Seismic mitigation performance and optimization design of NPP water tank with internal ring baffles under earthquake loads

Seismic mitigation performance and optimization design of NPP water tank with internal ring baffles under earthquake loads

Nuclear Engineering and Design 318 (2017) 182–201 Contents lists available at ScienceDirect Nuclear Engineering and Design journal homepage: www.els...

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Nuclear Engineering and Design 318 (2017) 182–201

Contents lists available at ScienceDirect

Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes

Seismic mitigation performance and optimization design of NPP water tank with internal ring baffles under earthquake loads Chunfeng Zhao a,d, Jianyun Chen b, Jingfeng Wang a, Na Yu c,⇑, Qiang Xu b a

School of Civil Engineering, Hefei University of Technology, Hefei 230009, China Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China c School of Economics, Hefei University, Hefei 230009, China d State Key Laboratory for Geo Mechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China b

h i g h l i g h t s  FSI of water tank under earthquake are simulated by FEM.  The influences of internal ring baffle on seismic response reduction are investigated.  ALE algorithm is applied to study the fluid-structure interaction effects.  The effects of different ring baffle types in reducing seismic response are compared.  The optimal type of ring baffle under seismic loads is obtained.

a r t i c l e

i n f o

Article history: Received 9 November 2015 Received in revised form 12 April 2017 Accepted 14 April 2017

Keywords: Nuclear power plant Ring baffle Fluid-structure interaction Seismic performance Optimal design

a b s t r a c t The shield building of AP1000 is designed to protect the steel containment vessel of nuclear power plant. Therefore, the safety and integrity must be ensured during the plant life in any conditions such as earthquake. The purpose of this paper is to study the fluid-structure interaction of water in water tank and effects of internal ring baffle on the response of AP1000 shield building under strong ground motions. For this purpose, a fluid-structure interaction algorithm of finite element technique is employed to investigate the seismic response of water tank with internal baffles of different shapes and arrangements under artificial, El-Centro and Kobe earthquakes with peak acceleration of 0.3 g. Four optimal designed schemes of different ring baffle types are considered and the influences of various parameters such as vertical baffle height, arrangement locations, baffle height ratio and length of baffle on the dynamical response of shield building are discussed. The numerical results clearly show that the water tank with vertical ring baffle near the bottom of tank can limit the vibration of shield building and can more efficiently dissipate the kinematic energy of the shield building under different earthquake. Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction AP1000 is a GEN III+ nuclear reactor designed by Westinghouse Electric Company and certified by U.S. Nuclear Regulatory Commission (NRC) (Huang et al., 2010). It is an improved pressurized water reactor (PWR) designed with the advanced features of passive cooling, which relies on natural forces of gravity, natural circulation and compressed gases to prevent the core or containment from overheating (Chen et al., 2014; Zhao and Chen, 2014). AP1000 has a gravity drain water tank above the shield building to cool the containment vessel by spray water when the nuclear

⇑ Corresponding author. E-mail addresses: [email protected] (C. Zhao), [email protected] (N. Yu). http://dx.doi.org/10.1016/j.nucengdes.2017.04.023 0029-5493/Ó 2017 Elsevier B.V. All rights reserved.

reactor is shut down. The volume and mass of the water storage tank of AP1000 are approximately 3000 m3 and 3000 t, thus, fluid-structure interaction (FSI) effects of water tank may affect the dynamic response of the shield building subjected to earthquake loads (Zhao et al., 2014b). FSI and water sloshing are common and important phenomenon widely in storage tank, land-transport vehicles, elevated water towers under ground motion, and fuel tanks in aircrafts (Lo Frano and Forasassi, 2009), which can cause serious problems in liquid storage tanks subjected to seismic loads. In order to prevent the damage of the sloshing, various internal and external methods can be utilized to increase the liquid damping which lead to the reduction of sloshing effects. One of the practices is to install internal baffles inside the liquid containers, which is considered to be an effective means in mitigating the sloshing amplitude. These

C. Zhao et al. / Nuclear Engineering and Design 318 (2017) 182–201

devices include the fixed horizontal baffle, the fixed vertical baffle and the ring baffle. Therefore, the study of liquid vibration in water tank of AP1000 with internal baffle and associated structural behavior has rather been in engineering applications (Xue and Lin, 2011; Zhao et al., 2015). As the fast advance of computer technology, there are several numerical studies on different aspects of liquid vibration being reported in last decades. In general, Maleki and Ziyaeifar (2008) developed an estimation of hydrodynamic damping ratio of liquid sloshing in baffled tanks undergoing horizontal excitation using Laplace’s differential equation solution, concerning horizontal ring and vertical blade baffles. Xue and Lin (2011) and Jung et al. (2012) developed a numerical model to study three-dimensional liquid sloshing in a tank with horizontal and vertical baffles. Ozdemir et al. (2010) employed a fully nonlinear fluid-structure interaction (FSI) algorithm of finite element method for the seismic analysis of anchored and unanchored steel liquid storage tanks. Armenio and La Rocca observed that the presence of a vertical baffle at the middle of the tank dramatically changed the sloshing response by analyzing sloshing of water in rectangular open tanks (Armenio and La Rocca, 1996). Cho and Lee (2004) studied numerically the effects of baffle on liquid sloshing in a tank using a FEM model. Zhao et al. and Xu et al. employed a FSI algorithm of finite element technique to analyze dynamic response of water storage tank of AP1000 with various water levels (Xu et al., 2016; Zhao et al., 2015, 2016). Lo Frano and Forassassi presented a validated methodology based on FEM approach and ALE coupling to evaluation of FSI effects of an innovative liquid metal nuclear reactor (Frano, 2015; Lo Frano and Forasassi, 2009, 2012). Liu and Lin (2009) studied 3-D liquid sloshing in a tank with a horizontal baffle and a vertical baffle, respectively, and pointed out that a vertical baffle is more effective on reducing the sloshing amplitude. Panigrahy et al. studied liquid sloshing in a rectangular tank with ring baffles and assessed the pressure variation on the tank walls and the surface elevation (Panigrahy et al., 2009). Eswarana et al. compared the numerical results from ADINA with the available experimental data and discussed the effects of ring baffle (Eswaran et al., 2009). However, the above mentioned works mainly concentrate on the fluid sloshing and the damping effects of baffles for naval, aerospace and automobile industry liquid tanks under impact or earthquake loads. Very few studies focus on the FSI effects and damping mechanism of gravity water storage tank of NPPs with baffles, especially for AP1000 under impact or earthquake loads. Furthermore, different types of baffles are not still yet to be fully understood in the previous papers. The primary objective of this paper is to numerically investigate the FSI effects and seismic performance mitigation of water tank, and the damping effects of water tank with different types of internal baffles of AP1000 under earthquake loads by explicit dynamic finite element code LS-DYNA. Furthermore, the best type of baffle is also obtained by comparison the effects of various types of baffles. The numerical results may improve the optimal parametric design for the AP1000 or CAP1400 of China in the future. In section 2, numerical model and materials are briefly introduced. Section 3 presents the dynamic analysis of shield building considering FSI effect. Section 4 describes the results and discussions of dynamic response of water tank with internal baffles of different shapes. Finally, the conclusions and future work are summarized in the last section.

outside cooling air intakes, steel containment vessel and air baffle, which cool surface of steel containment vessel using natural circulation of air by outside cooling air intakes and water evaporation. Fig. 1 presents a cutaway view and operation principle of sample NPP of AP1000 shield building analyzed in this study. The water tank of AP1000 is partially filled with water and the initial height of water is approximately 10.8 m. For liquid sloshing in a tank with baffles, different arrangements of baffles may have different effect on reducing liquid sloshing. In the present study, in order to evaluate the baffle effects on reducing seismic response of shield building of AP1000 under different earthquake excitations, four different internal baffle types, namely, a vertical ring baffle near the roof, a vertical ring baffle on the bottom and two horizontal ring baffles on two sides in water tank, are used respectively, as shown in Fig. 2. Four cases of water storage tank with different shapes and arrangements of baffles are optimal designed in order to reduce the water sloshing and strong dynamical response excited by FSI effects, as presented in Fig. 3. The geometry and principal dimensions of the shield building and water storage tank are shown and listed in Fig. 4 and Table 1, the water tank, which is h in height, and hB in height of baffle. Dout is the outer diameter of water tank, Din is the inner diameter of water tank, Dcv is the diameter of containment vessel and Ds is the diameter of shield building, respectively. 2.2. Finite element model Fine three-dimensional finite element model of the shield building with four cases of ring baffles is constructed as accurate

Fig. 1. The operation principle and cutaway view of AP1000 shield building.

2. Numerical model and materials 2.1. AP1000 PCS AP1000 passive containment cooling system (PCS) is composed of natural convection air discharge, PCS gravity drain water tank,

183

Fig. 2. The sketch of the water tank with baffles.

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as possible in this study. Since the limitation of the computational time and memory space of the computer, it is hard to construct the finite element model of the totally assembled reactor internals for one time as its complex shapes, boundary conditions (Zhao et al., 2014a). In order to focus on FSI effects and seismic reduction of internal baffles, some simplifications should be assumed, thus, the internal components and equipment of NPP are simulated by mass or shell elements due to its complicated shapes and arrangements. Water and air is simulated by Eulerian element, while shield building, water tank and ring baffles are simulated by shell element of shell163. Furthermore, the soil-structure interaction is ignored in this analysis as the NPP assumed to be set up on rigid foundation (rock soil type or rock foundation). Therefore, the shield building is assumed to be fixed at the base of ground, and water and air of the model is calculated by multiple-material coupling algorithm. In the current study, the arrangements and distribution of reinforcement in AP1000 are very complicated, and it is difficult to simulate the detailed interaction between reinforcement and concrete. Consequently, smeared model is adopted to investigate the baffle effects in reducing seismic response of the water tank. Smeared model has the advantages of less elements, small calculations and good precision and has been widely adopted to simulate the complicated reinforced concrete (RC) structures. In this model, smeared element can be deemed as continuous and homogeneous material due to the reinforcement smeared uniformly in concrete element. Moreover, the stiffness matrix of reinforced concrete element combines the stiffness matrix of steel and concrete, the reinforcement is deemed as equivalent concrete material, and the steel quantity can go through reinforcement percentage (Zhao et al., 2016).

Fig. 3. Optimal design of gravity water storage tank.

Table 2 Material characteristics of shield building. Material

Parameter

Symbol

Unit

Value

Concrete

Density Yong’s modulus Poisson’s ratio

q

m

kg/m3 MPa 1

2300 3.35  1010 0.2

Water

Density

q

kg/m3

1000

Air

Density

q

kg/m3

1

E

Table 3 Parameters of RC.

Fig. 4. The geometry and dimension of shield building with water tank.

Material

RO (Pa)

E(Pa)

PR

SIGY (Pa)

RC ETEN (Pa) 3.35  109

2.4  103 BETA 0.0

3.35  1010 SRC 0.4

0.2 SRP 0.5

32.4  106 FS 0

Table 1 The geometric details of shield building and water tank. Components of AP1000

Parameter

Symbol

Unit

Value

Shield building

Diameter Height Thickness

Ds Hs Ws

m m m

44.2 71 0.92

Out diameter Inner diameter Height Thickness

Dout Din H Ww

m m m m

27.13 10.668 11.8 0.6

Diameter Thickness

Dcv Wc

m m

39.6 0.045

Water tank

Containment vessel

Table 4 Error of different mesh sizes.

Error (%)

Element size (mm)

Acceleration responses in X direction P1

P2

P3

200 500 800

– 6.88% 34.33%

– 6.02% 29.29%

– 1.65% 21.9%

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C. Zhao et al. / Nuclear Engineering and Design 318 (2017) 182–201 Table 5 The first five mode shapes and frequencies for various height ratio of vertical baffles.

0.30

hB/h=0 hB/h=0.2 hB/h=0.6

Natural frequency (Hz)

0.25

hB/h=0.9 hB/h=1.0 0.20

0.15

0.10 1st

2nd

3rd

4th

Mode Fig. 5. Modal analysis for various height ratios of vertical baffles in case 1.

5th

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2.3. Material model of analysis 2.3.1. Material of reinforced concrete The finite element code LS-DYNA contains several material models for reinforced concrete (RC). To simplify the simulation and save the computational time to satisfy the requirement of the analysis, MAT_PLASTIC_KINEMATIC material model from LSDYNA is adopted to represent the RC. The detailed parameters of the material for RC, are RO, E, PR, SIGY, ETAN, BETA, SRC, SRP and FS, which are mass density, young’s modulus, poisson’s ratio, yield stress, tangent modulus, hardening parameter, strain rate parameter C, strain rate parameter P, and failure strain for eroding element of RC, respectively, are shown and listed in Tables 2 and 3.

Table 6 The first five mode shapes and frequencies for various lengths of baffles.

2.3.2. Material for air and water LS-DYNA applies a fluid-structure coupled algorithm of ALE approach to simulate the interaction among the water, air and baffles. Using this approach, different domains of physical problem such as structures and fluids can be modeled simultaneously using Lagrangian and Eulerian approaches. These different domains are then coupled together in space and time. The features make this computer program especially suitable for the study of interaction problems involving multiple materials of fluids and structures. In this study, water and air are simulated by Eulerian element and the shield building is modeled by Lagrange element, respectively. In this model, air is modeled by linear-polynomial equation of state (EOS) and linear internal energy, the material of air is represented by MAT-NULL. The pressure related to the energy can be expressed as follows:

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P ¼ C 0 þ C 1 l þ C 2 l2 þ C 3 l3 þ ðC 4 þ C 5 l þ C 6 l2 ÞE0

ð1Þ

where E0 is the specific initial energy, and l = q/q0  1, Ci (i = 0–6) are the coefficients. For the ideal gases, the coefficients in the EOS are setting as C0 = C1 = C2 = C3 = C6 = 0, and C4 = C5 = c  1, c is the polytropic ratio of specific heats. Since, the pressure is then given by

P ¼ ðc  1Þ

q E q0 0

ð2Þ

where q/q0 is the ratio of current density to reference density, the initial density of air is q, the ratio of specific heats c = 1.4, the specific initial energy E0 = 2.5  105 J/kg (Zhao and Chen, 2013), respectively. The material model and EOS of water are also modeled by the linear-polynomial equation of state (EOS) and MAT-NULL. The density of water and other parameters are assumed as 1000 kg/m3, C0 = C2 = C3 = C6 = 0, C1 = 1.5  109 Pa, C4 = 0.11, C5 = 0.3 and E0 = 0 J/kg. As well known that the accuracy of numerical results is strongly dependent on the mesh size used, thus, mesh size convergence analysis is conducted to obtain the acceptable mesh size in the current study before calculation. Finally, the acceleration errors of element sizes among 200, 500, 800 mm in horizontal X direction at different point are listed in Table 4. Consequently, it is finally decided to mesh the shield building with mixed sizes, internal ring baffles, around air intake with a mesh size of 200 mm. 3. Dynamical analysis

first five mode shapes and natural frequencies of baffle arrangement for case 1 with various heights of baffles, the baffle locates on the bottom of water tank. As shown in Table 5 and Fig. 5, it can be found that the natural frequencies decrease as the increase of height ratios for ring baffles. The decrease ratio of the natural frequency amplitude in the second and third frequencies is the fastest in the range of height ratio hB/h 0 to 0.6. The reason is that the baffle in the water tank adds to the damping force of the structure which leads to a natural frequency decrease with the height ratio of baffle hB/h increase. Table 6 and Fig. 6 show the first five mode shapes and natural frequencies of baffle arrangement for case 2 with various lengths of baffles, the baffle locates inside of the water tank. It can be seen from the Table 6 and Fig. 6 that the natural frequencies decrease as the increase of lengths of baffles, the decrease ratio is larger than that of vertical baffle. The variation of the natural frequency for baffle of 0 m is different from the other cases of baffles. The first five mode shapes and natural frequencies of baffle arrangement for case 4 with various heights of vertical of baffles are shown in Table 7 and Fig. 7, the baffle locates near the top of the water tank. As shown in Table 7 and Fig. 7, it can be seen that the natural frequencies decrease as the increase of baffle lengths, the decrease ratio is different for various heights of vertical baffles. The natural frequency amplitude in the first and second is almost same in the range of heights of vertical from 0 to 5 m. The participation factors for several mode shapes are also shown in Tables 8–10.

3.1. Modal analysis

3.2. Time history analysis

It is should be carried out modal analysis for NPP to obtain the vibration and mode of the water storage tank before dynamical analysis. The effects of ring baffle in the water tank on the natural frequencies of AP1000 shield building are analyzed. The effects of different ring baffles on the first five mode shapes and natural frequencies considering FSI effect of AP1000 shield building are illustrated in this section. Table 5 and Fig. 5 show the

Three different ground acceleration time histories (ATH) records (artificial earthquake wave, El-Centro, 1940, CALIF, Kobe, 1995, KJM), which were often used as the input data in seismic analysis of NPP by some researchers, are inputted at the base of foundation of shield building for dynamical analysis. The input acceleration data, in form of ATHs is derived from the registered seismic data (U.S. Geological Survey) (NRC, 2007). The ATH with

0.30

Length of baffle 0 m Length of baffle 2 m Length of baffle 4 m Length of baffle 5 m

Natural frequency (Hz)

0.25

0.20

0.15

0.10

0.05 1st

2nd

3rd

4th

Mode Fig. 6. Modal analysis for various lengths of baffles in case 2.

5th

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C. Zhao et al. / Nuclear Engineering and Design 318 (2017) 182–201 Table 7 The first five mode shapes and frequencies for various heights of vertical baffles.

peak acceleration of 0.3 g, as shown in Fig. 8, are adopted for time history analysis. The horizontal acceleration with PGA of 0.3 g and the vertical acceleration with PGA of 0.2 g are applied for the seismic analysis. In addition, the acceleration response spectrum of the three earthquake ATHs with 5% damping ratio obtained by SeismoSoft are also shown in Fig. 9, which can reflect the frequency characteristics of the ATHs. The Rayleigh damping for RC structure and the viscous damping for fluid are applied in the dynamical analysis. In dynamical analysis, equation of motion can be expressed as follow:

and displacement for the structure. Rayleigh damping is also used to simulate the structural damping, and the damping matrix C in a system can be defined as

€g þ Cfug _ þ Kfug ¼ F ¼ M u € g ðtÞ Mfu

a ¼ 2n2 x2  bx22

ð3Þ

where M is the mass matric, C is the damping matrix, K is the stiffness matrix, and F is the load vector caused by acceleration € g, fug _ and fug are vectors of acceleration, velocity time history. fu

C ¼ aM þ bK

ð4Þ

where a and b are predefined constants, that for given damping ratios (n1 and n2) and frequencies (x1 and x2) can be computed as:



2n2 x2  2n1 x1 x22  x21

ð5Þ

ð6Þ

The damping coefficients n1 and n2 are assumed as to be equal to 5% and 7% of steel and reinforced concrete structures (Lo Frano et al., 2010).

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0.30

Height of baffle 0 m Height of baffle 2 m Height of baffle 4 m Height of baffle 5 m

Natural frequency (Hz)

0.25

0.20

0.15

0.10 1st

2nd

3rd

4th

5th

Mode Fig. 7. Modal analysis for various heights of vertical baffles in case 4.

4. Results and discussion In order to investigate the ring baffle’s effects under different earthquake loads, numerical simulations are conducted in this section. Four different arrangements of baffles are considered and the influence of various parameters such as vertical baffle height, arrangement locations, baffle height ratio and length of baffle on the dynamical response of shield building is discussed. Fig. 10 shows the water tank with ring baffle, where hB is the ring baffle height, LB is the ring baffle width and h is the height of water tank. 4.1. Optimal design scheme 1 for water storage tank 4.1.1. Effect of ring baffle height on acceleration response In this section, five different hB/h ratios are taken as 0, 0.2, 0.6, 0.9 and 1, respectively. And the installation of ring baffle is considered to be fixed. The movement of the water tank follows the twodimensional horizontal acceleration time histories with PGA 0.3 g and vertical time acceleration history with PGA 0.2 g of Artificial, El-Centro and Kobe earthquake and time of 20 s. Fig. 11 and Table 11 show the peak acceleration response in horizontal X and Z directions at top point for different vertical ring baffle heights under three ATHs. It can be seen that the variation of maximum acceleration response in horizontal X and Z directions at top point decreases with increasing hB/h ratio as a whole, but different earthquakes have various results. For example, the maximum acceleration in horizontal X direction decreases with the hB/h ratio increase, but during the 0.85 has a peak value under artificial ATH. While the peak acceleration in X direction increases in the first hB/h ratio from 0 to 0.3 and then decreases during the hB/h ratio from 0.3 to 1 under El-Centro ATH. Whereas the variation tendency of maximum acceleration decreases as a function of hB/h increasing under Kobe ATH in horizontal X direction at the top point of the shield building, as can be observed in Fig. 11(a). From the plot, it is also observed that the peak acceleration responses for shield building with vertical ring baffles in horizontal Z direction have similar variation tendency with moving the

ring baffle to the top of the water tank under different earthquakes. However, the significant difference of these variations compared to X direction is that the artificial excitation has two peak value phase, as shown in Fig. 11(b). Comparison the different height of ring baffle for case 1, we found that the higher vertical ring baffle has small acceleration response, especially for EL-Centro ATH. As shown in Fig. 11, one can also extract the same information from the maximum value of acceleration response at the top point for different earthquakes, implying that the minimum value of maximum acceleration occurs when the hB/h ratio is 1. The maximum acceleration are reduced by about 17.19% and 33.34% in horizontal X direction, and 26.27% and 26.28% in horizontal Z direction, due to the effectiveness of ring baffle with hB =h ¼ 1 comparing with reference case hB =h ¼ 0 under artificial and El-Centro ATHs. The phenomenon of acceleration response of water tank with various vertical ring baffles as a function of hB/h is concluded as the irregular annular shape of water tank (which changes the vibration characteristics) or interaction between the water and ring baffles when the structure being subjected to different earthquakes. The ring baffles with various height, which result in additional viscosity and energy dissipation, may be also the other influence factors for changing the peak acceleration response of shield building.

4.1.2. Effect of ring baffle height on displacement response In this section, the case setup is the same as that in Section 4.1.1 while the tank is subjected to the same earthquakes. The maximum displacements at top point of shield building for water tank with ring baffle under earthquake loads are studied. Fig. 12 and Table 12 illustrate the peak displacement response variations versus variations of ring baffle height ratio hB/h only along the horizontal X and Z directions. It is noted that the maximum displacement responses at top point in horizontal X and Z directions are changed with the baffle height increase and these trends of variation are slightly similar with acceleration response.

X

X

Z

Direction

Direction

Y

hB/h = 0.2

hB/h = 0

0.32733 3.735E4 3.003E3 0.0317 0.2406 0.0289 0.012 0.6678 1.0426 0.0141

0.251E3 1148.6 928.52 0.958E5 0.165E4 0.123E3 12.351 14.636 0.768E4 0.849E4

Direction X

X

Z

Direction

Y

lB = 2 m

1462.8 55.492 0.301E4 0.428E4 0.212E3 14.182 22.511 0.107E3 0.188E4 2.8678

Y

lB = 0 m

Participation Factor of length of baffle lB 1 1204.8 816.3 2 816.30 1204.8 3 4.044E6 2.602E5 4 4.489E5 3.884E5 5 5.656E5 1.812E5 6 21.746 1.6611 7 1.6611 21.746 8 2.127E5 8.323E7 9 0.396E4 8.541E5 10 430.47 355.16

Mode

Table 9 Participation factor of various lengths of baffles in case 2.

Participation Factor of height ratio of vertical baffles hB/h 1 1204.8 816.30 0.32733 55.756 2 816.30 1204.8 3.735E4 1469.8 3 4.044E6 2.602E5 3.003E3 0.125E4 4 4.489E5 3.884E5 0.0317 0.978E4 5 5.656E5 1.812E5 0.2406 0.401E4 6 21.746 1.6611 0.0289 23.028 7 1.6611 21.746 0.012 14.509 8 2.127E5 8.323E7 0.6678 0.391E4 9 0.396E04 8.541E5 1.0426 0.882E4 10 430.47 355.16 0.01413 566.88

Mode

Table 8 Participation factor of height ratio of vertical baffles in case 1.

0.123E3 928.52 1148.6 0.824E6 0.162E4 0.195E4 14.636 12.351 0.208E4 0.204E4

Y

0.0341 0.0345 0.0106 1.5534 0.5262 0.0284 0.271E3 0.7961 2.1796 0.0241

Z 0.0111 0.0679 0.0319 0.0254 0.21657 0.0325 0.0083 18.465 0.0086 0.0153

Z

0.397E03 884.07 1216 0.215E4 0.364E5 0.126E3 15.495 3.5617 0.151E4 0.297E5

X

Direction

lB = 4 m

153.47 1442.9 5.023E6 4.2674E5 3.541E4 16.675 7.2872 1.762E5 295.45 280.28

Y

1740.3 0.267E3 0.991E4 0.947E5 0.444E4 0.751E4 0.173E4 0.104E5 19.999 59.021

Z

1442.9 153.47 3.618E5 6.268E5 5.656E5 7.2872 16.675 4.876E6 280.28 295.45

X

Direction

hB/h = 0.6

0.248E3 1216 884.07 0.176E4 0.484E4 0.143E3 3.5617 15.495 0.688E5 0.797E5

Y

1043.3 369.09 48.107 820.97 2.606E5 2.364E5 2.5581 0.2302 4.353E5 6.421E5

X

Direction

hB/h = 0.9

1603.2 0.775E4 0.466E3 0.122E5 0.475E5 0.121E4 0.986E5 0.921E5 13.049 97.641

Z

369.09 1043.3 820.97 48.107 6.095E5 1.232E3 0.2301 2.5581 1.894E5 1.131E5

Y

Direction

1102.1 4.3082 825.2 31.23 5.255E5 3.804E5 1.242 1.4389 1.126E5 4.968E6

Y

2.111E4 558.36 1382.1 7.609E5 3.285E5 3.343E5 9.033 9.3636 6.033E6 3.538E5

Y

4.3082 1102.1 31.23 825.2 1.689E4 9.223E5 1.4389 1.2419 4.682E6 1.384E5

X

1.131E4 1382.1 558.36 8.547E5 6.003E5 2.375E4 9.3636 9.033 2.572E5 3.788E6

X

Direction

lB = 5 m

0.0032 0.0115 1.191E4 0.0065 0.0107 0.0208 0.0107 0.0112 0.0037 0.0097

Z

hB/h = 1

1283.2 1.502E4 1.178E4 7.434E6 1.543E5 1.362E4 1.097E5 2.588E5 7.1924 172.27

Z

0.0149 0.01402 0.0013 0.0114 0.0152 0.0126 0.0085 0.0156 0.0046 0.006

Z

190 C. Zhao et al. / Nuclear Engineering and Design 318 (2017) 182–201

Participation 1 2 3 4 5 6 7 8 9 10

Mode

Factor of height of vertical baffle lv 1204.8 816.30 816.30 1204.8 4.044E6 2.602E5 4.489E5 3.884E5 5.656E5 1.812E5 21.746 1.6611 1.6611 21.746 2.127E5 8.323E7 0.396E04 8.541E5 430.47 355.16 0.32733 3.735E4 3.003E3 0.0317 0.2406 0.0289 0.012 0.6678 1.0426 0.0141

920.72 1134.7 4.288E6 1.057E5 2.111E5 167.84 134.09 0.2666 24.872 9.728E5

Direction X

X

Z

Direction

Y

lv = 2 m

lv = 0 m

Table 10 Participation factor of various heights of vertical baffles in case 4.

1134.7 920.72 1.985E5 1.797E5 1.803E5 134.09 167.84 24.872 0.2666 1.303E4

Y 0.0281 0.0366 0.0345 0.0161 4.7604 0.0211 0.0017 0.0399 0.0408 0.0418

Z 1062.3 991.51 0.268E4 0.142E4 0.432E5 0.8552 3.1568 17.893 2.6807 0.793E4

X

Direction

lv = 4 m

991.51 1062.3 0.392E5 0.919E5 0.372E5 3.1568 0.85526 2.6807 17.894 0.101E3

Y 0.0257 0.0472 5.439 0.0231 0.0324 0.0191 0.0041 0.0452 0.0216 0.3117

Z 477.87 1361.5 0.218E4 0.151E3 84.812 22.029 0.241E3 0.0853 16.921 0.135E04

X

Direction

lv = 5 m

1361.5 477.87 0.762E5 0.132E3 22.029 84.812 0.213E3 16.921 0.0853 0.242E4

Y

0.0579 0.0193 -6.2417 0.0325 0.0101 0.0213 0.0399 0.0292 0.0322 0.0217

Z

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Fig. 8. Acceleration time histories.

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Fig. 9. Response spectra for three different ATHs.

Fig. 10. Schematic diagram of water tank with different ring baffles.

It is can be seen that the peak value of displacement at top point slightly decreases in the first phase and increases in the last phase with gradually moving the ring baffle towards the water tank roof in X direction, while it is increasing almost in horizontal Z direction under artificial ATH. Meanwhile, the changing tendency of displacement in horizontal directions for El-Centro is small and keeping stable with ring baffle increase. Furthermore, the variation of displacement for Kobe ATH increases firstly and then decreases, the tendency in X direction is almost the same as the Z direction. These differences of displacement response for various ring baffle are likely due to the ring baffle changing the vibration frequency of shield building. Moreover, the water is divided into different parts by ring baffle, which may alter the dynamical characteristic of the water tank. The shield building may have resonance when the natural frequency of water tank with ring baffle closed to the frequency of earthquake.

4.2. Optimal design scheme 2 for water storage tank 4.2.1. Effect of ring baffle width on acceleration response In this section, four different ring baffle widths are conducted herein, i.e., the LB is taken as 0, 2, 4 and 5 m. The installation height of ring baffle is considered to be fixed and the movement of the water tank follows the same ATH as the Section 4.1. The maximum acceleration at top point for the tank with horizontal ring baffle under different earthquake loads are studied and listed in Table 13, as shown in Fig. 13. It is noted that the variation trend of maximum acceleration response in horizontal X and Z directions at top point is irregularly, and results have distinctions. In fact, the maximum accelerations both in horizontal X and Z directions decrease in the first phase of width and then increase at the last phase under artificial ATH, but the amplitude of variation is different. Meanwhile, the

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Fig. 11. Maximum acceleration at top point for vertical ring baffle near the bottom of water tank.

peak acceleration in horizontal directions increases in the first width from 0 to 2 meters and then decrease during the phase from 2 to 5 meters under Kobe ATH. Whereas the variations of maximum acceleration are small and becoming stably under El-Centro ATH both in horizontal X and Z directions, as can be observed in Fig. 13. In addition, the Kobe ATH has a strong dynamical response with respect to other earthquake with the same size and duration. Therefore, the ring baffle located inside of outer ring of water tank has some influences on the dynamic response of the structure,

Fig. 12. Maximum displacement at top point for vertical ring baffle near the bottom of water tank.

but the extent is different. In conclusion, not all the ring baffle height can reduce the seismic response of the shield building under earthquake loads compared with water tank without baffle. Hence, the horizontal ring baffle has a little effect on reducing seismic response of shield build. The ring baffles with various widths, which result in additional viscosity and energy dissipation, are also the main influence factors for changing the peak acceleration response of shield building.

Table 11 Maximum acceleration at top point of water tank with vertical ring baffle under earthquake loads. Height ratio of baffle hB/h

Maximum acceleration response (m/s2) 0.0 0.2 0.6 0.9 1.0

Artificial ATH

El-Centro ATH

Kobe ATH

X-direction

Z-direction

X-direction

Z-direction

X-direction

Z-direction

16.9342 15.6715 15.4936 17.3072 14.0233

12.6901 14.7186 13.7727 14.2270 12.4892

11.9268 11.2101 10.1024 8.7310 7.9501

11.4214 10.4010 11.4105 9.3611 8.4212

16.2101 19.2231 20.1204 18.6069 17.2108

16.6004 19.9024 20.8121 18.6201 17.6213

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Table 12 Maximum displacement at top point of water tank with vertical ring baffle under earthquake loads. Height ratio of baffle hB/h

Artificial ATH X-direction

Maximum displacement response (cm) 0.0 4.9286 0.2 4.5437 0.6 4.5273 0.9 4.7802 1.0 4.8710

El-Centro ATH

Kobe ATH

Z-direction

X-direction

Z-direction

X-direction

Z-direction

3.0519 3.2136 3.6068 3.6161 4.0165

2.5202 2.4113 2.5045 2.4059 2.4907

2.5408 2.4214 2.5115 2.4056 2.4908

4.1004 4.8705 5.5441 5.4632 5.2217

4.1107 4.8805 5.5514 5.4816 5.2111

Table 13 Maximum acceleration at top point of water tank with horizontal ring baffle under earthquake loads. Width of ring baffle (m)

Artificial ATH X-direction

Maximum acceleration response (m/s2) 0 16.9342 2 14.3445 4 17.4208 6 17.0877

El-Centro ATH

Kobe ATH

Z-direction

X-direction

Z-direction

X-direction

Z-direction

12.6901 13.8514 12.8755 13.2923

11.9268 12.9668 12.1469 12.6184

11.4214 13.6247 14.2552 13.6396

16.2123 23.3045 23.1067 22.1124

16.6023 24.4214 22.1345 22.6086

Fig. 13. Maximum acceleration at top point for horizontal ring baffle.

Fig. 14. Maximum displacement at top point for horizontal ring baffle.

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C. Zhao et al. / Nuclear Engineering and Design 318 (2017) 182–201 Table 14 Maximum displacement at top point of water tank with horizontal ring baffle under earthquake loads. Width of ring baffle (m)

Artificial ATH X-direction

Maximum displacement response (cm) 0 4.9286 2 4.4226 4 4.6696 6 4.6287

El-Centro ATH

Kobe ATH

Z-direction

X-direction

Z-direction

X-direction

Z-direction

3.0519 3.5044 3.5158 3.5464

2.5205 2.8513 2.8124 2.8115

2.5416 2.8642 2.8237 2.8207

4.1011 5.5024 5.4410 5.5307

4.1141 5.5105 5.4509 5.5404

Fig. 15. Comparison of the maximum acceleration at top point for inner and outer horizontal ring baffles.

Fig. 16. Comparison of the maximum displacement at top point for internal and outer horizontal ring baffles.

4.2.2. Effect of ring baffle width on displacement response In this section, the effects of horizontal ring baffle on influence the maximum displacement response are studied by changing its width under different earthquakes, which are the same as in Section 4.2.1, as shown in Fig. 14. Fig. 14 and Table 14 show the peak displacement response at top point for different ring baffle widths. It can be seen that the maximum displacement responses at top point in horizontal X and Z directions increase with increasing the ring baffle width

when the structure being subjected to El-Centro and Kobe ATH with same amplitude of acceleration. Whereas the variation trends of peak displacement for artificial earthquake are different from the other earthquakes such as El-Centro or Kobe ATH, and increase slightly with the baffle width increases in horizontal Z direction. It is obviously observed that the peak displacement response of the structure under Kobe ATH is influenced by the width of ring baffle significantly with regard to the other earthquakes of ElCentro and artificial earthquakes. According to the figure, it is

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Fig. 17. Maximum acceleration at top point for vertical ring baffle near the roof of water tank.

Fig. 18. Maximum displacement at top point for vertical ring baffle near the roof of water tank.

clearly indicated that the horizontal ring baffle cannot play an positive part in reducing the displacement response.

In conclusion, comparing with the case of water tank with ring baffles near the inner surface and outer surface, the ring baffle has greater influence on the acceleration response of tank when it is placed near to the inner surface and the influence is gradually reduced when it moved towards the outer surface of the tank, located at the same height, as shown in Fig. 15(b). The phenomenon of acceleration response of water tank with inner and outer ring baffles, which is located at the same height, considering FSI effects is concluded as the irregular annular shape of water tank or interaction between the water and ring baffles when the structure being subjected to different earthquakes. The installed locations of ring baffles, which result in additional viscosity and energy dissipation, are also the main influence factors for changing the peak acceleration response of shield building.

4.3. Optimal design scheme 3 for water storage tank 4.3.1. Effect of ring baffle arrangement location on acceleration response In this section, we shall look into the maximum acceleration response to different earthquake excitations for horizontal inner ring baffle and outer ring baffle with width of 4 meters arranged at the same height inside of water tank. The motion of water tank is still the same as that in Sections 4.1 and 4.2. Fig. 15 shows comparison of the maximum acceleration at top point for inner and outer horizontal ring baffles under artificial, El-Centro and Kobe ATHs with the same peak ground acceleration and duration of 0.3 g and 20 s, respectively. It can be seen that the peak acceleration of water tank with inner ring baffle under artificial ATH is much larger than the water tank with outer ring baffle under El-Centro and Kobe ATH with the same degree of earthquake and duration in horizontal X direction. Whereas one can extract the adverse information from the maximum acceleration in horizontal Z direction at top point for various seismic loads. In other words, The peak acceleration value with regard to artificial ATH is the smallest, and the value for El-Centro ATH is very closed to value of Kobe earthquake. Furthermore, the value of peak acceleration for ring baffle near the inner surface of water tank is larger than that of near the outer surface of the tank.

4.3.2. Effect of ring baffle arrangement location on displacement response In this section, the effects of horizontal ring baffle on influence the maximum displacement response are studied by changing its installation position under different earthquakes, which are the same as in Section 4.3.1, as shown in Fig. 16. Fig. 16 illustrates the comparison of the maximum displacement response at top point for inner and outer horizontal ring baffles under artificial, El-Centro and Kobe ATHs with the same peak ground acceleration and duration of 0.3 g and 20 s, respectively. It is clearly observed that the trends of peak displacement of water tank with inner and outer ring baffles under different earthquakes

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Fig. 19. Acceleration response spectra of case 1 under artificial earthquake. Fig. 20. Acceleration response spectra of case 1 under El-Centro earthquake.

are almost the same as the changing of peak acceleration. Meanwhile, the maximum displacement values of water tank with inner ring baffle are smaller than that of with outer ring baffle in horizontal X direction under artificial ATH. However, the adverse information can be extracted from the maximum displacement in horizontal Z direction at top point, when the structure is being subjected to the same seismic load. 4.4. Optimal design scheme 4 for water storage tank 4.4.1. Effect of ring baffle height on acceleration response In this section, five ring baffle heights near the roof of water tank are conducted herein, i.e., the vertical ring height hB is taken as 0, 2, 3.5, 4 and 5 m. The installation location of ring baffle is regard as fixed. The movement of the water tank follows the two-dimensional horizontal and one vertical dimensional acceleration time histories of Artificial, El-Centro and Kobe earthquake with peak acceleration 0.3 g and time of 20 s. The peak acceleration responses in horizontal X and Z directions at top point for different vertical ring baffle heights under three ATH are shown in Fig. 17. From the figure, it is obviously indicated that the variation of maximum acceleration response in horizontal X and Z directions at top point increases with increasing ring baffle height hB as a whole, but the variation trends for El-Centro and Kobe earthquakes have some fluctuation during some certain

phase. The maximum acceleration in horizontal X direction increases with the hB increase when the structure being subjected to artificial or Kobe ATHs, while the range of variation for artificial ATH is smaller than that of Kobe ATH. Meanwhile, the peak acceleration in X direction increases in the first status and then becomes stable during the last phase with the height of ring baffle increasing under El-Centro ATH. From the plot, it is also observed that the peak acceleration responses for shield building with vertical ring baffles in horizontal Z direction have similar variation tendency with moving the ring baffle towards the bottom of the water tank under different earthquakes. However, the significant difference of these variations compared to X direction is that the artificial excitation has two peak value phases, as shown in Fig. 17(b). Therefore, the ring baffles located at the roof of water tank have a significant influence on the dynamic response of the structure. Consequently, some ring baffle height can reduce the seismic response of the shield building under earthquake loads compared with water tank without baffle. Vertical ring baffle located at the roof of the water tank is not the best choice on reduction seismic response when the structure being subjected to different seismic loads. The location of ring baffles change the natural frequency of the shield building, and the close extent of frequencies between water tank and vibration frequency of earthquake determines the values of dynamic response.

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Fig. 21. Maximum the von Mises stress distribution for El-Centro ATH of (a) vertical ring baffle at the bottom, (b) inner horizontal ring baffle, (c) outer horizontal ring baffle and (d) vertical ring baffle near the roof.

4.4.2. Effect of ring baffle height on displacement response Fig. 18 shows the peak displacement response variation versus variation of ring baffle height near the roof of water tank only along horizontal X and Z directions. It is clearly observed that the maximum displacement responses at top point of water tank in horizontal Z direction under different earthquakes are changed with the height of ring baffle increases and these trends of variation are almost similar, as shown in Fig. 18(b). From the plot, we can also extract the same information from the variation of displacement response at top point under ElCentro and Kobe earthquakes in horizontal X direction with regard to the Z direction. However, the variation trend of acceleration response is not sensitively and kept stable with the ring baffle height increases when the structure being subjected to artificial ATH, as shown in Fig. 18(a). 4.5. Seismic reduction ratio and floor response spectrum for optimal scheme In the previous sections, we investigate the dynamic response of different ring baffle types of water tank and compare the maximum acceleration and displacement of various optimal schemes

under three earthquake loads. We find the optimal scheme 1 has small dynamical response with respect to other cases. In order to quantify the effect of seismic reduction of optimization scheme, the seismic reduction ratio (SRA) and floor response spectrum of the scheme should be investigated and provided. The expression of SRA is given by

SRb  SRa  100% SRA ¼ SRb

ð7Þ

Here SRA, SRb and SRa are seismic reduction ratio, structural response of water tank without ring baffle and with ring baffle, respectively. From Table 11, it is clearly observed that the SRAs of acceleration responses at the top point of water tank are 17.19% and 33.34% in horizontal X direction, and 26.67% and 26.28% in horizontal Z direction under artificial and El-Centro ATHs for the case of optimal scheme 1 comparing with water tank without ring baffle. These may clearly highlight the effectiveness of ring baffle in case 1 in reduction of acceleration response of the shield building. Overviews the obtained numerical results in terms of floor response spectra for optimal scheme 1, calculated at the chosen reference point are shown in Figs. 19-20 as an example for different earthquakes. It can be indicated that the value of floor response

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Fig. 22. Maximum the von Mises stress distribution for Artificial ATH of (a) vertical ring baffle at the bottom, (b) inner horizontal ring baffle, (c) outer horizontal ring baffle and (d) vertical ring baffle near the roof.

spectrum in scheme 1 with hB =h ¼ 1 is the smallest compared with the other height ratio of baffle. These results highlight the positive influence of the ring baffle in case 1 in mitigating the seismic response and this case of hB =h ¼ 1 with regard to other cases is the better choice of the shield building in reducing the seismic acceleration when the structure being subjected to earthquake loads.

As shown in figure, that the maximum stresses are 14.8, 14.8, and 13.5 MPa, which are less than the failure criterion of AP1000 safety. Thus, the corner and air intake have no damage during the earthquake excitation.

5. Conclusions 4.6. Stress state for various schemes The stress of shield building with various ring baffles is the main factor of the AP1000 safety, so the stress distribution of structure should be investigated to evaluate the safety of the shield building subjected to earthquakes. The failure criterion states that the von Mises stress must be less than the yield stress of a material, and the yield stress of reinforced concrete 22 MPa, is used for the stress analysis, and is selected from the report AP1000 Safety, Security, and Environment in the U.K (The AP1000 European DCD; Zhao et al., 2014b). The von Mises stresses (in Pa) of shield building due to different arrangement ring baffles under various excitations are shown in Figs. 21–23. As shown in the figure, the stress distribution of the shield building are influenced by the ring baffle, and the maximum von Mises stress at the corner of shield building and water tank is largest. Therefore, the corner and air intake of shield building are the weakest location of the shield building.

The key objective of this paper is to numerically investigate the effects of FSI, ring baffle heights, lengths and arrangement locations on dynamic response and reduction seismic response of shield building of AP1000 under different earthquake loads. The numerical results of this study indicate that the values of peak accelerations at the same point for different height and length of ring baffles are variously. Scheme 1 with vertical ring baffle height ratio hB/h of 1 at the bottom of water tank is found to be more effective in controlling the seismic response of the structure, compared with other schemes. This case is the optimal design due to the present of vertical ring baffle. The ring baffle is more effective in reducing dynamic response of the shield building when it is placed near the bottom of water tank. Nevertheless, NPP is system engineering, as continue of this research study, a deeply parametric study about vertical ring baffle is in progress to investigate application of ring baffle in practice of NPP engineering in future.

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Fig. 23. Maximum the von Mises stress distribution for Kobe ATH of (a) vertical ring baffle at the bottom, (b) inner horizontal ring baffle, (c) outer horizontal ring baffle and (d) vertical ring baffle near the roof.

Acknowledgements This work is financially supported by the National Natural Science of China (Grant No. 51508148, 51138001, 51409074), Fundamental Research Funds For the Central Universities (Grant No. JZ2015HGBZ0113 and 2015HGQC0216), State Key Laboratory for GeoMechanics and Deep Underground Engineering (Grant No. SKLGDUEK1508) and the China Postdoctoral Science Foundation (Grant No. 2015M581980 and 2016T90563). Constructive comments from anonymous reviewers are also gratefully acknowledged.

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