
5,5
7,5
a
h
b
p
b
T
p
N.A
1.26E5 x a
(h).7 x Tp x Ep
yp x Tp
It
Ep
Ec
y
p
LN ( )
LN ( )
V
P/2
x
CL
Acier
A
d'
lc
int
A
Figure 3. Cracks propagation and a teeth
behaviour.
This equation explains the debonding cr
i
teria due to
the concrete cover failure and failure a
p
pears, when the
shear stress value at the interface reaches
adm
. This
prop
osed theoretical model also depends on the crack
spacing size (
c
l
). To determine
c
l
(Zhang et al. 1995)
present the method calculus upper and lower zone. This
mean debonding load could be variable between
minimum a
nd maximum load. For simplified this
calculation due to experimental results of the di
f
ferent
large scale beams show that,
c
l
is more or less equal to
the average stirrup di
s
tance (S) in the shear zone
(Varastehpur et al. 1996b). When
p
b
b
the
admissible shear stress obtain by:
)
6
(
.
d
S
f
t
adm
(9)
3 SHEAR STRESS DISTRIBUTION AT THE
INTERFACE
It is obvious that in order to anticipate the debonding of
the plate, it is necessary to d
e
termine the dis
tribution of
the shear stresses at the level of the interface during the
loa
d
ing. In this part, we suggest a new equation to
determine the average shear stresses at the interface
plate/concrete on the basis of a p
a
rametric study
(Varastehpour et al. 1997).
Figure 4. Regression to evaluate the shear stress

load
r
e
lationships
.
To simulate the non

linear behaviour of material in
the distribution of the maximum stress at the interface,
we examined the e
f
fect of the different variables, such
as rig
i
d
ity and thickness of the plate, geometry of the
section, the loading mode,etc. As a co
n
sequence of this
parametric study, we intr
o
duce a factor
of the different variables which have an important
infl
u
ence on the distribut
ion of shear stress at the
interface. Figure (4) shows the dispe
r
sion of the
maximum normalized value of (multiplied by
) the
shear stress for diffe
r
ent examples determined by a
non

linear software as a function of
logarithmic scale. By using regre
s
sion analysis, the
best fit line was traced in order to d
e
termine the
relationship between shear force and shear stress.
5
.
1
5
.
0
int
)
.
.(
.
2
1
V
(10)
4
R
ELATIONSHIPS BETWEEN
LOAD AND
SHEAR STRESS
The theoretical study of the beam strengt
h
ened with a
FRP plate, allows thinking that the mechanical
behaviour (rigidity, resi
s
tance) depends strongly on the
interaction of the plate/concrete interface. The ultimate
capacity of the
beam can be determined by the
premature failure due to the debonding of the plate.
The failure criterion defined in this paper shows
rupture of the co
n
crete layer situated between the
reinforced steel and the FRP plate or by failure due to
debonding of end
plate at interface. Equ
a
tion
(
10
)
suggested in this study.
a
llows us to estimate the
di
s
tribution of the shear stress at the interface. To
determine the separation load, it is necessary to solve
this equation knowing the admissible interface stress
(
int
), and the relation b
e
tween the applied load and
the shear force. For example in the case of a beam
under four points bending (V=p/2) :
3
1
3
2
.
2
.
3
adm
sep
p
(11)
The admissible shear stress, in this equ
a
tion, is
given by the minimum of Eq
ualation
s
(
5
)
and
(
9
)
according to the premature failure criteria. In the case
of beams reinforced by thick plates, this separation
load (
sep
p
) corresponds to the ultimate capacity of the
beam (Varastehpour et
al. 1997).
5 RESULT AND VALIDATION OF THE
MODEL
The present theory has been validated by comparing the
predicted moment

curvature relatio
n
ships and the
ultimate capacity with experimental results. A series of
six recta
n
gular RC beams strengthened with a
FRP
Debonding failure mechanism in RC beam strengthening with CFRP
Energy and Hydro Technology/
Vol:1
/2008/No.1
4
0,00
0,02
0,04
0,06
0,08
0
20
40
60
80
P0 (The.)
P1 (The.)
P1 (Exp.)
Couvature (1/m)
Moment (KN.m)
P/2
P/2
600 mm
2000 mm
2300 mm
150mm
250
2 14
6@80mm
0
50
100
150
200
250
P1
P2
P3
P4
Test specimens
Ultimate capacity (KN)
Theoret ical capacit y wit hout int erface effect (software)
Theoret ical capacit y wit h interface effect (soft ware)
Equat ion 11
plate were tested up to failure (Varastehpour et al.
1996a). A
n
unidire
c
tional FRP plate of 2.5 mm
thickness was used during the tests. It is constituted of
HR carbon fiber su
b
merged in an epoxy resin. The
CFRP plate has a tensile strength of 1380
pa
M
and an
average elastic modulus of 117
pa
G
. The theoretical and
experimental results of the beams are compared in
figure
(
5
)
.
The theoretical study was led with mea
s
ured
mechanical properties by a nonlinear software. T
he
result shows that the moment

curvature relationships
can be approached with a satisfying precision by the
theor
i
tical model.
Figure5.Relationships between moment and curvature
.
In the
f
igure
(
6
)
, we compare the ultimate capacity
of the beams
with theor
i
tical va
l
ues. The failure was
obtained by a plate separation due to the concrete cover
rupture. The ultimate capacity obtained by the sof
t
ware
without interface effect is 238
kN
. The theoretical
result realizing the bond

slip and premature fail
ure
mode is 210
k
N. U
l
timate capacity using the equation
11 is 177.5
k
N.
Figure 6.
Theoretical ultimate
capacity of beam
.
To obtain the theoretical results in the
Eq
ualation
s
(
11
)
the following
parameters were used:
mm
b
b
p
150
mm
h
250
mm
T
p
5
.
2
mm
a
700
Mpa
E
p
117000
Mpa
E
c
30000
33
.
4
/
c
p
E
E
mm
Y
p
64
.
164
4
6
4
.
114
mm
E
I
t
t
p
p
I
T
Y
/
)
.
.
(
6
64
.
15
E
p
p
E
T
h
a
E
.
.
.
26
.
1
7
.
0
5
31
.
6
The admissible shear stress obtained by the
minimum of
Eq
ualation
s
(
5
)
or
(
9
)
. In this case the
admissible shear stress is equal to
adm
=2 N/mm2 and
obtained by
Eq
ualation
s
(
9
)
with the following
param
e
ters:
Mpa
f
t
2
.
4
mm
S
l
c
80
mm
d
28
mm
b
b
p
150
6 CONCL
U
S
ION
The theor
i
tical study of the beam strengt
h
ened with a
FRP plate, allows thinking that the mechanical behavior
(rigidity, resi
s
tance) depends strongly on the interaction
of the plate/concrete interface. The u
ltimate capa
c
ity of
the beam could be determined by the premature failure
due to the debonding of the plate.
Eq
ualation
s
(
10
)
is
suggested in this study. It a
l
lows us to estimate the
distribution of the shear stress at the i
n
terface. To
determine the separ
ation load, it is necessary to solve
this equation knowing the admissible inte
r
face stress
(
int
), and the relation between the a
p
plied load and the
shear force. For example in the case of a beam u
n
der
four points ben
d
ing (V=p/2), the
Eq
ualation
s
(
11
)
give
us the separation load. The admissible shear stress, in
this equation, is given by minimum of
Eq
ualation
s
5 and
9 according to the premature failure criteria. In the case
of beams reinforced by thick plates, this separ
a
tion load
(
sep
p
) corr
e
sponds to the ultimate capacity of the beam.
Figure
(
7
)
shown comparison of the ultimate load, result
of different experimental test and theoretical value when
we used cla
s
sical method (without debonding mode) or
Eq
ualation
s
(
11
)
.
These comparisons shown premature fai
l
ure mode due
debondig of external plate d
e
termine capacity of beams
strengthened with CFRP plate. Eqs11 helps us to o
b
tain
debonding load use for designing of these types of
concrete beams.
0
50
100
150
200
250
300
0
50
100
150
200
250
300
Theoretical load
(
KN
)
Equation
[
5
]
Experimantal load ( KN)
pexp
. (
s
1991
)
pexp
. (
p
1991
)
pexp
. (
P
1994
)
pexp
. (
R
1991
)
pexp
. (
V
1995
)
pexp
. (
Z
1994
)
pexp
. (
T
1992
)
pexp
. (
K
1992
)
0
50
100
150
200
250
300
0
50
100
150
200
250
300
Theoretical load (KN) Classical method
Pexp
.(
S
.
1991
)
Pexp
.(
P
.
1991
)
Pexp
.(
P
.
1994
)
Pexp
.(
R
.
1991
)
Pexp
.(
V
.
1995
)
Pexp
.(
Z
.
1994
)
Pexp
.(
T
.
1992
)
Pexp
.(
K
.
1992
)
Debonding failure mechani
sm in RC beam strengthening with CFRP
Energy and Hydro Technology/
Vol:1
/2008/No.1
Figure
7. Comparison between experimental and
theoretical r
e
sult.
7 RE
F
ERENCE

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RC beams strengthened with FRP plate., II: Anal
y
sis
and Parametric study", Journal of structural eng.,
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3455

ME
IER U., KAISER H. (1991)" Strengt
h
ening of
structures with CFRP laminates", Proceeding of the
ASCE Conference, ACM materials in civil
engineering stru
c
tures, P224

232

ROBERTS T.M. (1989)" Approximate anal
y
sis of
shear and normal stress concentrations
in the
adhesive layer of plated RC beams", The structural
engineer, Vo. 67, No. 12, P. 229

233

VARASTEHPOUR H., HAMELIN P.(1995)"
Structural Behavior of Reinforced Concrete Beams
Strengthened by Epoxy Bonded FRP Plate", Second
international symposium
on non

metallic (FRP)
Reinforcement of co
n
crete Structures, P. 559

567,
23 aoûT, Ghent, Belgium

VARASTEHPOUR H., HAMELIN P
(1997)"Strengthening of concrete beams using fiber
reinforced pla
s
tics", Journal of materials and
structures, Vol 30, No197, Lon
don, UK

VARASTEHPOUR H., HAMELIN P.(1996a)"
Experimental study of RC beams strengthened with
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m
posium on
composite material in bridges and structures, P. 555

563, 11 août , Montreal, CANADA

VARASTEHPOUR H., HAME
LIN P.(1996b)"
Analysis and study of failure mechanism of RC beam
strengthened with RP plate", Se
c
ond international
symposium on composite material in bridges and
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ZHANG S., RAOOF M., WOOD L.A. (1995)"
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Energy and Hydro Technology/
Vol:1
/2008/No.1
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