Fragility analysis of a containment structure under far-fault and near-fault seismic sequences considering post-mainshock damage states

Engineering Structures 198 (2019) 109511

Contents lists available at ScienceDirect

Engineering Structures journal homepage: www.elsevier.com/locate/engstruct

Fragility analysis of a containment structure under far-fault and near-fault seismic sequences considering post-mainshock damage states

T

⁎

Xu Baoa,b,c, Mao-Hua Zhangd, , Chang-Hai Zhaia,b,c a

School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China c Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150090, China d School of Civil Engineering, Northeast Forestry University, Harbin 150040, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Containment structure Fragility analysis Seismic sequence Post-mainshock damage state Near-fault sequence Far-fault sequence Copula technique

Due to the unique characteristics of near-fault ground motions with an intense pulse, near-fault seismic sequences have the potential to cause more severe damage to structures compared to far-fault seismic sequences. This study focuses on quantitatively comparing the seismic response and fragility of a containment structure subjected to near-fault and far-fault seismic sequences. For this purpose, both as-recorded and artificial seismic sequences are used as input to conduct the nonlinear dynamic analysis. The effect of fault types of aftershocks on a mainshock-damaged containment is investigated in terms of the global response and local damage, respectively. Seismic demands on secondary systems are also studied through floor response spectra considering postmainshock damage states. To evaluate the influence of near-fault and far-fault seismic sequences on the fragility of a containment structure, a new methodology is used to generate fragility curves, which can effectively consider the effect of post-mainshock damage states when computing the exceedance probability. The results show that near-fault seismic sequences can cause greater dynamic responses of a containment than far-fault ground motions, and the fragility evaluation without considering near-fault seismic records can overestimate the safety margin of a containment structure.

1. Introduction Man-made structures located in earthquake-prone regions are exposed not only to a single seismic event, but also to a seismic sequence. During the Tohoku earthquake [1], the Fukushima Daiichi nuclear power station suffered the seismic sequence. The nuclear structures were damaged by the mainshock and corresponding secondary disaster, and then these damaged structures were subjected to the following aftershocks. It is impossible to repair the damaged structures before the subsequent aftershocks occurred, because the time interval between mainshock and aftershock is too short, which may intensify the structural damage caused by the mainshock during aftershock events. So it is necessary to check the safety of the nuclear structures under seismic sequences. Many researchers studied the impact of seismic sequences on various types of structures, such as frame [2], dam [3], bridge [4] and steel structure [5], but the related research for nuclear structures is quite limited. As the final safety barrier of systems, the containment structure plays an irreplaceable role in protecting nuclear systems. The

⁎

reliability of a containment structure will affect the safety margin of a nuclear system directly. Some scholars [6–8] have studied the dynamic response and seismic capacity of containment structures under earthquake excitations. Although great progress has been made in the seismic design and evaluation of containment structures, one limitation of past studies is that most researchers performed the nonlinear seismic analysis or seismic evaluation of containment structures considering only one single earthquake excitation, which obviously underestimate the shaking effect of aftershocks. Near-fault earthquakes usually differ from ground motions recorded away from the source location due to the unique characteristics of large velocity and displacement pulses. The intense pulses are linked to the forward directivity effect generating when the fault rupture propagates towards the site at a speed close to the shear wave velocity. The consequence is that structures are exposed to most of the input energy from the rupture at the beginning of an earthquake [9]. For the same intensity and duration of ground motions, near-fault seismic excitations with an intense pulse can induce higher seismic demands on buildings

Corresponding author. E-mail address: [email protected] (M.-H. Zhang).

https://doi.org/10.1016/j.engstruct.2019.109511 Received 27 February 2019; Received in revised form 2 July 2019; Accepted 6 August 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Fig. 1. Cutaway view of the containment structure.

new seismic data, it is necessary to carry out the seismic safety assessment for existing nuclear power plants. Thus, more research on the fragility analysis under new seismic conditions (i.e., near-fault seismic sequences) is warranted to check the seismic safety margin of containment structures. This paper mainly conducts a comparative research on the dynamic response and safety assessment of a containment structure under nearfault and far-fault mainshock-aftershock sequences. A set of as-record and artificial seismic sequences is selected to conduct the nonlinear analysis of a containment structure. According to the dynamic analysis, the values of peak displacement, local cracking and damage dissipated energy are analyzed to study the fault type effect on a mainshock-damaged containment structure. Seismic demands on secondary systems are also studied through the floor response spectra considering postmainshock damage states. Finally, the fragility analysis of a containment structure under different types of seismic sequences is performed using a new methodology, which can directly incorporate the effect of post-mainshock damage states on the seismic capacity into the computation of exceedance probability. This study provides quantitative information on the impact of near-fault and far-fault seismic sequences on containment structures, which is a valuable reference for the safety margin assessment of nuclear power plants.

than far-fault ground motions [10]. Much work was conducted to identify the seismic response of many civil engineering structures under near-fault seismic excitations [11–13]. It is worth noting that although near-fault ground motions have larger acceleration spectrum values during the medium and long period [9], they can also cause greater structural damage on short-period structures like gravity dams compared with far-field ground motions [14]. Because of the limitation of exploration technology, several risk factors were not taken into account at the design stage of nuclear power plants. For example, some fault segments were discovered near the site of the Jinshan nuclear power plant in Taiwan, and the Quaternary fault system was located near the nuclear power plant in Korea [8,15]. However, the impact of characteristics of ground motions like intense pulses on structures was not considered in the design of nuclear power plants. In addition, the epicenter of a mainshock is frequently different from locations of subsequent aftershocks in the same earthquake event [16]. During the Northridge earthquake in 1994, the near-fault mainshock and aftershocks were recorded, while the far-fault mainshock following by nearfault aftershocks were measured in the Canterbury earthquake event [17]. When the structure sustains damage caused by a mainshock, nearfault aftershocks may further intensify the structural damage, which can lead to more loss of property and life. Therefore, there is an urgent need to study the impact of near-fault aftershocks on the seismic response of mainshock-damaged containment structures. The fragility analysis is an effective tool for conducting the safety assessment of structures, and the fragility evaluation of nuclear structures has been widely conducted by many researchers. Choi et al. [8] performed the nonlinear dynamic analysis to estimate the fragility of CANDU containment structure. Cho and Joe [18] introduced an improved method to conduct the fragility analysis of nuclear structures based on seismic records in Korea. Mandal et al. [19] carried out the fragility analysis of containment buildings and exploited these advantages provided by the IDA-based approaches. Perotti et al. [20] made use of the Response Surface Methodology and Monte Carlo approach to estimate the failure probability of base-isolated nuclear power plant buildings. Nakamura et al. [21] used a high accuracy model to evaluate the fragility of nuclear buildings considering soilstructure interaction and basemat uplift behavior. However, these studies mainly focused on the fragility analysis under single ground motions without considering seismic sequences, which can neglect the aftershock effect on the safety margin. According to requirements of International Atomic Energy Agency (IAEA) [22,23], after acquiring

2. Numerical modeling The case study is a reinforced concrete containment structure consisting of a cylindrical shell, a dome and a base, which is shown in Fig. 1. The cylindrical shell that is 44 m in height is connected to the base lab with a diameter equal to 44 m. The dome with 0.762 m thickness is attached at the top of a cylindrical shell. The shell has 37.796 m internal diameter and 39.93 m external diameter. The detailed design information is available in the Ref. [24]. The ABAQUS software is adopted to build the numerical model for the three-dimensional containment. The rebars are simulated by truss elements, which are embedded in the cylindrical shell. The solid element is used in the simulation of the containment shell and base. For the concrete material properties, the elastic modulus, Poisson's ratio, density, tensile strength and compressive strength of the containment concrete are assumed to be 36,000 MPa, 0.2, 2400 kg/m3, 2.85 MPa and 40 MPa, respectively. The concrete damaged plasticity model is selected to capture the accumulative damage of structures during seismic sequences, which can reflect the structural damage through normalized 2

Engineering Structures 198 (2019) 109511

X. Bao, et al.

¯ ) at the of containment structures, the average tensile damage index (dt bottom of the cylindrical shell (within the range of 6 m) is selected to measure the initial damage states [24]. There are four initial damage states defined in this research, namely DS0 (no damage) and three damage states. When the average tensile damage factor is equal to 0.1, the tensile damage appears in the body of a containment, which is set as ¯ = 0.9) represents that the slight cracks can be obDS1. DS2 (i.e., dt served at the bottom of the shell. The damage state in which cracks completely overspread the bottom of a containment is defined as DS3.

3. Selection of ground motions To examine the impact of fault types of seismic sequences considering post-mainshock damage states, two cases of seismic sequences: the far-fault mainshock followed by a far-fault aftershock and the farfault mainshock followed by a near-fault aftershock, are employed in this dynamic analysis. Both types of seismic sequences are selected from the same earthquake events under the same site conditions (i.e., the Northridge earthquake and Chi-Chi earthquake). In this study, a set of real far-fault sequences is selected from the database of PEER, and this selection is conducted based on the following criteria: (a) magnitudes of mainshocks and corresponding aftershocks are more than 6.0 and 5.0, which are more likely to cause the structural damage; (b) the selected seismic sequences are measured in a free field or low-height floor of buildings, and then the interaction between soil and structure can be neglected; (c) the closest distances of mainshocks and following aftershocks to rupture planes are both more than 20 km; and (d) acceleration records of seismic sequences are measured on the site where the shear velocity is greater than 360 m/s, because nuclear structures are usually built on rock or stiff soil. The 10 seismic sequence records are chosen through these criteria, and the related information is shown in Table 1. Because there are less actual near-fault seismic sequences recorded on rock or stiff soil site, the artificial mainshock-aftershock records are used as near-fault seismic sequences to perform the dynamic analysis. Currently, two approaches are frequently adopted to generate artificial seismic sequences. The first method [25,26] assumes that the characteristics of mainshocks is the same to that of following aftershocks, and use the mainshock record as a seed to simulate the corresponding aftershocks. But this situation is less likely to occur in reality. In the second approach [5,27], seismic sequences are derived by randomizing the set of selected ground motions. In the absence of real mainshockaftershock records [13], the latter method could be more preferable for

Fig. 2. Considered constitutive behavior of concrete in tension (a) and compression (b).

indicators dt and dc. The relationship of stress and normalized indicator can be seen in Fig. 2. The dt values of 0 and 1 correspond to no tensile damage and concrete cracking. Similarly, the dc values of 0 and 1 correspond to no compressive damage and the crush of concrete. In this numerical model, the rebars are considered as the uniaxial material with bilinear restoring force. The yield strength and ultimate stress of the steel are 350 MPa and 510 MPa. Rayleigh damping equal to 5% of critical value is assigned to the containment structure model. The dynamic analysis is conducted adopting the implicit algorithm Newton method with initial time increment and maximum time increment equal to 0.005 s and 0.01 s to improve convergence. To examine the effect of post-mainshock damage states on the seismic response during aftershocks, the initial damage levels should be quantified in terms of structural damage indicators. The containment is used to prevent the release of radioactive material, and thus cracking is an important damage state for containment structures due to their function. Moreover, the cracking damage mainly occurs at the bottom of containment structures. Therefore, according to the cracking pattern Table 1 Detailed information on selected far-fault seismic sequences. No.

Earthquake event

Station

Comp.

Time

Mw

PGA (g)

Vs30 (m/s)

Distance (km)

1

Chi-Chi, Taiwan

CHY046

E

2

Chi-Chi, Taiwan

CHY086

E

3

Chi-Chi, Taiwan

HWA005

N

4

Chi-Chi, Taiwan

HWA032

E

5

Chi-Chi, Taiwan

HWA034

E

6

Northridge

Griffith Park Observatory

90

7

Northridge

La Crescenta

90

8

Northridge

City Terrace

180

9

Northridge

Angeles Nat F

TUJ262

10

Northridge

Old Ridge Route

90

1999-09-20 1999-09-20 1999-09-20 1999-09-20 1999-09-20 1999-09-22 1999-09-20 1999-09-22 1999-09-20 1999-09-22 1994-01-17 1994-03-20 1994-01-17 1994-03-20 1994-01-17 1994-01-17 1994-01-17 1994-03-20 1994-01-17 1994-01-17

7.62 6.2 7.62 6.2 7.62 6.2 7.62 6.20 7.62 6.2 6.69 5.28 6.69 5.28 6.69 6.05 6.69 5.28 6.69 5.93

0.081 0.051 0.051 0.052 0.051 0.068 0.089 0.059 0.068 0.066 0.263 0.027 0.11 0.046 0.135 0.023 0.179 0.049 0.217 0.061

442.15 442.15 665.2 665.2 459.32 459.32 573.04 573.04 379.18 379.18 1015.88 1015.88 411.55 411.55 365.22 365.22 550.11 550.11 450.28 450.28

24.1 38.14 28.42 33.66 47.58 33.61 47.31 32.27 44.32 33.48 23.77 21.69 18.5 22.9 36.62 33.8 19.74 25.83 20.72 25.17

3

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Table 2 Detailed information on selected near-fault aftershocks. No.

Earthquake event

Station

Comp.

Tp (s)

Mw

PGA (g)

Vs30 (m/s)

Distance (km)

1 2 3 4 5 6 7 8 9 10

Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Northridge Northridge Northridge Northridge Northridge

CHY006 TCU075 TCU076 TCU102 TCU136 Jensen Filter Plant Generator LA Dam Pacoima Dam Converter Station East Olive View Med FF

E E E E W JGB022 LDM334 PAC265 SCE281 SYL360

2.6 5.1 4 9.7 10.3 3.5 1.7 0.5 3.5 3.1

7.62 7.62 7.62 7.62 7.62 6.69 6.69 6.69 6.69 6.69

0.215 0.228 0.281 0.177 0.114 0.764 0.319 0.191 0.476 0.536

438.19 573.02 614.98 714.27 462.1 525.79 628.99 2016.1 370.52 440.54

9.8 0.9 2.8 1.5 8.3 5.4 5.9 7.0 5.2 5.3

with different fault types from two events is used as input to conduct the nonlinear time-history analysis.

4.1. Displacement response analysis The maximum peak displacement is frequently adopted to examine the seismic response and global performance of containment structures [8]. In this analysis, the variation of maximum peak displacement subjected to seismic sequences considering initial damage states is studied. The post-mainshock damage state is simulated by scaling the peak ground acceleration (PGA) of mainshocks until the seismic response reaches the given damage state, and then the corresponding aftershocks scaling to different intensities (i.e., PGA = 0.2 g, 0.3 g, 0.4 g and 0.5 g respectively) are applied on the damaged containment. It is worth noting that there is a significant difference in damage potentials of mainshocks due to their characteristics, and these records need to be scaled with different scale factors to reach a given damage state. For DS0, the intensities of all mainshock records are scaled to 0.1 g. The variation of intensity levels for DS1 is from 0.3 g to 0.5 g. The seismic intensity is varied from 0.5 to 1.0 g for DS2. The DS3 is considered by using mainshocks with the intensity of 0.8–1.5 g. To stabilize the response of a structure after the mainshock excitation, a time gap of 100 s is added between seismic excitations. The brief summary of the basic procedure for implementing this dynamic analysis is shown in Fig. 4. As shown in Fig. 5(a), the near-fault aftershocks can cause a larger average peak displacement compared to far-fault aftershocks. As the intensity of aftershocks increases, the difference in displacement demands under different fault-type aftershocks is more evident. Comparing Fig. 5(a)–(d), it can be seen that post-mainshock damage states have a significant influence on displacement responses under aftershocks. When the structure remains minor damage (DS1), there is no obvious difference in displacements between DS0 and DS1. In contrast, when the structure is subject to severe damage, both types of aftershocks can lead to greater displacement responses, and the gap between displacement responses under near-fault and far-fault aftershocks becomes more obvious. Near-fault ground motions are generally characterized by their intensity and pulse period, which can reflect frequency and energy content of earthquakes [11]. To better study the impact of characteristics of pulse-type ground motions on structures, the effect of near-fault aftershocks with various pulse periods on the peak displacement is investigated in which the PGA is selected to measure the intensity of earthquakes [29]. As shown in Fig. 6, the dots represent samples of displacement responses corresponding to aftershocks with different pulse periods, and the trend line obtained by linear regression is used to reflect the relationship of displacement demands and pulse periods. For a structure with DS0, the effect of pulse periods is not obvious when the PGA is lower. As the intensity increases, the slope of trend line tends to decrease, which indicates that the ground motion with a pulse period close to the fundamental period of the containment (0.2 s) has a more significant effect on the dynamic response. It is worth noting that when

Fig. 3. Response spectrum for far-fault and near-fault aftershocks (5%damped).

generating seismic sequences because it can consider stochastic dependence between mainshocks and aftershocks. In this study, the second method is adopted to develop near-fault seismic sequences. It should be noted that the mainshock records is mainly used to simulated initial damage states of a containment structure, and thus the impact of fault types of mainshocks is not considered in this study. In addition, to investigate the aftershock fault type effect and minimize the influence of other factors, mainshock records from far-fault sequences are still used as mainshocks in near-fault seismic sequences. Baker [28] used wavelet analysis to identify 91 near-fault ground motions with largevelocity pulses. The 10 near-fault aftershocks used in this study are selected from 91 provided records. These records exhibiting an intense velocity pulse are also measured on the site where the shear velocity is greater than 360 m/s, while the fault distance of these ground motions are less than 10 km. The detailed information on selected near-fault aftershocks is listed in Table 2. The selected mainshocks and aftershocks from the same earthquake event are randomly assembled to generate 10 near-fault seismic sequences. The acceleration response spectrum for selected aftershocks is presented in Fig. 3. 4. Dynamic response analysis under far-fault and near-fault seismic sequences The near-fault ground motions with an intense velocity pulse contains a high input energy at the beginning of record, which may result in a large dynamic response of structures. Moreover, when the structure sustains damage during a mainshock, near-fault aftershocks are likely to cause more serious accumulative damage to this post-mainshock structure. In this section, to provide quantitative knowledge about the influence of near-fault sequences, the dynamic behavior of a postmainshock containment structure is studied. A set of seismic sequences 4

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Fig. 4. Flowchart for the dynamic analysis of a containment structure under seismic sequences.

In this section, the impact of the number of aftershocks on accumulation of damage is also investigated. Two kinds of sequence-type ground motions, containing one aftershock or two aftershocks, are considered in this study. For the seismic sequence with one aftershock, the selected mainshock-aftershock seismic sequences (presented in Section 3) are still used and the intensity of aftershocks is adjusted to target intensities (i.e., PGA1AS = 0.2 g, 0.3 g, 0.4 g and 0.5 g). In case of the combination of mainshock-aftershock-aftershock ground motions, the second aftershock can be generated by seeding the as-recorded

the pulse period exceeds 2.5 s, the effect of pulse periods is less obvious and the difference in displacement responses is minor. The similar tendency can be observed for the structure with minor damage. With the increase in the initial damage level, the peak displacement responses under aftershocks increase considerably compared with the intact structure, and the influence of pulse periods on the structure is more significant. The reason may be that the fundamental period of a mainshock-damaged containment structure becomes longer, which is closer to the pulse period of selected aftershocks.

Fig. 5. Peak displacement responses of a mainshock-damaged containment structure under far-fault and near-fault aftershocks. 5

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Fig. 6. The effect of pulse periods on the peak displacement of a containment structure.

and near-fault aftershocks.

aftershock using the repeated approach, and two aftershocks are scaled with reasonable scale factors to the same target intensities. For simplicity, the intensity ratios of aftershocks in two types of seismic sequences are set as 0.8 and 0.5 (i.e., PGA2AS/PGA1AS = 0.8 and 0.5). The value of 0.8 is used to conduct the comparison of multiple relative moderate aftershocks and the largest aftershock, and the value of 0.5 is used as the smallest relative intensity ratio which can cause the structural damage. The relationship of the magnitude and the number of seismic events can be described by Eq. (1) according to GutenbergRichter law [30].

N = 10 A − BM

4.2. Cracking damage analysis Due to the function of containment structures, the cracking is an important damage state and should be paid more attention. In this analysis, the effect of different types of aftershocks on the local cracking damage is studied. Fig. 8 shows the cracking of concrete in the containment structure under near-field and far-field aftershocks from two earthquake events. The red area in Fig. 8 represents the cracking in the body of a containment under earthquake excitations. It can be observed that cracking damage occurs at the bottom of the containment. In both earthquake events, near-field aftershocks can introduce more severe cracking damage to a containment structure than far-field ground motions. In order to quantify and examine the cracking damage under mainshock-aftershock sequences, a damage ratio (defined as the ratio of cracking area to total area of the cylindrical shell) is used in this research which is shown as follow:

(1)

where N is the number of earthquakes with the magnitude M, and A and B are constants. It can be observed that the intensity decreases with the increase in the number of earthquakes. So the aftershock intensity ratio of 1.0 (i.e., PGA2AS/PGA1AS = 1.0) is not considered in this study. Fig. 7 presents the average ratios of peak displacements of seismic sequences with two aftershocks to those of seismic sequences with one aftershock for various initial damage states. It can be seen that all ratios in Fig. 7(a) are less than 1.0, which indicates that seismic sequences with one aftershock have a more significant effect on the global response of a containment than seismic sequences with two aftershocks when the PGA2AS/PGA1AS is equal to 0.5. With the increase in initial damage level, the ratios of peak displacements under both near-fault and far-fault aftershocks at a given PGA increase gradually compared to the intact structure. Results in Fig. 7(b) indicate that for most cases the largest aftershock can also cause the higher damage with respect to multiple relative moderate aftershocks with a PGA2AS/PGA1AS of 0.8. However, seismic sequences consisting of two aftershocks with a PGA of 0.4 g (=0.8 × 0.5 g) have a larger influence on a containment structure with DS3, with the displacement ratios of 1.22 and 1.28 for far-fault

DR =

∫ (dt ) ds/∫ ds

(2)

where dt is the tensile damage index, and s is the total dimension of the cylinder. Fig. 9 shows the damage ratios for a structure with different damage states under near-fault and far-fault aftershocks. The horizontal axis represents the ground motion number, and the points are the damage ratios of a structure under corresponding ground motions. The lines in Fig. 9 reflect the average damage ratios of a containment structure under different fault-type aftershocks. It can be seen in Fig. 9 that nearfield aftershocks can lead to larger damage ratios, which is similar to 6

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Fig. 7. Ratios of displacement responses of a containment structure subjected to sismic sequences with one aftershock and multiple aftershocks.

sequences with one aftershock and two aftershocks. As shown in Fig. 10(a), one aftershock with a PGA of 0.2 g can cause a larger local damage than multiple aftershocks when PGA2AS/PGA1AS is equal to 0.5, and the ratios for cracking damage are a mere 0.32 and 0.37 for farfault and near-fault aftershocks respectively. With the damage level and PGA increase, the difference between damage effects of sequence-type ground motions with one aftershock and two aftershocks gradually narrows. For the aftershock intensity ratio of 0.8 presented in Fig. 10(b), the mean ratios of cracking damage increase to 1.19 and 1.24 at a PGA of 0.5 g, which implies that multiple aftershocks with

the result shown in Fig. 8. The development of structural cracking is significantly affected by initial damage levels. It should be noted that the local damage of a containment with DS1 is noticeably intensified compared to the structure with DS0, but the peak displacement response (presented in Section 4.1) does not exhibit any remarkable change. The reason may be that the global indicator like peak displacement is not much sensitive to the local damage of a containment structure, while the damage index related to material damage can better reflect the local damage situation. Fig. 10 illustrates mean ratios for damage ratios (DR) from seismic

Fig. 8. Cracking profiles for a containment structure under far-fault and near-fault aftershocks with a PGA of 0.3 g and DS2 damage state. 7

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Fig. 9. Damage ratios for a post-mainshock containment structure under far-fault and near-fault aftershocks with a PGA of 0.3 g.

Fig. 10. Ratios of damage ratio (DR) of a containment structure subjected to seismic sequences with one aftershock and multiple aftershocks. 8

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Fig. 11. Damage dissipation energy curves for a post-mainshock containment structure under far-fault and near-fault aftershocks with a PGA of 0.3 g in Chi-Chi earthquake event (left plot) and Northridge earthquake event (right plot).

widely adopted to measure the accumulative damage of structures [14]. The effect of different types of ground motions on a mainshock-damaged containment structure is investigated in terms of damage dissipated energy. Fig. 11 presents the damage dissipated energy curves of a structure with various damage states under near-fault and far-fault aftershocks. The curves in the right panels represent average values of damage dissipated energy under selected earthquakes from the Chi-Chi event, and curves in the left reflect average values from the Northridge event. In this dynamic analysis, the variation of energy in the first 15 s

higher intensity have a larger damage potential in a mainshock-damaged containment regardless of types of aftershocks. 4.3. Damage dissipated energy analysis The response of structures under seismic excitations, in essence, is the process of energy transfer, transformation and absorption. So energy can better reflect the effect of ground motions and seismic performance of inelastic structures. The damage dissipated energy is 9

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Fig. 12. Ratios of damage dissipation energy (DDE) of a containment structure subjected to seismic sequences with one aftershock and multiple aftershocks.

of as-recorded Chi-Chi ground motions and the first 40 s of selected Northridge records are shown in Fig. 11, because the damage dissipated energy after these specified durations is constant. It can be observed that near-fault aftershocks at the same intensity level can cause higher damage dissipated energy to the containment structure compared to far-fault aftershocks in both seismic events, and this gap is likely to widen as the initial damage level increases. Fig. 12 illustrates mean ratios of damage dissipation energies subjected to seismic sequences with one aftershock and two aftershocks. The ratios of damage dissipation energies under two types of seismic sequences have a similar tendency for the ratios of DRs observed in Fig. 10. A comparison between two types of sequence-type ground motions indicates that, with few exceptions, the impact of seismic sequences on the damage dissipation energy is stronger for seismic sequences consisting of one aftershock compared to the case of two aftershock events. Only when the containment structure sustains severe damage during the mainshock, can multiple aftershocks with larger intensity induce the comparable or higher damage dissipation energy, in comparison to seismic sequences with one aftershock.

characterize seismic demands on secondary systems. The six key secondary systems, such as reactor assembly and steam generator, are distributed at 7 m, 18 m and 39 m, respectively [31]. So the effect of near-fault and far-fault aftershocks on floor response spectra in these floor levels (i.e., 7 m, 18 m and 39 m) is investigated in the following part. For a given containment structure, the absolute acceleration response at the concerned floor height is obtained by the nonlinear timehistory analysis using selected ground motions, and this response of a primary structure is used as input for a single-degree-of-freedom (SDOF) to generate the floor response spectrum (FRS). It should be noted that the obtained results are valid for the following basic assumptions: (1) Interaction between structure and subsystem is neglected because the mass of secondary systems is far less than that of the primary structure; (2) The damping ratio of SDOF is 5%; (3) The primary structure is able to experience inelastic behavior, and the secondary systems behave elastically.

5.2. Floor response spectra for far-fault and near-fault sequences Because of the dynamic filtering effect, the containment structure has a significant effect on the frequency content of ground motions, and then the secondary systems are subjected to large seismic forces [32]. Identifying the characteristics of peak floor acceleration (PFA) for a post-mainshock structure can lead to better seismic design of secondary systems under seismic sequences. To understand the floor acceleration amplification with height, the normalized PFA (denoted as the ratio of PFA to PGA) under selected ground motions is plotted along the structural height, which represents the average acceleration responses

5. Seismic demands on secondary systems 5.1. Floor response spectrum method This section mainly focuses on near-fault and far-fault aftershock demands on the secondary systems in a post-mainshock containment structure, because a large portion of total cost belongs to secondary systems. The floor response spectrum method, which is frequently used for the estimation of equipment attached in structures, is adopted to 10

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Fig. 13. Floor acceleration amplification with height for a post-mainshock containment structure under far-fault and near-fault aftershocks.

of secondary systems at different floor levels. As shown in Fig. 13, it can be observed that the location of the secondary system has a significant impact on the values of PFA/PGA. For a containment structure with various damage states, the distribution of normalized PFA along height of building shows an almost linear trend, with the maximum floor acceleration magnification occurring at the top floor (39 m). The amplification values obtained from near-fault aftershocks are slightly higher than those for far-fault aftershocks at all floor levels. When the structure sustains none damage (DS0), the values of PFA/PGA at 39 m are 2.35 and 2.16 for near-fault and far-fault aftershocks, whereas the values of PFA are slightly smaller than PGA (i.e., the amplification values are less than 1) at 7 m for both types of aftershocks. As the initial damage level increases, the amplification values gradually decrease at different heights. It should be noted that the variation of amplification values with the increasing of damage level at the top floor is remarkable, but the variation at the lower location is not obvious. The difference between amplification values for different types of aftershocks is also reduced with the increase in damage level. For a containment structure with DS3, the reductions in the values of PGA/PFA at 39 m are up to 14.2% and 9.2% for near-fault and far-fault aftershocks, respectively. Moving from PFA to FRS, Fig. 14 presents the mean floor response spectra for a post-mainshock containment structure subjected to farfault and near-fault aftershocks. By comparing the floor response spectra for the intact structure under far-fault and near-fault aftershocks, it is observed that there is less difference during short period range, while the average acceleration values of FRS under near-fault aftershocks are higher than the values subjected to far-fault aftershocks throughout the long period range. The similar trend is also shown in the floor acceleration spectra at different heights for a post-mainshock structure with various damage states. With the increase in the location of secondary systems, the peak values of floor acceleration spectra

increase under both types of aftershocks. When the structure is subjected to none or minor damage (DS1), the gap between FRS is not obvious. As the initial damage level increases, the impact of the inelastic primary structure on the reduction of FRS values is even more noticeable. The reason is that more energy can be dissipated by inelastic behavior of the damaged structure, and then acceleration demands on secondary systems are reduced. It is worth noting that the above provided results are related and limited to a reinforced concrete containment structure under selected ground motions, and a more extensive parametric analysis is needed to be carried out in order to generalize the results. 6. Fragility analysis under seismic sequences According to analyses mentioned above, the effect of post-mainshock damage states on the seismic performance of structures during aftershock events is significant. So it is necessary to incorporate the influence of initial damage conditions in the fragility analysis under seismic sequences. In this section, a new framework for fragility analysis considering the effect of post-mainshock damage states is adopted, and the impact of far-fault and near-fault seismic sequences with one aftershock on the fragility of a containment structure is studied. 6.1. Framework for fragility analysis under mainshock-aftershocks The post-mainshock damage can lead to the deterioration of structural stiffness and strength, thus affecting the performance and seismic capacity of this structure during subsequent aftershocks. The current aftershock fragility assessments assume that the threshold values associated to limit states of a structure are invariable, and then the effect of initial damage states on the residual seismic capacity of a mainshock11

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Fig. 14. Comparison of mean floor response spectra for a post-mainshock containment structure under far-fault and near-fault aftershocks.

Fig. 15. The mean and standard deviation of peak displacements under mainshocks.

12

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Fig. 16. The mean and standard deviation of peak displacements under far-fault and near-fault aftershocks. Table 3 The values of selected criterion for five copula functions under far-fault sequences with PGAAS/PGAMS = 1.0. Intensity

Criterion

Normal

t

Gumbel

Frank

Clayton

0.5 g

AIC value d2

−190.5341 0.0466

−200.9943 0.0575

−208.5086 0.0398

−185.8866 0.0630

−158.1419 0.1098

1.0 g

AIC value d2

−253.6995 0.0162

−252.3774 0.0167

−274.7853 0.0107

−255.2064 0.0158

−264.4787 0.0131

1.5 g

AIC value d2

−114.3196 0.2639

−114.8399 0.2612

−144.0248 0.1457

−111.3921 0.2798

−114.1508 0.2648

2.0 g

AIC value d2

−164.8977 0.0960

−161.2208 0.1033

−167.3972 0.0913

−164.9812 0.0958

−161.5394 0.1026

2.5 g

AIC value d2

−194.7553 0.1522

−141.8189 0.0528

−206.6833 0.0408

−196.9646 0.0505

−190.5322 0.0575

3.0 g

AIC value d2

−183.4060 0.0663

−139.5704 0.1593

−190.8611 0.0569

−184.6478 0.0646

−185.7304 0.0633

normal and t copula belong to the class of elliptical copula, and these functions are defined according to the normal and t distribution, respectively. The bivariate normal copula function is given by:

damaged structure is ignored in the computation of exceedance probability, which can underestimate the seismic risk. To address this issue, the new framework is adopted to conduct the fragility analysis under mainshock-aftershocks, which can directly consider the dependence between the damaged levels caused by mainshocks and structural responses under aftershocks when computing the exceedance probability. The copula theory provides an efficient tool for characterizing the nonlinear correlation among random variables when modeling a joint probability distribution. In this theory [33], a joint probability distribution of multiple random variables can be characterized by a copula function in terms of their marginal probability distributions. For characterizing the dependence, the use of two classes of elliptical and Archimedean copula is prevalent, and the major difference between these functions is the ability to capture the tail dependence of data. The

CθN (u, v; θ) =

Φ−1 (u)

∫−∞

Φ−1 (v )

∫−∞

1

exp ⎛− 2π 1 − θ 2 ⎝ ⎜

s 2 − 2θst + t 2 ⎞ dsdt 2(1 − θ 2) ⎠ ⎟

(3) where Φ−1 (∙) represents the inverse standard normal distribution of two random variables, and θ is the intrinsic parameter measuring the dependence between variables. The bivariate t copula function can be written as:

13

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Table 4 The values of selected criterion for five copula functions under near-fault sequences with PGAAS/PGAMS = 1.0. Intensity

Criterion

Normal

t

Gumbel

Frank

Clayton

0.5 g

AIC value d2

−200.3258 0.0472

−197.8975 0.0496

−220.5117 0.0347

−208.8912 0.0398

−184.3681 0.0650

1.0 g

AIC value d2

−297.5145 0.0068

−286.6590 0.0084

−306.4333 0.0057

−276.5460 0.0103

−240.6354 0.0211

1.5 g

AIC value d2

−184.1731 0.0653

−140.1820 0.1573

−192.7502 0.0471

−181.5828 0.0687

−183.5514 0.0661

2.0 g

AIC value d2

−133.0577 0.1814

−105.1808 0.3168

−144.9296 0.1547

−132.8958 0.1820

−129.6932 0.1940

2.5 g

AIC value d2

−207.1253 0.0412

−205.4188 0.0427

−210.5517 0.0401

−206.0197 0.0422

−186.7851 0.0619

3.0 g

AIC value d2

−191.8754 0.0559

−151.4919 0.1255

−207.0898 0.0416

−190.5748 0.0574

−193.8224 0.0538

Fig. 17. Probability density functions following Gumbel copula for displacement responses under different fault-type seismic sequences.

Cθt, k (u, v; θ , k ) =

tk−1 (u)

∫−∞

tk−1 (v )

∫−∞

Cθ (u, v ) = −

−(k + 2)/2

2 2 ⎛1 + s − 2θst + t ⎞ 2) 2 k (1 θ − 2π 1 − θ ⎝ ⎠

1

⎜

⎟

dsdt

(4)

Cθ (u, v ) = (u−θ + v−θ − 1)−1/ θ

where tk−1 (∙) denotes the inverse t distribution with k which can be obtained by maximizing the log-likelihood function. Another popular copula family is the Archimedean copula function. The family of Archimedean copula includes Gumbel, Frank and Clayton copulas, and their mathematical formula are expressed as:

Cθ (u, v ) = exp(−[(−ln u)θ + (−ln v )θ]1/ θ )

(exp( −θu) − 1)(exp( −θv ) − 1) ⎞ 1 ⎛ ln ⎜1 + ⎟ exp(−θ) − 1 θ ⎝ ⎠

(6) (7)

In this method, two parameters under mainshocks and aftershocks are selected to represent the post-mainshock damage levels and aftershock demands, and the concept of bivariate distribution is used to model the probability distribution of these two variables. The proposed methodology introduces the bivariate seismic demand modeling using copula technique to describe the correlation of data. According to the features of data obtained from IDA under mainshock-aftershocks, the marginal distribution modeling for each demand parameter is determined and the suitable copula function is selected in terms of the AIC

(5)

14

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Fig. 18. Damage profiles for four limit states of the containment structure.

Fig. 19. The bi-dimensional limit-state functions for four limit states.

Relying on the combination of joint seismic demand models and bidimensional limit state functions, this approach enables the effect of post-mainshock damage states on the residual seismic capacity to be incorporated directly in the calculation of exceedance probability, and various damage states caused by mainshocks during the IDA can be taken into account simultaneously, which can improve the accuracy of the fragility evaluation and facilitate the use.

values and minimum squared Euclidean distances. The bi-dimensional limit state functions, which can consider the effect of post-mainshock damage levels on the seismic capacity of structures, are determined by the regression analysis of IDA results. In these functions, the two demand parameters representing the mainshock-damaged levels and dynamic responses under aftershocks are combined to indicate performance levels associated to limit states after mainshock-aftershock events. The Monte Carlo simulation method is used to calculate the probability that the structure exceeds the limit state under the mainshock-aftershock shakings. This procedure is repeated to calculate the probability of exceedance at each intensity level of ground motions, and then fit the data over the full range of intensities to form the fragility curve.

6.2. Fragility analysis of a containment structure under far-fault and nearfault seismic sequences To obtain the seismic demands of a containment structure, the incremental dynamic analysis (IDA) is performed by scaling the intensity 15

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Fig. 20. Comparison of fragility curves for a containment structure under far-fault and near-fault seismic sequences with PGAAS/PGAMS = 0.5.

information criterion is also widely-used for measuring the goodness of fit for statistical models, which can be calculated by the equation as follows:

of mainshock-aftershock sequences over the range of 0.1–3.0 g with the increment of 0.1 g. During scaling process, the intensity of earthquakes is measured in terms of PGA. The peak displacement is a useful damage index and usually used to indicate the performance level of a containment structure, because it is a simple cantilever type structure [8]. In this study, the maximum peak displacements under mainshocks and aftershocks are selected to measure the post-mainshock damage levels and aftershock demands. Previous research [34] indicated that the Frechet distribution is adequate to characterize the displacement demands. So the Frechet distribution is adopted to model the displacement demands of a containment structure under mainshocks and aftershocks. The mean and standard deviation are important statistical parameters of a marginal probability model using the Frechet distribution. The statistical values of displacements at different intensity levels of mainshocks are calculated and shown in Fig. 15. The statistical analysis is also carried out for the peak displacements of a containment structure under aftershocks. Two intensity ratio values (i.e., PGAAS/ PGAMS = 0.5 and 1.0) are considered in this analysis to study the effect of relative intensity of mainshock-aftershocks. Fig. 16 shows the mean and standard deviation of displacements under aftershocks. The determination of the copula function is the final step to construct the joint seismic demand model. To identify a reasonable copula function for displacement demands, the AIC and minimum squared Euclidean distance are used to examine the suitability of copula fitting for five alternative copula functions. The formula for the squared Euclidean distance is given by:

AIC = 2k − 2 ln(L)

where k is the number of parameters and L is the likelihood function. The fitted model with the smaller values of the AIC and squared Euclidean distance can fit better to the original data. The AIC and squared Euclidean distance values for five copula functions under farfault and near-fault sequences with PGAAS/PGAMS = 1.0 are listed in Tables 3 and 4. The corresponding values of Gumbel copula are the smallest among these copula functions. According to the results mentioned above, for the displacement demands of a containment structure under mainshocks and aftershocks, the Gumbel copula is preferable for characterizing the nonlinear dependence of data at various seismic intensity levels. Fig. 17 shows probability density functions following Gumbel copula for different fault-type seismic sequences. To consider the effect of initial damage states on the residual seismic capacity, the bi-dimensional limit-state functions combining displacements under mainshocks and aftershocks to define performance levels are provided through the IDA. The containment structure has a higher seismic capacity compared to other types of civil buildings. In addition, the IDA analysis is conducted by the Abaqus software, and jobs are submitted automatically through batch files. Thus, for convenience, the upper limit for PGA is directly set as 2.0 g, which ensures that most of selected earthquake records can induce the failure of the containment and then more data related to limit states can be obtained. In order to define the limit-state functions, the nonlinear time history analyses are carried out on the containment structure using mainshocks with a given intensity, and then the corresponding aftershocks whose intensities are scaled from 0.1 g to 2.0 g are applied on the post-mainshock

n

d2 =

∑ |CE (u, v ) − C (u, v )|2 i=1

(9)

(8)

CE (∙)

is an empirical copula function and C (∙) is a considered where copula function; n denotes the total number of data. The AIC 16

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Fig. 21. Comparison of fragility curves for a containment structure under far-fault and near-fault seismic sequences with PGAAS/PGAMS = 1.0.

simulation method. According to the obtained joint probability distribution model, the simulated samples are generated and then the number of data points that exceed the given bi-variable limit state is counted. The probability of exceeding the limit state can be obtained by the number of failure points divided by the total number of simulation runs. Finally, the fragility curve is developed by fitting the exceedance probabilities over a wide range of seismic intensity. The comparisons of fragility curves for near-fault and far-fault seismic sequences are shown in Figs. 20 and 21. To quantify the difference between fragility curves, fragility curves are characterized in terms of Sct (i.e., the median failure intensity at which one-half of selected ground motions can cause the dynamic behavior of a structure exceeding the given limit state) [35]. It is observed in Fig. 20 that the values of Sct obtained from far-fault sequences are higher than those from near-fault sequences for all limit states, which means that nearfault aftershocks can impose larger demands on a containment structure. For the minor damage state corresponding to LS1, the difference between Sct values for different fault-type sequences is small, with 0.36 g and 0.39 g for near-fault and far-fault seismic sequences. As the damage level associated to limit state increases, the gap between fragility curves gradually widens. It is because the fundamental period of the containment structure is elongated when suffering the serious damage, resulting in the enhanced influence of velocity pulses on the dynamic response. As shown in Fig. 21, there is similar tendency for seismic sequences with PGAAS/PGAMS = 1, regardless of fault types of earthquakes. Comparing Fig. 20 with 21, it can be seen that the seismic sequences with larger PGAAS/PGAMS can lead to a lower Sct for the same limit states, indicating the increase in the exceedance probability. Moreover, the difference between fragility curves for various fault types of ground motions becomes more obvious when the structure is subjected to seismic sequences with higher intensity aftershocks. Based on the fragility analyses mentioned above, near-fault sequences can cause

containment. This procedure is repeated by scaling the intensity of mainshocks over the range of 0.1–2.0 g with the increment of 0.1 g. During the IDA, the maximum peak displacements under various mainshocks and corresponding aftershocks are monitored, and the pairs of displacements reaching the onset of a given limit state are selected. The limit-state functions for limit states are proposed by the regression analysis of these selected data. For the containment structure, four limit states (i.e., LS1-LS4) are defined in this study. When the tensile damage factor (dt) equals 1, cracks begin to occur in the body of a containment, which is set as LS1. LS2 represents the damage state which the tensile stress of rebars reaches the yield strength of 350 MPa. The concrete crushing (i.e., the index of compressive damage dc = 1) is defined as LS3. The failure of a containment structure (denoted as LS4 herein) is identified by the crushing area corresponding to the intact containment with 85% of the ultimate capacity. The damage level of a containment structure can be observed directly and visually through concrete cracking or crushing, and Fig. 18 presents concrete damage profiles corresponding to different limit states. For LS1 and LS2, no concrete crushing occurs and then the cracking profiles are used to describe the damage level. When the containment reaches severe damage, cracks have already overspread the bottom of a containment structure, and the development of cracking damage is not as sensitive as that of crushing damage under earthquakes. So crushing profiles associated to LS3 and LS4 are adopted to reflect damage levels of a structure, which are shown in Fig. 18(c)–(d). Fig. 19 shows the limit-state functions corresponding to four limit states. It can be observed in Fig. 19 that the mainshock and aftershock displacements are unrelated for the limit state LS1, while the dependence between post-mainshock damage levels and residual seismic capacities (represented by displacements under mainshocks and aftershocks) gradually becomes obvious with the increase in the damage level. The exceedance probability is calculated through the Monte Carlo 17

Engineering Structures 198 (2019) 109511

X. Bao, et al.

Acknowledgments

more serious damage to a structure and then increase the probability of exceedance corresponding to various limit states, especially seismic sequences with higher PGAAS/PGAMS. Thus, the effect of near-fault sequences should be taken into account in the safety margin assessment of containment structures.

The authors are grateful to Dr. Xiaotian Fang of Peking University for her kind help. This study was supported by the National Key Research and Development Program of China (2016YFC0701108) and the National Natural Science Foundation of China (No. 51238012, 51322801, 51708161). This support is gratefully acknowledged. Finally, the authors express their gratitude to the anonymous reviewers that helped to improve the quality of the paper.

7. Summary and conclusions In this paper, the seismic performance and fragility analysis of a containment structure are investigated under far-fault and near-fault seismic sequences. The concrete damage plasticity model is used in the numerical model to capture the accumulative damage. A set of as-record and artificial seismic sequences is used as input to analyze the dynamic behavior of a containment structure. The nonlinear responses for a post-mainshock containment structure under near-fault aftershocks are compared with those obtained from far-fault aftershocks. Seismic demands on secondary systems are also studied through floor response spectra considering post-mainshock damage states. Finally, a new methodology incorporating the effect of post-mainshock damage levels is adopted to evaluate the fragility of a containment structure under different types of seismic sequences. The following conclusions can be made:

References [1] Institute of Nuclear Power Operations. Special report on the nuclear accident at the Fukushima Daiichi Nuclear Power Station. INPO 11-005. [S.1.]: INPO; 2011. [2] Tesfamariam S, Goda K, Mondal G. Seismic vulnerability of reinforced concrete frame with unreinforced masonry infill due to main shock-aftershock earthquake sequences. Earthq Spectra 2015;31(3):1427–49. [3] Zhang SR, Wang GH, Sa WQ. Damage evaluation of concrete gravity dams under mainshock-aftershock seismic sequences. Soil Dyn Earthq Eng 2013;50:16–27. [4] Dong Y, Frangopol DM. Risk and resilience assessment of bridges under mainshock and aftershocks incorporating uncertainties. Eng Struct 2015;83:198–208. [5] Li QW, Ellingwood BR. Performance evaluation and damage assessment of steel frame buildings under main shock-aftershock earthquake sequences. Earthq Eng Struct Dyn 2007;36(3):405–27. [6] Hirama T, Goto M, Shiba K, Kobayashi T, Tanaka R. Seismic proof test of a reinforced concrete containment vessel (RCCV) Part2: Results of shaking table tests. Nucl Eng Des 2005;235:1349–71. [7] Nakamura N, Tsunashima N, Nakano T, Tachibana E. Analytical study on energy consumption and damage to cylindrical and I-shaped reinforced concrete shear walls subjected to cyclic loading. Eng Struct 2009;31(4):999–1009. [8] Choi IK, Choun YS, Ahn SM, Seo JM. Probabilistic seismic risk analysis of CANDU containment structure for near-fault earthquakes. Nucl Eng Des 2008;238:1382–91. [9] Somerville P, Smith N, Graves R, Abrahamson N. Modification of empirical strong ground motion attenuation relations to include the amplitude and duration effects of rupture directivity. Seismol Res Lett 1997;68:199–222. [10] Loh CH, Liao WI, Chai JF. Effect of near-fault earthquake on bridges: Lessons learned from Chi-Chi earthquake. In: Proc 3rd National Seismic Conf and Workshop on Bridges and Highways, FHWA Western Resource Center and MCEER, Portland, Ore.; 2002. p. 211–22. [11] Dicleli M, Mehta A. Effect of near-fault ground motion and damper characteristics on the seismic performance of chevron braced steel frames. Earthq Eng Struct Dyn 2007;36:927–48. [12] Kunnath SK, Erduran E, Chai YH, Yashinsky M. Effect of near-fault vertical ground motions on seismic response of highway overcrossings. J Bridge Eng 2008;13(3):282–90. [13] Ruiz-Garcia J, Negrete-Manriquez JC. Evaluation of drift demands in existing steel frames under as-recorded far-field and near-fault mainshock-aftershock seismic sequences. Eng Struct 2011;33(2):621–34. [14] Zhang SR, Wang GH. Effects of near-fault and far-fault ground motions on nonlinear dynamic response and seismic damage of concrete gravity dams. Soil Dyn Earthq Eng 2013;53:217–29. [15] KINS. Development of Seismic Safety Evaluation Technology for NPP Sites. KINS/ GR-206; 2000. [16] Li Y, Song RQ, Lindt JWVD. Collapse fragility of steel structures subjected to earthquake mainshock-aftershock sequences. J Struct Eng 2014;140(12):04014095. [17] Ruiz-García J, Aguilar JD. Aftershock seismic assessment taking into account postmainshock residual drifts. Earthq Eng Struct Dyn 2015;44:1391–407. [18] Cho SG, Joe YH. Seismic fragility analyses of nuclear power plant structures based on the recorded earthquake data in Korea. Nucl Eng Des 2005;235:1867–74. [19] Mandal TK, Ghosh S, Pujari NN. Seismic fragility analysis of a typical Indian PHWR containment: Comparison of fragility models. Struct Saf 2016;58:11–9. [20] Perotti F, Domaneschi M, Grandis SD. The numerical computation of seismic fragility of base-isolated Nuclear Power Plants buildings. Nucl Eng Des 2013;262:189–200. [21] Nakamura N, Akita S, Suzuki T, Koba M, Nakamura M. Study of ultimate seismic response and fragility evaluation of nuclear power building using nonlinear threedimensional finite element model. Nucl Eng Des 2010;240:166–80. [22] International Atomic Energy Agency. Evaluation of seismic safety for existing nuclear installations: safety guide, Safety standard series No. NS-G-2.13. Vienna: IAEA; 2009. [23] International Atomic Energy Agency. Seismic evaluation of existing nuclear power plants Safety reports series No.28. Vienna: IAEA; 2003. [24] Zhai CH, Bao X, Zheng Z, Wang XY. Impact of aftershocks on a post-mainshock damaged containment structure considering duration. Soil Dyn Earthq Eng 2018;115:129–41. [25] Amadio C, Fragiacomo M, Rajgelj S. The effects of repeated earthquake ground motions on the non-linear response of SDOF systems. Earthq Eng Struct Dyn 2003;32:291–308. [26] Hatzigeorgiou GD, Beskos DE. Inelastic displacement ratios for SDOF structures subjected to repeated earthquakes. Eng Struct 2009;31:2744–55. [27] Hatzigeorgiou GD. Ductility demand spectra for multiple near- and far-fault earthquakes. Soil Dyn Earthq Eng 2010;30:170–83.

(1) For an intact containment structure, near-fault aftershocks can cause greater displacement responses than far-fault ground motions, and the gap between two types of aftershocks rises from 0.10 cm to 0.25 cm as the intensity of earthquakes increases. Postmainshock damage states can enhance the effect of pulse-type aftershocks remarkably, with up to the displacement of 2.57 cm and 3.11 cm for a containment with DS3 subjected to far-fault and nearfault aftershocks respectively. (2) Near-fault aftershocks lead to more severe cracking damage (causing an average damage ratio of 0.005), compared with 0.002 under far-fault earthquakes. The initial damage states have a significant impact on the development of structural cracking, increasing to 0.232 and 0.276 under far-fault and far-fault aftershocks when the structure sustains severe damage (DS3). The similar tendency can also be observed in terms of damage dissipated energy. (3) The distribution of PFA/PGA along the height of the structure shows an almost linear trend, reaching 2.16 and 2.35 for far-fault and near-fault aftershocks at 39 m. The floor acceleration magnifications obtained from near-fault aftershocks are slightly higher than those for far-fault aftershocks at all floor levels, and the largest gap is only 0.19. As for FRS, there is less difference in acceleration values during short period range, while spectra for near-fault aftershocks have richer spectral content in longer period range. As the initial damage level increases, the impact of the inelastic primary structure on the reduction in FRS values is more noticeable. (4) The values of Sct obtained from far-fault seismic sequences are higher than those from near-fault earthquakes for various limit states. The gap between fragility curves gradually widens as the damage level associated to limit states increases, ranging from 0.03 g to 0.19 g. Seismic sequences with higher PGAAS/PGAMS can lead to lower values of Sct for both types of ground motions. For LS4, the Sct values for far-fault and near-fault sequences with the PGAAS/PGAMS of 1.0 decrease by approximately 12.1% and 13.4% compared to seismic sequences with the intensity ratio of 0.5. Based on this study, near-fault ground motions have a significant effect on the dynamic responses and fragility of a containment structure because of the intense pulse with high input energy. Near-fault seismic sequences can impose more serious damage on a containment structure compared to far-fault sequences. Thus, the near-fault seismic sequences should be taken into account when performing the safety margin assessment of containment structures. 18

Engineering Structures 198 (2019) 109511

X. Bao, et al.

[32] Petrone C, Magliulo G, Manfredi G. Floor response spectra in RC frame structures designed according to Eurocode 8. Bull Earthq Eng 2016;14:747–67. [33] Nelsen RB. An introduction to copulas. New York: Springer; 2006. [34] Goda K. Statistical modeling of joint probability distribution using copula: Application to peak and permanent displacement seismic demands. Struct Saf 2010;32:112–23. [35] Federal Emergency Management Agency. Quantification of building seismic performance factors. FEMA P695; 2009.

[28] Baker JW. Quantitative classification of near-fault ground motions using wavelet analysis. Bull Seismol Soc Am 2007;97(5):1486–501. [29] Makris N, Black CJ. Evaluation of peak ground velocity as a “good” intensity measure for near-source ground motions. J Eng Mech-ASCE 2004;130(9):1032–44. [30] Gutenberg B, Richter CF. Seismicity of the earth and associated phenomena. 2nd edition Princeton: Princeton University Press; 1954. [31] Huang YN, Whittaker AS, Constantinou MC, Malushte S. Seismic demands on secondary systems in base-isolated nuclear power plants. Earthq Eng Struct Dyn 2007;36:1741–61.

19