This paper presents a simplified modeling strategy for reproducing the behavior of beam-column structures reinforced with Polymer Reinforced Fibers (FRP). A 1D concrete constitutive model has been recently proposed, suitable for both monotonic and cycling loadings. The model is inspired on two well-known concrete laws, one based on damage mechanics theory (La Borderie concrete damage model) and one based on experimental studies (Eid & Paultre's confined concrete model). Spatial discretization is done using multifiber Timoshenko beam elements. Validation of the strategy is provided using two case studies: a retrofitted bridge pier and a vulnerability analysis on an existing building

B-TRUDEAU, M.

Desprez, C.

Kotronis, Panagiotis

Mazars, J.

English

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Submitted on 13 Nov 2019
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Seismic vulnerability reduction: numerical modeling of
FRP reinforcement using multifiber beams elements
C. Desprez, Panagiotis Kotronis, J. Mazars, M. B-Trudeau
To cite this version:
C. Desprez, Panagiotis Kotronis, J. Mazars, M. B-Trudeau. Seismic vulnerability reduction: numerical
modeling of FRP reinforcement using multifiber beams elements. Provence 2009: Seismic risk in
moderate seismicity area: from hazard to vulnerability, Jul 2009, Aix en Provence, France. ￿hal-
01008877￿
SEISMIC VULNERABILITY REDUCTION: 
NUMERICAL MODELING OF FRP REINFORCEMENT 
USING MULTIFIBER BEAMS ELEMENTS.
Cedric Desprez1, Saber El Arem1, Panagiotis Kotronis2 and Jacky Mazars1.
1  Laboratoire Sols Solides Structures et Risques (3S-R) UJF/INPG/CNRS UMR 5521
Domaine Universitaire BP 53 38041 Grenoble cedex 9, France.
Cedric.Desprez@hmg.inpg.fr, Jacky.Mazars@hmg.inpg.fr
2 Research Institute of Civil Engineering and Mechanics (GeM), UMR CNRS 6183
Ecole Centrale de Nantes, 1 rue de la Noë, BP 92101, 44321 Nantes Cedex 3, France.
Panagiotis.Kotronis@ec-nantes.fr
Abstract. This paper presents a simplified modeling strategy for reproducing the behavior of beam-
column structures reinforced with Polymer  Reinforced Fibers  (FRP). A  1D concrete  constitutive 
model has been recently proposed, suitable for both monotonic and cycling loadings [1]. The model 
is inspired on two well-known concrete laws, one based on damage mechanics theory (La Borderie 
concrete damage model) and one based on experimental studies (Eid & Paultre's confined concrete 
model). Spatial discretization is done using multifiber Timoshenko beam elements. Validation of the 
strategy is provided using two case studies: a retrofitted bridge pier and a vulnerability analysis on 
an existing building.
Keywords. FRP, seismic loading, vulnerability, concrete, damage mechanics, retrofitting.
Acknowledgement. The  authors  gratefully  acknowledge  the  support  of  the  Sherbrooke  civil 
engineering department and the French ANR ARVISE research project.
1 INTRODUCTION
Nowadays,  Reinforced  Polymer  Fibers  (FRP)  are  often  used  in  retrofitting  of  civil 
engineering structures. Their role is mainly to confine existing columns and to increase the 
bearing capacity of beams or walls through axial reinforcement. This paper deals with a 
simplified model to simulate the behavior of FRP confined columns and beams or walls. A 
uniaxial  (1D)  concrete  constitutive  model,  suitable  both  for  monotonic  and  cycling 
loadings, is presented. Two case studies are used for validation: a retrofitted bridge pier and 
a vulnerability analysis on an existing building. 
2 MODELING TOOLS
In order  to decrease the  number  of  degrees of  freedom and thus to simplify the  finite 
element  mesh,  Timoshenko  multifiber  beam elements  are  often  used  to  discretise  RC 
specimens [2]. This approach is also adopted for the calculations presented in this paper. 
1
Shear is considered linear, allowing thus using 1D constitutive laws. Regular concrete is 
modeled using La Borderie’s model [3]. Based on damage mechanics, it takes into account 
the opening and closing of cracks. In order to reproduce the behavior of confined concrete 
under monotonic loading, the predictive model of Eid & Paultre [4] is adopted. It is a global 
model  taking  into  account  internal  (due  to  Transverse  Shear  Reinforcement  TSR)  and 
external (due to FRP) confinement (Figure 1).  The cyclic behavior of steel is simulated 
using the classical Menegotto-Pinto model.
3 SIMULATING RC COLUMNS CONFINED WITH FRP
.3.1 RC columns confined with FRP: principle of modeling
In concrete columns, the main mechanical effect of the internal and external confinement is 
to reduce the development of lateral expansions that cause the most part of the damage. A 
simplified way to take this effect into account using a 1D damage mechanics law is to adapt 
the damage evolution law due to compression. The proposed strategy consists in adapting 
the damage evolution of the La Borderie model to fit  the evolution proposed in Eid & 
Paultre's model [1].
Figure 1 . Monotonic model for confined 
concrete available for different  confinement 
ratio (Eid & Paultre)
Figure 2 . Cyclic model for confined concrete 
(LMCC model)
.3.2 Case study: Bridge pier under axial and flexural load.
Experimental setting
A RC mockup, representative of an existing bridge (1/3 scale) with partial retrofitting, has 
been recently cyclic  tested at  the University of Sherbrooke.  The bridge pier  contains  3 
identical columns of 2.1m height and a transverse beam (Figure 3).  Only the two outer 
columns are retrofitted with FRP (the central column and the beam are not retrofitted). The 
axial load on each column varies from 10% to 20% of its estimated capacity in uniaxial 
compression during the cycles. The lateral imposed displacement is cyclic with increasing 
intensity. During the test, the force-displacement curve is measured (Figure 4).
2
Figure 3. Bridge pier mockup with partial 
retrofitting.
Figure 4. Numerical result Vs experimental 
data.
 Numerical modeling
Each column is modeled using Timoshenko multifiber beam elements. They are considered 
fixed at the bottom. The transverse beam is assumed elastic with a reduced section to take 
into account the initial  cracks in concrete. Each multifiber section contains 24 concrete 
fibers and 15 fibers representing the longitudinal steel bars. Material parameters are based 
on experimental  tests  [5]. The material  model used for the unconfined concrete (central 
column) is the La Borderie model; for the confined concrete (outer columns) the LMCC 
model and for the steel bars the Menegotto-Pinto model. In Figure 4, numerical results show 
relatively good agreement with the experimental data in terms of maximum values but also 
hysteretic cycles.
4 SEISMIC VULNERABILITY ANALYSIS OF AN EXISTING RC 
BUILDING:  SIMULATING  RC  ELEMENTS  AXIALLY 
RETROFFITED BY FRP
.4.1 Axial reinforcement with FRP: principle of modeling
FRP reinforcement, bonded on one side of a RC element (beam, wall…), has a function 
similar to the one of an external reinforcement bar (Figure 5). Using multifiber beams, one 
can  easily  numerically  reproduce  this  contribution  by  adding  a  specific  fiber  in  the 
multifiber beam section (Figure 6). The role of FRP is then simulated adopting a linear 
elastic brittle material law. Concrete and steel are again modeled again using La Borderie 
and Menegotto-Pinto models respectively.
3
Figure 5. Beam retrofitting with 
FRP bonding on lower side.
Figure 6. FRP addition in 
multifiber beam section 
Figure 7. Grenoble city hall
.4.2 Case study:  RC building
The proposed  method is used to simulate the nonlinear behavior of an existing structure 
(Figure  7)  before  and  after  retrofitting.  This  building  is  a  reinforced concrete  structure 
constructed in1966. Only the tall tower (witch is separated from the rest of the building) is 
considered (Figure 8).  The dimensions are,  43m long,  13m large,  and 50m height.  The 
structure is  composed of  four  very stiff  rectangular  elements  (containing the stairs and 
elevators), slabs, beams and columns. 
The building has been modelled using nonlinear multifiber beams for the vertical elements 
and linear shell elements for the horizontal slabs. The linear dynamic behavior of the model 
has been validated by in-situ ambient vibration records [6].
Figure 8. Model (no retrofitting): Damage 
due to traction (D1) in concrete.
Figure 9. Model (no retrofitting): Maximum drift ratio 
(a) steel strain (b).
4
4.2.1Vulnerability analysis (without retrofitting)
The first part of the study concerns the analysis of the seismic vulnerability of the structure 
before applying  the FRP retrofitting.  A synthetic  three-directional  signal  based on EC8 
design code is used for the dynamic nonlinear simulations. Figure 8 presents the results of 
the numerical analysis in terms of damage, drift ratio and steel strain. More specifically: 
The behavior of the structure is found mainly flexural without significant torsional effects. 
This  beam-type  behavior  allows  a  flexural  reinforcement  using  FRP.  Damage  due  to 
traction is concentrated on four large areas but no damage due to compression appears. The 
steel stress-strain evolution shows that plastic hinges are developed in the building. 
4.2.2Vulnerability analysis (with retrofitting)
The second part of the study considers the structure this time (numerically) retrofitted. More 
specifically, FRP is applied at the four principal  piers. The design of the FRP sheets is 
chosen such as to avoid the plastic behavior of steel bars. According to the results of the 
previous calculation (Figure 9), FRP is added on the first floor, at the base of the structure 
and on the five first floors of the upper part. After retrofitting, a classical nonlinear static 
analysis  (pushover) shows that the flexural  capacity increases (Figure 10).  Indeed, FRP 
sheets allow reducing the strain localization due to plastic behaviour of reinforced steel 
bars.  However,  modifications  on the structural  dynamic  response  are surprisingly.  FRP 
allows decreasing the steel strains but new localization patterns appears (e.g. above the last 
reinforced floor),  Figure 11.  Moreover, displacements and drift ratio values are slightly 
modified. One can clearly see the necessity of having numerical tools, as the one presented 
in this paper, in order to be able to proceed to nonlinear vulnerability studies. 
Figure 10. Pushover in the transverse direction: 
bearing capacity before and after retrofitting.
Figure 11. Model (with retrofitting): Maximum 
drift ratio (a) steel strain (b).
5
5 CONCLUSION
In this work, a simplified modeling strategy is presented in order to reproduce the nonlinear 
cyclic behavior of FRP RC structures. More specifically:
• Multifiber beam elements are used for the spatial discretization.
• A modification of the evolution law for the damage variable of the La Borderie
model is adopted [1]. The new evolution is based of the Eid & Paultre concrete
model. Validation is provided using the experimental results of a retrofitted bridge.
• Extra fibers are added on the multifiber beam element discretization to reproduce
the FRP axial reinforcement. A vulnerability analysis on an existing building is
performed to validate the approach.
The  modeling  strategy developed  in  this  paper  can  serve  as  a  simplified  tool  to  do 
comparative studies on the vulnerability of RC structures before and after FRP retrofitting.
Bibliographie
[1].  Desprez,  C,  et  al. 2009.  Retrofitting  reinforced  concrete  structures  with  FRP:  Numerical  
simulation  using  multifiber  beam  elements.  Rhodes,  Greece :  Proceedings  of  COMPDYN, 
ECCOMAS  Thematic  Conference  on  Computational  Methods  in  Structural  Dynamics  and 
Earthquake Engineering.
[2]. Mazars, J, et al. 2006. Using multifiber beams to account for shear and torsion : Applications  
to concrete structural elements.  52, , Computer  Methods in Applied Mechanics and Engineering, 
Vol. 195, pp. 7264-7281.
[3].  La  Borderie,  C. 1991.  Phénomènes  unilatéraux  dans  un  matériau  endommageable: 
Modélisation et application à l'analyse des structures en béton. Thèse de doctorat. Université Paris 
VI, Paris, France. 
[4].  Eid, R et Paultre, P.  2008 Analytical model for FRP-confined circular reinforced concrete  
columns. 2008, Journal of Composites for Construction, Vol. 12, pp. 541-552.
[5].  Roy,  N. 2006  Réhabilitation  parasismique  performantielle  des  ponts  avec  des  polymères  
renforcés de fibres de carbone; Thèse de doctorat. Université de Sherbrooke, Canada (Quebec).
[6]. Michel,  C, et al.  2009.  Full-scale dynamic response of an RC building under weak seismic  
motions using earthquake recordings, ambient vibrations and modeling, Earthquake Engineering & 
Structural Dynamics, http://dx.doi.org/10.1002/eqe.948 (Early View).
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