Collapse Vulnerability and Fragility Analysis of Substandard RC Bridges Rehabilitated with Different Repair Jackets Under Post-mainshock Cascading Events

4.1 Hybrid Repair Jacket

Recently, the authors have proposed and experimentally validated a hybrid jacket for the repair of severely damaged RC bridge piers (Fakharifar et al. 2015b). The hybrid jacket comprised of passive and active confining pressure. The hybrid jacket application on the plastic hinge region of a severely damaged RC bridge column is illustrated in Fig. 4. The hybrid jacket is composed of a thin cold-formed steel sheet wrapped around the column with prestressing strands placed over the column. While the prestressing strands can prevent buckling of the confining steel sheet, the thin steel sheet can in turn prevent the prestressing strands from penetrating into cracked cover concrete (i.e., preventing loss of confining pressure in the active strands). The thin cold formed sheet metal is directly wrapped and welded around the existing column. The repair is completed by placing and prestressing the strands around the column. The hybrid jacket exhibits advantageous features over traditional repair jackets such as feasibility of rapid application after a MS event (no heavy equipment required); no additional seismic weight introduced due to small thickness of sheet metal and negligible weight of cables (similar to FRP jackets); and no requirement for column surface preparation and adhesive material application (required for FRP jackets). The most prominent structural feature of the hybrid jacket is resisting the shear crack opening in both the vertical and horizontal directions (see Fig. 5), while the prestressing strands (similarly any unidirectional jacket such as FRP or SMA wires) can resist the shear crack opening in the transverse direction only (Jirawattanasomkul 2013). Thus, due to the enhanced aggregate interlock provided, concrete shear strength in the hybrid jacketed column—similarly conventional steel jacketed column—is larger than that in column with prestressing strands (FRP or SMA) only.

4.2 Repair Techniques

Three different repair techniques were considered, including a CFRP repair jacket, a conventional thick steel repair jacket, and hybrid repair jacket (discussed in Sect. 4.1). The CFRP jacket was chosen as the first repair technique due to the excellent high strength-to-weight ratio which is becoming increasingly attractive for structural repair/retrofit projects (Priestley et al. 1996; Buckle et al. 2006; He et al. 2013; Grelle and Sneed 2013). The steel jacket was the first and the most widely used retrofit technique (Priestley et al. 1996; Buckle et al. 2006; ElGawady 2009; Fakharifar et al. 2013;), due to its availability, price, and ductile behavior when compared with FRP materials with brittle failure (Fakharifar et al. 2015c). However, in addition to the labor intense work required for steel plate or RC jacketing, one major concern, is the increase of the original cross section (i.e., increased stiffness and reduced natural vibration period (Haroun and Elsanadeby 2005) results in alteration of the system dynamic response). The additional flexural strength of a member with a thick repair jacket would increase the plastic shear demand on the retrofitted/repaired column. Thus, the conventional steel or RC concrete jackets need to be detailed so as not to trigger other failure modes such as cap beam damage or cause damage to other capacity protected elements (Priestley et al. 1996; Buckle et al. 2006; Fakharifar et al. 2014b). Therefore, active prestressing strands were considered as another repair technique. Active cables have the advantage of providing the active confining pressure without increasing the column cross section (Saatcioglu and Yalcin 2003). However, tests proved that for retrofitted columns with prestressing strands, penetration of the prestressed cables into the cracked cover concrete caused loss of confining force in the active cables (Buckle et al. 2006). To incorporate the economical price of steel jackets with the benefit of active confining pressure, the hybrid confining jacket was proposed and considered as the third seismic repair intervention in this study.

4.3 Seismic Repair Design and Repair Performance Objectives

The bridge column repair design aimed at restoring the shear strength, providing the required confining pressure in the plastic hinge and inhibiting the lap splice failure. Repair jacket design procedure is briefly described as follow.

Figure 6 illustrates the schematic of the studied repair jackets. The jacket height for the studied repair techniques was calculated as L _pz  = 1220 mm.

The CFRP jacket was assumed to have a tensile strength of 3800 MPa, modulus of elasticity of 227 GPa, and a rupture strain of 1.67 %. The selected composite CFRP repair system consisted of unidirectional high strength carbon fabric with fibers perpendicular to the column longitudinal axis (Fig. 6a). The required jacket thickness for the studied bridge column was calculated as 5.81 mm (using nominal fiber thickness).

A 7.5-mm thick A36 steel with minimum yield strength of 400 MPa was required for the thick steel repair technique. For practicality, a 10-mm thick steel jacket with yield strength of 400 MPa and modulus of elasticity of 200 GPa, with a 25 mm gap left between the column and the jacket to be filled with repair grout (Fig. 6b), was required.

For the hybrid jacket, the thin sheet metal with yield strength of 680 MPa; tensile strength of 771 MPa; and elastic modulus of 207 GPa was considered. Considering field-application and formability of the sheet metal around the existing column without specialized equipment in the field, a 1220 mm wide sheet with a thickness of 1.27 mm was calculated. The nominal 12 mm diameter seven-wire strands with the ultimate tensile strength of 1937 MPa and modulus of elasticity of 200 GPa were considered for repair design. The spacing between strands and the required prestressing pressure in the cables were calculated as 1045 MPa and 100 mm, respectively (Fig. 6c).

5.1 Nonlinear Numerical Model Details

The fiber discretized cross section of a numerical RC column and representative stress–strain behavior associated to fibers are shown in Fig. 7. For confined core fibers either steel-confined (for thick steel and hybrid jackets), or FRP-confined would be considered. Column elements were modelled through inelastic frame elements. The effect of lap-splice reinforcement was desired to be somewhat represented in the numerical models hysteresis behavior. For RC columns with spliced reinforcement, a multilinear smooth polygonal hysteresis loop, developed in the work of Sivaselvan and Reinhorn (1999, 2001) through a zero length rotational spring (available in Seismostruct) could be used to model the plastic hinge to include the hysteresis pinching associated with reinforcement slippage. However, the state of rebar stress at splice failure was needed to be determined. FEMA 356 (2000) provisions on lap-spliced bars was used to determine the rebar stress at failure, however the predicted response was not accurate especially in the post-peak degrading behavior. Study by Cho and Pincheira (2006) indicated that FEMA 356 underestimates the lapped rebar stress. Using bond-slip models are a proven method for inelastic analysis of RC columns with lap-splice failure (Xiao and Ma 1997; Harajli et al. 2002; Cho and Pincheira 2006). However, bond-slip model could not be directly incorporated in the numerical model, since a zero length stress–displacement section was not available. Besides, the effect of the lateral confining pressure from different repair jackets was also important. To achieve this, the stress–strain relationship of the longitudinal steel reinforcement for lap spliced reinforcement was reduced to simulate the expected backbone of lateral force–displacement relationship. It’s noteworthy to mention that the Xiao model (Xiao and Ma 1997) could be used to establish the average bond stress–lateral displacement relationship for columns with lap-spliced reinforcement in the as-built and with the consideration of the lateral confining pressure conditions in retrofitted ones, and then reduce the steel properties accordingly. When ignoring the lap-splice, monotonically increasing lateral force–displacement relationship with ascending post-peak behavior was observed. However, reduced material properties captured the bar-pullout and the associated softening behavior evident from lap-spliced columns hysteresis behavior. The method used was approximate, however resulted in fairly accurate predictions of the numerical models, as shown later in the paper. Note that fiber discretized sections with uniaxial constitutive laws were used in the finite element model and the fiber element is incapable of accurately aggregating shear deformations. However, the studied columns in the current investigation constitute primarily flexural dominant (column aspect ratio well above 2.5) hysteresis response.

The increase of lateral confining pressure on the constitutive confined concrete model in this study is illustrated in Fig. 8a. A typical stress–strain relationship for the virgin steel reinforcement versus damaged reinforcement is illustrated in Fig. 8b. For the retrofit case, the jacket is applied on the intact column cross section prior to any major event, while for the repair scenario the repair jacket is implemented after column experiences some extent of damage. As it can be seen, in the case of a repaired column the initial stiffness of steel reinforcement is reduced, as well as the post-yield strain hardening. Representative lateral force-drift relationship for an identical RC column depending on the reinforcement detailing, is also illustrated in Fig. 8c. It can be seen brittle failure could be avoided through inclusion of seismic reinforcement, such as external jackets.

5.2 Verification of Numerical Models with Experimental Test Results

Extensive verification of the numerical models for their capability of capturing and simulating the global and local forces and deformations were implemented first. The authors have also verified their analytical models for FRP jacketed concrete columns under both monotonic and dynamic timehistory loading elsewhere (Fakharifar et al. 2014c). To evaluate the accuracy of the developed numerical models for evaluating the behavior of bridges subjected to MS-AS sequences, experimental models were selected from full scale RC column/bridge structures subjected to multiple series of ground motions.

Experimental tests on RC columns tested under incrementally increasing reversed cyclic loading and constant axial load with lap spliced reinforcement (l _s  = 20d _b ) as part of another study by the authors was selected to evaluate the accuracy of the developed numerical models in predicting the force–displacement relationship of columns with lap-spliced reinforcement. Figure 9a depicts backbone of the predicted force–displacement relationship from the numerical model versus experimental test results. It is clear that, ignoring the slip effect would not capture post-capping degradation in the numerical model. However, the reduced steel allows capturing the post-peak strength degradation.

An RC cantilever column with continuous reinforcement (Column BG-2) tested under constant axial load and unidirectional quasi-static incrementally increasing lateral displacement up to failure was selected (Saatcioglu and Grira 1999). The selected column was chosen for verification since unlike regular RC columns with stirrups or spirals, welded reinforcement grids were used as confinement reinforcement. Therefore the equivalent confining pressure from the grids was considered in the model. Figure 9b indicates the high accuracy of the numerical model in predicting the hysteretic behavior of the experimental column specimen in terms of strength, stiffness and displacement capacity. Besides, it was concluded that alternative forms of confinement can also be considered in the numerical analysis, as long as the appropriate lateral confinement pressure is provided in the model.

A full-scale RC bridge pier subjected to series of six incremental ground motions developed by PEER and NEES (PEER 2010) as part of a blind prediction contest was selected. The input ground motions commenced with the low intensity excitations succeeded by high intensity motions to bring the bridge pier to the incipient collapse state. The numerical model was verified adopting the proposed recommendations by Bianchi et al. (2011). Figure 9c demonstrates the capability of the numerical model in reproducing the dynamic hysteresis behavior of the studied bridge pier. The selected bridge pier specimen exhibits significantly high level of nonlinearity (both material inelasticity and geometric nonlinearity). Damage was observed in the form of concrete spalling, concrete cracking, longitudinal bar buckling (thirteen of the eighteen bars were buckled), and longitudinal bar fracture in the plastic hinge region formed at column-footing interface (Schoettler et al. 2012). The numerical model could successfully capture the seismic response of the pier specimen subjected to six seismic sequences of various intensities.

To evaluate the adequacy of the developed numerical models in the case of steel-jacketed RC columns, a full scale concrete-filled steel tube bridge pier under incrementally increasing reversed cyclic loading and constant axial load (Marson and Bruneau 2004) was selected. Figure 9d depicts the predicted force–displacement relationship of the numerical model with reasonable accuracy as compared to the experimental test results.

To evaluate the accuracy of the numerical models in predicting the system response, the large scale bridge specimen tested in pseudo-dynamic type test was selected (Pinto et al. 1996). The bridge specimen was subjected to two successive input motions on shake table tests, including the design earthquake, followed by the 1.2 times the design level earthquake. The bridge deck was modelled using elastic frame elements with mass lumped along the centerline (Seismosoft 2013b). Both distributed plasticity (inelastic distributed element) and lumped plasticity (inelastic plastic hinge element) elements were adopted to model the bridge columns. The predicted displacement time history of the middle pier from the distributed plasticity and lumped plasticity models are compared versus experimental results in Fig. 9e. The results indicate the adequacy of both types of element formulations in predicting the displacement time history and the maximum displacement with reasonable accuracy.

Finally, to further evaluate the accuracy of the developed numerical models under cumulative seismic damage (expected for MS-AS), series of RC bridge column specimens tested under various loading histories were chosen (A2, A4, A8 and A10 column specimens) (Kunnath et al. 1997). Each of the selected bridge column specimens were tested under a constant axial load and a unique lateral load path, specifically, specimen A2: standard cyclic load with three full symmetric cycles at increasing ductility up to failure; specimen A4: constant amplitude reversed cyclic displacement of ±3Δy (Δy = yield displacement level); specimen A8: random earthquake displacement histories, representing four scenario earthquake sequence (minor, minor, damaging and severe earthquakes), and A10: representing five scenario earthquake sequence (major, minor, moderate, minor and severe earthquakes) (Kunnath et al. 1997). Comparison of calculated force–displacement relationship of the studied column specimens against experimental results are illustrated in Fig. 9f–i for A2, A4, A8 and A10 column specimens, respectively. The obtained results indicate the high accuracy of the numerical models to simulate the obtained experimental results under different loading histories—including multiple earthquakes—in terms of strength, stiffness and ductility. The developed numerical models exhibited to provide sufficient accuracy, and these modeling assumptions were adopted for performance-based evaluation of the bridge in the current study.

6.1 Damage/Limit State

Four damage states, namely minor, moderate, extensive and collapse as defined by HAZUS-MH (2003) were adopted herein, in which they were correlated with the quantitative engineering demand parameters. The drift-based limit states developed by Dutta and Mander (1998) were adopted to define the bridge columns drift limits. The drift limits considered for the bridge columns were 0.005, 0.007, 0.015, 0.025 and 0.05 for no damage, minor, moderate, extensive and collapse damage states, respectively. However, the constant drift limits better serve as a global (system) response quantity. For a more accurate evaluation, the strain limit sates (local response quantity) developed by Priestley et al. (2007) were incorporated as well. Using moment curvature and pushover analysis the strain limits were related to drift limit states. The maximum compressive strain in the confined core concrete and the maximum tensile strain in the longitudinal reinforcing steel were considered as the strain-based limit states (Priestley et al. 2007).

The bar buckling and bar fracture damage states were calculated according to the equations developed by Berry and Eberhard (2007). The equation proposed by Mackie and Stojadinovic (2007) for calculating the drift at column failure (i.e., lateral drift level beyond the peak strength that column reaches zero strength) was adopted to define the complete failure limit state. Incorporating the effect of load history on reinforcement bar buckling limit state—as shown in past studies (e.g., Rodriguez et al. 1999)—under the first seismic event may significantly alter the obtained results for the subsequent seismic event. Nevertheless, effects of seismic load-path history on reinforcement bar buckling were not considered.

6.2 Mainshock-Aftershock Seismic Ground Motion Records

The ground motions were selected from the Pacific Earthquake Engineering Research Center (PEER) Strong Motion Database, specifically, from the study by Baker et al. (2011) providing several standardized sets of ground motions for the PEER’s Transportation Research Program. The selected ground motions are neither site-specific nor structure specific (i.e., unbiased) (Baker et al. 2011). The earthquake ground motions records in this study include both type of far-fault (also referred to as far-field) and near-fault records.

Two bins of earthquake records were considered to generate the MS-AS sequences, namely, ensemble 1 and ensemble 2. Ensemble 1 constitutes far-fault records where ensemble 2 included records with near-fault effects. Each ensemble constitutes records of large and moderate magnitude. The acceleration response spectra of ensemble 1 and 2 record sets (unscaled) are illustrated in Fig. 10.

Two seismic sequences from ensemble 1 and two seismic sequences from ensemble 2 were considered, namely (1) severe MS-moderate AS, and (2) severe MS-severe AS. Eighty MS-AS seismic sequences from the ensemble 1 and eighty MS-AS seismic sequences from the ensemble 2 record sets were generated. Subsequently, for each ensemble, records were selected from the corresponding intensity record set. For instance for severe MS-moderate AS from ensemble 1, large magnitude (response spectra in Fig. 10a) and moderate magnitude (response spectra in Fig. 10b) records were paired. Similarly, for severe MS-severe AS from ensemble 1, large magnitude records followed by the same set of records were paired. Similar seismic sequences were generated from ensemble 2 bin of records. No paired seismic sequence from ensemble 1 to 2 and opposite were considered (i.e., no near fault MS-far fault AS or opposite). Hence, total of 160 paired accelerations (40 severe MS-moderate AS and 40 severe MS-severe AS from ensemble 1 and 2) were generated.

To simulate the free vibrating response of the bridge at the end of the MS, 20 s of zero acceleration was introduced between the MS and AS acceleration time histories, to assure that the bridge was at rest prior to the AS event.

For each intensity level, the selected ground motions were scaled to match the Los Angeles-California site response spectrum for two different hazard levels, namely 10 % probability of exceedance in 50 years (moderate earthquake), and 2 % probability of exceedance in 50 years (severe earthquake) (Fig. 10). The target response spectra were utilized to scale the original records at each intensity level. The selected unscaled ground motions from the severe (Fig. 10a) and moderate (Fig. 10b) intensity record sets from ensemble 1 were scaled considering the 2 and 10 % in 50 years target response spectra, respectively, to calculate the scaled severe and moderate magnitude records for ensemble 1. The same procedure was adopted to scale the original records from the ensemble 2 set of records. The characteristics of ensemble 1 and 2 record sets are detailed below.

Ensemble 1 (far-fault): for this set the large magnitude suite of records consists of 40 broad-band ground motions that their response spectra match the median and log standard deviations predicted for a large magnitude (M_w = 7) strike-slip earthquake at a distance of 10 km. The moderate magnitude motions constitutes 40 broad-band ground motions with their response spectra matching the median and log standard deviations predicted for a moderate magnitude (M_w = 6) strike-slip earthquake at a distance of 25 km. The selected set of ground motions as the far fault records represent a very broad range of spectral amplitudes up to two orders of magnitude. These set of records cover a broad range of intensities at sites located near active crustal earthquake sources (Baker et al. 2011). The acceleration response spectra of the severe and moderate intensity records from ensemble 1 ground motions are presented in Fig. 10a, b. Detailed information on the adopted records can be found elsewhere (Baker et al. 2011).

Ensemble 2 (near-fault): For this set the large magnitude ground motions consists of 40 records containing strong velocity pulses of varying periods. The velocity pulses are typically observed in the near fault ruptures due to directivity effects. This set of records are somewhat intense that constitute motions having a strike parallel peak ground velocity up to 250 cm/s. Figure 11 illustrates one original ground motion with strong velocity pulse along with the extracted pulse and non-pulse (residual) part of the original motion. The moderate magnitude ground motions consist of 40 records each obtained from scaling the large magnitude records (Bearman 2012). The acceleration response spectra of the ensemble 2 ground motions are presented in Fig. 10c, d. These set of near fault motions are similar to near-fault motions included in ATC-63 (2009), except these motions have a variety of pulse periods (1–12.9 s). This is important, since the pulse period, relative to the period(s) of vibration of a structure is not negligible. Besides, these set of records are somewhat intense that constitute motions having a strike parallel peak ground velocity of 250 cm/s (see Fig. 11a).

6.3 IDA Analysis Results Under Severe MS-Severe AS and Discussion

For brevity results from an extensive series of IDA analyses are presented only in terms of structural collapse capacity and maximum drift. For each series of analyses four cases of the studied bridge were considered: unrepaired bridge, column repaired with CFRP jacket, column repaired with conventional steel jacket, and column repaired with hybrid jacket. Each individual IDA curve corresponds to one MS-AS pair of ground motion. The IDA results were utilized to construct the IDA curves under back-to-back time histories. Extensive data from IDA analyses were generated and the IDA curves only for the severe MS-severe AS are plotted in Fig. 12. The IDA results under the severe MS-moderate AS are summarized at the end of this section.

The IDA results for the unrepaired case and the CFRP, conventional steel and hybrid repair cases subjected to severe MS-severe AS of ensemble 1 bin of records are presented in Fig. 12a–d, respectively. Similarly, IDA results under severe MS-severe AS from ensemble 2 suite of records for the unrepaired, CFRP, conventional steel and hybrid repaired cases are presented in Fig. 12e–h, respectively. To evaluate the impact of damage from the MS-AS sequence compared to an MS event only, the median of IDA results for the bridge subjected to severe MS only (i.e., no AS event) is superimposed on Fig. 12a, e accordingly (red dotted line).

The obtained mean structural collapse capacity for the MS only compared to MS-AS (Fig. 12a, e) is reduced as from 0.83 to 0.33 g; and from 0.69 to 0.36 g, for the ensemble 1 and 2 bin of records, respectively (60.0 and 47.8 % reduction in mean structural collapse capacity, respectively). This observation clearly indicates the effect of existing damage under a severe MS on the post-MS collapse capacity when severe AS is considered. Similarly, the obtained mean maximum drift level that the bridge could sustain prior to collapse for the MS only compared to MS-AS (Fig. 12a, e) is reduced from 3.42 to 2.35 %; and from 3.33 to 2.58 %, for the ensemble 1 and 2 bin of records, respectively (31.3 and 22.5 % reduction in maximum attainable drift level prior to collapse, respectively). The obtained mean structural collapse capacity/maximum drift for the original bridge subjected only to one seismic event (i.e., no AS) reveals the unsatisfactory performance of the bridge column with lap-splice deficiency, as expected. The original bridge could not reach drift capacity recommended by different seismic codes of practice (e.g. CALTRANS 2004). It is also shown that the accumulated damage under severe MS had impact on the post-MS collapse strength/deformability of the MS-damaged bridge when subjected to severe AS.

Usually the term MS-AS implies a severe MS followed by a minor/moderate AS, and the presented results herein is an extreme scenario, where the first severe earthquake is succeeded by another severe earthquake. Hence, the obtained results may not be realistic and represent the lowest bound to the mean structural collapse capacity. It is unlikely a severe MS is followed by a similar severe AS.

The mean structural collapse capacity for the CFRP, conventional steel, and hybrid repaired bridge columns under severe MS-severe AS from ensemble 1 record set (Fig. 12b–d) was 0.47, 0.48 and 0.43 g, respectively [i.e., 42.4, 45.5 and 30.3 % increase in the structural mean collapse capacity, respectively, compared to the unrepaired bridge (0.33 g)]. Similarly, the mean structural collapse capacity for the CFRP, conventional steel, and hybrid repaired bridge columns under the severe MS-severe AS from ensemble 2 record set (Fig. 12f, h) was 0.5, 0.46 and 0.5 g, respectively [i.e., 38.8, 27.7 and 38.8 % increase in the mean structural collapse capacity, respectively, compared to the unrepaired bridge (0.36 g)]. The obtained mean structural collapse capacities for the repaired bridge indicate the efficacy of confining repair jackets to be significant (up to 45.5 %) for the post-MS collapse capacity of the earthquake-damage bridge.

Similar results on significance/necessity of repair jackets application were found for the severe MS-moderate AS sequences. However, the decrease in the mean structural collapse capacity between the MS only and severe MS-moderate AS was less significant compared to the severe MS-severe AS case. It is due to the fact that the major/primary damage is accumulated during the higher intensity seismic event, either during the FS or AS, and not depending on the sequence of events. For this reason, repair jackets were less effective for the severe MS-moderate AS compared to severe MS-severe AS sequence. The repair jackets were still required for the severe MS-moderate AS sequence as lapped reinforcement bars are seismically deficient in the plastic hinge region. The results under severe MS-moderate AS seismic sequences confirm that the primary damage occurred under the severe MS and not the moderate AS, but numerous inelastic excursions are critical for lap-spliced columns even when subjected to minor or moderate AS. For instance, checking some of the steel reinforcement fibers stress–strain histories under single seismic event indicated the steel linear response up to proximity of yielding. However, same fiber under two seismic events exhibited highly nonlinear (post-yield) stress–strain response.

Comparison of Fig. 12a, e indicate that the mean structural collapse capacity of the original bridge under MS-only from ensemble 2 (near-fault) is smaller compared to ensemble 1 (far-fault) (0.69 g for near-fault records versus 0.83 g for far-fault records). The forward directivity effect and permanent displacement effect resulting in long period and large velocity pulse of near-fault ground motions (e.g. Fig. 11) have been addressed in previous studies.

The abovementioned results clearly indicate that the CFRP, steel and hybrid repair jackets were essential for post-MS collapse resilience of earthquake damaged bridge piers subjected to potential aftershocks of moderate or severe intensity. However, the repair jackets were most effective for the severe MS-severe AS scenario, and conversely were least effective for severe MS-moderate AS. Overall, the obtained results prove the efficacy of the studied repair jackets on post-MS seismic resilience of substandard RC bridge piers under aftershocks.

7.1 Fragility Analyses Results and Discussion

The fragility curves for the studied bridge in the repaired and unrepaired condition under severe MS-severe AS set of records from ensemble 1 (far-fault) and ensemble 2 (near-fault) for minor, moderate, extensive and collapse damage states are presented in Fig. 13a–h, respectively (Fig. 13a–d for ensemble 1 and Fig. 13e–h for ensemble 2). Similarly, the results under severe MS-moderate AS sequences from ensemble 1 and 2 for minor, moderate, extensive and collapse damage states are presented in Fig. 14a–h, respectively.

The obtained fragilities indicate that the fragility curves for the unrepaired scenario almost overlaps the repaired cases under the slight damage state, where the extent of damage is somewhat negligible (i.e., the damage state is cosmetic and repairable, and the onset of bar buckling did not occur). All the fragility curves irrespective of the repair jacket material, intensity of seismic sequences (i.e., severe MS-severe AS or severe MS-moderate AS) and earthquake type (i.e., far-fault and near-fault) indicate the increase of difference (shift) between fragilities of the unrepaired and repaired bridge as the damage state progresses. While Fig. 13a, e (similarly, Fig. 14a, e) clearly indicate that the fragility curves for the unrepaired bridge almost overlaps the repaired bridge under the minor damage state, the unrepaired bridge’s vulnerability is significantly larger than the repaired bridge for the extensive and collapse damage states (Figs. 13c, d, g, h, 14c, d, g, h). For instance, given the same probability of damage under the collapse damage state, the associated Sa of the unrepaired bridge is significantly less than that of the repaired bridge, irrespective of the repair jacket material. The fragilities accord to the obtained results from the IDA analyses results, where the repair jackets were more significant/critical for the severe MS-severe AS compared to the severe MS-moderate AS sequence. The fragilities clearly indicate the importance of repair jackets as the damage state increases. However, the influence of different intensity MS-AS sequences is clear through comparison of Figs. 13 versus 14. The obtained fragilities demonstrate the decrease of vulnerability for the unrepaired and repaired bridge under severe MS-moderate AS compared to severe MS-severe AS. It also suggests that the fragilities of unrepaired and repaired bridge are shifted more toward right under severe MS-moderate AS compared to severe MS-severe AS, which signals the lesser significance of repair jackets under moderate AS.

The fragilities also reveal that the steel jacketed bridge exhibits the highest vulnerability compared to CFRP and hybrid repair jackets at all damage states under both earthquake types. The increased vulnerability of the steel jacketed bridge over the other two repair interventions is due to the increased seismic action attracted by the thick steel jacketed bridge pier (inertia force of the dynamic system is increased due to thick jacket). For the conventional thick steel jacketing, the column cross section (deadweight) is increased, which in turn absorbs larger seismic actions (Priestley et al. 1996). On the other hand, the CFRP and hybrid jackets demonstrated comparable fragilities under all damage states and earthquake types. Although the hybrid jacket showed marginal decreased vulnerability compared to the CFRP jacket. Although the conventional steel jacket was shown to be the most vulnerable repair alternative, however, the steel jacket exhibited larger hysteresis loops compared to the CFRP jacket. Thus, fragility function for different repair interventions should be considered along with further investigation to better select the appropriate repair alternative. The reduced service stiffness of earthquake damaged RC bridge piers is an issue which steel jackets may be more advantageous over CFRP jackets, as they could provide higher service stiffness for the repaired RC pier (Youm et al. 2006).

Moreover, the fragility functions provide additional valuable information in regards to far-fault and near-fault records effects under different damage states. The obtained fragilities indicate that the vulnerability under near-fault records is larger than far-fault records for the minor and moderate damage states under severe MS-severe AS sequence (e.g. Fig. 13b vs. f). However, for collapse damage state, the fragilities under far-fault ground motions were slightly higher than those of the near-fault records (e.g. Fig. 13d vs. h). The obtained results indicate higher vulnerability for far-fault AS under collapse damage state for severe MS-severe AS. For minor and moderate damage states the near-fault record aftershocks are more prominent over far-fault aftershocks. For severe MS-moderate AS the near-fault records were more prominent. The obtained results suggest that maybe there is a relation between significance of earthquake type (far-fault or near-fault) and intensity of the seismic sequence considered (severe MS-severe AS or severe MS-moderate AS) at different damage states which requires further studies. Needless to mention, this observation on earthquake type effect at various damage states is limited only to the present study, and may not be generalized.