Development of a Risk Assessment Method Under the Multi-Hazard of Earthquake and Tsunami for a Nuclear Power Plant ^†

Abstract

Based on lessons learned from the Fukushima Daiichi Nuclear Power Plant accident caused by the 2011 off the Pacific coast Tohoku Earthquake, and the subsequent tsunamis, Japanese utilities have been upgrading their tsunami countermeasures. To understand the residual risk from beyond-design-basis events, it is important to assess seismic and tsunami risks independently while also recognizing how a plant’s risk profile changes when these events occur concurrently. This study developed a framework for a multi-hazard probabilistic risk assessment (PRA) to evaluate risks to nuclear power plants (NPPs) resulting from the superposition of earthquake and tsunami events. The framework is proposed on the assumption that the targeted plant has previously conducted single-hazard PRAs for both earthquakes and tsunamis. This study presents an approach to define the scope of risk assessment for the superposition of earthquake and tsunami events, based on the results from single-hazard PRAs for each hazard. It provides an analytical framework for superposition scenario analysis and a simplified method for multi-hazard assessment using data from single-hazard assessments. Moreover, a series of steps for the multi-hazard fragility assessment of superposed earthquake and tsunami events are proposed, clarifying the relationship between superposed impacts and the damaged parts and damage modes, accompanied by illustrative examples.

1. Introduction

This article is a revised and expanded version of a study conducted by Yamada et al. [1].

On 11 March 2011, the 2011 off the Pacific coast of Tohoku Earthquake and the subsequent tsunamis caused damage to several nuclear reactors. The Fukushima Daiichi Nuclear Power Plant accident released radioactive materials into the environment due to core damage. In response to this accident, the International Atomic Energy Agency (IAEA) created a nuclear safety action plan. As part of this action plan, the IAEA held an international expert meeting that brought together leading experts from various fields, including research, industry, regulatory, and safety assessment [2]. The knowledge gained through these international efforts to protect nuclear power plants (NPPs) from extreme earthquakes and tsunamis was subsequently used to strengthen nuclear safety in various countries.

The Nuclear Regulation Authority (NRA) in Japan has implemented new regulatory standards for the safety review of NPPs, based on insights gained from the Fukushima Daiichi Nuclear Power Plant accident. Nuclear operators are taking steps to enhance plant safety by implementing comprehensive tsunami protection and severe accident measures that comply with the new regulatory standards. Furthermore, operators must submit a Safety Assessment Report (SAR) [3] after the periodic operator inspection following the resumption of the plant’s operations. The SAR requires an assessment of risks from internal and external events to inform the implementation of activities to improve safety. The operation guide NRA SAR [4] states that the events covered by the assessment should be expanded step by step as the maturity of the probabilistic risk assessment (PRA) methods advances. This guide presents examples of simultaneous earthquakes and tsunamis. Based on knowledge of damage caused by earthquakes and tsunamis affecting NPPs and surrounding areas, a risk assessment concept (hereinafter referred to as the seismic-tsunami PRA) for NPPs in the event of a tsunami triggered by an earthquake has been proposed [5].

The IAEA has studied multi-hazard events involving the combined impact of earthquakes and tsunamis and published a Safety Report [6]. In addition, studies on seismic-tsunami PRAs have been conducted, focusing on evaluation methods such as hazard and fragility assessment [7] and accident sequence assessment [8,9]. These guides and prior studies do not provide descriptions of conventional methods that are based on assessment techniques, such as those employed by Japanese nuclear operators in their previously submitted SARs.

This study develops a methodology for risk assessment in multi-hazard conditions, specifically addressing earthquakes and tsunamis, to establish a practical multi-hazard evaluation approach for SAR implementation. The proposed method enables the assessment of seismic-tsunami PRAs at NPPs by utilizing an enhanced approach based on internationally recognized external-event PRA methods (e.g., Seismic Probabilistic Risk Assessment Implementation Guide [10], PRA standard [11]). Section 2 presents fundamental equations and key points for evaluating plant risk in the context of a superposed earthquake and tsunami event. Section 3 describes a methodology for scenario analysis based on the proposed superposition assessment framework for the plant. Section 4 proposes a simplified multi-hazard assessment method for practical implementation. Section 5 presents modeling and assessment methods for multi-hazard fragility assessment pertaining to earthquakes and tsunamis. Section 6 concludes the paper.

2. Framework for Assessing Plant Risk Under the Superposition of Earthquake and Tsunami

2.1. Prerequisite for Development of an Evaluation Methodology

When expanding the scope of events to include the superposition of an earthquake and a tsunami, it is essential to maintain methodological consistency with how single-hazard risks are assessed. Therefore, existing methods (such as event tree (ET), fault tree (FT), and hazard assessment data) developed for seismic and tsunami PRAs are recommended for application in seismic-tsunami PRAs.

This study focuses on a cascading event in which a tsunami follows an earthquake. Aftershocks were intentionally excluded from consideration, and for tsunamis, only the largest tsunami was targeted, with the effects of repeated tsunamis deliberately not taken into account. The scope of this study encompasses at level 1 PRA, focusing on the assessment of core damage frequency (CDF).

2.2. Relationship Between Independent Events and Superposition Events

The conceptual framework for the multi-hazard earthquake and tsunami addressed in this study is shown below. Figure 1 illustrates the relationship between the PRA for the multi-hazard earthquake and tsunami (considering a superposition event as examined in this study) and the single-hazard PRAs regarding an earthquake and a tsunami. This study excludes far-field tsunamis without seismic impact at the site, focusing instead on earthquake and tsunami events originating from the same seismic source. Earthquakes with inland hypocenters or those that do not generate tsunamis are also not considered.

This study focuses on earthquakes within the seismic source regions that generate tsunamis impacting the site. The CDF of the superposition event shown in Figure 1, which is the focus of this study, illustrates a plant risk profile that cannot be identified in each single-hazard PRA, despite individual evaluations of earthquakes and tsunamis originating from the same seismic source. Therefore, it is important to consider changes in seismic and tsunami inputs that affect plant response when previously evaluated as single-hazard PRAs, in order to properly account for multi-hazard effects and to understand changes in conditional core damage probability (CCDP) resulting from the impact of superposition events involving both earthquakes and tsunamis.

Figure 1. Scope of the seismic-tsunami PRA, single-hazard seismic PRA and tsunami PRA.

Figure 1. Scope of the seismic-tsunami PRA, single-hazard seismic PRA and tsunami PRA.

2.3. Range of Hazard Input Levels on the Seismic-Tsunami PRA

The first step in setting the scope of the seismic-tsunami PRA is to identify the combination of tsunami and seismic sources affecting the plant, based on the result of the probabilistic seismic hazard assessment (PSHA) and probabilistic tsunami hazard assessment (PTHA). The next step is to identify the scope of the impact from the superposition of earthquakes and tsunamis. Figure 2 illustrates the scope of the risk assessment for the multi-hazard of earthquakes and tsunamis. Moreover, Figure 2 illustrates the relationship between seismic intensity of peak ground acceleration (PGA) and tsunami height. The white area indicates an area where the tsunami’s impact on the plant does not need to be considered, as no significant tsunami impact is expected. Therefore, it may be reasonable to focus only on seismic effects in this area.

The orange area shown in Figure 2 is the range where the CCDP is close to 1.0 for both the seismic and tsunami PRAs. Hence, the evaluation of detailed accident scenarios is considered to have relatively low importance in this context. The yellow area in Figure 2 represents the range of hazard input levels to be evaluated. It should be noted that under high seismic acceleration conditions, the tsunami height to be considered may be reduced due to ground subsidence or damage to tsunami protection facilities.

2.4. Fundamental Considerations Under the Multi-Hazard of Earthquake and Tsunami

In multi-hazard scenarios involving earthquakes and tsunamis, it is anticipated that accident scenarios will differ from those caused by single hazards. Figure 3 provides a simplified overview of the progression of accidents following an earthquake and a tsunami.

Since seismic waves reach the site earlier than tsunamis, seismic motions affect the site first, potentially causing damage or degradation to tsunami protection facilities and equipment associated with initiating events (IEs) and accident mitigation systems, as well as triggering topographical changes. Furthermore, they may damage or impair the function of protective structures designed to prevent inundation. Subsequently, the tsunami reaches the site, causing additional damage to safety-related or mitigation structures, systems, and components (SSCs) and further impacting accident mitigation efforts.

Accident scenarios unique to multi-hazard conditions are anticipated, including events that would not occur under a single-hazard earthquake, increased difficulty in accident mitigation, and damage to protective systems that would remain intact under a single-hazard tsunami but are degraded by seismic impacts. These may result in a reduction in the tsunami capacity of SSCs, leading to damage under lower tsunami loads, and the emergence of alternative inundation pathways. Based on these considerations, the multi-hazard PRA must account not only for the single-event PRA but also for the following additional factors [12].

• Occurrence of IEs due to preceding hazards, and damage or degradation of accident mitigation systems.
• Damage or degradation of tsunami protection equipment caused by preceding hazards.
• Complex accident scenarios unique to the multi-hazard conditions, as influenced by the two aforementioned factors.

Moreover, given the discussions in Section 2.2 and Section 2.3, the dependency between earthquake and tsunami hazards should be considered.

In order to effectively respond to these challenges, the following aspects are identified as key issues: (1) scenarios that consider tsunami effects during the mitigation of accidents caused by earthquake-induced events; (2) the dependency between earthquakes and tsunamis in the frequency of the multi-hazard events; and (3) damage or function failure considering both the correlated and independent effects under earthquake and tsunami multi-hazard conditions.

2.5. Framework of the Risk Assessment Under the Multi-Hazard of Earthquake and Tsunami

A framework for the assessment of risk under the multi-hazard of earthquake and tsunami is shown in Figure 4.

This figure shows the model development and risk quantification, which are the focus of this study. These assessment items and their correspondence to the sections of this study are outlined. It should be noted that documentation and analysis of results are assumed to be conducted as appropriate at each step and therefore are not explicitly depicted in the diagram. The scope of this framework is limited to level 1 PRA. The arrows in the diagram represent the flow of data and assessment results exchanged among each assessment element.

2.5.1. Analysis of General Plant Response Scenarios Due to the Multi-Hazard of Earthquake and Tsunami

Referencing the identification of accident scenarios conducted in the seismic PRA and tsunami PRA, the analysts involved in the PRA will collaboratively analyze and develop comprehensive scenarios to identify the impacts of the multi-hazard of earthquake and tsunami on the plant, hereinafter referred to as “superposition scenarios”. One of the characteristics of superposition scenarios to be noted is events in which an earthquake or superposed action changes the behavior of the plant’s tsunami response. Seismic motion acts simultaneously on the SSCs of the NPPs. Therefore, the presence or absence of damage to SSCs is determined with a certain probability according to the characteristics of the seismic motion and the plant and its components. On the other hand, it is important to note that a tsunami is a phenomenon characterized by the mass inundation of seawater. The possibility and/or probability of damage to SSCs depend not only on the characteristics of the tsunami and the accident mitigation SSCs, but also on earthquake damage to tsunami protection facilities and other structures along the tsunami’s path. The concept of scenario identification is described in Section 3.

2.5.2. Hazard Assessment

As previously mentioned, this study used the single-hazard assessment data from PSHA and PTHA. The information also includes the following.

(1)

Quantification of the Multi-hazard of Earthquake and Tsunami

Based on a previous study by Nakajima et al. [13], this study develops an analysis method for the superposition hazard of earthquake and tsunamis in a simplified, approximate manner, considering the correlation between seismic intensity and tsunami height. For further details, refer to Section 4. In the seismic-tsunami PRA, seismic sources must be selected to ensure that both the subsequent ground motion and the associated tsunami have the potential to have significant impacts on the site. The procedure of earthquake determination for the seismic-tsunami PRA is shown in Figure 5.

Accordingly, from the list of earthquakes considered in the single-hazard tsunami PRA, those capable of generating tsunamis with significant wave heights and simultaneously inducing substantial ground motion at the site are identified.

It is necessary to identify tsunami source condition scenarios that correspond to the range of tsunami heights required for evaluation in the seismic-tsunami PRA. This range is specifically defined based on the “Range of hazard input levels for risk quantification” presented in Section 2.3. Since the evaluation of tsunami wave heights involves both epistemic and aleatory uncertainties, hazard assessments consider a wide range of tsunami source condition scenarios. The likelihood of tsunamis occurring under different source conditions is evaluated for each scenario, with a corresponding weight assigned in the logic tree. The scenario consists of tsunami source characterization and propagation models with aleatory uncertainty, and the inter-model uncertainty is assessed as epistemic uncertainty. Variations in tsunami height and characteristics reaching the site, driven by different source conditions, result in different impacts on the risk to NPPs.

Figure 5. Procedure of earthquake determination in the seismic-tsunami PRA.

Figure 5. Procedure of earthquake determination in the seismic-tsunami PRA.

In this study, it is assumed that seismic and tsunami hazard curves are derived from PSHA and PTHA conducted separately. Therefore, we have mathematically modeled the degree of correlation between seismic and tsunami events by evaluating the joint probability function, which consists of variabilities in ground motion and tsunami height, as one of the simplified methods for practical purposes. The contribution analysis of tsunami input conditions, i.e., fragility input conditions, can be evaluated using methods such as those of Kihara et al. [14]. As a result of the above process, a set of tsunami input conditions, each weighted according to tsunami height, is generated and used for fragility assessment. We think that there is room for further investigation of the superposed seismic and tsunami hazard evaluation. Therefore, we have compared the developed method with the detailed method based on fault rupture-modeled simulation, enabling more accurate evaluation of the correlation, though it requires heavy computation.

(2)

Quantification of Fragility Input Conditions

Inputs for evaluating tsunami response (hereinafter referred to as tsunami input conditions) should be based on those defined in the tsunami PRA. NPPs subject to seismic-tsunami PRA are considered to have relatively high tsunami hazard risks. Therefore, in the tsunami PRA, multiple tsunami input conditions are considered based on their contributions to the tsunami hazard curve across different tsunami heights. Tsunami input conditions for fragility assessment are generated based on the wave source conditions from the identified earthquake described in the previous section. Since the seismic sources generating seismic motions differ for each PGA level, the shapes of the tsunami occurrence probability density function (PDF) in Figure 2 also differ. As a result, tsunami responses are evaluated using datasets with different tsunami input conditions for each PGA. To account for earthquake effects, the seismic motion applied in fragility assessments should be derived from the results of the single-hazard seismic PRA conducted for the target NPPs. Care must be taken when the reference seismic motion derived from the source model in the seismic-tsunami PRA exhibits significantly different characteristics (e.g., periodicity of seismic motion) compared to that used in the single-hazard PRA.

2.5.3. Site and Plant Condition Surveys Under the Multi-Hazard of Earthquake and Tsunami

A site impact investigation is performed based on the site inundation propagation analysis under tsunami input conditions identified from the multi-hazard assessment of earthquake and tsunami. The fragility analyst identifies the impacts of superposition events on the damage probability of target SSCs, including damaged parts and damage modes. To this end, an analysis is conducted based on the design document surveys, and a plant walk-down is performed as appropriate. This process focuses on identifying impact areas and understanding the superposition effects of earthquake and tsunami hazards on the site. To ensure a comprehensive investigation, the plant walk-down should involve collaboration among experts from plant vendors, constructors, and specialists in seismic and tsunami-resistant technologies. This collaboration allows for a thorough examination of diverse perspectives.

2.5.4. Fragility Assessment

In seismic-tsunami PRA, in addition to the impacts of single hazards such as earthquakes or tsunamis, superposition or cascading hazards may generate distinct effects. These include hazard interactions and the reduction in system capacity to withstand subsequent events due to the influence of preceding ones. Safety-related components, for which the influence of preceding hazards on the capacity to damage modes from subsequent hazards must be considered, are typically installed outdoors. Components subject to multi-hazard fragility assessment for the superposition of earthquake and tsunami events are selected from the component lists for each seismic and tsunami PRA. Therefore, the first step is to conduct an analysis and organize the fragility assessment results into a single-hazard PRA. The seismic fragility model is based on the Separation of Variables (SOVs) method [15]. Tsunami fragility is quantified as a cumulative damage probability, calculated from damage probabilities assessed under multiple tsunami input conditions, each weighted by its contributions to the hazard curve. This is achieved by applying the detailed analysis approach (Seismic Safety Margins Research Program (SSMRP) method [16]) derived from seismic PRA, using tsunami input conditions weighted by tsunami height.

The next step involves identifying the SSCs that require consideration of the multi-hazard fragility for the superposition of earthquake and tsunami events. Once the SSCs subject to assessment have been selected, the damaged parts and damage modes caused by superposition effects need to be clarified. Suppose the damaged modes and damage parts in the seismic response of the SSCs differ from those in the tsunami response. In that case, there is no dependence between the seismic and tsunami responses, and the seismic response does not affect the tsunami capacity of the SSCs. Therefore, seismic damage and tsunami damage can be considered independent events. Therefore, it might be helpful to consider the following Boolean algebra expression, which could be used to calculate the damage probability considering the multi-hazard of earthquake and tsunami ($P_{s+t})$. Equation (1) shows that the multi-hazard fragility for the superposition of earthquake and tsunami events is calculated from the single-hazard seismic damage probability ${(P}_s)$ based on the PGA and the single-hazard tsunami damage probability ${(P}_t)$ based on the tsunami height.

$$P_{s+t}=\left(\left(1-P_t\right)\times P_s\right)+\left(P_s\times P_t\right)+\left(\right(1-P_s)\times P_t)$$

(1)

On the other hand, if the seismic response affects the tsunami capacity of SSCs, it is necessary to determine the damage probability while accounting for potential dependencies. Since the damage mechanisms under multi-hazard conditions may differ from those under a single hazard, it is important to re-examine the conditions under which the SSC being evaluated is expected to maintain its function identifying the part of damage, damage modes, and damage scenarios of SSCs considering the multi-hazard of earthquake and tsunami, which is a crucial aspect of this process. Moreover, the damage probabilities of SSCs for each scenario need to be evaluated and incorporated into the system reliability model. Assessment methods and examples for damage probabilities under multi-hazard conditions are described in Section 5.

2.5.5. Accident Sequence Assessment

To set the success criteria necessary to prevent core damage after an IEs, scenarios are identified, including the number and combination of SSCs required to achieve safety functions, the tsunami following an earthquake, and the mission time based on the time difference between earthquake motion and tsunami arrival. Due to the large number of potential inundation scenarios resulting from the tsunami inundation patterns at the site and the locations of inundation entry points caused by seismic damage, it is recommended that representative inundation patterns be identified and set as accident scenarios to be assessed, thereby facilitating comprehensive accident sequence assessment.

The frequencies of the IEs are quantified based on the identified “superposition scenarios”. In that case, fragility datasets corresponding to each scenario would be provided. The FT model used for the system reliability analysis is constructed, broadly speaking, by incorporating the influence of one hazard into the FT model of the other hazard in a single-hazard PRA. It is also necessary to verify whether any human error events have been overlooked in the Human Reliability Analysis (HRA) for the single-hazard seismic PRA and the single-hazard tsunami PRA.

This study proposes using PGA as the X-axis for risk profiles in seismic-tsunami PRA. The CDF for the multi-hazards of earthquakes and tsunamis, referred to as $CDF\left(superposition event\right)$, is obtained by incorporating the tsunami height (${\alpha }_T$), the PGA (${\alpha }_s$), the CCDP for each combination of the PGA and tsunami height (${\alpha }_s$, and ${\alpha }_T$), the frequency of earthquakes exceeding ${\alpha }_s$, and the conditional probability of the tsunami height (${\alpha }_s$) given the PGA (${\alpha }_T$). The proposed basic equation is presented in Equation (2).

$$CDF\left(superposition event\right)=\iint -{\displaystyle \frac{dH\left({\alpha }_S\right)}{d{\alpha }_S}}T({\alpha }_T|{\alpha }_S)·CCDP\left({\alpha }_S{,\alpha }_T\right)d{\alpha }_{T}d{\alpha }_S$$

(2)

$CDF\left(superposition event\right)$: core damage frequency under the superposition of earthquake and tsunami [/(reactor∙ year)].

${\alpha }_s$: peak ground acceleration (PGA) [Gal, cm/s²].

${\alpha }_T$: tsunami height [m].

$H\left({\alpha }_S\right)$: frequency of seismic motions exceeding the ${\alpha }_s$ [/year].

$T\left({\alpha }_T\right|{\alpha }_S)$: conditional probability density function of the tsunami height (${\alpha }_T$) given the PGA is ${\alpha }_s$.

CCDP (${\alpha }_s$, ${\alpha }_T$): conditional core damage probability when the PGA (${\alpha }_s$) and tsunami height (${\alpha }_T$) [-].

3. Methodology of Superposition Scenario Analysis

In the superposition scenario analysis, events related to reactor safety arising from the multi-hazard occurrences at the site are examined. Based on this analysis, the scenarios to be evaluated in the seismic-tsunami PRA are identified. This section focuses on the sequence from the occurrence of seismic and tsunami hazards to their arrival at the plant, which results in damage to various SSCs and triggers the IEs. Scenarios related to accident mitigation following the IEs will be addressed in the accident sequence assessment. Figure 6 outlines the procedure for analyzing superposition scenarios. This process is essential for conducting superposition PRA and provides the basis of the subsequent assessments, including hazard, fragility, and accident sequence assessments. The following presents the tasks that constitute the procedure, along with the steps performed within each task.

Figure 6. Procedure for analyzing superposition scenarios.

Figure 6. Procedure for analyzing superposition scenarios.

3.1. Task (1): Defining a Generalized Superposition Scenarios

To ensure a common understanding among analysts and maintain consistency in assessing superposition events and scenarios, it is desirable to establish a general chronological sequence under superposition hazard conditions.

This sequence can be developed using analytical tools such as chronological diagrams, in accordance with the assessment objectives and prerequisites.

3.2. Task (2): Identification of Superposition Events Subject to Evaluation

Based on the generalized superposition scenarios and plant information, the superposition events to be assessed are identified. This task is divided into four steps.

First, the multi-hazard events expected to occur in an NPP are identified using generalized superposition scenarios (Step 1). During the identification process, the focus is on the following three aspects.

• Changes in the behavior of subsequent hazards caused by the influence of preceding hazards acting on the plant.
  • Tsunami inundation conditions influenced by ground deformation, differing from those caused by a single hazard.
  • Tsunami inundation conditions that differ from those caused by a single hazard, due to the impact of preceding hazards or damage to tsunami protection facilities resulting from combined hazard effects.
• Changes in the characteristics of subsequent hazard impacts due to the influence of preceding hazards acting on the plant.
  • Damage to SSCs, including secondary effects, caused by the impact of preceding hazards or by combined hazard effects that results in conditions that differ from those under single-hazard scenarios.
  • Accident response conditions differ from those under single-hazard scenarios, due to the impact of preceding hazards or the combined effects of the multi-hazards.
  • Impact on accident response due to differences in hazard arrival times.
• Events and scenarios arising from a combination of aspects 1 and 2.

As a starting point for the examination of superposition events, this study proposes a standardized list of superposition events (referred to as general superposition events). A list of general superposition events is presented in Table 1. The general superposition events presented in this study are formulated under the assumption of a hypothetical Japanese plant and are not based on any specific actual plant conditions. Therefore, in practical applications, plant-specific superposition events are identified by examining each power plant’s conditions and reviewing general superposition events to identify any omissions or excesses.

Table 1. List of general superposition events.

	General Superposition Events
1	Change in the route of tsunami arrival at the site due to seismic damage to civil engineering structures around the site.
2	Change in tsunami behavior due to ground deformation (uplift/subsidence) over the entire site.
3	Damage to tsunami protection facilities due to rock slope collapse caused by seismic motion.
4	Changes in site inundation behavior due to seismic or superposed impacts on the tsunami prevention facility or drainage facilities.
5	Change in tsunami propagation path due to topographical changes in the site (landslide, etc.).
6	Damage to outdoor SSCs by superposed impacts.
7	Water intake function failure due to seismic-induced sloshing.
8	Generation of drifting of outdoor SSCs damaged by seismic impact (or superposed impact).
9	Inundation of buildings and propagation of tsunamis between buildings due to damage to tsunami inundation protection facilities caused by seismic impact (or superposed impact).
10	Change in the tsunami propagation path inside the building due to damage to internal flooding prevention equipment, etc., caused by seismic impacts (or superposed impacts).
11	Damage to indoor SSCs by superposed impacts.
12	Generation of new inundation paths or bypassing of inundation due to inundation in the system and containment due to damage to storage tanks, piping, containment, etc., caused by seismic impacts (or superposed impacts).
13	Tsunami inundation due to damage to the building structural wall caused by seismic impacts (or superposed impacts).
14	Impact of seismic impacts on tsunami protection response and countermeasures.
15	Changes in post-earthquake evacuation response and routes under superposition events.
16	Damage to facilities to ensure water intake when water levels drop due to seismic motion (or superposed action).
17	Restoration of work sites, access routes, and other areas that are newly generated or are more complicated than when a single hazard was present due to superposition events.
18	The actions for accident mitigation differ from those for a single hazard because hazards are superposed.
19	Interruption of accident management or damage to mitigation facilities due to the tsunami arrival during the response to an accident caused by an earthquake
20	Insufficient resources (equipment, personnel, time margin) when responding to superposed seismic and tsunami impacts.

Table 1. List of general superposition events.

	General Superposition Events
1	Change in the route of tsunami arrival at the site due to seismic damage to civil engineering structures around the site.
2	Change in tsunami behavior due to ground deformation (uplift/subsidence) over the entire site.
3	Damage to tsunami protection facilities due to rock slope collapse caused by seismic motion.
4	Changes in site inundation behavior due to seismic or superposed impacts on the tsunami prevention facility or drainage facilities.
5	Change in tsunami propagation path due to topographical changes in the site (landslide, etc.).
6	Damage to outdoor SSCs by superposed impacts.
7	Water intake function failure due to seismic-induced sloshing.
8	Generation of drifting of outdoor SSCs damaged by seismic impact (or superposed impact).
9	Inundation of buildings and propagation of tsunamis between buildings due to damage to tsunami inundation protection facilities caused by seismic impact (or superposed impact).
10	Change in the tsunami propagation path inside the building due to damage to internal flooding prevention equipment, etc., caused by seismic impacts (or superposed impacts).
11	Damage to indoor SSCs by superposed impacts.
12	Generation of new inundation paths or bypassing of inundation due to inundation in the system and containment due to damage to storage tanks, piping, containment, etc., caused by seismic impacts (or superposed impacts).
13	Tsunami inundation due to damage to the building structural wall caused by seismic impacts (or superposed impacts).
14	Impact of seismic impacts on tsunami protection response and countermeasures.
15	Changes in post-earthquake evacuation response and routes under superposition events.
16	Damage to facilities to ensure water intake when water levels drop due to seismic motion (or superposed action).
17	Restoration of work sites, access routes, and other areas that are newly generated or are more complicated than when a single hazard was present due to superposition events.
18	The actions for accident mitigation differ from those for a single hazard because hazards are superposed.
19	Interruption of accident management or damage to mitigation facilities due to the tsunami arrival during the response to an accident caused by an earthquake
20	Insufficient resources (equipment, personnel, time margin) when responding to superposed seismic and tsunami impacts.

Next, for each superposition event, potentially related SSCs, responses, and phenomena are extracted as either sources or targets of impact, and the specific event is identified (Step 2). At this stage, plant visits are conducted to ensure completeness in the extraction process, while referencing Piping and Instrumentation Diagrams (P&IDs), layout drawings, and information from previously conducted single-hazard PRAs.

For the events extracted in the previous step, screening is conducted from the perspectives of the likelihood of occurrence and the degree of impact on risk, considering related SSCs, responses, and phenomena (Step 3). The likelihood of superposition event occurrence is assessed from the perspectives of the impact and capacity of SSCs, based on engineering judgment, qualitative analysis, or quantitative analysis when the necessary information is readily available or can be easily generated. The screening criteria are presented below.

• Screening based on the defined scope and the potential for simultaneous occurrence of initiating events.

To streamline the investigation and analysis process, elements such as equipment and response measures that are clearly outside the scope of consideration are identified and excluded through a screening process. In this step, screening is conducted based on the following four criteria. If any of these criteria are met, the item is considered outside the scope of evaluation.

• The applicability of the event should be evaluated to determine whether it falls outside the scope of the multi-hazard PRA to be conducted.
• As a result of the detailed examination, it may be determined that the SSCs and related components are not associated with the occurrence of superposition events.
• Verification is required to determine whether the equipment is installed in a location that is demonstrably unaffected by potential hazards.
• An evaluation is required to determine whether the capacity of other SSCs, which may contribute to the same superposition event, is significantly lower than that of the SSCs under consideration.

2.

Screening based on the impact difference depending on event occurrence.

Determine whether the occurrence of an event has a significant impact. If the occurrence of that event does not have a significant impact, the relevant equipment or countermeasures are screened out.

3.

Screening based on capacity/fragility.

For components, countermeasures, and other relevant equipment where a significant impact cannot be ruled out, it is necessary to determine whether they possess sufficient capacity at the hazard level defined within the scope of the evaluation. Items determined to have sufficient capacity may be excluded from consideration as contributors to superposition events and treated as functioning properly in the PRA.

Finally, for events remaining after screening, it is recommended to determine whether probability estimation is necessary and whether tsunami effects or superposition effects should be evaluated (Step 4).

3.3. Task (3): Determining Superposition Scenarios

For the superposition events identified in Task (2), organize their relationships with other events, define strategies for developing superposition scenarios, and determine the resulting scenarios.

3.3.1. Step 1: Confirmation of the Scope of Influence of Superposition Events, the Dependency Between Superposition Events, and the Envelopment of Their Effects

For the superposition events determined in Task (2), confirm their scope of impact, dependencies on other events, and any underlying common factors. Additionally, confirm the extent and comprehensiveness of the impact resulting from their occurrence.

• Scope of impact of superposition events.
  • Utilized to assess the necessity of introducing scenario branching in the development of multi-hazard scenarios.
• Dependence among events and potential common cause factors.
  • Utilized to establish the order of scenario branching during the development of superposition scenarios.
• Inclusiveness of potential impacts.
  • Utilized to investigate the necessity of incorporating scenario branching and to establish representative superposition scenarios for evaluation.

3.3.2. Step 2: Determination of Superposition Scenarios

For superposition events that are interrelated or produce similar effects, the inclusiveness of potential impacts is examined. Taking these relationships into account, the overlapping events are arranged in chronological order, and the superposition scenarios (including their variations) are organized using tools such as event flow diagrams (e.g., Figure 7). Accident scenarios are grouped based on available resources for evaluation, risk significance, and similarities, thereby enabling a more efficient and focused assessment process.

Figure 7. Organization of scenarios using event flow diagrams.

Figure 7. Organization of scenarios using event flow diagrams.

4. Proposal of Simplified Multi-Hazard Assessment Method

The fundamental concept for treating multi-hazard scenarios involving earthquakes and tsunamis is presented in “A Standard for Procedure of Seismic Probabilistic Risk Assessment for Nuclear Power Plants: 2024” issued by the Atomic Energy Society of Japan (AESJ) [17]. However, in their formulation of exceedance probability calculations for multi-hazard metrics, they assume that there is no correlation between the variability of tsunami height and seismic ground motion. As a result, the hazard assessment does not extend to scenarios in which a single earthquake induces a single consequential tsunami.

Although a fully rigorous multi-hazard assessment could be conducted by applying a unified model from the source level, this study proposes a simplified method. The approach focuses on identifying the levels of seismic ground motion and tsunami height that are highly sensitive to quantifying combined risk to derive effective safety enhancement measures.

When probabilistic seismic hazard analysis and tsunami hazard analysis have been conducted independently for the target site, and seismic and tsunami hazard curves have been obtained, respectively, it can be considered possible to approximately calculate the combined seismic-tsunami hazard (defined as the exceedance probability of tsunami height over an analysis period of T₀, conditional on a given level of seismic ground motion) based on the following equation [18].

$$\begin{array}{c}{P}_0\left({H>h,T_0 under condition A}_1<A<A_2\right)\\ \cong \sum \left(\mathit{earthquake} \mathit{occurrence} \mathit{rate} \mathit{at} \mathit{the} \mathit{target} \mathit{source}\right)\\ \times \iint \left[\left(\begin{array}{c}Probability density function of the variability \\ in seismic ground motion intensity\end{array}\right)\right.\\ \times \left(\begin{array}{c}Joint probability density function of the variability\\ in seismic ground motion intensity and tsunami height\end{array}\right)\\ \times \left(\begin{array}{c}The probability that the seismic ground motion intensity \\ falls within the range{ A}_1<A<A_2\end{array}\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\times \left(\begin{array}{c}The probability that the tsunami height H \\ exceeds a threshold h.\end{array}\right)\end{array}$$

(3)

Here,

$P_0$(): Annual exceedance probability based on the conditions specified in parentheses.

$A$: Variable representing seismic ground motion level.

($A_1$ and $A_2$ represent specific values of seismic ground motion level for the target under consideration).

$H$: The variable representing tsunami height level.

(The value $h$ denotes a specific tsunami height for the target under consideration).

Each term in the above equation is presented as follows.

• Probability density function of seismic ground motion level variability: provided by the model used in the single-event PSHA.
• Joint probability density function of the variability in seismic ground motion intensity $A$ and tsunami height $H$: provided in the form of a joint probability density function defined by the combination of variability from the seismic ground motion model and the tsunami height model.
• Probability that seismic ground motion intensity $A$ falls within the interval $A_1$ < $A$ < $A_2$: this represents the exceedance probability within a specified ground motion intensity range and is calculated and output by the probabilistic seismic hazard analysis (PSHA).
• Probability that tsunami height $H$ exceeds a given value h: this represents the exceedance probability of tsunami height $H$ over a specified threshold h and is calculated and output through probabilistic tsunami hazard analysis (PTHA).

In general, seismic ground motion models used in single-event PSHA are based on ground motion prediction equations (GMPEs). Therefore, it is difficult to directly construct a joint probability density function from observational records or simulations. As a result, a practical approach to developing the joint probability density function is to follow the procedure outlined below.

(a)

The uncertainty in seismic ground motion intensity is represented by the dispersion around the median predicted by the GMPE adopted in the seismic ground motion model based on single-event PSHA.

(b)

The uncertainty in tsunami height is adopted from the logic tree used in the single-event PTHA.

As shown above, by assigning numerical values—specifically probability masses—for the joint probability density function representing uncertainties in seismic ground motion and tsunami height, and incorporating them into Equation (3), it is possible to approximately calculate the multi-hazard by linking the seismic hazard and tsunami hazard curves.

The simplified method proposed in this study can be applied when PSHA and PTHA are conducted separately. However, it should be noted that this approach provides only an approximate solution. It is important to recognize that, under the following conditions, (a) dependence on the problem setting related to the characterization of seismic sources and seismic motion, resulting in a low contribution from sources that dominate the superposition hazard assessment results, and (b) multiple sources having comparable levels of contribution, the extent of deviation from the exact solution may fluctuate. An example of the joint probability density function of ground motion intensity and tsunami height is shown in Figure 8. Additionally, Figure 9 shows an example of the multi-hazard curve surface which represents the seismic and tsunami multi-hazard.

5. Development of a Multi-Hazard Fragility Assessment Method

This section presents examples of fragility assessment that address cases where superposition effects must be considered. After identifying the SSCs subject to assessment, the multi-hazard fragility assessment for the superposition of earthquake and tsunami events is conducted in the following steps.

• Determination of damaged parts and damage modes.
  • Investigate the spatial layout, structure, and functions of the SSCs under assessment, including the inundation protection equipment, seismic capacity, tsunami capacity, and tsunami inundation routes, to identify the damaged parts and damage modes of the SSCs.
• Analysis of superposition damage scenario.
  • Investigate the impact of seismic effects from a single hazard (earthquake) on the damaged parts and damage modes of functional systems affected by post-earthquake tsunamis. Furthermore, identify the dependency and envelope relationships between the events and their effects.
• Establishment of a method for quantifying superposition damage probability.
  • Establish a method for quantifying realistic capacity and response under superposition events, which is based on the analysis of damaged parts, damage modes, and superposition damage scenarios.
• Assessment of superposition damage probability.
  • The damage probability is derived from ultimate-strength tests, numerical analysis, and other relevant methods that implement the approach established in the preceding step.

In the seismic-tsunami PRA, two primary types of multi-hazard fragility can be considered:

(a) Same damaged part/same damage mode;

(b) Different damaged parts/different damage modes.

This study presents examples of both fragility evaluation approaches and explains the process of the corresponding assessment method. The assessment process for the outdoor condensate tank (type A) and the seawater pump (type B) is shown below.

5.1. Multi-Hazard Fragility Assessment for the Same Damaged Part and Damage Mode

5.1.1. SSCs Subject to Evaluation

The outdoor condensate tank was selected as the SSC, with assessment type A applied, and the relevant parameters used in the assessment were based on published information [19]. The tank specifications are listed in Table 2, and Figure 10 shows its schematic diagram.

Table 2. Specifications of the condensate tank [19].

Item	Specification
Material (Body plate, Anchor bolt)	SS400
Plate thickness t [mm]	6
Height L1 [mm]	12,000
Liquid level (Height) L2 [mm]	11,680
Radius R [mm]	4400
R/t	733
L1/R	2.73

Table 2. Specifications of the condensate tank [19].

Item	Specification
Material (Body plate, Anchor bolt)	SS400
Plate thickness t [mm]	6
Height L1 [mm]	12,000
Liquid level (Height) L2 [mm]	11,680
Radius R [mm]	4400
R/t	733
L1/R	2.73

Figure 10. Schematic diagram of a condensate tank.

Figure 10. Schematic diagram of a condensate tank.

5.1.2. Determination of Damaged Part and Damage Mode

Table 3. Investigation of the damaged part and damage mode.

Seismic event	Damaged part	(1) Body plate. (2) Anchor bolt.
	Damage mode	(1) Buckling fracture. (2) Shear failure due to seismic motion.
Tsunami event	Damaged part	(1) Body plate. (2) Anchor bolt. (3) Soil.
	Damage mode	(1) Buckling fracture due to wave force. (2) Tensile fracture due to buoyancy. (3) Loss of ground support due to corrosion.
Superposition of seismic events and tsunami events	Damaged part	(1) Body plate. (2) Anchor bolt.
	Damage mode	(1) Buckling fracture. (2) Shear failure due to seismic motion and tensile fracture due to seismic motion and buoyancy. (3) Ground support failure due to seismic and tsunami wave forces and corrosion.
	Adjoint scenario	(1) None. (2) Damage to the anchorage or supporting ground may cause the tank to become a driftage.

shows an example of evaluations of damaged parts and modes for outdoor tanks. For seismic events, the damaged parts are the body and the anchor. The damage modes were identified as body plate buckling and shear failure at the anchor, as shown in Table 3. Tsunami events may include body plate buckling from wave forces, anchor damage from buoyancy, boundary damage from drifting debris, and loss of ground support from scouring. The loads acting on the body plates during earthquakes and tsunamis include accumulated stress from seismic motion, wave force effects, and impacts from drifting objects. For anchor sections and the ground, loads may result from seismic motion, wave forces, accumulated drift impact effects, and ground deformation due to scouring. As shown in Table 3, seismic-tsunami PRA requires consideration of multiple factors. It is important to note that if the support structure is damaged due to an earthquake, tsunami, or their superposition effects, the outdoor tank could become floating debris and potentially damage other SSCs or cause them to lose function.

5.1.3. Analysis of Superposition Damage Scenario

Figure 11 shows an example of an analysis flow for a damage scenario.

The flowchart illustrates the classification of cases in which identified damaged parts are affected by seismic and tsunami forces, resulting in a loss of function. When tank failure is primarily due to anchor bolt damage, the evaluation methods for seismic and tsunami capacities differ depending on whether the stress falls within the elastic or plastic range, as shown in Figure 11. In prior study [19], an ultimate strength test of the condensate tank exemplified in this study was conducted under seismic loading, and the tank’s body plate was identified as the critical damaged part leading to loss of function. Based on the assumption that the same part governs function loss under post-earthquake tsunami load, the following evaluation is conducted.

Figure 11. Damage scenario of the condensate tank.

Figure 11. Damage scenario of the condensate tank.

5.1.4. Establishment of a Method for Quantifying Superposition Damage Probability

This study focuses on providing a method for conducting the multi-hazard fragility assessment for NPPs, where single-hazard seismic PRA and tsunami PRA have already been completed. Therefore, this study assumes that the prior study provides publicly available information relevant to the target plant’s seismic evaluation results. As mentioned earlier, the condensate tanks subject to assessment have undergone ultimate strength tests and the seismic response analyses in prior studies [19]. According to the studies, an ultimate horizontal displacement of 333 mm at the top of the condensate tank under seismic load was determined as the ultimate strength. In this study, it was assumed that the damage caused by the combined effects of earthquakes and tsunamis on condensate tanks was identical to that caused by single-hazard earthquakes or tsunamis. The median realistic capacity was assumed to be the displacement at ultimate strength. The horizontal displacement at the top of the tank, calculated through seismic and tsunami response analyses, was assumed to represent the median value of realistic responses (probability distribution of responses). Figure 12 shows a conceptual diagram of the realistic response and capacity, which is assumed to follow a lognormal distribution. This distribution is characterized by the displacement at the top of the tank due to both seismic motion during an earthquake and wave force during a tsunami.

5.1.5. Assessment of Superposition Damage Probability

(1) Capacity

Table 4 shows the tolerance limit and median capacity of the condensate tank, determined from the previous study [19]. Body plate buckling was assumed to be the dominant failure mode for the condensate tank.

The median capacity under the multi-hazard of earthquake and tsunami was assumed in this study to be the sum of the earthquake-induced and tsunami-induced displacements, with the latter specified as 333 mm for function loss.

Table 4. Tolerance limit and median capacity of the condensate tank.

Type of External Force	Tolerance Limit	Median Capacity (Displacement of the Top of the Tank Roof)
Seismic (Dynamic load)	Buckling of body plate [19]	50 mm [19]
Tsunami (Static load)	Ultimate displacement [19]	333 mm [19]
	Breakage of the body plate due to buckling	720 mm (Based on the breaking strain of SS400 is 17% [19])
Seismic and tsunami (Dynamic load + Static load)	Ultimate displacement [19]	333 mm [19]

Table 4. Tolerance limit and median capacity of the condensate tank.

Type of External Force	Tolerance Limit	Median Capacity (Displacement of the Top of the Tank Roof)
Seismic (Dynamic load)	Buckling of body plate [19]	50 mm [19]
Tsunami (Static load)	Ultimate displacement [19]	333 mm [19]
	Breakage of the body plate due to buckling	720 mm (Based on the breaking strain of SS400 is 17% [19])
Seismic and tsunami (Dynamic load + Static load)	Ultimate displacement [19]	333 mm [19]

(2) Seismic Response Analysis and Tsunami Response Analysis

Numerical data from seismic response analysis could not be obtained from the publicly available literature [19]. Furthermore, to perform tsunami inundation response analysis, a model was developed using publicly available information presented in Figure 13.

The evaluation of superposition damage probability as a function of seismic ground motion and tsunami height requires assessing damage probabilities across the multi-hazards. These analytical cases are defined based on the bin widths of seismic ground motion and tsunami height, as specified in the seismic-tsunami PRA, along with the input ranges presented in Section 2.3.

Figure 13. Seismic response analysis model parameters and geometric features.

Figure 13. Seismic response analysis model parameters and geometric features.

In this study, the seismic response due to dynamic loading and the tsunami response due to static maximum inundation loading were evaluated using the lumped-mass model shown in Figure 13.

A representative ground motion capable of inducing plastic deformation in part of the condensate tank was applied, and the analysis was performed. In the tsunami response analysis, static wave forces up to the height of the condensate tank were calculated in accordance with the Design Code for Seismic and Tsunami Resistance of Nuclear Power Plants (JEAC 4629-2014) [20]. Suppose the maximum inundation depth exceeds the tank’s height. In that case, the tsunami load on the tank is evaluated as the sum of the horizontal static wave force acting on the tank up to its top and the weight of the water above the tank from its top to the maximum inundation depth. The response analysis was conducted using the same model as in the seismic response analysis. Figure 14 illustrates the tsunami wave force evaluation in the tsunami inundation response analysis model.

To illustrate the evaluation process, this study deliberately refrains from specifying input conditions for any particular site or plant. Instead, the analysis is conducted using representative waveforms to ensure general applicability and methodological clarity. Accordingly, in the seismic response analysis, the reference seismic motion level was set to 1.0 (in normalized units). The seismic input was set to induce plastic deformation in part of the condensate tank, and the displacement at the top of the tank roof was calculated using nonlinear time-history analysis. The results of the response analysis are shown in

Table 5. Result of the seismic response analysis.

Seismic Input Level [Times]	Displacement (Absolute Value)	Deformed State
0.2	5.5 mm	Elastic
0.5	13.8 mm	After buckling (Buckling occurred at 12.3 mm)
1.0	27.3 mm	After buckling
1.5	35.9 mm	After buckling
2.0	43.4 mm	After buckling
3.0	79.1 mm	After buckling
3.5	91.1 mm	After buckling

and

Table 6. Result of the tsunami inundation response analysis.

Tsunami Input Level	Displacement (Absolute Value)	Deformed State
12 m	21.5 mm	After buckling
14 m	27.9 mm	After buckling
16 m	62.2 mm	After buckling
17 m	97.1 mm	After buckling
18 m	143.4 mm	After buckling
19 m	202.2 mm	After buckling
20 m	282.0 mm	After buckling

.

(3) Logarithmic Standard Deviation of Realistic Capacity and Realistic Response

The realistic capacity and realistic response to a multi-hazard earthquake and tsunami were assumed to follow a lognormal distribution. The values for the logarithmic standard deviations of the aleatory uncertainties (${\beta }_r$) and epistemic uncertainties (${\beta }_u$) were evaluated based on engineering judgment. Quantifying uncertainty is an important evaluation factor. However, since it could not be obtained from the information referenced in this study, it was determined based on engineering judgment. The evaluation results are shown in

Table 7. The logarithmic standard deviation of uncertainties.

	Seismic	Tsunami	Seismic + Tsunami
Capacity	${\beta }_r$$= 0.32, {\beta }_u$ = 0.32	${\beta }_r$$= 0.24, {\beta }_u$ = 0.24	${\beta }_r$$= 0.24, {\beta }_u$ = 0.24
Response	βr = --- 1, βu = 0.19	${\beta }_r$$= 0.15, {\beta }_u$ = 0.15	${\beta }_r$$= 0.21, {\beta }_u$ = 0.21

¹ The uncertainty from the epicenter to the installation ground is not taken into account because the input seismic motion is assumed to be at the condensate tank installation location.

. These uncertainties are assumed based on engineering judgment, with reference to examples of uncertainty settings in similar components used in seismic PRA [15].

(4) Realistic Response Under the Multi-Hazard of Earthquake and Tsunami

The probability density function of the realistic response for a given value of input A due to an earthquake or tsunami, $f_R(A,x)$, is expressed as a lognormal distribution with median, $R_m\left(A\right)$, and logarithmic standard deviation, ${\beta }_R\left(A\right)$, as follows.

$$f_R\left(A,x\right)={\displaystyle \frac{1}{\sqrt{2\pi }{\beta }_R\left(A\right)·x}}exp\left\{-{\displaystyle \frac{1}{2}}{\left({\displaystyle \frac{ln\left(x/R_m\left(A\right)\right)}{{\beta }_R\left(A\right)}}\right)}^2\right\}$$

(4)

$f_R(A,x)$: Probability density function of realistic response following a lognormal distribution.

$A$: Seismic input (PGA [Gal]) and tsunami input (Tsunami height [m]).

$x$: Parameters representing realistic response values (displacement of the top of the condensate tank roof).

$R_m\left(A\right)$: median of the realistic response.

${\beta }_R\left(A\right)$: logarithmic standard deviation.

As mentioned earlier, this study assumed that the displacement of the top of the condensate tank is evaluated as the combined effect of the earthquake and tsunami. The occurrence probabilities of displacement $x$ due to earthquakes and tsunamis are assumed to be independent events. In addition, the tsunami-induced displacement was assumed to be the difference between the total displacement of an earthquake and tsunami and the seismic-induced displacement. The following equation was applied based on the aforementioned assumptions. The probability function ($P_{S+T}\left(x_{total}\right)$) is an approximation of the PDF of the total displacement at the top of the condensate tank resulting from the combined effects of an earthquake and tsunami. Therefore, the $P_{S+T}\left(x_{total}\right)$ is obtained by the following equation. Here, the sum of the displacement due to the earthquake and tsunami is $x_{total}.$

$$P_{S+T}\left(x_{total}\right)\cong {\int }_0^{x_{total}}{P}_S\left(x\right)\times P_T\left(x_{total}-x\right)dx$$

(5)

$P_S\left(x\right)$: probability density function where the displacement caused by an earthquake is $x$.

$P_T\left(x\right)$: probability density function where the displacement caused by a tsunami is $x$.

$x_{total}$: displacement of the superposition of earthquake and tsunami.

$P_{S+T}\left(x\right)$: probability density function where the displacement caused by the superposition of the impact of the earthquake and tsunami is $x$.

In this study, the probability was evaluated by discretizing the variable $x$ into 1 mm intervals. The probability density function of the realistic response under the multi-hazard of earthquakes and tsunamis is shown in Figure 15.

Figure 15 shows an example of realistic response evaluation at a seismic input level of 3 times and a tsunami height of 18 m. The blue line represents the distribution of realistic responses for a tsunami input with a height of 18 m. The green line represents a realistic response to the superposition effects of seismic and tsunami events. Additionally, the black line in Figure 15 represents a realistic capacity.

(5) Quantification of Superposition Damage Probability

The superposition damage probability, which is a function of the failure probability, is assessed for each tsunami height level using the realistic capacity and response obtained in the previous section, and the resulting damage probability is used to assess the seismic PGA. The damage probability for a tsunami height $H$ given a seismic acceleration is expressed as $F\left(H\right)$. $F\left(H\right)$ is calculated as the conditional probability that the probability density function of the realistic response at the tsunami height $H,$ $f_R(H,x_R)$, exceeds the probability density function of the realistic capacity, $f_S\left(x_R\right),$ as shown in Equation (6). Figure 16 shows an example of the fragility evaluation results under the multi-hazard earthquakes and tsunamis.

$$F\left(H\right)={\int }_0^{\infty }{f}_S\left(x_R\right)\left({\int }_{x_R}^{\infty }{f}_R\left(H,x_R\right)dx\right)d{x}_R$$

(6)

5.2. Multi-Hazard Fragility Assessment for Different Damaged Parts and Damage Modes

In this study, the seawater pump was selected as an example of assessment type (b), in which the damaged part and damage modes during a tsunami event were assumed to differ depending on the presence or absence of seismic effects. The assessment method was developed based on hypothetical structural capacity and response values, without relying on detailed design information.

5.2.1. SSCs Subject to Evaluation

To evaluate superposition damage resulting from degradation of tsunami protection performance caused by preceding seismic effects, a seawater pump was selected as a representative case. The seawater pump is protected by tsunami protection equipment, an inundation protection wall. It should be noted that the equipment evaluated in this study does not reflect the actual specifications, as the primary objective is to demonstrate the evaluation method and its procedural framework.

5.2.2. Determination of Damaged Part and Damage Mode

This study assumes that the damaged parts and damage modes of seawater pumps have been evaluated, as shown in

Table 8. Example of damaged part and damage mode for seismic and tsunami events on the seawater pump.

Seawater pump	Seismic event	Structural damage	Damaged part	(1) Pump mount bolt (2) Anchor bolt
			Damage mode	(1) Tensile fracture due to seismic motion (2) Tensile fracture due to seismic motion
		Functional damage	Damaged part	(1) Pump with an electric motor
			Damage mode	(1) Dynamic functional failure due to seismic motion
	Tsunami event	Functional damage	Damaged part	(1) Pump motor main unit
			Damage mode	(1) Submersion
Tsunami protection equipment (inundation prevention wall)	Seismic event	Structural damage	Damaged part	(1) Plate (2) Anchor bolt (3) Plate connection section
			Damage mode	(1) Bending fracture (2) Tensile fracture due to seismic motion (3) Gap occurrence due to seismic motion
	Tsunami event	Structural damage	Damaged part	(1) Plate (2) Anchor bolt (3) Plate joint section
			Damage mode	(1) Bending fracture due to wave force/floating debris (2) Tensile fracture due to wave force/floating debris (3) Plate joint section destruction due to wave force/floating debris
		Functional damage	Damaged part	(1) Entire unit
			Damage mode (Function failure)	(1) Overflow

. The subsequent discussion is based on these evaluations. For NPPs where seismic and tsunami PRAs have been completed, fragility assessments for the safety-related SSCs have also been conducted. Therefore, the damaged parts and damage modes shown in Table 8 can be assessed by referring to the results of these previously conducted PRAs.

In evaluating seawater pump failure, the pump and associated tsunami protection equipment are treated as an integrated system to assess their combined performance under a superposition event. It should be noted that if the tsunami protection equipment has sufficient seismic capacity, the probabilities of seawater pump damage due to an earthquake or a tsunami can be evaluated independently based on their respective hazard responses.

5.2.3. Analysis of Superposition Damage Scenario

The damage scenarios for the seawater pump, which is installed outdoors and protected by the tsunami protection equipment shown in Figure 17, are as follows. As illustrated in Figure 17a, if the tsunami protection equipment remains intact following an earthquake, the seawater pumps will remain unaffected by tsunami inundation up to the water level below the inundation prevention level. Meanwhile, suppose the tsunami protection equipment loses its inundation protection capability due to the formation of gaps or damage to the part underpinning components caused by seismic motion. In that case, the seawater pump’s tolerance to tsunami-induced inundation (specifically, its allowable inundation depth) will be reduced, as illustrated in Figure 17b.

5.2.4. Establishment of a Method for Quantifying Superposition Damage Probability

Since the seawater pump and tsunami protection equipment are installed under identical ground conditions, the seismic motion can be considered identical for both systems, indicating that their seismic responses are interdependent. Furthermore, since the integrity and damage of tsunami protection equipment are mutually exclusive states, it is difficult to assess the damage probability of seawater pumps using simple calculations as treated seismic and tsunami impacts independently.

Therefore, this study developed a method for estimating the probability of superposition damage through scenario analysis.

The section presents an evaluation example of the seawater pump using the developed method. The framework for the seismic-tsunami PRA developed in this study assumes that a single-hazard PRA for earthquakes and tsunamis has already been conducted. Accordingly, the information presented in Table 9 is assumed to be available. Hypothetical parameter values are assigned in this study to demonstrate the proposed evaluation method. It should be noted that, although actual NPPs may apply different seismic responses between seawater pumps and tsunami protection systems, this evaluation assumes identical seismic responses for both components.

As previously noted, it is necessary to account for event dependency and mutual exclusivity. This section presents the use of a Monte Carlo approach. Figure 18 shows the flowchart for assessing the probability of damage due to earthquakes, tsunamis, or superposition effects.

Table 9. Required parameters for the evaluation of the proposed fragility assessment method.

		Realistic Response and Realistic Capacity	Seawater Pump	Tsunami Protection Equipment
Seismic		Median of R 3: μ	${\mu }_{s,R,sp}$	${\mu }_{s,R,tp}$
		LSD 2 of R 3: σ	${\sigma }_{s,R,sp}$	${\sigma }_{s,R,tp}$
		Median of C 4: μ	${\mu }_{s,C,sp}$	${\mu }_{s,C,tp}$
		LSD 2 of C 4: σ	${\sigma }_{s,C,sp}$	${\sigma }_{s,C,tp}$
Tsunami		Median of R 3: μ	${\mu }_{T,R,sp}$
		LSD 2 of R 3: σ	${\sigma }_{T,R,sp}$
	Integrity of TPE 1 is maintained	Median of C 4: μ	${\mu }_{T,C,sp}$
		LSD 2 of C 4: σ	${\sigma }_{T,C,sp}$
	TPE 1 is damaged	Median of C 4: μ	${\mu }_{T,C^{\prime },sp}$
		LSD 2 of C 4: σ	${\sigma }_{T,C^{\prime },sp}$

¹ TPE: tsunami protection equipment; ² LSD: logarithmic standard deviation; ³ R: realistic response; ⁴ C: realistic capacity.

Table 9. Required parameters for the evaluation of the proposed fragility assessment method.

		Realistic Response and Realistic Capacity	Seawater Pump	Tsunami Protection Equipment
Seismic		Median of R 3: μ	${\mu }_{s,R,sp}$	${\mu }_{s,R,tp}$
		LSD 2 of R 3: σ	${\sigma }_{s,R,sp}$	${\sigma }_{s,R,tp}$
		Median of C 4: μ	${\mu }_{s,C,sp}$	${\mu }_{s,C,tp}$
		LSD 2 of C 4: σ	${\sigma }_{s,C,sp}$	${\sigma }_{s,C,tp}$
Tsunami		Median of R 3: μ	${\mu }_{T,R,sp}$
		LSD 2 of R 3: σ	${\sigma }_{T,R,sp}$
	Integrity of TPE 1 is maintained	Median of C 4: μ	${\mu }_{T,C,sp}$
		LSD 2 of C 4: σ	${\sigma }_{T,C,sp}$
	TPE 1 is damaged	Median of C 4: μ	${\mu }_{T,C^{\prime },sp}$
		LSD 2 of C 4: σ	${\sigma }_{T,C^{\prime },sp}$

¹ TPE: tsunami protection equipment; ² LSD: logarithmic standard deviation; ³ R: realistic response; ⁴ C: realistic capacity.

Figure 18. Damage probability assessment flow for seismic, tsunamis, or superposition effects.

Figure 18. Damage probability assessment flow for seismic, tsunamis, or superposition effects.

The first step is to determine the seismic response. In this assessment, identical seismic responses are assumed for both the seawater pump and the tsunami protection equipment. Next, determine the capacity of both the seawater pump and the tsunami protection equipment. For each component, damage is assumed to occur when the seismic or tsunami response exceeds its corresponding capacity, i.e., when response ≥ capacity. If the seawater pump is determined to be damaged at this stage, the trial is terminated.

If the integrity of the seawater pump is confirmed, the next step is to assess the damage caused by the tsunami. This assessment begins with the determination of the tsunami response. If the tsunami protection equipment is not damaged by seismic motion, its capacity is used in an intact condition. If it is damaged, the capacity in the damaged condition is used. Damage is considered to occur when the response exceeds the evaluated capacity, i.e., when response ≥ capacity. The above procedure is repeated until the assessed damage probability converges. Then, the final damage probability is calculated by dividing the number of trials resulting in damage by the total number of trials.

5.2.5. Assessment of Superposition Damage Probability

In this study, the damage probability due to seismic, tsunami, and superposition effects was assessed based on 100,000 trials. The realistic capacities are shown in Table 10. For the seismic response of seawater pumps and tsunami protection equipment, values ranging from 0.5 to 5 times the median reference response acceleration were used as linear scaling factors. For the tsunami response, the tsunami height at the installation site was assigned a median value within the range of 7 m to 14 m. A logarithmic standard deviation of 0.3 was adopted for the realistic response, both for seismic and tsunami events. The results obtained by implementing the proposed fragility assessment method are presented in Figure 19. As the intensity of seismic motion and tsunami height increase, the probability of structural damage correspondingly rises, thereby confirming the anticipated trend associated with multi-hazard fragility.

Table 10. Parameters for realistic capacity for assessment.

		Realistic Capacity	Seawater Pump	Tsunami Protection Equipment
Seismic		$\mathrm{Median}: \mu$	1600 [Gal]	1200 [Gal]
		LSD 2: σ	0.1	0.1
Tsunami	Integrity of TPE 1 is maintained	Median: μ	12 [m]
		LSD 2: σ	0.15
	TPE 1 is damaged	Median: μ	8 [m]
		LSD 2: σ	0.15

¹ TPE: tsunami protection equipment, ² LSD: logarithmic standard deviation.

Table 10. Parameters for realistic capacity for assessment.

		Realistic Capacity	Seawater Pump	Tsunami Protection Equipment
Seismic		$\mathrm{Median}: \mu$	1600 [Gal]	1200 [Gal]
		LSD 2: σ	0.1	0.1
Tsunami	Integrity of TPE 1 is maintained	Median: μ	12 [m]
		LSD 2: σ	0.15
	TPE 1 is damaged	Median: μ	8 [m]
		LSD 2: σ	0.15

¹ TPE: tsunami protection equipment, ² LSD: logarithmic standard deviation.

Figure 19. Example of the fragility evaluation result of the seawater pump.

Figure 19. Example of the fragility evaluation result of the seawater pump.

The fragility assessment results, as presented in Figure 16 and Figure 19, are used as input parameters to determine the branching probabilities of IEs and the basic events within the FT model.

6. Conclusions

This study developed a seismic-tsunami PRA method that emphasizes practical applicability. It was developed with a focus on obtaining insights into multi-hazard risks for NPPs, without incurring excessive resources for risk assessment. The developed method enables the assessment of seismic-tsunami PRA in cases where seismic and tsunami PRA have been implemented at NPPs by applying an expanded approach based on internationally employed external event PRA methods. In this study, a multi-hazard PRA framework was developed to evaluate risks applicable to NPPs arising from the superposition of the earthquake and tsunami events. This study clarifies the relationship between multi-hazard and single-hazard assessments of earthquakes and tsunamis. Furthermore, it presents an approach to defining the scope of risk assessment for the superposition of earthquake and tsunami based on the results of a single-hazard PRA conducted for both seismic and tsunami hazards.

Section 2 presented a framework for seismic-tsunami PRAs. This framework identified assessment factors that are not considered in single-hazard PRAs but should be taken into account in the context of superposition events, and it also presents a fundamental equation for CDF due to superposition events under earthquakes and tsunamis. Furthermore, it emphasized the importance of identifying scenarios in which safety-related SSCs or mitigation SSCs may be damaged or degraded due to the impact of an earthquake on tsunami protection equipment that is not accounted for in a single-hazard PRA. In addition, it highlighted the need to consider the dependency between seismic and tsunami hazards, which may contribute to the loss of these functions. To enhance the clarity of risk assessments that address these perspectives, it was proposed that scenario analysis under multi-hazard conditions is crucial before each evaluation that constitutes a level 1 PRA. Section 3 provided the analytical procedure for the superposition scenario analysis developed in this study and organized general superposition events that can serve as references during scenario analysis for actual plant evaluations. Section 4 provided a simplified method for multi-hazard assessment using data from single-event PSHA and PTHAs that were developed in this study. Furthermore, Section 5 proposed assessment steps for multi-hazard fragility of earthquakes and tsunamis, clarified the relationship between superposition effects and damaged parts and damage modes, and presented evaluation examples.

The assessment process for superposition scenarios, which plays a critical role in the evaluation, is designed to be broadly applicable in practical implementations. It should be noted that, in actual plant evaluations, additional scenario considerations specific to the plant (e.g., site conditions and reactor type) are necessary. This study does not incorporate HRA into the proposed framework of risk assessment under the multi-hazard of earthquake and tsunami. However, for practical applications involving actual plants, HRA specialists must be involved in analyzing superposition scenarios. In particular, when addressing post-earthquake tsunami events, a key challenge lies in identifying human error events that may not be captured in single-hazard PRAs. Moving forward, these factors could be quantified, for example, by using the HRA guidelines developed by the NRRC [21].

The simplified multi-hazard assessment method developed in this study can be broadly applied to actual plants where seismic PRA and tsunami PRA have been conducted. For plants where the multi-hazard risks are dominant or where site-specific tsunami characteristics are significant, the application of more detailed methodologies may be considered. Furthermore, the proposed multi-hazard assessment method may serve as a practical tool for hazard-based screening to determine whether a seismic-tsunami PRA is necessary for individual plants.

A multi-hazard fragility assessment method for the superposition of earthquake and tsunami events was developed in this study. It focused on low-resource evaluation using data from single-hazard seismic PRA and single-hazard tsunami PRAs. Regarding the quantification of realistic capacity and realistic response for superposition damage probability, prior studies have conducted time-history analyses in which tsunami loads were applied after seismic loads using methods such as the finite element method (FEM). For SSCs identified as risk-dominant in the simplified assessment, it is expected that a detailed analysis will obtain more elaborate evaluation results. Also, this study evaluates the uncertainty in realistic capacity and realistic response related to the probability of superposition damage solely through engineering judgment. To address the challenges in quantifying these uncertainties, there is a need to expand the body of commonly applicable knowledge through structural experiments, numerical analyses, and other approaches. However, further refinement of uncertainty is required when the SSCs under evaluation have a dominant or significant impact on plant risk. Therefore, it is essential to first assess the influence of uncertainty through a sensitivity analysis of the values set based on existing knowledge and engineering judgment.

The framework and assessment method developed in this study covers the scope of hazard assessment, fragility assessment, and accident sequence assessment required in addition to single-event PRA. They serve as a technical foundation for PRA analysts and researchers conducting model plant studies.

In the future, the seismic-tsunami PRA method is expected to mature to a practical level through iterative model plant studies using actual plant data, based on the findings of this study.