EQE International
The use of Fragility
Analysis in Seismic Safety
Cases for Nuclear Power
Stations
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LAYOUT
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BACKGROUND
OBJECTIVES
OUTLINE METHODOLOGY
FRAGILITY CURVE DEVELOPMENT
ALARP ANALYSIS
CONCLUSIONS
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BACKGROUND
• LTSR and PSR completed to deterministic
principles
• Regulator driven requirement to confirm that
the risk posed is ALARP
• Not a Seismic PSA
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OBJECTIVES
• To confirm that the current level of qualification
renders the risk of unacceptable seismically
induced damage as ALARP
• To understand the relative contributions of different
items of plant, equipment and structures to the risk
profile
• To identify areas of plant, the modification of
which would decrease the annual failure frequency
to the lowest reasonably practicable level
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OUTLINE METHODOLOGY
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Identify claimed safety functions and associated
equipment/structures
Identify deterministic margins, and the methods of
assessment used. Normalise margins.
Characterise Variance in Capacity. Calculate
“median” margins
Convolute the hazard and fragility curves and
screen out items with an annual failure
frequency below a defined cut off
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OUTLINE METHODOLOGY cont
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Identify modifications to increase the margin
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Associate a bounding fault categorisation to a loss
of safety function. Convert the fault category to
an associated environmental cost as defined in the
Safety Review Guidebook
Calculate Cost Benefit Ratio (CBR)
Review results, and provide information to the
Client to assist in the decision making process
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FRAGILITY CURVE DEVELOPMENT
• Identify Assessment Types
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Code Based eg BS 5950, 8110, 5628,
806, ACI 349
Other Codes eg R6, SQUG
Comparison with available experimental data
Engineering Judgement
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FRAGILITY CURVE DEVELOPMENT
• Use EPRI and other research work previously
undertaken to derive fragility curve parameters
• Development of the application of standard curves
for other assessment types eg R6
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Illustrative Family of Fragility Curves
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95% Confidence
0.9
5% Confidence
0.8
50% Confidence
Mean
Failure Probability
0.7
0.6
0.5
0.4
0.3
0.2
0.1
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0
HCLPF
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MEDIAN
Peak Ground Acceleration (g)
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DERIVATION OF MEDIAN FRAGILITY
The median fragility â is a function of the following
parameters:
a) the normalised assessed margin Ma
b) the Code factor Fc (default value 1.0)
c) the HCLPF factor
d) the combined logarithmic standard deviation c
e) the peak ground acceleration for the site’s
10-4 p.a. URS event, å
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NORMALISATION OF MARGINS
Aim to place all margins on a common basis
Examine basic input for all calculations, and
acknowledge degree of sophistication applied to
assessments
Identify appropriate fragility parameters
This process is to a certain degree iterative,
particularly for items with apparently anomalous
margins
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NORMALISATION OF MARGINS- KEY FACTS
• Margins have been derived over c 15 years using a
variety of approaches
• The current state of the art is more advanced than when
the LTSR work began
• For some cases, seismic margins cannot be readily
extracted, for example elements with high working
stresses, where only margins against total load have been
assessed
• Margins are often calculated against eg a code allowable,
not a true measure of the loss of functionality
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Typical URS Seismic Hazard Curve
1.E+00
Expected Annual Probability of Exceedance H
1.E-01
1.E-02
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
0
0.2
0.4
0.6
Peak Ground Acceleration (g)
0.8
1
1.2
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Convolution of Hazard Gradient and Fragility Curve For a Normalised Median Fragility of 1.5.  c = 0.42
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3.0E-04
Density Function
0.9
2.5E-04
Fragility Curve
0.7
2.0E-04
Hazard
Gradient
0.6
0.5
1.5E-04
0.4
1.0E-04
0.3
0.2
5.0E-05
0.1
0
0.0E+00
0
0.1
0.2
0.3
0.4
0.5
0.6
Peak Ground Acceleration (g)
0.7
0.8
0.9
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Annual Failure Frequency Density Function
Hazard Gradient & Failure Probability
0.8
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ALARP ANALYSIS
Quantifiable Cost Elements
• Basic time and materials costing
• Costs as an overrun of outage
• Costs of safety case preparation
Non-Quantifiable Cost Elements
eg
• Worker Dose (qualitative ALARP)
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CALCULATION OF COST BENEFIT RATIO
Annual Safety Function Failure Frequency =
Annual Equipment Failure Frequency
X Probability of Safety Function Failure
Risk cost (valuation) =
Accident cost x Remaining Station Life
C.B.R. =
X
Annual Safety Function Failure Frequency
Modification Cost for the Plant Item in Question
Current Risk Cost - Risk Cost Post Modification
• Rank
• Review
• Report
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CLOSURE
• The approach has been very useful in acting as a ranking
tool to better understand the key contributors to the risk
profile
• The approach used has shown the absolute necessity for
normalisation of margins
• The approach used allows judgment to be applied in a
quantifiable manner. This has overcome the limitations
inherent in alternative, purely mechanical evaluation
methods