Debonding Failure of
CFRP Reinforced Concrete Beams and
In-Situ Monitoring Schemes
By
Ryan Sieber
Bachelor of Science, Civil and Environmental Engineering
Northeastern University, 2009
Submitted to the Department of Civil and Environmental Engineering
In Partial Fulfillment of the Requirements of the Degree of
.
.
Master of Engineering
In Civil and Environmental Engineering
At the
Massachusetts Institute of Technology
MASSAC HUSETTS
LI
INSTfTUTE
OFTECHNOLOGY
L 15 2010
LI BRARIES
June 2010
@ 2010 Ryan Sieber. All rights reserved.
ARCHIVES
The author hereby grants to MIT permission to reproduce and distribute publicly paper and
electronic copies of this thesis document in whole or in part in any medium now known or
hereafter created.
Signature of Author:
Ryan Sieber
Department of Civil and Environmental Engineering
May 10, 2010
Certified by:
Jerome J.Connor
Professor of Civil and Environmental Engineering
PJesis~iupervisor
Accepted by:
Daniele Veneziano
Chairman, Departmental Committee for Graduate Students
Debonding Failure of
CFRP Reinforced Concrete Beams and
In-Situ Monitoring Schemes
By
Ryan Sieber
Submitted to the Department of Civil and Environmental Engineering on May 10, 2010
In Partial Fulfillment of the Requirements for the Degree of
Master of Engineering
In Civil and Environmental Engineering
ABSTRACT
Fiber Reinforced Polymer (FRP) systems have gained much popularity as a method for reinforcing
existing concrete structures.
However a variety of sudden failure methods, such as debonding,
delamination, and creep rupture have led to the development of code limitations on the strength that
an FRP system can be considered to provide. The uncertainty brought on by the failure methods
mentioned above has become the topic of much research. Researchers have proposed fracture and
strength based methods to predict debonding. However, there are many environmental and durability
issues that have not been considered in these prediction. These uncertainties make FRP strengthened
concrete beams a good candidate for a health monitoring system. In this a paper a detailed look at
current methods of predicting debonding is presented. Additionally, effects that the environment and
durability have on debonding are presented. Finally, monitoring systems for FRP strengthened concrete
beams are discussed. Two monitoring schemes are proposed.
Thesis Supervisor: Jerome J.Connor
Title: Professor of Civil and Environmental Engineering
Acknowledgments
.
I would like to first acknowledge my parents, Deborah and Tony Sieber. Without their support I would
never have reached MIT and thus never had the opportunity to write this thesis. Their constant support
during this strenuous year was invaluable.
I would like to thank Professor Connor and Simon Laflamme for introducing to me a new way of looking
at structures. An introduction to motion based design has increased my knowledge of and appreciate
for how structures behave. I'm sure this will prove to be very valuable throughout my career.
Thanks to Chakrapan who helped me get through some stumbling blocks at the early stages of my
research. Your knowledge of FRP helped me to be able to continue to move forward on my research.
Thanks to Rebecca and Chris for allowing me to use them as a way to distract myself from my work.
Although sometimes it turned into procrastination, the distractions were necessary and much
appreciated.
Thanks to the 2010 MEng class. It has been a fun ride and I couldn't have asked for a better group of
people to spend this year with.
Table of Contents
1
Introduction ............................................................................................................................
2
M echanics of Debonding Failure .........................................................................................
Fracture M echanics Approach ......................................................................................................
2.1
Bond Slip Law ..............................................................................................................................
2.1.1
Global Energy Fracture M echanics ........................................................................................
2.1.2
Strength Approach...........................................................................................................................16
2.2
Interfacial Stress M odels.............................................................................................................16
2.2.1
2.2.2 Strength Based Equations for Design......................................................................................
2.3
Crack Band Method .........................................................................................................................
Durability & Debonding .........................................................................................................
3
Cyclic/Fatigue Loading ................................................................................................................
3.1.1
3.1.2 Sustained Load & Creep ..............................................................................................................
Freeze-Thaw................................................................................................................................24
3.1.3
3.1.4 High & Low Temperatures ......................................................................................................
Moisture & Salt ...........................................................................................................................
3.1.5
4
M onitoring of Debonding ......................................................................................................
Monitoring Instrum ents...................................................................................................................31
4.1
Fiber Bragg Grating.....................................................................................................................31
4.1.1
4.1.2 OTD R Sensors ..............................................................................................................................
4.1.3 Introduction to Distributed Systems ......................................................................................
Ideal M onitoring Schem e.................................................................................................................34
4.2
In-Situ M onitoring Scheme ..............................................................................................................
4.3
Accurate Bi-Linear M odel Available........................................................................................
4.3.1
4.3.2 Abstract Approach Without Bi-Linear M odel.........................................................................
Conclusions...........................................................................................................................40
5
References.......................................................................................................................................42
6
9
10
10
13
18
18
20
20
23
26
27
31
32
33
35
35
36
4
List of Figures
9
Figure 1: FRP Debonding Types [2].......................................................................................................
Figure 2: Interfacial Stresses Along Cracked Beam [3]............................................................................. 9
10
Figure 3: Bi-Linear Bond Slip Law [4]......................................................................................................
11
Figure 4: Bilinear Model vs. "Simplified" Model vs. "Precise" Model [2] ............................................
11
Figure 5: Schematic of FRP-Concrete Interface Showing the Cohesive Zone. .......................................
Figure 6: Theoretical Dual Crack M odel Analyzed [5]............................................................................ 12
Figure 7: Results from Num erical Analysis of M odel [5]........................................................................ 12
Figure 8: Theoretical Debonding Process Between Two Parallel Cracks [5]..........................................12
Figure 9: Load vs. Deflection Plot Showing Energy Dissipation Due to Debonding [6]..........................14
Figure 10: Simply Supported, Uniformly Loaded Beam and Corresponding Moment Diagram............15
16
Figure 11: Internal Forces in FRP Strengthened RC Beam [7]...............................................................
Figure 12: (a) Discrete Crack Model vs. (b) Crack Band Model [9]........................................................ 18
19
Figure 13: Crack Band FEM Model Predicted Damage vs. Experimental Damage [9] ...........................
Figure 14: Load vs. Displacement for Fatigue Loading Double Shear Test [12]....................................21
Figure 15: Strain Curve of Monotonically Loaded T-Beam Bridge Girder [13]......................................22
Figure 16: FRP and Rebar Strain vs. Cycle Number (a) Wet Lay-Up (b) Plate [10].................................23
Figure 17: Strain vs. Time for Four-Point Bending Sustained Load [16]............................................... 24
Figure 18: Summary of Reviewed Freeze-Thaw Experiments...............................................................25
25
Figure 19: Schem atic of Direct Shear Test [2] ........................................................................................
0
0
0
Figure 20: Load vs. Deflection (a) Room Temp. (b) +40 C (c) -30 C (d) -100 C [21]...........................27
28
Figure 21: Schem atic of Peeling (M ode 1) Test [22] ..............................................................................
28
Figure 22: Num erical M ode 1 Fracture Energy vs. ................................................................................
28
Figure 23: Cohesive Zone M odel for Varying IRRH [22] .......................................................................
Figure 24: Load vs. Deflection for Varying No. of Wet-Dry Cycles for Plate [23]...................................29
Figure 25: Load vs. Deflection for Varying No. of Wet-Dry Cycles for Sheet (Wet Lay-Up) [23]............30
32
Figure 26: Schem atic of FBG Sensor [27] ..............................................................................................
Figure 27: Schem atic for OTDR Crack Detection [28]............................................................................. 33
......... 33
Figure 28: Power Loss vs. Crack Width for Varying Crack to Fiber Angles [28]............
35
Figure 29: Basic Strain Gage Schem atic .................................................................................................
36
Figure 30: 3 Gage Monitoring Scheme for Known Slip Model ...............................................................
37
Figure 31: Schematic of Proposed Debonding Monitoring Scheme ......................................................
Figure 32: Example Plot of Concrete and FRP strain vs. Time...............................................................38
38
Figure 33: Example Plot of Concrete Strain vs. Time and A-Strain vs. Time ..........................................
1
Introduction
Fiber reinforced polymer (FRP) has drawn increasing interest from engineers as an acceptable method of
performing civil structure remediations and upgrades. A majority of the applications currently used are
for concrete structures. FRP can be used as containment for concrete columns or as shear and/or
flexural reinforcement for concrete beams. As for FRP as flexural reinforcement, it takes on a role
identical to that of reinforcing steel. The addition of FRP increases the available tensile capacity of the
cross-section which in turn leads to a larger and more efficiently used concrete compressive section.
The combination of these two leads to an increased flexural capacity. With the larger flexural capacity
and corresponding larger stresses, additional possible methods of failure are introduced to the beam.
The introduction of FRP increases the number of possible materials to fail from two (concrete and steel)
to four (concrete, steel, FRP, and the epoxy adhesive). Concrete beams are designed to perform in a
ductile manner, meaning the ductile material, steel, is designed to yield prior to concrete crushing, a
brittle failure. The possible failure modes for an FRP strengthened beam include [1]:
1. Crushing of the concrete in compression before yielding of the reinforcing steel
2. Yielding of the reinforcing steel in tension followed by rupture of the FRP laminate
3. Yielding of the steel in tension followed by concrete crushing
4. Shear/tension delamination of the concrete cover
5. Debonding of the FRP from the concrete substrate
Modes 1, 4, and 5 show no ductile behavior and thus fail in a brittle manner with little or no warning.
Failure mode 1 can be avoided with a high level of certainty by considering it during the initial design.
Similar to typical concrete design, where the amount of tensile reinforcement is limited in order to
ensure the yielding of the steel prior to the failure of the concrete, the amount of FRP used can be
controlled to ensure the compressive concrete does not reach a critical strain value, approximately
0.003 in/in, (in which is crushes) prior to another failure mode occurring. The concrete strain levels can
be easily calculated using strain compatibility. The other two brittle failure methods, FRP debonding
and delamination are less understood, more variable and therefore less predictable. Variability comes
due to various initial conditions such as cracks or exposure to different environments and corresponding
material degradation. The American Concrete Institute (ACI) handles this variability and uncertainty by
setting limits on certain stresses, strains, and by using reduction/safety factors. Equation 1 below is
from ACI 440 and is the general equation used for computing the moment capacity of a reinforced
concrete beam strengthened by FRP.
Equation 1
QMn
= 0 [Asfs (d
)+
A1ffe
()
4= overall strength reduction factor (0.65 + 0.9)
A= area of steel reinforcement
f= stress in steel reinforcement
d = dist. from extreme compression fiber to centroid of tension reinforcement
1= 0.85 for equivalent rectangular stress block
c = distance from extreme compression fiber to neutral axis
4f = FRP strength reduction factor (recommended 0.85)
Af = area of FRP reinforcement
ffe = effective stress in the FRP
h = overall thickness or height of member
The overall strength reduction factor, 4), is0.9 for typical reinforced concrete beams. The factor is
reduced as the FRP makes the failure less ductile and more brittle. Afactor of 0.65 represents a section
in which the reinforcing steel does not yield and thus has no ductility.
4
f is simply an uncertainty factor.
It represents the uncertainty of the data used to formulate the design equations for FRP and can expect
to increase as the level of confidence in research goes up.
Equation 2
ffe = EfEfe
Ef = tensile modulus of elasticity of FRP
Efe= effective strain level in FRP reinforcement attained at failure
Equation 3
Efe
=
(Ecuc
bi
Efd
Ecu = ultimate axial strain of unconfined concrete
df= effective depth of FRP reinforcement
Ebi = strain level in concrete substrate at time of FRP installation
Efd = effective debonding strain of externally bonded FRP reinforcement
(typ. range of 0.6efu - 0.9Efu)
ACI limits the strain allowed in the FRP using Equation 3. This limit ensures that the stress at the FRPconcrete interface does not get above an allowable limit. At this limit either the FRP-concrete interface
may get overstressed and begin to slip/fail (debonding) or the concrete will begin to crack under the
combination of shear and tension (delamination).
Efd
Equation 4
= 0. 08 3
Efg= design rupture strain of FRP reinforcement
Equation 5
Efu = CEEfu
exposure factor (ranges from 0.95 4 0.85 for carbon fiber FRP)
Eu = ultimate rupture starin of FRP reinforcement
CE = environmental
Equation 5 includes the final form of a reduction factor shown in the above equations. The
environmental exposure factor takes into consideration the degradation of the FRP and possible loss of
strength or functionality.
The reduction factors highlighted above are ACI's attempt to design for the uncertainties that are
associated with FRP flexural strengthening. This series of reduction factors has two effects on the use of
FRP. Firstly, for certain situations the design may end up being extremely conservative. Secondly, the
uncertainty that a list of reduction factors portrays may deter engineers from using FRP retrofits on
higher importance structural members. There are two possible solutions to cut back on the uncertainty
and thus the reduction factors. The most obvious one is continuing research. The Lf factor, a factor not
found in front of the steel portion of the flexural strength equation, is solely a function of uncertainty
within research data. Continuing research and growing confidence in data can lead to the elimination of
such a factor. The second option, which is addressed in this paper, is the use of health monitoring.
Proper health monitoring could be a reason to lower reduction factors. Limiting certain stress levels
during design would still be necessary, however monitoring would give some warning of possible system
failure and thus relieve some anxiety associated with FRP retrofits' brittle failures.
Health monitoring is a multi-step process that includes: i) a full understanding of the possible failure
modes, ii) preliminary detailed inspection of the concrete member to be strengthened, iii) a balance of
choosing the right combination of a monitoring scheme and analytical model to process the monitoring
data, and iv) follow up maintenance. This paper focuses on the understanding of an individual possible
failure mode, debonding and the implementation of monitoring schemes to recognize the initiation of
debonding.
2 Mechanics of Debonding Failure
Debonding failures are the failures of most concern to the effectiveness of an FRP strengthened beam.
As explained above, debonding failures are brittle and hard to predict. These failures encompass the
fourth and fifth failure modes presented by ACI, namely shear/tension delamination of the concrete
cover and debonding of the FRP from the concrete substrate. Debonding can be further categorized
into four failure modes; intermediate crack (IC)debonding, concrete cover separation, plate-end
interfacial debonding, and critical diagonal crack debonding [2]. See Figure 1for sketches of these
failure modes.
lxural-
Debonding
A ehondino
Intermediate Crack Debonding
Plate-End Interfacial Debonding
DeDebonding
Critical diagonal crack
Debonding
Concrete Cover Separation Debonding
Critical Diagonal Crack Debonding
Figure 1: FRP Debonding Types [2]
For all modes of debonding, the driver of the failure ishigh interfacial stresses. These stresses, normal
and shear, tend to be higher at concrete cracks and FRP plate ends which iswhere debonding initiates.
Figure 2 shows the increase of stresses at the bond interface at crack locations.
-
Stress Analysis
---
Section Analysis
-- - Actual Stresses
Figure 2: Interfacial Stresses Along Cracked Beam [3]
Two different approaches to understanding and analyzing debonding are often recognized. These
approaches are the strength based approach and the fracture based approach [3]. While the strength
based approach was generally researched first, it only predicts a debonding load/stress and does not
recognize the process in which debonding happens. The fracture based approach also works to find a
debonding load/stress, however it also focuses greatly on the steps prior, during and after debonding, in
particular crack propagation. Since the fracture based approach best considers debonding as a process,
it will be presented first.
2.1 Fracture Mechanics Approach
Debonding is essentially a crack propagation promoted by local stress intensities [3]. A failure method
involving crack propagation lends itself to be studied using a fracture mechanics based approach. The
bond-slip law and a global fracture energy approach will be reviewed below. The bond-slip law, while
being purely a fracture mechanics based law, is used in combination with a strength based approach to
analyze the propagation of debonding over time of increasing load. The global fracture energy approach
is a pure fracture mechanics approach which using global energy balance and dissipation to predict an
ultimate load at which debonding causes failure.
2.1.1
Bond Slip Law
Along with the desire of finding an ultimate stress/load/strain that will cause debonding, it is also
desired to understand and model the debonding process itself. Early simplified models considered the
bond failure to act in a linear elastic manner throughout the complete debonding process. However it
has been shown through experiments that failures actually act in a non-linear way [4] and a bi-linear
model more appropriately represents the failure of the concrete/FRP interface, see Figure 3 and Figure
4. The slip, 5, is the relatively displacement between the top of the FRP and the top of the cohesive
zone.
0 for 6<-Sf
Tf
--
1f for - Sf ! 6 < -1
(
:Gff
T =
<
r
for
Tf
-
61
f or S 1
0 for Sf
Figure 3: Bi-Linear Bond Slip Law [4]
5S < 51
S < 5f
6
--
-Bilinear
o
model
Simplified model
Precise model
,
5f
Figure 4: Bilinear Model vs. "Simplified" Model vs. "Precise" Model [2]
The bond-slip model isessentially acohesive zone model (CZM). The cohesive zone refers to the
"fracture processing area" [4]. The bi-linear model best represents ICdebonding, where the failure
most often takes place with-in the first few millimeters of the concrete layer, although occasionally in
the adhesive itself. It isin this zone of concrete in which the "fracture processing" occurs. Inthe case of
ICdebonding, the initial formation of the flexural or shear/flexural crack at the FRP-concrete interface
causes an initial interface slip and therefore a concentration of stresses at the crack edges [4]. This
concentration of stresses introduces/increases the local shear stress t. As the applied load increases,
fractures continue to happen at the interface which results in a relative slip between the FRP and
concrete. During this initial stage the FRP-concrete interface acts as a spring with the value Kb. As the
fracturing process continues the interface continues to act as a spring Kb until the shear force reaches
the critical value of Tf and the slips corresponding value of 61. Tf is not a property of the concrete or the
adhesive, it instead isa property of the two acting together as a cohesive zone, see Figure 5. This istrue
because there is microscopic interaction that occurs between the two layers that makes every different
combination of epoxy and concrete have a unique cohesive zone and corresponding unique value of Tf.
Concrete
one
Epoxy
FRP
Figure 5: Schematic of FRP-Concrete Interface Showing the Cohesive Zone.
This isan important fact because it means that an appropriate value of Tf has to be found by testing and
can't be derived solely on material properties. At this value of t the point of the interface located
closest to the crack enters a softening stage. The softening stage isrepresented by the negative sloping
line as 5 continues to grow. Additional load can be applied, however the softening stage will propagate
away from the crack and the point at the crack will eventually enter the debonding stage. At this point
in time the point closest to the crack has debonded and throughout the process released a quantity of
energy equal to Gf (total area under the curve), the fracture energy. Additional load can continue to be
applied as the softening and debonding regions continue to migrate across the interface. This istrue
until the full interface has no more elastic regions and consists only of softening and debonded regions.
Astudy done by Chen and Qiao [5] using the bi-linear bond slip law analyzed the debonding at two
intermediate cracks in a simply supported beam. Results from the study are shown in Figure 6,
Figure 7, and Figure 8 below and help illustrate the debonding process described above. Note the
reduction of the slope of load-slip curve as additional load isadded. This beam model has no steel
reinforcement, so the change in slope isnot a function of steel yielding, but rather solely afunction of
more of the bond entering the softening and/or debonding stage.
concrete
cracks
2
Z
Si
Lt
adhesive layer
FRP plate
L
5
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
LO
1
1.1 1.2 1.3
Bond slip at x-L (am)
Figure 7: Results from Numerical Analysis of Model [5]
Figure 6: Theoretical Dual Crack Model Analyzed [5]
T=TY
E
ES
(A)
(B)
(C)
(=F
(
EE
(D)
T
(E)
(F)
D=Debonded
S=Softenina State
E= ElasticState
Beam isnot symmetricallyloaded, thus debondinq propaaates from one crack and not from both
Figure 8: Theoretical Debonding Process Between Two Parallel Cracks [5]
Although this isa simplified model it does require asignificant amount of inputs. Inputs for this model
include standard properties such as geometry, material properties and loading (magnitude and
location), but also includes inputs concerning the dimensions of the cracks. The dimensions of the crack
are used to replace the remaining intact concrete with a rotational spring. This is used to accurately
model the affect the crack will have on the flexibility of the beam and thus the stress that get applied at
the interface. One interesting aspect of this is that the rotational spring, kr, used in this model is
calculated at the beginning of the modeling and not adjusted for the possibility of changing crack
dimensions. Overall the blond-slip law proves useful as a simplified model for the understanding of the
debonding process and the local stresses that occur during it.
2.1.2
Global Energy Fracture Mechanics
Another fracture mechanics approach to understanding and predicting debonding is a global energy
approach. A global energy approach looks at the balance of external energy acting on a structure and
stored "potential" energy within the structure. For an FRP strengthened beam or any structure, the
external energy comes in the form of loads, while the potential energy is stored as strains. The structure
is stable while these two energies are balanced. While the external energy can be limitlessly applied,
the total possible potential energy is limited by the structure's geometry and material properties. In the
case where the external loads exceed the possible potential energy the structure can still be in balance.
This is dependent on a structure's ability to dissipate energy, remove it from the system. Energy is
dissipated through materials failing or yielding. The structure as a whole will not fail until the difference
in external energy and potential energy exceeds the structure's ability to dissipate energy. Gunes et. al.
[6] studied the possibility of using this concept to predict debonding failure loads. As mentioned above,
a structure has a certain quantifiable ability to dissipate energy. In the case of FRP there are three areas
of possible energy dissipation; concrete cracking/crushing, steel yielding or pullout, and FRP debonding
[6]. Gunes et. al. approached the global energy technique by concentrating on the energy dissipation
during debonding, AID, represented in the equation below.
f
f
f
AD = Ydfl + adEPdf + Gf dAf > 0
Equation 6
JYdQ represents the bulk energy dissipation (mostly concrete cracking), fjEcdQ represents the plastic
energy dissipation due to steel reinforcement yielding, and JGfdAf represents the energy dissipation due
to interface fracture/debonding. According to Gunes et. al. most of the concrete cracking happens prior
to the debonding process, so the bulk energy dissipation is considered insignificant and dropped for
further calculations.
The model in this study is represented by a simply supported beam undergoing symmetrical four-point
bending. The simplified bi-linear load vs. deflection figures below, Figure 9, are used to represent the
beams response under load. The steeper portion represents the beam prior to steel yielding, while the
less steep portion represents the beam after the steel yields.
dV=fTd[2+fGdA,
d=f
..
stengthened
f2d
strengthened
beam
P
beam
0
oP2d
P
0
Td+fGdA,+ fa-de'dQ
..........----
-
-
-
-
-
-y
-
-
-
- - --........-
unstrengthened
------
-
beam
-
unstrengthened
beam
0
K2
KI
K2
/DKI
Beam deflection under load points, 5,
Beam deflection under load points,
9,
Figure 9: Load vs. Deflection Plot Showing Energy Dissipation Due to Debonding [6]
Gunes et. al. explains that AI is approximately equal and opposite to the change in potential energy
during debonding. A further assumption is made that the unloading "springs" Ki and K2 or equivalent to
the K, and K2 from the initial loading prior to yielding of the steel reinforcement. Given these
assumptions and the four-point loading scheme, the potential energy prior to debonding is PE2 and the
potential energy after debonding is PE1.
2
PE2 =
p2
PE1'2K,
f2d
2K 2
Equation 7
All)=PE 2 -PE,
d
Equation 8
Equation 9
Given these Equations 7-9, AID from Equation 9 can be set equal to Ao from Equation 6 to solve for a
failure load, P2- P2 is solved for by Gunes et. al. by making the following substitutions for the energy
dissipated by the steel and the energy dissipated by the FRP.
M) =
fa(dEPdfl+
fGfdAf
P2
2
22K2
P
2K1
Equation 10
This equation becomes extremely simple to solve under this loading scheme and under some additional
assumptions that are discussed below. The following substitutions can be made:
fadEdfl = fyEc-
c'
)Ac
Equation 11
f Gf dAf = Gfljbf
Equation 12
where c' and c are the depths of the compressive zone after and prior to debonding respectively and le is
the length of the "constant moment" area, the area between the two point loads. GfJI isthe mode 11
fracture energy of concrete and Ifand bf are the length and width of the FRP reinforcement.
The first major assumption made in Equation 11 isthat the steel yields prior to FRP debonding and
secondly that the curvature of the beam stays constant after FRP debonded. These assumptions can be
justified, however the Ieterm istroubling from design point of view. The thought behind the le term is
that under four-point bending the region between the point loads will have aconstant moment equal to
the maximum moment. This means that all of the steel in this section will yield at the same time and
thus all contribute to the energy dissipation. Atypical design load does not have a constant moment
region, this isonly achieved in symmetrical four-point bending. Anything other than a symmetrical fourpoint scheme will not have a constant moment region and thus according to this equation will have no
energy dissipation from the steel. Negating the dissipation due to steel yielding for a loading without a
constant moment region would be extremely conservative. Consider the uniformly loaded simply
supported beam and corresponding moment diagram in Figure 10.
Figure 10: Simply Supported, Uniformly Loaded Beam and Corresponding Moment Diagram
Assume that the uniform load, w, isthe load at which the steel reinforcement yields. If it holds true that
debonding occurs after steel yielding then that means that additional load will be applied prior to the
FRP debonding. Given the above moment diagram, one can see that the slope of the curve isminimal
around the maximum moment location at the center. This means that as w increases to w+ that the
span of steel yielding will increase as the other portions of the moment diagram reach the moment that
causes yielding. Thus there will be a significant length of steel that will yield prior to debonding, not the
length of zero that issuggested by Equation 11. It was not the authors' intention to suggest that no
energy dissipation would occur without a constant moment region, however looking at such a situation
complicates the energy dissipation process as not all of the steel enters ayielded state at the same time.
The major assumptions concerning the FRP energy dissipation are that the debonding occurs in the
concrete and that it acts in a mode 11,shear, failure mode. This isjustified by past experiments that have
resulted in debonding occurring in the concrete and that the debonding process quickly turns from
mixed mode to solely mode 11.
Although the theory of aglobal fracture mechanics approach isapplicable to the prediction of a
debonding load, it appears that many simplifications have to be made to create computational efficient
equations. Given complex modeling capabilities, a global energy approach should be able to predict a
debonding failure load.
2.2 Strength Approach
As mentioned earlier in the fracture mechanics section, debonding isessentially a propagation of cracks
caused by intense local stresses. The strength based approach essentially uses structural mechanics to
map the interfacial stresses. These stresses compare the materials ultimate strengths and an
approximate failure load can be found. Methods of finding detailed interfacial stresses as well as
empirical formulas for ultimate debonding strength are discussed below.
2.2.1
Interfacial Stress Models
Essentially there are two forces at the FRP-concrete interface, the normal force, a(x), and the shear
force, t(x). The differential beam element shown in Figure 11 shows these forces in addition to the
other internal forces that occur in a FRP strengthened concrete beam.
q
M(x)
N
)+ dM1(x)
M
~)
Nl(x)+dN,(x)
+
V,(x:
dVI(x)
t ti t t t t t t
st
Mi(x) V2(x)
t
t
tt
dx
t
i
t
M,(,) +dug()
VIx) +dVzfx)
Figure 11: Internal Forces in FRP Strengthened RC Beam [7]
The common assumption across all methods of finding interfacial stresses is that both the concrete
beam and the FRP act in a linear elastic manner [3,5,7]. The methods of analysis can then be
differentiated based on the additional assumption they make and approaches they take. The first major
dividing point in analyses iswhether or not constant stresses are assumed throughout the depth of the
adhesive. Realistically the adhesive has variant stresses through its depth and this is modeled in what
researchers called a high-order analysis [3,5]. A high-order analysis requires a very intensive model
which yields more accurate solutions. However, the only major increase in accuracy is only noticed at
the very end of the FRP reinforcement [5]. That being said, the majority of models assume invariant
stresses throughout the adhesive. Models that assume invariant stresses in the adhesive can further be
broken into to two groups based on their approach to find interfacial stresses. These two methods are
grossly broken into direct deformation compatibility approach and a staged analysis approach [7].
The direct deformation compatibility approach relates its interfacial stresses to the difference between
the displacement of the top of the FRP reinforcement and that of the bottom of the concrete beam.
Shear stresses are found by comparing the longitudinal displacements, while the normal stresses are
found comparing the vertical displacements [7]. Multiple models have been formed around this
approach and their differences come in the selection of which deformations to include in the
displacement values. For example two models are addressed in [7], one model includes shear
deformations of the beam while the other does not. Displacements that are considered in all the
models include those from bending in the concrete beam and those from axial forces in the FRP.
A staged approach uses multiple steps to get the interfacial stresses. An example of this found in [7],
uses the deformation compatibility approach to get initial shear stresses in stage one. In the second
stage a bending moment and shear force equal to those found in the first stage are applied to the FRP
layer. The FRP is then treated as a beam on an elastic foundation to get the normal stresses and
additional shear stresses. The stresses found in stage one are combined with stage two to get the final
interfacial stresses.
A large variety of these types of approaches exist and each one makes unique assumptions to try to
create a more accurate or simple model, ideally both. Whatever the approach taken, these models are
used in combination with fracture mechanic concepts to understand interface crack propagation. This is
seen in the example mentioned in the bond-slip law section. In that paper the beam and FRP
reinforcement are assumed to act linear elastically, however a bond-slip model is substituted in for the
otherwise assumed linear elastic interface. Additionally rotational springs are used to represent cracks
in order to more accurately model the beam stiffness and therefore the interface stresses. The addition
of rotational springs and the bond-slip law are just examples of building on the more simple models
mentioned above.
.. ...........
2.2.2
......
.....
-
.........
...
Strength Based Equations for Design
The methods above are useful for mapping interfacial stresses and being used in combination with
models such as the bi-linear slip model to understand the propagation of cracks, however in design the
main concern is not the path of cracks but preventing debonding from ever occurring. Prevention of
failure through initial design isthe goal of every government's code and engineer and thus researchers
have focused on finding the most accurate and simple methods of generally avoiding debonding failures.
Asummary of empirical design equations proposed by researchers was put together by Saxena et. al.
[8]. Different equations are proposed for the prevention of different debonding failures, intermediate
crack vs. plate end debonding. The variety of equations include producing limits on applied shear, V,
strain in the FRP, strain in the concrete, stress in the FRP, and some interaction equations which balance
the effects of shear and moment forces and their potential for causing debonding. The strain limitation
in these type of equations refer to the strains calculated using a linear stress-strain beam analysis, not
the local strains that may occur due to intensified forces at cracks. This makes sense for a design
approach in which the location of future cracks is not known. There isone stress limit approach
presented by [2] that limits local stresses in the FRP to prevent debonding.
2.3 Crack Band Method
So far no finite element modeling (FEM) approaches have been discussed, however FEM isa plausible
approach to predicting debonding failures. Two methods of FEM are discussed by Coronado and Lopez
[9], which include adiscrete crack approach and a crack band approach. The difference between these
methods is how the FRP-concrete interface ismodeled, see Figure 12.
1 1 1
"Cbeami
nd surface
FRP laminate
Interfacial
elements
(a)
P
RC beam
laminate
SFRP
CrackBand
(b)
Figure 12: (a) Discrete Crack Model vs. (b) Crack Band Model [9]
In the discrete crack approach the debonding failure ismodeled as a crack with zero thickness
propagating along the bond surface. The FRP istypical attached to the concrete by some sort of non-
... ..
........................................................................
....
. ....
....
ii
...
linear spring to represent the interface stiffness. This can be numerically efficient if the crack path can
be accurately assumed, however it has been found that during debonding failure that occurs within the
concrete that the crack path continuously changes direction [9]. This means that in order to obtain
accurate crack propagation modeling the model would have to continuously be re-meshed. In the case
of the crack band approach a certain thickness of FRP-concrete interface isdefined. It isassumed that
micro-cracking related to debonding will occur within the assigned crack band. Giving a depth to the
crack area allows for the crack to change direction while propagating. The crack band is defined by
giving it non-linear properties similar to the ones discussed in the bi-linear slip law. This does require
the input of an accurate bi-linear model, which requires preliminary testing to define the limiting values
associated with the bi-linear model. However, beyond the need for the bi-linear inputs the necessary
inputs for the model are relatively simple. Inputs consist of the basic material properties for each
element of the model (FRP, Concrete, and Epoxy), such as elastic moduli, limiting compressive stresses,
and tensile strains. The benefit of this model isthe accuracy to which it models crack propagation and
debonding load. The crack band model allows for cracking to follow the path of least resistance. The
accuracy of the failure path can be seen in Figure 13. What's most intriguing about this example isthe
transition the model makes from damage due to debonding to damage due to a shear crack. In a
discrete crack model this propagation upwards would not have been addressed. Overall the crack band
model isaformidable model for predicting debonding failure, however it does require preliminary
testing to get an accurate bi-linear model.
Load
Expermental damage
S1
FRP End
D
e
FRP End
Figure 13: Crack Band FEM Model Predicted Damage vs. Experimental Damage [9]
3 Durability & Debonding
Static loading is not the only possible cause of premature failure due to debonding. Other aspects such
as fatigue and environmental exposure can also affect the load carrying capacity of an FRP strengthened
concrete beam.
3.1.1
Cyclic/Fatigue Loading
One of the main reasons for the growing interest in FRP strengthening is the deteriorating infrastructure
that society relies heavily on for transportation. This is particularly true with bridges, many of which
have been labeled "structurally deficient". Furthermore a large portion of the bridges that make up the
transportation system are concrete girder bridges. One of the main reasons for the deterioration is the
cyclical nature of the loading that is applied to vehicular bridges. FRP has been proposed to help
reinforce these cyclically loaded structures, whether to help strengthen already fatigue damaged girders
or strengthened girders for increased fatigue loads, thus preventing fatigue damage from ever
occurring.
For normal reinforced concrete beams it has been well documented that its fatigue behavior is
controlled by the fatigue behavior of the reinforcing steel. In addition to the relatively high stresses in
the steel, concrete is known to soften under fatigue loading and thus the FRP stress is increased even
more [10]. This process leads to fracture of the steel reinforcement and thus the fatigue failure of the
beam. It is for this reason that it is typical in reinforced concrete design to maintain steel stress well
below the steels actual fatigue limit [10].
In theory, applying FRP to a fatigue damaged beam or any cyclically loaded reinforced concrete beam
helps relieve some stress from the reinforcing steel and thus increases the number of loading cycles
under the same load before failure. Additionally, applying FRP can increase the load capacity under
fatigue loading. Tests have found that given the same steel stress for an un-retrofitted beam and an FRP
strengthened beam (additional load is applied to the strengthened the beam to reach equivalent unretrofitted stresses) that the fatigue lives will be equivalent. This helps conclude the idea that steel
stress/fatigue is still the controlling factor in the fatigue failure of FRP strengthened beams. The
preceding information holds true assuming that there is no debonding failure at the FRP-concrete
interface. However it will be seen that debonding can have an effect on the fatigue capacity of an FRP
strengthened beam.
It has been found that the fatigue performance of FRP itself is a function of the matrix and not as much a
function of the fiber [10, 12]. That being said, in general FRP is considered to have very good fatigue
resistance. Additional studies have been done to study the effects cyclic loading has on the bond-slip
properties. Figure 14 shows the load vs. displacement for the double shear test performed by [12] to
study the bond-slip properties of fatigue loaded interfaces. Figure 14 shows plastic deformation upon
unloading after each cycle in addition to lowering stiffness with each cycle. The lowering stiffness
correlates with the softening stage of the bond-slip model. The interface fracture energy was also found
to reduce slightly.
5
25-
-.
....
-
10
15
5
0.0
0
10
..
-c
0.5
1
1.5
2
lsplbcOment(mm)
2.5
CAL
3
0
0.5
1
1.5
2
2.5
3
Dsplacement(mm)
Figure 14: Load vs. Displacement for Fatigue Loading Double Shear Test [12]
The reduction of fracture energy is small enough to be rather insignificant however debonding in
general can have a significant effect on the fatigue performance of beam. When debonding occurs the
stress that the FRP was helping to carry gets transferred back to the steel. This means that the beam is
essentially working as an un-strengthened member at this point and will take on the fatigue properties
of an un-strengthened beam. The strain relationship throughout the depth of the T-beam shown in
Figure 15 should remain relatively linear with the maximum strain located at the bottom of the beam,
the location of the FRP. However, it can be seen that from an early loading stage that the linear strain
curve is not true. The only explanation for this digression from linearity is slip between FRP and
concrete at the interface. It can be seen that the slip gradually gets worse as the difference between
distance 0 and 2 gets greater. Eventually the FRP is fully debonded and a huge jump in the strain at the
steel reinforcement is noticed. Since this is a fatigue load, lower than an ultimate load, the beam is not
at risk of failing under a single cycle, however the earlier the debonding occurs the more cycles are
applied to the steel at this higher stress level and the lower the fatigue life will be.
16
-400
T14
350
1200
k3p4ch
0
-10ki4
:10
e
~ ~-e
I as
-s
0
250
ip-imc
A
410
-2000
0
2000
4000
6000
U000
MicrostraIf (at MidspeaSeeden)
10000
12000
Figure 15: Strain Curve of Monotonically Loaded T-Beam Bridge Girder [13]
Additional insight into debonding of FRP under fatigue loading can be found in Figure 16. With the same
linear theory in mind as above, the slopes of these curves can be analyzed to recognize slip and the
onset of debonding. Under ideal conditions, no-slip and no softening of the concrete, the slopes of
these curves should be zero. Consider a more realistic situation where softening of the concrete does
occur however no slip, in this case the curvature of the beam should slightly increase over the time of
the cyclical loading. The increase in curvature should lead to an increase in slope of the strain curves for
both the rebar and the FRP, furthermore with the FRP slope increasing faster than the rebar's due to its
location further from the neutral axis. It isapparent that in the case of this experiment that this was not
true. What isseen in both cases instead isa larger increase in slope of the rebar and not the FRP. This is
an indication of slip at the interface. In the case of the wet lay-up, the results are more drastic with the
rebar strain level eventually exceeding the FRP strain levels, a clear sign of debonding. More drastic
results are to be expected in the wet lay-up since the small thickness of the FRP makes the strains
naturally close even under ideal conditions. In the case of the plate, the rebar strain never exceeds the
FRP strain however it can be seen the slope of the rebar starts to increase at a higher rate than the FRP
at around 103 cycles, a sign of slip. The sudden increase in rebar strain and decrease FRP strain at the
end of plot b isrepresentative of full debonding. Please note that although the gap between the FRP
and rebar strains isexpected to be larger for the plate due to its larger thickness, the y-axes, strain, are
not the same scale. Despite the onset of debonding in the Figure 15Figure 16, experiments have shown
improved fatigue behavior in FRP strengthened beams when compared to un-strengthened beams. As
mentioned earlier, the mode of failure between the two are still noted as being the same, however the
FRP lowers the stress levels in the rebar for the cycles prior to debonding and thus increases the fatigue
life of the steel and the entire beam.
4000
(a)
* 3500
rebar
3000-
2500
.2000;
-
CFRP
1500
-
1
10
10
-
10'
10'
10,
10'
10V 10'
10V
cycle number
1700
S(b)
. 1600
15001400-
1300 -
-_ _
-
_
rebar
1200
1100
1000-
1
10'
10
10V 10,
cycle number
Figure 16: FRP and Rebar Strain vs. Cycle Number (a)Wet Lay-Up (b) Plate [10]
3.1.2
Sustained Load &Creep
Another concern for concrete structures isthe softening or loss of stiffness in the compressive concrete
over time under a sustained service load. The loss of stiffness leads to an increase in deflection, a
serviceability issue, but not typically failure. However, it isof interest to understand the behavior of the
FRP during sustained loads. Carbon FRP (CFRP), the most popular FRP for structural use, isalso the FRP
with the best resistance to creep [1]. Creep-rupture tests have been performed on 0.25 inch diameter
FRP bars and it was found that a linear relationship exists between creep-rupture strength and the
logarithm of time [1]. It was found that after 50 years of sustained load that the ultimate strength of the
CFRP was reduced by approximately 10% [1]. Beyond the slight loss of strength in the FRP, the elastic
modulus isalso affected. It was proposed that the elastic modulus of the FRP at time "t" after the
application of the sustained load follows the equation below [14, 15]:
Efrpt =
where
Efrp
is the initial modulus and
frp
Efr
4
l+ Ofrp
Equation 13
is the creep coefficient for a specific composite laminate.
Ofrp = tm -
1
Equation 14
where m isa coefficient determined experimentally from the relationship between
Efrp,t and
t. Although
m seems difficult to get, the above equations show how the modulus will decrease over time. A
decreased modulus will have the same effect asoftening concrete has and help lead to increasing
deflections over time. Additionally this leads to increased strains in the FRP, however not additional
stresses because the reduced modulus allows for increased strains without increased stresses. Figure 17
shows the strains versus time for afour-point bending experiment. Uand Lare used to denote two
different beams. Note the negative strains for compressive concrete and positive strains for FRP and
tension portion of concrete section. It can be seen that over time the strains in the FRP get larger.
Intuitively when the beam deflects more the curvature gets larger and both the FRP strain and "Bottom"
strain should get larger, with the FRP stain growing at a faster rate. Although the "Bottom" is not
showing an increase in strain, the FRP isshowing an increase and one that isobviously larger than that
of the "Bottom". The above information leads to the conclusion that creep should not have a significant
effect on the ultimate strength of a beam, however the change in strain over time under the same load
isimportant to recognize when trying to differentiate between strains due to additional loads and
strains due to other reasons.
2000
-o
1o
.100
2000
.30 00--
-
- --
---
200
250
300
3
FRP-U
Bom-U --Top-U
Top-L
-0-Boom-L -FRP-L
- -- -- - - - - - - - - - - - . . .
-4000
.5000
Time (days)
Figure 17: Strain vs. Time for Four-Point Bending Sustained Load [16]
3.1.3
Freeze-Thaw
An initial review of literature concerning the effects of Freeze-Thaw on the bond strength of FRP
strengthened concrete beams revealed contradicting results. The first paper reviewed presented two
references to past experiments which concluded that freeze-thaw had negative effects on both the
ultimate load carrying capacity of beams, the bond shear strength, and the peak slip value (6f from
Figures 3 & 4) [17]. However the paper itself concluded after its experiment that there were no effects
of freeze-thaw cycles. This contradiction led to the review of a total of four experiments, summaries of
the experiments and conclusions from this review can be found below in Figure 18.
....
..
....
...........
# of
FreezeThaw Cycles
Paper
Type of Test
FRP Type
[10]
Direct Shear*
CFRP: Plate &
CFRP: Wet Lay-up
0, 100, 200
Direct Shear*
CFRP: Wet Lay-Up
0, 100, 300
[11]
Exposure to
AirExosr toairWater
Entramment
None
None Mentioned
Mentioned
Sprayed In
Middle of
None
onclusion
on FreezeThaw Effect
Insignificant
Reduced
Capacity
Thawing Process
I
[121
Direct Shear* &
4-Point Bending
[13]
4-Point Bending
CFRP: Wet Lay-Up
GFRP: Wet Lay-Up
0,50,
150,300
Thawed in Water
(15 "C)
6%
Insignificant
0,50,200
Thawed in Water
(15 *C)
6%
Insignificant
*Schematic of direct shear test found below in Figure 19
Figure 18: Summary of Reviewed Freeze-Thaw Experiments
P
~~J~b.fz
Figure 19: Schematic of Direct Shear Test [2]
Each experiment has highly specific and unique test setups and material properties, however the
conclusions on the effect of freeze-thaw cycles are drawn from the differences found in the summary
above. The first paper read, "[17]", concluded that freeze-thaw has an insignificant effect, while the
second paper read, "[18]", concluded that freeze-thaw has a significant effect on the bond properties. A
comparison of these two papers revealed that while "[17]" used ASTM C666 for freeze-thaw testing,
there was no mention of interaction with water during the thawing, while "[18]" mentioned the
spraying of water on test specimens during thawing. The main driver in deterioration of concrete under
freeze-thaw cycles isthe water inside the pores freezing, expanding and creating local stresses. This
made the absence of the mention of water in "[17]" significant. The third and fourth papers read were
"[19]" and "[20]". These experiments included soaking of the specimens in water during thawing,
however both concluded that freeze-thaw had insignificant effects on the bond properties. A
comparison of "[17]" with "[19]" and "[20]" found the only major difference to be the absence of airentrainment in "[17]". It is noted that if appropriate are entrainment is provided in concrete, freezethaw deterioration of concrete can essentially be eliminated [20]. The conclusion is made that airentrainment helps prevent micro-cracking from occurring in the concrete at the interface and thus
allows the full fracture energy of the interface to be used to resist applied loads rather than some of this
energy being used by fracturing during the freeze-thaw process.
Although air-entrainment appears to prevent reduction in bond strength due to freeze-thaw, it is still
useful to look at the effects freeze-thaw has on non-air-entrained samples. The lower bond strength can
be contributed to the fracture energy used up during the freeze-thaw process. The reduction in fracture
energy however does not result in a lowered value of critical shear, Tf, according to [17]. The reduction
in fracture energy comes from the lower 5i value and critical slip value (when debonding starts), 6 f. This
is consistent with a more brittle failure which is commented on in [17, 18, 19]. It was also found that the
decrease in fracture energy continued as the number of freeze-thaw cycles increased. However, not
enough data is available to generate an equation for the rate at which this available fracture energy
decreases with number of freeze-thaw cycles.
3.1.4
High & Low Temperatures
Freeze-thaw experiments typically perform the loading part of the experiment at room temperature. In
this case the specimens are being tested to see what damage the freeze-thaw process has on them. In
addition to the effects of freeze-thaw, extreme temperatures can play a role on the performance of an
FRP strengthened beam during loading. It is well documented that FRP and its adhesives tend to behave
in a more brittle manner at lower temperatures and tend to get softer at higher temperatures [21]. The
effects of extreme temperatures can be seen in the figure below from the experiment performed by
[21]. It can be seen from these results of a three-point bending test that the colder temperature
samples failed in a more brittle manner while the samples above room temperature failed in a more
ductile manner. It should also be noted that all the samples at high temperatures failed through the
epoxy, a manner of failure which is unconventional. This can be explained by the softening interface
due to the temperature and its inability to transfer high loads, thus never transferring loads into the
concrete high enough to damage the concrete. Conversely the samples in the extreme cold
environment all failed by debonding starting within concrete at the intermediate flexural crack and
transitioning into epoxy. This also is an unusual failure pattern. It can be explained by the interface's
ability to take high loads initially and thus damage the concrete, but then the slip gets too large and the
brittle property of the cold epoxy takes over and the failure proceeds into the epoxy.
14 - F, kN
12 -
14 - F, kN
12 -b
10 -
10-
*8
8
64
2
0
0.20 0.70 1.20
6, mm
1.70 2.20 2.70
,mm
1.70 2.20 2.70
14- F, kN
14 - F,kN
12-
12 -
10 -
...
-
6 4 2 0
0.20 0.70 1.20
C
d
10
8 6 4 -4
8 6-
2~ -,mm
I I
I
0
0.20 0.70 1.20 1.70 2.20 2.70
2
0
0
0.20 0.70
f
u,mm
1.20
1.70 2.20 2.70
Figure 20: Load vs. Deflection (a) Room Temp. (b) +40"C (c)-30'C (d) -100*C [21]
(--) for E=300 GPa
(-) for E=170 GPa
It can be seen from Figure 20 that extreme temperatures can have asignificant effect on the behavior of
FRP strengthened concrete beams.
3.1.5
Moisture & Salt
As mentioned earlier many applications of FRP strengthening are found in reinforced concrete bridge
girders. Inaddition to freeze-thaw and variant extreme temperatures these applications have to
withstand high levels of moisture and de-icing salts during winter months. The prevalence of this type
of application has led to many experiments on the effects of moisture and salt on the performance of
FRP retrofits.
As with most of the environmental effects mentioned above, experiments have been done on aglobal
level with bending tests and at a bond level with either shear or peeling tests. Peeling tests, see Figure
21, were done on CFRP-concrete bonded joints that were immersed in water for avarying amount of
time [22]. The objective of the test was to evaluate the effects of water on mode 1 fracture energy and
the cohesive zone model. Figure 22 shows the change in fracture energy for given water immersion
periods. The fracture energy was found by inputting the test data such as load and crack length into an
empirical formula presented in [22]. The loss of fracture energy isshown in amore specific manner in
Figure 23. This figure shows the variation of the cohesive zone model with interface region relative
humidity (IRRH) where Hd isdeterioration rate of the interfacial fracture energy, @isthe retention
coefficient, and ko isthe initial stiffness at the quasi-linear stage of the cohesive zone model and is
assumed to be unaffected by moisture [22]. Although all the specimens were immersed in water the
IRRH isa function of the diffusion rate of the water into the concrete and the time the samples are
immersed, thus the longer immersed specimens have a higher IRRH. It can be seen that the higher the
IRRH the lower the fracture energy as well as the critical stress and separation. It isimportant to stress
that this ismode 1fracture energy and as mentioned earlier, debonding failure tends to converge to
mode 2 failure, however it isexpected that comparable results would occur for mode 2 failure.
t meds
Side view
I load
sysan
191 mn
Figure 21: Schematic of Peeling (Mode 1) Test [22]
500
400
300
200
100
0
0
2
3
4
5
6
7
8
Water immersion time (weeks)
Figure 22: Numerical Mode 1 Fracture Energy vs.
Immersion Time [221
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Normal interfacial separation (mm)
Figure 23: Cohesive Zone Model for Varying IRRH [22]
Many experiments have been done on the effects of wet-dry cycles with the inclusion of de-icing
chemicals. As mentioned earlier, this ispopular because it represents the environmental conditions a
transportation structure might see over its lifetime. Three experiments were reviewed and all of them
recorded adecrease in load carrying capacity and ductility with the increase in the number of wet-dry
cycles in the de-icing chemicals [23, 24, 25]. It is noted that for a typical reinforced concrete beam the
damage due to de-icing chemicals comes in the form of steel reinforcement deterioration [23]. The
reinforcement deterioration was found to decrease in FRP strengthened beams compared to
unstrengthened ones [23]. This is believed to be a factor of the FRP acting as a line of protection against
the infiltration of the chemicals into the concrete. This creates a two-fold benefit to applying the FRP,
the strengthening of the cross-section as well as the barrier against steel corrosion. The FRP
strengthened beam however is still affected by the wet-dry cycles as can be seen in Figure 24 and Figure
25. In all of these cases besides the unstrengthened one, the method of failure was debonding. There
are two possible explanations for the increased deflections with the number of cycles, either the
deterioration of steel or that of the FRP-concrete interface. It was found that the steel reinforcement
lost a mass equal to 0, 1, and 1.33% of its mass under 100, 200, and 300 cycles respectively for the
beams strengthened with the FRP plate, while the change in the mass of the steel for the FRP sheet
strengthened beams was found to be so low that it was unreadable. Additionally, strain at failure in the
plate decreased from 1.057% at 0 cycles to 0.578% at 300 cycles (a45% decrease), while the strain at
failure in the sheet decreased from 0.917% at 0 cycles to 0.842% at 300 cycles (an 8% decrease). The
difference in loss of steel mass and change in failure strain is very interesting. Looking at the crosssections of the specimens it is clear that the plate exposes more of the concrete. Considering the
experiment above it would be expected that the plated samples would have a higher IRRH due to the
smaller amount concrete area covered by FRP, see Figure 24 and Figure 25. This leads to lower fracture
energy in addition to the above mentioned steel mass reduction. Both beams exhibit more brittle
failure and lower maximum loads with increase in the number of cycles, however the plated beam sees
a greater change. Note that both beams use transverse FRP for longitudinal FRP anchorage, not just the
"sheet" beams.
140
120100-10Cc.
1 80
r
.......
- --- 200 Cycles
--
20
0
10
20
30
40
50
Dlctiononne
300 Cycls
0
80
CFRP
PLATE
Figure 24: Load vs. Deflection for Varying No. of Wet-Dry Cycles for Plate [23]
140
-- 0 Cycles
------- 100Cyles
120
50
- -200Cycles
300 Cycles
-
N
-Lutmngiened
604
40
20
0
10
20
30
40
Deflectn (nw)
50
0
70
8
LONGITUDINAL
CFRP SHEET
TRANSVERSE
CFRP SHEETS
Figure 25: Load vs. Deflection for Varying No. of Wet-Dry Cycles for Sheet (Wet Lay-Up) [23]
4
Monitoring of Debonding
4.1 Monitoring Instruments
Chapters 2 and 3 have provided good insight into the behavior of FRP strengthened reinforced concrete
beams and their failure due to debonding. It is clear that these failure modes are predicted and
analyzed on the basis of strain and relative slip. Similarly the behaviors of structural members are often
monitored using strain based instruments. These instruments, strain gages, have historically been based
on electric resistance, however more recently fiber optic sensors have gained popularity as a method of
strain recording. The concept behind fiber optics as strain gages is relatively simple. The most simple
fiber optic strain gages work by having a light wave sent through one end of a fiber optic cable and
simply received on the other end. The difference in the light wave that is initially sent through the fiber
optic and the light wave that is received on the other end provides the necessary data that when used in
combination with analysis software and instruments can provide information such as strain,
temperature, and pressure. The difference in the light wave can be recognized by either a change in
wavelength or a change in power. The property analyzed is dependent on the type of fiber optic used
and the type of receiver. Fiber optic systems can get very complicated, using amplifiers to amplify
output wavelengths, complicated instruments called interferometers that manipulate the wavelengths
for accurate analysis and varying types of fiber optics themselves. Details on the workings of the fiber
optic sensors are beyond the scope of this paper, however a few examples of proposed monitoring
schemes will be summarized below to help provide a necessary introduction into the possible fiber optic
schemes. It is important to note that fiber optics systems can either be singular or distributed. A
singular sensor is simply what it says, one sensor on a fiber optic. A distributed scheme is a series of
sensors on the same strand of fiber optics. A distributed scheme requires complicated equipment that
is able to differentiate between the waves lengths coming from different sensors. Two singular schemes
are presented below as well as an introduction to distributed schemes.
4.1.1
Fiber Bragg Grating
One example of a fiber optic is the Fiber Bragg grating (FBG). The most simple form of fiber optics were
mentioned above, ones in which the light simply transmits through. FBGs however work on a reflection
basis. These optical fibers have a periodic variation in the refractive index in the core, see grey rings in
Figure 26 [26]. The Bragg grating acts as a light reflector with maximum reflection occurring for a
certain wavelength, AB the Bragg wavelength. AB is a function of neff and A, the effective index of
refraction and grating periodicity respectively, see Equation 15.
....
.......
.
AB
2
neffA
Equation 15
Strain and Temperature
Optical fiber
Incident Light
Reflected Light
Clad
g
Trnsmitted Light
Bragg Grating
o
o
Figure 26: Schematic of FBG Sensor [27]
The FBG has the ability to sense change in strain and temperature as is noted in Figure 26. Both a
change in strain and temperature lead to a change in AB, this changes the wavelength being reflected.
This change in reflection is picked up by the instrumentation and computer and then isconverted to a
change in temperature and change in strain according to Equation 16 [26]
=
AB
(1
-
pe)AE + (a + )AT
Equation 16
where AE isthe change in strain, AT isthe change in temperature, Pe isthe strain optic coefficient, a is
the thermal-expansion coefficient, and kisthe thermo-optic coefficient. AT can be removed from the
list variables easily by providing another instrument in the form of athermometer and thus AE can be
solved for. One of the most important drawbacks of the FBG sensor isits ineffectiveness in areas of high
strain contour. The concept beyond the FBG assumes that one wavelength will be reflected back and
analyzed, if there isa large strain gradient then there ispotential for multiple wavelengths to be sent
back and effectively make the sensor worthless. Most importantly, large stresses that occur at finite
locations such as at cracks, would not necessarily be recognized. That being said, the FBG sensor is best
used with a small gage length and thus provides strain values for afinite location.
4.1.2
OTDR Sensors
An optical time domain reflectometer (OTDR) isnot a type of fiber optic, but it isatype of optical
transmitter and receiver. The OTDR sends a pulse of light and then senses the reflected light. Certain
changes in the fiber will induce an increase in reflected light while others lead to a decrease in reflected
light. Abend in the fiber optic induces a decrease in the reflected light and thus a decrease in the power
received back at the OTDR. It was proposed to use this characteristic to measure crack width in
concrete structures, see Figure 27 & Figure 28 [28].
Crack width
Transmni sion light
.d d
Sensnfie
Figure 27: Schematic for OTDR Crack Detection [28]
L
12 - -- -
I
0
0.5
i- -
--
-
-
-
301
-
--
---45 -4
I- - - -
1
1.5
2
2.5
3
Crack width(mm)
Figure 28: Power Loss vs. Crack Width for Varying Crack to Fiber Angles [28]
By placing the optic sensor at an angle relative to the crack (in this plot angles are measured in reference
to horizontal) any growth in the crack will cause bending and thus a power loss. It can be seen that by
placing the fiber at a larger angle that more bending occurs and thus more power is lost. OTDR has the
capability of differentiating changes that occur at different location within the fiber optic, however the
disadvantage isthe OTDR isits inability to pick up the small power losses that may occur in FRP
debonding where strains are relatively small [28].
4.1.3
Introduction to Distributed Systems
The two examples above both have the disadvantage of only sensing/observing strains at a single
location along a beam. However it iscertainly desired to observe the strain at multiple locations along
the beam. With the examples above, multiple sensing locations would require multiple strings of
sensors, an expensive and most likely quiet cluttered approach. Distributed fiber optic sensors refer to
sensors that are distributed along the same fiber strand. As mentioned earlier, this requires aspecial
piece of equipment called an interferometer which differentiates the signals coming from each
individual sensor along the strand. Afurther introduction to distributed systems can be found in
[29,30,31,32].
4.2
Ideal Monitoring Scheme
In Chapter 2 the mechanics of debonding were investigated. From this understanding of the mechanics
of debonding it becomes clear what information would be useful for its monitoring. From the fracture
mechanics section it can be concluded that a relative slip value at the interface would be most useful
towards predicting debonding. We start with a simply supported beam being acting on solely by vertical
loads, see Figure 29. Theoretically the value of slip can be found using two strain gages, that is if the
depth of the neutral axis is known and a linear strain relationship is assumed. In this scheme one strain
gage is needed on the concrete at some position below the neutral axis, preferably near the bottom
face, but not within the interface slip zone. With a known location of a neutral axis and this strain gage
a beam curvature, <p can be found. With this curvature, theoretical values for the strain at the bottom
of the FRP and bottom of the concrete can be found, Efrp,1in.E and Ebot.conc. respectively. A measured strain
value isfound at the bottom of the FRP, Egage. Given this information and a relationship between the
theoretical relative displacement and the actual relative displacement, the difference between these
two relationships provides a value for slip, see Equation 17 and Figure 29. Assuming that preliminary
interface testing has been done, 61 and 5f (from the slip model) are known, measured slip values from
the monitoring at the interface can be compared to these two values and thus the onset of debonding
could be monitored.
6
= (Alfrp,lin.e
-
(Algage
Albot,conc.)
-
Albot,conc)
Equation 17
where:
Al,
10
= E*
10
= length of gages chosen (assume same lengths for all)
Efrp,lin,E = <p(di
+
dfrp)
Ebot,conc = <p(dtotai - c)
<p
=
e d,
5
EC'
1 & gage are measured values from monitoring
....
N
Z/0
Strain Gage
c
FRP
EPP
isreally at the same depth as Efrp,iin.E and isjust shown below for clarity
Note that Egage
Figure 29: Basic Strain Gage Schematic
In this scheme only two gages are used because the location of the neutral axis isassumed to be known,
however accurately knowing this value isdifficult. The location of the neutral axis isconstantly changing
as the applied loads and corresponding stresses and strains change. Two schemes are proposed below.
Both neglect the location of the neutral axis. As mentioned a few times before, 61 and 6f require testing
to obtain, additionally it has been discussed in Chapter 3that these values can be affected by
environmental exposure. For these reasons, once the two schemes proposed below takes an abstract
interpretive approach to monitoring debonding without knowledge of the critical slip values.
4.3 In-Situ Monitoring Scheme
4.3.1
Accurate Bi-Linear Model Available
With the assumption of aknown bi-linear model, ascheme similar to the one presented in the previous
section should work. However, as mentioned earlier this scheme will have to work without knowledge
of the location of the neutral axis. To solve this problem athree gage scheme is presented, see Figure
30. The concept of finding slip stays the same as earlier, however curvature is now found through the
relationship of two strain gages mounted on the side of the beam. Adjusted equations are found below
and can be substituted into Equation 17 to find a value for slip.
OEc,2 ~ Ec,1
~d2 - d1
Efrp,1in,e = <p(d 3)
+ -c,2
Ebot,conc = <(d3 - tfrp)
+ Ec,2
StrainGage
FRP
m
7
Figure 30: 3 Gage Monitoring Scheme for Known Slip Model
With the use of the equations presented above a variety of useful plots can be created. The plot of most
interest is obviously the slip vs. time plot. With this one plot and a known slip model, the slip process
can be monitored, thus potential debonding can recognize prior to actually occurring. Notice that
distributed sensors are drawn on the schematic. Part of designing the monitoring system would be
deciding the number of sensors, the spacing and their gage lengths. The ideal scheme would have an
infinite number of sensors spaced infinitesimally close and with infinitesimally small gage lengths. This
ideal situation would essentially give you a continuous strain field over the length of the beam, however
this is obviously impractical. The number of sensors can be limited for a number of reasons including
cost, the amount of power that would be necessary to overcome the slight losses at each sensor. As a
general note it is suggested to space the sensors more densely near the plate ends and the mid-span, as
well as at locations of any pre-existing cracks whether they are repaired or not. In addition to looking at
the slip value for individual sets of three sensors, it is suggested to compare the slip values of
neighboring sets of sensors. Ifthe sets show shallow sloping linearity amongst them then the slip is due
to regular, uniform interfacial stresses. Ifthe comparison of the sets proves one set to have much
higher slip values than its neighbors then this is a crack location. Close attention should be paid to these
sets of sensors in order to see ifthis high slip propagates. Finally, although it was stated that the bilinear model is known, factors such as the environment or non-perfect installation can cause anomalies
along the interface and thus the bi-linear model may not perfectly represent the whole interface. These
factors should be considered when choosing final slip values to compare the monitoring results to.
4.3.2
Abstract Approach Without Bi-Linear Model
It was deemed appropriate to consider monitoring without knowledge of the slip model. This
conclusion was made as an attempt to avoid the preliminary interface testing and the interface variation
factors mentioned above. The foundation for this proposed scheme was presented in the Cyclic/Fatigue
Loading section of Chapter 3. Inthis section a concept analyzing the slope of the Strain vs. No. of Cycles
curve was presented. It was understood that with cyclic loading came softening of the beam and thus
larger beam curvatures. Theoretically, larger curvatures should lead to an increase in both rebar strain
and FRP strain, with the FRP strain increasing more due to its further distance from the neutral axis.
When the pattern of strains deviated from this concept based on linear strains it was assumed that
slipping was occurring, furthermore when drastic deviation occurred that debonding had happened. It is
proposed to use a relative monitoring scheme comparing strain slopes over time to monitor slip
recognize when debonding may occur.
It isproposed to use a distributed fiber optic sensor system in which two fiber optic "rows" are placed
on the FRP strengthened beam. One row on the side the concrete beam, located as close to the bottom
of the beam without being placed in the predicted slip zone (the first few millimeters of concrete) as
possible. The second row will be placed on the underside of the FRP, see Figure 31.
Concrete
Strain Gage
FRP Strain
FRPage
Figure 31: Schematic of Proposed Debonding Monitoring Scheme
These sensors will record data at finite locations at finite time intervals. The main product of this data
will be a strain vs. time plot for each sensor which will be used to monitor the behavior of the beam.
Ideally the data from each set of corresponding FRP and concrete strain gages will be used to produce
two master plots. The first plot would consist of the strain vs. time data for each of the individual
sensors and would be used to monitor the trends of the strain over the lifetime of the structure, see
Figure 32. However these strains will vary sporadically with constantly changing loads. Amore useful
plot is a plot of the difference between the concrete strain value and the FRP strain value. Under
perfect bonding, no slip, an increase in concrete strain should correspond to a larger increase in FRP
strain. This means that if the strain in the concrete increases so should the difference between the
strain in the FRP and concrete, see Figure 33.
2000
-4--Concrete
Strain
-.
0
. FRP Strain
.
1000
0
0
5
10
15
20
Time
Figure 32: Example Plot of Concrete and FRP strain vs. Time
2000
-4-- Concrete Strain
-e--..
Difference Between FRP and Conc Strain
C
40
0
1000
0
5
10
15
20
Time
Figure 33: Example Plot of Concrete Strain vs. Time and
A-Strain vs. Time
Notice that the plot of the difference between the FRP strain and concrete strain follows a trend pattern
similar to that of the concrete strain plot. Upon slipping or debonding the strain in the FRP will start to
react less to changes in beam curvature. That being said a flattening of the "A-Strain" plot relative to
the concrete strain plot implies slipping. It is understood that this monitoring scheme is very
interpretive, however, in the absence of accurate slip models due to environmental effects interpretive
monitoring measures are most likely necessary. Additional data manipulation may be useful in the
interpretation of slipping. One possibility isto create a concrete strain vs. "A-strain" plot as large
amounts of data isreceived. Naturally similar concrete strain values will be recorded many times over
the lifetime of the structure and a plot such as this would help to recognize any loss in A-strain vs. a
given concrete strain over time and thus help recognize any softening or the interface.
5
Conclusions
Debonding failure in FRP strengthened concrete beams is an interesting failure which is complicated and
difficult to predict. Fracture based models have been used to understand the process and progression
of debonding, while strength based models have focused on deriving the local stresses at the interface
and predicting a failure load. Combinations of the two have been used to understand the process of
debonding by using local stresses derived from the strength method in combination with a bi-linear slip
model derived from the fracture approach. The local stresses derived correspond to a point of stress on
the bond-slip model and thus provide a value of slip. This can be used to understand when the interface
enters leaves the elastic stage and enters the softening stage on its way to complete debonding.
Additionally, many empirical formulas have been proposed to predict debonding loads. These empirical
formulas tend to be formulated using strength based models and limit the design strains and/or stresses
to prevent debonding from ever occurring. Additionally, the majority of these empirical formulas only
address the stresses and strains calculated based on linear stress and strain curves, which means they
fail to address local intensified stresses and strains that may form at cracks or plate ends. This makes an
accurate empirical formula useful for initial design, but of little help for monitoring where the local
stresses tend to be the driving force behind debonding.
The most convenient monitoring scheme would use an accurate bond-slip model and local strains
measured in the field. An accurate bond-slip model however is difficult to obtain. Bond-slip models
require physical testing because although mostly a function of the epoxy, the interface model is
additionally a function of the interaction between the epoxy and the concrete. Furthermore the
accuracy of a bond-slip model has been seen to be affected by the interface's environment and loading
over its life. Cyclic loading has been found to slightly reduce the fracture energy, freeze-thaw of non-airentrained concrete has been found to reduce both the 61 and 6 f values, and exposure to salt in
combination with moisture has been found to reduce both the critical shear and critical slip values for
the bond-slip model. With these findings it can be concluded that an accurate bi-linear model is difficult
to obtain for ever changing state of the structure over its full lifetime.
A monitoring scheme for a beam with a well understood interface (bond-slip model) would only require
two sets of strain gages, one on the side of the concrete and one on the bottom of the FRP. The strain
values measured would easily be able to be translated to relative slip values and thus compared to
critical slip values. This comparison would provide insight to whether or not debonding is occurring or
about to occur. A monitoring scheme neglecting the bond-slip model would be extremely useful due to
the difficulty in obtaining an accurate model. It has been proposed to compare the expected behavior
of the beam based on a linear strain model with the actual behavior of the beam. Under the linear
strain model increases/decreases in the FRP should occur at the same time as increases/decreases in the
concrete strain. However the increases/decreases in the FRP should be larger due to its location further
from the neutral axis in comparison with the concrete sensor. As the difference between
increases/decreases in strains becomes closer under similar loads it can be expected that the beam is no
longer acting in a linear manner. This lack of linearity leads to the conclusion that slippage is occurring.
A proposed scheme such as this one is obviously very theoretical and requires judgment rather than
providing an absolute answer. Additionally the jumps in strain over the life of the structure may be very
small, making it very difficult to accurately see any difference in the behavior of the beam concerning its
strain linearity. It is suggested that more advanced monitoring schemes be proposed, however
attention be paid to trends of the strains during testing, thus making a monitoring scheme without the
use of a bi-linear slip model more feasible.
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