Microsoft Word - ETASR_V12_N5_pp9160-9165 Engineering, Technology & Applied Science Research Vol. 12, No. 5, 2022, 9160-9165 9160 www.etasr.com Vu et al.: Correlation Analysis of Earthquake Intensity Measures and Engineering Demand Parameters … Correlation Analysis of Earthquake Intensity Measures and Engineering Demand Parameters of Reactor Containment Structure Xuan-Hung Vu Department of Civil Engineering, Vinh University Vinh, Vietnam vxhlkc@gmail.com Thanh-Tung Thi Nguyen Department of Civil Engineering, Vinh University Vinh, Vietnam ntttung@gmail.com Van-Long Phan Department of Civil Engineering, Vinh University Vinh, Vietnam phanlongkxd@vinhuni.edu.vn Duy-Duan Nguyen Department of Civil Engineering, Vinh University Vinh, Vietnam duyduankxd@vinhuni.edu.vn Received: 4 July 2022 | Revised: 24 July 2022 | Accepted: 25 July 2022 Abstract-This study aims to analyze the correlation between earthquake Intensity Measures (IMs) and seismic responses of a reactor containment building in an APR-1400 nuclear power plant. A total of 20 IMs were employed to develop Seismic Demand Regression Models (SDRMs), which show the relationship between IMs and engineering demand parameters. A numerical model of the structure was constructed using the Lumped-Mass Stick Model (LMSM) in SAP2000. Additionally, a three-dimensional finite element model was developed to validate the simplified LMSM approach. A set of 90 ground motion records was used to perform a time-history analysis, where the motions cover a wide range of amplitude, intensity, epicenter distance, significant duration, and frequency of earthquakes. Engineering demand parameters were monitored in terms of floor accelerations and displacements. Consequently, strongly correlated IMs were identified based on the evaluation of SDRMs using four statistical indicators: coefficient of determination, standard deviation, practicality, and proficiency. The results showed that the strongest IMs were Sa(T1), Sv(T1), and Sd(T1) followed by ASI, EPA, PGA, and A95. On the other hand, the weakly correlated IMs were PGD, DRMS, SED, VRMS, PGV, HI, VSI, and SMV. Keywords-reactor containment structure; earthquake intensity measure; seismic demand regression model; floor acceleration; floor displacement I. INTRODUCTION Currently, seismic design codes and guidelines use Peak Ground Acceleration (PGA) and Spectral Acceleration (Sa) as intensity measures. These parameters are widely employed to evaluate the probabilistic seismic damage of structures. However, each structure has specific characteristics, such as structural dimensions, material properties, and details. Therefore, the correlation between seismic structural responses and earthquake intensity measures may differ for different structure types. Numerous studies evaluated the correlation between seismic Intensity Measures (IMs) and responses of different structures such as buildings [1-6], bridges [7-12], intake tanks [13], chimneys [14], and underground structures [15-17]. These studies concluded that PGA and Sa were not the optimal parameters to evaluate seismic responses and fragility analyses of structures. There is a need to systematically identify efficient earthquake IMs for seismic risk analysis of Nuclear Power Plants (NPPs), where the reactor containment building is one of the crucial structures. Some studies investigated the interrelation of the responses of NPP structures and earthquake IMs. In [23], the correlation coefficients between typical IMs and seismic fragility of the Canada Deuterium Uranium reactor building were determined, pointing out that spectral acceleration Sa(T1) and spectral displacement at the fundamental period Sd(T1) are the most correlated IMs. In [24], time-history analysis was performed to recognize the strongly correlated earthquake IMs with the structural responses of base-isolated nuclear power plant structures, considering the high-frequency content of earthquakes. As a result, PGA, A95, and Sustained Maximum Acceleration (SMA) had the largest correlation with structural behaviors subjected to low-frequency earthquakes. Meanwhile, Specific Energy Density (SED), Characteristic Intensity (Ic), and Arias Intensity (Ia) were the strongest IMs under high- frequency ground motions. However, a systematic study on the correlation analysis between seismic IMs and structural behaviors of the 1400 NPP containment structure has not been performed. Since this structure is designed according to the US Nuclear Regulation Commission 1.60 (NRC 1.60) with PGA=0.3g, a selection of large ground motions is required, where the mean spectrum matches the design. Moreover, a simplified numerical model called the Lumped Mass Stick Model (LMSM) and a full Three-Dimensional Corresponding author: Duy-Duan Nguyen Engineering, Technology & Applied Science Research Vol. 12, No. 5, 2022, 9160-9165 9161 www.etasr.com Vu et al.: Correlation Analysis of Earthquake Intensity Measures and Engineering Demand Parameters … Finite Element Model (3D FEM) have been used to evaluate nuclear structures [18]. However, since 3D FEM takes a long time for time-history analysis and occupies a large amount of memory, LMSM is preferred. Several studies demonstrated that LMSM was capable of evaluating fragility analyses of NPP structures [19-22]. This study conducted a correlation analysis between IMs and Engineering demand Parameters (EDPs) of reactor containment structures. A total of 20 IMs were considered to establish seismic demand regression models representing the relationship between IMs and EDPs. A numerical model of the containment structure was developed using the simplified LMSM in SAP2000. Additionally, a solid- based 3D FEM was built to validate the LMSM. A set of 90 seismic ground motion records was selected for time-history analysis. The EDPs were measured in terms of floor accelerations and displacements. Four statistical properties were used to evaluate the efficiency of seismic demand regression models, including coefficient of determination (R2), standard deviation, practicality, and proficiency. II. EARTHQUAKE INTENSITY MEASURES AND INPUT GROUND MOTIONS This study selected 20 IMs to develop the seismic demand regression models, as shown in Table I. These IMs were classified in by amplitude, frequency, intensity, and energy. TABLE I. CONSIDERED EARTHQUAKE INTENSITY MEASURES No Earthquake IMs Formula Unit Ref. 1 Peak ground acceleration PGA = max |a(t)| g - 2 Peak ground velocity PGV = max |v(t)| m/s - 3 Peak ground displacement PGD = max |d(t)| m - 4 Root-mean-square of acceleration ���� = � �� � �(�)��� � g [25] 5 Root-mean-square of velocity ���� = � �� � �(�)��� � m/s [25] 6 Root-mean-square of displacement ���� = � �� � �(�)��� � m [25] 7 Arias intensity �� = ��� � �(�)��� � m/s [26] 8 Characteristic intensity �� = (���� )�/������ m1.5/s2.5 [27] 9 Specific energy density SED = !(�)�"�� # m2/s - 10 Cumulative absolute velocity CAV = |%(�)|"�� # m/s [28] 11 Acceleration spectrum intensity ASI = &� '( =#.*#.� 0.05, ./". g*s [29] 12 Velocity spectrum intensity VSI= &� '( =�.*#.� 0.05, ./". m [29] 13 Housner spectrum intensity HI = 0&� '( =�.*#.� 0.05, ./". m [30] 14 Sustained maximum acceleration SMA = the 3rd of PGA g [31] 15 Sustained maximum velocity SMV = the 3rd of PGV m/s [31] 16 Effective peak acceleration EPA= �1�2(34�.56�.7(89#.#*))�.* g [28] 17 Spectral acceleration at T1 &� (.�) g [32] 18 Spectral velocity at T1 &� (.�) m/s - 19 Spectral displacement at T1 &� (.�) m - 20 A95 parameter A95 = 0.764 ��#.:�; g [33] A group of 90 ground motion records was selected from worldwide earthquakes provided by the PEER center, considering a wide range of amplitude, magnitude, epicentral distance, duration, fundamental period, and frequency. Figure 1 shows the response spectra of the 90 motion records. It should be noted that the mean spectrum of these motions is close to the design response spectrum of the US NRC 1.60 [34]. Fig. 1. Response spectra of 90 motion records. III. FINITE ELEMENT MODEL OF CONTAINMENT STRUCTURE The reactor containment structure in the Advanced Power Reactor 1400 (APR-1400) NPP was employed to develop the modeling. This structure is made of reinforced concrete with a cylinder and a top dome. The diameter and height of the cylinder are 47m and 54m respectively. The thickness of the RC cylinder wall is 1.22m. The radius and thickness of the dome are 23.2m and 1.07m respectively. Figure 2 shows the structural dimensions of the containment structure. Fig. 2. Configurations of the containment structure. Since the containment structure is a vertically symmetric cantilever column, its FEM can be developed using the simplified LMSM. This numerical model was based on beam elements with nodal masses assigned at the nodes of the elements. The model consisted of 14 beam elements, where their length was determined based on the change of vertical stiffness of the structure and the location where secondary systems are connected to the containment structure. The lumped masses and structural section properties of elements were calculated based on the real cross-section of the structure [35]. The LMSM of the containment structure was constructed in SAP2000, a commercial structural analysis program. Figure 3(a) shows the LMSM of the containment structure in SAP2000 and Table II shows the material properties. 0 0.5 1 1.5 2 2.5 3 0.1 1 10 100 S p ec tr al A cc el er at io n ( g ) Frequency (Hz) Average spectrum NRC 1.6 spectrum 1.22 m 22.8 m 1.07 m 5 4 m 2 3 .5 m 1.22 m Reinforcement details D18 @300 1.22 m D18 @300 Engineering, Technology & Applied Science Research Vol. 12, No. 5, 2022, 9160-9165 9162 www.etasr.com Vu et al.: Correlation Analysis of Earthquake Intensity Measures and Engineering Demand Parameters … 3D FEM is known to be the most accurate numerical approach and was used to validate the simplified LMSM. In this study, 3D FEM was developed using solid elements in ANSYS. The structural model was meshed into 13,571 prism elements, after conducting a sensitivity meshing analysis as shown in Figure 3(b). The elastic modulus of the material was 30,500MPa, Poisson’s ratio was 0.17, and volumetric density was 24.0KN/m3. (a) LMSM (b) 3D FEM Fig. 3. Finite element models. TABLE II. MATERIAL PROPERTIES USED IN LMSM Model Elastic modulus (kN/m 2 ) Volumetric density (kN/m 3 ) Poisson’s ratio Containment structure 3.05E+07 0.00 0.170 IV. SEISMIC RESPONSES OF THE CONTAINMENT STRUCTURE A series of linear time-history analyses was performed since the stiffness of the containment structure was very high and was expected to behave elastically under earthquakes. Acceleration records were imposed on the horizontal direction, and the effects of vertical motion were neglected. The EDPs (seismic responses) of the structure were quantified in terms of floor accelerations and displacements. These parameters are commonly used in structural and earthquake engineering analyses [36-38]. Figure 4 displays the time-history responses of the containment structure at the top and middle nodes using LMSM and 3D FEM, showing that the results of the two models are highly compatible. Figure 5 shows the Floor Response Spectra (FRS) at different elevations of the structure, which also implies that LMSM results are very close to 3D FEM and highlights the capability of the former to perform a seismic time-history analysis of the NPP structure. V. SEISMIC DEMAND REGRESSION MODEL The Seismic Demand Regression Model (SDRM) has been widely used to represent the relationship between earthquake IMs and EDPs. This model was also applied to seismic designs according to the probabilistic approach [6, 39]. The popular expression of SDRM is [7, 10, 40]: &< = % × (�>)? (1) where SD is the mean seismic response of the structure, a and b are regression coefficients, and IM is the intensity measure considered. Equation (1) can be also written as: @A(&< ) = @A(%) + C × @A(�>) (2) Fig. 4. Time-history responses of the structure subjected to the 1940 El Centro earthquake. Fig. 5. FRS at different elevations of the structure under the 1940 El Centro earthquake. A total of 40 SDRMs of the structure were constructed for 20 IMs and EDPs. Optimal IMs were evaluated using four statistical indicators: coefficient of determination (R2), efficiency (standard deviation), practicality, and proficiency. It should be noted that R2 represents the percentage of data closest to the regression line, and a higher R2 value indicates a more optimal SDRM. On the contrary, efficiency denotes the scattering (standard deviation) of SDRM, and smaller efficiency indicates more optimal SDRMs. It practicality indicates the slope of the regression line, and smaller practicality means more correlated IM. Similarly, proficiency represents the balance between efficiency and practicality, and smaller proficiency means a more proficient SDRM. Figure 6 shows the SDRMs for floor displacement for the 20 IMs. The results demonstrate that the IMs corresponding to SDRMs with the highest R2 values and having the smallest scattering were: Sa(T1), Sv(T1), Sd(T1), ASI, EPA, PGA, and A95. Displacement-based regression models using Sa(T1), Sv(T1), and Sd(T1) had R 2 greater than 0.95. Similarly, R2 values were also greater than 0.85 in acceleration-based regression models using Sa(T1), Sv(T1), Sd(T1). The trend of SDRMs was similar for both using floor displacement and acceleration as EDPs. Overall, a high correlation was observed for acceleration-based IMs, attributed to the large mass and stiffness of the investigated structure, so it was sensitive to acceleration rather than velocity and displacement [24]. Moreover, Sa(T1), Sv(T1), Sd(T1) had the strongest correlation with EDPs since they combine the earthquake characteristic and structural property (i.e. the fundamental period T1). -20 -15 -10 -5 0 5 10 15 0 10 20 30 40 D is p la ce m en t (m m ) Time (s) LMSM 3D FEM Top node -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 A cc el er at io n (g ) Time (s) LMSM 3D FEM Top node -10 -8 -6 -4 -2 0 2 4 6 8 0 10 20 30 40 D is p la c em en t (m m ) Time (s) LMSM 3D FEM Middle node -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0 10 20 30 40 A cc el er at io n (g ) Time (s) LMSM 3D FEM Middle node 0 2 4 6 8 10 1 10 100 A cc el er at io n (g ) Frequency (Hz) Top node LMSM 3D FEM 0 2 4 6 8 10 1 10 100 A cc el er at io n (g ) Frequency (Hz) Middle node LMSM 3D FEM Engineering, Technology & Applied Science Research Vol. 12, No. 5, 2022, 9160-9165 9163 www.etasr.com Vu et al.: Correlation Analysis of Earthquake Intensity Measures and Engineering Demand Parameters … Fig. 6. SDRMs concerning floor displacement for 20 IMs. Figure 7 summarizes four statistical indicators (R2, efficiency, practicality, and proficiency), which were calculated based on SDRMs that combined 20 IMs and two EDPs. The results showed that the trend in each indicator was similar for the acceleration and displacement responses. It was also found that SDRMs using Sa(Sa(T1), Sv(T1), Sd(T1) had the smallest efficiency and proficiency and the largest R2 and practicality. The following-up IMs were ASI, EPA, PGA, and A95. In other words, these IMs were strongly correlated with EDPs (i.e. seismic responses) of the NPP structure. By contrast, PGD, DRMS, SED, VRMS, PGV, HI, VSI, and SMV are weakly correlated with EDPs of the containment structure. These findings emphasize that it is necessary to select strong correlation IMs to evaluate the seismic performance of containment structures. Fig. 7. Calculated statistical parameters of SDRMs. y = 0.8721x + 3.7995 R² = 0.7662 1 2 3 4 5 -3 -2 -1 0 1 ln (E D P ) ln(PGA) y = 0.4986x + 3.4106 R² = 0.3796 1 2 3 4 5 -3 -2 -1 0 1 ln (E D P ) ln(PGV) y = 0.172x + 3.2978 R² = 0.0772 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 ln (E D P ) ln(PGD) y = 0.8524x + 5.5014 R² = 0.6396 1 2 3 4 5 -5 -4 -3 -2 -1 ln (E D P ) ln(ARMS) y = 0.3843x + 3.9891 R² = 0.2297 1 2 3 4 5 -5 -4 -3 -2 -1 ln (E D P ) ln(VRMS) y = 0.1088x + 3.3267 R² = 0.0323 1 2 3 4 5 -6 -5 -4 -3 -2 -1 0 ln (E D P ) ln(DRMS) y = 0.4362x + 2.7896 R² = 0.6226 1 2 3 4 5 -3 -2 -1 0 1 2 3 ln (E D P ) ln(Ia) y = 0.6005x + 4.5592 R² = 0.6539 1 2 3 4 5 -5 -4 -3 -2 -1 0 ln (E D P ) ln(Ic) y = 0.1666x + 3.2494 R² = 0.187 1 2 3 4 5 -6 -5 -4 -3 -2 -1 0 1 2 3 ln (E D P ) ln(SED) y = 0.5569x + 1.7109 R² = 0.3061 1 2 3 4 5 1 2 3 4 ln (E D P ) ln(CAV) y = 0.9801x + 4.1101 R² = 0.8746 1 2 3 4 5 -3 -2 -1 0 1 ln (E D P ) ln(ASI) y = 0.5519x + 2.7691 R² = 0.445 1 2 3 4 5 -2 -1 0 1 2 ln (E D P ) ln(VSI) y = 0.485x + 2.8386 R² = 0.3765 1 2 3 4 5 -2 -1 0 1 2 ln (E D P ) ln(HI) y = 0.8434x + 4.0894 R² = 0.6986 1 2 3 4 5 -3 -2 -1 0 ln (E D P ) ln(SMA) y = 0.5326x + 3.6857 R² = 0.3536 1 2 3 4 5 -4 -3 -2 -1 0 ln (E D P ) ln(SMV) y = 0.8891x + 3.8372 R² = 0.7853 1 2 3 4 5 -3 -2 -1 0 1 ln (E D P ) ln(EPA) y = 0.8674x + 3.8076 R² = 0.7648 1 2 3 4 5 -3 -2 -1 0 1 ln (E D P ) ln(A95) y = 0.9979x + 3.1674 R² = 0.9982 1 2 3 4 5 -2 -1 0 1 2 ln (E D P ) ln(Sa(T1)) y = 0.9433x - 0.2184 R² = 0.957 1 2 3 4 5 1 2 3 4 5 6 ln (E D P ) ln(Sv(T1)) y = 1.0011x + 2.6516 R² = 0.9987 1 2 3 4 5 -2 -1 0 1 2 ln (E D P ) ln(Sd(T1)) 0 0.2 0.4 0.6 0.8 1 1.2 R 2 va lu e Intensity measure Max acceleration Max displacement 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 E ff ic ie nc y (σ D |I M ) Intensity measure Max acceleration Max displacement 0 0.2 0.4 0.6 0.8 1 1.2 P ra ct ic al it y (b ) Intensity measure Max acceleration Max displacement 0 5 10 15 20 25 P ro fi ci en cy ( ξ ) Intensity measure Max acceleration Max displacement Engineering, Technology & Applied Science Research Vol. 12, No. 5, 2022, 9160-9165 9164 www.etasr.com Vu et al.: Correlation Analysis of Earthquake Intensity Measures and Engineering Demand Parameters … VI. CONCLUSION This study examined the correlation between earthquake IMs and EDPs of the containment structure of an APR-1400 NPP. Numerical modeling was developed using LMSM and validated using a 3D FEM. A set of 90 ground motion records and 20 typical IMs were considered in time-history and correlation analyses. The correlation of IMs with EDPs was evaluated using statistical indicators. Based on the numerical results, the following conclusions can be drawn: • LMSM is reliable for performing time-history analysis of containment structures in NPPs. • The strongest correlated IMs with EDPs of the containment structure were Sa(T1), Sv(T1), Sd(T1), followed by ASI, EPA, PGA, and A95. • The weakest correlated IMs with EDPs of the containment structure were PGD, DRMS, and SED, followed by VRMS, PGV, HI, VSI, and SMV. • It is necessary to select strongly correlated IMs to evaluate the seismic performance and fragility of NPP containment structures. REFERENCES [1] A. Elenas and K. 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