Boudy, B

Graf, C

Liebig, K,

Moussallam, N

robin-boudaoud, marie-cécile,

English

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Submitted on 16 Apr 2019
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Progress in the understanding and modelling of
components that could drive the overall fragility of a
nuclear power plant
Marie-Cécile Robin-Boudaoud, B Boudy, C Graf, K Liebig, N Moussallam
To cite this version:
Marie-Cécile Robin-Boudaoud, B Boudy, C Graf, K Liebig, N Moussallam. Progress in the under-
standing and modelling of components that could drive the overall fragility of a nuclear power plant.
BEST PHSANI, May 2018, cadarache, France. ￿hal-02100930￿
 
Progress in the understanding and modelling of components that could drive 
the overall fragility of a nuclear power plant 
 
MC.  ROBIN-BOUDAOUD1,  B. BOUDY1,  C. GRAF2,  KD. LIEBIG2, N. MOUSSALLAM1  
1 AREVA NP, 10 rue Juliette Récamier, 69456 Lyon CEDEX, FRANCE   
2 NEW NP GMBH, Paul-Gossen-Str. 100, 91052 Erlangen, GERMANY 
 
This work has been carried out under the SINAPS@ project received French funding 
managed from the National Research Agency under the program “Future Investments” 
(SINAPS@ reference No. ANR-11-RSNR-0022).  
The content of this paper has been presented at workshop BESTPSHANI, 2018. 
 
1. Introduction 
The aim of seismic risk analysis of nuclear power plants is to ensure that the chances of safety goals 
not being met in case of a severe earthquake are extremely small. It requires performing the fragility 
estimates of a large list of components which are mandatory to ensure these safety goals during and 
after an earthquake event. In practice, it is known that some classes of equipment and components 
very often appear as major contributors to the seismic risk, irrespectively of the nuclear power plant 
under consideration. It happens that some of these components need hardware modifications in 
order to improve their robustness in case of severe earthquake. It also occurs that the engineering 
methods used to evaluate their ultimate capacity are too conservative, leading to an overestimation 
of their real contribution to the seismic risk.  
R&D efforts of the industry practitioners should then focus on the improvement of the 
understanding and modelling of the ultimate capacity of those generic high contributors to the 
seismic risk. The aim is to be able to determine if equipment needs reinforcement at the earlier stage 
of the seismic re-assessment.  
Rigorous identification of those generic high contributors to the seismic risk is not an easy task. In 
this article, we present  the approach retained by Framatome to define this generic seismic 
equipment list (GSEL). Its characteristic feature is to take advantage of the existing database of 
Seismic Margin Assessments and Seismic Probabilistic Safety Assessments. 
Critical analyses of the engineering methods used to evaluate the fragility of GSEL shows that there is 
place for improvements in order to better assess their seismic risk.  
In this paper, we focus on the improvement of modeling of energy dissipation of elastic structures 
supported by non-linear supports, and on the improvement of the prediction of fragility of electrical 
and instrumentation and control cabinets. 
2. Identification of major generic contributors to the seismic risk – GSEL 
 
2.1 Identification from available results of SPSA and SMA studies 
The purpose of the Seismic Margin Assessment (SMA) is to show that the systems, structures and 
components (SSCs) critical to achieve a safe shutdown state following an earthquake are designed 
with large safety margins so that they have a low probability of failure in the Seismic Margin 
Earthquake (SME)1. 
The Seismic Probabilistic Safety Assessment (SPSA) of a nuclear power plant has the purpose to 
demonstrate that the contribution of seismic events to overall risk is not excessive.  
Both approaches rely on the definition and analysis of a Seismic Equipment List (SEL), collecting the 
SSC contributing to meet the safety goals.  The results of SMA or SPSA give then valuable information 
on the seismic performance and risk of the components of the SEL like: their dominant failure mode, 
their High  Confidence of Low  Probability of Failure (HCLPF) and fragility parameters,  their PSA 
importance metrics (such as the Fussel-Vesely importance). It is noted that these metrics are 
conditional on the way it the fragility has been determined (with generic or specific method), as well 
as on the assumptions adopted in the PSA with respect to the dependence between seismic-induced 
failures and to the fragility of distributed systems. 
In order to identify the generic high contributors to the seismic risk, the available data for several 
projects are gathered in a common database. Several metrics are built in order to rank the 
component of the SEL in terms of seismic risk. The different metrics are then weighted to reach a 
unique criterion, which is normalized. Hence, the most penalizing component is attributed a value of 
100%.  At the end, the components for which the indicator exceeds a given threshold are considered 
to be part of the GSEL (generic seismic equipment list).  
Thanks to this method, the classes of components that often drive the seismic vulnerability are 
rigorously identified. The outcome of this work is that HVAC systems, cable trays, electrical 
equipment and I&C panels are significant generic contributors to the seismic risk. 
 
2.2 From experience of seismic re-assessment 
 
In order to get a complete overview of the generic contributors to the seismic risk, it is also 
interesting to review the experience of seismic re-assessment for different industrial sites. It appears 
that the following issues often lead to a need for in-depth studies in order to achieve justification: 
-Justification of reinforced concrete building when damages appear, 
-Sliding and rocking structures or components (unanchored equipment, handling cranes and 
machinery), 
-Structures and systems on nonlinear supports (seismically isolated buildings, yielding supports), 
-Immersed components with high fluid-structure interaction effects. 
 
Hence those components should be added to the GSEL. 
 
 
3. Critical analysis of the engineering methods 
 
Once the major generic contributors to the seismic risk are known, it is important to evaluate and, if 
necessary, improve the analysis methodologies that have led to identify those components as critical. 
1 The SME is the seismic demand level assumed in the SMA; the margin between the SME and the design basis 
earthquake (DBE) is the minimum acceptable margin. 
                                                          
Hence, if the fragilities estimates of those components are based on too conservative methods, then 
their seismic vulnerability is overestimated, which is not the goal of a SMA or SPSA.  
 
The present paper follows up on the observation that the modelling of the dissipation of linear 
structures on nonlinear supports can be improved in order to better assess the seismic demand on 
those structures.  
Furthermore, the paper elaborates on improvements in predicting the fragility of electrical cabinets. 
 
 
4. Improvement of damping modeling in case of sliding or yielding structures 
This section sums up a work presented in detail in [1]. 
4.1 State of the art 
The sources of energy dissipation in structures are multiple and potentially rather complex to model. 
For elastic structures, it is common practice to model damping forces thanks to a linear viscous 
damping model. Usually this damping is introduced considering the proportional damping model, 
called Rayleigh damping. 
The Rayleigh damping model is based on two coefficients that define the viscous damping matrix as a 
combination of terms proportional to the mass matrix, α [M], and the stiffness matrix, β [K]. 
While the stiffness matrix proportional term induces damping proportional to the deformations of 
the structures, the mass matrix proportional term induces damping when rigid motions are applied, 
which is not acceptable. 
As a consequence, in presence of rigid body motion, cautious engineers only use the β [K] part, 
leading to a conservative modeling of the damping of the lower frequency modes. 
 
 
 
4.2 Development of the “GHOST” methodology 
The “ghost” methodology aims at producing damping forces on the linear structure which are only 
proportional to the structure deformation velocities. To achieve this goal, the velocity corresponding 
to the rigid body motion 𝑈𝑈𝑔𝑔  of the linear part of the model is subtracted from the overall velocity ?̇?𝑈  
when constructing the damping force vectors, as presented in equation (1). 
 
�𝐹𝐹𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑔𝑔� = 𝛼𝛼[𝑀𝑀]. �?̇?𝑈 − ?̇?𝑈𝑔𝑔� + 𝛽𝛽[𝐾𝐾]. �?̇?𝑈�                                                                                          (1) 
 
The rigid body motion is evaluated thanks to a rigid model of the structure that follows the 
displacements and rotations of the structure, defined as a function of the kinematics of some key 
nodes. Thanks to this technique, full Rayleigh damping can be introduced. 
 
4.3 Improvements in seismic demand assessment 
In order to show the benefit of such an improvement of modeling, the case of a building on a seismic 
isolation system is considered. In that situation, the building remains linear whereas isolators 
undergo significant deformation. Hence the isolated building belongs to the category of nonlinearly 
supported linear structures.  Figure 1 shows the building model, supported at its bottom. 
 
Figure 1. Overview of the building model 
 
Figure 2 compares results obtained using only β [K] part and using the ghost methodology, both with 
a target of 7% reduced damping.  
 
Figure 2. Comparison of the floor response spectra (a) horizontal (b) vertical 
 
 
Clearly, the use of the more realistic ghost methodology results in a reduced seismic demand, and 
hence in a less conservative estimation of the fragility of the equipment. 
 
5. Improvement in the determination of capacity of electrical equipment  
 
5.1 State of the art 
 
The estimation of the capacity of electrical cabinets of Nuclear Power Plants is often based on the 
qualification tests of the cabinet on a shaking table. It can be assumed that the capacity is defined by 
the required response spectra defined for the test qualification. This spectrum can then be compared 
to the seismic demand at the floor anchorage. 
It is conservative in the sense that even though the cabinet did not effectively fail during the test, the 
equipment behavior beyond tested levels remains unknown and in the standard fragility 
methodology based on EPRI TR-103959 de-facto no significant margin can be credited.  
This contributes to the consequence that electrical cabinets are identified as generic high contributor 
to the seismic risk. 
 
5.2 Better understanding and characterization of the failure modes 
 
Electrical cabinets contain a large number of electrical components. Among them, relays are known 
to be weak points (“bad actors”), because of possible chattering. Chattering induces an interruption 
of electrical signal during few milliseconds that could have detrimental consequences on the plant 
operation during the earthquake. This is considered to be one of the most likely failure modes of an 
electrical cabinet. 
 
In order to better assess the dynamic behavior of relays, sine sweep tests are performed on 
individual components. The sine sweeps are unidirectional, acceleration controlled, with constant 
amplitude. Several tests with increasing acceleration amplitudes are performed in order to identify 
maps of failure, as presented in Figure 3. 
 
 
 
Figure 3. Illustrative failure map of a relay 
 
In order to evaluate the capacity of the component, an artificial sine sweep test is built. Its amplitude 
varies with the frequency in order to match the limit of the safe zone. Its response spectrum defines 
the capacity of the component.  
 
 
5.3 Estimation of the capacity to seismic demand of the electrical cabinet 
 
At this stage, it is mandatory to build the link between the seismic demand at the anchorage level of 
the cabinet and the seismic demand at the level of the electrical / I&C devices. 
 
In – depth analysis 
 
In order to define the seismic demand at the level of the component, the transfer function of the 
cabinet between the anchorage and the device has to be determined. 
 
Tests performed on cabinets, sine sweep tests or seismic excitation tests, can be used for extracting 
damping and Eigen frequencies of dominant modes. These are then supplemented by numerical 
simulations in order to retrieve transfer function for any positions within the cabinet, or to identify 
the dynamic behavior of a non-tested cabinet, providing its design is similar to tested cabinets. 
 
Electrical cabinets are rather stiff and low damped structures. In general, electrical cabinets exhibit 
few modes in the frequency range of the seismic excitations, Eigen frequencies are typically higher 
than 10 Hz. Figure 4 shows the typical behavior of an electrical cabinet. 
 
 
Figure 4. Illustrative transfer function of a cabinet between the anchorage and an inner position 
 
The capacity to demand ratio for the cabinet can then be established by performing the following 
steps. Firstly, time histories for a given seismic scenario are generated, either by direct calculations or 
from the floor response spectrum. Then the corresponding time histories at the level of the devices 
are estimated thanks to the transfer function of the cabinet. Their response spectrum is compared to 
the capacity of the device, in order to get the minimum capacity to demand ratio for each 
component. Particular attention is paid to the zero period acceleration which is compared to the 
maximum quasi static acceleration measured in tests. Finally, the minimum ratio of all the safety-
relevant devices is the capacity to demand ratio of the cabinet devices. 
Considering the large number of cabinets in a nuclear power plant, this method would require a large 
effort in order to analyze all cabinets. 
 
Simplified method 
 
In order to get a quick view of the electrical cabinets that could be significant contributors to the 
seismic risk, a simplified method is developed, taking advantage of the dynamic properties of the 
electrical cabinets. 
In a first stage, for each device, the corresponding capacity at the anchorage level is determined by 
applying the inverse transfer function of the cabinet to the sine sweep defining the safe zone of the 
devices. The minimum of all the evaluated capacities defines the capacity of the electrical cabinets at 
the anchorage level. This capacity can then directly be compared to the probabilistic seismic demand 
at the floor level to get the capacity to demand ratio of the cabinet. 
 
This simplified method is approximate. Nonetheless, it permits a first analysis of the seismic risk for 
the electrical cabinets in a very efficient way. 
Figure 4 and 5 show a comparison of the in-depth method and simplified method.  In Figure (4), the 
comparison of the capacity of a component and of the seismic demand is performed at the 
anchorage level (base level), following the simplified methodology.  Figure (4a) shows the 
comparison in terms of response spectrum. Figure (4b) illustrates the evolution of the capacity to 
demand ratio as a function of frequency. Figure (5) presents the same data but this time following 
the in-depth methodology, i.e. comparison of the capacity and the demand at the level of the 
component. A very good agreement is found validating the simplified method. 
Hence, all electrical cabinets presenting a large ratio capacity to seismic demand ratio with the 
simplified method do not need a deeper investigation. For the remaining cabinets, it is necessary to 
perform an in-depth study, in particular to characterize the ZPA seen by the device. 
 
 
  
 
                      Figure 4. Comparison of the capacity to demand at the anchorage level; (a) response 
spectrum, (b) ratio  
  
                      Figure 5. Comparison of the capacity to demand at the device level; (a) response 
spectrum, (b) ratio  
 
 
5.4  Towards an integrated tool 
 
Considering the nature of the analyses, it is envisioned to develop a generic database and automatic 
query to assess the seismic risk of electrical cabinets at an early stage. 
This database is composed of 4 tables: plant, seismic demand, electrical cabinet and device tables.  
 
 
6. Conclusion 
Identification of generic high contributors allows concentrating R&D on the understanding and 
modelling of ultimate capacity of those components. In particular, methodological improvements are 
a way to increase the robustness of the prediction of the seismic risk associated with those 
components. In this paper, two methodological developments that can lead to a better prediction of 
the capacity of high contributors to the seismic risk have been presented.   Hence, as dissipation is 
known to play an important role in the estimation of the capacity of structures, a new method has 
been developed to better model dissipation of linear structures supported by non-linear supports. 
What’s more, as electrical cabinets have been identified as potentially high contributors to the 
seismic risk, in this paper, an innovative strategy in order to better assess their capacity to demand 
ratio has been presented. In particular, a simplified method that allows performing a first evaluation 
in a very efficient is proposed. 
 
References: 
[1] Nadim Moussallam et al. 2015- SMIRT 23 
Application of proportional “ghost” damping for sliding or yielding structures in time history dynamic 
analyses 


Progress in the understanding and modelling of components that could drive the overall fragility of a nuclear power plant

Robin-Boudaoud, Marie-Cécile,

HAL Descartes

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Progress in the understanding and modelling of components that could drive the overall fragility of a nuclear power plant

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