Treatment of Uncertainties in Seismic PRA

Presented byM.K. Ravindra

MKRavindra ConsultingIrvine, CA

USA

L:\pubs\1206063KKG\PRA Training\Seismic PSA Methodology.ppt – Page 2

Seismic Probabilistic Risk Assessment

Component-FragilityEvaluation

Seismic Hazard Analysis

Seismic MotionParameter

Freq

uenc

y of

Exce

edan

ce

Event TreesFault Trees

Containment Analysis

P i

P i

P i

Systems Analysis

Seismic MotionParameter

Release Frequency Consequence Analysis

Frequency Damage

Freq

uenc

y of

Exce

edan

ce

1 32

ReleaseCategory

Pro

babi

lity

Den

sity

•Weather Data•Atmospheric

Dispersion•Population•Evacuation

•Health Effects•Property Damage

Risk

Con

ditio

nal P

roba

bilit

yof

Fai

lure

Dictionary on Uncertainty in SPRA Seismic Hazard

- Aleatory uncertainty- Epistemic uncertainty- “Informed” community distribution- SSHAC Process- Hazard curves with subjective probability weights

Fragility- Randomness in Capacity (aleatory uncertainty)- Uncertainty in Median Capacity (Modeling uncertainty) (Epistemic uncertainty)- Fragility curves at different confidence levels

Risk Metrics: CDF and LERF- Probability Distribution on CDF and LERF

Estimation of Hazard Frequencies

Seismic Hazard Curves

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Peak Ground Acceleration, g

Ann

ual P

roba

bilit

y of

Exc

eeda

nce

Uniform Hazard Spectra

Develop Seismic Sytem Models(Event Trees and Fault Trees)

Utilize/modify existing event trees and fault trees from internal events PRA.

Little or no event tree modification is expected; fault trees will require several modifications.

Seismically-induced initiating events to consider are:– Loss of offsite power (no recovery).– Loss of offsite power and small LOCA.– Either of the above combined with other support or frontline

system failures important to plant risk (seismically-induced or random failures).

Must account for both seismic and non-seismic (random) impact on important safety equipment.

Output: Seismic Equipment List

Seismic Fragility Curves

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4

95%Confidence

Median

5%Confidence

PEAK GROUND ACCELERATION (g)

PRO

BAB

ILIT

Y O

F FA

ILUR

E

ßR = 0.25ßU= 0.35

Am= 0.87 g

0.068

Mean

0.20

0.79

HCLPF 0.32g

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4

95%Confidence

Median

5%Confidence

PEAK GROUND ACCELERATION (g)

PRO

BAB

ILIT

Y O

F FA

ILUR

E

ßR = 0.25ßU= 0.35

Am= 0.87 g

0.068

Mean

0.20

0.79

HCLPF 0.32g

Seismic Fragility vs Random Unavailability

Rate of failure to start or run as random events can be obtained by routine periodic testing during the life of the plant.

Starting point is industry wide generic data; it is used as “prior” and subjected to Baysian updating using plant specific test data.

Testing for random unavailability is relatively cheap and data will be accumulated over the life of the plant

Failure rate is generally not affected by external stresses Seismic fragility has to be calculated using a combination of analysis,

qualification test data and earthquake experience data.

Seismic Fragility vs Random Unavailability (contd)

Seismic fragility (and hazard) varies with the input earthquake motion

Screening of components is done using plant walkdown which is an expensive task.

Fragility tests are not routinely done to obtain failure statistics; instead, qualification test data results are extrapolated.

Seismic PRA is not regularly updated whereas internal event PRAs are conducted often (e.g., risk monitors).

Component Fragility Fragility parameters Am, ßR and ßU

With perfect knowledge, conditional probability of failure fo, for a given peak ground acceleration level a is:

Fragility

R

)mA/aln(of

R

1Um )Q()A/aln( F

Fragility Model

A = Am R U

R and U are lognormal variables

Parameters: Am, R, U

HCLPF capacity = Am exp [-1.65 (R + U)]= Am exp [-2.33C]

C = R2 + U

2

Fragility Model (Cont.)

Am = Fm ASSE

Fm = FC FRS FRE

FC = FS F

FRS = FSA F FM FMC

FRE = FSA F FM FMC

F = (S2 + 2 + SA

2 + ...)1/2

Fragility Analysis

Variables considered: Strength Inelastic energy absorption Spectral shape Damping Soil-structure interaction Modeling Method of analysis/testing Combination of modes Combination of earthquake components

Seismic Walkdown and Screening Screening of high capacity components from SEL Identify potential failure modes Record any obvious seismic deficiencies (e.g., missing

anchor bolts, loose mounting relays and excessive cracking of concrete)

Identify spatial system interaction concerns that are judged to be potentially serious problems

Evaluate the fire protection systems in the plant for seismic induced fire and inadvertent actuation of fire protection system issues and sources of seismic induced flooding

1988 Saguenay,Quebec (M6.0)

1986 Adak Island,Alaska (M7.7 and 6.5)

1988Armenia,

USSR (M6.9)

1983 Borah Mt.,Idaho (M6.9)

1986 Painesville,Ohio (M5.0)

1975 Lice, Turkey (M6.8)1978 Miyagi-Ken-oki, Japan (M7.4)

1976 Friuli, Italy (M6.5)

1986 Northern Taiwan (M6.8)1990 Central Luzon, Philippines (M7.7)

1990 Manjil,Iran (M7.7)

1990 Bishop’s Castle, Wales (M5.4)

1993 Nansei-oki Hokkaido, Japan (M7.8)

1992 Roermond, Netherlands (M5.8)

1993 Scotts Mill,OR (M5.3)

1992 Erzincan, Turkey (M6.8)

1992 Cairo,Egypt (M5.9)

1993 Klamath Falls,OR (M5.7)

1994 Toho-oki Hokkaido, Japan (M8.1)

1977 Vranchia,Romania (M7.4)

1985 Santiago, Chile (M7.8 and 7.2)1995 Antofagasta, Chile (M7.4)

1987 Bay of Plenty,New Zealand (M6.2)

1985 Mexico City, Mexico (M8.1 and 7.5)

1986 San Salvador, El Salvador (M5.4)1972 Managua, Nicaragua (M6.3)1973 Managua, Nicaragua (M5.8)

1978 Izu Peninsula, Japan (M6.7)

1989 Newcastle,Australia (M5.5)

1991 Valle de la Estrella, Costa Rica (M7.4)

1989 Acapulco, Mexico (M6.8)

1993 Agana, Guam (M8.2)

1995 Kobe, Japan (M7.2)

1995 Pereira, Colombia (M6.5)

1987 Cerro Prieto, Mexico (M5.4)

1996 Duvall,WA (M5.3)

1997 Umbria (Assissi),Italy (M5.5)

1999 Armenia, Colombia (M5.0)

1998 Adana-Ceyhan, Turkey (M6.2)

1999 Izmit, Turkey (M7.4)

1999 Central Taiwan (M7.6)

1999 Duzce, Turkey (M7.2)

1999 Puerto Escondido, Mexico (M7.5)

1999AthensGreece(M5.9)

1999 WesternWashington (M5.8)

1999 Algeria (M5.5)

1994 Northridge (M6.7)

1983 Coalinga (M6.7)

1980 Livermore(M5.5 and 5.8)

1988 Alum Rock (M5.1)

1979 Gilroy (M5.5)

1990 Upland(M5.5)

1988 Gorman (M5.2)

1975 Ferndale (M5.5)

1992 Cape Mendocino(M7.0, 6.0,6.5)

1986 Chalfant Valley(M6.0 and 5.5)

1984 Morgan Hill (M6.2)

1978 Santa Barbara (M5.1)

1973 Point Mugu (M5.9)1971 San Fernando (M6.5)

1987 Whittier (M5.9)

1986 North Palm Springs (M6.0)

1992 Landers-Big Bear (M7.6 and 6.7)

1987 SuperstitionHills (M6.3)1981 Brawley (M5.6)&

1979 Imperial Valley (M6.6)

1992 Desert HotSprings (M6.1)

1991 Sierra Madre(M5.8)

1980 Eureka (M7.0)

1979 Bishop (M5.8) &1980 Mammoth Mt.

(M6.5, 6.5, 6.7)1997 Calico (M5.0)

1999 Hector Mine (M7.1)

1989 Loma Prieta (M7.1)

2000 Tottori, Japan (M6.7)

2000 Napa, CA (M5.2)

1995 Sakhalin Islands,Russia (M7.2)

1995 Manzanillo, Mexico (M7.6)

2000 Events2001 Events 1999 Events

2001 Gujarat, India (M7.6)

2001 Seattle (Nisqually),WA (M6.8)

Over 100 Earthquakes Investigated

L:\pubs\1206063KKG\PRA Training\Seismic Margin Assessment Methodology.ppt – Page 17

Seismic Fragility

"FAILURE" IS DEFINED AS THE EVENT WHEN AN ELEMENT REACHES A LIMIT STATE

ElementStructures

Piping

Equipment

Limit States Inelastic Deformations Exceeding Operability Limits for

Equipment

Fracture or Collapse of Pressure Boundary Failure of Supports Attachment Failure

Structural - Bending, Buckling of Supports Anchor Bolt Pull-Out, Nozzles, etc.

Functional - Binding of Valve, Excessive Deflection, Relay Chatter

Data Sources

Plant specific– Design analysis documents– Qualification tests

Generic– Shock test data– Past performance– Fragility tests

Systems Modeling Initiating events

– Loss of offsite power– Small break LOCA– etc.

Safety functions and associated front line and support equipment

Event trees Fault trees Detailed equipment list Booleans for accident sequences Plant level fragility

Simplified Event Tree For A Large LOCA

PA

PA x PE1

PA x PD1

PA x PD1 x PE2

PA x PC1

PA x PC1 x PD2

PA x PB

PE1

PE2

PD1

PD2

PC1

PB

PAInitiating Event

A

PipeBreak

B

ElectricPower

C

ECCS

E

ContainmentIntegrity

D

FissionProductRemoval

Example Fault Tree Loss of Electric Power (EP)

to Engineered SafetyFeatures (ESFs)

Loss of DCPower to ESFs

OR

Loss of ACPower to ESFs

AND

Loss of Off-SitePower to ESFs

Loss of On-SiteAC Power to ESFs

Service water pumpsAuxiliary building -- failure of concrete shear wallRefueling water storage tankInterconnecting piping/soil failure beneath reactor buildingCondensate storage tankCrib house collapse of pump enclosure roof125 VDC batteries and racksService water system buried pipe 1020 mm diameterCST piping 500 mm diameterCollapse of pressurizer enclosure roof

Example Boolean CD = 4 + 8 + 10 + 14 + 17 + 21 + (12 + 22 + 26) * 9

+ = OR* = AND

26

22

21

12

14

17

10

9

8

4

Propagation of Uncertainty Uncertainties in seismic hazard, fragilities, random failure

rates, and operator errors Develop point estimates for different accident sequences

using mean hazard curve, mean fragilities and failure rates For significant accident sequences, conduct uncertainty

analysis Important to consider success terms Softwares available based on DPD and Monte Carlo

simulation

-

DPD Method for Sequence Fragility Each component is modeled by “n” fragility curves. We perform the required operation (union or intersection)

on two components at a time for each of the “n” fragility curves.

If the median uncertainties are independent, we obtain “n2” fragility curves which is condensed back to “n” curves (if the median uncertainties are dependent, we obtain “n” curves).

The “n” fragility curves of the combined event are then combined with the “n” curves of another component.

This process is continued until all the component fragilities have been combined as given in the Boolean equation, finally resulting in “n” sequence fragility curves.

Sequence Failure Frequency Each of the n sequence level fragility curves are

convolved with each of the m seismic hazard curves for the site

The convolution is expressed by the following

The result is a probability distribution on the frequency of accident sequence

oo

o

daS(a)da

dH(a)

dadHwhere the frequency with which earthquakes occur in the

size range da about aS(a) = conditional probability of accident sequence

Plant Fragility Curve, Including Random and Nonseismic Failures

Results of a Probabilistic Risk Assessment

Sources of Uncertainty: Hazard Hazard modeling

- Earthquake Sources- Ground motion- Local site response- Other hazards (liquefaction, landslide etc)

Aleatory and Epistemic uncertainties Methodology

- Earthquake history- Theoretical and empirical models- Expert elicitation SSHAC Process

Development of family of seismic hazard curves

Sources of Uncertainty: Fragility Seismic capacity modeled as a product of multiple variables Limited empirical data to describe these variables Analyst is asked to estimate the aleatory and epistemic

uncertainties for each variable Functional failure modes are not clearly tied to the structural

deformations. Fragility is described in terms of a family of fragility curves. Limited test data for electrical components (one

qualification test and no fragility tests) Loss of offsite power fragility Generic conversion of HCLPF to fragility

Sources of Uncertainty: Plant Response and Quantification

Propagation of uncertainty-software

Large uncertainty mainly from hazard uncertainty Simplifications

- system model: initiating events and SSCs- correlation- human errors under seismic conditions- screening of components

Comparison and integration with other events

Model Uncertainty Significance Seismic Hazard HIGH

- Process stabilizing Seismic Fragility MEDIUM

- Process stable- Lack of test data- Limited resources

Plant Response and Quantification LOW to MED- Process stabilizing- Software availability

Concluding… Seismic PRAs have been conducted for over 50

plants in the US and worldwide; useful insights have been obtained in spite of large uncertainties for plant safety upgrades and regulatory decisions

Seismic PRA methodology allows and requires full treatment and propagation of uncertainty

Seismic hazard uncertainty dominates the uncertainty in risk metrics CDF and LERF

Seismic PRA and SMA Projects for Existing Plants Around the World

17000-15\EQEWorld.drw (10/94)

.

I

Atomic Energyof Canada,

PSA of Candu 6

Ontario HydroSMA of

Pickering

OKG/ForsmarkSMA of

Oskarshamn &Forsmark

IVO/TVOSeismic PSAof Loviisa &

Olkiluoto

Seismic PSAGösgen, Mühleberg

& BeznauCzech Power Board

Seismic PSA of Temelin

Seismic PSA of Krsko

PNCSeismic PSA of

Monju

Korea ElectricPower Company Seismic PSA of

Kori, Yonggwong, Ulchin, and Wolsong

TaipowerSeismic PSAof Kuosheng,

Maanshan,Chinsan,Lungmen

SMA ofPaks,

Hungary

IberdrolaSMA of

Vandellos,Cofrentes

SMA of GCRs

PSA of HIFAR

SMA ofKozloduy

SMA of Bohunice