Buildings Facilitieswebarchiv.ethz.ch/lsa/education/vorl/snpp_slides_11/PSHA... · 2011. 5. 12. ·...

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Spring Semester 2011Dr. M. Raschke

Methods of Technical Risk Assessment in a Regional Context

www.lsa.ethz.ch/education/vorl Methods of Technical Risk Assessment in a Regional Context - PSHA 1

Buildings and facilities can be endangered by earthquakes.

How to design facilities against earthquake?

What is an appropriate design load – level of local impact?

Probabilistic Seismic Hazard Analysis (PSHA) ‐ Introduction

BuildingsFacilities




"Earthquakes Don't Kill People, Buildings Do"S. Hough and L. Jones, USGS

Seismic resistance design

Seismic resistance design is part of engineering science.The estimation of the level of local ground motion is part of seismology and earthquake engineering.

Dwellings are designed for an impact with a return period of 475 years according to modern design codes. The safety level has to be defined by the entire society.

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Seismic resistance designSeismic impact:- simple load factor: factor*weight; without consideration of dynamic interaction; NOT STATE OF THE ART- response spectrum: maximum response values form SDOF for computation of replacement load; dynamic of the system can be simply considered or more in detail- time history analysis: complex model of dynamic system and interactionDesign details:- linear or non-linear behaviour of the structural response

Time history analysis and a system of moment frames

Response force for system with two degree of freedoms

The load/impact level for the seismic resistance design is provided by PSHA, independent on design details.

RC-frame, high ductilityRC-walls, high ductilityRC-walls unreinforced masonry

Generation of design code in Switzerland

Equi

val e

nt fo

r ce




Deterministic approach

Probabilistic Seismic Hazard Analysis ‐ Approaches

- simple rules, e.g.: The largest observed earthquake within a radius of 100 km being placed

near the site is the design earthquake.

- older codes

- design load depends on historical records (settlement history)

- No statements about frequency or probability.

- simple and straightforward

x

y

Site

5 8.5

6.58

100km

x

y

Site8

Distance

Loca

l Im

pact

histor.Design

Selection of histor. earthquake Change of position Resulting impact (design load)

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Probabilistic approach- state of the art of seismic hazard assessment

- statements about frequency or probability

- earthquake hazard can be compared with other hazards

- modeling and computation is much more complicate

dmdrrmzFrfmfzZi

iirimi ,)()())(( s

Probability integral for the occurrence frequency

Probabilistic Seismic Hazard Analysis ‐ Approaches




Components of the Model and functional chain of the earthquake process

soil deposit

bedrockrupture

site

Magnitude-recurrence-relation(Seismicity of the surrounding area) – TS and FM

Attenuation-relation (decrease of seismic loads with increasing distance site to source) – WP and FM

Transfer function soil layers(subsoil effects) - WP

Scheme of earthquake process (side view)

source: Habenberger, 2007

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dmdrrmzFrfmfzZi

iirimi ,)()())(( s

The probability integral

Area

Line(Fault)

SitePoint

x

y

Point

Site

Line

Point

y

x

22 hdr 2

222

11 )()( ststd

h

Site Epicenterd

r h

Hypocenter

s=(s ,s )1 2 t=(t ,t )1 2y

x

Local shaking levle, random variable

Annual frequency of exceedance of Z

Annual frequency of occurrence (M>mmin)

Annual intensity of occurrence (M>mmin)

PDF of M

PDF of H

Conditional probability of exceedance

dxdydhdmrmzFhfmfzZ hm ,)()())(( s

),)((,)()(

))(()(

rmzZPrmzF

hfmf

zZZ

h

m

s

ss




Magnitude-recurrence-relation Attenuation-relation Transfer function soil layers

Seismic sources (faults, regions)Magnitude-recurrence-relation:e.g.: Gutenberg-Richter

M: magnitude (e.g.: Mw, Ms, Ml)N: number of magnitudes m>=M per

yeara, b: regression parameters of the

Gutenberg-Richter-law

bMamMN )(log

Attenuation relation for spectral accelerations or intensitiese.g.:

aleatoric uncertaintyregression parameters

R: distance site-hypo-/epicentrecoefficient (deviation from average)

)log(log 321 RCMCCZ

::nC

:

Site response: damping or amplification of seismic waves due to soft soil layers

-analytical (e. g. frequency domain)-numerical (e.g. FEM)

PSHA – Details of some Components

source: Habenberger, 2007

mFmMN m )(log

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PSHA – Uncertainties

epistemic uncertainty: incomplete knowledge (lack of data)

aleatory uncertainty: inherent randomness of ground motion generation

estimation error, confidence interval or residual variance

spreading of random variables

Uncertainty in PSHA Analogy in Stochastic and Statistic




•It is an approach to estimate the epistemic uncertainty.•It can be a simple mixture of models (probability distributions).•Weighting factors based on expert opinions or special approaches.•It is not an event (fault) tree!

seismiczonation model Mu

a attenuationrelation

0.3

0.7

0.3

0.3

0.4

0.5

0.5

0.25

0.75

0.0113

0.0338

…

…

…

1

Branches

1

2

K

PSHA – Logic Tree Approach

Logic tree

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response spectraset of hazard curves

PSHA – Surface Ground Motion Spectra

Scheme of data disaggregation source: Habenberger, 2007




•Lack of data - Some functions of the PSHA for a site or region are estimated with data of other regions.

•Some regression functions are used for extrapolations.

•Which estimation method is right?

•Sensitivity analysis is not equivalent to the statistical estimation of confidence range (logic tree).

•The uniform distribution of earthquake intensity in a source region seems to be inadequate.

•Not all possible statistical methods are applied in PSHA (everyday problem in all sciences).

•Not al statistical models being applied in PSHA are in agreement with state of the art in statistics.

PSHA – Some issues

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PSHA – The conditional Probability of Z

•The distribution type of Zm,h influences the hazard estimation.•If Z is an extreme value, an extreme value distribution should be appropriate.•But it is often assumed that Z m,h is log-normal distributed.

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0 200 400 600 800 1000z - PGA [cm/s2]

(Zz

)

Gumbel, case A

Log-normal, case A

Gumbel, case B

Log-normal, case B

A: Var(ln(Z) m,h)=0.462B: Var(ln(Z) m,h)=0.692




Example I – Model for Switzerland of SED (2004)

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source: SED

Example I – Model for Switzerland




Recent hazard map Recent frequency functions for >0.0001

Example I – Model for Switzerland

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Example II – Recent Model for NPP Beznau

• example is of Reichner et al. (Insights gained from the Beznau Seismic PSA, 10th Conference of PSAM, Seattle, 10. Juni 2010)• PEGASOS study: a PSHA with highest elaborated Level 4 according to SSHAC•SSHAC: “Senior Seismic Hazard Analysis Committee, Recommendations for PSHA, Guidance on Uncertainty and Use of Experts”, NUREG/CR-6372, 1997 (Logic tree)•Earlier PSHA :

• ETH Zurich, “Seismic Hazard Maps of Switzerland”, 1977.• Basler&Hofmann, “Beznau NPP, Site-Specific Seismic Hazard

Functions for Probabilistic Risk Assessment”, 1984.





1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

0 0.2 0.4 0.6 0.8 1 1.2Peak Ground Acceleration [g]

Exce

edan

ce F

requ

ency

[per

yea

r]

Median

Mean

84th Percentile

Beznau PEGASOS

Paks HungaryBeznau old

Seismic Hazard for Beznau (PEGASOS and Old Analysis) and for Paks Site

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Summary of Spectra of 30 Time Histories Used

0

1

2

3

4

5

6

0.1 1 10 100

Frequency (Hz )

Acc

ele

rati

on

(

TH 1

TH 2

TH 3

TH 4

Th 5

TH 6

TH 7

TH 8

TH 9

TH 10

TH 11

TH 12

TH 13

TH 14

TH 15

TH 16

TH 17

TH 18

TH 19

TH 2 0

TH 2 1

TH 2 2

TH 2 3

TH 2 4

TH 2 5

TH 2 6

TH 2 7

TH 2 8

TH 2 9

TH 3 0





Resulting Median and 84th-Percentile UHS from Time Histories compared to PEGASOS Target

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0 1 10 100

Frequency (Hz)

Acc

eler

atio

n (g

Ensemble Median Ensemble 84th

Target Median Target 84th

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Probabilistic Floor Response Spectra (5% Damping) for Operating Floor of Reactor Building compared with Deterministic Design Spectra

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.1 1.0 10.0 100.0Frequency [Hz]

Spe

ctra

l Acc

eler

atio

n [g

Prob. Median XProb. Median YProb. Median ZProb. 84% XProb. 84% YProb. 84% ZDet. XDet. YDet. Z





Contributions of Seismic Acceleration Levels (Spectral Acceleration 5 Hz) to core damage frequency (CDF) and large early release frequency (LERF) of Power Operation

0.00E+00 5.00E-06 1.00E-05 1.50E-05 2.00E-05 2.50E-05

Power Modes

Hot Shutdown

Cold Shutdown

Frequency [per calendar year]

All Initiators except Seismic

Seismic

Core/Fuel Damage

Large Release

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Contributions of SSCs to LERF of Power Operation

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Contribution to Large Early Release [-]

Seismic Failure

Random Failure




The large earthquake near Honshu and the impact on Fukushima

The energy magnitude is 8.6, the moment magnitude is 9.0. The locale shaking level has a return period of around 475 years. This is the design level of simple buildings. (source: USGS)

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The Tsunami problem

A Tsunami is a complex hydraulic phenomena and can be caused by an earthquake.The local wave height strongly depends on profile of the sea ground in front of the cost.The classical PSHA does not cover Tsunami hazard.

Buildings Facilitieswebarchiv.ethz.ch/lsa/education/vorl/snpp_slides_11/PSHA... · 2011. 5. 12. ·...

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