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Seismic Safety ofNuclear Power Plants
Bozidar Stojadinovic, ProfessorCEE Department, UC Berkeley
What is Safety?• The state of being safe
• The state of beingprotected fromconsequences ofundesirable events: – Accidents – Errors
– Failures
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Nuclear Power Plants
• Complex energy conversionmachines
• Engineered: – Not naturally occurring – Made and operated by humans
• Introduce a layer of hazard notpresent before we inventedthem: – RadiaVon hazard – Explosion hazard – Other hazards (environmental,
occupaVonal…)
Safety Goal• Protect the public from empirically detectable
harm: – No more: protecVng against what is not
empirically detectable is near-impossible
– No less: causing a detectable change in the hazardenvironment is not acceptable
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Safety Goal
• Focus on radiaVon dose at exclusion areaboundary:
An#cipated opera#onaloccurrences
Design basis events
Beyond design basisevents
Hazard and Risk
Risk = P(event occurring) x (Impact of event occurrence)
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Seismic Safety of NPPs
• Earthquakes
• CharacterisVcs ofground moVons
• Effect of ground moVonon simple structures
• Measures of earthquakehazard
• Effect of earthquakeground moVon on realstructures
• Demand, damage anddecisions: performance
• Probability-based risk-informed technology –
neutral designframework
Cause of EarthquakesIn Japan, peoplebelieved that acatfish that livedunder the landcausedearthquakes everytime it wiggled.
The people in the
picture are strikingthe catfish to stop itfrom shaking theearth.
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Tectonic Plates
iew of a Geo-ScienVst• An earthquake is the result of the sudden
release of energy in the Earth's crust thatcreates seismic waves
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Earthquake Faults
• Earthquake faultsoccur at theedges of tectonicplates (wherethey slip by eachother)
• These arecomplex rock andsoil fracturephenomena
How Do Faults Slip?• An earthquake is caused by a build up of strain on
the edges of the tectonic plates.• The strain becomes so great that rocks give way and
slipping occur along the fault.
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Seismic Wave PropagaVon
• Waves reect from andrefract through crustlayers of differentdensity
h p://www.uwgb.edu/DutchS/EarthSC202Notes/quakes.htm
Wave PropagaVon Through Soil• Body wave:
– Pressure – Shear
• Surface waves: – Lowe – Rayleigh – They are slowest, but
they do most of thedamage when theyarrive at the site of thestructure
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Ground MoVon at the Site
• Depends on: – Energy released at the
source (fault)
– Path, distance the wavestravel to the site
– Local condiVons at thesite:
• Soil
• Focusing• Other structures
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Ground MoVon at the Siteof an NPP Structure
Surfacewaves
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Types of
Ground MoVon• Great variety!
Principal Types of Ground MoVon• Delineated by:
– Magnitude – Distance between the
hypocenter and the site – Local soil condiVons
• Near-Fault – Pronounced direcVvity
• Perpendicular• Parallel
• Near-Field – Strong pulse, ing – High-frequency content
• Far-Field – Longer duraVon – Moderate and low
frequency content
Samedistance
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Magnitude : Measure
of Energy Release• Many versions:
ObservaVons• Intensity of
ground shakingdecreases withincreasingdistance from theepicenter
(1994 M6.7
NorthridgeEarthquake, USGSShake Map)
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How Ground MoVons Affect
Structures?
Dynamic Equilibrium:EquaVon of MoVon
• Total displacement: – Ground displ.
– RelaVve displ.
• Forces: – InerVa
– Damping
– Structural resistance
• Equilibrium
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ElasVc Structural Response
• Characterizedby: – Natural
period(frequency)of vibraVon
– Damping:energy
dissipaVonduringvibraVon
ElasVc Response Spectrum
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ElasVc
Response Spectrum• Displacement: D
• Pseudo-velocity:
• Pseudo-acceleraVon: A
• Note on effecVve force
• Note on strain energy:
Spectra ary, too!• El Centro 1940,
different damping
• More damping: lessdeformaVon
• El Centro, differentearthquakes
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ElasVc Design Spectra
• Average of a largenumber of similarground moVonspectra
• Smoothing occursalong the way
• Note: PGA on the
T=0 axis• Note: Cap at the
maximum values
• Describes elasVcseismic response ofsimple structures
Seismic Hazard and Risk• Seismic Hazard Analysis:
Describes the potenValfor dangerousearthquake-relatednatural phenomena(such as groundshaking)
• Seismic Risk Analysis:
Assesses the probabilityof occurrence of losses(human, social,economic) associatedwith seismic hazard
Risk = P(event occurring) x (Impact of event occurrence)
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Probability of Recurrence:
Magnitude and Likelihood of Occurrence
Physical Limits on Magnitude
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Ground MoVon A enuaVon
• Reasons: – Geometric spreading of
waves
– AbsorpVon (damping) inthe rock/soil
Empirical A enuaVon RelaVons
h p://peer.berkeley.edu/products/nga_project.html
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Model-Based A enuaVon RelaVons
• Complex, regionalmodels: – Sources
– Faults – Geographic features
– Rock and soil layers
• Huge computer
resources• h p://www.scec.org/
Seismic Hazard Curve
• For a given site,provide theprobability that aground moVonintensity parameterwill be exceeded
• P(IM>im)
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Use of Seismic Hazard Curves
Seismic Risk from NPP Structures• Losses to society due to a large radiaVon
release induced by earthquake ground moVon
JNES web site
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How Ground MoVons Affect
Real Structures
How Ground MoVon Affects Structures
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How Ground MoVon Affects Structures
How Ground MoVon Affects Structures
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Measure of Seismic Demand
Engineering Demand Parameters (EDP)Deforma#on duc#lity
• Story dri : relaVve moVonbetween top and bo om ofa story
Energy absorp#on ability
• Quality of structural systemand structural detailing
Seismic Demand Model• A relaVon between ground moVon intensity and
demand(s) on the structure• Method:
– Develop a computer model of the structure – Develop a por olio of site-specic ground moVons
scaled to reect different hazard levels – Conduct (a possibly large number of) analyses to
determine demand on the structure imposed by eachground moVon – Do a staVsVcal t
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Seismic Demand Model:
Log-log Linear• A condiVonal probability: P(EDP>edp|Im=im)
Damage to Structures• Local damage affects
global loss of stability
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Damage to Non-Structural Content
• Affects ability toconVnue using thestructure
Seismic Damage Model• A relaVon between demand on the structure
and structural and non-structural damage
• Method: – Gather data (experimental, empirical, from
manufacturers) on the types of damage, whenthey occur and how they affect the structure
– Do a staVsVcal t – Determine probabiliVes of excessive damage
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Seismic Damage Model:
Fragility Curves• CondiVonal probability P(DM>dm|EDP=edp)
Performance of the Structure• HolisVc evaluaVon of risk
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Discrete Performance Levels
Seismic Decision Model• A relaVon between structural and non-
structural damage and the performance ability(or lack there off) of a structure from thestandpoint of its intended funcVon
• Method: – Establish Decision ariables
– Establish threshold values and associate themwith acceptable recurrence intervals
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Seismic Decision Model:
Fragility Curves• CondiVonal probability: P(D >dv|DM=dm)
Risk EvaluaVon• Given a seismic hazard environment and a structure,
the probability that a performance objecVve is notachieved (D exceeds a threshold) is:
• Consider probability distribuVons of seismic hazard,
of demand, damage and decision variables due to: – Lack of knowledge (epistemic uncertainty) – Record-to-record randomness (aleatory uncertainty)
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Performance ObjecVve:
ProbabilisVc DescripVon of RiskPerformance Level Performance Recurrence
Performance ObjecVve Table
R e c u r r e n c e I n t e r v a l
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Acceptance Criteria
• A comparison of Demand and Capacity: – Failure (to saVsfy a performance objecVve)occurs
when (some staVsVcal expression of) demand islarger than (some staVsVcal expression of)capacity
D m e a n
C m e a n
threshold
DemanddistribuVon Capacity
distribuVon
Risk-Informed Design• Formulate design acceptance/rejecVon criteria
such that there is High Condence in LowProbability of Failure (HCLPF) to saVsfy aperformance objecVve
• Example: – 99% condence that the probability of collapse is
less or equal 1% in any 50-year interval
• Accounts for rst and second moments of theinterim model probability distribuVons
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Structural Engineering of NPPs
ASCE 43-05• Two acceptance criteria:
– Less than 1% probability of unacceptableperformance for the Design Basis ground moVon
– Less than 10% probability of unacceptableperformance for 150% of Design Basis groundmoVon
• Both must be saVsed: – Trying to control the shape of the fragility curve by
these two points
Safety Goal• A ain 10-6 annual probability of seismic core
damage
An#cipated opera#onaloccurrences
Design basis events
Beyond design basisevents
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Common Design Framework
• Performance-based design is, in essence,technology-neutral design: – Dene what we want to achieve, not how
• Acceptance criterion units must be selected toenable use of different technologies: – Ability to model and analyze is crucial
• Design must be risk-informed: – HCLPF to perform as desired – Basis for comparaVve evaluaVon of different
technologies
Seismic Safety ofNuclear Power Plants
• Complex energy conversionmachines
• Engineered by teamsrepresenVng all branches ofengineering
• Engineered to perform theirfuncVon in a manner that issafe even under mostextreme hazards
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Thank you!