Bauhaus Summer School in Forecast Engineering: Global Climate change and the challenge for built environment
17-29 August 2014, Weimar, Germany
Modelling of circular concrete columns with CFRP sheets under
monotonic loads by ATENA-3D
ALRAYES, Omar
Institute of Structural Mechanics, Bauhaus-Universität Weimar, Germany.
KÄSEBERG, Stefen
Department of Civil Engineering and Architecture Leipzig, Germany.
Abstract
Over the last years, performance based design has become acceptable in abnormal events assessment
of structures. Therefore, using this design method, performance of existing and retrofitted
reinforcement concrete (RC) buildings can be evaluated using nonlinear analysis. In this case, the
performance of a fiber reinforced polymer (FRP)-retrofitted column is assessed under monitoring
loading and the result is compared with unstrengthened ones. The results are examined and compared
with models reported in literature such as Teng and Lam model ( Teng, et al., 2007). The reliability of
the model is assessed through comparison with experiment results that were done in Institut für
Betonbau (IFB), Leipzig in 2009. The comparison shows that within the practical range of the
confinement model variables, the ATENA analytical model is in very good agreement with the
empirically model (Vladimír, et al., 2012). This model is based on smeared crack method in order to
develop a nonlinear finite element method that describes the behavior of the plasticity and mechanical
damage of the material. Also,
The number of structures in the world continues to increase, as does their average age. The need for
increased maintenance is inevitable. Complete replacement is likely to become an increasing financial
burden and is certainly a waste of natural resources if upgrading is a viable alternative. Therefore,
maintenance, strengthening and monitoring of existing buildings have become more important. The
way in which FRP composite material as carbon fiber reinforced polymer (CFRP) can apply in
strengthening structures like buildings and bridges is illustrated in EUROCOMP Design Code
(December 2004) and ACI committee 440 (Technical committee document 440. 2R-02, 2002). The
predictions are confirmed as confinement efficiency depends on the strength of both concrete and
confinement, the shape of cross section, lateral ties hoop and fiber orientation.
1. Introduction
1.1. CFRP Confinement
The repair of deteriorated, damaged and substandard civil infrastructure has become one of the
important issues for civil engineers worldwide. The rehabilitation of existing structures is fast
growing; as a matter of fact, especially in developed countries, which completed most of their
infrastructure in the middle period of the last century. Furthermore, structures which were built after
World War II had little attention paid to durability issues
Numerous experiments since the 1980s have demonstrated the effectiveness of CFRP composites for
confining RC columns such as (De Lorenzis, et al., 2005). The increase of the load-carrying capacity
of columns being reinforced with Textile Reinforced Concrete (TRC) is partly achieved by the
additional concrete cover. But then it is also decisively caused by the confinement effect of the textile
reinforcement.
ALRAYES, Omar, KÄSEBERG, Stefen / FE 2014 2
An important application of fiber-reinforced polymer composites is to provide confinement to RC
columns to enhance their load-carrying capacity and ductility. This method of strengthening is based
on the well-known phenomenon that the axial compressive strength and ultimate axial compressive
strain of concrete can be significantly increased through lateral confinement.
Various methods have been used to achieve confinement to columns using CFRP composites. In situ
CFRP wrapping has been the most commonly used technique, in which unidirectional fiber sheets or
woven fabric sheets are impregnated with polymeric resins and wrapped around columns in a wet lay-
up process, with the main fibers orientated in the hoop direction. In addition, filament winding and
prefabricated CFRP jackets have also been used. The filament winding technique uses continuous
fiber strands instead of sheets/straps so that winding can be achieved automatically by means of a
computer-controlled winding machine. When prefabricated CFRP jackets are used, the jackets are
fabricated in half circles or half rectangles and circles with a slit or in continuous rolls, so that they can
be opened up and placed around columns.
Figure 1. Confining action of CFRP jacket under Axial Load
Regardless of the type of FRP jacket used, any vertical joint in the FRP jacket should include an
adequate overlap to ensure that failure of the joint will not precede failure of the jacket away from the
joint when subjected to hoop tension. In the strengthening of rectangular columns, the sharp corners of
the columns should be rounded to reduce the detrimental effect of the sharp corners on the tensile
strength of the FRP, and to enhance the effectiveness of confinement.
The confinement of concrete with FRP is based on a well-understood mechanism and denoted in
Figure 1. When the concrete is subject to axial compression, it expands laterally. This expansion is
resisted by the FRP jacket, which provides a confining pressure to the concrete. Eventual failure
occurs when the FRP jacket ruptures as a result of tensile stresses in the hoop direction. Concrete in a
circular jacket is uniformly confined, while concrete in a jacket of any other sectional shape is non-
uniformly confined. Most existing studies of FRP-confined concrete have been concerned with
uniformly confined concrete by testing FRP-confined circular concrete specimens (lam, et al., 2003b).
The FRP confinement action is passive. It arises as a result of the lateral expansion of the concrete
core under an axial load (LAM , et al., 2003). The confining reinforcement develops a tensile stress
balanced by pressures reacting against the concrete lateral expansion. FRP displays an elastic behavior
up to failure and therefore exerts a continuously increasing confining action. Failure normally results
by tensile rupture of the FRP. Hence, the confined concrete strength is closely related to the tensile
rupture strain of the FRP on the confined element. Experimental evidence shows that this failure strain
is usually lower than the ultimate strain obtained by standard tensile testing of the FRP sheet.
1.2. Proposed Model
Many researchers carry out a lot of embedded test and research work in confined concrete specimens.
They investigated the mechanical behavior of large number of experimental test, and discussed the
results by their models. Such as Lam and Teng model (LAM , et al., 2003), Richart model (Richart,
11
1 - 1
ALRAYES, Omar, KÄSEBERG, Stefen / FE 2014 3
1994), Samaan and Mirmiran model (Samaan, et al., 1998), Mander moel (Mander, et al., 1998), and
Teng and Lam model ( Teng, et al., 2007).
Lam and Teng model is built on results from a parametric study using an accurate analysis-oriented
stress-strain model for FRP-confined concrete. This model allow the effects of confinement stiffness
and the jacket strain capacity to be separately reflected and accounts for the effect of confinement
stiffness explicitly instead of having it reflected only through the confinement ratio. The test database
used in the model based on key features.
For ease of discussion, three basic ratios are first defined: the confinement ratio (
), the confinement
stiffness ratio ( ); with sufficiently confined concrete ( ) illustrated in figure 2 and equation
2 also, the strain ratio ( ). The mathematical expressions of these three ratios are as follows:
(
)
Figure 2. Schematic of stress strain model ( ( Teng, et al., 2007))
Where, is the confining pressure provided by the FRP jacket when it fails by rupture due to hoop
tensile stresses (i.e. the maximum confining pressure possible with the jacket), is the elastic
Axia
l S
tress
𝜎𝑐
Axial Strain
Unconfined
> 0.01
ALRAYES, Omar, KÄSEBERG, Stefen / FE 2014 4
modulus of FRP in the hoop direction, t is the thickness of the FRP jacket, is the hoop rupture
strain of the FRP jacket and D is the diameter of the confined concrete cylinder.
The confinement ratio is a commonly used parameter in the existing literature. The confinement
stiffness ratio represents the stiffness of the FRP jacket relative to that of the concrete core. The strain
ratio is a measure of the strain capacity of the FRP jacket. The confinement ratio is equal to the
product of the other two ratios. Based on Lam and Teng (2003) and on the interoperation of the test
results database, the following improved equation for the ultimate axial strain of FRP confined
concrete is proposed and showed in figure 2:
The compressive strength equation was refined on a combined experimental and analytical basis.
Parametric study was conducted using the refined version (Jiang and Teng 2007) of the analysis-
oriented stress-strain model for FRP-confined concrete. The equation (5) illustrates the axial stress
when it reaches ( ):
A careful examination of the present tests data showed that the second portion of all the experimental
axial stress-lateral strain curves intercepts the axial stress axis at a stress value which is very close to
the unconfined concrete strength when this portion is approximated by a best-fit straight line. The
slope of this straight line is (k), as proposed:
The new ultimate strain and compressive strength equations account for the effects of confinement
stiffness and jacket strain capacity separately and provide close predictions of test results. The
modified model of Lam and Teng’s model provide much closer predictions of test stress-strain curves
than the other models. And, it is suitable for direct use in practical design and for inclusion in design
cods/specifications. Also, this model is more compatible with current experiments data that are
compared.
1.3. Numerical Analysis
Finite element method (FEM) is a numerical technique to find approximate solutions for boundary
value problems, for partial differential equations and also for integral equations. These differential
equations are solved by either eliminating the differential equations completely or by rendering these
differential equations into ordinary differential equations which are then numerically integrated using
standard techniques. FEM is a good choice for solving partial differential equations over complex
domains.
The technique of FE Method is described by: discretizing the continuum, selecting interpolation
functions, finding and assembling the material properties to obtain the system equations, imposing the
boundary conditions, solving the system equations, and making additional computations if desired.
ALRAYES, Omar, KÄSEBERG, Stefen / FE 2014 5
In fact, the nonlinear fracture models based on the numerical approach are relatively more involved in
the computations as ATENA program. For this reason, probably, the fracture models based on the
modified linear elastic fracture mechanics may bridge the gap between the computational efficiency
and the model predictive capability of results; because, they are relatively more computationally
efficient, but have limited capacity to predict the fracture parameters.
FEM is well suited for superimposition of material models for the constituent parts of a composite
material. Advanced constitutive models implemented in the finite element system ATENA serve as
rational tools to explain the behaviour of connection between steel and concrete. Nonlinear simulation
using the models in ATENA can be efficiently used to support and extend experimental investigations
and to predict behaviour of structures and structural details. Several constitutive models covering these
effects are implemented in the computer code ATENA, which is a finite element package designed for
computer simulation of concrete structures. The graphical user interface in ATENA provides an
efficient and powerful environment for solving many anchoring problems. ATENA enables virtual
testing of structures using computers, which is the present trend in the research and development.
Because of material properties play an important role in modeling of structural elements, each material
inside the program is defined; concrete is represented by solid brick element, reinforcement by bar
elements and FRP by shell elements.
2. Materials and Methods
2.1. Experiment Data Base
The test database used in the present study (i.e., the present test database) has been reported for the
assessment of analysis oriented stress strain models. The study is divided the database of many tests
on concrete cylinders to four groups’ results. Table 1 illustrate the specimens’ geometry with (150
mm) diameter and (300 mm) height for all specimens and steel detailing for both unconfined and
confined groups. Also, figure 3 and figure 4 showed the cross section details, CFRP layer thickness
(T) and steel bars distributions. The mechanical priority of concrete material as concrete strength (i.e.,
the compressive strength) is with concrete class C35/37. All these tests were recently conducted
under standardized test conditions at HTWK University for applied science-Leipzig by the writers’
group.
Table 1. Specimen grouping and basic parameters
PC: Plain concrete, RC: Reinforcement concrete, CFRP: Carbon fibre reinforced polyethylene.
Also, the material properties for the concrete and steel that used in lab are inserted in table 2. Same specimens after the tests were retrofitted with FRP sheets in the damage area to restore their strengths. Four types of specimens were constructed with different detailing; two were unconfined and the other two confined. The monitoring load had been applied using Quasi-static testing technique. CFRP wrapping was used for retrofitting of damaged specimens with epoxy resin.
The test procedure that made in laboratory to get the test database is summarized as: the FRP jackets
were formed via the wet lay-up process and had hoop fibers only, for each batch of concrete, three
No. Group
Name
Specimen Group Specimen
Size (mm)
Longitudinal
Reinforcement
Stirrups CFRP
T. (mm)
1 Z0 Unconfined PC 300*150 ------ ------ ------
2 Z 6/10 Unconfined RC 300*150 6 T 8 T 6 /100mm ------
2 Z 6/5 Unconfined RC 300*150 6 T 8 T 6 /50mm ------
3 Z0 CFK Confined PC with CFRP 300*150 ------ ------ 2*0.11
4 Z 6/10CFK Confined RC with CFRP 300*150 6 T 8 T 6 /100mm 2*0.11
4 Z 6/5 CFK Confined RC with CFRP 300*150 6 T 8 T 6 /50mm 2*0.11
ALRAYES, Omar, KÄSEBERG, Stefen / FE 2014 6
plain concrete cylinders were tested as control specimens to determine the average values of the
unconfined concrete strength and the corresponding axial strain .
Figure 3. Reinforcement detailing and cross section details of unconfined specimen
Figure 4. Reinforcement detailing and cross section details of confined specimen
Table 2. Material Properties
Strength classes of normal concrete C: C35/37
Cylinder compressive strength
Initial elastic modulus 29 GPa
Poisson’s ratio = 0.2
Tensile Strength
Reinforcement bars
Compressive strength
Initial elastic modulus 200 GPa
ALRAYES, Omar, KÄSEBERG, Stefen / FE 2014 7
Also, for each specimen was tested in Figure 5, the behaviour of the load-displacement curve and
cracks pattern were controlled. Table 1, Figure 3 and Figure 4 show the cross section of cylinder
specimens included the longitudinal bars and stirrups that are used. Also, table 2 shows the material
properties that are used.
(a)
(b)
Figure 5. (a) CFRP Confined RC specimen (b) unconfined RC specimen; test loading are appeared.
Finally, the CFRP jackets hoop fibers with two layers of unidirectional, woven carbon fiber fabric for
confined specimens are used. The material property of this kind of carbon fiber (SikaWrap-200c)
shows in table 3.
Table 3. Carbon fiber material property
2.2. Numerical Method
The program ATENA offers a variety of material models for different materials and purposes. The
most important material models in ATENA for RC structure are damage model for concrete and
reinforcement based on smeared crack method. This advanced model considers all the important
aspects of real material behaviour in tension and compression as well the CFRP material modeling is
also considered.
This model which is determined for nonlinear finite element analysis of structures, used ATENA offer
tools specially designed for computer simulation of concrete and reinforced concrete structural
behavior. ATENA program system consists of a solution core and several user interfaces. The solution
core offers capabilities for variety of structural analysis tasks, such as: stress and failure analysis,
transport of heat and humidity, time dependent problems (creep, dynamics), and their interactions.
Technical Data
Fiber type High strength carbon fibers
Fiber orientation 0° (unidirectional)
Areal weight 200 g/m2 ± 5 %
Fiber Density 1.80 g/cm3
Fabric design thickness 0.11 mm (based on total carbon content
Tensile strength of fibers 3´900 N/mm2 (nominal)
Tensile E-Modulus of fibers 230´000 N/mm2 (nominal)
Construction Warp: Carbon fibers (98 % of total areal weight)
Weft: Thermoplastic heat-set fibers (2 % of total areal weight)
Fabric length/roll Fabric width 300/600 mm
Shelf life 2 years from date of production
ALRAYES, Omar, KÄSEBERG, Stefen / FE 2014 8
Solution core offers a wide range of 2D and 3D continuum models, libraries of finite elements,
material models and solution methods. User interfaces are specialized on certain functions and thus
one user interface need not necessarily provide access to all features of ATENA solution core. This
limitation is made on order to maintain a transparent and user friendly user environment in all specific
applications of ATENA.
ATENA 3D program is designed for 3D nonlinear analysis of solids with special tools for reinforced
concrete structures. However, structures from other materials, such as soils, metals etc. can be treated
as well. The program has three main functions; pre-processing, run and post-processing. The pre-
processing step includes input of geometrical objects (concrete, reinforcement, interfaces, etc.),
loading and boundary conditions, meshing and solution parameters. Also, the analysis procedure
makes possible a real time monitoring of results during calculations, and the last step, post-processing,
it accesses to a wide range of graphical and numerical results.
2.3. FEM Modeling of cylinder specimens in ATENA
Element geometric modeling of concrete has been done using 3D solid brick element with 8 up to 20
nodes in ATENA. The 3D solid brick elements having three degree of freedom at each node:
translations in the nodal x, y and z directions. This is an isoperimetric element integrated by Gauss
integration at integration points. This element is capable of plastic deformation, cracking in three
orthogonal directions, and crushing. The most important aspect of this element is the treatment of non-
linear material properties.
Reinforcement modeling could be discrete or smeared. In our work, a discrete modeling of
reinforcement has been done. The reinforcement has been modeled using bar elements in ATENA.
Reinforcement steel is a 3D bar element, which has three degrees of freedom at each node; translations
in the nodal x, y and z direction. Bar element is a uniaxial tension-compression element. The stress is
assumed to be uniform over the entire element. Also plasticity, creep, swelling, large deflection, and
stress-stiffening capabilities are included in the element.
The FRP modeling can be done as a 3D shell element in ATENA. The Ahmad shell element
implemented in ATENA, is described in ATENA theory manual. The present Ahmad element belongs
to group of shell element formulation that is based on 3D elements concept. It can be used to model
thin as well as thick shell or plate structures.
There are many methods to model the fiber material. A better option is to model the CFs as discrete
bars at/near the concrete surface (Vladimír, et al., 2012). About 2 bars per element (with the area
corresponding to the total CF cross section area per the concrete element width) should be enough.
However, it is not possible to capture debonding/delamination with this modeling. Another
recommended option is to use shell elements to model the wraps. Then, the user can model the
interface between the concrete and the wrap using contact elements.
The method, in this research, of how carbon fiber wraps strengthening in ATENA model is built on
the linear relation between the elastic modulus of the CFRP material and the thickness of the CFRP
layer. In fact, the thickness of CFRP layer is modeled as (10 mm) with elastic modulus (5060 MPa),
but in real the thickness of the CFRP layer is (2*0.11 mm) with elastic modulus (230000 MPa), the
material proprieties of the CFRP material is shown in Table 4.
Table 4. CFRP Material Properties modeling
Material Type (ATENA) 3D Elastic Isotropic
Elastic modulus E 5060 MPa
Poisson’s ratio ν 0.3 -
Material Type (Lab) 3D Elastic Isotropic
Elastic modulus E 230000 MPa
Poisson’s ratio ν 0.3 -
ALRAYES, Omar, KÄSEBERG, Stefen / FE 2014 9
The steel plates and the resin material properties of the models are considered. The function of the
steel plate in the ATENA is for support and for loading. The property of steel plate is the same as the
reinforcement bar yield strength. And for resin material perfect connection material is proposed as
epoxy material properties that used in lab tests.
3. Results and Discussion
In pre-processing window the model is built and the processing steps are performed by create the
geometry of FE model as shown in Figure 6. Then the material properties are assigned to the various
elements of each cylinder specimens. After that, the structural element boundaries are come, various
supports, loadings, FRP and monitoring points are defined in Figure 6. Also, the finite element
meshing parameters are given and meshing of the model is generated accordingly. Various analysis
steps are defined. The FE non-linear analysis is done in Run window.
The FE non-linear static analysis calculates the effects of steady loading conditions on a structure. A
static analysis can, however, include steady inertia loads (such as gravity and rotational velocity), and
time-varying loads that can be approximated as static equivalent. Static analysis is used to determine
the displacements, stresses, strains, and forces in structures or components by loads.
When the FE nonlinear static analysis is completed the, the results are shown in third part of the
ATENA i.e. Post processing. The stress- strain values at every step, crack pattern and cracks
propagation at every step shown help in to analyse the behaviour of the elements at every step of load
deflection.
(a) (b) (c)
Figure 6. (a) FE mesh of unconfined specimen; (b) Monitoring points of specimens; (c) FE mesh of confined
specimen
3.1.Unconfined Plain Concrete Columns
Load deflection curve for unconfined specimen has been plotted in Figure 7. It can be observed from
Figure 7 that the structure behaved linearly elastic up to the value of load around100 kN at 0.1 mm. At
this point the minor cracks started to get generated at the specimen. After this point there is a slight
curvature in the plot and load started increasing with the deflection increments. When the load reached
to the value of 521 kN, the graph depicted non-linearity in its behavior and the maximum load taken
by cylindrical specimen is 690 kN at deflection of 0.9 mm. Subsequently, deflection started increasing
without any significant increment in load; it has reached to the value of 0.7 mm with the load value
around 600 KN. As the analysis continued, the load carrying capacity decreased progressively.
Further, the load has been found to be 220 kN at the deflection of 2 mm.
ALRAYES, Omar, KÄSEBERG, Stefen / FE 2014 10
Figure 7. Load-Displacement curves of unconfined plain concrete cylinders
Results of analytical modeling are compared with Experimental Results of Unconfined plain concrete
specimen, the results vary but the behavior remains almost same. The analytical results vary due to
actual experimental conditions and conditions of fixed end. The modeling parameters are constant for
the analytical specimen but for actual specimen some parameters are different. The same model for
concrete has been modeled but the actual behavior may not resemble exactly the same. Considerable
increase in strength of around 12% was shown by experimental modeling. In figure 7, there are four
developments of fracture zones. At the first zone, the initial stiffness in ATENA model is not the same
as in lab data because of the boundary conditions (supports, loads, symmetry planes, etc.), the E-
modulus, and reinforcement ratio differences. At the second zone, the main difference is in the peak
point position. In fact, the main reason of gap between lab results and analytical data is meshing size
of the element. At the third and fourth zones, the cracking and material yielding are different because
of the material definition at ATENA program database. Also, neglecting shrinkage effect of relaxation
concrete material affects the behaviour of stress-strain curve under monitoring loading. The same
discussion for unconfined reinforcement concrete specimens with different ties spacing is proposed.
3.2. CFRP Confined Reinforced Concrete Columns
The load and deflection for a confined specimen has been depicted through Figure 8. It can be
observed from this plot that the load-deformation behavior is the same as for unconfined specimen.
The structure behaved linearly elastic up to the value of load around 228 kN at 0.15 mm. At this point
the minor cracks started to get generated at the confined specimen. After this point there is a slight
curvature in the plot and load started increasing with the deflection increments. When the load reached
to the value of 858 kN, the graph depicted non-linearity in its behavior with deflection of 1 mm.
Subsequently deflection started increasing without any significant increment in load; it has reached to
the value of 3 mm with the load value of 1170 kN. The maximum value of load has been observed to
be 1540 kN at deflection of 4.78 mm.
In Figure 8, at the first zone, the initial stiffness in ATENA model is nearly the same as in lab data
because of the boundary conditions (supports, loads, symmetry planes, etc.), the E-modulus, and
reinforcement ratio differences. At the second zone, the behavior of ATENA curve is approximately
the same. At the third and fourth zones, the cracking and reinforcement yielding (and eventually, other
nonlinearities) developed. We see that the ATENA model at this zone not similar in lab curves and
this because of the material definition at ATENA program database. Finally, the same behavior of
0
100
200
300
400
500
600
700
800
900
0.0 0.5 1.0 1.5 2.0 2.5
ATENA
LAB-S1
LAB-S2
LAB-S3
Displacement [mm]
Co
mp
ress
ive
axia
l L
oad
[k
N]
ALRAYES, Omar, KÄSEBERG, Stefen / FE 2014 11
ATENA curve can be predicted if the first elastic zone is shifted. Also, some differences will be made
because of relatively common source of differences is neglecting shrinkage effect. The same
discussion for unconfined reinforcement concrete specimens with different ties spacing is proposed.
Figure 8. Load-Displacement curves of confined Reinforcement concrete cylinders with stirrups spacing
S1= 10 cm
3.3.Extension to the behaviour of concrete under fatigue loading
Because of the traditional approach that used to describe damaged caused by static load is not
applicable for fatigue loading so it is thus necessary to modify the traditional formulation of these
models (Alliche, 2004). To describe fatigue degradation of concrete material, the concept of damage
mechanics is denoted as (Papa, 1993) model. This model is based on strain damage theory and
assumed that degradation of material is mainly due to nucleation and growth of the micro cracks.
Some numerical simulation was created by (Alliche, 2004) and show that strain can be divided into
three stages of degradation with different percentage under fatigue load. In experimental fatigue
behaviour for concrete material the increasing of damage is described as extension of pre-existing
cracks until the stable state is reached and it will be the first stage. Then the second stage start with
nucleation of new cracks and creep. Finally, the instable crack propagation leading to failure as third
stage. Also, during fatigue test the indication of damage occurring in the material is the decrease of the
Young modulus. In order to check the validity of previous model and parameters, experimental results
are proposed from (Kim, et al., 1996) on concrete specimens subjected to compressive fatigue loading.
Some indications of fatigue results obtained from (Alliche, 2004) study is denoted in table 5. The
experimental evolution of axial strain showed in figure 9 and compared with damage analytical model
of (Alliche, 2004) model. The model based on damage theory described the material degradation
under fatigue loading and uses tensorial damage (Dragon, et al., 2000) parameters in conjunction with
fatigue damage evolution.
Table 5. Fatigue results
Compressive
Strength (Mpa)
Young’s
Modulus
(Mpa)
Maximum
Stress
(Mpa)
Fatigue
cycles
80 38000 63 4284
0
200
400
600
800
1000
1200
1400
1600
1800
0 1 2 3 4 5 6
ATENA
LAB-S1
LAB-S2
LAB-S3
Displacement [mm]
Com
pre
ssiv
e ax
ial
Load
[kN
]
ALRAYES, Omar, KÄSEBERG, Stefen / FE 2014 12
The comparison which obtained showed also good agreement with experimental results and the
validity of the damage model under axial load. Furthermore, several phenomenon observed in fatigue
test: the progressive stiffness decay during fatigue loading, three stages of strain during fatigue life and
accumulation of permanent strains under constant amplitude fatigue load.
Figure 9. Comparison between experimental and computed axial strain evolution for one fatigue test (Alliche,
2004)
These results will be used later in a new study related to the development of the model in case of
strengthening system with CFRP sheets under fatigue loading. The study will investigate the fatigue
performance of RC concrete material and fiber reinforced concrete. These authors developed some
damage models incorporating fiber reinforced concrete enhanced sensitivity of fatigue.
4. Conclusion
The four types of concrete cylinders before and after confined them by FRP jackets were tested to
study the fundamental stress–strain behavior of confined concrete. In this progress the test results and
analysis declared the behavior of CFRP concrete cylinders. Based on the results of this study, the
following conclusions can be drawn: significant increase in strength and ductility of concrete can be
achieved by CFRP composite jackets, the confinement modulus and the confinement strength of the
composite jacket have been identified as the two critical parameters in describing the system
confinement effectiveness. Also, the ultimate confined concrete which is determined by the rupture of
the composite jacket (rupture strain), is much lower than the rupture strain obtained from flat tensile
coupon samples which refined constitutive model of concrete confined by FRP. In addition to
validation model, the results of cyclic tests of compressive fatigue load for unconfined specimens
show the demand of applying such test to CFRP specimens in terms of extending fatigue service life.
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Number of cycles N
3
2.8
2.4
2.2
2
1.8
1.6
2.6
(10-3
)
Axia
l S
trai
n
Experiment
Analytical Alliche 2004
ALRAYES, Omar, KÄSEBERG, Stefen / FE 2014 13
Furthermore, this study is important because of the whole procedure is guided to economic view of the
lab experiments. The progress is summarized with prediction the post behavior of the confined
concrete circular columns with two layers of Carbon fiber polymer material by studying the most
parameters that affect the behavior of the composite material. Then create a finite element model with
ATENA program simulate the experimental one. This progress will save a lot of experiment material
and also save time in the future.
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