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 (SL2), the UHS generated by the safety evaluation report, and the US RG1.60 spectrum, respectively, a threedimensional 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 largescale 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 [
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, earthquakesafe 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 SL2 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 [
NPP location.
In this study, the stochastic method was used to simulate ground motion [
The simplest and most commonly used source is the classic singlecornerfrequency model [
The corner frequency is related to seismic moment
This paper uses the generalized additive doublecornerfrequency (ADCF) model [
The constancy of the highfrequency acceleration spectral level requires that the following constraint be satisfied:
The highfrequency level is
Atkinson and Silva’s [
The simplified path effect
Geometrical spreading function.
The NPP is at the bedrock site; therefore, the quality factor
The site and path effect are each considered. The amplification and attenuation can be conveniently separated as follows:
Amplification vs. frequency.
The attenuation operator
The
Site amplification combined effect of pathindependent diminution.
A total of 43 earthquakes of
Historical earthquake records near the NPP site (
No.  Earthquake time  Epicenter location  Magnitude  Distance (km)  Accuracy  

Yearmonthday  Longitude  Latitude  
1  BC70.06.01  36.3  119.2  7  306.46  4 
2  495.04.01  37.6  120.9  5.25  160.25  5 
3  1046.04.24  36.9  121.4  5  100.6341  4 
4  1346.03  37.5  119.5  5  274.6924  5 
5  1408.02.28  37.6  121.1  4.75  144.5236  4 
6  1409.02.13  37.6  121.1  4.75  144.5236  4 
7  1506.09.07  36.3  120.7  4.75  179.5199  1 
8  1509.04.21  35.4  119.7  4.75  308.3935  3 
9  1517.10.01  37.6  119.2  5.5  302.8976  4 
10  1543.05.08  35.2  118.5  5  412.4283  3 
11  1548.09.22  38.0  120.7  7  197.9331  5 
12  1584.03  37.5  119.2  5  300.7126  3 
13  1588.07.02  37.5  118.5  5  361.7426  5 
14  1597.10.06  38.5  120.0  7  280.1267  5 
15  1597.12  37.7  121.6  5.25  115.4321  4 
16  1598.02.13  37.4  121.3  5.75  118.8754  3 
17  1621.11.22  37.9  121.2  5.25  156.405  4 
18  1642.08.11  37.2  120.6  4.75  173.0536  4 
19  1668.07.26  36.4  119.2  6.75  303.7531  3 
20  1668.08.24  36.5  118.5  5.75  363.078  — 
21  1672.06.17  35.6  118.8  6  367.6132 

22  1686.01.18  37.7  121.8  4.75  103.5937  4 
23  1687.11.20  37.6  121.5  4.75  114.8229  4 
24  1736.12.25  37.8  121.6  5  123.4755  4 
25  1796.03  36.0  119.4  5  300.0419  3 
26  1829.11.19  36.6  118.5  6.25  361.4066  2 
27  1852.11.17  36.0  118.8  5  350.6615  3 
28  1854.06.04  36.3  118.7  4.75  349.9403  3 
29  1888.06.13  38.5  119.0  7.5  354.0953  4 
30  1910.01.08  35.0  122.0  6.75  224.4953  5 
31  1910.01.09  35.0  122.0  4.9  224.4953  2 
32  1924.02.19  35.0  120.0  5  316.16 

33  1932.08.22  36.1  121.6  6.3  127.6046  2 
34  1939.01.08  37.1  121.6  5.2  83.661 

35  1948.05.23  37.6  121.9  6  89.3951  4 
36  1969.07.18  38.2  119.4  7.4  307.9253  2 
37  1969.07.18  38.1  119.3  4.8  311.368  3 
38  1969.07.18  38.1  119.3  4.9  311.368  2 
39  1969.07.18  38.0  119.0  5.1  331.954  2 
40  1969.07.19  38.2  119.4  4.7  307.9253  2 
41  1992.01.23  35.3  121.13  5.2  224.464  1 
42  1992.11.04  35.33  123.33  4.7  196.3993  1 
43  2002.07.23  35.53  122.21  4.8  184.8908  3 
Earthquake distribution (regional scope: 118.5°–124° east longitude and 35.0°–38.5° north latitude; time range: 70 BC–May 2006; magnitude range:
SMSIM was used to obtain typical timeseries earthquake data (Figure
Time series for the example.
PSA for all point sources (
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
Hazard curves at 0.2 s and 1 s.
UHS. 1 × 10^{−4} rate of exceedance.
The UHS (obtained from the SER generated using the probability method), SL2 spectrum (from SER, enveloped by the probabilistic and deterministic methods at a zeroperiod acceleration of 0.12 g), and RG1.60 spectrum (zeroperiod acceleration equal to SL2 spectrum) were compared with the UHS generated by the stochastic method (hereafter referred to as the new UHS; Figure
Comparison of the new UHS with other spectra.
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
NPP layout. (a) Plan graph. (b) Reactor and spent fuel direction profile. (c) Reactor and auxiliary direction profile. (d) 3D FEM.
Acceleration timehistory curve in the
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
Interlayer drift angle of NPP.
Figure
Displacement peaks in different layers.
Figures
Interlayer shear force.
Interlayer bending moment.
The acceleration timehistory and Fourier spectrum of the firstloop pressure release and the bottom plate (elevation 7.5 m) of the absorbing ball shutdown system were analysed as shown in Figures
Acceleration timehistory curve at 7.5 m.
Fourier spectrum at 7.5 m.
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 sitespecific conditions of the selected NPP. The new UHS was compared with the SL2 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 SL2 spectrum. Then, the threedimensional FEM of the NPP was established, and its dynamic timehistory 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.
The authors declare no conflicts of interest.
This work was supported by the National Key R&D Program of China (2017YFC1500604).