Expected seismic fragility of code-conforming RC moment resisting frames under twin seismic events

Journal Pre-proof Expected seismic fragility of code-conforming RC moment resisting frames under twin seismic events A. Kalantari, H. Roohbakhsh PII:

S2352-7102(19)31363-4

DOI:

https://doi.org/10.1016/j.jobe.2019.101098

Reference:

JOBE 101098

To appear in:

Journal of Building Engineering

Received Date: 25 July 2019 Revised Date:

27 November 2019

Accepted Date: 29 November 2019

Please cite this article as: A. Kalantari, H. Roohbakhsh, Expected seismic fragility of code-conforming RC moment resisting frames under twin seismic events, Journal of Building Engineering (2020), doi: https://doi.org/10.1016/j.jobe.2019.101098. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

Expected Seismic Fragility of Code-Conforming RC Moment Resisting Frames under Twin Seismic Events A. Kalantari1

H. Roohbakhsh2

Abstract Seismic design codes require buildings to be designed only for one seismic event, neglecting the neglecting the possibility of multiple earthquake events. However considerable damage and loss is observed due to aftershocks where buildings have been affected by the first event. The purpose of this research is to introduce fragility curves of code-conforming reinforced concrete moment resisting frames (RCMRFs) under aftershock. Three RC moment resisting frames of 4, 8 and 15 stories, are loaded and designed based on the latest three editions of the Iranian code of seismic design for buildings referred to as Standard No. 2800 (STD-2800). The nine designed frames are then numerically simulated in OpenSees software to perform nonlinear dynamic analysis. Twenty natural ground motion sequences, each including two seismic events, were selected from previous studies for the purpose of nonlinear incremental dynamic analysis. Maximum inter-story drift was employed as a damage index, to capture performance of the RC frames under the sequences. The accepted performance for the collapse level was taken from Iranian instructions for seismic rehabilitation of existing buildings, PBOPublication No. 360, 2007, which is similar to ASCE 41-13. Seismic fragility values are calculated for the buildings in the second event after being damaged in different first event intensity scenarios. Assuming a lognormal distribution for the failure probability function, corresponding values of median, µ, and standard deviation, β, for each case are calculated and discussed. Results indicate how the probability of failure in the seismic fragility curves may differ as a result of the effects of a first event scenario. It is also shown how updating the design criteria as well as the height of frames can affect fragility in a second event.

Key Words: Seismic sequence, nonlinear dynamic analysis, RC buildings, seismic performance, fragility curve

1)

International Institute of Earthquake Engineering and Seismology, No. 21, Arghavan St., North Dibajee, Farmanieh. Tehran-Iran P.O. Box: 19537-14453 [email protected]

2)

International Institute of Earthquake Engineering and Seismology, No. 21, Arghavan St., North Dibajee, Farmanieh. Tehran-Iran P.O. Box: 19537-14453 [email protected]

Acknowledgments The research described in this paper was supported by the Iran National Science Foundation under the Grant No. 96005525.

1

1 Introduction Seismic design or assessment of structures in current codes and regulations is usually performed only for one given event. A mainshock usually with a higher magnitude is often followed by several aftershocks. The sequence can continue for one year or longer. The events may have damaging effects on the structures. This is observed as reduction of strength or deterioration of stiffness which is accompanied by reduction of capacity. The reduction of strength or ductility of the structure in this condition can increase the vulnerability and fragility for the next events in a seismic sequence. The information on the effect of mainshock on seismic vulnerability and fragility of buildings can be valuable when assessment of building stocks under aftershocks. Previous studies on the subject have shown that aftershocks occurred after severe mainshocks make structures more vulnerable (Karsan et al. 1969) and may result in collapse of buildings which suffered damage by the mainshock (Amadio et al. 2003). Foreshocks with smaller magnitude than mainshock originate at or near the rupture region of mainshock (Reasenberg et al. 1989). For example, the Sarpol-e Zahab (Mw 7.3, 2017), Iran earthquake was preceded by a number of foreshocks, where the largest one was a magnitude 4.5 event 43 minutes before the mainshock. More than 900 aftershocks have been reported for this major earthquake (Farzanegan et al. 2017). A second (foreshock) event with a lower intensity than the design earthquake may result in collapse of the structure if the building has suffered damage due to the mainshock. The corresponding cumulative damage can also influence the assignment of macro-seismic intensity in seismic risk studies as shown by Grimaz and Malisan (2017) on a stock of masonry buildings taken from real cases. Several researches have been conducted to examine the effect of earthquake sequences on structures. Amadio et al. (2003) assessed the effect of repeated earthquakes on the response of SDOF systems with nonlinear behavior. The results of this research showed that multiple earthquakes can imply an accumulative damage and reduction in the behavior factor q. Based on the research the authors expressed that the modern codes should consider qfactor reduction and damage index increase in areas where historically affected by multiple earthquakes. Luco et al. (2004) developed a “calibrated” static approach for computing residual capacity for repeated events based on nonlinear dynamic analysis of case study buildings. This calibrated computation takes into account residual capacity for repeated events as either measured in field or expected state of damage based on nonlinear dynamic analysis. Li et al. (2007) investigated the effect of aftershock on steel moment frame structures. In the research the frame connections are modeled by a moment-rotation relationship. A simple probabilistic method for assessing the structural rapid evaluation was proposed. The results showed that as the initial damage ratio caused by the main shock increased, the aftershock damage estimates under the two assumptions became closer. Replication and randomization are two assumptions on aftershock characteristics in this research. Hatzigeorgiou et al. (2010) purposed a new method for ductility demand of SDOF systems under repeated earthquakes. In this method ductility demands and cumulative damage will be achieved using force reduction factor. As a result of this study the repeated earthquakes lead to more conservative force reduction factors in comparison with the “design earthquake”. Jalayer et al. (2011) employed an equivalent single-degree of freedom structure with cyclic stiffness degradation in order to evaluate the progressive damage caused by a sequence of aftershock events. Given the time history of the main-shock and the residual damage caused by it, they calculated the probability of exceeding a set of discrete limit states in a given interval of time. Ezzatfar et al. (2012) verified the performance of Mesh Reinforced Mortar application for retrofitting RC structures as a perused method in Turkish code under consecutive earthquakes. The study showed that is observed as result of no significant strength degradation during repeated events. Goda (2012) investigated the effect of aftershocks on ductility demand of inelastic SDOF systems using real and artificial mainshock-aftershock sequences. The result indicated the similarity of ductility demand for real and artificial sequence, so artificial sequences could be substituted for real sequence. Garcia (2012) examined the behavior of existing buildings under 92 real mainshock-aftershock sequences in Northridge and New Zealand earthquakes. The result of this research showed that: a) Inherent self-centering in degradation of stiffness is significant for constraining permanent displacement under strong aftershock, b) The response of structures for real and artificial sequences is not like each other and c) Predominant period of the aftershock has special influence on post mainshock response. Ates et al. (2013) represented a field observation of RC structures damage under consecutive earthquakes occurred in Van event Turkey.

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Raghunandan et al. (2015) investigated the vulnerability of modern RC structures in California subjected to mainshock-aftershock sequences. The RC frames were modeled as MDOF systems and based on incremental dynamic analysis, fragility curves were generated. The result of this study showed that the collapse fragility increase in aftershock if the structure subjected to a major mainshock. Faisal et al. (2013) conducted a comprehensive procedure to evaluate the influence of repeated earthquakes on storey ductility demand of RC structures. In this study 3,6,12 and 18 storey RC frames with 1.5, 2, 4 and 6 behavior factor were modeled. The result of this study showed that the repeated earthquake significantly increases ductility demand. For example, the average increment of ductility demand is 1.4 to 1.3 times when double or triple events are imposed. Li et al. (2014) investigated the collapse capacity of mainshock damaged steel structures in aftershock. In the research a four storey steel moment frame designed by code was analyzed. The results showed when the structure was subjected to a high intensity mainshock, the capacity reduced significantly and structure collapsed by aftershock with a small intensity in the following. The effects of mainshock records, fault type and spectral shape of aftershock on structural collapse capacity were evaluated in this study. Zhai C., Wen W., Li S., Xie L. (2015) studied the strength reduction factor of a single degree of freedom system with constant ductility performance subjected to the mainshock-aftershock sequence-type ground motions using recorded and artificial sequence-type ground motions. Abdelnaby (2018) conducted a research to investigate the behavior of RC structures under repeated earthquakes. In this study a tool was developed to model damage features of RC structures in numerical analysis subjected to repeated earthquake. A parametric study for estimating the behavior of RC moment frame is done in this study. Rinaldin et al. (2017) investigated the effect of repeated events on structures by different hysteretic behavior. SDOF systems were subjected to ten earthquake sequences. The results showed that reduction of behavior factor from 15% for bilinear with hardening and pivot hysteretic rules to 35% for elasto-plastic systems with high ductility should be adopted in design to increase the seismic resilience Moshref et al. (2017) performing incremental dynamic analysis (IDA) on several RC columns correlated the maximum and residual drift ratios. They also developed a method to compute the fragilities of mainshockdamaged columns by performing IDA with a sequence of mainshock–aftershock ground motions. Kashani et al. (2018) investigated the non-linear flexural behavior of RC columns including bar buckling and fatigue degradation. The results can be effectively employed in nonlinear modeling of RC structures. Salami et al. (2019) investigated the seismic behavior of RC structures using comprehensive modeling that considered low cyclic fatigue and inelastic buckling of longitudinal bars. A comprehensive ground motion data were selected by considering subduction earthquake, deep in slab and shallow crustal. A range of fragility curves were developed by accounting the effect of aftershocks. The results of this study showed that slight and moderate damage level are not affected by future aftershock however major aftershocks increase probability of failure up to 5% and 10% when structures are damaged under mainshocks in complete and extensive level respectively. Tolentino et al. (2018) proposed an approach to describe the evolution of damage that a structure could accumulate by the action of seismic sequences at the end of a time interval. They used a damage index which quantified the cumulative damage. The index considers both the demanded drift and ultimate drift. Using this proposal, they also obtained the structural reliability expressed it in terms of reliability functions. In spite of considerable previous research on this subject, the effects of changes in seismic design codes in different editions, on seismic fragility of buildings under a sequence of earthquakes needs to be investigated. This is important, especially when building stacks designed based on different editions of seismic codes are under assessment in a project. The need for development of seismic fragility functions for code-conforming buildings in Iran have been recently emphasized by Taherian and Kalantari (2019). The purpose of this research is to introduce fragility curves for aftershocks for code-conforming RC frames in Iran. The result may be employed immediately after a mainshock event when receiving the mainshock intensity information alarm in a rapid assessment system. This means the resulted functions will be required when still there is no clear data about the exact or certain damage state of the buildings yet. So the system, having the intensity distribution of the first event, will provide a rapid estimation of probable damage distribution under different mainshock intensity scenarios for the probable aftershocks. This study was planned to answer the following questions; (i) how the probability of failure of RCMRFs has changed with revising the STD-2800, (ii) What is the height effect on the results in question (i), (iii) if the frame is affected with a damaging first seismic event, how the probability of collapse may be affected

3

under s second seismic event if repair is not possible due to time and logistic limitations. (iv) how the seismic fragility of the code-conforming RCMRFs under aftershocks varies, when subjected to different mainshock intensity scenarios. Three RC frames of 4, 8 and 15 stories are loaded and designed based on the latest edition of the Iranian code of seismic design for buildings referred as Standard No. 2800 (STD-2800). The frames are then simulated in OpenSees software to perform nonlinear dynamic analysis. Twenty natural ground motions sequences each including two seismic events were selected from previous studies and employed for the purpose of nonlinear incremental dynamic analysis. Maximum inter-story drift was employed as a damage index, to capture performance of the RC frames under the sequences. The accepted performance for the collapse level was taken from Iranian instructions for seismic rehabilitation of existing buildings (PBO-Publication No. 360, 2007) which is similar to ASCE 41-13. Assuming a log-normal distribution for the fragility function, values of median, µ, and standard deviation, β, for each case are calculated and discussed.

2 Iranian code of practice for seismic design of buildings 2nd edition of STD-2800 has been approved by government in 1999. There were more safety level and technical points in this edition comparing with the first edition. The 3rd and the 4th edition of the code have been applied since 2000 and 2014, respectively. The latest edition was modified in different parts such as updating the relative seismic hazard map, modification of design response spectrum, modifying the classification of soil profile, modifying and updating the building behavior factor, and etc. Based on the document, the horizontal seismic load acting on structures should be determined by either equivalent static or dynamic procedure. Equivalent static procedure can be used for specific structures such as regular structures shorter than 50 meters in height from base and irregular structures with less than 5 storey or 18m in height from the base level where the overall dynamic behavior can be predicted based on the characteristics of the first mode. In this study the equivalent static procedure is used to calculate horizontal seismic load and design the structure. In equivalent static procedure the horizontal seismic load in each direction is calculated by Eq. 1.

V = CW

(1)

Where V is the base shear force and W is the total seismic weight of building including dead load and a percentage of live and snow load. C is the seismic coefficient that is calculated by Eq. 2.

C=

ABI R

(2)

Here A is the ratio of seismic acceleration to gravity acceleration in terms of g, B is the building response factor determined from the design response spectrum, R and I stand for behavior and importance factor, respectively. In this study the last three editions of Iranian seismic code are considered for designing RC structures. As mentioned previously the editions of the STD-2800 are mainly different in determining R factor as well as response factor B for buildings. This may lead to different seismic design demands on the structure consequently. Some of these differences are summarized in Table 1 when defining B factor. As shown, the factor is express by different equations in each edition of the standard. 2nd edition

= . (

)

Table 1. Expression of B factor in different editions of STD-2800 3rd edition 4th edition = 1+ 0 ≤ ≤ ! + (! − ! + 1) # $ 0 < < = 1 + ≤ ≤ = ! + 1 < < ( + 1)

(! + 1) #

≥

$ >

Here T is the fundamental period of vibration of the structure and follows simplified criteria in each edition of the STD-2800. , and S are determined based on the soil type and level of seismicity and N is the spectrum modification factor. In 4th edition of the standard, the behavior factor (R) is represented based on Strength Design method but in 3rd and 2nd editions, the parameter was determined based on the Allowable Stress Design method. To investigate how the regulations in different editions of the STD-2800 have affected the structural performance, the RCMRFs are designed based on seismic loads resulted from each of the three latest edition of the standard and the fragility parameters are calculated for each case as explained in the following. The results are then presented and discussed. 4

3 Representative Frames Three sets of RCMRFs with 4, 8 and 15 stories are designed using the latest three editions of STD-2800. Considered buildings are assumed to be residential with a similar importance factor of I=1.0 for three editions. The structure is taken to be located in a very high seismic zone (A=0.35 for all three editions). Soil type II is considered for the site assuming Vs30= 375~750 m/s. B factor is calculated based on soil condition and following the criteria included in each edition of STD-2800 and introduced in Table 1. . The lateral bearing system is assumed to be a special moment resisting frame (R=10, 10 and 7.5 in 2nd, 3rd and 4th edition of STD-2800, respectively). The fundamental period of the structures are calculated following the criteria presented in each edition Assuming properties of ST-37 for the reinforcement and concrete specific strength in 28 days as fc=280 kg/cm2, the designed beam and column section specifications for each of the nine resulted frames have been introduced in Table 2. A three-digit code is used to refer each frame of which the first two digits refer to the number of stories and the third digit introduces the edition of code applied for design. Table 2. Section properties for the nine RCMRFs Column Beam

153

154

Transverse Rebar

152

Longitudinal Rebar (top & bot.)

084

Section

083

Transverse Rebar

082

Longitudinal Rebar

044

Section

043

Story 1-2 Story 3-4 Story 1-2 Story 3-4 Story 1-2 Story 3-4 Story 1-2 Story 3-5 Story 6-8 Story 1-2 Story 3-5

35×35 30×30 40×40 35×35 45×45 35×35 45×45 40×40 35×35 45×45 40×40

8φ18 8φ16 12φ20 8φ18 16φ22 8φ22 12φ20 8φ18 8φ16 12φ22 8φ20

Φ10@20 Φ10@20 Φ[email protected] Φ10@20 Φ[email protected] Φ[email protected] Φ[email protected] Φ[email protected] Φ[email protected] Φ10@15 Φ10@15

25×25 25×25 25×25 25×25 35×35 35×35 30×30 30×30 30×30 35×35 35×35

3φ14 3φ14 3φ14 3φ14 4φ20 4φ20 3φ16 3φ16 3φ16 3φ16 3φ16

Φ8@20 Φ8@20 Φ[email protected] Φ[email protected] Φ[email protected] Φ[email protected] Φ[email protected] Φ[email protected] Φ[email protected] Φ[email protected] Φ[email protected]

Story 6-8 Story 1-2 Story 3-5 Story 6-8 Story 1-3 Story 4-9 Story 10-15 Story 1-3 Story 4-9 Story 10-15 Story 1-3 Story 4-9 Story 10-15

35×35 50×50 40×40 35×35 60×60 50×50 35×35 60×60 50×50 35×35 60×60 50×50 40×40

8φ18 12φ22 8φ20 8φ18 16φ22 12φ22 12φ18 20φ22 12φ22 12φ20 20φ24 12φ22 12φ20

Φ10@15 Φ10@15 Φ10@15 Φ10@15 Φ[email protected] Φ[email protected] Φ[email protected] Φ[email protected] Φ[email protected] Φ[email protected] Φ10@15 Φ10@15 Φ10@15

35×35 35×35 35×35 35×35 35×35 35×35 35×35 35×35 35×35 35×35 45×45 45×45 45×45

3φ16 3φ16 3φ16 3φ16 3φ20 3φ20 3φ20 4φ20 4φ20 4φ20 4φ20 4φ20 4φ20

Φ[email protected] Φ10@15 Φ10@15 Φ10@15 Φ[email protected] Φ[email protected] Φ[email protected] Φ[email protected] Φ[email protected] Φ[email protected] Φ10@15 Φ10@15 Φ10@15

Story

Frame 042

4 Modeling

5

The structures were modeled as 2D RC frames of four spans. A schematic illustration of the frames is shown in Fig. 1.

Fig. 1 Schematic of a N-story 2D frame The Open System for Earthquake Engineering Simulation (OpenSees) software is employed to analyze the structural response of RC frames under earthquake sequences (McKenna et al. 2011). The models of the RCMRFs were developed in the software and dynamic analyses were performed. In the models, the flexural behavior of beams and columns was modeled as distributed plasticity with sufficient number of fibers in the section. This resulted in 400 fiber elements in the core and about 80 elements for concrete cover. Damping ratio of 5% Rayleigh damping and P-delta effect were considered in models. The nonlinear beam-column elements were used to model the frame columns and beams. This element is force-based with distributed plasticity. The element is subdivided by five integration points. Ignoring the soilstructure interaction effects, the lower node of the column is fixed and has no rotation and displacement. Reinforcement slippage of longitudinal bars at joints has not been considered in this research. The schematic finite element shape of RC members with fiber section distribution is demonstrated in Fig. 2. Each section is divided into three fiber parts: concrete core, concrete cover and steel reinforcement using the material properties introduced in the following.

Fig. 2 fiber details of RC beam-column components

5 Material Properties In this study, the confined core concrete of the component was modeled using uniaxial Popovic’s concrete material object with degraded linear unloading-reloading stiffness according to the work of Karsan et al. (1969). The confined concrete (core) and unconfined concrete (cover) are defined using the Concrete04 material within OpenSees software, which assumes that the concrete material has no tensile strength. The longitudinal reinforcement was modeled with a bi-linear stress-strain relation that accounts for strain hardening in OpenSees using the Steel02 material. This model does not consider failure of bars in analyses. MinMax material is used to model failure of longitudinal reinforcements. The yield strength of rebar is assumed to be 400 MPa and the slope of strain hardening section is assumed 0.01 of the initial slope. For unconfined concrete with 28Mpa compressive strength, a strain of 0.002 under the maximum stress and a strain of 0.005 as a yield value were assumed. The concrete model developed by Mander et al. (1988) is used to

6

simulate the confined concrete stress strain behavior. Based on this model, the behavior of confined concrete depends on section confinement. The concrete modulus of elasticity, Ec, is calculated by Eq. 3 for the normal weight concrete (ACI 318-08 2008). '( = 4700+,(-

(3)

Where ,(- is concrete compressive strength in Mpa.

6 Model Verification To verify the numerical models developed in this research, a valid experimental study on reinforce concrete columns has been employed. Wehbe (1998) conducted an experimental research on four rectangular RC columns with moderate confinement to investigate the ductility of each member. Confinement ratio and axial force were different in each column. Column A1 has been selected to verify the numerical modeling. The A1 specimen is a 2050 mm height column with a cross section of 610*380 mm. The member is reinforced by 18 φ

19 longitudinal bars and φ 6&10 @ 11 mm transvers rebar. The yield strength of steel and compressive strength of concrete is 414 MPa and 27.6 MPa, respectively. The initial axial load for A1 specimen is 615 kN. In experimental test the specimen is subjected to lateral load. The yield and ultimate lateral displacement and ductility of the specimen are reported. In this study the A1 specimen was modelled with FE and subjected to lateral load. The calculated capacity curve of A1 specimen is illustrated in Fig. 3

Fig 3. Capacity curve of column A1 The yielding of section is reported as the first longitudinal bar yields. Column ultimate displacement is reported as onset of occurrence of one of the followings: - Concrete core crushing, - Longitudinal bar rupturing and %20 decrease in column capacity curve. Table 3 presents a comparison between the experimental results and the results obtained from numerical model in the current study. Table 3 comparison of calculated result with experimental test Yield Displacement (mm) Current Wehbe A1 Diff. % study 23 18.45 19.80

Ultimate Displacement (mm) Current Wehbe A1 Diff. % study 121 114.8 5.10

Wehbe A1 5.3

Ductility Current study 6.2

Diff. % 17.4

As mentioned previously MinMax material model is used to simulate the degradation of bars after reaching ultimate strain. MinMax material model fails a predefined material when reaches below or above certain threshold values. Fig. 4 shows the stress-strain curve of longitudinal tensile bar in A1 model. It is observed that exceeding the tensile bar strain above the threshold level the stress fails to zero.

7

Stress (MPa)

Fig. 4 stress-strain cure of reinforcement

7 Ground Motions For the earthquake sequences, the records could be selected as synthesized or as-recorded for seismic evaluation (Li et al. (2014) or Abdelnaby (2018)). Here, for the purpose of nonlinear dynamic analysis under a sequence of two events, a set of twenty natural ground motion sequences was selected. Details of these sequences are summarized in Table 4. Table 4 List of ground motion records First event PGA (g) Date

Second event PGA (g) Date

No.

Event Name

1

China: Northwest China

0.273

1997-04-05

0.144

1997-04-06

2

Italy: Emilia Romagna

0.259

2012-05-20

0.294

2012-05-29

3

Italy: Friuli

0.190

1976-05-06

0.328

1976-09-11

4

Italy: Nocera Umbra

0.491

1997-09-26

0.502

1997-10-06

5

Japan: Fukushima

0.505

2011-04-11

0.127

2011-04-11

6

Japan: Niigata

0.547

2004-10-23

0.553

2004-10-23

7

USA: Mammoth Lakes

0.410

1980-05-25

0.161

1980-05-25

8

Chile: Valparaiso

0.712

1985-03-03

0.190

1985-03-04

9

New Zealand: Christchurch

0.334

2011-02-22

0.222

2011-06-13

10

New Zealand: Weber

0.199

1990-02-19

0.248

1990-05-13

11

Armenia: Spitak

0.191

1988-12-07

0.098

1988-12-07

12

Italy: Irpinia

0.316

1980-11-23

0.033

1980-11-23

13

Taiwan: Chi Chi

1.026

1999-09-20

0.150

1999-09-25

14

India: Chamoli

0.359

1999-03-28

0.064

1999-03-28

15

Iran:Varzaghan

0.426

2012-08-11

0.531

2012-08-15

16

USA: Whittier Narrows

0.381

1987-10-01

0.216

1987-10-04

17

Turky: Duzce

0.293

1999-11-12

0.204

1999-11-12

18

USA: Chalfant Valley

0.402

1986-07-21

0.432

1986-07-31

19

New Zealand: Edgecumbe

0.436

1987-03-02

0.109

1987-03-02

20

Greece: Kalamata

0.296

1986-09-13

0.152

1986-09-13

8 Incremental Dynamic Analyses - Consideration of Sequence Effects For evaluation of behavior of RC frames under repeated earthquakes, an incremental dynamic analysis (IDA) procedure is defined (Vamvatsikos et al. 2002). In the previous research different intensity levels have been employed for performing IDA analysis such as peak ground velocity (PGV), peak ground acceleration (PGA), peak ground displacement (PGD) and etc. Daneshjoo et al (2015) showed that some spectral intensity measures are more practical than PGA. Bojórquez et al. (2017) investigated the efficiency of the first mode spectral acceleration in comparison with new nonlinear intensity measure (INP) and advantages of INP are reported. In current research because of the final purpose of development of the fragility functions, PGA has been considered as the seismic intensity measure in the IDA. The RC frames are subjected to a series of twenty 8

Acceleration (g)

earthquake sequences. Fig. 5 demonstrates a sequence of two events of Niigata, Japan, 2004 event. Duration of 20s is considered after the first event and before the second to represent the state in which structure comes to the rest after ending the first event while preserving the damage effects on the model.

Fig. 5 A repeated event applied to analyses (Niigata, Japan, 2004) For the purpose of this research, incremental dynamic analyses were performed using 20 ground motion sequences on 9 RC moment frames. To assess the effect of first event on the probability of collapse of structure subjected to a second event, three PGA scenarios of 0.4g, 0.7g and 1.0g are considered for the first event. The second-event analysis is repeated by scaling the corresponding aftershock record applied to the structure affected by the first. The IDA using the second event continues till the structural collapse limit state is achieved. The peak ground acceleration of the second event that caused structural collapse, quantifies the sequence intensity for collapse.

9 IDA Analysis Result 9.1 Limit states As mentioned, maximum inter-story drift was selected to represent the damage state of RC moment frames in IDA analysis. The maximum inter-story drift ratios for RC structures are 2% and 4% for life safety and collapse prevention, respectively (ASCE 41-13 (2013) and PBO-Publication No. 360 (2007)). 9.2 IDA Curves The IDA analyses are performed to evaluate the probability of collapse and estimate the collapse capacity of the structure which experienced the first event of the sequence with different PGA scenarios in first event. As mentioned previously, the RC frames are analyzed under three different intensities of the first event. Fig. 6 illustrates the IDA results for the 4 storey RC frame, designed based on the second edition of the code of practice (042) and affected by three mainshock scenarios. To compare the results, the median of the IDA curves is also depicted in solid line in each figure. It is observed that by increasing the intensity of the first event, the PGA intensity corresponding to collapse limit state – referred as collapse capacity - in the second event will decrease. For example, the corresponding intensity levels for 2% drift are 1.11g, 0.62g and 0.22g when the PGA of the mainshock ground motion is scaled to 0.4g, 0.7g and 1.0g respectively.

9

(a)

(b)

(c) Fig. 6 IDA results for Frame 042 subjected to repeated events, with PGA of the first event = a) 0.4g, b) 0.7g and c) 1.0g The corresponding values of median of IDA results in the second event for Frame 042 at the onset of the two performance levels are summarized in Table 5. It is observed that by increasing the mainshock PGA intensity level, to what extent the PGA of second event for the onset of life safety and collapse prevention performance levels may decrease. Table 5 PGA Median of IDA results for Frame 042 at the onset of the two performance levels PGA(g) First event intensity (PGA in g) Collapse Life safety prevention 1.11 2.18 0.4 0.62 1.77 0.7 0.22 1.65 1.0

10 Fragility Curves A fragility function represents the probability of exceedance of a selected Engineering Demand Parameter (EDP) from a selected structural limit state (LS) when subjected to a ground motion intensity measure (IM). Mathematically, seismic fragility function is illustrated by the following expression: ./0123245 = 678!|:; = 5<

(4)

Where IM and LS are already described and y is a specific IM level. Probability of failure is also calculated using the following equation: => = 67 ≥ 1< ? @

(5)

Where D and C are drift demand and capacity of the structure, respectively. After estimation of the dispersion, which is a conditional value on the earthquake intensity, assuming a log normal function for the distribution, the fragility function can be estimated by using Eq. 6: 6(A|:; = B) = Φ(

DEFGH I

)

(6)

Where P(C | IM=x) is the probability that a ground motion with IM = x will cause the demand parameter in the model to exceed the limit state C, Φ is the log normal cumulative distribution function (CDF) and β is the standard deviation of the natural logarithm of (IM). Fig. 8 shows the steps to develop fragility curve in the current study.

10

Fig. 8 Procedure of development of fragility curves in current study

Probability of Failure

Probability of Failure

In this procedure, the frame is assumed to experience the effects of the first event. As mentioned, three scenarios for the first event of the sequences with three PGA intensity levels of 0.4g, 0.7g and 1.0g are considered. The IDA analysis is then performed on the frame using the corresponding second event in each sequence. Based on the IDA results for the earthquake sequences, the PGA intensity of the second event corresponding to a drift ratio of %4 (collapse level) is calculated. This is considered as the capacity of the frame affected by the first excitation and will be referred hereafter as the collapse capacity. It is assumed that the values corresponding to collapse capacity are distributed log-normally. So the Median and standard deviation of PGA corresponding to collapse are employed to define the fragility functions. Fig. 9 illustrates the resulted fragility curves for collapse limit state calculated for 4, 8 and 15 storey RCMRFs. As shown, each Figure contains three plots illustrating the fragility curve, corresponding to the three mainshock scenarios.

(b) Frame 043

Probability of Failure

Probability of Failure

(a) Frame 042

(c) Frame 044

(d) Frame 082

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Probability of Failure

Probability of Failure

(f) Frame 084

Probability of Failure

Probability of Failure

(e) Frame 083

(h) Frame 153

Probability of Failure

(g) Frame 152

(i) Frame 154 Fig. 9 Fragility curves for the case of collapse prevention level as failure It is observed how occurrence of a mainshock increases the probability of failure of the frame during a second event. Frames affected by larger intensity level of mainshock, have larger probability of failure. As an example, the fragility values of RC frames for 1.0g intensity level of aftershock were extracted from the Fig. 9. The probability of failure of the 4 storey frame designed based on the 4th edition of the code when affected by 1.0g mainshock is 70%. The value is just 10% for the case affected by the mainshock events with an intensity of 0.4g. The median, µ, and standard deviation, β of the log normal distribution function representative for the calculated fragility values are shown in Table 6 below where PGA is the peak ground acceleration of the first event. The Table presents the values for each of the 4, 8 and 15 storey frames designed based on the second, third and fourth edition of SDT-2800 referred in the Table as 2nd E., 3rd E. and 4th E., respectively.

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Table 6 Median and standard deviation values for all frames in collapse under repeated event PGA=0.4g PGA=0.7g PGA=1.0g µ β µ β µ β 2nd E. 1.24 0.89 0.98 0.91 0.85 0.93 4 3rd E. 1.11 0.77 0.83 0.82 0.77 0.92 storey 4th E. 1.89 0.81 1.79 0.92 1.27 1.04 2nd E. 1.73 0.99 1.67 1.07 1.45 1.17 8 3rd E. 1.74 0.94 1.64 0.98 1.65 1.09 storey 4th E. 1.75 0.94 1.69 1.01 1.66 1.11 2nd E. 1.71 1.00 1.65 1.02 1.42 1.05 15 3rd E. 1.73 0.99 1.69 1.03 1.49 1.07 storey 4th E. 1.69 0.96 1.69 1.03 1.50 1.06

Based on the results demonstrated in Table 6, the effects of different editions of STD-2800, height of the frames and different first event scenarios may be interpreted as follows: (i) Effect of revising of the STD-2800 on fragility values As shown values of the median of the fragility function, µ, for the four storey frames 042, 043 and 044 when affected by a first event with a PGA intensity of 0.7g are 0.98g, 0.83g and 1.79g, respectively. This indicates that although the 4th edition of design code increased the median as much as 0.81g relative to the 2nd edition, a reduction of 0.15g is observed when the 2nd edition of code has been updated to the 3rd edition. (ii) Effect of height of the frames on the fragility functions The effect of height of frames on median of the fragility function, µ, is also reflected in Table 6. As shown, in 8 and 15 storey frames affected by a first event with PGA of 0.7g, the median for different design editions of STD-2800 varies between 1.64g and 1.69g. However there is a notable difference between the results for four story frames designed based on different editions of the code and experienced a first event with a PGA of 0.7g (iii) Effect of the first event on the fragility As evident in the Table 6, increasing the PGA intensity level of the first event, results in reduction of median of the fragility function, µ. For example, the 15 storey frame designed based on the 2nd edition of STD-2800 and experienced the first event with PGA values of 0.4g, 0.7g and 1.0g, the median values are obtained as 1.71g, 1.65g and 1.42g respectively.

10 Conclusions Structures in seismically prone regions may be exposed to repeated earthquakes. The short duration between such events often make it difficult or even impossible to repair the probable damage occurred in the mainshock. This may lead to exceeding the probability of failure (collapse) of the structure from expected limits when subjected to aftershocks. In spite of considerable previous research on the aftershock effects on seismic fragility of RC moment frames, the effects of changes in seismic design codes in different editions, on seismic fragility of buildings under a sequence of earthquakes is needed to be investigated. This is important, especially when building stacks designed based on different editions of seismic codes are under assessment in a project. In this research, three sets of RC frames of 4, 8 and 15 stories have been modeled and analyzed for different seismic sequence conditions. There are three RC frames in each set designed based on the 2nd, 3rd and 4th edition of Iranian code of practice for seismic design. Seismic sequences were selected and applied to the numerical model. Inter-story drift as an engineering demand parameter was calculated during numerical analysis of the frames. Fragility curves have been calculated for multi-excitation cases. The followings are the main conclusion of the study: -

Fragility functions for the buildings under aftershock effects were developed when considering three different mainshock scenarios.

-

The median of the IDA curves was investigated for Frame 042 to study the effect of the intensity of the first event on the performance of the frame during the second event. It was observed how by increasing the intensity of the first event, the collapse capacity in the second event may decrease. For example, the median values of PGA corresponding to 2% maximum inter-storey drift (as life safety level) are 1.11g, 13

0.62g and 0.22g when the PGA of the mainshock ground motion is scaled to 0.4g, 0.7g and 1.0g respectively. -

Based on the aftershock IDA results for maximum interstory drift for all frames, the aftershock fragility curves were generated. As for fragility parameters also, increasing the PGA intensity level of the first event, resulted in reduction of median of the fragility function, µ. For example, the 15 storey frame designed based on the 2nd edition of STD-2800 and experienced the first event with PGA values of 0.4g, 0.7g and 1.0g, the median values are obtained as 1.71g, 1.65g and 1.42g respectively.

-

It was shown how 4th edition of STD-2800 could enhance expected performance of the RCMRFs. As an example, the median of the fragility function, µ, for Frame 044 when affected by a first event with an intensity of 0.7g is 1.79g, which is larger than 0.98g and 0.83g for Frame 042 and Frame 043, respectively. It was also discussed that although the 4th edition of design code increased the median as much as 0.81g relative to the 2nd edition, a reduction of 0.15g was observed when the 2nd edition of code has been updated to the 3rd edition.

-

The effect of height of frames on median of the fragility function, µ, was also reflected in results.

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Kashani, M. M., Salami, M. R., Goda, K., & Alexander, N. A. (2018) Non-linear flexural behavior of RC columns including bar buckling and fatigue degradation. Magazine of Concrete Research, 70(5), 231247. Li Q, Ellingwood BR (2007) Performance evaluation and damage assessment of steel frame buildings under main shock–aftershock earthquake sequences. Earthquake engineering & structural dynamics 36(3) 405427. Li Y, Song R, Van De Lindt JW (2014) Collapse fragility of steel structures subjected to earthquake mainshockaftershock sequences. Journal of Structural Engineering 140(12) 04014095. Luco N, Bazzurro P, Cornell CA (2004) Dynamic versus static computation of the residual capacity of a mainshock-damaged building to withstand an aftershock. 13th World Conference on Earthquake Engineering. Mander JB, Priestley MJ, Park R (1988) Theoretical stress-strain model for confined concrete. Journal of structural engineering 114(8) 1804-1826. McKenna F, Mazzoni S, Fenves GL (2011) Open System for Earthquake Engineering Simulation (OpenSees) Software Version 2.2.0. University of California, Berkeley, CA. Available from http://opensees. berkeley. edu. Moshref A, Khanmohammadi M, Tehranizadeh M (2016) Assessment of the seismic capacity of mainshock damaged reinforced concrete columns. Bull Earthquake Eng. No S. (2005) 2800 Iranian Code of Practice for Seismic Resistant Design of Buildings. Third Revision, Building and Housing Research Center, Tehran. No S. (2007) 360 Instruction for Seismic Rehabilitation of Existing Buildings. Building and Housing Research Center, Tehran. PBO Planning and Management Organization of Iran (2007) Iranian instructions for seismic rehabilitation of existing buildings Publication No. 360. Management and Planning Organization of Iran Raghunandan M, Liel AB, Luco N (2015) Aftershock collapse vulnerability assessment of reinforced concrete frame structures. Earthquake Engineering & Structural Dynamics 44(3) 419-439. Reasenberg PA, Jones LM (1989) Earthquake hazard after a mainshock in California. Science 243(4895) 11731176. Rinaldin G, Amadio C, Fragiacomo M (2017) Effects of seismic sequences on structures with hysteretic or damped dissipative behaviour. Soil Dynamics and Earthquake Engineering 97 205-215. Ruiz-García J (2012) Issues on the response of existing buildings under mainshock–aftershock seismic sequences. 15th World conference on earthquake engineering. Salami, M. R., Kashani, M. M., & Goda, K. (2019). Influence of advanced structural modeling technique, mainshock-aftershock sequences, and ground-motion types on seismic fragility of low-rise RC structures. Soil Dynamics and Earthquake Engineering, 117, 263-279. Taherian, A R, Kalantari, A (2019) Risk Targeted Seismic Design Maps for Iran J Seismology. https://doi.org/10.1007/s10950-019-09867-6. Tolentino D, Flores R B, Alamilla J L (2018) Probabilistic assessment of structures considering the effect of cumulative damage under seismic sequences. Bulletin of Earthquake Engineering 16(5) pp. 2119–2132. Vamvatsikos D, Cornell CA (2002) Incremental Dynamic Analysis. Earthquake Engineering & Structural Dynamics pp. 31(3) pp.491-514. Wehbe, N. (1998). EERI annual student paper award confinement of rectangular bridge columns in moderate seismic area. Earthquake spectra, 14(2), 397-406. Zhai C., Wen W., Li S., Xie L. (2015) The ductility-based strength reduction factor for the mainshock– aftershock sequence-type ground motions, Bulletin of Earthquake Engineering 13(10).

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Highlights: • Probability of failure under an aftershock may significantly increase if the structure was already affected by a mainshock. • There is an increase in maximum curvature of RC column up to 58% subjected to a mainshock-aftershock sequence in comparison with a single event.

• IDA results of the aftershock records for RC frame affected by a mainshock with specific intensities indicates the decrease of MAIC when the mainshock intensity increases.

• Probability of failure of frames designed based on the latest edition of the Iranian code is less in comparison with those of designed according former editions.

Respected Editor of Journal of Building Engineering Hereby the authors declare that they have no financial or other conflict of interest. With regards

Author statement Afshin Kalantari: Conceptualization; Funding acquisition; Investigation; Methodology; Project administration; Resources; Supervision; Validation; Writing – review & editing.

Hamed Roohbakhsh: Data curation; Formal analysis; Software; Supervision; Validation; Visualization; Roles/Writing – original draft;