Seismic vulnerability assessment of CFRP strengthened RC structures

Seismic vulnerability of a Reinforced Concrete (RC) frame retrofitted with the Carbon Fibre Reinforced Polymer (CFRP) is analysed in this paper. An experimental programme was conducted to determine the way in which concrete strength is affected by CFRP. The improved properties were modelled for different levels of concrete strength using a finite element based software. Using the results obtained during analysis, seismic vulnerability curves were derived for the unstrengthened and strengthened frames. The curves show significant improvement in the performance of unstrengthened RC structure after retrofitting.


Introduction
The seismically deficient and non-engineered (not designed by a qualified Engineer) building stock in many countries including Pakistan has become an issue of great concern, as it was partially or completely damaged by the jolts of earthquake in recent past.In Pakistan, Kashmir earthquake (2005) and Balochistan earthquake (2008,2013) caused devastating damage to both property and lives and severely affected the socio-economic situation in these areas and in the country as a whole [1].Almost 10-15 % of the total building stock of Pakistan consists of reinforced concrete buildings [2] and most of them are non-engineered and designed to withstand gravity loads only [3].Prior to Kashmir earthquake (2005), local designers were unaware of the need for seismic detailing and, hence, many of the buildings were designed without considering seismic loads.Many of such buildings were severely damaged in Kashmir earthquake [3].Postearthquake damage analyses exposed many deficiencies in the construction and design that caused the damage.These deficiencies are mostly due to the unawareness of the need to conduct seismic design, and to the lack of skilled manpower.Some of deficiencies of this type are: soft storey mechanism, irregular plans and elevations, poor quality and low strength construction materials, provision of insufficient reinforcement in joints, weak column-strong beam, exposed rebars in structural members, anchorage and development length, insufficient lap splices, deficient or no seismic hooks, inadequate transverse reinforcement, etc. [1,4].Some of these deficiencies are shown in Figure 1.It is therefore essential to strengthen the existing deficient building stock by means of suitable retrofitting techniques, so that earthquake forces can properly be harnessed, and in order to prevent further loss of human lives and infrastructure.The retrofitting of structural members such as beams, columns, etc. has been conducted as a means to strengthen RC structures.Among all structural members, reinforced concrete (RC) columns are of critical importance for the performance and the safety of structures as they are mostly compression controlled members, and they carry the load of other members.The confinement of concrete is an efficient technique for increasing the load carrying capacity and/ or ductility of a column.It is precisely the lateral pressure that induces in concrete a tri-axial state of stress and, consequently, an increment of compressive strength and ultimate axial strain, [5].Strengthening of RC columns was first conducted by means of steel jackets grouted to the concrete core, but the use of Fibre Reinforced Polymer (FRP) jackets gained more importance from the beginning of the 1990s.The FRP confinement is accomplished by placing the fibres mainly transverse to the longitudinal axis of the column providing passive confinement, which is activated once the concrete core starts dilating as a result of Poisson's effect and internal cracking.The confinement of non-circular columns is widely accepted to be less efficient than the confinement of circular columns, since in the latter case, the wrapping provides circumferentially uniform confining pressure to the radial expansion of the concrete.In non-circular columns, the confinement is concentrated at the corners rather than across the entire perimeter [6].Extensive work in both the experimental and analytical areas has been conducted on both full scale RC frames and smallscale plain concrete specimens of circular and non-circular cross-sections confined with FRP and subjected to pure axial compressive loading [6][7][8][9][10].The effect of CFRP strengthening on hollow steel members has also been studied by Kabir et al. [11].Studies focusing on RC columns of both circular and non-circular cross-sections of considerable size (minimum dimension cross-section of about 300 mm [12]) have also been conducted [12][13][14][15][16][17]; however, these researches were focused on the effect of confinement on structural behaviour, while insignificant research has been done on Earthquake Risk Assessment (ERA).ERA is the first step required for earthquake risk mitigation.To carry out ERA, seismic hazard and vulnerability assessment are required.In Pakistan, insignificant work has been done on seismic vulnerability assessment of reinforced concrete (RC) buildings [3].In recent work on seismic vulnerability assessment in Pakistan as conducted by Ahmed Seismic vulnerability assessment of CFRP strengthened RC structures [3] and Muhammad [18], analytical fragility functions and socioeconomic loss functions were derived for a particular segment of building stock in Pakistan.The purpose of the seismic hazard and vulnerability assessment is to develop damage indicators of buildings for different levels of hazard, and to represent them with vulnerability curves.In different parts of the world the vulnerability of structures may differ considerably, which is due to the difference in available construction materials, different construction methods and practices.The seismic vulnerability assessment was conducted in this study on CFRP wrapped deficient RC structures.For that purpose, an experimental program was conducted, which involved testing of cylindrical concrete specimens.The specimens were wrapped with CFRP in single and double layers and then tested in compression.The test results were used for modelling and analysis in a finite element based software.Finally, vulnerability curves were generated for the un-strengthened and strengthened frames.

Experimental program
An experimental program was conducted to investigate behaviour of cylindrical concrete specimens confined by wrapping CFRP composites in different arrangements, under monotonic (axial) load.The materials, concrete and instrumentation details are presented in the following sections.

Fibre reinforced polymer composite
The Carbon Fibre Reinforced Polymer (CFRP) was used in this study as confining material, while epoxy resin was used to adhere it to the specimens.The CFRP was chosen on the basis of availability in the local market.The properties of CFRP, as provided by the supplier, are shown in Table 1.

Epoxy adhesive
The epoxy adhesive used in this research was also obtained from local market.The properties are shown in Table 2.The epoxy contained two mixtures named resin (A) and hardener (B).As per manufacturer's guidelines, the mix ratio was set to 4(A) to 1(B) by weight and cured for seven days at room temperature.

Concrete
Keeping in view the compressive strength typically used in Pakistan for low and medium rise structures, a normal strength concrete with compressive strength of 20 MPa was used throughout the program.No additive was added.The mix ratio of concrete was 1:2:4 (cement: sand: gravel) by weight to achieve the target strength.

Test specimen details
The total of 9 cylindrical specimens 150 mm in diameter and 300 mm in height were cast and tested in axial compression during the experimental work.The following designations were used for these specimens: controlled specimens were designated as C1, C2 and C3.For CFRP wrapped specimens, the letter W indicates wrapped specimen; it is followed by the number designating the number of layers, and by the second number denoting the sample number.For example, W-1-1 denotes the first wrapped specimen with one CFRP layer.Other specimens were: W-1-2, W-1-3, W-2-1, W-2-2, and W-2-3.

Instrumentation
All tests were performed using a 2000 kN capacity testing machine at the loading rate of 0.15 MPa/s.A data logger was used for data acquisition while an extensometer was fixed onto the specimens to measure axial strain.Figure 2 shows the test setup and specimens ready for testing with load cell and extensometer.

Test results
All confined specimens failed abruptly by rupture of FRP jackets.Figure 3.a and 3.b shows typical failure of FRP wrapped specimens.There was a good bond between the FRP wrap and concrete, as a thin layer of concrete was still attached to FRP sheet after failure.Due to sufficient overlap of FRP wraps, no failure was observed at this location.For all confined specimens, the failure was sudden and there were no warning signs.Moreover, specimens confined with the double layer of FRP failed explosively, and the specimens were fully disintegrated.

Axial stress-strain response
The average stress-strain curves for controlled, CFRP single (W-1) and double layered (W-2) confined specimens, obtained from the test results, are shown in Figure 4.The stress-strain behaviour shows a visible improvement of ductility and peak strength when CFRP wrapped specimens are used.The controlled specimens gave an average strength of 20.3 MPa with the peak strain of 0.0018, while the specimens with a single layer of CFRP gave an average strength of 43.1 MPa and the ultimate strain of 0.019.An increase in ultimate strain was also observed.When two layers of CFRP were used, there was a remarkable increase in both ultimate stress and strain to an average of 68 MPa and 0.021, respectively.

Comparison with existing stress-strain models
The existing stress-strain models, suggested by different researchers, had to be compared with the experimental stress-strain curves for the purpose of analytical modelling.Many researchers proposed stress-strain models for different confinement mechanisms.Some of them predicted the values that are quite close to experimental values, and are therefore widely used to predict the stress-strain values.Out of those models, the ones proposed by Saman [19], Mander [20] and Lam and Teng [6] were compared with experimental results.As will be discussed later in Section 3, the RC frame, which was used for modelling, had square columns, and the specimens used in the testing were circular in shape.The effective confinement reduces drastically due to shape effect [21], so the shape factor k s1 for strength modification and k s2 for strain modification was incorporated.
As the stress-strain model by Lam and Teng [6] provides a more accurate prediction, stress-strain curves for 3 and 4 Seismic vulnerability assessment of CFRP strengthened RC structures layers can also be predicted by changing the number of layers in the equations and, after converting them to an equivalent square, the predicted behaviour is obtained as shown in Figure 6.a, 6.b, 6.c and 6.d.

Modelling and analysis
A generic RC frame was selected for the analysis based on the existing building stock in Pakistan where about 10-15 % The length of FRP confinement was chosen from largest of plastic hinge lengths, 0.5D and 12.5 % of member length as suggested by [22].The plastic hinge length was taken as l p = 0.5h using guidelines as recommended by ATC-40 [23], where l p is plastic hinge length, and h is the overall section depth.Figure 7 shows the geometry of the selected frame with regions confined with CFRP, and Figure 8 shows reinforcement details of beam and column cross-sections.The modelling was conducted using the PERFORM 3D software [24].It is a finite element based analytical tool with graphical user interface, capable of assigning different material properties to the same structural members, while also allowing the use of the bar pullout effect during analysis.

Bar pullout effect
Different levels of confinement and other parameters influence the bond strength and hence the type of bond failure [25,26].
Harajli [27] proposed a relationship that is widely used for predicting bond strength improvement due to confinement, and also for the bar pullout failure.The model is shown in Figure 9.The monotonic envelope (pull-out failure) describes the stressslip behaviour of concrete confined with FRP.For well confined concrete, the bond stress slip relationship is given in Equation ( 1). ( where: u -bond stress s -slip Seismic vulnerability assessment of CFRP strengthened RC structures u 1 -the maximum stress that the bar can develop and is given by (MPa), s 1 = 0,15 c o , where c o -clear distance between the ribs of reinforcing bars and can be taken as 10 in the absence of bar data.s 2 = 0,35c o , s 3 = c o and u f = 0,35u 1 .
The pull-out failure curve was used to model the bond stress-slip relation of steel and concrete in regions where CFRP is used for confinement.

Modelling of beam and column Cross-sections
Beams and columns were modelled in Perform 3D [24] using the in-elastic fibre section.The cross-section of the beam was split into different number of fibres for both concrete and steel, with 6 fibres for concrete and 2 fibres for 4 bars at the top and bottom of the beam, as illustrated in Figure 10.The area and local axis were used to define the fibre sections.Modelling details of column cross-sections are shown in Figures 11  and 12.

Analysis
The non-linear static cyclic analysis was run for the reference and all retrofitted frames and their hysteresis loops were generated.From the hysteresis loops, backbone curves (plot of displacement and base shear) were produced for all frames, as shown in Figure 13, where "n" represents the number of layers of CFRP confinement.Hysteresis loops for all four cases clearly point to improvement in base shear when CFRP wrap is used in the areas near joints in RC columns.

Analytical seismic vulnerability assessment
The Results of analytical model in terms of backbone curves were used for development of the seismic vulnerability curve (PGA vs Damage Index) for different PGA levels for reference and strengthened frames.For this reason, a methodology for seismic vulnerability assessment as suggested by Kyriakides [28] was used.Kyriakides proposed a technique based on the Capacity Spectrum Method (CSM) by FEMA 440 [29].The CSM modification was done by Kyriakides who reversed the order to reach peak ground accelerations for a specific damage level.
The design spectrum of UBC-97 [30] is used in this research as it is also implemented by the local building code i.e.Building Code of Pakistan [31].As this design spectrum depends on different factors such as the type of soil, earthquake zone, and location of active fault line nearest to the site, the design spectrum preparation was done in accordance with UBC 97, and the soil type for the case structure was assumed to be SD, and the near source factor as being equal to one.
To apply CSM, the design spectrum was transformed into the SA-SD space known as Acceleration-displacement response spectrum ADRS (β 0 ).The back bone curves obtained after the analysis represented capacity of a Multi Degree of Freedom System.CSM requires this curve to be converted to the representative curve of an equivalent Single Degree of Freedom System.The capacity curve was idealized to an elastic perfectly plastic form, so as to establish ductility levels for every displacement.The non-linearity of the structure was incorporated by multiplying the acceleration ordinate with the reduction factor M to get MADRS (β eff , M).Each point on the capacity curve was taken to be a performance point and the corresponding hazard level, described in terms of PGA, was the required output for developing a vulnerability curve.The next step in developing the vulnerability curve was to quantify damage potential at an approximated structural response.Kyriakides [32] obtained the damage index (DI) for each performance point and suggested no damage state at DI=0 and total collapse at DI = 100.Kyriakides [32] further correlated the Damage Index (DI) with the Mean Damage Ratio (MDR) i.e. ratio of repair to replacement cost, and linearly correlated the DI with the MDR by assuming correlation coefficient to be equal to 1 (Equation 2).

Seismic vulnerability curves
By using the aforementioned procedure, seismic vulnerability curves were developed for the reference frame and four strengthened frames.The vulnerability curves for the frames are shown in Figure 14.Four different damage levels as suggested by HAZUS [33] are also marked on the curves showing Slight Damage (SD) ranging from 0-40 % MDR, Moderate Damage (MD) ranging from 40-70 % MDR, Extensive Damage (ED) ranging from 70-100 % and Collapse at 100 % MDR.It can be seen in Figure 14 that 100 % damage is predicted for the reference frame at 0.42 PGA, and that the slope of vulnerability curve becomes very steep at 0.38 PGA, which shows that the structure exhibits brittle failure.This is due to brittle failure of joints due to slip in the main reinforcement in the reference frame.The initial slope of all frames is almost the same as the CFRP starts assuming stress after failure of concrete, and improvement due to confinement is effective thereafter.The structure with a single layer CFRP wrap showed improved behaviour and complete damage occurred at 0.52 PGA, though the slope was as steep as the reference frame with some improvement in the bond slip behaviour.The two layers CFRP strengthened frame showed further improvement both in complete damage PGA and in the slope of damage.The slope for this structure was gradual which means the damage was gradual due to further improvement in bond between the bar and concrete and more effective confinement provided by CFRP.The frames with three and four layers of CFRP showed further improvement at all damage levels with an overall increase in confinement effect, bar slip behaviour and frame ductility that led to ductile failure.The PGA at damage levels for all frames is shown in Table 3, and improvement percentage at 100 % damage for all frames is shown in Figure 15.

Figure 1 .
Figure 1.a) Improper beam column joint; b) Poor quality construction material; c) Exposed rebars near beam column joint

Figure 2 .
Figure 2. Specimen ready for testing with full set up 2.4.Experimental results

Figure 4 .
Figure 4. Axial Stress-strain Behaviour of unconfined and confined test specimens

Figure 5 .
a and 5.b show the comparison of these three models with experimental values of CFRP single layer and CFRP double layer results, respectively.The comparison clearly shows that the model proposed by Lam and Teng [6] closely predicts the stress-strain behaviour for both single layered and double layered CFRP wrapping.

Figure 5 .Figure 6 .
Figure 5.Comparison of experimental stress-strain curve with other models: a) Single wrap CFRP; b) Double wrap CFRP

Figure 8 .
Figure 8. Reinforcement details of beam and column cross-sections

Figure 14 .
Figure 14.Comparison of vulnerability curves for reference and strengthened frames at different damage levels