Advancements in Design and Analysis of Protective Structures 2019View this Special Issue
Research Article | Open Access
Generation of Uniform Hazard Spectrum Based on the Stochastic Method of Simulating Ground Motion and Its Use in Nuclear Power Plants
To obtain an accurate uniform hazard spectrum (UHS), this paper proposes combining a stochastic simulation with probabilistic seismic hazard analysis. The stochastic method fully accounts for the effect of the source mechanism, path, and site effect. Historical ground motions in the site specific to the nuclear power plant (NPP) are simulated, and a UHS with an equal exceeding probability is proposed. To compare the seismic performance of the NPP under different ground motions generated by the existing site spectrum (SL-2), the UHS generated by the safety evaluation report, and the US RG1.60 spectrum, respectively, a three-dimensional finite element model is established, and dynamic analysis is performed. Results show that the structural responses to different spectra varied; the UHS response was slightly larger than that of RG1.60. This finding is relatively more reasonable than prior research results. The UHS generated using the stochastic simulation method can provide a reference for the seismic design of NPPs.
In recent years, nuclear power plant (NPP) construction in China entered a stage of mass development. By the end of 2016, China was operating 14 NPPs, and 27 are scheduled to be built. However, given the large-scale construction and operation of NPPs, associated safety problems have become prominent. Once an accident occurs in an NPP, the core can melt and radioactive substances can leak out, causing potentially disastrous consequences. To ensure the NPP safety, various sudden disasters (e.g., tsunamis, earthquakes, debris flows, landslides, and aircraft crashes) are considered possibilities during operation, with earthquakes being the most probable one. The Fukushima nuclear accident and its catastrophic consequences raised global awareness of the gravity of seismic safety problems in NPPs. Strong earthquakes occur frequently in China and can lead to secondary disasters. Therefore, improving the safety of NPPs and ensuring their seismic performance is very important.
The aseismic design spectrum is the foundation of the design of NPPs and associated facilities. Throughout the last few decades, the United States Regulatory Guide 1.60 (RG1.60) spectrum  was used in the seismic design of NPPs, but the RG1.60 spectrum contains no site-specific conditions. Therefore, probabilistic seismic hazard analysis (PSHA) with such conditions has attracted increasing attention. PSHA is a methodology used to estimate the probability of various extents of earthquake-cause ground motion being exceeded at a given location in the future . The main goal of PSHA is to provide a design response spectrum for structural analysis. This generated spectrum is called the uniform hazard spectrum (UHS) because every ordinate has an equal exceeding probability. United States Regulatory Guide 1.208  provides a method to obtain the UHS, the purpose of which is to provide guidance for the establishment of a site-specific ground motion response spectrum. Choi et al.  developed the UHS using available seismic hazard data for four Korean NPP sites. Desai and Choudhury  analysed site-specific seismic hazards and one-dimensional equivalent linear ground responses of important sites in Mumbai, and a designed UHS with 5% damping was obtained from the PSHA at each site.
However, many countries such as China do not maintain sufficient strong motion and seismological information; most strong earthquake data in historical records are simply described narratively. Thus, seismic hazard curves remain highly uncertain. For major projects such as NPPs and projects in which serious secondary disasters may occur, earthquake-safe requirements should be determined based on the results of an earthquake safety evaluation report (SER). Current Chinese NPP earthquake safety assessments are based on the maximum construction method, maximum historical earthquake method, and integrated probability method for response spectrum design. The response spectrum obtained by SER is called the SL-2 spectrum, but this spectrum does not represent the same exceeding probability over the entire frequency range of interest. Additionally, the UHS obtained from the probability method only accounts for the attenuation of bedrock ground motion. Hence, a new method should be applied to generate a new spectrum that fully considers factors such as the source mechanism, path, and site effect.
The stochastic method has mainly been used to compute ground motion at frequencies of engineering interest . Since its introduction by Hanks and McGuire  and subsequent enhancements by Boore , the method has been extended to analyse stochastic finite-fault effects [9, 10] and equivalent linear site response [11, 12]. These applications rely on point-source formulation in the stochastic method, which has changed little in the last few years. In this paper, a method of simulating ground motion using the stochastic method to determine UHS is proposed. To analyse reaction characteristics, a high-temperature gas-cooled reactor plant is selected, and a three-dimensional finite element model of the NPP is established to analyse the dynamic response of the NPP under UHS excitation. The NPP is approximately 23 kilometers south of Rongcheng City, 14 kilometers northwest of Shidao, and 68 kilometers southeast of Weihai City, Shandong Province, China, as shown in Figure 1.
2. Generation of Regional Historical Ground Motion
In this study, the stochastic method was used to simulate ground motion . The point-source stochastic model, implemented with the software package Stochastic-Method SIMulation (SMSIM) , was used to generate regional historical ground motion. By separating the spectrum of ground motion into source, path, and site components, models based on the stochastic method can be easily modified to account for specific situations.
The simplest and most commonly used source is the classic single-corner-frequency model . The Fourier acceleration amplitude spectrum (abbreviated here as A) is given bywhere is the seismic moment and is the corner frequency . The high-frequency level is given by
The corner frequency is related to seismic moment and stress drop , with the corresponding formula given bywhere is the shear-wave velocity in the source vicinity.
This paper uses the generalized additive double-corner-frequency (ADCF) model  in which the acceleration source spectrum is proportional towhere and are the double-corner frequencies; is the weighting parameter; and and denote the frequency power and denominator power, respectively. The subscripts and refer to quantities appearing in the two parts of the double-corner-frequency source model. For high frequencies ( and ), the formula becomes
The constancy of the high-frequency acceleration spectral level requires that the following constraint be satisfied:
The high-frequency level is
Atkinson and Silva’s  correlation between and is used in this paper. and are from the study of Boore et al. . According to observational data from Shandong , the density and shear-wave velocity at the source were 2.7 g/cm3 and 3.2 km/s, respectively.
2.2. Path Effect
The simplified path effect is given by the multiplication of the geometrical spreading and functions,where is the seismic velocity, and the geometrical spreading function is given by a piecewise continuous three-segment straight line as follows:where is the closest distance to the rupture surface. Based on the crust thickness in Shandong and references in the literature from the Shandong Seismic Network , , , , , and , as shown in Figure 2.
The NPP is at the bedrock site; therefore, the quality factor Q can be obtained using the rock site in eastern North America .
The site and path effect are each considered. The amplification and attenuation can be conveniently separated as follows:where the amplification function is usually relative to the source and the diminution function is used to model the path-independent loss of energy. Applications must specify reference conditions for the and functions. The square-root-impedance approach  is applied to the crustal amplification function in this case, as presented in Figure 3.
The filter is applied in this paper. The combined effect of amplification and attenuation for a series of diminution parameters is displayed in Figure 4 for the hard rock site.
2.4. Generation of Regional Historical Ground Motion
A total of 43 earthquakes of were recorded in the NPP site region from 70 BC to May 2006 (Table 1), in which five were 7.0–7.9 earthquakes; six were 6.0–6.9 earthquakes; 17 were 5.0–5.9 earthquakes; and 15 were 4.7–4.9 earthquakes. The distribution of earthquakes is shown in Figure 5. The 17th earthquake record, with a magnitude of 5.25 and distance of 156 km, was selected as an example.
SMSIM was used to obtain typical time-series earthquake data (Figure 6) and the pseudoabsolute response spectral acceleration (PSA) of all historical regional ground motion. Assuming all sources involve a point-source model, the 5% damped PSA of all earthquakes is shown in Figure 7.
3. UHS Generation
The natural logarithm of PSA appeared normally distributed for each period; as such, the probability of exceeding any PSA level can be computed using knowledge of the mean and standard deviation :where is the standard normal cumulative distribution function. Two thousand years of earthquake records were counted; hence, the return period of every earthquake was equal to 2000. The annual rate of recurrence was 1/2000 = 0.0005. The annual rate of exceedance in each period was calculated by combining the probability of exceedance and recurrence. Figure 8 shows the hazard curve at individual periods of 0.2 s and 1 s, after which an annual rate exceeding 10−4 was selected. The UHS with a 10−4 exceedance rate for the NPP site was plotted by combining the PSAs from all periods, as depicted in Figure 9.
The UHS (obtained from the SER generated using the probability method), SL-2 spectrum (from SER, enveloped by the probabilistic and deterministic methods at a zero-period acceleration of 0.12 g), and RG1.60 spectrum (zero-period acceleration equal to SL-2 spectrum) were compared with the UHS generated by the stochastic method (hereafter referred to as the new UHS; Figure 10). The RG1.60 spectrum was largest before 0.15 s, and the SL-2 spectrum was largest at 0.16 s only. After 0.16 s, the SL-2 spectrum began to exhibit a downward trend with an amplitude below that of the RG1.60 spectrum and UHS. The amplitude of UHS was larger than that of RG1.60, except at 0.4 s.
4. Finite Element Model Analysis of NPP
4.1. Establishment and Calculation of FEM
To verify the dynamic response of UHS for the NPP, FEM was established in SAP2000. The base elevation was −15.55 m, the roof elevation of the reactor building was 44.1 m, and there were eight floors in total. The roof elevation of the spent fuel plant and auxiliary plant was 36.08 and 21.6 m, respectively. The layout is depicted in Figure 11. The main components of the plant were shear walls and floors that were quite thick. A thick shell element was therefore adopted to simulate the linear state of the NPP. According to the response spectrum in Figure 9, the artificial acceleration time-history curves of each response spectrum were generated, as shown in Figure 12. Two-directional horizontal earthquakes were used as dynamic excitations in the NPP.
4.2. Result Analysis
The simulation results indicate that the natural period of NPP was 0.22 s. Due to space limitations, this paper only analyses the results in the X direction. Figure 13 presents the interlayer drift angle of the NPP at different heights. The height of the maximum interlayer drift angle varied for seismic waves generated by different response spectra. The maximum of RG1.60 was in the third layer, whereas others were in the 6th layer. The angles of the 1st to 3rd layers increased gradually and reduced in the 4th layer; a clear inflexion occurred in the 3rd layer. The angle demonstrated a slight increase from the 5th to 6th layer, and the 6th layer to the top declined gradually. The UHS (SER) angle was smallest. The SL-2 angle was less than that of new UHS and RG1.60. The new UHS and RG1.60 angles were close, but the new UHS angle was larger at the top; the amplitude of the two response spectra was quite small for the natural vibration period, and the NPP response was therefore similar in each.
Figure 14 presents the peak displacement at different elevations. The peak increased along with the elevation. At the same height, the maximum displacement was the peak of the new UHS. Comparing the elevation at 44.1 m, the peak of the new UHS was 5.19 mm, and the peak value of RG1.60 was close to that of SL-2.
Figures 15 and 16 depict the interlayer shear force and bending moment, respectively. The shear force showed a minor change within the first three layers and then decreased from the 3rd layer to the top. The bending moment declined from the bottom to the top, but a slight inflection point appeared in the 5th layer. The force and moment values of UHS and RG1.60 were close and larger than that those of SL-2.
The acceleration time-history and Fourier spectrum of the first-loop pressure release and the bottom plate (elevation 7.5 m) of the absorbing ball shutdown system were analysed as shown in Figures 17 and 18. The peak value of the RG1.60 spectrum acceleration was largest, nearly 0.26 g, and that of SER UHS was smallest with a peak value of 0.14 g. For the Fourier spectrum, RG1.60 and the new UHS each had a widely distributed range within 7 Hz. The Fourier spectrum of the new UHS was more homogeneous than that of Sl-2. These results indicate that the response of different spectra to the NPP varied. The dynamic response of the new UHS to NPP was larger than that of others.
This paper combines stochastic simulation ground motion and a probabilistic method to generate a UHS with an annual exceedance probability of 10−4. Compared with previous studies, the effects of various parameters were fully accounted for when generating the response spectrum, including the source mechanism, propagation path, and site effect. Key parameters were discussed with regard to site-specific conditions of the selected NPP. The new UHS was compared with the SL-2 spectrum, SER UHS, and RG1.60 spectrum, revealing that the new UHS and the SER UHS obtained using the simplified attenuation relation differed substantially in spectrum shape and amplitude. The amplitude of the new UHS and RG1.60 was close to the short period and slightly larger than the SL-2 spectrum. Then, the three-dimensional FEM of the NPP was established, and its dynamic time-history analysis was implemented in SAP2000. The simulation results indicate that different response spectra presented unique dynamic responses to the NPP. UHS exhibited a large response; as such, the UHS generated using the stochastic simulation method can provide a necessary reference for design and aseismic checking of NPPs.
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare no conflicts of interest.
This work was supported by the National Key R&D Program of China (2017YFC1500604).
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