Consideration of safety margin of safety-related ssc for implementation of the defence in depth concept for seismic risk

Division IX (include assigned division number from I to X)

CONSIDERATION OF SEISMIC MARGIN OF SAFETY-RELATED SSC

FOR IMPLEMENTATION OF DIFENCE IN DEPTH CONCEPT FOR

SEISMIC SAFETY

Tatsuya Itoi1

1 _{Associate Professor, School of Engineering, The University of Tokyo, Japan}

ABSTRACT

In this paper, implementation of defence-in-depth concept to seismic design of nuclear power plant and nuclear-related facilities is discussed. A framework that combines diversity in the dynamic characteristics of items and additional seismic margin to items important for mitigating the consequences of accidents is utilized. The proposed framework is useful, e.g., when an emergency operations facility is additionally designed next to a reactor building. Whether a base-isolated structure is more effective than an earthquake-resistant structure for this emergency operations facility or not is discussed on basis of the proposed framework.

INTRODUCTION

Defence in depth is considered to be the primary mean to prevent and mitigate the consequences of accidents by implementing through the combination of a number of consecutive and independent levels of protection. The concept of the defence in depth was originally developed for accidents due to internal events. Therefore, there appears to be no standard approach to achieve defence in depth for seismic risk. Under seismic excitation, it is fundamentally impossible and unrealistic to assume that each level of protection for defence in depth is completely independent from each other, which is different from accidents of internal origins. It is because items used for each level of defence are excited by earthquake simultaneously and could lead to simultaneous malfunction or damage, i.e., common cause failure. Therefore, it is realistic to consider that the degree of dependence between each level of defence should be reduced as far as practicable.

For that purpose, this paper proposes one possible framework to implement the defence in depth concept for seismic risk. Among the possible methodologies, this paper discusses a framework in terms of the required amount of safety margin for different types of safety-related SSCs. A proposed method specifies the required safety margin to each item by combining regional seismicity and information about vulnerability of a plant, then identifies most probable source characteristics as well as ground motion at a nuclear power plant that corresponds to most probable accident scenario.

IMPLEMENTATION OF DEFENCE IN DEPTH FOR SEISMIC RISK

The strategy for combination of items important for safety needs to be developed by combining diversity, physical separation and functional independence. Especially, implementation of diversity to seismic excitation needs to be discussed further. In the seismic design of nuclear power plants, diversity is to be provided through differences in location of items (e.g., plan layout or elevation) and by different dynamic characteristics between items (e.g., structural type, natural period and damping characteristics). It is, however, not always possible to introduce diversity, because of the limitation due to the characteristics of item. Providing an additional seismic margin is considered to be effective as a means of supplementing for such cases. Appropriate combination of seismic margin and diversity needs to be discussed in a risk-informed manner to implement the defence in depth concept to seismic design for nuclear power plants. In following chapters, a method to assign additional seismic margin required to each item depending on the characteristics of diversity (Itoi et al., 2017) is utilized.

ADDITIONAL SEISMIC MARGIN REQUIRED FOR ITEMS FOR MITIGATING THE CONSEQUENCES OF ACCIDENTS

A system which contains two items (items A and B) and whose items are located at the same place is assumed for a simplified case. It is assumed that an accidental condition occurs if item A fails. Item B is then used to mitigate the consequences of the accident. In such case, item B should be designed based on a different concept from that of item A, because a role of item B is different from that of item A as discussed above.

Hereafter, item A is assumed to be a single-degree-of-freedom-system that has a natural period 𝑇𝑇_𝐴𝐴. Item B is also assumed to be a single-degree-of-freedom system with a natural period 𝑇𝑇_𝐵𝐵. 𝑇𝑇_𝐵𝐵 can be different from

𝑇𝑇𝐴𝐴. One of typical examples related to this simplified model is the case that an emergency operations facility

additionally designed next to a reactor building. Whether a base-isolated structure is better than an earthquake-resistant structure for this emergency operations facility or not should be discussed not only by the performance of a single facility to seismic excitation but also based on the performance of nuclear power plant during the accidental condition. The proposed framework can be used to discuss the latter issue.

Probabilistic seismic hazard analysis is usually used to determine design ground motion. An example of the annual exceedance probability of design ground motion required for nuclear power plants is usually around 10-4 _{or smaller. Statistical equations, i.e., ground motion prediction equations (GMPEs), are conventionally}

used to predict ground motions. 5% damped acceleration response spectra are conveniently used to characterise a variety of frequency contents in ground motions. A GMPE for 5% damped spectral acceleration that are used in this study was initially developed for crustal earthquakes in Japan by Itoi et al. (2015). The functional form of the equation is as follows:

log10𝑆𝑆𝐴𝐴(𝑇𝑇) = 𝑎𝑎(𝑇𝑇) + 𝑏𝑏(𝑇𝑇)𝑀𝑀𝑊𝑊− 𝑐𝑐(𝑇𝑇)𝑋𝑋 − log10(𝑋𝑋 + 𝑑𝑑(𝑇𝑇) ∙ 100.5𝑀𝑀𝑊𝑊)

− 𝑒𝑒(𝑇𝑇)(log10𝑉𝑉𝑆𝑆30)2+ 𝑓𝑓(𝑇𝑇)log10𝑉𝑉𝑆𝑆30

+ 𝑔𝑔(𝑇𝑇)log10�max�min(𝑍𝑍1500, ℎ(𝑇𝑇) ), 𝑘𝑘(𝑇𝑇)��

+ 𝜎𝜎𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼(𝑇𝑇)𝐸𝐸𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼(𝑇𝑇) + 𝜎𝜎𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴(𝑇𝑇)𝐸𝐸𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴(𝑇𝑇)

(1)

where, 𝑆𝑆_𝑎𝑎(𝑇𝑇) is the 5% damped spectral acceleration at period 𝑇𝑇. 𝑀𝑀_𝑊𝑊, 𝑋𝑋(km), 𝑉𝑉_𝑆𝑆30(m/s), and 𝑍𝑍₁₅₀₀(m) are the moment magnitude, the shortest distance from fault to site, the 30 m average shear wave velocity, and the depth to shear wave velocity which is equal to 1500 m/s, respectively. 𝐸𝐸_{𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼}(𝑇𝑇) and 𝐸𝐸_{𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴}(𝑇𝑇) are standard normal variables for inter-event and intra-event residuals respectively, while 𝜎𝜎_{𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼}(𝑇𝑇) and

The most probable level of spectral acceleration 𝑠𝑠_𝐴𝐴∗ at 𝑇𝑇 = 𝑇𝑇_𝐴𝐴 for accident occurrence is obtained using the first order reliability method (FORM) (Rackwitz & Fiessler, 1978). Seismic margin 𝑚𝑚_𝐵𝐵(𝑇𝑇_𝐵𝐵|𝑇𝑇_𝐴𝐴) that is additionally required for item B is given as follows:

𝑚𝑚𝐵𝐵(𝑇𝑇𝐵𝐵|𝑇𝑇𝐴𝐴) = max �1,𝑠𝑠̅𝐵𝐵

∗_(𝑇𝑇 𝐵𝐵|𝑇𝑇𝐴𝐴)

𝑠𝑠𝐵𝐵𝐵𝐵(𝑇𝑇𝐵𝐵) � (2)

where, 𝑠𝑠_{𝐵𝐵𝐵𝐵}(𝑇𝑇_𝐵𝐵) is the spectral acceleration at period 𝑇𝑇_𝐵𝐵 for the original seismic design obtained using the same concept as that of item A, i.e., annual exceedance probability is around 10-4 _{or smaller in this case.} 𝑠𝑠̅𝐵𝐵∗(𝑇𝑇𝐵𝐵|𝑇𝑇𝐴𝐴) is the most probable level of spectral acceleration at 𝑇𝑇 = 𝑇𝑇𝐵𝐵 for occurrence of accident, i.e.,

malfunction of item A. 𝑠𝑠̅_𝐵𝐵∗(𝑇𝑇_𝐵𝐵|𝑇𝑇_𝐴𝐴) is calculated as follows:

log10𝑠𝑠̅𝐵𝐵∗(𝑇𝑇𝐵𝐵|𝑇𝑇𝐴𝐴)

= 𝑎𝑎(𝑇𝑇𝐵𝐵) + 𝑏𝑏(𝑇𝑇𝐵𝐵)𝑚𝑚𝑊𝑊∗− 𝑐𝑐(𝑇𝑇𝐵𝐵)𝑥𝑥∗− log10�𝑥𝑥∗+ 𝑑𝑑(𝑇𝑇𝐵𝐵) ∙ 100.5𝑚𝑚𝑊𝑊∗�

− 𝑒𝑒(𝑇𝑇𝐵𝐵)(log10𝑉𝑉𝑆𝑆30𝑆𝑆)2+ 𝑓𝑓(𝑇𝑇𝐵𝐵)log10𝑉𝑉𝑆𝑆30𝑆𝑆

+ 𝑔𝑔(𝑇𝑇𝐵𝐵)log10�max�min(𝑍𝑍1500𝑆𝑆, ℎ(𝑇𝑇𝐵𝐵) ), 𝑘𝑘(𝑇𝑇𝐵𝐵)��

+ 𝜎𝜎𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼(𝑇𝑇𝐵𝐵)𝜀𝜀̅𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼∗(𝑇𝑇𝐵𝐵|𝑇𝑇𝐴𝐴) + 𝜎𝜎𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴(𝑇𝑇𝐵𝐵)𝜀𝜀̅𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴∗(𝑇𝑇𝐵𝐵|𝑇𝑇𝐴𝐴)

(3)

where, 𝑚𝑚_𝑊𝑊∗, 𝑥𝑥∗, 𝜀𝜀̅_{𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼}∗(𝑇𝑇_𝐵𝐵|𝑇𝑇_𝐴𝐴) and 𝜀𝜀̅_{𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴}∗(𝑇𝑇_𝐵𝐵|𝑇𝑇_𝐴𝐴), respectively, are the most probable values for 𝑀𝑀_𝑊𝑊,

𝑋𝑋, the conditional means of the bivariate normal distribution given 𝜀𝜀_{𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼}∗(𝑇𝑇_𝐴𝐴) and 𝜀𝜀_{𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴}∗(𝑇𝑇_𝐴𝐴) given that

𝑆𝑆𝐴𝐴(𝑇𝑇𝐴𝐴) = 𝑠𝑠𝐴𝐴∗ that is obtained by a method of seismic hazard deaggregation (McGuire, 1995, Takada et al.,

2003). 𝜀𝜀̅_{𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼}∗(𝑇𝑇_𝐵𝐵|𝑇𝑇_𝐴𝐴) and 𝜀𝜀̅_{𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴}∗(𝑇𝑇_𝐵𝐵|𝑇𝑇_𝐴𝐴) are as follows:

𝜀𝜀̅𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼∗(𝑇𝑇𝐵𝐵|𝑇𝑇𝐴𝐴) =𝜌𝜌𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼(𝑇𝑇𝐴𝐴, 𝑇𝑇𝐵𝐵)𝜀𝜀𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 ∗_(𝑇𝑇

𝐴𝐴)

�1 − 𝜌𝜌𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼(𝑇𝑇𝐴𝐴, 𝑇𝑇𝐵𝐵)2

(4)

𝜀𝜀̅𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴∗(𝑇𝑇𝐵𝐵|𝑇𝑇𝐴𝐴) =𝜌𝜌𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴(𝑇𝑇𝐴𝐴, 𝑇𝑇𝐵𝐵)𝜀𝜀𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴 ∗_(𝑇𝑇

𝐴𝐴)

�1 − 𝜌𝜌𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴(𝑇𝑇𝐴𝐴, 𝑇𝑇𝐵𝐵)2

(5)

where, 𝜀𝜀_{𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼}∗(𝑇𝑇_𝐴𝐴), and 𝜀𝜀_{𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴}∗(𝑇𝑇_𝐴𝐴) are respectively the most probable values for 𝐸𝐸_{𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼}(𝑇𝑇_𝐴𝐴) and

𝐸𝐸𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴(𝑇𝑇𝐴𝐴) given that 𝑆𝑆𝐴𝐴(𝑇𝑇𝐴𝐴) = 𝑠𝑠𝐴𝐴∗. This concept is identical to that of the conditional mean spectrum

proposed by Baker (2011). From Equations (3)-(5), it can be understood that the additional seismic margin

𝑚𝑚𝐵𝐵(𝑇𝑇𝐵𝐵|𝑇𝑇𝐴𝐴) is almost unity if the difference between 𝑇𝑇𝐴𝐴 and 𝑇𝑇𝐵𝐵 is large enough, because both

𝜌𝜌𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼(𝑇𝑇𝐴𝐴, 𝑇𝑇𝐵𝐵) and 𝜌𝜌𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴(𝑇𝑇𝐴𝐴, 𝑇𝑇𝐵𝐵) decrease as difference between 𝑇𝑇𝐴𝐴 and 𝑇𝑇𝐵𝐵 increases (Itoi et al., 2015).

On the other hand, a larger additional margin 𝑚𝑚_𝐵𝐵(𝑇𝑇_𝐵𝐵|𝑇𝑇_𝐴𝐴) is required if 𝑇𝑇_𝐴𝐴 and 𝑇𝑇_𝐵𝐵 are close to each other, i.e., if the diversity in the characteristics of items is not introduced in the seismic design.

EXAMPLE CALCULATION

An area source is assumed for an example calculation. Point sources are uniformly distributed within a radius of 100 km where their focal depth is 10 km. The nuclear power plant is assumed to be located on the ground surface above the center of the area source. The probability distribution of the earthquake magnitude is assumed to be in agreement with the Gutenberg-Richter law. Uniform hazard response spectra calculated at the facility are shown in Figure 1. The design ground motion for a system is assumed to correspond to the exceedance probability of 10-4_{/year. The natural period of item A,} 𝑇𝑇

𝐴𝐴, is assumed to be 0.02 s. As for

item B, three alternative options (items B0, BS and BT) are assumed as listed in Table 1. It is also assumed

of failure at the level of design ground motion is assumed to be 0.01. An additional seismic margin of 1.49 for item BS, as compared to item B0, is obtained for this example, whereas an additional seismic margin is

not required for item BT.

Monte Carlo simulations are conducted where the number of samples for the simulation is 108_{.Samples of}

hypocenter and magnitude of earthquakes, 5% damped acceleration response spectra and capacity of items are generated to calculate simultaneous malfunction of both items. The annual failure probability of the system is calculated to discuss the effectiveness of diversity in the natural period of items and additional seismic margins. The results are tabulated in Table 2. For case 0, item B0 is not so much effective to mitigate

the consequences of accidents, because the failure probability of the system does not decrease less than 0.449-0.640 times as compared to that of item A. The failure probability of the system decreases 0.165-0.213 times as compared to that of item A for case S, and it decreases 0.14 times as compared to that of item A for case T. Both cases T and S are effective in mitigating the consequences of accidents, while case 0 is not because of the effects of common cause failure.

Figure 1 Uniform hazard spectra at the location of the facility (Itoi et al., 2017)

Table 1 Three alternative options for item B (Itoi et al., 2017) Case 0

(item B0)

Natural period of item B is 0.02 s, which is identical to that of item A. Item B is designed for design ground motion corresponding to the exceedance

probability of 10-4 _/year.

Case S (item BS)

Natural period of item B is 0.02 s, which is identical to that of item A. Seismic margin is provided based on the proposed method Case T

(item BT)

Natural period of item B is 0.97 s.

Seismic margin is provided based on the proposed method

Table 2 Calculated failure probabilities for different option (Itoi et al., 2017) Case Failure probability of the

system (/year)

Ratio to failure probability of item A

Item A (reference) 1.54 × 10−5 - Case 0 6.91 × 10−6 ( ρ = 0.0 )

9.86 × 10−6 _{( ρ = 0.6 )} 0.449_0.640 ( ₍ ρ = 0.0 _{ρ = 0.6} ) ₎

Case S 2.54 × 10−6 ( ρ = 0.0 )

3.28 × 10−6 _{( ρ = 0.6 )} 0.165_0.213 (₍ ρ = 0.0 _{ρ = 0.6} ) ₎

Case T 2.08 × 10−6 0.135

10-2 10-1 100

0 500 1000 1500 2000 2500 3000

Period of 1DOF T(s)

Ac

ce

le

ra

ti

o

n r

es

n

po

n

se

S a

(cm/

s

2 )

Based on the results obtained, some of benefits and challenges to introduce a base-isolated structure instead of an earthquake-resistant structure for an emergency operations facility can be discussed and those which had not been discussed previously are described as follows:

 Simultaneous occurrence of damage both to a reactor building and an emergency operations facility can be avoided relatively easily if a reactor building is an earthquake-resistant building and an emergency operations facility is a base-isolation building. It is important to avoid cliff edge, little attention is paid to this benefits.

 In the area where earthquakes with large magnitude may occur, design basis ground motion for a base-isolation building tends to be critical compared to that for an earthquake-resistant building. It is because larger level of ground motion may occur for longer period ground motions compared to shorter period ground motions, because coefficient for magnitude 𝑏𝑏(𝑇𝑇) of GMPE is larger for longer period as shown in. e.g., Itoi et al. (2015).

SUMMARY

In this paper, a challenge of seismic design of nuclear power plants was discussed from the

viewpoint of seismic design of items that are important in mitigating the consequences of accidents.

A method to assign additional seismic margin required to those items was utilized which estimates required seismic margin depending on the degree of diversity introduced. One of typical examples related to the case study in this paper was useful when an emergency operations facility is additionally designed next to a reactor building. Whether a base-isolated structure is better than an earthquake-resistant structure for this emergency operations facility or not could be discussed on basis of the proposed framework.

ACKNOWLEDGEMENT

Part of this paper is based on master thesis of Mr. Yuki Iita (former graduate student of School of Engineering, the University of Tokyo).

REFERENCES

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Budnitz, R.J., Amico P.J., Cornell C.A., Hall, W.J., Kennedy, R.P., Reed, J.W., and Shinozuka, M. (1985). “An Approach to the Quantification of Seismic Margins in Nuclear Power Plants”, NUREG/CR-4334, Lawrence Livermore National Laboratory and U.S. Nuclear Regulatory Commission.

Itoi, T., Murakami, M., Sekimura, N. (2015). “Statistical Equations of Response Spectra of Crustal Earthquake for Assessment of Multiple Facilities Seismic Risk”, Journal of Japan Association for Earthquake Engineering, 15(6), pp.126-141. (in Japanese with English abstract)

Itoi, T., Iita, Y., Sekimura, N. (2017). “A Framework for Seismic Design of Items in Safety-Critical Facilities for Implementing a Risk-Informed Defense-in-Depth-Based Concept”, Front. Built Environ., 05 May 2017 | https://doi.org/10.3389/fbuil.2017.00027.

McGuire, R. K. (1995). “Probabilistic Seismic Hazard Analysis and Design Earthquakes – Closing the Loop”, Bulletin of the Seismological Society of America , 85(5), 1275-1284.

Rackwitz, R. & Fiessler, B. (1978). “Structural reliability under combined random load sequences”

Computers and Structures, 9, 489–494.