Performance-based seismic retrofit of a bridge bent - CiteSeerX

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Performance-based seismic retrofit of a bridge bent: Design and experimental validation Nathalie Roy, Patrick Paultre, and Jean Proulx

Abstract: Changes in the 2005 edition of the National building code of Canada resulted in an increase in earthquake hazard for some regions in Canada. This project studied the impact of this increase on a selected highway bridge. A seismic retrofit scheme, using carbon-fiber-reinforced polymers (CFRPs), was developed and applied to the selected highway bridge bent. The retrofitting technique is based on specific performance criteria under which the retrofitted structure must meet prescribed ductility levels corresponding to selected seismic events, and its design includes a new confinement model for reinforced-concrete columns wrapped with CFRP. Using this performance-based approach, the amount of required composite materials to achieve the specified criteria was found to be much more economical when compared with the ductility requirements in the 2000 edition of the Canadian highway bridge design code. The performance of the retrofitting technique was evaluated by pseudo-dynamic tests carried out on a 1:3 scale model of one of the bridge bents. Using the substructuring approach, the remainder of the structure was modeled, and the bridge bent was subjected to increasing levels of seismic loading, corresponding to various limit states of the bridge. The measured response of the test specimen compared well with the predictions of a three-dimensional (3D) nonlinear finite-element model calibrated with dynamic properties obtained from on-site ambient vibration tests. During the highest intensity test corresponding to a return period of 2500 years for a region of high seismicity, the CFRP retrofit showed no sign of distress, and the strain values measured on the fibers were very low, indicating that the performance-based design procedure is conservative. Key words: highway bridge, reinforced concrete, seismic retrofit, performance objectives, damage criteria, fiber-reinforced polymer, large-scale test, pseudo-dynamic test, substructuring test, nonlinear modeling. Re´sume´ : Les changements apporte´s dans la dernie`re e´dition du Code National du Baˆtiment ont entraıˆne´ une augmentation de l’ale´a sismique conside´re´ pour plusieurs re´gions. Une me´thode de dimensionnement de re´habilitation sismique a` l’aide de polyme`res renforce´s de fibres de carbone (PRFC) a e´te´ optimise´e afin d’e´tudier l’impact de cette augmentation sur les appuis d’un pont d’e´tagement typique. La me´thode de re´habilitation est base´e sur des crite`res de performance spe´cifiant les niveaux de ductilite´s correspondant a` diffe´rents niveaux d’intensite´s sismiques. La me´thode inclut un nouveau mode`le de confinement des sections en be´ton arme´ a` l’aide de PFRC. La quantite´ de PRFC calcule´e a` l’aide de cette approche a` la performance est beaucoup plus e´conomique que la quantite´ qui serait requise afin de rencontrer le taux de confinement requis dans la zone de rotule plastique tel que prescrit dans le Code canadien de calcul des ponts routiers, 2000. La re´habilitation a` l’aide de PRFC a e´te´ valide´e par la re´alisation d’essais pseudo-dynamiques par sous-structures sur un mode`le a` e´chelle 1/3 du viaduc choisi. Selon l’approche par sous-structures, la superstructure a e´te´ mode´lise´e et un mode`le a` e´chelle 1/3 de l’appui du pont a e´te´ construit en laboratoire. L’ensemble a e´te´ soumis a` des niveaux croissants de chargement sismique, correspondant a` diffe´rents e´tats-limites du pont. La re´ponse mesure´e du spe´cimen a e´te´ compare´e aux pre´visions d’un mode`le 3D par e´le´ments finis non-line´aire lequel a e´te´ pre´alablement calibre´ avec les proprie´te´s dynamiques obtenues a` partir d’essais dynamiques sous vibrations ambiantes re´alise´s in situ. Pendant l’essai d’intensite´ sismique la plus e´leve´e correspondant a` une pe´riode de retour de 2500 ans pour la re´gion d’activite´ sismique e´leve´e, le PRFC n’a montre´ aucun signe d’endommagement et les valeurs de de´formations mesure´es sur les fibres e´taient tre`s basses, indiquant que la me´thode de re´habilitation des poteaux a` l’aide de PRFC propose´e est conservatrice. Mots-cle´s : viaduc, be´ton arme´, re´fection parasismique, objectifs de performance, crite`res d’endommagement, polyme`res renforce´s de fibres, essais a` grande e´chelle, essais pseudo-dynamiques, essais par sous-structures, mode´lisation non-line´aire.

Received 11 April 2008. Revision accepted 10 June 2009. Published on the NRC Research Press Web site at cjce.nrc.ca on XX XX) 2010. N. Roy, P. Paultre,1 and J. Proulx. Department of Civil Engineering, Universite´ de Sherbrooke, 2500, boul. de l’Universite´, Sherbrooke, QC J1K 2R1, Canada. Written discussion of this article is welcomed and will be received by the Editor until 30 June 2010. 1Corresponding

author (e-mail: [email protected]).

Can. J. Civ. Eng. 37: 1–13 (2010)

Introduction Transportation plays a key role in support of Canada’s economic activity and in the day-to-day lives of Canadians. Throughout Canada’s early development, measures were adopted to enhance transportation safety, accessibility, and economic efficiency (Transport Canada 2003). However, a large number of existing highway bridges in North America were built when standards of seismic design were at an early stage of development. Moreover, the earthquake hazard levels have been increased for some regions of Canada in the latest editions of the National building code of Canada

doi:10.1139/L09-138

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of reinforced concrete (RC) bridge columns for their load and corrosion resistance, light weight, and ease of installation. They were also selected to demonstrate their effectiveness in protecting the circular RC columns against the devastating effects of an earthquake by increasing their flexural ductility. In the last step, the bridge evaluation and rehabilitation methodologies were validated by performing pseudo-dynamic tests with substructuring on a 1:3 scale model of a typical highway bridge.

Evaluation of the seismic capacity Description of the bridge The bridge selected for this study is shown in Fig. 1. It is a multispan continuous concrete girder bridge supported by two three-column bents located near Trois-Rivie`res, Quebec. The structure was selected for its regular geometry and symmetrical properties. With these characteristics, the bridge is suitable for an evaluation of its seismic capacity using a unimodal nonlinear static analysis. Its symmetry is also used to simplify the finite element model of the bridge substructure used in the pseudo-dynamic tests.

Fig. 2. Performance-oriented test protocol matrix. Tr, return period.

(NBCC) (NRCC 2005). This underlines the need to develop reliable procedures for the evaluation of the structural capacity of our existing infrastructure, before and after an earthquake, and to evaluate effective techniques for retrofitting deficient bridges. This paper presents a performancebased approach to seismic retrofitting and its experimental validation using pseudo-dynamic tests. Retrofit design methodology with carbon-fiber reinforced polymers (CFRPs) The project presented herein integrates the newest approaches in seismic design. In a first step, an evaluation of the transverse seismic capacity of the bridge bents for a typical highway bridge was carried out using a performancebased approach. A design methodology for bridge rehabilitation using carbon-fiber-reinforced polymers (CFRPs) was then optimized. CFRPs were selected for the rehabilitation

Performance-based evaluation In the field of bridge engineering, the 1971 San Fernando earthquake constituted a turning point involving important modifications to the American standards. Since then, other earthquakes (e.g., Loma Prieta in 1989, Northridge in 1994, and Kobe in 1995) alerted owners, managers, and design engineers to the need to design and retrofit the structures according to performance objectives. In addition to safeguarding of human lives, these objectives should reduce damage and the inherent repair costs generated by more moderate earthquakes. The fundamental differences of the new seismic design approaches are related to (i) the use of performance objectives, and (ii) the definition of acceptable displacement criteria to meet the performance objectives. To show the evolution of the performance-based approach, a comparison was made between the performance objectives, performance criteria, and corresponding seismic hazard recommended in the ATC-6-2 Seismic retrofitting guidelines for highway bridges (Applied Technology Council 1983), the ATC-32 Improved seismic design criteria for California bridges: provisional recommendations (Applied Technology Council 1996), the MCEER/ATC-49 Recommended LFRD guidelines for the seismic design of highway bridges (Applied Technology Council and Multidisciplinary Center for Earthquake Engineering Research 2003), and the 2000 edition of the Canadian highway bridge design code (CHBDC) (CSA 2000). In the ATC-6-2 guidelines, the only objective is related to survival, defense, and safety. In the ATC-32 design criteria, MCEER/ATC-49 guidelines, and the CHBDC, the performance objectives consist of a service level known as ‘‘operational’’ or ‘‘functional,’’ guaranteeing the occupation or the immediate use of the structure after a seismic event having a high probability of exceedance, and of an ultimate level guaranteeing the safeguard of human life in the case of an earthquake of high severity with a low probability of exceedance. An intermediate objective, limiting the inherent damage and cost of repair due to earthquakes, is also considPublished by NRC Research Press

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Fig. 3. Mode shapes obtained from ambient vibration tests. fexp, experimental frequency; xexp, experimental damping ratio.

Fig. 4. Stiffness degradation. Modified Takeda hysteretic model (Takeda et al. 1970). M, bending moment; ku, unloading stiffness; k0, initial stiffness; q, rotation; qr, plastic rotation.

Fig. 5. Capacity and demand spectrum. Teq, equivalent period.

Fig. 6. Moment–curvature response of the confined and unconfined concrete sections.

ered in the 2000 edition of the CHBDC. In all guidelines, the actual design recommendations are based on a force reduction factor to meet qualitative criteria of performance. Quantitative criteria (i.e., displacements, curvature) and design rules related to those performance criteria are still needed. Seismic hazard The seismic risk considered in the various guidelines has evolved from a deterministic approach (maximum probable earthquake) to a probabilistic approach (with probability of exceedance). The design earthquake for the 2000 CHBDC has a period of recurrence of 475 years, and the actual peri-

ods of recurrence for a rare event vary from 1000 years (2000 edition of CHBDC) to 2500 years (MCEER/ATC-49). It is worth mentioning that, in the latest edition of the Published by NRC Research Press

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Fig. 7. Pseudo-dynamic testing with substructuring.

Fig. 8. Reinforcement details of the bridge bent model. f, bar diameter.

NBCC, the new uniform hazard spectrum (UHS) approach describes the site-specific frequency content of the expected ground motions by plotting, for each spectral period, the spectral amplitude at a specified probability of exceedance. New UHSs at 2% in 50 years (2500 year return period) have been developed by the Geological Survey of Canada for the NBCC 2005 (Adams and Halchuk 2003). The change from 10% to 2% in 50 years probability level (475 to 2500 year return period) was intended to achieve uniform reliability across the country. This change has a significant impact on moderate seismic activity regions like Eastern

Canada. Indeed, the rate at which ground motion amplitudes increase as probability decreases varies regionally and is more pronounced for the areas having moderate seismic activity (Adams and Atkinson 2003). The adoption by the Geological Survey of Canada of two distinct probabilistic models, namely the H (historical seismicity) model and the R (regional) model, for Eastern Canada also led to significant changes. For example, the R model implies that currently aseismic regions between adjacent seismicity clusters (e.g., the St. Lawrence Valley near Trois-Rivie`res, Que.) are susceptible to large earthquakes (Adams and Atkinson Published by NRC Research Press

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2003).The bridge considered in this study is therefore located in a moderate seismic activity region of the province of Quebec, where there is a great difference between the peak ground accelerations prescribed in the 1995 and 2005 editions of the NBCC (NRCC 1995, 2005). For this particular region, the peak ground acceleration (PGA) was 0.12g for a probability of exceedance of 10% in 50 years, as prescribed in the 1995 edition of the NBCC and in the 2000 CHBDC. For this same probability of exceedance (10% in 50 years), this value has been modified to 0.18g due to the adoption of the R model by the Geological Survey of Canada. For a probability of exceedance of 2% in 50 years, on a firm soil site, the PGA prescribed in the 2005 NBCC for the bridge location is 0.40g (Adams and Halchuk 2003). The 2000 CHBDC recommends that the earthquake level and procedure used for evaluating lifeline bridges shall be specified by the owner or those having jurisdiction. In this study, a performance-oriented test protocol was developed as shown in Fig. 2. The horizontal axis indicates the desired performance level in terms of damage. The vertical axis represents the seismic demand, where the lowest level is associated with a moderate seismic activity region (the actual bridge location) and a return period of 475 years (design earthquake) (CHBDC (CSA 2000)). The intermediate level of seismic demand corresponds to the same region, but with an increased return period of 2500 years (NRCC 2005). In the case of the bridge considered for this project, the increase in seismic hazard mentioned previously and the current CHBDC requirements indicated the need to retrofit. However, a refined seismic evaluation of the structure showed that the bridge bent has sufficient ductility capacities to resist the increase in seismic demand (intermediate level in Fig. 2). Therefore, to demonstrate the efficiency of the retrofitting methodology developed in this research project, the bridge was also considered to be located in a higher seismic activity region in Que´bec, which represents the hazard corresponding to the maximum level of the performance matrix in Fig. 2. Numerical modeling A three-dimensional (3D) numerical model was developed with the Ruaumoko nonlinear analysis program (Carr 2002) and used for the seismic evaluation of the prototype bridge. The superstructure was modeled with shell and beam ele-

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ments and is considered to remain elastic under a seismic event. The mechanical properties of cracked concrete were considered for the crossbeams, deck, and bridge bents, and uncracked values were considered for the prestressed beams. The effective stiffness of the elements of the bridge bents were derived from the idealization of their moment–curvature responses obtained with the WMNPhi sectional analysis computer program (Paultre 2000). Added masses were provided for the 50 mm asphalt cover and parapets. A dynamic analysis was carried out using the 3D model with spring elements at the abutments and bents to simulate foundation interaction. A difference in spectral acceleration of approximately 4% was observed between the model with spring elements and the rigid foundation model. This small value justified using fixed conditions at the abutments and bents for the remainder of the analysis. Moreover, these are the conditions that were reproduced in the laboratory. On-site dynamic test under ambient vibration Ambient vibration dynamic tests were carried out on the actual bridge to extract the key dynamic properties (frequencies, mode shapes, and damping). Vertical and horizontal motions were recorded on both sides of the deck to allow for the detection of horizontal, vertical, and torsional modes. Data were recorded with six velocity transducers placed evenly on the deck at 9 m intervals at a total of 22 locations. As can be seen on Fig. 3, six modes were identified from the tests, three of which were transverse modes. Nonlinear modeling The calibration of the numerical model in the linear domain was carried out with the ambient vibration test results. The calibration was performed through the modification of the effective stiffness of the deck elements. Nonlinear properties were then assigned to the bridge bents (the remainder of the structure was assumed to behave linearly). The effective properties for the columns and the crossbeams of the two bridge bents were obtained with the program WMNPhi (Paultre 2000). This is a sectional analysis program used to predict the moment–curvature response, which includes several stress–strain models for the reinforcement and the confined and unconfined concrete. A modified Takeda hysteretic behaviour was assumed in the plastic hinge regions of the columns as shown in Fig. 4 (Takeda et al. 1970). In Fig. 4, the unloading stiffness depends on the parameter a, which is taken as 0.25. The postyield stiffness is a percentage of the initial stiffness, which is taken as r = 0.05. The reloading stiffness after yielding is characterized by the parameter b, which is taken as 0 in this research program. The values of all these parameters were based on numerical prediction of the column force–displacement response, in which qy is the yield rotation and qu is the unloading rotation. The equivalent combined plastic hinge lengths lp were calculated with the following relationship (Priestley et al. 1996): ½1

lp ¼ 0:08l þ 0:022dbl fy  0:044fy dbl

where l is the distance from the critical section of the plastic hinge to the point of contraflexure, dbl is the diameter of the longitudinal bars, and fy is the yield stress of the reinforcement steel. For the bridge considered in this research proPublished by NRC Research Press

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Can. J. Civ. Eng. Vol. 37, 2010 Table 1 . Experimental program. Test No. 1

Intensity level 1

2

1

3 4 5

2 2 3

Details CHBDC 2000; before retrofit CHBDC 2000; after retrofit NBCC 2005 El Centro NBCC 2005

Return period (years) 475

Seismic site activity Moderate

PGA (g) 0.180

475

Moderate

0.180

2500 — 2500

Moderate — High

0.373 0.400 1.450

Fig. 10. Accelerograms used for pseudo-dynamic tests with substructuring (scaled values of time and acceleration used for the tests are given along the bottom and left axes, and corresponding real values in italic along the top and right axes). amax, maximum acceleration.

Fig. 11. Tested substructure.

gram, the plastic hinge length was found to be lp = 469 mm. A Rayleigh damping model proportional to the initial stiffness and mass matrices was used with a damping ratio of 1.5% on the first two transverse modes. The value of 1.5% was chosen based on the damping ratios obtained from the in situ ambient vibration tests.

N2 method The evaluation of the seismic vulnerability of the bridge was performed with the N2 method (Fajfar 1999). This method combines the capacity spectrum method, which graphically compares the capacity of a structure with the demands of specified earthquake ground motions, with the use of inelastic demand spectra. The seismic demand is obtained from a comparison between the uniform hazard spectrum considered and idealized force–displacement response of the structure. This response is converted into an elastic – perfectly plastic curve of an equivalent single-degree-of-freedom (SDOF) system. The monotonic displacement ductility capacity mmD of the bridge bent was obtained from a nonlinear pushover analysis with the 3D numerical model of the complete bridge and accounting for applied axial load – displacement (P–D) effects. The monotonic displacement ductility capacity of the bridge bent is defined as mDm = Du/Dy, where Du is the ultimate top lateral displacement, and Dy is the top lateral displacement of the bridge bent at yielding. As described in Shinozuka et al. (2000), the initial lateral loads are applied to the structure in proportion to the fundamental mode shape: Published by NRC Research Press

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Table 2. Tests results and damage levels. Test No. 1 2 3 4 5

Intensity level 1 1 2 2 3

K (kN/mm) 18.0a 18.0 14.2 13.2 7.2

umax (mm) 3.77 4.52 10.28 12.38 31.67

Vmax (kN) 90.0 85.4 162.5 174.8 262.9

mD 0.36 0.43 0.98 1.18 3.01

Drift (%) 0.17 0.20 0.46 0.56 1.43

Behaviour Elastic Elastic Elastic limit Elastic limit Inelastic

Damage level Almost none Almost none Slight Slight Moderate

Performance objective Immediate use Immediate use Operational Operational Life safety

Note: K, stiffness; umax, maximum top lateral displacement; Vmax, maximum base shear. a

Before test 1, K = 26.00 kN/mm.

Fig. 12. Displacement ductility (measured values of displacement and base shear are given along the bottom and left axes, and corresponding real values in italics along the top and right axes).

Fig. 13. Test 1 (intensity level 1, before retrofit) comparison between (a) measured and (b) computed time history. Tapp, apparent period; umax, maximum displacement.

0

½2

1 w f i Fi ¼ @XN i AV wf i¼1 i i

where Fi is the lateral load acting on degree of freedom i (i

Fig. 14. Test 1 (intensity level 1, before retrofit) hysteretic response.

Fig. 15. Test 2 (intensity level 1, after retrofit) comparison between (a) measured and (b) computed time history.

= 1, 2, . . ., N); wi is the permanent load assigned to node i; fi is the amplitude of the fundamental mode at node i; and V is the base shear. The base shear versus top lateral displacement curve is then transformed into a spectral acceleration (Sa) versus Published by NRC Research Press

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Fig. 16. Test 2 (intensity level 1, after retrofit) hysteretic response.

Fig. 17. Test 3 (intensity level 2, UHS-compatible ground motion) comparison between (a) measured and (b) computed time history.

spectral displacement (Sd) response spectrum (ADRS) according to the following equations: ½3

Sa ¼

V=W a

Fig. 18. Test 3 (intensity level 2, UHS-compatible ground motion) hysteretic response.

Fig. 19. Test 4 (intensity level 2, El Centro accelerogram) comparison between (a) measured and (b) computed time history.

XN

½5

ðwi fi Þ=g G ¼ XNi¼1 ðwi f2i Þ=g i¼1

½6

ðwi fi Þ=g2 i¼1 a ¼ XN XN ½ i¼1 wi =g½ i¼1 ðwi f2i Þ=g

and ½4

up Sd ¼ G fp

where W is the total weight of the bridge; up and fp are, respectively, the lateral displacement and amplitude of the fundamental mode at the top of the bent; and G and a are the modal participation factor and modal mass coefficient, respectively, and are defined as follows:

½

XN

where g is the acceleration due to gravity. The effects of the higher modes are not considered. However, the percentage of the effective modal mass corresponding to the first mode calculated for an earthquake in the transverse direction is 84%, which clearly indicates the prevalence of this mode. Assuming a linear distribution of curvature along the columns, displacement at yielding, as well as the column ductility, are calculated geometrically us-

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Fig. 20. Test 4 (intensity level 2, El Centro accelerogram) hysteretic response.

Fig. 22. Test 5 (intensity level 3, UHS-compatible ground motion) hysteretic response.

Fig. 21. Test 5 (intensity level 3, UHS-compatible ground motion) comparison between (a) measured and (b) computed time history.

Results of the analysis For the bridge considered here, the displacement at yield obtained for the bridge is Dy = 0.027 m, and the displacement ductility is mDm = 1.87. This monotonic displacement ductility capacity is then reduced with due consideration to cumulative damage to obtain the cyclic ductility capacity mDc, using the following relationship: ½9

ing the following equations and considering the column double curvature: ½7

Dy ¼

4y l2 3

where 4y is the yield curvature of the concrete section. Assuming localization of constant curvature in the plastic hinge region after yielding, the column displacement ductility can be expressed as follows: ! 4u  4y lp ðl  0:5lp Þ ½8 mDm ¼ 1 þ 4y l2 =3

mDc 1 ¼ mDm 1 þ bg 2 mDc

where b is a strength degradation parameter, taken to be equal to 0.15 (Park et al. 1984); and g is a dimensionless parameter function of the dissipated hysteretic energy, the maximum displacement, and the natural frequency of the structural system, which can be taken equal to 1 (Fajfar 1999). The computed cyclic ductility capacity for the selected bridge is mDc = 1.52. The resulting capacity spectrum is presented in Fig. 5. The uniform hazard elastic spectrum with return periods of 100, 475, and 2500 years for the bridge site are also shown in Fig. 5. The uniform hazard spectrum for a more seismically active region (located in Quebec), with a return period of 2500 years, is also shown in its elastic and inelastic form, for a value of the seismic force reduction factor the seismic force reduction factor R = 1.92. In this method, the ductility demand is determined using the equal displacement rule and the inelastic design spectra. As can be seen in Fig. 5, with R = m in the high seismic activity region and a return period of 2500 years, the demand in terms of displacement ductility of the bridge bent exceeds its capacity and is equal to mD,demand = 1.92. The advantages of this type of analysis are that (i) the displacement ductility values are directly obtained for the system, and (ii) UHScompatible ground motion time histories do not have to be generated. In the next section, a retrofit scheme is developed for the bridge bent columns to meet the 1.92 ductility demand.

where 4a is the ultimate curvature of the concrete section.

Retrofit design methodology A retrofit solution using jacketing with CFRP was dePublished by NRC Research Press

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Table 3. Comparison between measured responses (PSD laboratory tests) and those computed with the Ruaumoko program. Test No. 1 2 3 4 5

umax (mm) PSD test 3.77 4.52 10.28 12.38 31.67

Intensity level 1 1 2 2 3

Vmax (kN) Ruaumoko 4.14 4.60 10.66 12.62 29.39

d (%) +9.0 +1.6 +3.7 +2.0 –7.2

PSD test 90.0 85.4 162.5 174.8 262.9

Ruaumoko 99.1 77.1 168.2 165.0 187.2

d (%) +10.1 –9.7 +3.5 –5.6 –28.8

Note: d, percent difference between the measured and computed responses.

signed with the following steps to increase the displacement ductility of the RC columns (Priestley et al. 1996): 1. Determine the cyclic ductility demand in terms of displacement, based on the evaluation of the seismic vulnerability of the bridge bents. For the bridge studied, we have: ½10

mD;demand ¼ 1:92

2. Calculate the corresponding curvature ductility demand, mf with the following geometric relationship (Park and Paulay 1975): ½11

mf ¼

4u mD  1   ¼1þ lp l 4y 3 1 p l

2l

where 4u and 4y are the ultimate and yield curvature of the concrete section and lp is an equivalent confined plastic hinge length given by Priestley et al. (1996) as: ½12

lp ¼ g þ 0:044dbl fy

where g is the gap between the jacket and the supporting member and dbl longitudinal bar diameter. 3. Calculate the demand in terms of the maximum concrete compression strain 3cu,demand according to the following equation: ½13

3cu;demand ¼ 4u c

where c is the neutral axis depth calculated with the sectional analysis program WMNPhi (Paultre 2000). 4. Determine the required ratio of confinement such that the following inequality between the provided ultimate strain and the demand in strain holds: ½14

3cu;provided  3cu;demand

The required number of CRFP layers is calculated with a material-dependent relationship between the ultimate compression strain and the volumetric ratio of jacket confinement. The equations used in this project are derived from the Eid and Paultre (2006) confinement model. This new model has two important advantages: (i) it considers the two confinement sources acting on the concrete section, i.e., the action due to the CFRPs and the action due to steel ties; and (ii) the definition of the confinement action due to CFRPs was expressly derived for composite materials (not from equivalent steel). In this new model, the ultimate strain of the section confined with CFRPs, 3cu,provided, is calculated with the following expression derived by Lam and Teng (2004):

½15

    Ash f hy 2tEf 3fu 3fu 0:45 3cu;provided ¼3c0 1:75þ5:53 ke þ  sDc f c0

Df c0

3c0

where fc0 and 3c0 are the unconfined concrete strength and corresponding strain, respectively; ke is a coefficient introduced by Sheikh and Uzumeri (1982) and Mander et al. (1987) that reflects the effectiveness of the lateral steel in confining the concrete; Ash is the total cross-sectional area of the transverse reinforcement; fhy is the yield stress of the transverse reinforcement steel; s is the steel tie spacing; Dc is the concrete core diameter; D is the full column diameter; and t, Ef, and 3fu are the thickness, elastic modulus, and ultimate tensile strain of the CFRP. The material chosen for this project has the following properties (from the manufacturer): t = 1.016 mm, Ef = 70.6 GPa, the ultimate tensile strength, ffu = 849 MPa, and 3fu = 0.0112. 5. Calculate the cyclic displacement ductility capacity for the confined section. With three layers of the material chosen for the confinement, the retrofitted columns have a cyclic displacement ductility capacity of mDc = 2.80, which exceeds the displacement ductility demand of mD,demand = 1.92. 6. Check the capacity design principles. The moment–curvature curves calculated with the WMNPhi program shown in Fig. 6 for the confined and unconfined sections clearly outline the significant increase in terms of curvature and displacement ductility in the case of the retrofitted bridge bent. It is also shown that, under the axial force considered (0:1Ag f 0 c , where Ag is the gross section area, and f ’c is the compressive strength of unconfined concrete), the flexural capacity of the circumferentially retrofitted RC column is not significantly enhanced (7% increase in ultimate moment). Although this value is low, capacity design principles were still followed. Additional stresses that were potentially induced in the other parts of the bent (footing and crossbeam) did not exceed their capacities. The crossbeam was modeled with Response2000 (Bentz and Collins 2000), a sectional analysis program that calculates the strength and ductility of a reinforced concrete cross section subjected to shear and moment according to the modified compression field theory. Requirements of the 2000 Canadian highway bridge design code As the bridge was designed in 1975, the columns do not have the minimum ratio of transverse reinforcement currently prescribed for new bridges in the 2000 edition of the CHBDC. The 2000 CHBDC recommendations for confinement in members subjected to flexure, particularly in plastic Published by NRC Research Press

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hinge regions, correspond to a ratio of transverse reinforcement of rs = 0.99% for the selected bridge. With a crosssectional area of Ash = 275 mm2 for the ties and a spacing of s = 300 mm, the actual ratio of transverse reinforcement is a much lower rs = 0.51%. Column rehabilitation would therefore be required to match the current CHBDC requirements. However, the comparison of the 2000 CHBDC requirements with the ratio of confinement required to satisfy the performance-based displacement criteria shows that this approach is advantageous. The number of layers of CFRP required to meet the 2000 CHBDC requirements in terms of confinement was calculated by first computing the maximum strain (3cu) that would have been reached with a ratio of transverse reinforcement rs = 0.99% with the following relationship: ½16

3cu ¼ 0:004 þ

1:4rs fhy 3su f 0 cc

where the reinforcement ultimate strain 3su = 0.04, and f 0 cc is the compressive strength of confined concrete. The thickness, t, of CFRPs was then obtained with eq. [15]. Indeed, for the bridge under investigation, meeting the 2000 CHBDC code requirements would require twice the amount of CFRPs (six layers) compared with the three layers that were computed to satisfy the needs in terms of ductility corresponding to the hazard of a higher seismic activity region in Quebec (maximum level of the performance matrix in Fig. 2).

Pseudo-dynamic test with substructuring The experimental evaluation of the performance-based retrofitting scheme was carried out using the pseudo-dynamic (PSD) technique with substructuring. This method, which represents the state-of-the-art in earthquake testing, was used to develop the performance-oriented test protocol considering input motions corresponding to various limit states of the bridge (Fig. 2). With this hybrid testing technique, the restoring forces of a structure are determined experimentally, and the time-dependent forces, i.e., damping and inertia, are simulated numerically. The test can thus be performed in a quasi-static manner, which is much simpler than a real-time test. When substructuring is used, a selected portion of a structure (that is expected to behave nonlinearly) is tested, and the remainder of the structure is numerically modeled. Substructuring is implemented by two different processes. The PSD controller process is responsible for simulating the dynamic effects of the scaled model of the three-column bridge bent and for controlling the testing machine, and the substructuring process simulates the linear part of the structure, the deck in this case, with a finite-element model (FEM) (Fig. 7). The two processes have to exchange information related to the common degrees of freedom. The time-integration scheme adopted in this project is based on the a method, which is an unconditionally stable implicit algorithm (Hilber et al. 1977). More details on the implementation of the method can be found in Weber et al. (2007).

Experimental program A 1:3 scale factor was selected for the model to accommodate the facilities of the Sherbrooke laboratory. Similitude relationships were used between the actual bridge and the model. Virtual substructure The scaled FEM of the superstructure was implemented in MATLAB. Symmetric boundary conditions were considered, and only half of the bridge was modeled. This simplified model with beam elements was calibrated with the dynamic properties obtained from the ambient vibration tests carried out on the actual bridge. The same value of damping of 1.5% used for the evaluation was assumed for the substructure model. Tested substructure The geometric characteristics of the bent scaled model are presented in Fig. 8. The bent was instrumented with several strain gauges to measure deformations in the column longitudinal and transverse reinforcement. Displacement transducers were used to record the top lateral displacement, joint displacement, and curvature at the top and bottom of the columns ( Fig. 9). Ground-motion time histories The test specimen was subjected to three levels of increasing simulated earthquake excitation as described in Table 1. The four accelerograms shown in Fig. 10 were used for the tests. The time and acceleration values were scaled for test purposes (using similitude relationships); the real values are shown in italics on the right and top axes. The first accelerogram, used for tests 1 and 2, is compatible with the design requirements of the 2000 CHBDC for a region of moderate seismic activity in eastern Canada with a return period of 475 years. The second and fourth accelerograms, used for tests 3 and 5, are compatible with the uniform hazard spectrum recommended by the 2005 edition of the NBCC for regions in Eastern Canada with moderate and high seismic activity, respectively. The third accelerogram, used for test 4, is the El Centro, California, recording of the 1940 Imperial Valley earthquake, with the peak ground acceleration scaled to 0.40g. Accelerograms 1, 2, and 4 are uniform hazard spectrum compatible time histories inputs (Atkinson and Beresnev 1998). Test procedure The lateral seismic load was applied to the test specimen with a 500 kN dynamic-rated servohydraulic actuator attached to a reaction wall. An axial force of 236 kN (corresponding to 0:1Ag f 0 c ) was applied with a total of six hydraulic jacks, two per column (Figs. 9 and 11). The initial stiffness of the tested substructure was determined by carrying out a static displacement test on the bridge bent specimen before each test. The test specimen was then subjected to the first level of earthquake. Two of the three columns were then retrofitted with CFRPs, and tests 2–5 were subsequently carried out ( Fig. 11).

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Analysis of test results Table 2 summarizes the earthquake response of the test specimen. For each test, the table includes the stiffness, top lateral displacement, base shear, displacement ductility, and lateral drift. The observed behaviour, damage level, and performance objective are also presented in Table 2. These values correspond to the expected behaviour of a normal bridge according to the performance matrix shown in Fig. 2. Figures 12, 14, 16, 18, 20, and 22 show the hysteretic responses of the bridge bent for the five tests. After the first two earthquake simulations (accelerogram 1), the specimen exhibited no visible cracking and performed with no yielding of the reinforcement. During tests 3 and 4 (accelerograms 2 and 3), yielding was measured on some longitudinal bars, but the centre column of the bridge bent exhibited no significant cracking. During test 5 (accelerogram 4), the centre column exhibited more significant yielding and cracking but no spalling of the concrete cover. These data can be referred to when establishing quantitative criteria for performance-based retrofit methods. Moreover, these values are similar to those reported elsewhere for a highway bridge bent (Dutta 1999) and for a ductile momentresisting RC frame (Ghobarah 2004). The displacement ductility reached a value of 3.01 after the highest intensity test, corresponding to a return period of 2500 years for a region of high seismicity, which is more than the displacement ductility value of 2.80 calculated for the retrofit design ( Fig. 12). During this high-intensity test, the CFRPs showed no signs of distress, and the strain values measured on the fibres were very low, indicating that the design procedure is conservative. Comparison between test results and numerical predictions One of the main reasons for performing PSD tests is the difficulty modeling the nonlinear behaviour of structures under seismic loading. Tests results are needed to validate numerical modeling assumptions. Table 3 shows a comparison between the measured responses from the PSD laboratory tests and the computed responses with the Ruaumoko program for the five tests. Note that stiffnesses of the columns were reduced in the model between each test to account for cumulative damage. Figures 13, 15, 17, 19, and 21 show comparisons between the measured and computed responses of the bridge bent specimen for the three intensities of ground motion. The graphics show the time history of the top lateral displacement of the specimen. Good agreement between the predicted and measured responses can be observed for the overall motion, the maximum top lateral displacement, and the apparent period. More specifically, Fig. 21 demonstrates that the nonlinear bridge bent behaviour was accurately predicted using the Ruaumoko and WMNPhi programs.

Conclusions An optimized retrofitting scheme using carbon-fiber-reinforced polymers (CFRPs) was developed and applied to a selected highway bridge. The retrofitting technique is based on specific performance criteria where the retrofitted structure must meet prescribed ductility levels corresponding to

Can. J. Civ. Eng. Vol. 37, 2010

selected seismic events, and its design includes a new confinement model for reinforced concrete circular columns wrapped with CFRP. The seismic demand considered in this study is based on the changes in the latest edition of the National building code of Canada (NRCC 2005), which led to an increase in earthquake hazard for some regions in Canada. Using this performance-based approach, the amount of required composite material to achieve the specified criteria was found to be much more economical when compared with the ductility requirements of the 2000 edition of the Canadian highway bridge design code (CHBDC (CSA 2000)). The performance of the retrofitting technique was evaluated by pseudo-dynamic tests carried out on a 1:3 scale model of one of the bridge bents. Using the substructuring approach, the remainder of the structure was modeled, and the bridge bent was subjected to increasing levels of seismic loading, corresponding to various limit states of the bridge. The measured response of the test specimen compared well with the predictions of a three-dimensional nonlinear finiteelement model calibrated with dynamic properties obtained from on-site ambient vibration tests. During the highest intensity test (return period of 2500 years, region of high seismicity), the CFRP retrofit showed no sign of distress, and the strain values measured on the fibres were very low, indicating that the performance-based design procedure is conservative. These conclusions are based on a test performed on only one type of pier bent. Therefore, other bridge types need to be examined to generalize the method.

Acknowledgements The authors would like to acknowledge the financial support of ISIS Canada, the Natural Sciences and Engineering Research Council of Canada (NSERC), the Que´bec Fonds pour la recherche sur la nature et les technologies (FQRNT), the Que´bec Ministry of Transportation, the City of Que´bec, Sika-Canada, and Centre d’expertise et de recherche en infrastructures urbaines (CERIU). Benedikt Weber developed the PSD test algorithm in MATLAB. Special thanks to Benedikt Weber, Rami Eid, Thien Phu Le, Claude Aube´, Jeason Desmarais, Se´bastien Gauthier, Laurent Thibodeau, Philippe Grandmaison-Audette, Andre´ Bernard, and Ce´dric Poirier for their collaboration on various aspects of the project.

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