Seismic Probabilistic Risk Assessment of a Nuclear Power Plant

Figure 7. Uniform Hazard Spectrum and (a) the response spectra of 11 scaled ground motion b) median spectrum of the 11 scaled SGSM ground motion (Huang et al., 2011b).

Figure 8. Definition of accelerograms (Medel-Vera and Ji, 2016)

Figure 9. Scaling ground motions for the time-based assessment of the NPP structure (Huang et al., 2008).

Figure 10. Distributions of responses in demand parameters matrix (Shen et al., 2014).

Table of Equations

Equation 1: Design Response Spectrum…………………………………………………………………9

Equation 2: Design Factor……………………………………………………………………….………9

Equation 3: Slope of seismic hazard……………………………………………………………..…..…9

Equation 4: Probability of unacceptable performance………………………………………………….14

Equation 5: Annual frequency of unacceptable performance………………………………………….14

The unfortunate event of Fukushima Daiichi nuclear-power plant accident in 2011 boosted the need for assessing the seismic risk in-order to determine the unacceptable performance of the component of nuclear power plant (such as core melt, radiation release, property damage etc.). This was the main reason which heavily impacted the expansion of the Nuclear Industry in the UK. Approved methodologies for the investigation of seismic risk by NUREG-1407 are Seismic Probabilistic Risk Assessment (SPRA) and Seismic Margin Assessment (SMA).(Huang et al. 2011a). In the late 1970s, SPRA was most commonly used methodology by the nuclear power plant industry for the effective evaluation of seismic risk of an existing Nuclear Power Plant (NPP). Seismic Probabilistic Risk Assessment is defined as a “systematic process to evaluate the safety of a nuclear reactor”. This document will mainly focus on SPRA methodologies which are used by research experts for seismic probabilities risk assessment of the nuclear plant. American nuclear regulator were the first to publish a guide for using the methodology for performing SPRA, NUREG/CR-2300 (USNRC, 1983). It mentioned about the two methods of SPRA namely Zion and Seismic Safety Margin (SSM). Initially, the Zion method was experimented for the probabilistic risk assessment of the Oyster Creek which was later modified for estimating the seismic risk assessment of the Zion Plant. The SSM method was first introduced in an NRC-funded project, that was undertaken at Lawrence Livermore National Laboratory.

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1.2 Scope

The project aims at performing a probabilistic risk assessment to determine the probability of unacceptable performance of a nuclear reactor in a hypothetical rock site in UK. The nuclear power plant site selected for analysis in this project is Sizewell B, Suffolk, East England. In this project numerical modelling analysis will be carried out using OpenSees and MATLAB.

2. Literature Review

2.1 Conventional Method of SPRA for Nuclear Power Plant

Four simplified steps for conducting this method are: (i) seismic hazard analysis; (ii) component fragility evaluation; (iii) plant-system and accident-sequence analysis; and (iv) consequence analysis (Huang et al. 2011a).

Figure 1. SPRA for Nuclear Power Plant (Huang and Whittaker, 2014)

Huang and Whittaker (2014) suggested the following steps for conventional SPRA of NPP’s:

Step 1: Illustrates the characterisation of the maximum frequencies for varied intensity of earthquake intensities effecting on the particular NPP.

Step 2: Generate a sets of fragility curves for parts of Nuclear reactor structure.

Step 3: Determining all the probable sequence of failure event by developing event trees and fault tress.

Step 4: Estimating the probability of occurrence of failure event for the considered earthquake intensity (Figure 1(c)). This can be achieved by computation of fragility curves for the failure events with the use of component fragility curve from Step 2 (Figure 1(a)) and the sequence of accident determined from the Step 3 (Figure 1(b)).

Step 5: Finally, development of seismic fragility curves for structural and non-structural member of NPP. The distribution of frequency of failure event is computed by integrating hazard curves and fragility curves obtained in Step 1over the range of earthquake intensity used in the analysis(Figure 1(e)). The failure event frequency is utilised for developing the annual frequency of exceedance against the damage (i.e. human loss, financial loss) (Figure 1(f)).

2.2 Huang et al. Methodology

Huang et al. (2011a; 2011b) presented a SPRA methodology that differs from the conventional method in such a way that it uses the analysis of nonlinear response history to estimate response of each parts of NPP structure instead of using fragility curves. Floor spectral acceleration and story drift are the two main structural response parameters whose functions will deliver the seismic fragility curves.

Huang et al.(2011a) projected following steps for a new approach of SPRA:

Figure 2. Steps involved in Huang et al.(2011a) Methodology for SPRA

Step 1: Development of fragility curves for the parts of the NPP structure.

Step 2: Characterization of the seismic hazard

Step 3: Analysis of nonlinear response-history using the ground motions acquired from Step 2 for estimating the deformations in structural system (primary) as well as to estimate the forces, displacement and acceleration which will aid as demands on the non-structural components (secondary) and systems of the NPP’s.

Step 4: Assessment of damage caused to the varied parts of the reactor structure and systems with the use of fragility curves produced in Step 1 and demands computed in the Step 3.

Step 5: Optimization of the seismic risk using the results procured from the step 4 and the accident sequence developed in Step 1.

2.2.1 Sample Nuclear Reactor (Huang et al. 2008)

Figure 3. represents a sectional view demonstrating different components of nuclear power plant considered for the analysis proposed by Huang et al. (2008). The lumped mass model has been widely used for the analysis. Figure 4, comprises of two stick models: (a) External (containment) structure (b) Internal structure. Both the stick models shares the same base and are structurally independent. The calculation of the mechanical property of the elements involves the use of 3D model of the reactor building. The height of external and internal structure in Figure 4 is 59.5 m and 39 m, respectively along with a thickness of 1.2 m for the wall of the containment structure (Huang et al. 2008). The period of first mode for both external and internal structure is 0.2 s and 0.14 s respectively. The total weight (W) of the structure is considered as 75,000 tons. Huang et al.(2011b), presented a study which focused on the seismic assessment of secondary structure of the reactor building which may result in effective cost saving, since the cost of design, analysis, testing, regulatory approval and construction of secondary structure is less as compared to that of NPP structure. Supports are provided at a specific height for holding the internal structure to secondary system (as shown in figure 3, nodes 201, 1006, 1009, 215 and 216).

Figure 3. Sectional view of Containment Structure (Huang et al., 2008)

First mode of stick model in SAP2000 b. Stick model of internal structure

Figure 4. Lumped mass model (Huang et al., 2008)

2.2.2 Plant System and Accident-Sequence Analysis

Figure 5, illustrates a sample event and fault trees proposed by smith et al. (1981) which is used to explain the system analysis of the plant and accident-sequence analysis in this section. The research of Huang et al.(2011a), emphasized on discovering frequencies of occurrence of failure events. Investigation of earthquake induced initiating events which might lead to radiation release and core melt, plays a key role for the Plant-system and accident-sequence analysis. The failure will not be caused by an initiating event as it will trigger the mitigation and safety measurements in the reactor building. While computing the frequency of the failure event, all the possible sequences are required to be considered. This could be successfully achieved by the use of event trees for classifying all the possible accident sequence.

Yawson and Lombardi, (2018) emphasized on the cause of unacceptable performance due to the failure of any secondary components which are comprised inside the internal structure of the power plant (i.e. reactor assembly, feeders & feeder heads, heat transport system, steam generator and maintenance crane). The NPP structures are designed in order to resist the massive internal and external pressure, therefore the inclusion of secondary structure is effective since the NPP structures are not designed to withstand the seismic effects. The structural response parameters(such as spectral acceleration, peak story drift and floor acceleration) are used as an input to develop the seismic fragility of curve of each which help in the identification of the damage status of the component.

The research conducted by Klügel, (2009) emphasised on the separation of the dispersion in fragility curves into for improving the quality of SPRA(Huang et al 2011a). On the other hand, Kennedy (1999) proposed that it is unnecessary to separate the dispersion of fragility curves as it would not only intensify the complexity while computing the fragility curves also would not contribute towards the accuracy in estimation of the seismic risk. The single mean fragility curve is computed by a median capacity and a logarithmic standard deviation . The combination of mean hazard curve and single mean fragility are used for the computation of seismic risk.

2.2.2.1 Event Trees

Event trees delivers a simplified output for investigation of varied outcomes of an initiating events. Figure 3, illustrates a sample event tree, which comprises of an initiating event and a failure event. The initialisation of accident sequences by the initiating events may affect the three safety systems namely A,B and C.

Figure 5. Sample event and fault trees (Smith et al., 1981).

Figure 5(a) shows a hierarchical order of the sample event and fault trees, where, all the cases are branched excluding the initialising event. The upper division of the branches represents the success of the safety systems, whereas, the lower division of the branches represents the failure in safety systems.

There are six sequences constituted in the event tree. The sequence designation column presents the probability of occurrence of each events along with an assumption that all the events are independent and the probability of occurrence of each event ( , and ) is known. Identification of the sequence of failure event is dependent on the success or failure of each safety system in each sequence. Finally, probability of failure event can be estimated by combining all the results from initiating events.

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2.2.2.2 Fault Trees

Fault trees method, estimates the values of , and for above computation of probability of the failure event in the previous section 2.2.2.1. The computation of probability of the events can be achieved by developing a fault tree for each of the events in the event tree. Figure 5(b), demonstrates an example of a fault tree for System A where an “AND” gate denotes the failure of system above the gate if both the system below it fails and an “OR” gate denotes the failure of system above the gate if any of the system below it fails.

2.2.3 Characterization of Seismic Hazard

In this step, mean seismic hazard curve plays a key role in estimation of the annual frequency of failure event which is used for establishing the mean annual frequency of exceedance (MAFE).

The design and analysis of nuclear structure on the basis of characterisation of seismic hazard risk was first executed in the DOE Guidelines set by United states “Natural phenomena hazards design and evaluation criteria for Department of Energy facilities”(DOE, 1994). As per the ASCE standards 43-05, the design response spectrum (DRS) is estimated by multiplying the uniform hazard spectrum (UHS) with a design factor, DF:

$DRS = DF x UHS$

(1)

DF = max (1.0,0.6 ${(A_{R})}^{α}$

) (2)

$A_{R} = \frac{{SA}_{0.1 H_{D}}}{{SA}_{H_{D}}}$

(3)

Where, UHS	–	probabilistic seismic hazard analysis for specified annual frequency of exceedance, $H_{D}$
$α$	–	A parameter depending on Seismic Design Category
$A_{R}$	–	Slope of seismic hazard curve
${SA}_{0.1 H_{D}}$ and ${SA}_{H_{D}}$	–	5%-damped spectral accelerations corresponding to annual frequencies of exceedance of 0.1 HD and HD, respectively.

In 2006, Baker and Cornell (2006) proposed a theory that uses horizontal ground motion for the analysis of structure of NPP. Recent researches explains the use of conditional spectrum for dissemination of spectral demand from the mean spectrum.(see NEHRP Consultant Joint Venture, 2011 for detailed methodology and tools required for selection and scaling of ground motion.) Huang et al., (2011a 2011b) presented a study which demonstrated the use of uniform hazard spectrum as the criteria for the selection and scaling of ground motion. Yawson and Lombardi (2018), stated the importance for consideration of multiple seismic hazard (such as liquefaction, surface rupture, tsunami runup) in order to perform effective assessment of seismic risk assessment of NPP’s. Their study emphasized on the earthquake-induced ground shaking which causes damage to the NPP’s. There are several approaches for estimating ground shaking effects, namely: (i) intensity-based approach. (ii) scenario-based approach. (iii) time-based approach. Medel-Vera and Ji, (2016a, 2016b) proposed a study which emphasize on the elimination of GMPE and scaling procedures for estimation of suitable accelerograms. It also eliminates the use Monte-Carlo-type algorithm for estimating the damage state of NPP as the structural responses are directly calculated.

Figure 6. Approach for estimation of ground shaking effects

2.2.3.1 Intensity-based Approach

Intensity-based approach includes a single reference spectrum to play a significant role in the estimation of an earthquake shaking intensity. Scaling of either sets of accelerogram or single spectral acceleration of a reference spectrum act as an input for the estimation of ground shaking intensity (Yawson and Lombardi, 2018) .

(a) (b)

Figure 7. Uniform Hazard Spectrum and (a) the response spectra of 11 scaled ground motion b) median spectrum of the 11 scaled SGSM ground motion (Huang et al., 2011b).

Huang et al.(2011b) presented a methodology which uses intensity-based approach for estimation of ground shaking hazards. Figure 8, represents (a) Uniform risk spectrum/Uniform hazard spectrum developed using the methodology presented in ASCE 43-05 (ASCE 2005) and the response of 11 scaled ground motion which are developed by using “Strong Ground Motion Simulations (SGMS)” . In this graph, the thick black lines represents uniform risk motion and the thin grey lines represents the ground motions generated by SGMS, (b) Uniform risk spectrum and the median of SGMS motions. Both the graphs are further used for the response-history analysis.

2.2.3.2 Scenario-based Approach

In this approach, it is efficient to identify the single scenario which will cause massive damage to the NPP. This scenario can be estimated by de-aggregation of the hazard curve, as in (Medel Vera and Ji,(2016)). Further, estimation of spectral shape is achieved by computing ad-hoc Ground motion prediction equations (GMPE) and this spectral shape are used to scale the available accelerogram.

A detailed study explaining the use of scenario-based approach for computing the spectral acceleration of 11 accelerogram, that are scaled for its corresponding GMPE, was carried out by Medel-Vera and Ji, (2016b), and the definition of accelerograms for the same are demonstrated in Figure 8.

Figure 8. Definition of accelerograms (Medel-Vera and Ji, 2016)

2.2.3.3 Time-based Approach

Time-based Approach involves computation of series of intensity-based approaches. (Huang et al., 2008) All the earthquake scenarios are considered in relation to magnitude and location as well as ground motion produced by each scenario at the site for estimating the ground-shaking hazard by the use of probabilistic seismic hazard analysis.(Yawson and Lombardi, 2018). Firstly, it is essential to compute the mean hazard curve of the NPP which will be divided into 8 equal interval as shown in Figure 10. Thereafter, target intensity is denoted by the midpoint of each interval, for which intensity-based analyses is carried out. Finally, accelerograms are scaled using varied scaling methods.

a. Computation of target spectral ordinates b. Response spectra of the ground motions

Figure 9. Scaling ground motions for the time-based assessment of the NPP structure (Huang et al., 2008).

2.2.4 Simulation of Structural Responses

Simulation of structural responses can be achieved by utilizing the ground motion in the previous section to compute nonlinear response-history analysis. Each nonlinear response history analysis perform in this section will provide a value for each response parameter considered for computation of component fragility curve in section 2.2.2, and therefore empower the development of a vector of demand parameters. This simulation will generate demand-parameter matrix for every sets of ground motion estimated in the section 2.2.3. The number of columns in demand-parameter matrix is directly proportional to the sets of ground motion. The quantity of rows in this matrix are similar to the product of total numerical model and the total sets of ground motion.

The ATC-58 Guidelines (ATC, 2012) published a methodology, which was originally stated in Yang et al. (2009), that uses statistical manipulation of structural analyses for computing varied number of simulation (i.e., generating rows to a new demand-parameter matrix) . Shen et al. (2014) proposed a study that demonstrated the use of the methodology mentioned in Yang et al. (2009) and ATC Guidelines (ATC, 2012) for increasing the number of rows in the demand-parameter matrix from 20 to 5000. Figure 10, illustrates the simulations of structural responses conducted by Shen et al. (2014). It demonstrates the response distribution from 20 x 34 matrix to 50,000 x 34 matrix for RHR operated valves and RHR piping which are generated as per Yang et al. Generation of the values per the Yang et al. makes no effect on magnitude and the relationship in the responses acquired from the response-history analysis. The 20 solid circles indicate results for response history analysis and red plus sign indicates the results obtained from methodology of Yang et al. (2009).

Figure 10. Distributions of responses in demand parameters matrix (Shen et al., 2014).

In general, the use of actual accelerogram data as the input for time-history should only be considered for the areas with occurrence of strong ground motions. Instead it is advisable to use synthetic accelerogram (Medel-Vera and Ji, 2016b) or the data from the other regions with strong ground motion. Yawson and Lombardi, (2018) strongly recommend to use real accelerogram for more accurate analysis.

2.2.5 Damage Assessment of NPP Component

Damage assessment of structural and non-structural component uses the data from component fragility curve along with response history data from the analysis conducted in section 2.2.4. A new row vector of response quantities is created in demand-parameter matrix for each analysis conducted in section 2.2.3, which is further utilized as demands to the components of the NPP. Thereafter, damage is estimated for the demands produced by the analysis with the use of component fragility curve previously generated for structural and non-structural component of NPP. Huang et al. (20011a, 2011b) proposed two damage possibility namely: failed or passed. The component is said to be passed if it functions effectively during and after the occurrence of earthquake and it does not leads to the activation of unfortunate events. The component fails if it is unable to function effectively or it activates the occurrence of unacceptable performance. The operational status of a NPP component can be evaluated by a random test. This includes generation of random number between 0 and 1 through a uniform and relating it with the failure probability. The component is evaluated as pass if the random number is greater than the failure probability; else, the component is evaluated as failed.

2.2.5 Computation of risk

The Last Step includes estimation of probability of unacceptable performance at a particular intensity of ground motion(Huang et al., 2011a). $P_{UP} (S_{a, i})$

is largely affected if the capacity of the component are wider than the distribution range of response demand and vice versa. Following is the equation proposed by Huang et al.,(2011a) :

$P_{UP}$

= $\frac{n_{UP}}{n_{all}}$

(4)

$λ_{UP} = \sum_{i}^{8} P_{UP} (S_{a, i}) . ∆ λ_{H, i}$

(5)

Where, $P_{UP}$	–	Probability of unacceptable performance
$n_{UP}$	–	Number of rows related with unacceptable performance
$n_{all}$	–	Total number of rows in demand parameter matrix
$λ_{UP}$	–	Annual frequency of unacceptable performance
$S_{a, i}$	–	Mean spectral acceleration
$∆ λ_{H, i}$	–	Mean Annual frequency of core melt

3. Conclusion

This documents demonstrates the review of different methodology used for seismic probabilistic risk assessment of a nuclear power plant. A detailed review on widely used methodology in industries : conventional method and Huang et al. (2011a ,2011b) methodology for SPRA of NPP is presented in this document. The main aim of SPRA is to compute the recurrence of event of unsatisfactory functioning of a NPP structure under seismic effect. The new Huang et al. (2011a,2011b) methodology uses non-linear response history analysis and structural response-based fragility curves. In this method, the fragility curves are established from the structural response parameters (such as spectral floor acceleration) instead of using the ground motion intensity as used in conventional method. The use of structural responses is greatly emphasised as the damage cause to NPP components is majorly due to the structural responses than the ground motions. Basically, there are three approaches for performing this methodology namely: (i) intensity based approach (ii) scenario-based approach (iii) time-based approach. In intensity-based and scenario-based approach , the outcome is the probability of unsatisfactory performance of the NPP structure under a specified shaking intensity and a single scenario which is the main cause for the damage of a NPP structure, respectively. On the other hand time-based approach, the annual frequency of probability of unacceptable performance of NPP structure is the final products. Medel-Vera and Ji (2016) proposed a methodology based on direct stochastic simulation of seismic input which focuses on the elimination of GMPE and Scaling /matching procedures for the estimation of sets of accelerogram as well it eliminate the use of Monte Carlo-type algorithm for the simulation of damage status of the NPP structure.

3.1 Research Gaps:

For SPRA of NPP, it is a common practise to use simplified model of a sample nuclear reactor since the component data of a particular nuclear power plant are confidential. However the detailed modelling of NPP structure may result in acquisition of the more accurate and realistic analysis as each component of nuclear reactor is important for the assessment. Very few research focuses on the soil-structure interaction analysis in SPRA of NPP, it is of great interest to explore the outcomes of the probability of unacceptable performance by inclusion of foundation along with the NPP Structure.

3.2 Research Questions:

What is the impact of using detailed model of NPP structure on the probability of unacceptable performance?
Is the use of synthetic accelerograms suitable for effective study of SPRA of NPP?
What would be the impact on the SPRA of NPP with the inclusion of the foundation in the sample NPP model?
Comparison of results obtained from intensity-based, scenario-based and time-based assessment for characterising seismic hazard ?

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