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Identifying significant earthquake intensity measures for evaluating seismic damage and fragility of nuclear power plant structures
Nuclear Engineering and Technology xxx (xxxx) xxx
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Original Article
Identifying significant earthquake intensity measures for evaluating seismic damage and fragility of nuclear power plant structures Duy-Duan Nguyen a, b, Bidhek Thusa a, Tong-Seok Han c, Tae-Hyung Lee a, * a
Department of Civil and Environmental Engineering, Konkuk University, Seoul 05029, South Korea Department of Civil Engineering, Vinh University, Vinh 461010, Vietnam c Department of Civil and Environmental Engineering, Yonsei University, Seoul 03722, South Korea b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 March 2019 Received in revised form 14 May 2019 Accepted 12 June 2019 Available online xxx
Seismic design practices and seismic response analyses of civil structures and nuclear power plants (NPPs) have conventionally used the peak ground acceleration (PGA) or spectral acceleration (Sa) as an intensity measure (IM) of an earthquake. However, there are many other earthquake IMs that were proposed by various researchers. The aim of this study is to investigate the correlation between seismic responses of NPP components and 23 earthquake IMs and identify the best IMs for correlating with damage of NPP structures. Particularly, low- and high-frequency ground motion records are separately accounted in correlation analyses. An advanced power reactor NPP in Korea, APR1400, is selected for numerical analyses where containment and auxiliary buildings are modeled using SAP2000. Floor displacements and accelerations are monitored for the non- and base-isolated NPP structures while shear deformations of the base isolator are additionally monitored for the base-isolated NPP. A series of Pearson's correlation coefficients are calculated to recognize the correlation between each of the 23 earthquake IMs and responses of NPP structures. The numerical results demonstrate that there is a significant difference in the correlation between earthquake IMs and seismic responses of non-isolated NPP structures considering low- and high-frequency ground motion groups. Meanwhile, a trivial discrepancy of the correlation is observed in the case of the base-isolated NPP subjected to the two groups of ground motions. Moreover, a selection of PGA or Sa for seismic response analyses of NPP structures in the high-frequency seismic regions may not be the best option. Additionally, a set of fragility curves are thereafter developed for the base-isolated NPP based on the shear deformation of lead rubber bearing (LRB) with respect to the strongly correlated IMs. The results reveal that the probability of damage to the structure is higher for low-frequency earthquakes compared with that of high-frequency ground motions. © 2019 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Nuclear power plant Earthquake intensity measure High-frequency ground motion Pearson's correlation coefficient Seismic fragility curve
1. Introduction The 2011 Great East Japan Earthquake caused significant damage to infrastructures in the region and immediately made a shutdown state of the eleven reactors at four nuclear power plants (NPPs) in Fukushima Daiichi. In the 2011 Mineral Virginia US earthquake, the ground motion exceeded the level of the operating basis and design basis earthquakes at the North Anna NPP. It was the first US nuclear plant to be shut down due to an earthquake. The 1999 Chichi earthquake caused three nuclear reactors in Northern Taiwan (Kuosheng and Chinshan areas) were shut down
* Corresponding author. E-mail address: [email protected] (T.-H. Lee).
automatically. The 2016 Gyeongju and 2017 Pohang earthquakes occurred in South Korea, nearby the NPPs, showed that the peak ground acceleration can be larger than 0.3 g, the safe shutdown earthquake design level of NPPs. Therefore, studies on seismic response analyses of NPP structures are always needed. The peak ground acceleration (PGA), velocity (PGV) or spectral acceleration (Sa) is commonly selected as an intensity measure (IM) of an earthquake for the seismic performance analysis of civil engineering structures. However, several studies showed that such parameters might not always be the best selections for seismic responses and damage analysis of civil structures [1e9]. Additionally, many other IMs were proposed by researchers and these IMs might be strongly correlated with seismic damage of different kinds of structures. In specific, the correlation between earthquake IMs
https://doi.org/10.1016/j.net.2019.06.013 1738-5733/© 2019 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
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and seismic damage of building structures was the most sufficiently studied [6e15]. Cao and Ronagh [8,9] they pointed out that velocity spectrum intensity (VSI), Housner intensity, and Sa are the best indicators correlated to seismic damage of low-rise buildings. Additionally, various researchers demonstrated that other IMs also have a strong correlation with the seismic response of buildings such as frequency-dependent parameters [10], Arias intensity [11], Sa(T1) and velocity-based parameters [12], and PGV and spectral response parameters [13,14]. An improved earthquake IM was proposed by Lu et al. [15] for super high-rise buildings, which showed to be more reliable and efficient than PGA and Sa(T1) in estimating collapse simulation. The relation between different earthquake IMs and responses of other civil structures were also investigated numerously. Optimal IMs for seismic responses of different types of bridges are conducted by Padgett et al. [16], Jahangiri et al. [17], Zelaschi et al. [18], Avs¸ar et al. [19], and Nguyen et al. [20]. Correlation analyses between ground motion parameters and damage of mountain tunnels were implemented by Chen and Wei [1]. Nguyen et al. [21] demonstrated that PGV/Vs30 is the optimum seismic IM for developing the fragility curves of underground structures. Phan and Paolacci [22] identified the efficient IMs for seismic response analysis of liquid steel storage tanks. Seismic probabilistic risk assessment (SPRA) and seismic margin assessment (SMA) are two kinds of effective approaches for safety examination of NPPs under seismic events. The seismic fragility evaluation is a crucial step in the seismic risk assessment of NPPs. During the evaluation process, to represent the seismic capacity of structures and equipment, high confident of low probability of failure (HCLPF) values and fragility curves are developed. The HCLPF value is defined as an earthquake level corresponding approximately to a 95% confidence that the probability of failure is less than 5%. There are many methods to derive fragility curves as well as calculate the HCLPF such as probabilistic fragility analysis (PFA), conservative deterministic failure margin method (CDFM), and test results. For the PFA methodology [23,24], the fragility curves and HCLPF are derived from a function of seismic median capacity and composite standard deviation. In this method, numerous seismic factors are considered as uncertainty parameters, which are ground motion, damping, modeling, mode shape combination, time history simulation, strength, inelastic model, and soil-structure interaction. Each factor is estimated in a statistic way to establish a median and a composite standard deviation. It is noted that the PFA methodology is reflected in the calculation process of seismic margin factors. While the PFA method calculates the seismic margin factors using a lognormal distribution in probabilistic methodology, CDFM method [25] determines the seismic margin factor based on finite element analysis. The three common deterministic seismic factors are the strength, inelastic energy absorption, and damping. The test data method [26] is widely used to evaluate electrical equipment with sufficient experimental data. Based on the response curves obtained from various failure modes, the lower bound of the curves can represent the deterministic fragility level. Zero period acceleration and average spectral acceleration are two indicators for fragility level in both deterministic and probabilistic approaches. Recently, many studies performed the seismic fragility assessment of NPP structures and equipment adopting the conventional aforementioned methodologies [27e33] or modified conventional method [34,35]. Additionally, many studies adopted general approaches such as the maximum likelihood estimation (MLE), the incremental dynamic analysis (IDA), and the regression, which have been used in seismic fragility assessment of general civil engineering structures (e.g. buildings, bridges, and underground structures), for NPP structures and components [27,31,33,37e40]. Some studies used the ground motions compatible to uniform
hazard response spectrum for developing fragility curves [27,29,36,37], while other studies used arbitrary ground [30,31,33,39]. The advantage of using arbitrary ground motions is to consider a wide range of magnitude, period, rupture distance, or amplitude as uncertainty characteristics in fragility analysis. In particular, Mandal et al. [30,31] performed comparative studies on fragility assessments using the conventional method for NPPs and the general approaches for civil structures. They used a set of arbitrary ground motions for analyses and concluded that the IDAand MLE-based fragility analyses give highly reasonable estimates compared to the conventional method, which produces an overestimation of the fragility by a great margin. Until now, correlations between seismic IMs and responses of buildings and other civil engineering structures were systematically studied, but those of NPP structures are still not studied yet. Therefore, the purpose of this study is to investigate the relationship between 23 earthquake IMs and seismic responses of NPP structures to identify the significant IMs to estimate damage of NPP. In particular, significant IMs for high-frequency and low-frequency ground motions are distinguished where a ground motion is referred to as a high-frequency motion when its' dominant frequency is over 10 Hz. An NPP containing an advanced pressurized water nuclear reactor, APR1400, designed in South Korea is selected as a case study example. Both NPP structures with and without base isolators are considered. Structural models of NPP structures are developed in SAP2000 program where lumped-mass stick model is used to model the containment and auxiliary buildings. A series of time history analysis is performed to monitor structural responses such as floor accelerations, floor displacements, and shear deformation of the base isolator. Thereafter, Pearson's correlation coefficients are calculated for each IM and strongly correlated IMs with seismic responses of NPP structures are identified. Finally, a set of fragility curves are developed based on the shear deformation of LRB with respect to the strongly correlated IMs. 2. Earthquake intensity measures and ground motions records 2.1. Earthquake intensity measures Earthquake IMs are crucial values for representing the characteristics of a seismic ground motion. In general, IMs characterize the amplitude, frequency content, and duration of motions [41]. The optimum IMs can reduce the deviation of seismic structural performances and predict the responses of structures accurately [15]. In this study, we select 23 available IMs proposed by many researchers for correlation analyses. These IMs are calculated for every ground motion time histories using SeismoSignal program [42]. The IMs adopted in this study and their definitions are presented in Table 1. It should be noted that the “intensity measure” (IM) terminology used herein represents all investigated ground motion parameters in this paper. 2.2. Selected ground motion records For this study, 80 ground motion records are selected from worldwide earthquakes that provided by the PEER center [53] and KMA [54]. Two groups of ground motions including low- and highfrequency content are classified separately, in which 40 records are in the low-frequency motion group and 40 records are in the highfrequency group. The low-frequency ground motions are collected from worldwide historic earthquakes while the high-frequency ground motion group consists of some earthquake events in North America and Korea, which can be categorized as mid-to lowseismicity zones. The frequency content of a ground motion is
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Table 1 Selected earthquake intensity measures. No. Earthquake parameter
Definition
Unit
Reference
1 2 3 4 5
Peak ground acceleration Peak ground velocity Peak ground displacement Ratio of PGV/PGA Root-mean-square of acceleration
g m/s m s g
e e e Kramer 1996 [41] Dobry et al., 1978 [43]
6
Root-mean-square of velocity
m/s
Kramer 1996 [41]
7
Root-mean-square of displacement
m
Kramer 1996 [41]
8
Arias intensity
m/s
Arias 1970 [44]
9
Characteristic intensity
PGA ¼ max ja(t)j PGV ¼ max jv(t)j PGD ¼ max jd(t)j PGV/PGA sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z ttot 1 Arms ¼ aðtÞ2 dt ttot 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Z ttot 1 Vrms ¼ vðtÞ2 dt ttot 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z ttot 1 Drms ¼ dðtÞ2 dt ttot 0 Z ttot p Ia ¼ aðtÞ2 dt 2g 0 2=3 pffiffiffiffiffiffiffi ttot Ic ¼ ðArms Þ
m1.5/ s2.5 m2/s
Park et al., 1985 [45]
m/s
Benjamin and Associates 1988 [46]
g*s
R ttot
10 Specific energy density
2
SED¼ 0 vðtÞ dt R t CAV ¼ 0tot aðtÞdt R 12 Acceleration spectrum intensity ASI ¼ 0:5 Sa ðx ¼ 0:05; TÞdT 0:1 11 Cumulative absolute velocity
13 Velocity spectrum intensity 14 Housner spectrum intensity 15 Sustained maximum acceleration 16 Sustained maximum velocity 17 Effective peak acceleration 18 19 20 21 22 23
Spectral acceleration at T1 Spectral velocity at T1 Spectral displacement at T1 A95 parameter Predominant period Mean period
VSI ¼
R 2:5 0:1
R 2:5 HI ¼ 0:1 PSv ðx ¼ 0:05; TÞdT SMA ¼ the 3rd of PGA SMV ¼ the 3rd of PGV EPA ¼
meanðS0:10:5 ðx ¼ 0:05ÞÞ a 2:5
Sa ðT1 Þ Sv ðT1 Þ Sd ðT1 Þ A95 ¼ 0.764 I 0:438 a Tp Tm ¼
SC 2i =fi Þ C 2i
m
Housner 1952 [47] & Thun et al., 1988 [48] Housner 1952 [47] & Thun et al., 1988 [48] Housner 1952 [47]
g
Nuttli 1979 [49]
m/s g
Nuttli 1979 [49] Benjamin and Associates 1988 [46]
g m/s m g s s
Shome et al., 1988 [50] e e Sarma & Yang 1987 [51] Kramer 1996 [41] Rathje et al., 1998 [52]
m
Sv ðx ¼ 0:05; TÞdT
; Ci is the Fourier amplitude, fi is the discrete frequency corresponding
e
to Ci
normally identified based on the response spectrum. In this study, 10 Hz is defined as the threshold to distinguish between low- and high-frequency earthquakes. In other words, the ground motions with large values of spectral accelerations fallen in the frequency range approximately larger than 10 Hz is considered as a highfrequency ground motion, otherwise discerned as low-frequency motions [55,56]. Fig. 1 shows the response spectra of two groups of ground motion records used in this study. 3. Structural modeling 3.1. Numerical modeling of NPP structures The Advanced Power Reactor 1400 (ARP1400), an advanced
pressurized water nuclear reactor designed in Korea is employed for a numerical example in this study. Fig. 2 shows a general view and cutting view of structural configuration of the APR1400 plant. We focus our modeling on the reactor containment building and the auxiliary building. The lumped-mass stick models of the structure are implemented in SAP2000 [57], a commercial structural analysis program. The containment and auxiliary buildings are modeled in terms of a simplified model using elastic beam elements. The equivalent section properties are calculated based on the designed cross sections of the structures [58,59]. The lumped masses are also assigned into associated element nodes. Elastic shell elements are applied for the base-mat foundation. The structural properties of the APR1400 NPP in the lumped-mass beam stick model are shown in Table 2.
Fig. 1. Response spectra of selected ground motion records.
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Fig. 2. Advanced power reactor 1400.
Table 2 Properties of the APR1400 NPP in the lumped-mass beam stick model. Node
Height frombase-mat (m)
Nodal mass(ton)
Area(m2)
Moment of inertia(m4)
Shear area(m2)
Torsional constant (m4)
87.07 166.52 185.42 189.29 170.39 234.68 314.15 333.05 318.02 310.43 376.80 279.92 355.52 352.09 147.80
202.90 202.90 202.90 202.90 202.90 202.90 202.90 202.90 202.90 202.90 202.90 179.76 179.76 166.11
56299.85, 56299.85, 56299.85, 56299.85, 56299.85, 56299.85, 56299.85, 56299.85, 56299.85, 56299.85, 56299.85, 47591.20, 35861.70, 12825.63,
56299.85 56299.85 56299.85 56299.85 56299.85 56299.85 56299.85 56299.85 56299.85 56299.85 56299.85 47591.20 35861.70 12825.63
101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 89.89, 89.89 89.89, 89.89 83.03, 83.03
112634.22 112634.22 112634.22 112634.22 112634.22 112634.22 112634.22 112634.22 112634.22 112634.22 112634.22 95199.65 71732.03 25651.25
184.17 341.40 796.48 523.67 273.10 296.29 296.86 355.47 80.51 264.64 255.68 271.76 81.38
833.15 883.97 857.92 313.78 254.60 221.94 261.38 202.76 202.76 202.76 103.23 97.93
51055.67, 79896.93 51262.81, 81942.48 51149.25, 80710.1 9908.34, 21253.36 9816.63, 19442.95 9515.25, 19384.02 9848.14, 20166.32 9630.81, 18524.13 9630.81, 18524.13 9630.81, 18524.13 1932.60, 4666.70 1918.14, 4642.60
662.77, 662.77 704.29,704.29 684.03, 684.03 221.77, 221.77 171.14, 171.14 144.33, 144.33 175.93,175.93 130.81, 130.81 130.81, 130.81 130.75, 130.75 94.90, 94.90 92.25, 92.25
164989.72 168389.13 165957.82 37753.43 35811.75 35233.94 36571.27 34566.87 34566.87 34566.87 7888.57 7840.37
4608.78 5265.66 4680.11 4150.72 3218.83 2000.28 1659.49 957.38
1660.45 1503.17 1529.65 1363.35 842.16 579.06 371.98
530766.3, 405355.4 466685.8, 332679.3 464101.2, 340852.6 368330.8, 292325.7 241060.5, 158771.4 142392.3, 121479.2 75850.4, 86362.9
770.35, 611.30 658.91, 582.41 659.42, 589.37 565.41, 558.81 358.88, 329.06 212.0, 261.6 160.3, 192.0
239729.53 198363.83 205791.05 187226.65 173747.81 76553.8 52753.99
Reactor containment building 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16.76 20.27 23.46 27.73 31.09 34.59 40.53 47.24 53.94 60.65 66.44 70.56 78.63 86.72 94.64
Internal structure 1201 1202 1203 1204 1204 1205 1206 1207 1208 1209 1210 1211 1212
16.76 18.28 20.26 23.46 25.75 27.73 31.09 32.61 34.59 36.57 40.53 46.32 51.20
Auxiliary structure 1001 1002 1003 1004 1005 1006 1007 1008
16.76 23.46 36.57 41.91 40.53 52.42 57.92 63.39
For the base-isolated model, 486 LRBs are installed beneath the base mat for improving the seismic performance of the NPP structures. Fig. 3 shows the finite element models of the non- and base-isolated NPP structures in SAP2000. Fig. 4 shows the layout of LRBs and the bilinear response model of LRBs due to shear forces. The mechanical properties of LRBs are described in Table 3. The results of the eigenvalue analysis are presented in Table 4. For the non-isolated NPP model, the 1st and 2nd modes are the horizontal translation modes of the containment building, while, the 3rd and 4th modes represent the translational modes of the auxiliary building, as shown in Fig. 5. For the base-isolated NPP
model, the 1st and 2nd modes are translational modes of the superstructure, while the 3rd mode represents the rotational mode and the 4th mode is the translational model of the containment building, as shown in Fig. 6. These results are also in good agreement with the findings elsewhere [60e62].
3.2. Verification of the lumped-mass stick model (LMSM) The LMSM is verified with a 3D finite element model (3D FEM) using ANSYS software. A set of time-history analyses for the nonisolated reactor containment building is performed to compare
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Fig. 3. Finite element lumped-mass stick model of APR1400: Non-isolated (left) and base-isolated model (right).
Fig. 4. Layout of LRBs and their bilinear response model.
Table 3 Mechanical properties of LRBs. Property
Value
Unit
Elastic stiffness, Ku Hardening stiffness, Kd Yield strength, Fy Characteristic strength, Qd Vertical stiffness, Kv Effective stiffness, Keff Equivalent damping ratio, x
537,703 4204.84 1009.65 1001.03 12.896 8970 0.335
kN/m kN/m kN kN kN/m kN/m
structures are expected to vibrate within an elastic range during a design earthquake. All ground motions were applied to the NPP models in the horizontal direction. The seismic responses of nonisolated NPP structures are obtained in terms of the maximum drift ratio and floor acceleration at each component, while for the base-isolated model, the additional shear deformation behavior of LRBs is observed. Figs. 10 and 11 show representative examples of the maximum floor displacements and examples of the displacement time-history responses of the NPP structure, respectively, for low-and high-frequency earthquakes. The acceleration floor response spectra at the top of the NPP components due to earthquakes are also plotted in Fig. 12. Fig. 13 shows shear force versus shear deformation behaviors of the LRB under different earthquakes. The responses of the NPP components are obtained for every ground motion records. A relationship between seismic responses of NPP structures and earthquake IMs is needed to identify the strong and the weak correlation indicators. In this study, the Pearson's coefficient is used to reflect the correlation between seismic responses of NPP structures and earthquake IMs. The correlation coefficient given by Ang and Tang [63] is defined as
r¼ Table 4 Eigenvalue analysis results. Mode shape
Translational Y of superstructure Translational X of superstructure Rotational Z of superstructure Translational Y of RCB Translational X of RCB Translational Y of auxiliary bldg. Translational X of auxiliary bldg.
Isolated base
e e e 3.858 3.859 5.077 5.351
0.476 0.477 0.709 3.786 3.812 e e
e e e e
Mode Mode Mode Mode
1 2 3 4
e e e e e
Mode Mode Mode Mode Mode
P
ðxi xÞðyi yÞ
sx sy
(1)
where x, y, are the sample means of variables xi and yi. xi represents the seismic responses of NPP components, while yi represents the values of intensity measures. sx , sy are the sample standard deviations of x and y, determined by
Natural frequency (Hz) Fixed base
1 n1
1 2 3 4 5
the seismic behaviors of two models. Fig. 7 shows the 3D FEM of the containment building modeled in ANSYS. Time-history responses and floor response spectra of LMSM and 3D FEM are shown in Figs. 8 and 9, respectively. It can be found that the results of the two models are in good agreement, demonstrating that the LMSM is sufficient for time-history analyses of NPP structures. 4. Seismic responses of NPP structures and correlation analyses A series of linear time-history analyses are performed since NPP
sx ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i i 1 h 1 h ðSxi Þ2 nðxÞ2 ; sy ¼ ðSyi Þ2 nðyÞ2 n1 n1 (2)
Fig. 14 shows the representative results of the calculated correlation coefficients for the non-isolated NPP structures associated with low- and high-frequency ground motions. It is found that for the low-frequency motions, the A95 and PGA are the strongest correlated parameters, followed by sustained maximum acceleration (SMA) and effective peak acceleration (EPA). The weakest correlated IMs are specific energy density (SED), root mean square of displacement (Drms), PGD, and Sv(T1). For the high-frequency motion group, the good correlation indicators are SED, characteristic intensity (Ic), and Arias intensity (Ia). The poor correlation IMs are PGV/PGA, predominant period (Tp), and mean period (Tm). The similar tendency is observed for all NPP components modeled. Fig. 15 shows the representative results of the correlation coefficients for the base-isolated NPP model. It can be demonstrated that for low-frequency ground motions, SED, Ia, and Ic are strongly
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Fig. 5. Mode shapes of the non-isolated NPP model.
Fig. 6. Mode shapes of the base-isolated NPP model.
correlated parameters. Meanwhile, the lowest correlation IMs are PGV/PGA, Tp, and Tm. Also, this trend is obtained for the base-isolated NPP structures associated with the high-frequency motions. Tables 5 and 6 summarize the strongly and weakly correlated IMs with seismic responses of NPP structures under low- and highfrequency earthquakes, respectively. It is highlighted that SED, Ia, and Ic are the best IMs in correlating with seismic responses of the base-isolated NPP structures for both low- and high-frequency earthquakes and the non-isolated structure in HF excitations. A95, PGA, and SMA are the also good indicators for correlation with damage of the non-isolated NPP structures in LF seismic zones. In contrast, Tp, Tm, and PGV/PGA are the weakest correlated IMs with seismic responses of the NPP structures under HF earthquakes and the base-isolated structures in LF earthquakes. Additionally, Drms, PGD, and Sv(T1) are also shown to be low correlation with seismic damage of the non-isolated NPP structure in LF earthquakes. For the non-isolated NPP model with regard to the lowfrequency motions, the strongly correlated intensity measures (PGA, A95, SMA, EPA) seem to be resulted from their definitions, in which these measures are related to the force (or the acceleration). Thus, it governs the floor responses of the fixed base structures for high amplitude of ground motions. Whereas, the poor correlation parameters (Drms and PGD), which are directly related to the deformation (or the displacement), seems to be less sensitive to the relatively rigid structures. For the base-isolated structures, most of input seismic energy is dissipated through the hysteretic behavior of LRBs. Therefore, it is obvious to find that the energy-based IMs (SED, Ia) are the strong correlated parameters. Meanwhile, the period-based parameters, Tp
and Tm, are less than 1.7 s and 0.7 s for the LF and HF groups, respectively. It is smaller than the fundamental period of the base-isolated structures, consequently, causing a less damage to the structure. 5. Fragility analyses 5.1. Limit states The seismic fragility is the conditional probability that a structural system exceeds a limit state when subjected to a specified level of earthquake intensity. For the base-isolated NPP structure, the superstructure should behave within the elastic range during the seismic excitation. However, the base isolator will experience a large deformation that may exceed the yield deformation and reach the ultimate deformation capacity. For developing fragility curves, a set of limit states should be pre-defined according to damage levels of components. In this study, the damage levels of an LRB with respect to the shear strain is considered as the limit states. The shear strain of LRB, g is expressed by
g¼
D H
(3)
where D and H are the maximum lateral deformation and the height of LRB, respectively. According to recent experimental studies [64e69], the LRB can reach to an ultimate capacity of beyond 400% shear strain. Therefore, we adopt these results to define three limit states, if the shear strain exceeds 100% (i.e. D 40 cm), the slight limit state (LS-1) is specified. Similarly, if the
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Shinozuka et al. [73] is used in this study. In this approach, the fragility function is assumed as a log-normal cumulative distribution function (CDF) expressed by
lnða=ck Þ Fk ðaÞ ¼ F
zk
(4)
where a is the earthquake intensity measure, ck and zk are the median and the log-standard deviation of the log-normal CDF, and Fð Þ is the standard normal CDF. In Equation (4), the subscript k indicates the k-th limit state when more than one limit state is considered. In the MLE, ck and zk are determined by maximizing the likelihood function. This function is defined by
L¼
Fig. 7. 3D FEM of the reactor containment building.
shear strain goes beyond 300% (i.e. D 120 cm) and 400% (i.e. D 160 cm), the moderate (LS-2) and extensive (LS-3) limit states are established. This approach was also used in previous studies [39,40,70e72]. Three limit states are summarized in Table 7. 5.2. Maximum likelihood estimation Among several methods to develop seismic fragility curves, the maximum likelihood estimation (MLE) approach proposed by
YN i¼1
½Fk ðai Þxi ½1 Fk ðai Þð1xi Þ
(5)
where Fk ðaÞ increases when damage occurs and 1 Fk ðaÞ, the probability of not experiencing a damage, increases when damage does not occur for the earthquake intensity of ai . In Equation (5), N is the number of ground motions considered and xi is a Bernoulli random variable that indicates whether the structure is damaged or not where 0 indicates no damage and 1 indicates damage. ck and zk are determined so that Equation (5) is maximized with respect to ck and zk as follows
vL vL ¼ ¼ 0; k ¼ 1; /; NLS vck vzk
(6)
where NLS is the number of limit states. 5.3. Fragility curves Since LRB is the crucial element in the base-isolated NPP, a set of fragility curves is developed for different limit states, which are defined based on the shear strain of LRB. The two spectrally equivalent ground motion suites (LF and HF motions) are used to
Fig. 8. Comparison of time-history responses between two models under the 1940 El Centro earthquake.
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Fig. 9. Floor response spectra of the structure under the 1940 El Centro earthquake.
Fig. 10. Maximum displacements at the top of the NPP structures under the LF and HF earthquakes.
Fig. 11. Displacement time-history responses at the top of the containment building under the LF and HF earthquakes.
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Fig. 12. Mean floor response spectra at the top of the NPP structures with different earthquakes.
Fig. 13. Responses of LRB under different earthquakes.
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Fig. 14. Correlation between responses of non-isolated NPP and earthquake IMs.
perform the incremental dynamic analysis (IDA) [74]. In IDA, the selected ground motions are scaled to multiple levels of intensity, herein, we select two strongly correlated IMs, which are SED and Ia, to develop fragility curves for the base-isolated NPP structure. For each analysis, the maximum deformation of LRB is monitored as the engineering demand parameter. In total, 800 dynamic analyses are performed (i.e. 2 suites x 40 records x 10 intensity levels). Fig. 16 shows the IDA curves in terms of deformation of LRB versus IMs for LF and HF motions. The solid curves represent the mean values. Due to higher input energy of the LF motions, the base isolator is deformed in a larger range during a stronger seismic intensity. Fragility curves of base-isolated NPP model are developed for three limit states considering two groups of ground motions. Fig. 17 shows the fragility curves for three limit states with different earthquake groups. It can be observed that the base-isolated NPP structure might behave without damage if the level of SED and Ia are less than 0.2 m2/s and 1.5 m/s, respectively. Fig. 18 shows a comparison of fragility curves for three LSs and two groups of earthquakes. It can be observed that the structural model under LF motions would be more vulnerable than that due to HF earthquakes. This can be attributed to the reason that the deformation of LRBs produced by LF motions is higher than that under HF motions. It can be clearly observed that the median values for LS-1 are 22% and 24% lower when LF motions are applied than applying HF ones for SED and Ia, respectively. Similarly, the median values for LS-2 and LS-3 are reduced by 15% and 9% with respect to SED, respectively, and also decreased 12% and 8% with respect to Ia,
respectively, under LF motions. Table 8 describes the fragility function parameters (i.e. median and standard deviation (SD)) for LF and HF earthquakes with different limit states. 6. Conclusions Significant intensity measures of earthquakes that are strongly correlated to seismic responses of NPP structures are identified. We consider the effect of low-frequency and high-frequency ground motions, separately. A series of time history analyses are performed for both non- and base-isolated numerical models of NPP structures to monitor the floor displacement, floor acceleration, and shear deformation of LRB. Pearson's correlation coefficients are calculated to identify the best earthquake IMs for indicating the seismic damage of NPP structures. A set of fragility curves is also developed with respect to the well-correlated IMs. Based on the numerical results, the following conclusions are drawn. (1) For the non-isolated NPP structures subjected to lowfrequency ground motions, the best IMs for correlating with seismic responses of such structures are PGA, A95, and SMA. For high-frequency earthquakes, the best IMs are SED, Ic, and Ia. (2) For the base-isolated NPP structures subjected to lowfrequency ground motions, SED, Ia, and Ic are the strongly correlated parameters. This trend is also obtained for the base-isolated NPP structures associated with the highfrequency ground motions.
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Fig. 15. Correlation between the responses of base-isolated NPP and earthquake IMs.
Table 5 Strongly correlated IMs with seismic responses of NPP structures. Low-frequency earthquakes
High-frequency earthquakes
Non-isolated model
Base-isolated model
Non-isolated model
Base-isolated model
A95 PGA SMA
SED Ia Ic
SED Ic Ia
SED Ia Ic
Table 6 Weakly correlated IMs with seismic responses of NPP structures. Low-frequency earthquakes
High-frequency earthquakes
Non-isolated model
Base-isolated model
Non-isolated model
Base-isolated model
Drms PGD Sv(T1)
Tp Tm PGV/PGA
Tp Tm PGV/PGA
Tp Tm PGV/PGA
Table 7 Definition of limit states. Limit state
Shear strain of LRB
Maximum lateral deformation of LRB (mm)
Slight damage (LS-1) Moderate damage (LS-2) Extensive damage (LS-3)
g 100% g 300% g 400%
400 1200 1600
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Fig. 16. Incremental displacement of LRB with respect to SED and Ia.
Fig. 17. Fragility curves for limit states with various ground motion groups.
(3) A selection of PGA or Sa for correlation analyses with seismic responses of the NPP structures in the high-frequency seismic regions may not be the best option. (4) The median values of fragility functions for three limit states in the case of base-isolated NPP are reduced by 9%e22% and 8%e24% for SED and Ia, respectively, when low-frequency ground motions applied than when high-frequency motions are applied. It implies that the considered NPP structure is more vulnerable to low-frequency ground motions than high-frequency ground motions.
Data availability All the data supporting the key findings of this paper are presented in the figures and tables of the article. Request for other data will be considered by the corresponding author.
Conflicts of interest The authors declare that they have no conflicts of interest.
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Fig. 18. Comparison of fragility curves for low- and high-frequency excitations.
Table 8 Fragility function parameters of the based-isolated NPP structure. Limit state LF earthquake
LS-1 LS-2 LS-3
HF earthquake
SED (m2/s)
Ia (m/s)
Median SD
Median SD
0.489 1.054 1.633
0.442 6.206 0.422 16.860 0.409 33.202
SED (m2/s)
Ia (m/s)
Median SD
Median SD
0.570 0.625 0.587 1.247 0.590 1.793
0.549 8.123 0.443 19.165 0.247 36.179
0.643 0.491 0.279
Acknowledgement This study is supported by project titled “Development of High Reliability Seismic Monitoring System for Precise Analysis of High Frequency Earthquake Motion in Nuclear Power Plants”, assignment number 20171510101860.
References [1] Z. Chen, J. Wei, Correlation between ground motion parameters and lining damage indices for mountain tunnels, Nat. Hazards 65 (3) (2013) 1683e1702. [2] M. Corigliano, C.G. Lai, G. Barla, January). Seismic vulnerability of rock tunnels using fragility curves, in: 11th ISRM Congress, International Society for Rock Mechanics and Rock Engineering, 2007. [3] S. Yaghmaei-Sabegh, Application of wavelet transforms on characterization of inelastic displacement ratio spectra for pulse-like ground motions, J. Earthq. Eng. 16 (4) (2012) 561e578. [4] M. Ghayoomi, S. Dashti, Effect of ground motion characteristics on seismic soil-foundation-structure interaction, Earthq. Spectra 31 (3) (2015) 1789e1812. [5] Y.Y. Zhang, Y. Ding, Y.T. Pang, Selection of optimal intensity measures in seismic damage analysis of cable-stayed bridges subjected to far-fault ground motions, J. Earthq. Tsunami 9 (01) (2015), 1550003. [6] A. Elenas, Correlation between seismic acceleration parameters and overall structural damage indices of buildings, Soil Dynam. Earthq. Eng. 20 (1e4) (2000) 93e100. [7] A. Elenas, K. Meskouris, Correlation study between seismic acceleration parameters and damage indices of structures, Eng. Struct. 23 (6) (2001)
698e704. [8] V. Cao, H.R. Ronagh, Correlation between seismic parameters of far-fault motions and damage indices of low-rise reinforced concrete frames, Soil Dynam. Earthq. Eng. 66 (2014) 102e112. [9] V. Cao, H.R. Ronagh, Correlation between parameters of pulse-type motions and damage of low-rise RC frames, Earthq. Struct. 7 (3) (2014) 365e384. [10] A. Massumi, F. Gholami, The influence of seismic intensity parameters on structural damage of RC buildings using principal components analysis, Appl. Math. Model. 40 (3) (2016) 2161e2176. [11] N. Nanos, A. Elenas, P. Ponterosso, Correlation of different strong motion duration parameters and damage indicators of reinforced concrete structures, in: The 14th World Conference on Earthquake Engineering, 2008. Beijing, China, 2008. [12] K. Kostinakis, A. Athanatopoulou, K. Morfidis, Correlation between ground motion intensity measures and seismic damage of 3D R/C buildings, Eng. Struct. 82 (2015) 151e167. [13] J. Pejovic, S. Jankovic, Selection of ground motion intensity measure for reinforced concrete structure, Procedia Eng. 117 (2015) 588e595. [14] J. Pejovic, N. Serdar, R. Pejovic, Optimal intensity measures for probabilistic seismic demand models of RC high-rise buildings, Earthq. Struct. 13 (3) (2017) 221e230. [15] X. Lu, L. Ye, X. Lu, M. Li, X. Ma, An improved ground motion intensity measure for super high-rise buildings, Sci. China Technol. Sci. 56 (6) (2013) 1525e1533. [16] J.E. Padgett, B.G. Nielson, R. DesRoches, Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios, Earthq. Eng. Struct. Dyn. 37 (5) (2008) 711e725. [17] V. Jahangiri, M. Yazdani, M.S. Marefat, Intensity measures for the seismic response assessment of plain concrete arch bridges, Bull. Earthq. Eng. (2018) 1e24. [18] C. Zelaschi, R. Monteiro, R. Pinho, Critical assessment of intensity measures for seismic response of Italian RC bridge portfolios, J. Earthq. Eng. (2017) 1e21. € Avs¸ar, G. Ozdemir, € [19] O. Response of seismic-isolated bridges in relation to intensity measures of ordinary and pulselike ground motions, J. Bridge Eng. 18 (3) (2011) 250e260. [20] D. Nguyen, H. Park, B. Thusa, T.-H. Lee, Identification of Earthquake Intensity Measures as the Seismic Damage Indicator of Bridges Considering Low- and High-Frequency Contents of Ground Motions, Submitted to Earthquakes And Structures, 2019. [21] D.D. Nguyen, D. Park, S. Shamsher, V.Q. Nguyen, T.H. Lee, Seismic vulnerability assessment of rectangular cut-and-cover subway tunnels, Tunn. Undergr. Space Technol. 86 (2019) 247e261. [22] H.N. Phan, F. Paolacci, Efficient intensity measures for probabilistic seismic response analysis of anchored above-ground liquid steel storage tanks, in: ASME 2016 Pressure Vessels and Piping Conference (pp. V005T09A010-
Please cite this article as: D.-D. Nguyen et al., Identifying significant earthquake intensity measures for evaluating seismic damage and fragility of nuclear power plant structures, Nuclear Engineering and Technology, https://doi.org/10.1016/j.net.2019.06.013
14
D.-D. Nguyen et al. / Nuclear Engineering and Technology xxx (xxxx) xxx
V005T09A010), American Society of Mechanical Engineers, 2016. [23] R.P. Kennedy, M.K. Ravindra, Seismic fragilities for nuclear power plant risk studies, Nucl. Eng. Des. 79 (1) (1984) 47e68. [24] EPRI, Methodology for Developing Seismic Fragilities, Report TR-103959, Palo Alto, CA, USA, 1994. [25] EPRI, A Methodology for Assessment of Nuclear Power Plant Seismic Margin, Report EPRI-NP-6041-M-REV.1, 1991 (Palo Alto, CA, USA). [26] U.S. NUREG, Nuclear Regulatory Commission, Seismic Fragility of Nuclear Power Plant Components (Phase II), NUREG/CR-4659, vols. 2e4, Department of Nuclear Energy, Brookhaven Laboratory, Long Island, NY, USA, 1987. BNLNUREG-52007. [27] A. Ali, N.A. Hayah, D. Kim, S.G. Cho, Probabilistic seismic assessment of baseisolated NPPs subjected to strong ground motions of Tohoku earthquake, Nucl. Eng. Technol. 46 (5) (2014) 699e706. [28] P.C. Basu, M.K. Ravindra, Y. Mihara, Component fragility for use in PSA of nuclear power plant, Nucl. Eng. Des. 323 (2017) 209e227. [29] S.G. Cho, Y.H. Joe, Seismic fragility analyses of nuclear power plant structures based on the recorded earthquake data in Korea, Nucl. Eng. Des. 235 (17e19) (2005) 1867e1874. [30] T.K. Mandal, N.N. Pujari, S. Ghosh, A comparative study of seismic fragility estimates using different numerical methods, in: 4th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, 2013. [31] T.K. Mandal, S. Ghosh, N.N. Pujari, Seismic fragility analysis of a typical Indian PHWR containment: comparison of fragility models, Struct. Saf. 58 (2016) 11e19. [32] F. Perotti, M. Domaneschi, S. De Grandis, The numerical computation of seismic fragility of base-isolated Nuclear Power Plants buildings, Nucl. Eng. Des. 262 (2013) 189e200. [33] T.T. Tran, A.T. Cao, T.H.X. Nguyen, D. Kim, Fragility assessment for electric cabinet in nuclear power plant using response surface methodology, Nucl. Eng. Technol. 51 (3) (2019) 894e903. [34] Y.N. Huang, A.S. Whittaker, N. Luco, A probabilistic seismic risk assessment procedure for nuclear power plants:(I) Methodology, Nucl. Eng. Des. 241 (9) (2011) 3996e4003. [35] Y.N. Huang, A.S. Whittaker, N. Luco, A probabilistic seismic risk assessment procedure for nuclear power plants:(II) Application, Nucl. Eng. Des. 241 (9) (2011) 3985e3995. [36] I.K. Choi, Y.S. Choun, S.M. Ahn, J.M. Seo, Seismic fragility analysis of a CANDU type NPP containment building for near-fault ground motions, KSCE J. Civ. Eng. 10 (2) (2006) 105e112. [37] I.K. Choi, Y.S. Choun, S.M. Ahn, J.M. Seo, Probabilistic seismic risk analysis of CANDU containment structure for near-fault earthquakes, Nucl. Eng. Des. 238 (6) (2008) 1382e1391. [38] S. De Grandis, M. Domaneschi, F. Perotti, A numerical procedure for computing the fragility of NPP components under random seismic excitation, Nucl. Eng. Des. 239 (11) (2009) 2491e2499. [39] D.D. Nguyen, B. Thusa, T.H. Lee, Seismic fragility of base-isolated nuclear power plant considering effects of near-fault ground motions, J. Korean Soc. Hazard Mitig. 18 (7) (2018) 315e321. [40] D.D. Nguyen, B. Thusa, T.H. Lee, Effects of significant duration of ground motions on seismic responses of base-isolated nuclear power plant, J. Earthq. Eng. Soc. Korea 23 (3) (2019) 149e157. [41] S.L. Kramer, Geotechnical Earthquake Engineering, Prentice Hall, New Jersey, USA, 1996. [42] SeismoSignal - a computer program for signal processing of strong-motion data, available from: http://www.seismosoft.com, 2017. [43] R. Dobry, I.M. Idriss, E. Ng, Duration characteristics of horizontal components of strong-motion earthquake records, Bull. Seismol. Soc. Am. 68 (5) (1978) 1487e1520. [44] A. Arias, A Measure of Earthquake Intensity, Massachusetts Inst. of Tech., Cambridge, 1970 (Univ. of Chile, Santiago de Chile). [45] Y.J. Park, A.H.S. Ang, Y.K. Wen, Seismic damage analysis of reinforced concrete buildings, J. Struct. Eng. 111 (4) (1985) 740e757. [46] J.R. Benjamin, A Criterion for Determining Exceedances of the Operating Basis Earthquake, Report No. EPRI NP-5930, Electric Power Research Institute, Palo Alto., California, USA, 1988. [47] G.W. Housner, Spectrum intensities of strong-motion earthquakes, in: Symposium on Earthquake and Blast Effects on Structures, 1952, pp. 20e36 (Los Angeles, California, USA). [48] J.L. Von Thun, Earthquake Ground Motions for Design and Analysis of Dams. Earthquake Engineering and Soil Dynamics II-Recent Advances in GroundMotion Evaluation, 1988. [49] O.W. Nuttli, The Relation of Sustained Maximum Ground Acceleration and Velocity to Earthquake Intensity and Magnitude, Report 16, US Army Engineer Waterways Experiment Station, Vicksburg, Mississippi, USA, 1979. Misc. Paper S-73-1.
[50] N. Shome, C.A. Cornell, P. Bazzurro, J.E. Carballo, Earthquakes, records, and nonlinear responses, Earthq. Spectra 14 (3) (1998) 469e500. [51] S.K. Sarma, K.S. Yang, An evaluation of strong motion records and a new parameter A95, Earthq. Eng. Struct. Dyn. 15 (1) (1987) 119e132. [52] E.M. Rathje, N.A. Abrahamson, J.D. Bray, Simplified frequency content estimates of earthquake ground motions, J. Geotech. Geoenviron. Eng. 124 (2) (1998) 150e159. [53] PEER Ground Motion Database, 2018. http://peer.berkeley.edu/peer_ground_ motion_database. [54] KMA, Korean Meteorological Administration, 2016, https://web.kma.go.kr/ eng/index.jsp [55] EPRI, Program on Technology Innovation: the Effects of High Frequency Ground Motion on Structures, Components, and Equipment in Nuclear Power Plants, Report 1015108, Electrical Power Research Institute, Palo Alto, California, USA, 2007. [56] EPRI, Advanced Nuclear Technology: High-Frequency Seismic Loading Evaluation for Standard Nuclear Power Plants, Report 3002009429, Electrical Power Research Institute, Palo Alto, California, USA, 2017. [57] SAP2000 Ver 15, Computers and structures Inc, Berkeley, CA, USA, 2013. [58] J.M. Kim, E.H. Lee, Development and Verification of Simplified Beam-Stick Model of Seismically Isolated ARP1400 Nuclear Power Plant Structure,” Research Report, Central Research Institute of KHNP, KETEP Project No. 2014151010170B, Korea, 2015. [59] E.H. Lee, J.M. Kim, K.H. Joo, H. Kim, Evaluation of the soil-structure interaction effect on seismically isolated nuclear power plant structures, J. Earthq. Eng. Soc. Korea 20 (6) (2016) 379e389. [60] G.J. Kim, K.K. Yang, B.S. Kim, H.J. Kim, S.J. Yun, J.K. Song, Seismic response evaluation of seismically isolated nuclear power plant structure subjected to Gyeong-Ju earthquake, J. Earthq. Eng. Soc. Korea 20 (7) (2016) 453e460. [61] J.W. Jung, H.W. Jang, J.H. Kim, J.W. Hong, Effect of second hardening on floor response spectrum of a base-isolated nuclear power plant, Nucl. Eng. Des. 322 (2017) 138e147. [62] S.G. Cho, S.M. Yun, D. Kim, K.J. Hoo, Analyses of vertical seismic responses of seismically isolated nuclear power plant structures supported by lead rubber bearings, J. Earthq. Eng. Soc. Korea 19 (3) (2015) 133e143. [63] A.H.S. Ang, W.H. Tang, Probability Concepts in Engineering: Emphasis on Applications in Civil & Environmental Engineering, vol. 1, Wiley and Sons, 2007. [64] J.H. Kim, M.K. Kim, I.K. Choi, Experimental study on the ultimate limit state of a lead-rubber bearing, in: ASME 2016 Pressure Vessels and Piping Conference (pp. V008T08A039-V008T08A039), American Society of Mechanical Engineers, Vancouver, BC, Canada, 2016, 2016. [65] H.P. Lee, M.S. Cho, J.Y. Park, K.S. Jang, Assessment of LRB seismic isolation device for nuclear power plant, in: Transactions of the Korean Nuclear Society Autumn Meating, 2013. Gyeongju, Korea, 2013. [66] I. Choi, J. Kim, M. Kim, Performance based design of lrb systems for nuclear power plants, in: Transaction of the 24th Structural Mechanics in Reactor Technology (SMiRT-24) Conference, Busan, Korea, 2017, 2017. [67] S. Eem, D. Hahm, Large strain nonlinear model of lead rubber bearings for beyond design basis earthquakes, Nucl. Eng. Technol. 51 (2) (2019) 600e606. [68] S. Yabana, K. Kanazawa, S. Nagata, S. Kitamura, T. Sano, Shaking table tests with large test specimens of seismically isolated FBR plants: Part 3 - ultimate behavior of upper structure and rubber bearings, in: ASME 2009 Pressure Vessels and Piping Conference, American Society of Mechanical Engineers, 2009, pp. 179e187. [69] T. Hiraki, S. Nagata, K. Kanazawa, T. Imaoka, T. Nakayama, Y.,. Umeki, H. Shimizu, Development of an evaluation method for seismic isolation systems of nuclear power facilities: Part 9 - ultimate properties of full-scale lead rubber bearings based on breaking test, in: ASME 2014 Pressure Vessels and Piping Conference (pp. V008T08A012-V008T08A012), American Society of Mechanical Engineers, 2014. [70] J. Zhang, Y. Huo, Optimum isolation design for highway bridges using fragility function method, in: The 14th World Conference on Earthquake Engineering, WCEE), Beijing, China, 2008. [71] J.H. Lee, J.K. Song, Seismic fragility analysis of seismically isolated nuclear power plant structures using equivalent linear-and bilinear-lead rubber bearing model, J. Earthq. Eng. Soc. Korea 19 (5) (2015) 207e217. [72] S.H. Eem, H.J. Jung, M.K. Kim, I.K. Choi, Seismic fragility evaluation of isolated NPP containment structure considering soil-structure interaction effect, J. Earthq. Eng. Soc. Korea 17 (2) (2013) 53e59. [73] M. Shinozuka, M.Q. Feng, J. Lee, T. Naganuma, Statistical analysis of fragility curves, J. Eng. Mech. 126 (12) (2000) 1224e1231. [74] D. Vamvatsikos, C.A. Cornell, Incremental dynamic analysis, Earthq. Eng. Struct. Dyn. 31 (3) (2002) 491e514.
Please cite this article as: D.-D. Nguyen et al., Identifying significant earthquake intensity measures for evaluating seismic damage and fragility of nuclear power plant structures, Nuclear Engineering and Technology, https://doi.org/10.1016/j.net.2019.06.013
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Original Article
Identifying significant earthquake intensity measures for evaluating seismic damage and fragility of nuclear power plant structures Duy-Duan Nguyen a, b, Bidhek Thusa a, Tong-Seok Han c, Tae-Hyung Lee a, * a
Department of Civil and Environmental Engineering, Konkuk University, Seoul 05029, South Korea Department of Civil Engineering, Vinh University, Vinh 461010, Vietnam c Department of Civil and Environmental Engineering, Yonsei University, Seoul 03722, South Korea b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 March 2019 Received in revised form 14 May 2019 Accepted 12 June 2019 Available online xxx
Seismic design practices and seismic response analyses of civil structures and nuclear power plants (NPPs) have conventionally used the peak ground acceleration (PGA) or spectral acceleration (Sa) as an intensity measure (IM) of an earthquake. However, there are many other earthquake IMs that were proposed by various researchers. The aim of this study is to investigate the correlation between seismic responses of NPP components and 23 earthquake IMs and identify the best IMs for correlating with damage of NPP structures. Particularly, low- and high-frequency ground motion records are separately accounted in correlation analyses. An advanced power reactor NPP in Korea, APR1400, is selected for numerical analyses where containment and auxiliary buildings are modeled using SAP2000. Floor displacements and accelerations are monitored for the non- and base-isolated NPP structures while shear deformations of the base isolator are additionally monitored for the base-isolated NPP. A series of Pearson's correlation coefficients are calculated to recognize the correlation between each of the 23 earthquake IMs and responses of NPP structures. The numerical results demonstrate that there is a significant difference in the correlation between earthquake IMs and seismic responses of non-isolated NPP structures considering low- and high-frequency ground motion groups. Meanwhile, a trivial discrepancy of the correlation is observed in the case of the base-isolated NPP subjected to the two groups of ground motions. Moreover, a selection of PGA or Sa for seismic response analyses of NPP structures in the high-frequency seismic regions may not be the best option. Additionally, a set of fragility curves are thereafter developed for the base-isolated NPP based on the shear deformation of lead rubber bearing (LRB) with respect to the strongly correlated IMs. The results reveal that the probability of damage to the structure is higher for low-frequency earthquakes compared with that of high-frequency ground motions. © 2019 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Nuclear power plant Earthquake intensity measure High-frequency ground motion Pearson's correlation coefficient Seismic fragility curve
1. Introduction The 2011 Great East Japan Earthquake caused significant damage to infrastructures in the region and immediately made a shutdown state of the eleven reactors at four nuclear power plants (NPPs) in Fukushima Daiichi. In the 2011 Mineral Virginia US earthquake, the ground motion exceeded the level of the operating basis and design basis earthquakes at the North Anna NPP. It was the first US nuclear plant to be shut down due to an earthquake. The 1999 Chichi earthquake caused three nuclear reactors in Northern Taiwan (Kuosheng and Chinshan areas) were shut down
* Corresponding author. E-mail address: [email protected] (T.-H. Lee).
automatically. The 2016 Gyeongju and 2017 Pohang earthquakes occurred in South Korea, nearby the NPPs, showed that the peak ground acceleration can be larger than 0.3 g, the safe shutdown earthquake design level of NPPs. Therefore, studies on seismic response analyses of NPP structures are always needed. The peak ground acceleration (PGA), velocity (PGV) or spectral acceleration (Sa) is commonly selected as an intensity measure (IM) of an earthquake for the seismic performance analysis of civil engineering structures. However, several studies showed that such parameters might not always be the best selections for seismic responses and damage analysis of civil structures [1e9]. Additionally, many other IMs were proposed by researchers and these IMs might be strongly correlated with seismic damage of different kinds of structures. In specific, the correlation between earthquake IMs
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and seismic damage of building structures was the most sufficiently studied [6e15]. Cao and Ronagh [8,9] they pointed out that velocity spectrum intensity (VSI), Housner intensity, and Sa are the best indicators correlated to seismic damage of low-rise buildings. Additionally, various researchers demonstrated that other IMs also have a strong correlation with the seismic response of buildings such as frequency-dependent parameters [10], Arias intensity [11], Sa(T1) and velocity-based parameters [12], and PGV and spectral response parameters [13,14]. An improved earthquake IM was proposed by Lu et al. [15] for super high-rise buildings, which showed to be more reliable and efficient than PGA and Sa(T1) in estimating collapse simulation. The relation between different earthquake IMs and responses of other civil structures were also investigated numerously. Optimal IMs for seismic responses of different types of bridges are conducted by Padgett et al. [16], Jahangiri et al. [17], Zelaschi et al. [18], Avs¸ar et al. [19], and Nguyen et al. [20]. Correlation analyses between ground motion parameters and damage of mountain tunnels were implemented by Chen and Wei [1]. Nguyen et al. [21] demonstrated that PGV/Vs30 is the optimum seismic IM for developing the fragility curves of underground structures. Phan and Paolacci [22] identified the efficient IMs for seismic response analysis of liquid steel storage tanks. Seismic probabilistic risk assessment (SPRA) and seismic margin assessment (SMA) are two kinds of effective approaches for safety examination of NPPs under seismic events. The seismic fragility evaluation is a crucial step in the seismic risk assessment of NPPs. During the evaluation process, to represent the seismic capacity of structures and equipment, high confident of low probability of failure (HCLPF) values and fragility curves are developed. The HCLPF value is defined as an earthquake level corresponding approximately to a 95% confidence that the probability of failure is less than 5%. There are many methods to derive fragility curves as well as calculate the HCLPF such as probabilistic fragility analysis (PFA), conservative deterministic failure margin method (CDFM), and test results. For the PFA methodology [23,24], the fragility curves and HCLPF are derived from a function of seismic median capacity and composite standard deviation. In this method, numerous seismic factors are considered as uncertainty parameters, which are ground motion, damping, modeling, mode shape combination, time history simulation, strength, inelastic model, and soil-structure interaction. Each factor is estimated in a statistic way to establish a median and a composite standard deviation. It is noted that the PFA methodology is reflected in the calculation process of seismic margin factors. While the PFA method calculates the seismic margin factors using a lognormal distribution in probabilistic methodology, CDFM method [25] determines the seismic margin factor based on finite element analysis. The three common deterministic seismic factors are the strength, inelastic energy absorption, and damping. The test data method [26] is widely used to evaluate electrical equipment with sufficient experimental data. Based on the response curves obtained from various failure modes, the lower bound of the curves can represent the deterministic fragility level. Zero period acceleration and average spectral acceleration are two indicators for fragility level in both deterministic and probabilistic approaches. Recently, many studies performed the seismic fragility assessment of NPP structures and equipment adopting the conventional aforementioned methodologies [27e33] or modified conventional method [34,35]. Additionally, many studies adopted general approaches such as the maximum likelihood estimation (MLE), the incremental dynamic analysis (IDA), and the regression, which have been used in seismic fragility assessment of general civil engineering structures (e.g. buildings, bridges, and underground structures), for NPP structures and components [27,31,33,37e40]. Some studies used the ground motions compatible to uniform
hazard response spectrum for developing fragility curves [27,29,36,37], while other studies used arbitrary ground [30,31,33,39]. The advantage of using arbitrary ground motions is to consider a wide range of magnitude, period, rupture distance, or amplitude as uncertainty characteristics in fragility analysis. In particular, Mandal et al. [30,31] performed comparative studies on fragility assessments using the conventional method for NPPs and the general approaches for civil structures. They used a set of arbitrary ground motions for analyses and concluded that the IDAand MLE-based fragility analyses give highly reasonable estimates compared to the conventional method, which produces an overestimation of the fragility by a great margin. Until now, correlations between seismic IMs and responses of buildings and other civil engineering structures were systematically studied, but those of NPP structures are still not studied yet. Therefore, the purpose of this study is to investigate the relationship between 23 earthquake IMs and seismic responses of NPP structures to identify the significant IMs to estimate damage of NPP. In particular, significant IMs for high-frequency and low-frequency ground motions are distinguished where a ground motion is referred to as a high-frequency motion when its' dominant frequency is over 10 Hz. An NPP containing an advanced pressurized water nuclear reactor, APR1400, designed in South Korea is selected as a case study example. Both NPP structures with and without base isolators are considered. Structural models of NPP structures are developed in SAP2000 program where lumped-mass stick model is used to model the containment and auxiliary buildings. A series of time history analysis is performed to monitor structural responses such as floor accelerations, floor displacements, and shear deformation of the base isolator. Thereafter, Pearson's correlation coefficients are calculated for each IM and strongly correlated IMs with seismic responses of NPP structures are identified. Finally, a set of fragility curves are developed based on the shear deformation of LRB with respect to the strongly correlated IMs. 2. Earthquake intensity measures and ground motions records 2.1. Earthquake intensity measures Earthquake IMs are crucial values for representing the characteristics of a seismic ground motion. In general, IMs characterize the amplitude, frequency content, and duration of motions [41]. The optimum IMs can reduce the deviation of seismic structural performances and predict the responses of structures accurately [15]. In this study, we select 23 available IMs proposed by many researchers for correlation analyses. These IMs are calculated for every ground motion time histories using SeismoSignal program [42]. The IMs adopted in this study and their definitions are presented in Table 1. It should be noted that the “intensity measure” (IM) terminology used herein represents all investigated ground motion parameters in this paper. 2.2. Selected ground motion records For this study, 80 ground motion records are selected from worldwide earthquakes that provided by the PEER center [53] and KMA [54]. Two groups of ground motions including low- and highfrequency content are classified separately, in which 40 records are in the low-frequency motion group and 40 records are in the highfrequency group. The low-frequency ground motions are collected from worldwide historic earthquakes while the high-frequency ground motion group consists of some earthquake events in North America and Korea, which can be categorized as mid-to lowseismicity zones. The frequency content of a ground motion is
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Table 1 Selected earthquake intensity measures. No. Earthquake parameter
Definition
Unit
Reference
1 2 3 4 5
Peak ground acceleration Peak ground velocity Peak ground displacement Ratio of PGV/PGA Root-mean-square of acceleration
g m/s m s g
e e e Kramer 1996 [41] Dobry et al., 1978 [43]
6
Root-mean-square of velocity
m/s
Kramer 1996 [41]
7
Root-mean-square of displacement
m
Kramer 1996 [41]
8
Arias intensity
m/s
Arias 1970 [44]
9
Characteristic intensity
PGA ¼ max ja(t)j PGV ¼ max jv(t)j PGD ¼ max jd(t)j PGV/PGA sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z ttot 1 Arms ¼ aðtÞ2 dt ttot 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Z ttot 1 Vrms ¼ vðtÞ2 dt ttot 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z ttot 1 Drms ¼ dðtÞ2 dt ttot 0 Z ttot p Ia ¼ aðtÞ2 dt 2g 0 2=3 pffiffiffiffiffiffiffi ttot Ic ¼ ðArms Þ
m1.5/ s2.5 m2/s
Park et al., 1985 [45]
m/s
Benjamin and Associates 1988 [46]
g*s
R ttot
10 Specific energy density
2
SED¼ 0 vðtÞ dt R t CAV ¼ 0tot aðtÞdt R 12 Acceleration spectrum intensity ASI ¼ 0:5 Sa ðx ¼ 0:05; TÞdT 0:1 11 Cumulative absolute velocity
13 Velocity spectrum intensity 14 Housner spectrum intensity 15 Sustained maximum acceleration 16 Sustained maximum velocity 17 Effective peak acceleration 18 19 20 21 22 23
Spectral acceleration at T1 Spectral velocity at T1 Spectral displacement at T1 A95 parameter Predominant period Mean period
VSI ¼
R 2:5 0:1
R 2:5 HI ¼ 0:1 PSv ðx ¼ 0:05; TÞdT SMA ¼ the 3rd of PGA SMV ¼ the 3rd of PGV EPA ¼
meanðS0:10:5 ðx ¼ 0:05ÞÞ a 2:5
Sa ðT1 Þ Sv ðT1 Þ Sd ðT1 Þ A95 ¼ 0.764 I 0:438 a Tp Tm ¼
SC 2i =fi Þ C 2i
m
Housner 1952 [47] & Thun et al., 1988 [48] Housner 1952 [47] & Thun et al., 1988 [48] Housner 1952 [47]
g
Nuttli 1979 [49]
m/s g
Nuttli 1979 [49] Benjamin and Associates 1988 [46]
g m/s m g s s
Shome et al., 1988 [50] e e Sarma & Yang 1987 [51] Kramer 1996 [41] Rathje et al., 1998 [52]
m
Sv ðx ¼ 0:05; TÞdT
; Ci is the Fourier amplitude, fi is the discrete frequency corresponding
e
to Ci
normally identified based on the response spectrum. In this study, 10 Hz is defined as the threshold to distinguish between low- and high-frequency earthquakes. In other words, the ground motions with large values of spectral accelerations fallen in the frequency range approximately larger than 10 Hz is considered as a highfrequency ground motion, otherwise discerned as low-frequency motions [55,56]. Fig. 1 shows the response spectra of two groups of ground motion records used in this study. 3. Structural modeling 3.1. Numerical modeling of NPP structures The Advanced Power Reactor 1400 (ARP1400), an advanced
pressurized water nuclear reactor designed in Korea is employed for a numerical example in this study. Fig. 2 shows a general view and cutting view of structural configuration of the APR1400 plant. We focus our modeling on the reactor containment building and the auxiliary building. The lumped-mass stick models of the structure are implemented in SAP2000 [57], a commercial structural analysis program. The containment and auxiliary buildings are modeled in terms of a simplified model using elastic beam elements. The equivalent section properties are calculated based on the designed cross sections of the structures [58,59]. The lumped masses are also assigned into associated element nodes. Elastic shell elements are applied for the base-mat foundation. The structural properties of the APR1400 NPP in the lumped-mass beam stick model are shown in Table 2.
Fig. 1. Response spectra of selected ground motion records.
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Fig. 2. Advanced power reactor 1400.
Table 2 Properties of the APR1400 NPP in the lumped-mass beam stick model. Node
Height frombase-mat (m)
Nodal mass(ton)
Area(m2)
Moment of inertia(m4)
Shear area(m2)
Torsional constant (m4)
87.07 166.52 185.42 189.29 170.39 234.68 314.15 333.05 318.02 310.43 376.80 279.92 355.52 352.09 147.80
202.90 202.90 202.90 202.90 202.90 202.90 202.90 202.90 202.90 202.90 202.90 179.76 179.76 166.11
56299.85, 56299.85, 56299.85, 56299.85, 56299.85, 56299.85, 56299.85, 56299.85, 56299.85, 56299.85, 56299.85, 47591.20, 35861.70, 12825.63,
56299.85 56299.85 56299.85 56299.85 56299.85 56299.85 56299.85 56299.85 56299.85 56299.85 56299.85 47591.20 35861.70 12825.63
101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 101.45, 101.45 89.89, 89.89 89.89, 89.89 83.03, 83.03
112634.22 112634.22 112634.22 112634.22 112634.22 112634.22 112634.22 112634.22 112634.22 112634.22 112634.22 95199.65 71732.03 25651.25
184.17 341.40 796.48 523.67 273.10 296.29 296.86 355.47 80.51 264.64 255.68 271.76 81.38
833.15 883.97 857.92 313.78 254.60 221.94 261.38 202.76 202.76 202.76 103.23 97.93
51055.67, 79896.93 51262.81, 81942.48 51149.25, 80710.1 9908.34, 21253.36 9816.63, 19442.95 9515.25, 19384.02 9848.14, 20166.32 9630.81, 18524.13 9630.81, 18524.13 9630.81, 18524.13 1932.60, 4666.70 1918.14, 4642.60
662.77, 662.77 704.29,704.29 684.03, 684.03 221.77, 221.77 171.14, 171.14 144.33, 144.33 175.93,175.93 130.81, 130.81 130.81, 130.81 130.75, 130.75 94.90, 94.90 92.25, 92.25
164989.72 168389.13 165957.82 37753.43 35811.75 35233.94 36571.27 34566.87 34566.87 34566.87 7888.57 7840.37
4608.78 5265.66 4680.11 4150.72 3218.83 2000.28 1659.49 957.38
1660.45 1503.17 1529.65 1363.35 842.16 579.06 371.98
530766.3, 405355.4 466685.8, 332679.3 464101.2, 340852.6 368330.8, 292325.7 241060.5, 158771.4 142392.3, 121479.2 75850.4, 86362.9
770.35, 611.30 658.91, 582.41 659.42, 589.37 565.41, 558.81 358.88, 329.06 212.0, 261.6 160.3, 192.0
239729.53 198363.83 205791.05 187226.65 173747.81 76553.8 52753.99
Reactor containment building 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16.76 20.27 23.46 27.73 31.09 34.59 40.53 47.24 53.94 60.65 66.44 70.56 78.63 86.72 94.64
Internal structure 1201 1202 1203 1204 1204 1205 1206 1207 1208 1209 1210 1211 1212
16.76 18.28 20.26 23.46 25.75 27.73 31.09 32.61 34.59 36.57 40.53 46.32 51.20
Auxiliary structure 1001 1002 1003 1004 1005 1006 1007 1008
16.76 23.46 36.57 41.91 40.53 52.42 57.92 63.39
For the base-isolated model, 486 LRBs are installed beneath the base mat for improving the seismic performance of the NPP structures. Fig. 3 shows the finite element models of the non- and base-isolated NPP structures in SAP2000. Fig. 4 shows the layout of LRBs and the bilinear response model of LRBs due to shear forces. The mechanical properties of LRBs are described in Table 3. The results of the eigenvalue analysis are presented in Table 4. For the non-isolated NPP model, the 1st and 2nd modes are the horizontal translation modes of the containment building, while, the 3rd and 4th modes represent the translational modes of the auxiliary building, as shown in Fig. 5. For the base-isolated NPP
model, the 1st and 2nd modes are translational modes of the superstructure, while the 3rd mode represents the rotational mode and the 4th mode is the translational model of the containment building, as shown in Fig. 6. These results are also in good agreement with the findings elsewhere [60e62].
3.2. Verification of the lumped-mass stick model (LMSM) The LMSM is verified with a 3D finite element model (3D FEM) using ANSYS software. A set of time-history analyses for the nonisolated reactor containment building is performed to compare
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Fig. 3. Finite element lumped-mass stick model of APR1400: Non-isolated (left) and base-isolated model (right).
Fig. 4. Layout of LRBs and their bilinear response model.
Table 3 Mechanical properties of LRBs. Property
Value
Unit
Elastic stiffness, Ku Hardening stiffness, Kd Yield strength, Fy Characteristic strength, Qd Vertical stiffness, Kv Effective stiffness, Keff Equivalent damping ratio, x
537,703 4204.84 1009.65 1001.03 12.896 8970 0.335
kN/m kN/m kN kN kN/m kN/m
structures are expected to vibrate within an elastic range during a design earthquake. All ground motions were applied to the NPP models in the horizontal direction. The seismic responses of nonisolated NPP structures are obtained in terms of the maximum drift ratio and floor acceleration at each component, while for the base-isolated model, the additional shear deformation behavior of LRBs is observed. Figs. 10 and 11 show representative examples of the maximum floor displacements and examples of the displacement time-history responses of the NPP structure, respectively, for low-and high-frequency earthquakes. The acceleration floor response spectra at the top of the NPP components due to earthquakes are also plotted in Fig. 12. Fig. 13 shows shear force versus shear deformation behaviors of the LRB under different earthquakes. The responses of the NPP components are obtained for every ground motion records. A relationship between seismic responses of NPP structures and earthquake IMs is needed to identify the strong and the weak correlation indicators. In this study, the Pearson's coefficient is used to reflect the correlation between seismic responses of NPP structures and earthquake IMs. The correlation coefficient given by Ang and Tang [63] is defined as
r¼ Table 4 Eigenvalue analysis results. Mode shape
Translational Y of superstructure Translational X of superstructure Rotational Z of superstructure Translational Y of RCB Translational X of RCB Translational Y of auxiliary bldg. Translational X of auxiliary bldg.
Isolated base
e e e 3.858 3.859 5.077 5.351
0.476 0.477 0.709 3.786 3.812 e e
e e e e
Mode Mode Mode Mode
1 2 3 4
e e e e e
Mode Mode Mode Mode Mode
P
ðxi xÞðyi yÞ
sx sy
(1)
where x, y, are the sample means of variables xi and yi. xi represents the seismic responses of NPP components, while yi represents the values of intensity measures. sx , sy are the sample standard deviations of x and y, determined by
Natural frequency (Hz) Fixed base
1 n1
1 2 3 4 5
the seismic behaviors of two models. Fig. 7 shows the 3D FEM of the containment building modeled in ANSYS. Time-history responses and floor response spectra of LMSM and 3D FEM are shown in Figs. 8 and 9, respectively. It can be found that the results of the two models are in good agreement, demonstrating that the LMSM is sufficient for time-history analyses of NPP structures. 4. Seismic responses of NPP structures and correlation analyses A series of linear time-history analyses are performed since NPP
sx ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i i 1 h 1 h ðSxi Þ2 nðxÞ2 ; sy ¼ ðSyi Þ2 nðyÞ2 n1 n1 (2)
Fig. 14 shows the representative results of the calculated correlation coefficients for the non-isolated NPP structures associated with low- and high-frequency ground motions. It is found that for the low-frequency motions, the A95 and PGA are the strongest correlated parameters, followed by sustained maximum acceleration (SMA) and effective peak acceleration (EPA). The weakest correlated IMs are specific energy density (SED), root mean square of displacement (Drms), PGD, and Sv(T1). For the high-frequency motion group, the good correlation indicators are SED, characteristic intensity (Ic), and Arias intensity (Ia). The poor correlation IMs are PGV/PGA, predominant period (Tp), and mean period (Tm). The similar tendency is observed for all NPP components modeled. Fig. 15 shows the representative results of the correlation coefficients for the base-isolated NPP model. It can be demonstrated that for low-frequency ground motions, SED, Ia, and Ic are strongly
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Fig. 5. Mode shapes of the non-isolated NPP model.
Fig. 6. Mode shapes of the base-isolated NPP model.
correlated parameters. Meanwhile, the lowest correlation IMs are PGV/PGA, Tp, and Tm. Also, this trend is obtained for the base-isolated NPP structures associated with the high-frequency motions. Tables 5 and 6 summarize the strongly and weakly correlated IMs with seismic responses of NPP structures under low- and highfrequency earthquakes, respectively. It is highlighted that SED, Ia, and Ic are the best IMs in correlating with seismic responses of the base-isolated NPP structures for both low- and high-frequency earthquakes and the non-isolated structure in HF excitations. A95, PGA, and SMA are the also good indicators for correlation with damage of the non-isolated NPP structures in LF seismic zones. In contrast, Tp, Tm, and PGV/PGA are the weakest correlated IMs with seismic responses of the NPP structures under HF earthquakes and the base-isolated structures in LF earthquakes. Additionally, Drms, PGD, and Sv(T1) are also shown to be low correlation with seismic damage of the non-isolated NPP structure in LF earthquakes. For the non-isolated NPP model with regard to the lowfrequency motions, the strongly correlated intensity measures (PGA, A95, SMA, EPA) seem to be resulted from their definitions, in which these measures are related to the force (or the acceleration). Thus, it governs the floor responses of the fixed base structures for high amplitude of ground motions. Whereas, the poor correlation parameters (Drms and PGD), which are directly related to the deformation (or the displacement), seems to be less sensitive to the relatively rigid structures. For the base-isolated structures, most of input seismic energy is dissipated through the hysteretic behavior of LRBs. Therefore, it is obvious to find that the energy-based IMs (SED, Ia) are the strong correlated parameters. Meanwhile, the period-based parameters, Tp
and Tm, are less than 1.7 s and 0.7 s for the LF and HF groups, respectively. It is smaller than the fundamental period of the base-isolated structures, consequently, causing a less damage to the structure. 5. Fragility analyses 5.1. Limit states The seismic fragility is the conditional probability that a structural system exceeds a limit state when subjected to a specified level of earthquake intensity. For the base-isolated NPP structure, the superstructure should behave within the elastic range during the seismic excitation. However, the base isolator will experience a large deformation that may exceed the yield deformation and reach the ultimate deformation capacity. For developing fragility curves, a set of limit states should be pre-defined according to damage levels of components. In this study, the damage levels of an LRB with respect to the shear strain is considered as the limit states. The shear strain of LRB, g is expressed by
g¼
D H
(3)
where D and H are the maximum lateral deformation and the height of LRB, respectively. According to recent experimental studies [64e69], the LRB can reach to an ultimate capacity of beyond 400% shear strain. Therefore, we adopt these results to define three limit states, if the shear strain exceeds 100% (i.e. D 40 cm), the slight limit state (LS-1) is specified. Similarly, if the
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Shinozuka et al. [73] is used in this study. In this approach, the fragility function is assumed as a log-normal cumulative distribution function (CDF) expressed by
lnða=ck Þ Fk ðaÞ ¼ F
zk
(4)
where a is the earthquake intensity measure, ck and zk are the median and the log-standard deviation of the log-normal CDF, and Fð Þ is the standard normal CDF. In Equation (4), the subscript k indicates the k-th limit state when more than one limit state is considered. In the MLE, ck and zk are determined by maximizing the likelihood function. This function is defined by
L¼
Fig. 7. 3D FEM of the reactor containment building.
shear strain goes beyond 300% (i.e. D 120 cm) and 400% (i.e. D 160 cm), the moderate (LS-2) and extensive (LS-3) limit states are established. This approach was also used in previous studies [39,40,70e72]. Three limit states are summarized in Table 7. 5.2. Maximum likelihood estimation Among several methods to develop seismic fragility curves, the maximum likelihood estimation (MLE) approach proposed by
YN i¼1
½Fk ðai Þxi ½1 Fk ðai Þð1xi Þ
(5)
where Fk ðaÞ increases when damage occurs and 1 Fk ðaÞ, the probability of not experiencing a damage, increases when damage does not occur for the earthquake intensity of ai . In Equation (5), N is the number of ground motions considered and xi is a Bernoulli random variable that indicates whether the structure is damaged or not where 0 indicates no damage and 1 indicates damage. ck and zk are determined so that Equation (5) is maximized with respect to ck and zk as follows
vL vL ¼ ¼ 0; k ¼ 1; /; NLS vck vzk
(6)
where NLS is the number of limit states. 5.3. Fragility curves Since LRB is the crucial element in the base-isolated NPP, a set of fragility curves is developed for different limit states, which are defined based on the shear strain of LRB. The two spectrally equivalent ground motion suites (LF and HF motions) are used to
Fig. 8. Comparison of time-history responses between two models under the 1940 El Centro earthquake.
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Fig. 9. Floor response spectra of the structure under the 1940 El Centro earthquake.
Fig. 10. Maximum displacements at the top of the NPP structures under the LF and HF earthquakes.
Fig. 11. Displacement time-history responses at the top of the containment building under the LF and HF earthquakes.
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Fig. 12. Mean floor response spectra at the top of the NPP structures with different earthquakes.
Fig. 13. Responses of LRB under different earthquakes.
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Fig. 14. Correlation between responses of non-isolated NPP and earthquake IMs.
perform the incremental dynamic analysis (IDA) [74]. In IDA, the selected ground motions are scaled to multiple levels of intensity, herein, we select two strongly correlated IMs, which are SED and Ia, to develop fragility curves for the base-isolated NPP structure. For each analysis, the maximum deformation of LRB is monitored as the engineering demand parameter. In total, 800 dynamic analyses are performed (i.e. 2 suites x 40 records x 10 intensity levels). Fig. 16 shows the IDA curves in terms of deformation of LRB versus IMs for LF and HF motions. The solid curves represent the mean values. Due to higher input energy of the LF motions, the base isolator is deformed in a larger range during a stronger seismic intensity. Fragility curves of base-isolated NPP model are developed for three limit states considering two groups of ground motions. Fig. 17 shows the fragility curves for three limit states with different earthquake groups. It can be observed that the base-isolated NPP structure might behave without damage if the level of SED and Ia are less than 0.2 m2/s and 1.5 m/s, respectively. Fig. 18 shows a comparison of fragility curves for three LSs and two groups of earthquakes. It can be observed that the structural model under LF motions would be more vulnerable than that due to HF earthquakes. This can be attributed to the reason that the deformation of LRBs produced by LF motions is higher than that under HF motions. It can be clearly observed that the median values for LS-1 are 22% and 24% lower when LF motions are applied than applying HF ones for SED and Ia, respectively. Similarly, the median values for LS-2 and LS-3 are reduced by 15% and 9% with respect to SED, respectively, and also decreased 12% and 8% with respect to Ia,
respectively, under LF motions. Table 8 describes the fragility function parameters (i.e. median and standard deviation (SD)) for LF and HF earthquakes with different limit states. 6. Conclusions Significant intensity measures of earthquakes that are strongly correlated to seismic responses of NPP structures are identified. We consider the effect of low-frequency and high-frequency ground motions, separately. A series of time history analyses are performed for both non- and base-isolated numerical models of NPP structures to monitor the floor displacement, floor acceleration, and shear deformation of LRB. Pearson's correlation coefficients are calculated to identify the best earthquake IMs for indicating the seismic damage of NPP structures. A set of fragility curves is also developed with respect to the well-correlated IMs. Based on the numerical results, the following conclusions are drawn. (1) For the non-isolated NPP structures subjected to lowfrequency ground motions, the best IMs for correlating with seismic responses of such structures are PGA, A95, and SMA. For high-frequency earthquakes, the best IMs are SED, Ic, and Ia. (2) For the base-isolated NPP structures subjected to lowfrequency ground motions, SED, Ia, and Ic are the strongly correlated parameters. This trend is also obtained for the base-isolated NPP structures associated with the highfrequency ground motions.
Please cite this article as: D.-D. Nguyen et al., Identifying significant earthquake intensity measures for evaluating seismic damage and fragility of nuclear power plant structures, Nuclear Engineering and Technology, https://doi.org/10.1016/j.net.2019.06.013
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Fig. 15. Correlation between the responses of base-isolated NPP and earthquake IMs.
Table 5 Strongly correlated IMs with seismic responses of NPP structures. Low-frequency earthquakes
High-frequency earthquakes
Non-isolated model
Base-isolated model
Non-isolated model
Base-isolated model
A95 PGA SMA
SED Ia Ic
SED Ic Ia
SED Ia Ic
Table 6 Weakly correlated IMs with seismic responses of NPP structures. Low-frequency earthquakes
High-frequency earthquakes
Non-isolated model
Base-isolated model
Non-isolated model
Base-isolated model
Drms PGD Sv(T1)
Tp Tm PGV/PGA
Tp Tm PGV/PGA
Tp Tm PGV/PGA
Table 7 Definition of limit states. Limit state
Shear strain of LRB
Maximum lateral deformation of LRB (mm)
Slight damage (LS-1) Moderate damage (LS-2) Extensive damage (LS-3)
g 100% g 300% g 400%
400 1200 1600
Please cite this article as: D.-D. Nguyen et al., Identifying significant earthquake intensity measures for evaluating seismic damage and fragility of nuclear power plant structures, Nuclear Engineering and Technology, https://doi.org/10.1016/j.net.2019.06.013
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Fig. 16. Incremental displacement of LRB with respect to SED and Ia.
Fig. 17. Fragility curves for limit states with various ground motion groups.
(3) A selection of PGA or Sa for correlation analyses with seismic responses of the NPP structures in the high-frequency seismic regions may not be the best option. (4) The median values of fragility functions for three limit states in the case of base-isolated NPP are reduced by 9%e22% and 8%e24% for SED and Ia, respectively, when low-frequency ground motions applied than when high-frequency motions are applied. It implies that the considered NPP structure is more vulnerable to low-frequency ground motions than high-frequency ground motions.
Data availability All the data supporting the key findings of this paper are presented in the figures and tables of the article. Request for other data will be considered by the corresponding author.
Conflicts of interest The authors declare that they have no conflicts of interest.
Please cite this article as: D.-D. Nguyen et al., Identifying significant earthquake intensity measures for evaluating seismic damage and fragility of nuclear power plant structures, Nuclear Engineering and Technology, https://doi.org/10.1016/j.net.2019.06.013
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Fig. 18. Comparison of fragility curves for low- and high-frequency excitations.
Table 8 Fragility function parameters of the based-isolated NPP structure. Limit state LF earthquake
LS-1 LS-2 LS-3
HF earthquake
SED (m2/s)
Ia (m/s)
Median SD
Median SD
0.489 1.054 1.633
0.442 6.206 0.422 16.860 0.409 33.202
SED (m2/s)
Ia (m/s)
Median SD
Median SD
0.570 0.625 0.587 1.247 0.590 1.793
0.549 8.123 0.443 19.165 0.247 36.179
0.643 0.491 0.279
Acknowledgement This study is supported by project titled “Development of High Reliability Seismic Monitoring System for Precise Analysis of High Frequency Earthquake Motion in Nuclear Power Plants”, assignment number 20171510101860.
References [1] Z. Chen, J. Wei, Correlation between ground motion parameters and lining damage indices for mountain tunnels, Nat. Hazards 65 (3) (2013) 1683e1702. [2] M. Corigliano, C.G. Lai, G. Barla, January). Seismic vulnerability of rock tunnels using fragility curves, in: 11th ISRM Congress, International Society for Rock Mechanics and Rock Engineering, 2007. [3] S. Yaghmaei-Sabegh, Application of wavelet transforms on characterization of inelastic displacement ratio spectra for pulse-like ground motions, J. Earthq. Eng. 16 (4) (2012) 561e578. [4] M. Ghayoomi, S. Dashti, Effect of ground motion characteristics on seismic soil-foundation-structure interaction, Earthq. Spectra 31 (3) (2015) 1789e1812. [5] Y.Y. Zhang, Y. Ding, Y.T. Pang, Selection of optimal intensity measures in seismic damage analysis of cable-stayed bridges subjected to far-fault ground motions, J. Earthq. Tsunami 9 (01) (2015), 1550003. [6] A. Elenas, Correlation between seismic acceleration parameters and overall structural damage indices of buildings, Soil Dynam. Earthq. Eng. 20 (1e4) (2000) 93e100. [7] A. Elenas, K. Meskouris, Correlation study between seismic acceleration parameters and damage indices of structures, Eng. Struct. 23 (6) (2001)
698e704. [8] V. Cao, H.R. Ronagh, Correlation between seismic parameters of far-fault motions and damage indices of low-rise reinforced concrete frames, Soil Dynam. Earthq. Eng. 66 (2014) 102e112. [9] V. Cao, H.R. Ronagh, Correlation between parameters of pulse-type motions and damage of low-rise RC frames, Earthq. Struct. 7 (3) (2014) 365e384. [10] A. Massumi, F. Gholami, The influence of seismic intensity parameters on structural damage of RC buildings using principal components analysis, Appl. Math. Model. 40 (3) (2016) 2161e2176. [11] N. Nanos, A. Elenas, P. Ponterosso, Correlation of different strong motion duration parameters and damage indicators of reinforced concrete structures, in: The 14th World Conference on Earthquake Engineering, 2008. Beijing, China, 2008. [12] K. Kostinakis, A. Athanatopoulou, K. Morfidis, Correlation between ground motion intensity measures and seismic damage of 3D R/C buildings, Eng. Struct. 82 (2015) 151e167. [13] J. Pejovic, S. Jankovic, Selection of ground motion intensity measure for reinforced concrete structure, Procedia Eng. 117 (2015) 588e595. [14] J. Pejovic, N. Serdar, R. Pejovic, Optimal intensity measures for probabilistic seismic demand models of RC high-rise buildings, Earthq. Struct. 13 (3) (2017) 221e230. [15] X. Lu, L. Ye, X. Lu, M. Li, X. Ma, An improved ground motion intensity measure for super high-rise buildings, Sci. China Technol. Sci. 56 (6) (2013) 1525e1533. [16] J.E. Padgett, B.G. Nielson, R. DesRoches, Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios, Earthq. Eng. Struct. Dyn. 37 (5) (2008) 711e725. [17] V. Jahangiri, M. Yazdani, M.S. Marefat, Intensity measures for the seismic response assessment of plain concrete arch bridges, Bull. Earthq. Eng. (2018) 1e24. [18] C. Zelaschi, R. Monteiro, R. Pinho, Critical assessment of intensity measures for seismic response of Italian RC bridge portfolios, J. Earthq. Eng. (2017) 1e21. € Avs¸ar, G. Ozdemir, € [19] O. Response of seismic-isolated bridges in relation to intensity measures of ordinary and pulselike ground motions, J. Bridge Eng. 18 (3) (2011) 250e260. [20] D. Nguyen, H. Park, B. Thusa, T.-H. Lee, Identification of Earthquake Intensity Measures as the Seismic Damage Indicator of Bridges Considering Low- and High-Frequency Contents of Ground Motions, Submitted to Earthquakes And Structures, 2019. [21] D.D. Nguyen, D. Park, S. Shamsher, V.Q. Nguyen, T.H. Lee, Seismic vulnerability assessment of rectangular cut-and-cover subway tunnels, Tunn. Undergr. Space Technol. 86 (2019) 247e261. [22] H.N. Phan, F. Paolacci, Efficient intensity measures for probabilistic seismic response analysis of anchored above-ground liquid steel storage tanks, in: ASME 2016 Pressure Vessels and Piping Conference (pp. V005T09A010-
Please cite this article as: D.-D. Nguyen et al., Identifying significant earthquake intensity measures for evaluating seismic damage and fragility of nuclear power plant structures, Nuclear Engineering and Technology, https://doi.org/10.1016/j.net.2019.06.013
14
D.-D. Nguyen et al. / Nuclear Engineering and Technology xxx (xxxx) xxx
V005T09A010), American Society of Mechanical Engineers, 2016. [23] R.P. Kennedy, M.K. Ravindra, Seismic fragilities for nuclear power plant risk studies, Nucl. Eng. Des. 79 (1) (1984) 47e68. [24] EPRI, Methodology for Developing Seismic Fragilities, Report TR-103959, Palo Alto, CA, USA, 1994. [25] EPRI, A Methodology for Assessment of Nuclear Power Plant Seismic Margin, Report EPRI-NP-6041-M-REV.1, 1991 (Palo Alto, CA, USA). [26] U.S. NUREG, Nuclear Regulatory Commission, Seismic Fragility of Nuclear Power Plant Components (Phase II), NUREG/CR-4659, vols. 2e4, Department of Nuclear Energy, Brookhaven Laboratory, Long Island, NY, USA, 1987. BNLNUREG-52007. [27] A. Ali, N.A. Hayah, D. Kim, S.G. Cho, Probabilistic seismic assessment of baseisolated NPPs subjected to strong ground motions of Tohoku earthquake, Nucl. Eng. Technol. 46 (5) (2014) 699e706. [28] P.C. Basu, M.K. Ravindra, Y. Mihara, Component fragility for use in PSA of nuclear power plant, Nucl. Eng. Des. 323 (2017) 209e227. [29] S.G. Cho, Y.H. Joe, Seismic fragility analyses of nuclear power plant structures based on the recorded earthquake data in Korea, Nucl. Eng. Des. 235 (17e19) (2005) 1867e1874. [30] T.K. Mandal, N.N. Pujari, S. Ghosh, A comparative study of seismic fragility estimates using different numerical methods, in: 4th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, 2013. [31] T.K. Mandal, S. Ghosh, N.N. Pujari, Seismic fragility analysis of a typical Indian PHWR containment: comparison of fragility models, Struct. Saf. 58 (2016) 11e19. [32] F. Perotti, M. Domaneschi, S. De Grandis, The numerical computation of seismic fragility of base-isolated Nuclear Power Plants buildings, Nucl. Eng. Des. 262 (2013) 189e200. [33] T.T. Tran, A.T. Cao, T.H.X. Nguyen, D. Kim, Fragility assessment for electric cabinet in nuclear power plant using response surface methodology, Nucl. Eng. Technol. 51 (3) (2019) 894e903. [34] Y.N. Huang, A.S. Whittaker, N. Luco, A probabilistic seismic risk assessment procedure for nuclear power plants:(I) Methodology, Nucl. Eng. Des. 241 (9) (2011) 3996e4003. [35] Y.N. Huang, A.S. Whittaker, N. Luco, A probabilistic seismic risk assessment procedure for nuclear power plants:(II) Application, Nucl. Eng. Des. 241 (9) (2011) 3985e3995. [36] I.K. Choi, Y.S. Choun, S.M. Ahn, J.M. Seo, Seismic fragility analysis of a CANDU type NPP containment building for near-fault ground motions, KSCE J. Civ. Eng. 10 (2) (2006) 105e112. [37] I.K. Choi, Y.S. Choun, S.M. Ahn, J.M. Seo, Probabilistic seismic risk analysis of CANDU containment structure for near-fault earthquakes, Nucl. Eng. Des. 238 (6) (2008) 1382e1391. [38] S. De Grandis, M. Domaneschi, F. Perotti, A numerical procedure for computing the fragility of NPP components under random seismic excitation, Nucl. Eng. Des. 239 (11) (2009) 2491e2499. [39] D.D. Nguyen, B. Thusa, T.H. Lee, Seismic fragility of base-isolated nuclear power plant considering effects of near-fault ground motions, J. Korean Soc. Hazard Mitig. 18 (7) (2018) 315e321. [40] D.D. Nguyen, B. Thusa, T.H. Lee, Effects of significant duration of ground motions on seismic responses of base-isolated nuclear power plant, J. Earthq. Eng. Soc. Korea 23 (3) (2019) 149e157. [41] S.L. Kramer, Geotechnical Earthquake Engineering, Prentice Hall, New Jersey, USA, 1996. [42] SeismoSignal - a computer program for signal processing of strong-motion data, available from: http://www.seismosoft.com, 2017. [43] R. Dobry, I.M. Idriss, E. Ng, Duration characteristics of horizontal components of strong-motion earthquake records, Bull. Seismol. Soc. Am. 68 (5) (1978) 1487e1520. [44] A. Arias, A Measure of Earthquake Intensity, Massachusetts Inst. of Tech., Cambridge, 1970 (Univ. of Chile, Santiago de Chile). [45] Y.J. Park, A.H.S. Ang, Y.K. Wen, Seismic damage analysis of reinforced concrete buildings, J. Struct. Eng. 111 (4) (1985) 740e757. [46] J.R. Benjamin, A Criterion for Determining Exceedances of the Operating Basis Earthquake, Report No. EPRI NP-5930, Electric Power Research Institute, Palo Alto., California, USA, 1988. [47] G.W. Housner, Spectrum intensities of strong-motion earthquakes, in: Symposium on Earthquake and Blast Effects on Structures, 1952, pp. 20e36 (Los Angeles, California, USA). [48] J.L. Von Thun, Earthquake Ground Motions for Design and Analysis of Dams. Earthquake Engineering and Soil Dynamics II-Recent Advances in GroundMotion Evaluation, 1988. [49] O.W. Nuttli, The Relation of Sustained Maximum Ground Acceleration and Velocity to Earthquake Intensity and Magnitude, Report 16, US Army Engineer Waterways Experiment Station, Vicksburg, Mississippi, USA, 1979. Misc. Paper S-73-1.
[50] N. Shome, C.A. Cornell, P. Bazzurro, J.E. Carballo, Earthquakes, records, and nonlinear responses, Earthq. Spectra 14 (3) (1998) 469e500. [51] S.K. Sarma, K.S. Yang, An evaluation of strong motion records and a new parameter A95, Earthq. Eng. Struct. Dyn. 15 (1) (1987) 119e132. [52] E.M. Rathje, N.A. Abrahamson, J.D. Bray, Simplified frequency content estimates of earthquake ground motions, J. Geotech. Geoenviron. Eng. 124 (2) (1998) 150e159. [53] PEER Ground Motion Database, 2018. http://peer.berkeley.edu/peer_ground_ motion_database. [54] KMA, Korean Meteorological Administration, 2016, https://web.kma.go.kr/ eng/index.jsp [55] EPRI, Program on Technology Innovation: the Effects of High Frequency Ground Motion on Structures, Components, and Equipment in Nuclear Power Plants, Report 1015108, Electrical Power Research Institute, Palo Alto, California, USA, 2007. [56] EPRI, Advanced Nuclear Technology: High-Frequency Seismic Loading Evaluation for Standard Nuclear Power Plants, Report 3002009429, Electrical Power Research Institute, Palo Alto, California, USA, 2017. [57] SAP2000 Ver 15, Computers and structures Inc, Berkeley, CA, USA, 2013. [58] J.M. Kim, E.H. Lee, Development and Verification of Simplified Beam-Stick Model of Seismically Isolated ARP1400 Nuclear Power Plant Structure,” Research Report, Central Research Institute of KHNP, KETEP Project No. 2014151010170B, Korea, 2015. [59] E.H. Lee, J.M. Kim, K.H. Joo, H. Kim, Evaluation of the soil-structure interaction effect on seismically isolated nuclear power plant structures, J. Earthq. Eng. Soc. Korea 20 (6) (2016) 379e389. [60] G.J. Kim, K.K. Yang, B.S. Kim, H.J. Kim, S.J. Yun, J.K. Song, Seismic response evaluation of seismically isolated nuclear power plant structure subjected to Gyeong-Ju earthquake, J. Earthq. Eng. Soc. Korea 20 (7) (2016) 453e460. [61] J.W. Jung, H.W. Jang, J.H. Kim, J.W. Hong, Effect of second hardening on floor response spectrum of a base-isolated nuclear power plant, Nucl. Eng. Des. 322 (2017) 138e147. [62] S.G. Cho, S.M. Yun, D. Kim, K.J. Hoo, Analyses of vertical seismic responses of seismically isolated nuclear power plant structures supported by lead rubber bearings, J. Earthq. Eng. Soc. Korea 19 (3) (2015) 133e143. [63] A.H.S. Ang, W.H. Tang, Probability Concepts in Engineering: Emphasis on Applications in Civil & Environmental Engineering, vol. 1, Wiley and Sons, 2007. [64] J.H. Kim, M.K. Kim, I.K. Choi, Experimental study on the ultimate limit state of a lead-rubber bearing, in: ASME 2016 Pressure Vessels and Piping Conference (pp. V008T08A039-V008T08A039), American Society of Mechanical Engineers, Vancouver, BC, Canada, 2016, 2016. [65] H.P. Lee, M.S. Cho, J.Y. Park, K.S. Jang, Assessment of LRB seismic isolation device for nuclear power plant, in: Transactions of the Korean Nuclear Society Autumn Meating, 2013. Gyeongju, Korea, 2013. [66] I. Choi, J. Kim, M. Kim, Performance based design of lrb systems for nuclear power plants, in: Transaction of the 24th Structural Mechanics in Reactor Technology (SMiRT-24) Conference, Busan, Korea, 2017, 2017. [67] S. Eem, D. Hahm, Large strain nonlinear model of lead rubber bearings for beyond design basis earthquakes, Nucl. Eng. Technol. 51 (2) (2019) 600e606. [68] S. Yabana, K. Kanazawa, S. Nagata, S. Kitamura, T. Sano, Shaking table tests with large test specimens of seismically isolated FBR plants: Part 3 - ultimate behavior of upper structure and rubber bearings, in: ASME 2009 Pressure Vessels and Piping Conference, American Society of Mechanical Engineers, 2009, pp. 179e187. [69] T. Hiraki, S. Nagata, K. Kanazawa, T. Imaoka, T. Nakayama, Y.,. Umeki, H. Shimizu, Development of an evaluation method for seismic isolation systems of nuclear power facilities: Part 9 - ultimate properties of full-scale lead rubber bearings based on breaking test, in: ASME 2014 Pressure Vessels and Piping Conference (pp. V008T08A012-V008T08A012), American Society of Mechanical Engineers, 2014. [70] J. Zhang, Y. Huo, Optimum isolation design for highway bridges using fragility function method, in: The 14th World Conference on Earthquake Engineering, WCEE), Beijing, China, 2008. [71] J.H. Lee, J.K. Song, Seismic fragility analysis of seismically isolated nuclear power plant structures using equivalent linear-and bilinear-lead rubber bearing model, J. Earthq. Eng. Soc. Korea 19 (5) (2015) 207e217. [72] S.H. Eem, H.J. Jung, M.K. Kim, I.K. Choi, Seismic fragility evaluation of isolated NPP containment structure considering soil-structure interaction effect, J. Earthq. Eng. Soc. Korea 17 (2) (2013) 53e59. [73] M. Shinozuka, M.Q. Feng, J. Lee, T. Naganuma, Statistical analysis of fragility curves, J. Eng. Mech. 126 (12) (2000) 1224e1231. [74] D. Vamvatsikos, C.A. Cornell, Incremental dynamic analysis, Earthq. Eng. Struct. Dyn. 31 (3) (2002) 491e514.
Please cite this article as: D.-D. Nguyen et al., Identifying significant earthquake intensity measures for evaluating seismic damage and fragility of nuclear power plant structures, Nuclear Engineering and Technology, https://doi.org/10.1016/j.net.2019.06.013