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Study on the dynamic behavior of isolated AP1000 NIB under mainshock-aftershock sequences
Progress in Nuclear Energy xxx (xxxx) xxx
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Study on the dynamic behavior of isolated AP1000 NIB under mainshock-aftershock sequences Chunfeng Zhao a, *, Na Yu b, **, Tao Peng a, Vincenzo Lippolis c, Aldo Corona c, Y.L. Mo d a
Department of Civil Engineering, Hefei University of Technology, Hefei, 230009, China Department of Economics, Hefei University, Hefei, 230601, China c Department of Engineering and Architecture, University of Parma, Parma, 43121, Italy d Department of Civil and Environmental Engineering, University of Houston, Houston, 77021, USA b
A R T I C L E I N F O
A B S T R A C T
Keywords: AP1000 nuclear island building (NIB) Isolation system Mainshock-aftershock Floor response spectrum Dynamic analysis
A mainshock can trigger several following severe aftershocks, which may take a threat to the structure. AP1000 nuclear power plant buildings (NPPB) may subject to severe mainshock and aftershock sequences during its whole life cycle. This paper mainly focuses on the seismic behavior of isolated AP1000 NPPB under mainshock and aftershock sequences. A 3D finite element model (FEM) of isolated AP1000 NPPB is established to perform the dynamic analysis. The effects of the mainshock-aftershock sequences on the maximum acceleration, peak displacement, acceleration response spectrum, and stress distribution are carried out using parametric analysis. The results indicate that the aftershock has a small impact on the seismic performance of the isolated nuclear island building (NIB) due to the isolation system. Mainshock and aftershock also influence the floor response spectrum in horizontal directions and the stress state to some extent, but the effects are relatively small compared with the non-isolated NIB.
1. Introduction AP1000 NPP as a type of generation III þ nuclear power plant (NPP) with advanced passive safety features (APS) is developed by Westing house Company and approved by the U.S. NRC (Zhao et al., 2017; Zhao and Yu, 2018). AP1000 NPP is advanced and low-cost due to its passive design philosophy for operation and maintenance(Wang et al., 2019; Zhao and Chen, 2014; Zhao et al., 2014, 2015). Although NPP has a series of advanced features and safety, it may also encounter a potential threat of earthquakes due to its uncertainty and randomness. Seismic or base isolation as an effective approach can reduce the dynamic response of the structure and keep the structure security, particularly for the NPP structure (Chen et al., 2014). A severe earthquake may trigger many strong aftershocks frequently, which take severe threats to the security of NPPs. In the past, several researchers have studied the dynamic response of NPPs under single earthquake excitations, which have made excellent progress in the security of NPPs. Zhao et al. investigated the dynamic response and the effectiveness of isolators in the NPP under SSE loading (Chen et al., 2014; Zhao and Chen, 2013). The results showed that the isolation system could
effectively reduce the structural response and protect the structure more security. Huang et al. (Huang et al., 2010) evaluated the benefits of base isolation in providing the safety of NPP compared with a conventional NPP by using performance assessment method. Nakamura et al. used a type of nonlinear material to establish a 3D FEM of NPP and investigated the influence of vertical ground motion on the structural lift. It indicated that the basement uplift was small under earthquake loads (Medel-Vera and Ji, 2015). Micheli et al. (2004) used a pure FEM to study the seismic behavior of an NPP with isolators under earthquake excitation. It was observed that the isolator could decrease the acceleration response drastically and make the NPP more safety (Micheli et al., 2004). Lo Frano adopted a numerical method to simulate the seismic isolation effects in EGIV NPP. The results showed that the isolation technology could reduce the seismic response the NPP compared with the non-isolated structure (Lo Frano and Forasassi, 2011). Xu et al. used SPH and FEM models to analyze the sloshing and oscillation of the water in the gravity water storage tank under different earthquakes. Jeltsov et al. (2018) used CFD and VOF methods to study the lead sloshing and seismic response of ELSY reactor under artificial earthquake. Liu et al. (2015) used an equivalent mechanical model to study the dynamic
* Corresponding author. . ** Corresponding author. E-mail addresses: [email protected] (C. Zhao), [email protected] (N. Yu). https://doi.org/10.1016/j.pnucene.2019.103144 Received 29 May 2019; Received in revised form 11 August 2019; Accepted 27 August 2019 Available online 5 September 2019 0149-1970/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Chunfeng Zhao, Progress in Nuclear Energy, https://doi.org/10.1016/j.pnucene.2019.103144
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Table 1 Mainshock-aftershock sequences. No.
Name
Country
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Hoover Hsinfengkiang Kariba Koyna Tangshan Friuli Imperial Valley Borach peak Nahanni Valparaiso Whittier Narrows Saguenay Loma Prieta Manjil Landers Chi Chi
USA China Zimb India China Italy USA USA Canada Chile USA Canada USA Iran USA Taiwan
Mainshock
Largest aftershock
Database
Year
Mw
PGA (g)
Delay
Mw
PGA (g)
1939 1962 1963 1967 1976 1976 1979 1983 1985 1985 1987 1988 1989 1990 1992 1999
5 6.1 6 6.3 7.8 6.5 6.5 7.3 6.9 7.8 6.1 5.9 6.5 7.3 6.9 7.6
– 0.6 – 0.5 – 0.35 0.4 0.08 0.2 0.3 0.3 0.16 0.3 0.7 0.3 0.8
2h 36 months 2 days 10 months 1 day 4 months 3 min 1 day 2 days 1 month 3 days 1 day 33 h 2 months 10 h 1 week
4 5.3 5.8 5.1 7.1 6.1 5 5.8 5.7 7.2 5.3 4.1 5 5 6.7 6.8
– – – 0.15 – 0.2 0.3 0.07 0.1 0.15 0.15 – – 0.25 0.5 –
response of AP1000 PCCWST under earthquake considering FSI effects. Zhao et al. studied the benefits of base isolation system in decreasing the seismic response of CPR1000 CCV. They also investigated the effect of dynamic response and structural damage for an integral structure of the nuclear island building with different heights of air takes. The effects of an internal ring baffle on the dynamic response of AP1000 NPPB were also considered subjected to seismic loads considering fluid-structure interaction of water(Zhao and Chen, 2013; Zhao et al., 2015, 2016, 2017; Zhao and Yu, 2018). As we all known, earthquakes are generally composed of foreshocks, mainshocks and aftershocks. Moreover, in the event of various earth quakes, strong aftershocks cause severe and potential danger to the safety of structures. some strong aftershocks caused by a mainshock are shown in Table 1. Several earthquake disasters indicated that the structure was not able to resist the strong aftershocks after the main shock excitation without recovery (Wang et al., 2017). Simultaneously, the aftershock might also take accumulative damage to the structure when it was subjected to strong mainshock ground motions. Whereas, strong earthquakes may trigger several severe aftershocks during earthquake events. Thus, many structures are not only subjected to an earthquake event, but also to some earthquake sequences in seismic activity zones (Pang et al., 2019; Zhai et al., 2018). In the past, several studies indicated that a mainshock might trigger the following mainshock. For example, 105 aftershocks with the magnitude between 4.1 and 6.1 were caused by the Wenchuan earth quake of 8.0 magnitude on May 12, 2008. The Tohoku earthquake with a magnitude of 9.0 was occurred on March 11, 2011, in Japan and caused more than 588 aftershocks with a moment magnitude of 5.0. Many works have demonstrated that aftershocks could aggravate the struc tural damage and trigger seriously failure or even the collapse of structures (Zhai et al., 2018; Zhang et al., 2013). Because the mainshock causes structural damage and then aftershocks aggravate the additional damage without any reparation. The accumulated damage of structure caused by mainshock-aftershock earthquake sequences should be investigated to protect the security of the structure (Zhai et al., 2018) (Foulger et al., 2018). Up to now, some researchers have started to investigate the dynamic behavior of structures under a series of mainshock-aftershock earth quakes. Some works have considered the seismic behavior of reinforced concrete buildings subjected to mainshock and aftershocks and provided some significative conclusions (Alliard and L� eger, 2008; Fragiacomo et al., 2004; Hatzigeorgiou and Liolios, 2010). Unfortunately, few re searchers have focused on the dynamic responses and the accumulative damage of NPP and isolated NPP subjected to aftershock. Zhai et al., 2015, 2018 investigated the dynamic response of reinforced concrete containment and the effects of duration of aftershocks on the
– – – NGDC NGDC PEER COSMOS PEER STRONGMO COSMOS COSMOS STRONGMO – ESD COSMOS PEER
Fig. 1. AP1000 NIB.
accumulative damage of CCV. The obtained results indicated that longer durations of aftershocks could trigger severe cumulative damage to the structure. Wang et al. studied elastic behaviors of AP1000 NIB under severe earthquake excitation, and the results indicated that the after shock took a minimal effect on the structural responses in horizontal and vertical directions under DBE earthquake (Wang et al., 2019). Yu et al. studied the seismic behavior of AP1000 nuclear power plant building under different mainshock and aftershock earthquakes. The results showed that the aftershock took accumulative damage and had a sig nificant effect on the floor acceleration response spectrum of the struc ture in the horizontal direction(Yu et al., 2019). In short, the limited works mainly paid attention to the CAP1000 NPP containment vessel or shield building of AP1000 NPP, and no research focused on the seismic behavior of isolated NPP under mainshock-aftershock earthquakes. Aftershocks may induce severe accumulative damage and cause potential danger to the AP1000 NIB. Therefore, it is important and necessary to study the seismic perfor mance and accumulative damage of isolated AP1000 NPPB under mainshock-aftershock sequences. In this study, the seismic response and factor of isolated AP1000 NIB are investigated under the different mainshock-aftershock sequences. A parametric analysis of aftershock magnitude on the structural behavior of isolated NIB is conducted under mainshock and aftershock. Lastly, acceleration response, displacement response and floor response spec trum of isolated NIB are also studied and compared with the results of non-isolated NIB.
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Table 2 Geometry of AP 1000 NIB [5]. Parameter Width of nuclear island Length of nuclear island Height of nuclear island Radius of shield building Radius of water tank Radius of CV Wall thickness Thickness of CV Height of water tank Height of auxiliary building
Table 3 Material characteristics. Value 26.67 77.42 81.98 22.1 13.565 19.8 0.92 0.041 11.8 39.42
Unit
Material
m m m m m m m m m m
Parameter
Concrete
Symbol
Density Yong’s modulus Poisson’s ratio Density Yong’s modulus Poisson’s ratio Density Density
Reinforced bar Water Air
Unit
Value 3
Kg/m MPa 1 Kg/m3 MPa 1 Kg/m3 Kg/m3
ρ
E
ν ρ
E
ν ρ ρ
2300 3.35 � 104 0.2 7800 2.06 � 105 0.3 1000 1
Fig. 2. The isolated AP1000 NIB and the layout of isolators.
2. AP1000 nuclear island 2.1. Numerical model
Fig. 3. Convergence of mesh size effects.
AP1000 NIB is composed of a shield building (SB), water storage tank (WST), air intake (AI), containment vessel (CV), as shown in Fig. 1. The geometry of AP1000 NIB is shown in Table 2. According to the total mass of the structure, the vertical live and dead load, we select GZY900 type of isolator for application in the AP1000 NIB, the details of the isolators are explained in the previous paper (Chen et al., 2014). The vertical stiffness, horizontal post yielding stiffness, yield force, vertical maximum load and the design maximum horizontal displacement of the isolators are described in the previous reference (Chen et al., 2014). Finally, 387 isolators are chosen after the calculation with a minimum of 29% safety margin against the extra-loads. The isolators are modeled by the elements of COMBIN 14 and COMBIN 14 in vertical stiffness and horizontal stiffness respectively. COMBIN 14 is a spring-damper element that has the longitudinal or torsional capacity for 1D, 2D or 3D appli cation(Chen et al., 2014). Each node of the spring-damper element has three degrees of freedom and translation in X, Y and Z directions. The element is defined by two nodes, a spring constant and damping co efficients. Combin40 is a combination of a spring-slider and damper in parallel, coupled with a gap in series(Chen et al., 2014). The element has one degree of freedom at each node, either a nodal translation, rotation, pressure, or temperature. The element can be used to represent the horizontal movement of the isolators. AP1000 NIB has many auxiliary buildings, it is tough to establish all the models including reactor in ternal pipeline and equipment once time due to its complicated boundary and structural shape. This study mainly focused on the CV and SB of AP1000 NIB under mainshock -aftershock sequences, so the in ternal equipment and pipelines are represented by shell and mass ele ments. Additionally, a reinforced concrete smear model is applied to simulate the seismic behavior of isolated AP1000 NIB, and the rigid foundation is assumed without consideration of soil-structure interac tion in this model. The detailed finite element model of isolated AP1000 NIB is shown in Fig. 2.
2.2. Model of material The compressive behavior of concrete material is described by the constitutive law of concrete (Yip, 1998). The compressive stress-strain relation of concrete can be given as follows:
σ con ¼
nðεcon =ε0 Þ n
1 þ ðεcon =ε0 Þnk
(1)
σcu
where σ con and εcon stand for the stress and strain of concrete. σ cu represent the ultimate compressive strength of concrete. n and k are the fitting parameters and slope parameter of the stress-strain curve. ε0 denotes the value of strain when σ con reaches to σ cu . The expressions of these parameters can be expressed as follows:
ε0 ¼
n¼
k¼
σcu
n n
σ cu 17
pffiffiffiffiffiffi ðEc ¼ 3300 σcu þ 6900Þ
1 Ec þ 0:8
or
n¼
�
Ec Ec
8 < 1:00
(2)
E0 ðεc =ε0 � 1Þ
: 0:67 þ σcu 62 � 1
ðεc =ε0 > 1Þ
E0 ¼
σcu ε0
� (3)
(4)
=
where Ec andE0 represent initial modulus and the tangent modulus of concrete at σcu . The behavior of the steel is simulated by a plastic hardening kinematic model, and the material parameters are shown in Table 3. 2.3. Mesh convergence analysis In the finite element model, a suitable element size can be obtained from a mesh convergence analysis due to the mesh influence on the 3
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accuracy of numerical results. In general, if you use a smaller mesh size, you will get more accurate results. We cannot use the minimum size of the element to calculate due to the cost of computation increases rapidly. In this section, three mesh sizes of 200 mm, 500 mm and 800 mm are used to perform the modal analysis of structure, and the different errors of mesh sizes are only 0.021% and 0.11%, as shown in Fig. 3. Lastly, the mesh size of 500 mm is applied for the analysis.
Table 4 Period and natural frequency of isolated AP1000 NIB. Mode
Frequency (Hz)
Period (s)
1 2 3 4 5 6
0.6394 0.6408 2.1968 3.2409 3.3586 4.3083
1.5641 1.5607 0.4552 0.3085 0.2977 0.2321
Participation mass ratio (%) x
y
z
0.817 99.16 0.001 0 0.019 0
0 0 0 0.074 0 2.405
99.14 0.817 0 0.034 0 0
3. Numerical simulation 3.1. Modal analysis The present study attempts to understand the seismic behavior of isolated AP1000 NIB under mainshock-aftershock sequences. First, the natural frequencies and mode shapes are obtained through the modal analysis. Then, time history analysis is conducted using the earthquake excitation to get the seismic behavior and floor response spectrum of isolated AP1000 NIB. The first six natural frequencies, periods, and the participation mass ratios of the isolated AP1000 NIB are shown inTable 4 . It is indicated that the frequencies are paired symmetrically, and the mass of the iso lated structure is mainly focused on the first two modes. For example, the first four periods are 1.5641 s, 1.5647 s, 0.4552 s and 0.3085 s for isolated NIB, while the first four periods of the non-isolated AP1000 NIB are 0.3086, 0.3067, 0.2299 and 0.2262, respectively. The results show that the first two periods of the isolated structure are larger than that of the non-isolated NIB (0.3056 s and 0.3067), which indicates that the structure can reduce the dynamic response by prolonging the period using isolation system with soft horizontal stiffness. Fig. 4 shows the first two modal shapes of isolated and non-isolated AP1000 NIB. The results indicate that the isolated NIB mainly has the horizontal translational movement, whereas the non-isolated NIB has rocking modes. 3.2. Time history analysis As the above reasons, mainshocks may trigger several aftershocks, which may cause potential danger to the structure, especially for the NPP. In the previous papers, some earthquakes cause a lot of aftershocks during the following 2 h. Some of which include the Indonesia earth quake with a magnitude of 8.2 in 2005, Wenchuan earthquake with a magnitude of 6.0 and M7.0 of Fukushima earthquake in 2011(He et al., 2013; Wang et al., 2019). Seismic response of the structure under a single earthquake is various from the structure subjected to mainshock-aftershock sequences. Although, the magnitude of main shock is greater than aftershock, on the contrary, disaster event trig gered by aftershock may be worse than that of mainshocks. For instance, the mainshock did not take severe damage even disaster in New Zealand earthquake with a magnitude of 7.1. However, its aftershock with a magnitude of 6.3 caused nearly 150 fatalities in addition to several
Fig. 4. The first two modes of NIB: (a) 1st and (b) 2nd modes of isolated NIB, (c) 1st and (d) 2nd mode of non-isolated NIB.
Fig. 5. Design response spectra in horizontal and vertical directions. 4
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Table 5 Properties of the mainshock-aftershock ground motion sequences. No.
Ground motion
Station
Sequence
No. of NGA
Mw
Vs30 (m/s2)
Rjb (km)
Rrup(km)
1 2 3 4 5 6
CHI–CHI CHI–CHI Northridge CHI–CHI CHI–CHI Northridge
CHY074 HWA031 LA Dam CHY074 HWA031 Pacoima. Kagel Canyon
Mainshock Mainshock Mainshock Aftershock Aftershock Aftershock
1227 1280 1013 2190 3018 1671
7.62 7.62 6.69 5.9 6.2 5.2
602.29 553.43 628.99 602.29 553.43 508.08
0.7 47.41 0 43.27 39.29 20.08
10.8 51.46 5.92 45.07 40.04 20.79
damaged buildings in some cities (Zhai et al., 2018). In the section, the influences of aftershock on the seismic perfor mance of isolated AP1000 NIB under mainshock-aftershock sequences are analyzed. Simultaneously, the seismic response of isolated AP1000 NIB under a single mainshock with the same magnitude are also discussed.
3.2.2. Mainshock-aftershock sequences A series of mainshock and aftershock earthquake records from PEER database are selected to study the dynamic behavior of isolated AP1000 NIB. The aftershock accelerations are revised to satisfy the target design acceleration response spectrum of RG 1.60 (Zhai et al., 2018). The mainshocks should satisfy the following criterion, such as (1) magnitude of mainshock between 6 and 7.9; (2) shear velocity in the above soil layer of 30 m is from 400 m/s to 800 m/s; (3) fault distance is from 0 to 100 km; (4) accelerations are recorded on rock or stiff soil. We select earthquakes following the above-mentioned criterions considering the duration, the peak value of acceleration and response spectrum, which are the critical points for dynamic analysis of structures. Under these criteria and design response spectra, three mainshocks and three after shocks are selected from different stations in PEER database. Table 5 shows the mainshock-aftershock sequences for the analysis.
3.2.1. Earthquake selection Aseismic design of NPP requires that structures, the system, and equipment resist earthquakes. It has two seismic levels of Operating Basis Earthquake (OBE) and Safe Shutdown Earthquake (SSE) with two different levels of probability of occurrence. In this section, the SSE excitation is used to calculate the seismic response of isolated AP1000 NIB. The input earthquake for analysis of isolated AP1000 NPP requires the acceleration response spectrum to not only match with RG 1.60 but also consider the high-frequency amplification effects. The maximum values of input acceleration are 0.3 g and 0.2 g in the horizontal and vertical directions respectively. Fig. 5 shows the design ground response spectra for AP1000 NPP.
3.2.3. Modification of mainshock-aftershock sequences The request of the duration for an earthquake is not less than 20 s in China seismic design code of NPP(Construction, 1998). What is more, the strong part of the earthquake is greater than 6 s and the interval is less than or equal to 0.01 s. Additionally, the duration of the earthquake is not less than the three or four times of fundamental period in the case
Fig. 6. Mainshock-aftershock earthquake sequence of RSN1280. 5
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Fig. 7. Mainshock-aftershock earthquake sequence of RSN1227.
Fig. 8. Mainshock-aftershock earthquake sequence of RSN1013.
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with the input peak acceleration ratio of 0.667, respectively. The peak acceleration ratio PAR is defined as follows: PAR ¼
PGAaftershock PGAmainshock
(5)
where PGAmainshock represents the peak acceleration of mainshock, and PGAaftershock represents the peak acceleration of aftershock. For convenience, three mainshock-aftershock sequences are named by the number of PEER mainshock. For instance, the mainshockaftershock sequence of RSN1280-RSN3018 is simplified as RSN1280, and the other two mainshock-aftershock sequences are expressed as RSN1227 and RSN1013, as shown in Fig. 6–8. 4. Results and discussion The peak acceleration, displacement response and floor response spectra of isolated AP1000 NIB are investigated under mainshock and aftershock sequences. They have the same peak acceleration and design response spectrum of RG 1.60. The measurement points of the isolated AP1000 NIB are shown in Fig. 9. The ratio of maximum acceleration (RMA) is expressed as Eq. (6) based on the “Code for seismic design of the building” (GB 50011-2010) (GB50011, 2010).
Fig. 9. Measurement points.
of AP1000 NIB. According to the requirement, the duration of Chi-Chi earthquake mainshock with a magnitude of eight is 30 s, and the other mainshock is assumed as 30 s, aftershock duration is uniformly assumed as 20 s. We connect the mainshock and aftershock earthquake with an interval of 10 s to create earthquake sequences. During the interval of 10 s, the structure is assumed to be static without movement before aftershock starts. Three-directional mainshock and aftershock ground motions are inputted at the basement of isolated AP1000 NIB model, the peak values of mainshock acceleration are 0.3 g and 0.2 g in the horizontal directions and vertical direction, respectively. The peak acceleration of aftershock in horizontal and vertical directions are assumed as 0.2 g and 0.133 g
RMA ¼
MARaftershock MARmainshock
(6)
where RMA represents the ratio of maximum acceleration of isolated AP1000 NIB, MARaftershock represents the maximum acceleration response under aftershock, and MARmainshock stands for the maximum acceleration response under mainshock.
Fig. 10. Acceleration responses of the isolated NIB under sequences of RSN1280. 7
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Fig. 11. Acceleration responses of the isolated NIB under sequences of RSN1227.
Fig. 12. Acceleration responses of the isolated NIB under sequences of RSN1013. 8
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Fig. 13. The ratio of acceleration at different points. Table 6 Maximum absolute acceleration at different points of the isolated AP1000 NIB. Earthquake sequences
RSN1280
Points
Direction
Mainshock (m/s2)
Aftershock (m/s2)
RMA
Mainshock (m/s2)
Aftershock (m/s2)
RMA
Mainshock (m/s2)
Aftershock (m/s2)
RMA
P1
X Y Z X Y Z X Y Z X Y Z
3.969 0.932 3.445 3.732 0.364 3.429 3.600 0.306 3.283 3.437 0.139 3.194
2.678 1.206 2.000 2.476 0.459 1.960 2.351 0.377 1.833 2.207 0.168 1.743
0.67 1.29 0.58 0.66 1.26 0.57 0.65 1.23 0.56 0.64 1.21 0.55
3.155 0.649 3.679 2.972 0.240 3.352 2.860 0.193 3.296 2.122 0.085 3.120
2.565 0.602 2.265 2.356 0.227 2.126 2.231 0.185 1.994 2.084 0.079 1.875
0.81 0.93 0.62 0.79 0.95 0.63 0.78 0.96 0.60 0.98 0.93 0.60
4.038 1.190 3.725 3.810 0.554 3.546 3.673 0.475 3.377 3.517 0.219 3.191
2.253 0.661 2.632 2.051 0.238 2.551 1.932 0.197 2.312 1.791 0.085 2.156
0.56 0.56 0.71 0.54 0.43 0.72 0.53 0.41 0.68 0.51 0.39 0.68
P2 P3 P4
RSN1227
RSN1013
*RMA is ratio of maximum acceleration of AP1000 NI, see Eq. (6).
4.1. Acceleration response
does not change with the height increasing. The reason is due to the isolation system provides the soft stiffness in horizontal, which can mitigate the acceleration response of the isolated AP1000 NIB. The isolated NIB mainly focuses on the lateral movement during the exci tation of the earthquake. For all cases, especially for the horizontal direction, the aftershock acceleration responses are smaller compared with the values of main shock acceleration. For instance, as shown in Table 6, RMA of P1 in horizontal X and Z directions are 0.67 and 0.58 while the input peak acceleration ratio (PAR) is 0.667 under mainshock-aftershock RSN1280, which shows that aftershock has a slight effect on the acceleration re sponses. Similarly, RMA of P1 is 0.56 and 0.71 in horizontal X and Z
The acceleration responses at different points of isolated AP1000 NIB are shown in Figs. 10–12. Fig. 13 and Table 6 show the maximum ac celeration responses ratio at different points. As shown in figures, the results show that the acceleration responses of isolated AP1000 NIB between 30 s and 40 s are approximately zero without earthquake input, the isolated AP1000 NIB vibrates again after the aftershock starts input. It is noted that the horizontal maximum accelerations reduce dramati cally using base isolation system. The horizontal acceleration responses at different points are almost the same with the height of AP1000 NIB increases, namely, the horizontal acceleration responses of the building 9
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Fig. 14. Acceleration response spectra at different points in earthquake sequences of RSN1280.
directions while the input peak acceleration ratio (PAR) is 0.667 under the same magnitude of mainshock-aftershock RSN1013. These variation trends of the isolated NIB are different from the results of non-isolated NIB under the mainshock-aftershock sequences. This is because of the isolation system can prolong the period of the NIB and reduce the seismic response of the structure. On the contrary, mainshock-aftershock sequences of RSN1227 have the reverse effects for P2, P3 and P4, which the aftershocks increase the
acceleration response of isolated AP1000 NI under the same magnitude of mainshock-aftershock sequence, as shown in Table 6. Fig. 13 plots the curves of a maximum acceleration response of isolated AP1000 NIB. It is observed that the acceleration response values of the mainshock sequence of RSN1227 with same PAR of 0.667 are larger than that of the response of RSN1013 and RSN1280. Namely, the RMA of RSN1227 is larger than those of RSN1013 and RSN1280 in horizontal X directions at different measurement points. Simultaneously, the RMA of isolated 10
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Fig. 15. Acceleration response spectra at different points in earthquake sequences of RSN1227.
AP1000 NIB in the vertical direction under mainshock-aftershock se quences of RSN1280 and RSN1227 are larger than that of the horizontal directions. The values of vertical RMA are greater than or approximately equal to 1.0. Moreover, all the RMA curves of aftershocks RSN1227 and RSN1013 are close to the line of PAR of aftershock-RSN1227 and aftershock-RSN1013. It means that the aftershock has small effects on the dynamic response of isolated AP1000 NIB due to the isolator system.
4.2. Floor acceleration spectrum The floor acceleration response spectrum of isolated AP1000 NIB is investigated in this section. In the calculation, the damping ratio of the model is defined as 5% based on the AP1000 NPP theory document. Fig. 14 shows the floor response spectrum of different points under earthquake sequence of RSN1280. It is indicated that the peak of the floor acceleration spectrum at all the points of isolated AP1000 NIB 11
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Fig. 16. Acceleration response spectra at different points in earthquake sequences of RSN1013.
under mainshock is greater than that of the aftershock of RSN1280 in the horizontal and vertical directions. The predominant periods for various points in the horizontal direction are larger than the results of the ver tical direction. Furthermore, the horizontal peak values are greater than the results of the vertical direction. In comparison, it is observed that the mainshock and aftershock sequences of RSN1280 have an essential in fluence on the dynamic response in the horizontal direction with responding to the vertical direction.
Similarly, as shown in Figs. 15 and 16, mainshock and aftershock sequences have a substantial effect on the floor acceleration response in the horizontal Z-direction corresponding to the other directions sub jected to the RSN1227 and RSN1013. However, the peak floor acceler ations at P1, P2, P3 and P4 of isolated AP1000 NIB under aftershock are larger than the results of the mainshock in the horizontal and vertical directions. Moreover, the predominant periods of the acceleration response spectrums are beyond of the natural period of the isolated 12
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Fig. 17. Displacement response of the isolated NIB under sequences of RSN1280.
AP1000 NIB. It indicates that the isolated structure does not occur resonance and has an excellent reduction of the dynamic response during the mainshock-aftershock sequence excitation.
displacements under the mainshock and aftershock are 0.095 m and 0.020 m for RSN1280, 0.089 m and 0.016 m for RSN1227, and 0.090 m and 0.031 m for RSN 1013, respectively. The results indicate that the maximum lateral displacement under mainshock is greater than the result of the aftershock, and much less than the limit lateral displace ment of the isolators. It is demonstrated that the isolation system can improve the seismic resistance of AP1000 NIB prominently. During this stage, the isolated AP1000 NI is also being elastic status and has not accumulative damage, the effect of aftershock can be neglected for this earthquake sequence.
4.3. Displacement response “Code for seismic design of buildings” regulates that the limit value of lateral deflection should be less than smaller values between the 0.55 time of the effectiveness diameter (0.495 m) and the 3 times of the total thickness of all the rubber (0.489 m) in isolator(GB50011, 2010). For the isolation system, the maximum lateral displacement or deflection is a key control index of the isolated structure.
4.4. Stress state
Figs. 17–19 show the displacement time histories for different points under mainshock-aftershock sequences. From the figure, the lateral displacement response of isolated NI building does not change with the height of measure point increasing, the lateral values of displacements are almost the same at different measurement points. For instance, the values of maximum relative lateral displacements are 0.095 m and 0.088 m at P1, 0.092 m and 0.085 m at P2, 0.090 m and 0.083 m at P3, 0.088 m and 0.081 m at P4 in the horizontal X and Z directions under the RSN1280 mainshock-aftershock sequence. The values are far less than the limit value of the isolator (0.489 m). These results indicate that the story drifts of the upper isolated NIB are very small because of the same maximum lateral displacement in different height. The reason is that the isolation system applied in this structure is mainly horizontal isolation with softer stiffness in horizontal direction compared with the vertical stiffness of the isolator. The isolated AP1000 NIB mainly occurs lateral movements, which are corresponding with the law of the results of modal analysis. Table 7 shows the maximum lateral displacement of isolated NIB under mainshock-aftershock sequences. The maximum lateral
Fig. 20 shows the first principal stress of isolated AP1000 NIB under different mainshock-aftershock records. The stress distribution with red color indicates the maximum first principal stress region. The region has the most probability of damage during ground motions. As shown in Fig. 20, it is observed that the first principal stress distributed on the shield building is worse than that of the auxiliary building. The maximum stress or accumulative damage distribute in two areas, the first place occurs at the corner between the AP1000 NIB and air intakes, the other at the connection between the shield building and auxiliary building. Due to the isolator installation between the basement and upper structure, stress concentration exists on the connection between isolators and NIB. Thus, the security of the connection should be checked, and the structure avoids collapse under strong earthquakes. In most cases, the maximum first principal stress is less than 3 MPa, and far less than the yield stress of the concrete as results of the application of the isolation system. It is indicated that the isolation system can effec tively reduce the stress and mitigate the damage extent of the NIB under the earthquakes. In summary, due to the base isolation, the first principle stresses of 13
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Fig. 18. Displacement response of the isolated NIB under sequences of RSN1227.
Fig. 19. Displacement response of the isolated NIB under sequences of RSN1013. 14
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Table 7 The maximum horizontal relative displacement of isolated AP1000 NIB. Earthquake
RSN1280
RSN1227
RSN1013
Direction
Mainshock (m)
Aftershock (m)
Mainshock (m)
Aftershock (m)
Mainshock (m)
Aftershock (m)
X Z
0.095 0.088
0.019 0.020
0.086 0.089
0.011 0.016
0.081 0.090
0.031 0.025
Fig. 20. The 1st principal stress contours in different mainshock-aftershock sequences.
the NIB are far less than the yield stress of the concrete and the results of non-isolated NIB under the same mainshock-aftershock sequences. It is concluded that the isolation system can significantly mitigate the effects of aftershock on the damage states or the accumulative damage of the NIB.
distribution of isolated AP1000 NIB are studied and compared with nonisolated NIB to evaluate the influence of aftershock on accumulate damage. The results show that the acceleration responses of the isolated NIB are far less than that of the non-isolated NIB under the mainshockaftershock sequences. The accelerations and displacements of the iso lated NIB under aftershock are much less than the results of the main shock. The aftershock has a small effect on the dynamic response of the isolated AP1000 NIB and the influence can be neglected. The isolation system can effectively decrease the first principle stress of the structure and mitigate the cumulative damage to the isolated NIB. Thus, the isolation system can improve the seismic resistance of the structure effectively. This work mainly considers every mainshock with one
5. Conclusions In this paper, the finite element method is used to investigate the effects of the mainshock-aftershock sequence on the seismic behavior and stress distribution of isolated AP1000 NIB. The acceleration response, displacement response, floor acceleration spectrum and stress 15
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aftershock, the results don’t show the cumulative damage of the struc ture. In the future, we will consider a mainshock with multiple after shocks, and then analyze the cumulative effect under the effect of multiple aftershocks.
Lo Frano, R., Forasassi, G., 2011. Preliminary evaluation of seismic isolation effects in a Generation IV reactor. Energy 36, 2278–2284. Medel-Vera, C., Ji, T., 2015. Seismic protection technology for nuclear power plants: a systematic review. J. Nucl. Sci. Technol. 52, 607–632. Micheli, I., Cardini, S., Colaiuda, A., Turroni, P., 2004. Investigation upon the dynamic structural response of a nuclear plant on aseismic isolating devices. Nucl. Eng. Des. 228, 319–343. Pang, R., Xu, B., Zhang, X., Zhou, Y., Kong, X., 2019. Seismic performance investigation of high CFRDs subjected to mainshock-aftershock sequences. Soil Dyn. Earthq. Eng. 116, 82–85. PEER Ground Motion Database. (http://ngawest2.berkeley.edu/). Wang, G., Wang, Y., Lu, W., Yan, P., Zhou, W., Chen, M., 2017. Damage demand assessment of mainshock-damaged concrete gravity dams subjected to aftershocks. Soil Dyn. Earthq. Eng. 98, 141–154. Wang, D., Wu, C., Zhang, Y., Ding, Z., Chen, W., 2019. Elastic-plastic behavior of AP1000 nuclear island structure under mainshock-aftershock sequences. Ann. Nucl. Energy 123, 1–17. Yip, W.K., 1998. Generic form of stress-strain equations for concrete. Cement Concr. Res. 28, 499–508. Yu, N., Zhao, C., Peng, T., Huang, H.-w., Roy, S.S., Mo, Y.L., 2019. Numerical investigation of AP1000 NIB under mainshock-aftershock earthquakes. Prog. Nucl. Energy 117, 103096. Zhai, C.-H., Zheng, Z., Li, S., Xie, L.-L., 2015. Seismic analyses of a RCC building under mainshock–aftershock seismic sequences. Soil Dyn. Earthq. Eng. 74, 46–55. Zhai, C.-H., Bao, X., Zheng, Z., Wang, X.-Y., 2018. Impact of aftershocks on a postmainshock damaged containment structure considering duration. Soil Dyn. Earthq. Eng. 115, 129–141. Zhang, S., Wang, G., Sa, W., 2013. Damage evaluation of concrete gravity dams under mainshock–aftershock seismic sequences. Soil Dyn. Earthq. Eng. 50, 16–27. Zhao, C., Chen, J., 2013. Numerical simulation and investigation of the base isolated NPPC building under three-directional seismic loading. Nucl. Eng. Des. 265, 484–496. Zhao, C., Chen, J., 2014. Dynamic characteristics of AP1000 shield building for various water levels and air intakes considering fluid-structure interaction. Prog. Nucl. Energy 70, 176–187. Zhao, C., Yu, N., 2018. Dynamic response of generation IIIþ integral nuclear island structure considering fluid structure interaction effects. Ann. Nucl. Energy 112, 189–207. Zhao, C., Chen, J., Xu, Q., 2014. Dynamic analysis of AP1000 shield building for various elevations and shapes of air intakes considering FSI effects subjected to seismic loading. Prog. Nucl. Energy 74, 44–52. Zhao, C., Chen, J., Xu, Q., Yang, X., 2015. Sensitive analysis of water levels and air intakes on natural frequency of AP1000 nuclear island building considering FSI effects. Ann. Nucl. Energy 78, 1–9. Zhao, C., Chen, J., Xu, Q., Wang, J., Wang, B., 2016. Investigation on sloshing and vibration mitigation of water storage tank of AP1000. Ann. Nucl. Energy 90, 331–342. Zhao, C., Chen, J., Wang, J., Yu, N., Xu, Q., 2017. Seismic mitigation performance and optimization design of NPP water tank with internal ring baffles under earthquake loads. Nucl. Eng. Des. 318, 182–201.
Acknowledgments This work is supported by National Natural Science of China (Grant No. 51508148, 51138001), China Postdoctoral Science Foundation Funded Project (Grant No.:2015M581980 and 2016T90563), and Fundamental Research Funds for the Central Universities (Grant No. JZ2015HGBZ0113 and 2015HGQC0216). We also would like to thank the Chinese Scholarship Council (CSC) for his visiting scholarship stipend. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.pnucene.2019.103144. References Alliard, P.-M., L�eger, P., 2008. Earthquake safety evaluation of gravity dams considering aftershocks and reduced drainage efficiency. J. Eng. Mech. 134, 12–22. Chen, J., Zhao, C., Xu, Q., Yuan, C., 2014. Seismic analysis and evaluation of the base isolation system in AP1000 NI under SSE loading. Nucl. Eng. Des. 278, 117–133. Construction, C.M.o., 1998. Code for Seismic Design of Nuclear Power Plants. GB 5026797. Foulger, G.R., Wilson, M.P., Gluyas, J.G., Julian, B.R., Davies, R.J., 2018. Global review of human-induced earthquakes. Earth Sci. Rev. 178, 438–514. Fragiacomo, M., Amadio, C., Macorini, L., 2004. Seismic response of steel frames under repeated earthquake ground motions. Eng. Struct. 26, 2021–2035. GB50011, C.S., 2010. Code for Seismic Design of Buildings. China Building Industry Press, Beijing. Hatzigeorgiou, G.D., Liolios, A.A., 2010. Nonlinear behaviour of RC frames under repeated strong ground motions. Soil Dyn. Earthq. Eng. 30, 1010–1025. He, P., Wen, Y., Xu, C., Liu, Y., 2013. The large aftershocks triggered by the 2011 Mw 9.0 Tohoku-Oki earthquake, Japan. J. Asian Earth Sci. 74, 1–10. Huang, Y.-N., Whittaker, A.S., Luco, N., 2010. Seismic performance assessment of baseisolated safety-related nuclear structures. Earthq. Eng. Struct. Dyn. 39, 1421–1442. Jeltsov, M., Villanueva, W., Kudinov, P., 2018. Seismic sloshing effects in lead-cooled fast reactors. Nucl. Eng. Des. 332, 99–110. Liu, Y., Lu, D., Dang, J., Wang, S., Zeng, X., 2015. Equivalent mechanical model for structural dynamic analysis of elevated tank like AP1000 PCCWST. Ann. Nucl. Energy 85, 1175–1183.
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Study on the dynamic behavior of isolated AP1000 NIB under mainshock-aftershock sequences Chunfeng Zhao a, *, Na Yu b, **, Tao Peng a, Vincenzo Lippolis c, Aldo Corona c, Y.L. Mo d a
Department of Civil Engineering, Hefei University of Technology, Hefei, 230009, China Department of Economics, Hefei University, Hefei, 230601, China c Department of Engineering and Architecture, University of Parma, Parma, 43121, Italy d Department of Civil and Environmental Engineering, University of Houston, Houston, 77021, USA b
A R T I C L E I N F O
A B S T R A C T
Keywords: AP1000 nuclear island building (NIB) Isolation system Mainshock-aftershock Floor response spectrum Dynamic analysis
A mainshock can trigger several following severe aftershocks, which may take a threat to the structure. AP1000 nuclear power plant buildings (NPPB) may subject to severe mainshock and aftershock sequences during its whole life cycle. This paper mainly focuses on the seismic behavior of isolated AP1000 NPPB under mainshock and aftershock sequences. A 3D finite element model (FEM) of isolated AP1000 NPPB is established to perform the dynamic analysis. The effects of the mainshock-aftershock sequences on the maximum acceleration, peak displacement, acceleration response spectrum, and stress distribution are carried out using parametric analysis. The results indicate that the aftershock has a small impact on the seismic performance of the isolated nuclear island building (NIB) due to the isolation system. Mainshock and aftershock also influence the floor response spectrum in horizontal directions and the stress state to some extent, but the effects are relatively small compared with the non-isolated NIB.
1. Introduction AP1000 NPP as a type of generation III þ nuclear power plant (NPP) with advanced passive safety features (APS) is developed by Westing house Company and approved by the U.S. NRC (Zhao et al., 2017; Zhao and Yu, 2018). AP1000 NPP is advanced and low-cost due to its passive design philosophy for operation and maintenance(Wang et al., 2019; Zhao and Chen, 2014; Zhao et al., 2014, 2015). Although NPP has a series of advanced features and safety, it may also encounter a potential threat of earthquakes due to its uncertainty and randomness. Seismic or base isolation as an effective approach can reduce the dynamic response of the structure and keep the structure security, particularly for the NPP structure (Chen et al., 2014). A severe earthquake may trigger many strong aftershocks frequently, which take severe threats to the security of NPPs. In the past, several researchers have studied the dynamic response of NPPs under single earthquake excitations, which have made excellent progress in the security of NPPs. Zhao et al. investigated the dynamic response and the effectiveness of isolators in the NPP under SSE loading (Chen et al., 2014; Zhao and Chen, 2013). The results showed that the isolation system could
effectively reduce the structural response and protect the structure more security. Huang et al. (Huang et al., 2010) evaluated the benefits of base isolation in providing the safety of NPP compared with a conventional NPP by using performance assessment method. Nakamura et al. used a type of nonlinear material to establish a 3D FEM of NPP and investigated the influence of vertical ground motion on the structural lift. It indicated that the basement uplift was small under earthquake loads (Medel-Vera and Ji, 2015). Micheli et al. (2004) used a pure FEM to study the seismic behavior of an NPP with isolators under earthquake excitation. It was observed that the isolator could decrease the acceleration response drastically and make the NPP more safety (Micheli et al., 2004). Lo Frano adopted a numerical method to simulate the seismic isolation effects in EGIV NPP. The results showed that the isolation technology could reduce the seismic response the NPP compared with the non-isolated structure (Lo Frano and Forasassi, 2011). Xu et al. used SPH and FEM models to analyze the sloshing and oscillation of the water in the gravity water storage tank under different earthquakes. Jeltsov et al. (2018) used CFD and VOF methods to study the lead sloshing and seismic response of ELSY reactor under artificial earthquake. Liu et al. (2015) used an equivalent mechanical model to study the dynamic
* Corresponding author. . ** Corresponding author. E-mail addresses: [email protected] (C. Zhao), [email protected] (N. Yu). https://doi.org/10.1016/j.pnucene.2019.103144 Received 29 May 2019; Received in revised form 11 August 2019; Accepted 27 August 2019 Available online 5 September 2019 0149-1970/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Chunfeng Zhao, Progress in Nuclear Energy, https://doi.org/10.1016/j.pnucene.2019.103144
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Table 1 Mainshock-aftershock sequences. No.
Name
Country
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Hoover Hsinfengkiang Kariba Koyna Tangshan Friuli Imperial Valley Borach peak Nahanni Valparaiso Whittier Narrows Saguenay Loma Prieta Manjil Landers Chi Chi
USA China Zimb India China Italy USA USA Canada Chile USA Canada USA Iran USA Taiwan
Mainshock
Largest aftershock
Database
Year
Mw
PGA (g)
Delay
Mw
PGA (g)
1939 1962 1963 1967 1976 1976 1979 1983 1985 1985 1987 1988 1989 1990 1992 1999
5 6.1 6 6.3 7.8 6.5 6.5 7.3 6.9 7.8 6.1 5.9 6.5 7.3 6.9 7.6
– 0.6 – 0.5 – 0.35 0.4 0.08 0.2 0.3 0.3 0.16 0.3 0.7 0.3 0.8
2h 36 months 2 days 10 months 1 day 4 months 3 min 1 day 2 days 1 month 3 days 1 day 33 h 2 months 10 h 1 week
4 5.3 5.8 5.1 7.1 6.1 5 5.8 5.7 7.2 5.3 4.1 5 5 6.7 6.8
– – – 0.15 – 0.2 0.3 0.07 0.1 0.15 0.15 – – 0.25 0.5 –
response of AP1000 PCCWST under earthquake considering FSI effects. Zhao et al. studied the benefits of base isolation system in decreasing the seismic response of CPR1000 CCV. They also investigated the effect of dynamic response and structural damage for an integral structure of the nuclear island building with different heights of air takes. The effects of an internal ring baffle on the dynamic response of AP1000 NPPB were also considered subjected to seismic loads considering fluid-structure interaction of water(Zhao and Chen, 2013; Zhao et al., 2015, 2016, 2017; Zhao and Yu, 2018). As we all known, earthquakes are generally composed of foreshocks, mainshocks and aftershocks. Moreover, in the event of various earth quakes, strong aftershocks cause severe and potential danger to the safety of structures. some strong aftershocks caused by a mainshock are shown in Table 1. Several earthquake disasters indicated that the structure was not able to resist the strong aftershocks after the main shock excitation without recovery (Wang et al., 2017). Simultaneously, the aftershock might also take accumulative damage to the structure when it was subjected to strong mainshock ground motions. Whereas, strong earthquakes may trigger several severe aftershocks during earthquake events. Thus, many structures are not only subjected to an earthquake event, but also to some earthquake sequences in seismic activity zones (Pang et al., 2019; Zhai et al., 2018). In the past, several studies indicated that a mainshock might trigger the following mainshock. For example, 105 aftershocks with the magnitude between 4.1 and 6.1 were caused by the Wenchuan earth quake of 8.0 magnitude on May 12, 2008. The Tohoku earthquake with a magnitude of 9.0 was occurred on March 11, 2011, in Japan and caused more than 588 aftershocks with a moment magnitude of 5.0. Many works have demonstrated that aftershocks could aggravate the struc tural damage and trigger seriously failure or even the collapse of structures (Zhai et al., 2018; Zhang et al., 2013). Because the mainshock causes structural damage and then aftershocks aggravate the additional damage without any reparation. The accumulated damage of structure caused by mainshock-aftershock earthquake sequences should be investigated to protect the security of the structure (Zhai et al., 2018) (Foulger et al., 2018). Up to now, some researchers have started to investigate the dynamic behavior of structures under a series of mainshock-aftershock earth quakes. Some works have considered the seismic behavior of reinforced concrete buildings subjected to mainshock and aftershocks and provided some significative conclusions (Alliard and L� eger, 2008; Fragiacomo et al., 2004; Hatzigeorgiou and Liolios, 2010). Unfortunately, few re searchers have focused on the dynamic responses and the accumulative damage of NPP and isolated NPP subjected to aftershock. Zhai et al., 2015, 2018 investigated the dynamic response of reinforced concrete containment and the effects of duration of aftershocks on the
– – – NGDC NGDC PEER COSMOS PEER STRONGMO COSMOS COSMOS STRONGMO – ESD COSMOS PEER
Fig. 1. AP1000 NIB.
accumulative damage of CCV. The obtained results indicated that longer durations of aftershocks could trigger severe cumulative damage to the structure. Wang et al. studied elastic behaviors of AP1000 NIB under severe earthquake excitation, and the results indicated that the after shock took a minimal effect on the structural responses in horizontal and vertical directions under DBE earthquake (Wang et al., 2019). Yu et al. studied the seismic behavior of AP1000 nuclear power plant building under different mainshock and aftershock earthquakes. The results showed that the aftershock took accumulative damage and had a sig nificant effect on the floor acceleration response spectrum of the struc ture in the horizontal direction(Yu et al., 2019). In short, the limited works mainly paid attention to the CAP1000 NPP containment vessel or shield building of AP1000 NPP, and no research focused on the seismic behavior of isolated NPP under mainshock-aftershock earthquakes. Aftershocks may induce severe accumulative damage and cause potential danger to the AP1000 NIB. Therefore, it is important and necessary to study the seismic perfor mance and accumulative damage of isolated AP1000 NPPB under mainshock-aftershock sequences. In this study, the seismic response and factor of isolated AP1000 NIB are investigated under the different mainshock-aftershock sequences. A parametric analysis of aftershock magnitude on the structural behavior of isolated NIB is conducted under mainshock and aftershock. Lastly, acceleration response, displacement response and floor response spec trum of isolated NIB are also studied and compared with the results of non-isolated NIB.
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Table 2 Geometry of AP 1000 NIB [5]. Parameter Width of nuclear island Length of nuclear island Height of nuclear island Radius of shield building Radius of water tank Radius of CV Wall thickness Thickness of CV Height of water tank Height of auxiliary building
Table 3 Material characteristics. Value 26.67 77.42 81.98 22.1 13.565 19.8 0.92 0.041 11.8 39.42
Unit
Material
m m m m m m m m m m
Parameter
Concrete
Symbol
Density Yong’s modulus Poisson’s ratio Density Yong’s modulus Poisson’s ratio Density Density
Reinforced bar Water Air
Unit
Value 3
Kg/m MPa 1 Kg/m3 MPa 1 Kg/m3 Kg/m3
ρ
E
ν ρ
E
ν ρ ρ
2300 3.35 � 104 0.2 7800 2.06 � 105 0.3 1000 1
Fig. 2. The isolated AP1000 NIB and the layout of isolators.
2. AP1000 nuclear island 2.1. Numerical model
Fig. 3. Convergence of mesh size effects.
AP1000 NIB is composed of a shield building (SB), water storage tank (WST), air intake (AI), containment vessel (CV), as shown in Fig. 1. The geometry of AP1000 NIB is shown in Table 2. According to the total mass of the structure, the vertical live and dead load, we select GZY900 type of isolator for application in the AP1000 NIB, the details of the isolators are explained in the previous paper (Chen et al., 2014). The vertical stiffness, horizontal post yielding stiffness, yield force, vertical maximum load and the design maximum horizontal displacement of the isolators are described in the previous reference (Chen et al., 2014). Finally, 387 isolators are chosen after the calculation with a minimum of 29% safety margin against the extra-loads. The isolators are modeled by the elements of COMBIN 14 and COMBIN 14 in vertical stiffness and horizontal stiffness respectively. COMBIN 14 is a spring-damper element that has the longitudinal or torsional capacity for 1D, 2D or 3D appli cation(Chen et al., 2014). Each node of the spring-damper element has three degrees of freedom and translation in X, Y and Z directions. The element is defined by two nodes, a spring constant and damping co efficients. Combin40 is a combination of a spring-slider and damper in parallel, coupled with a gap in series(Chen et al., 2014). The element has one degree of freedom at each node, either a nodal translation, rotation, pressure, or temperature. The element can be used to represent the horizontal movement of the isolators. AP1000 NIB has many auxiliary buildings, it is tough to establish all the models including reactor in ternal pipeline and equipment once time due to its complicated boundary and structural shape. This study mainly focused on the CV and SB of AP1000 NIB under mainshock -aftershock sequences, so the in ternal equipment and pipelines are represented by shell and mass ele ments. Additionally, a reinforced concrete smear model is applied to simulate the seismic behavior of isolated AP1000 NIB, and the rigid foundation is assumed without consideration of soil-structure interac tion in this model. The detailed finite element model of isolated AP1000 NIB is shown in Fig. 2.
2.2. Model of material The compressive behavior of concrete material is described by the constitutive law of concrete (Yip, 1998). The compressive stress-strain relation of concrete can be given as follows:
σ con ¼
nðεcon =ε0 Þ n
1 þ ðεcon =ε0 Þnk
(1)
σcu
where σ con and εcon stand for the stress and strain of concrete. σ cu represent the ultimate compressive strength of concrete. n and k are the fitting parameters and slope parameter of the stress-strain curve. ε0 denotes the value of strain when σ con reaches to σ cu . The expressions of these parameters can be expressed as follows:
ε0 ¼
n¼
k¼
σcu
n n
σ cu 17
pffiffiffiffiffiffi ðEc ¼ 3300 σcu þ 6900Þ
1 Ec þ 0:8
or
n¼
�
Ec Ec
8 < 1:00
(2)
E0 ðεc =ε0 � 1Þ
: 0:67 þ σcu 62 � 1
ðεc =ε0 > 1Þ
E0 ¼
σcu ε0
� (3)
(4)
=
where Ec andE0 represent initial modulus and the tangent modulus of concrete at σcu . The behavior of the steel is simulated by a plastic hardening kinematic model, and the material parameters are shown in Table 3. 2.3. Mesh convergence analysis In the finite element model, a suitable element size can be obtained from a mesh convergence analysis due to the mesh influence on the 3
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accuracy of numerical results. In general, if you use a smaller mesh size, you will get more accurate results. We cannot use the minimum size of the element to calculate due to the cost of computation increases rapidly. In this section, three mesh sizes of 200 mm, 500 mm and 800 mm are used to perform the modal analysis of structure, and the different errors of mesh sizes are only 0.021% and 0.11%, as shown in Fig. 3. Lastly, the mesh size of 500 mm is applied for the analysis.
Table 4 Period and natural frequency of isolated AP1000 NIB. Mode
Frequency (Hz)
Period (s)
1 2 3 4 5 6
0.6394 0.6408 2.1968 3.2409 3.3586 4.3083
1.5641 1.5607 0.4552 0.3085 0.2977 0.2321
Participation mass ratio (%) x
y
z
0.817 99.16 0.001 0 0.019 0
0 0 0 0.074 0 2.405
99.14 0.817 0 0.034 0 0
3. Numerical simulation 3.1. Modal analysis The present study attempts to understand the seismic behavior of isolated AP1000 NIB under mainshock-aftershock sequences. First, the natural frequencies and mode shapes are obtained through the modal analysis. Then, time history analysis is conducted using the earthquake excitation to get the seismic behavior and floor response spectrum of isolated AP1000 NIB. The first six natural frequencies, periods, and the participation mass ratios of the isolated AP1000 NIB are shown inTable 4 . It is indicated that the frequencies are paired symmetrically, and the mass of the iso lated structure is mainly focused on the first two modes. For example, the first four periods are 1.5641 s, 1.5647 s, 0.4552 s and 0.3085 s for isolated NIB, while the first four periods of the non-isolated AP1000 NIB are 0.3086, 0.3067, 0.2299 and 0.2262, respectively. The results show that the first two periods of the isolated structure are larger than that of the non-isolated NIB (0.3056 s and 0.3067), which indicates that the structure can reduce the dynamic response by prolonging the period using isolation system with soft horizontal stiffness. Fig. 4 shows the first two modal shapes of isolated and non-isolated AP1000 NIB. The results indicate that the isolated NIB mainly has the horizontal translational movement, whereas the non-isolated NIB has rocking modes. 3.2. Time history analysis As the above reasons, mainshocks may trigger several aftershocks, which may cause potential danger to the structure, especially for the NPP. In the previous papers, some earthquakes cause a lot of aftershocks during the following 2 h. Some of which include the Indonesia earth quake with a magnitude of 8.2 in 2005, Wenchuan earthquake with a magnitude of 6.0 and M7.0 of Fukushima earthquake in 2011(He et al., 2013; Wang et al., 2019). Seismic response of the structure under a single earthquake is various from the structure subjected to mainshock-aftershock sequences. Although, the magnitude of main shock is greater than aftershock, on the contrary, disaster event trig gered by aftershock may be worse than that of mainshocks. For instance, the mainshock did not take severe damage even disaster in New Zealand earthquake with a magnitude of 7.1. However, its aftershock with a magnitude of 6.3 caused nearly 150 fatalities in addition to several
Fig. 4. The first two modes of NIB: (a) 1st and (b) 2nd modes of isolated NIB, (c) 1st and (d) 2nd mode of non-isolated NIB.
Fig. 5. Design response spectra in horizontal and vertical directions. 4
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Table 5 Properties of the mainshock-aftershock ground motion sequences. No.
Ground motion
Station
Sequence
No. of NGA
Mw
Vs30 (m/s2)
Rjb (km)
Rrup(km)
1 2 3 4 5 6
CHI–CHI CHI–CHI Northridge CHI–CHI CHI–CHI Northridge
CHY074 HWA031 LA Dam CHY074 HWA031 Pacoima. Kagel Canyon
Mainshock Mainshock Mainshock Aftershock Aftershock Aftershock
1227 1280 1013 2190 3018 1671
7.62 7.62 6.69 5.9 6.2 5.2
602.29 553.43 628.99 602.29 553.43 508.08
0.7 47.41 0 43.27 39.29 20.08
10.8 51.46 5.92 45.07 40.04 20.79
damaged buildings in some cities (Zhai et al., 2018). In the section, the influences of aftershock on the seismic perfor mance of isolated AP1000 NIB under mainshock-aftershock sequences are analyzed. Simultaneously, the seismic response of isolated AP1000 NIB under a single mainshock with the same magnitude are also discussed.
3.2.2. Mainshock-aftershock sequences A series of mainshock and aftershock earthquake records from PEER database are selected to study the dynamic behavior of isolated AP1000 NIB. The aftershock accelerations are revised to satisfy the target design acceleration response spectrum of RG 1.60 (Zhai et al., 2018). The mainshocks should satisfy the following criterion, such as (1) magnitude of mainshock between 6 and 7.9; (2) shear velocity in the above soil layer of 30 m is from 400 m/s to 800 m/s; (3) fault distance is from 0 to 100 km; (4) accelerations are recorded on rock or stiff soil. We select earthquakes following the above-mentioned criterions considering the duration, the peak value of acceleration and response spectrum, which are the critical points for dynamic analysis of structures. Under these criteria and design response spectra, three mainshocks and three after shocks are selected from different stations in PEER database. Table 5 shows the mainshock-aftershock sequences for the analysis.
3.2.1. Earthquake selection Aseismic design of NPP requires that structures, the system, and equipment resist earthquakes. It has two seismic levels of Operating Basis Earthquake (OBE) and Safe Shutdown Earthquake (SSE) with two different levels of probability of occurrence. In this section, the SSE excitation is used to calculate the seismic response of isolated AP1000 NIB. The input earthquake for analysis of isolated AP1000 NPP requires the acceleration response spectrum to not only match with RG 1.60 but also consider the high-frequency amplification effects. The maximum values of input acceleration are 0.3 g and 0.2 g in the horizontal and vertical directions respectively. Fig. 5 shows the design ground response spectra for AP1000 NPP.
3.2.3. Modification of mainshock-aftershock sequences The request of the duration for an earthquake is not less than 20 s in China seismic design code of NPP(Construction, 1998). What is more, the strong part of the earthquake is greater than 6 s and the interval is less than or equal to 0.01 s. Additionally, the duration of the earthquake is not less than the three or four times of fundamental period in the case
Fig. 6. Mainshock-aftershock earthquake sequence of RSN1280. 5
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Fig. 7. Mainshock-aftershock earthquake sequence of RSN1227.
Fig. 8. Mainshock-aftershock earthquake sequence of RSN1013.
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with the input peak acceleration ratio of 0.667, respectively. The peak acceleration ratio PAR is defined as follows: PAR ¼
PGAaftershock PGAmainshock
(5)
where PGAmainshock represents the peak acceleration of mainshock, and PGAaftershock represents the peak acceleration of aftershock. For convenience, three mainshock-aftershock sequences are named by the number of PEER mainshock. For instance, the mainshockaftershock sequence of RSN1280-RSN3018 is simplified as RSN1280, and the other two mainshock-aftershock sequences are expressed as RSN1227 and RSN1013, as shown in Fig. 6–8. 4. Results and discussion The peak acceleration, displacement response and floor response spectra of isolated AP1000 NIB are investigated under mainshock and aftershock sequences. They have the same peak acceleration and design response spectrum of RG 1.60. The measurement points of the isolated AP1000 NIB are shown in Fig. 9. The ratio of maximum acceleration (RMA) is expressed as Eq. (6) based on the “Code for seismic design of the building” (GB 50011-2010) (GB50011, 2010).
Fig. 9. Measurement points.
of AP1000 NIB. According to the requirement, the duration of Chi-Chi earthquake mainshock with a magnitude of eight is 30 s, and the other mainshock is assumed as 30 s, aftershock duration is uniformly assumed as 20 s. We connect the mainshock and aftershock earthquake with an interval of 10 s to create earthquake sequences. During the interval of 10 s, the structure is assumed to be static without movement before aftershock starts. Three-directional mainshock and aftershock ground motions are inputted at the basement of isolated AP1000 NIB model, the peak values of mainshock acceleration are 0.3 g and 0.2 g in the horizontal directions and vertical direction, respectively. The peak acceleration of aftershock in horizontal and vertical directions are assumed as 0.2 g and 0.133 g
RMA ¼
MARaftershock MARmainshock
(6)
where RMA represents the ratio of maximum acceleration of isolated AP1000 NIB, MARaftershock represents the maximum acceleration response under aftershock, and MARmainshock stands for the maximum acceleration response under mainshock.
Fig. 10. Acceleration responses of the isolated NIB under sequences of RSN1280. 7
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Fig. 11. Acceleration responses of the isolated NIB under sequences of RSN1227.
Fig. 12. Acceleration responses of the isolated NIB under sequences of RSN1013. 8
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Fig. 13. The ratio of acceleration at different points. Table 6 Maximum absolute acceleration at different points of the isolated AP1000 NIB. Earthquake sequences
RSN1280
Points
Direction
Mainshock (m/s2)
Aftershock (m/s2)
RMA
Mainshock (m/s2)
Aftershock (m/s2)
RMA
Mainshock (m/s2)
Aftershock (m/s2)
RMA
P1
X Y Z X Y Z X Y Z X Y Z
3.969 0.932 3.445 3.732 0.364 3.429 3.600 0.306 3.283 3.437 0.139 3.194
2.678 1.206 2.000 2.476 0.459 1.960 2.351 0.377 1.833 2.207 0.168 1.743
0.67 1.29 0.58 0.66 1.26 0.57 0.65 1.23 0.56 0.64 1.21 0.55
3.155 0.649 3.679 2.972 0.240 3.352 2.860 0.193 3.296 2.122 0.085 3.120
2.565 0.602 2.265 2.356 0.227 2.126 2.231 0.185 1.994 2.084 0.079 1.875
0.81 0.93 0.62 0.79 0.95 0.63 0.78 0.96 0.60 0.98 0.93 0.60
4.038 1.190 3.725 3.810 0.554 3.546 3.673 0.475 3.377 3.517 0.219 3.191
2.253 0.661 2.632 2.051 0.238 2.551 1.932 0.197 2.312 1.791 0.085 2.156
0.56 0.56 0.71 0.54 0.43 0.72 0.53 0.41 0.68 0.51 0.39 0.68
P2 P3 P4
RSN1227
RSN1013
*RMA is ratio of maximum acceleration of AP1000 NI, see Eq. (6).
4.1. Acceleration response
does not change with the height increasing. The reason is due to the isolation system provides the soft stiffness in horizontal, which can mitigate the acceleration response of the isolated AP1000 NIB. The isolated NIB mainly focuses on the lateral movement during the exci tation of the earthquake. For all cases, especially for the horizontal direction, the aftershock acceleration responses are smaller compared with the values of main shock acceleration. For instance, as shown in Table 6, RMA of P1 in horizontal X and Z directions are 0.67 and 0.58 while the input peak acceleration ratio (PAR) is 0.667 under mainshock-aftershock RSN1280, which shows that aftershock has a slight effect on the acceleration re sponses. Similarly, RMA of P1 is 0.56 and 0.71 in horizontal X and Z
The acceleration responses at different points of isolated AP1000 NIB are shown in Figs. 10–12. Fig. 13 and Table 6 show the maximum ac celeration responses ratio at different points. As shown in figures, the results show that the acceleration responses of isolated AP1000 NIB between 30 s and 40 s are approximately zero without earthquake input, the isolated AP1000 NIB vibrates again after the aftershock starts input. It is noted that the horizontal maximum accelerations reduce dramati cally using base isolation system. The horizontal acceleration responses at different points are almost the same with the height of AP1000 NIB increases, namely, the horizontal acceleration responses of the building 9
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Fig. 14. Acceleration response spectra at different points in earthquake sequences of RSN1280.
directions while the input peak acceleration ratio (PAR) is 0.667 under the same magnitude of mainshock-aftershock RSN1013. These variation trends of the isolated NIB are different from the results of non-isolated NIB under the mainshock-aftershock sequences. This is because of the isolation system can prolong the period of the NIB and reduce the seismic response of the structure. On the contrary, mainshock-aftershock sequences of RSN1227 have the reverse effects for P2, P3 and P4, which the aftershocks increase the
acceleration response of isolated AP1000 NI under the same magnitude of mainshock-aftershock sequence, as shown in Table 6. Fig. 13 plots the curves of a maximum acceleration response of isolated AP1000 NIB. It is observed that the acceleration response values of the mainshock sequence of RSN1227 with same PAR of 0.667 are larger than that of the response of RSN1013 and RSN1280. Namely, the RMA of RSN1227 is larger than those of RSN1013 and RSN1280 in horizontal X directions at different measurement points. Simultaneously, the RMA of isolated 10
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Fig. 15. Acceleration response spectra at different points in earthquake sequences of RSN1227.
AP1000 NIB in the vertical direction under mainshock-aftershock se quences of RSN1280 and RSN1227 are larger than that of the horizontal directions. The values of vertical RMA are greater than or approximately equal to 1.0. Moreover, all the RMA curves of aftershocks RSN1227 and RSN1013 are close to the line of PAR of aftershock-RSN1227 and aftershock-RSN1013. It means that the aftershock has small effects on the dynamic response of isolated AP1000 NIB due to the isolator system.
4.2. Floor acceleration spectrum The floor acceleration response spectrum of isolated AP1000 NIB is investigated in this section. In the calculation, the damping ratio of the model is defined as 5% based on the AP1000 NPP theory document. Fig. 14 shows the floor response spectrum of different points under earthquake sequence of RSN1280. It is indicated that the peak of the floor acceleration spectrum at all the points of isolated AP1000 NIB 11
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Fig. 16. Acceleration response spectra at different points in earthquake sequences of RSN1013.
under mainshock is greater than that of the aftershock of RSN1280 in the horizontal and vertical directions. The predominant periods for various points in the horizontal direction are larger than the results of the ver tical direction. Furthermore, the horizontal peak values are greater than the results of the vertical direction. In comparison, it is observed that the mainshock and aftershock sequences of RSN1280 have an essential in fluence on the dynamic response in the horizontal direction with responding to the vertical direction.
Similarly, as shown in Figs. 15 and 16, mainshock and aftershock sequences have a substantial effect on the floor acceleration response in the horizontal Z-direction corresponding to the other directions sub jected to the RSN1227 and RSN1013. However, the peak floor acceler ations at P1, P2, P3 and P4 of isolated AP1000 NIB under aftershock are larger than the results of the mainshock in the horizontal and vertical directions. Moreover, the predominant periods of the acceleration response spectrums are beyond of the natural period of the isolated 12
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Fig. 17. Displacement response of the isolated NIB under sequences of RSN1280.
AP1000 NIB. It indicates that the isolated structure does not occur resonance and has an excellent reduction of the dynamic response during the mainshock-aftershock sequence excitation.
displacements under the mainshock and aftershock are 0.095 m and 0.020 m for RSN1280, 0.089 m and 0.016 m for RSN1227, and 0.090 m and 0.031 m for RSN 1013, respectively. The results indicate that the maximum lateral displacement under mainshock is greater than the result of the aftershock, and much less than the limit lateral displace ment of the isolators. It is demonstrated that the isolation system can improve the seismic resistance of AP1000 NIB prominently. During this stage, the isolated AP1000 NI is also being elastic status and has not accumulative damage, the effect of aftershock can be neglected for this earthquake sequence.
4.3. Displacement response “Code for seismic design of buildings” regulates that the limit value of lateral deflection should be less than smaller values between the 0.55 time of the effectiveness diameter (0.495 m) and the 3 times of the total thickness of all the rubber (0.489 m) in isolator(GB50011, 2010). For the isolation system, the maximum lateral displacement or deflection is a key control index of the isolated structure.
4.4. Stress state
Figs. 17–19 show the displacement time histories for different points under mainshock-aftershock sequences. From the figure, the lateral displacement response of isolated NI building does not change with the height of measure point increasing, the lateral values of displacements are almost the same at different measurement points. For instance, the values of maximum relative lateral displacements are 0.095 m and 0.088 m at P1, 0.092 m and 0.085 m at P2, 0.090 m and 0.083 m at P3, 0.088 m and 0.081 m at P4 in the horizontal X and Z directions under the RSN1280 mainshock-aftershock sequence. The values are far less than the limit value of the isolator (0.489 m). These results indicate that the story drifts of the upper isolated NIB are very small because of the same maximum lateral displacement in different height. The reason is that the isolation system applied in this structure is mainly horizontal isolation with softer stiffness in horizontal direction compared with the vertical stiffness of the isolator. The isolated AP1000 NIB mainly occurs lateral movements, which are corresponding with the law of the results of modal analysis. Table 7 shows the maximum lateral displacement of isolated NIB under mainshock-aftershock sequences. The maximum lateral
Fig. 20 shows the first principal stress of isolated AP1000 NIB under different mainshock-aftershock records. The stress distribution with red color indicates the maximum first principal stress region. The region has the most probability of damage during ground motions. As shown in Fig. 20, it is observed that the first principal stress distributed on the shield building is worse than that of the auxiliary building. The maximum stress or accumulative damage distribute in two areas, the first place occurs at the corner between the AP1000 NIB and air intakes, the other at the connection between the shield building and auxiliary building. Due to the isolator installation between the basement and upper structure, stress concentration exists on the connection between isolators and NIB. Thus, the security of the connection should be checked, and the structure avoids collapse under strong earthquakes. In most cases, the maximum first principal stress is less than 3 MPa, and far less than the yield stress of the concrete as results of the application of the isolation system. It is indicated that the isolation system can effec tively reduce the stress and mitigate the damage extent of the NIB under the earthquakes. In summary, due to the base isolation, the first principle stresses of 13
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Fig. 18. Displacement response of the isolated NIB under sequences of RSN1227.
Fig. 19. Displacement response of the isolated NIB under sequences of RSN1013. 14
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Table 7 The maximum horizontal relative displacement of isolated AP1000 NIB. Earthquake
RSN1280
RSN1227
RSN1013
Direction
Mainshock (m)
Aftershock (m)
Mainshock (m)
Aftershock (m)
Mainshock (m)
Aftershock (m)
X Z
0.095 0.088
0.019 0.020
0.086 0.089
0.011 0.016
0.081 0.090
0.031 0.025
Fig. 20. The 1st principal stress contours in different mainshock-aftershock sequences.
the NIB are far less than the yield stress of the concrete and the results of non-isolated NIB under the same mainshock-aftershock sequences. It is concluded that the isolation system can significantly mitigate the effects of aftershock on the damage states or the accumulative damage of the NIB.
distribution of isolated AP1000 NIB are studied and compared with nonisolated NIB to evaluate the influence of aftershock on accumulate damage. The results show that the acceleration responses of the isolated NIB are far less than that of the non-isolated NIB under the mainshockaftershock sequences. The accelerations and displacements of the iso lated NIB under aftershock are much less than the results of the main shock. The aftershock has a small effect on the dynamic response of the isolated AP1000 NIB and the influence can be neglected. The isolation system can effectively decrease the first principle stress of the structure and mitigate the cumulative damage to the isolated NIB. Thus, the isolation system can improve the seismic resistance of the structure effectively. This work mainly considers every mainshock with one
5. Conclusions In this paper, the finite element method is used to investigate the effects of the mainshock-aftershock sequence on the seismic behavior and stress distribution of isolated AP1000 NIB. The acceleration response, displacement response, floor acceleration spectrum and stress 15
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aftershock, the results don’t show the cumulative damage of the struc ture. In the future, we will consider a mainshock with multiple after shocks, and then analyze the cumulative effect under the effect of multiple aftershocks.
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Acknowledgments This work is supported by National Natural Science of China (Grant No. 51508148, 51138001), China Postdoctoral Science Foundation Funded Project (Grant No.:2015M581980 and 2016T90563), and Fundamental Research Funds for the Central Universities (Grant No. JZ2015HGBZ0113 and 2015HGQC0216). We also would like to thank the Chinese Scholarship Council (CSC) for his visiting scholarship stipend. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.pnucene.2019.103144. References Alliard, P.-M., L�eger, P., 2008. Earthquake safety evaluation of gravity dams considering aftershocks and reduced drainage efficiency. J. Eng. Mech. 134, 12–22. Chen, J., Zhao, C., Xu, Q., Yuan, C., 2014. Seismic analysis and evaluation of the base isolation system in AP1000 NI under SSE loading. Nucl. Eng. Des. 278, 117–133. Construction, C.M.o., 1998. Code for Seismic Design of Nuclear Power Plants. GB 5026797. Foulger, G.R., Wilson, M.P., Gluyas, J.G., Julian, B.R., Davies, R.J., 2018. Global review of human-induced earthquakes. Earth Sci. Rev. 178, 438–514. Fragiacomo, M., Amadio, C., Macorini, L., 2004. Seismic response of steel frames under repeated earthquake ground motions. Eng. Struct. 26, 2021–2035. GB50011, C.S., 2010. Code for Seismic Design of Buildings. China Building Industry Press, Beijing. Hatzigeorgiou, G.D., Liolios, A.A., 2010. Nonlinear behaviour of RC frames under repeated strong ground motions. Soil Dyn. Earthq. Eng. 30, 1010–1025. He, P., Wen, Y., Xu, C., Liu, Y., 2013. The large aftershocks triggered by the 2011 Mw 9.0 Tohoku-Oki earthquake, Japan. J. Asian Earth Sci. 74, 1–10. Huang, Y.-N., Whittaker, A.S., Luco, N., 2010. Seismic performance assessment of baseisolated safety-related nuclear structures. Earthq. Eng. Struct. Dyn. 39, 1421–1442. Jeltsov, M., Villanueva, W., Kudinov, P., 2018. Seismic sloshing effects in lead-cooled fast reactors. Nucl. Eng. Des. 332, 99–110. Liu, Y., Lu, D., Dang, J., Wang, S., Zeng, X., 2015. Equivalent mechanical model for structural dynamic analysis of elevated tank like AP1000 PCCWST. Ann. Nucl. Energy 85, 1175–1183.
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