1. Introduction
Recent events worldwide have demonstrated that natural hazards cannot be neglected in evaluating the risk of industrial facilities. Accordingly, several studies have been conducted related to natural hazard risk assessment [
1,
2,
3,
4]. Basco and Salzano [
1] analyzed the hazards related to tsunamis and their impact on the industrial equipment tanks. The fragility functions for this have been specifically defined with respect to tsunami waves and debris. Salzano et al. [
2] dealt with the seismic risk analysis of industrial facilities where tanks, reactors, and pumps are installed. Their study specifically discussed the simplified procedures and methodologies based on a historical database and literature data on natural-technological accidents for seismic risk assessment. Fabbrocino et al. [
3] studied the issue of integrating structural seismic risk into quantitative probabilistic seismic risk analysis by a representative study case regarding an oil storage plant. Prabhu et al. [
4] described a generalized probabilistic methodology for estimating facility downtime under multi-hazard scenarios. Using the Boolean logic, the component vulnerabilities to different hazards were combined. This research demonstrated the applicability of the methodology on industrial plants.
With this background, especially for the nuclear industry, since the cause of the 2011 Fukushima Nuclear Power Plant (NPP) accident turned out to be the multi-hazards from the earthquake and the tsunami, there has been a need to explore various accident scenarios in order to improve the nuclear safety. Multi-hazards can be manifested in a variety of forms, including concurrently occurred hazards (e.g., earthquakes and tsunamis) and sequentially occurred multiple hazards (e.g., earthquake-induced landslides and earthquake-induced fires) [
5]. The recent 2016 Kumamoto earthquake and the 2018 Hokkaido earthquake induced slope collapse, and such slope collapse subsequently caused the failures of adjacent major infrastructures, such as roads, buildings, and chemical plants. This accident shows the potential threat that such multi-hazards may also occur around nuclear facilities when they are located near a slope such as the ones in Korea.
Currently, the method to probabilistically evaluate the safety of nuclear facilities against the potential impact of external hazards is called External Event Probabilistic Safety Assessment (EE-PSA) [
6,
7,
8,
9]. Such assessments have been conducted to identify and improve the safety of nuclear plants from external accidents. Generally, for the nuclear facilities, the EE-PSA probabilistically predicts the possibility of damage to the reactor core due to external hazards. Thus, the safety of the overall nuclear facilities is assessed against external hazards based on this predicted assessment. Methodologically, the EE-PSA is an integrated process that obtains a single risk value by performing an external hazard analysis, fragility analysis, accident scenario analysis, and risk quantification. It also takes into account the randomness and uncertainty associated with these analyses and quantifications. However, the conventional EE-PSA of the nuclear facilities has been carried out for a single hazard, and the multiple hazards occurring simultaneously or sequentially have not been considered because of their low possibilities of occurrence and difficulties in handling these.
For the nuclear facilities, the integrated codes for quantifying the current single-hazard EE-PSA risks are SEISM, SEISMIC, EQESRA, and PRASSE. They are all probability distribution-based Boolean algebraic quantification methodologies [
10,
11,
12]. The commonality of the above mentioned codes is based on the Electric Power Research Institute (EPRI) separation-of-variable (SOV) method, which is a single-hazard fragility analysis method proposed by EPRI [
13]. These codes accept component fragility information as input data and evaluate the system fragility by using Boolean algebra. However, the risk quantification analysis method that uses Boolean algebra has a limitation in accurately evaluating the partial dependency between the components. The inter-component dependency is a phenomenon that may occur in the different components on the same floor or the same components on the same floor under an external hazard event, which can be quantified to different degrees of correlation coefficient values. Such inter-component dependency has been found to have a non-negligible impact on the single-hazard EE-PSA results through the risk sensitivity analyses regarding various actual nuclear power plants [
14]. Specifically, the method of dealing with such inter-component dependency basically assumes a joint log-normal probability distribution between the random variables, with respect to the fragility information having inter-component dependency information. Accordingly, the inter-component dependency information is represented by a correlation coefficient matrix composed of correlation coefficients between component fragilities. Here, the defined correlation coefficient value is the Pearson correlation coefficient, which shows the strength and direction of the linear relationship between two random variables and is defined as the covariance of the variables divided by the product of their standard deviations. The correlation coefficients between these components are obtained from analysis, testing, field measurements, empirical data, and expert judgment. Recently, there have been attempts to quantify the partial dependency between components by using a flexible relation of nodes and a conditional probability table within the Bayesian network technique in order to conduct the single- and multi- hazard PSA methods considering inter-component correlations [
15,
16,
17]. However, in the safety assessment of nuclear facilities, it is expected to apply the strictly proven concepts due to the significant impact that nuclear facilities can get in the event of an accident. Therefore, this new technique has not been applied yet to the risk quantification of the nuclear facilities.
Under these circumstances, Watanabe et al. [
18] developed a sampling-based risk quantification method (called SECOM2-DQFM) to consider precisely the partial dependencies between components based on the fragility method developed by JAERI (Japan Atomic Energy Research Institute) (also known as the response coefficient method) [
19]. From the SECOM2-DQFM’s fragility analysis stage, the component is sampled by separating this into a response
R and a capacity
C. Based on comparing the values from the samplings of
R and
C, the state of the component is classified into safety (“0”) and failure (“1”). Based on such component state information, the states of the sub-system and the top-system are evaluated as “0” and “1” through the various logic gates on the fault tree. The probability of failure of each component, sub-system, and top-system is also evaluated by the ratio between the number of total samples and the number of failure state samples (i.e., samples having “1”). By iteratively performing this procedure for each external hazard intensity, the component and system fragility curves are ultimately derived. Due to this method’s features, it is possible to take into account all of the partial dependencies between the components in the sampling stage. The method also has the advantage of being able to obtain an accurate solution if a sufficient number of samples is extracted. In addition, since the partial dependency relationship between the response and the capacity can be evaluated separately, it is possible to perform a more detailed analysis. However, since this method is a sampling-based method there is a disadvantage in that the computational time is relatively large because a large number of samples must be extracted in order to get a value close to the exact solution [
20,
21]. In addition, there is a disadvantage that a large number of input variables has to be defined in connection with the features of the JAERI fragility methodology compared to the risk quantification method based on the existing EPRI SOV fragility input-based method. Most importantly, there is a fundamental limitation that the analytical time is quite large because sufficient samples must be extracted for the response
R and the capacity
C for every single external hazard intensity. An analytical study has been conducted to assess the probabilistic reliability and fragility analyses under specific loads at a level of a single component and a structure in the nuclear industry [
22]. However, this study did not extend from the component level fragility to the overall plant level system fragility assessment stage.
For the safety analysis of the nuclear facility, most of the risk quantification methods developed so far are methodologies for single external-hazard events. Therefore, expanding the existing single-hazard EE-PSA methodology is essential for quantifying the risk of nuclear facilities for multiple hazards. Conceptually, multi-hazard risk quantification can be expressed in the following equation:
Here, ai represents the hazard intensity of each external hazard i considered. For a single external-hazard event case, the external event hazard information (H) and system fragility information (Pf|s) are expressed as a one-dimensional function in a conventional single external-hazard event, and the corresponding final risk is quantified through the one-dimensional integral. However, in quantifying multi-hazard risks, the hazard and fragility are expressed in a multi-dimensional space, and the final risk is quantified through multi-dimensional integration. Therefore, in deriving the multi-dimensional system fragility results, the Boolean algebra or the sampling extraction and comparison should be performed in a multi-dimensional area. In addition, the collection of reliable original data on the fragility and the hazard is essential for an accurate multi-hazard risk assessment. However, such data collection is one of the most challenging parts of the risk assessment process. Since the focus of this study was on improving risk assessment methods, detailed multi-hazard data collection has not been covered in detail.
Therefore, under this background, we propose a methodology for quantifying the multi-hazard risks of the nuclear facilities by extending the existing single-hazard EE-PSA methodology. Specifically, we develop an efficient multi-hazard PSA methodology by utilizing the current single-hazard EE-PSA methodology such as the probability distribution-based Boolean algebraic approach and the sampling-based method. Here, the limitations on not being able to deal with the partial dependencies of the probability distribution-based Boolean algebraic approach are solved through the sampling-based method. In addition, a more efficient algorithm is proposed to improve the current sampling-based method, which requires a long computational time. Finally, in the sampling-based method, the number of input variables is minimized by reducing the existing input variables to the basic input variables of the EPRI SOV’s fragility method. As a result, the originality and significance of this study are to present a multi-hazard PSA method that is not currently in the nuclear energy industry and to increase the computational efficiency of the existing sampling-based EE-PSA method (i.e., DQFM).
In order to verify the validity of the proposed multi-hazard PSA methodology for the nuclear facilities, four examples were applied, and the results from the different methods within the methodology were compared for accuracy and efficiency. The four selected examples were deployed in a way that increased the complexity of the system. In particular, the third and fourth examples were for the single EE-PSA and the multi-hazard PSA of an actual nuclear power plant, respectively.
5. Summary and Conclusions
In this study, we proposed a methodology to quantify multi-hazard risks by extending the existing single-hazard EE-PSA methodology. We developed an efficient multi-hazard PSA methodology based on the probability distribution-based Boolean algebraic approach and sampling-based method, which are currently basic methods of the single-hazard PSA methodology. Specifically, we extended the probability distribution-based Boolean algebraic approach, which is the basic method for quantifying existing single-hazard EE-PSA risks, to a method to quantify multi-hazard PSA risks. This is the most efficient way to assess exact solutions of system fragility and risks regarding a complete independent condition and a fully dependent condition between components within each hazard event. However, it has a limitation that it cannot consider a partially dependent condition between the component fragilities. Therefore, a sampling-based method was introduced to deal with this partial dependent problem. A single-hazard EE-PSA technique (DQFM) was previously proposed, which could take into account the partial correlations between the component’s vulnerabilities. However, this is a method that can basically consider single-hazard EE-PSA problems. Thus, in this study, we proposed an extended algorithm of the existing DQFM to consider multi-hazard PSA problems. In addition, we proposed a more efficient algorithm by improving the shortcomings of the basic algorithm of the current DQFM, which takes a great deal of computational time. Finally, in the sampling-based method, the existing input variables (Rm, Cm, βRr, βCr, βRu, βCu) of the existing DQFM method were reduced to the basic inputs of the EPRI SOV method (Am, βr, βu) to minimize the number of input variables.
The proposed multi-hazard PSA methodology was applied from the simple earthquake and tsunami multi-hazard examples to the single-hazard and multi-hazard PSA examples of the actual NPP, and the results are summarized as follows. The three methods developed within the multi-hazard PSA methodology yielded the same results with respect to a simple intersection example, a more general example of intersection and union, and an actual seismic-tsunami multi-hazard example of the NPP. Thus, the validity of methods could be verified mutually. Specifically, based on the results of the probability distribution-based Boolean algebraic method, which can obtain exact solutions for the independent and fully dependent conditions, the results of the E-DQFM method and those of the proposed method, which improves the existing DQFM algorithm, were compared. Such a comparison result shows that the proposed method secures similar accuracy in the solutions, even though it utilizes fewer samples than the E-DQFM method. Additionally, in the case of the partially dependent condition, the Boolean algebraic approach did not yield the result due to the characteristics of the method, but the E-DQFM method and the proposed method calculated similar results, which could prove the validity of the methods. In addition, the proposed methodology was applied to the PSA problem of a single earthquake hazard of an actual NPP, and the proposed methodology proved its accuracy by calculating almost the same value as the previous research results in the same problem. Finally, the numerical stability and accuracy of the results were investigated by changing the number of samples “N” with respect to the E-DQFM method and the proposed method for all the examples. The results showed that when N = 1 × 104 or more, the results of both sampling methods become almost close to the exact solutions, and the solution convergence patterns of both methods were similar.
A large amount of data is required to actually apply the multi-hazard PSA methodology proposed in this study. Since the Fukushima nuclear accident in 2011, as the awareness of a multi-hazard event has increased, many studies have been conducted to date [
1,
21]. In addition, one study was conducted on the quantification of dependencies between components in nuclear facilities in the event of an external hazard [
14]. From such a perspective, the proposed multi-hazard PSA methodology is considered to be applicable under the current dataset situation. In particular, it is believed that this methodology can be used to predict external hazard risks, even in situations where there is not enough data, through appropriate engineering judgments and data assumptions. As a result, it is expected that the proposed multi-hazard PSA method can be used to evaluate the risk quantification efficiently and accurately by taking into account all of the dependencies between the components under the multi-hazard events.