SPRA Methodology: Fragility Analysis

(1)

G. Hardy, Simpson Gumpertz & Heger

Senior Principal

SMiRT 25 Workshop

August 9, 2019

Seismic Fragility

Methodology

(2)

Seismic Fragility

§

Fragility is the conditional probability of "failure” of a structure or

component for a given peak ground acceleration.

§

Fragility is used:

–

To estimate the conditional probability of occurrence of initiating events

(e.g., LOSP, small LOCA)

(3)

Seismic Probabilistic Risk Assessment

Component-Fragility

Evaluation

Seismic Hazard Analysis

Seismic Motion

Parameter

Fre

qu

enc

y

of

exceed

an

ce

Event Trees

Fault Trees

Containment Analysis

P

_i

P

_i

P i

Systems Analysis

Seismic Motion

Parameter

C

o

n

d

iti

o

n

a

l

Pr

o

b

a

b

ili

ty

o

f

F

a

ilu

re

Release FrequencyConsequence Analysis

Risk

Frequency

P

rob

abi

li

ty

D

ens

it

y

Damage

Fr

eque

nc

y

of

Ex

ce

ed

an

ce

Property damage

Health effects

Evacuation

Population

dispersion

Atmospheric

Weather data

1

3

2

(4)

Example 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)

CO

N

DI

TI

O

N

AL

PR

O

B

A

B

ILI

TY

O

F

FA

ILU

R

E

b

_R

= 0.25

b

U

= 0.35

A

_m

_{= 0.87 g}

0.068 Mean

0.20

0.79

(5)

Some Basics on Random Distributions

Probability Density Function (PDF) for Normal Distribution

Failure data for many components exhibit the Lognormal Distributions

Parameter Measured

Nu

m

b

er

o

f

Sa

m

p

le

s

or

Fr

equency

of

S

am

pl

(6)

Selection of Distribution for Fragility Analysis

(7)

Form of Fragility Curve

(8)

Fragility Model

§

Lognormal model is typically assumed (all properties of variables have

lognormal distributions, e.g. the natural logs of the distributions are normally

distributed).

§

Strength and response tend to be lognormally distributed in nature.

§

Mathematical treatment is simple.

§

Entire fragility curve and its aleatory and epistemic variability can be expressed

by three parameters: A

_m

,

b

_R

,

b

_U

where:

–

A

_m

= median acceleration capacity (PGA or Sa may be used as the reference ground

motion parameter)

–

β

_R

= Logarithmic standard deviation of the aleatory uncertainty (randomness) of the

variables contributing to the fragility description

–

β

_U

= Logarithmic standard deviation of epistemic uncertainty (incomplete knowledge)

of variables contributing to the fragility description

(9)

Fragility Model (continued)

§

Single “Mean” Fragility Curve is expressed as:

§

where Z is the number of logarithmic standard

deviations from the median value of A

_m

§

From normal distribution tables,

Given:

A

_m

= 0.87g

β

_R

= 0.25

β

_U

= 0.35

β

_C

= 0.43

C

z

m

e

A

a

=

b

c

Am

a

n

Z

b

)

/

(

!

=

)

(

Z

PF

=

F

a

Value of Z

Probability of

Failure

0.32 -2.33

0.01 (HCLPF)

0.36 -2.05

0.02

0.43 -1.65

0.06

0.57 -1.0

0.16

0.87

0

0.5

1.34

1.0

0.84

1.77

1.65

0.94

2.1

2.05

0.98

(10)

Example 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)

CO

N

DI

TI

O

N

AL

PR

O

B

A

B

ILI

TY

O

F

FA

ILU

R

E

b

_R

= 0.25

b

U

= 0.35

A

_m

_{= 0.87 g}

(11)

Fragility Resources

§

Primary resource available for seismic fragilities is the 2018 EPRI

Seismic Fragility/Margin Guide (EPRI 3002012994)

§

Many earlier EPRI fragility and margin documents were subsumed

into this new report

(12)

Primary Resource – EPRI Seismic Fragility/Margin Guide

§

Seismic Fragility and Seismic Margin Guidance for Seismic

Probabilistic Risk Assessments, Sept 2018 (EPRI 3002012994)

§

A collection of EPRI seismic fragility documents from the past 25

years have been used for fragility analysis

§

Developed a single document that combines

past fragility knowledge and key new

developments

(13)

Seismic Fragility Research – Updated Fragility Guide

EPRI

3002012994

September 2018

Incorporated and

Superseded

TR-103959

1002988

1019200

Incorporated In Part

and Retained

(14)

Seismic Fragility Analysis – Updated Fragility Guide

1. INTRODUCTION AND SCOPE

2. BACKGROUND

a)

SPRA Background

b)

SMA Background

c)

Hybrid Method

3. FRAGILITY METHODOLOGIES

a)

Fragility Concepts

b)

Lognormal Fragility Model

c)

Separation of Variables

d)

Hybrid Fragility Approach

4. SEISMIC CAPACITY

a)

Capacity Factor

b)

Material Strengths

c)

Structural Failure Modes and Capacities

d)

Structure Inelastic Energy Absorption

e)

Equipment Failure Modes and Capacities

f)

Anchorage Failure Modes and Capacities

g)

Equipment Inelastic Energy Absorption

h)

Test Based Capacities

i)

Capacities Using NP-6041 and EQ Experience

5. SEISMIC DEMAND

a)

General

b)

Reference Earthquake

c)

Evaluation of Median and 84th Percentile Seismic Demand

d)

Response Variables for Fragility Analysis of Structures

e)

Response Variables for Fragility Analysis of Equipment

6. FRAGILITY IMPLEMENTATION TOPICS

a)

Seismic Walkdown

b)

Identification of High Capacity Components

c)

Screening and Representative Fragilities

d)

Relay Evaluations

e)

Special Considerations for High Frequency Demand

f)

Methods for Spectral Clipping

g)

Structural Models for Seismic Response Analysis

h)

Response Analysis Scaling Methods

(15)

Seismic Fragility Analysis – Updated Fragility Guide, Appendices

A. English to SI Unit Conversion

B. Walkdown Criteria: General Guidance

C. Walkdown Criteria: Basis for Seismic Capacity Guidelines for

Structures, Equipment, and Subsystems

D. Walkdown Criteria: Sampling Guidelines

E. Fragility Methods: Background on Recommendations for Hook

Anchors and Deeply Embedded Anchors

F. Fragility Methods: Influence of Small Concrete Cracks on Expansion

Anchors

G. Fragility Methods: Comparison of ASCE/SEI 43 Design Criteria and

CDFM Criteria for Low Ductility Failure Modes

H. Fragility Methods: Issues Concerning the Inclusion of Response

Spectral Peak and Valley Variability in Development of Fragility and

HCLPF Capacity Estimates

I. Fragility Methods: Horizontal Direction Peak Response Variability

J. Fragility Methods: Development of Test-Based Fragility Parameters

K. Fragility Methods: Treatment of Small-Small Loss of Coolant

Accidents in Fragility Analysis

L. Response Analysis: Refinement of In-Cabinet Amplification Factors

M. Response Analysis: Benchmark Studies to Verify an Approximate

Method for Spectra Scaling

N. Response Analysis: Development of In-Structure Response Spectra

for Seismic Margin or Seismic PRA Evaluation by Scaling

O. Example: Fragility Analysis of a Reinforced Concrete Shear Wall

P. Example: Cylindrical Concrete Wall CDFM Capacity

Q. Example: CDFM Analysis of Lightly Reinforced Non-Load Bearing

Masonry Walls

R. Example: Comparison of ASCE/SEI 43-05/Barda and Gulec/Whittaker

Strengths for an Example Low-Rise Shear Wall

S. Example: Fragility and CDFM Analysis of a Metal Flat-Bottom Vertical

Liquid Storage Tank

T. Example: Heat Exchanger Fragility by Separation of Variables and

Hybrid Approaches

U. Example: Fragility for Service Water Pump

V. Example: Expansion Anchor Fragility by Separation of Variables and

Hybrid Approaches

W. Example: CDFM Evaluation for Fillet Weld Anchorage

X. Example: Fragility Analysis for Equipment Qualified by Testing

Y. Example: Fragilities Derived from Experience Data

(16)

“What’s New” in the Updated Fragility Guide?

§

New Tools and Fragility Data

–

Walkdown Forms for SPRA/SMA provided in pdf

format

–

Excel version of fragility curves and HCLPF

calculations embedded in digital report

–

New (higher) seismic capacities based on

earthquake experience data documented

–

New high frequency test data referenced from EPRI

testing

–

Reviews of existing data

–

Consistent set of fragility parameters throughout

the report, including the examples

–

Examples for both SOV fragility and Hybrid (HCLPF

and generic β’s) provided

§

Update to Fragility Methods

–

Incorporate key elements of current

codes/standards (ASCE, AISC, ACI, etc.) criteria

–

Incorporate EPRI research projects over last decade

§

Deeply embedded anchor capacities

§

Refined cabinet horizontal amplification factors

§

Bounding vertical amplification factors

–

Incorporate latest methods/criteria from NTTF 2.1

SPRA experience

§

Reference earthquake definition

(17)

(18)

Failure Modes for Seismic Fragility

Element

Limit States

Structures

• _Collapse

• Loss of equipment anchorage due to excessive concrete cracking resulted

from inelastic deformations

• Seismic-induced sliding

Piping

• Fracture or Collapse of Pressure Boundary

• Failure of Supports

Equipment

• _{Structural – Bending, Buckling of Supports, Anchor Bolt Pull-Out, Nozzles,}

etc.

• Functional – Binding of Valve, Excessive Deflection, Relay Chatter

(19)

Failure Modes for Seismic Fragility (continued)

Element

Limit States

Soil-Related

Failure

Modes

• _Liquefaction

• Toe Bearing

• _{Base Slab Uplift}

• Slope Instability

Dams

• Cracking

• Rupture

(20)

(21)

(22)

Separation of Variables Fragility Derivation

§

Fragility typically expressed in terms of a reference earthquake

and developed from design information by quantifying factors of

conservatism and variability.

A

_m

= F

_C

F

_ER

F

_RS

A

_RE

F

_C

= Capacity Factor (Strength and Ductility Contribute)

F

_ER

= Response Factor for Equipment

F

_RS

= Response Factor for Structure

(23)

(24)

SOV Fragility Derivation

𝐹

_"

= 𝐹

_$

𝐹

_%

𝐹

_&$

= 𝐹

_$'

𝐹

_()*&

𝐹

₊

𝐹

_,-

𝐹

_.-

𝐹

_/-

𝐹

_0"

𝐹

₀₍

𝐹

_/"-

𝐹

_1/2

𝐹

_$$2

𝐹

_+$+

𝐹

_2&

𝐹

_3&

= 𝐹

_4/

𝐹

_$$

𝐹

_,5

𝐹

_.5

𝐹

_/5

𝐹

_/"5

𝐹

_3""5

𝛽

_"

=

𝛽

_$

7 + 𝛽

_%

7 9/7

(25)

SOV Fragility Derivation

F

_S

Elastic Strength Factor

F

_µ

Inelastic Energy Absorption Factor

F

_QM

Qualification method factor

F

_SS

Equipment in-structure spectral shape

factor

F

_δe

Equipment damping factor

F

_fe

Equipment model frequency factor

F

_Me

Equipment model fidelity factor

F

_MCe

Equipment mode combination factor

F

_ECCe

Earthquake component combination factor

for equipment response

F

_SA

Ground motion factor for spectral shape

F

_HDPR

Ground motion factor for horizontal

direction peak response

F

_V

Ground motion factor for vertical to

horizontal ground acceleration ratio

F

_δs

Structure damping factor

F

_fs

Structure model frequency factor

F

_Ms

Structure model fidelity factor

F

_TC

Structure model torsional coupling factor

F

_TH

Time-history phasing factor

F

_MCs

Structure mode combination factor

F

_GMI

Foundation structure interaction factor for

ground motion incoherence

F

_SSI

Foundation structure interaction factor for

soil-structure interaction

F

_VSV

Foundation structure interaction factor for

vertical spatial variation

F

_ECCs

Earthquake component combination factor

for structure response

(26)

(27)

Heat Exchanger Fragility

§

Example Problem in EPRI Fragility Training Course

§

HE dimensions, anchorage and weights provided

§

Seismic response provided

(28)

Potential Failure Modes Evaluated

§

Failure through the steel anchor bolt.

§

Failure of the anchor bolt in the concrete.

§

Failure of the support base plate due to bending.

§

Failure of the weld connection between the base and vertical

(29)

Summary of Fragility Results

§

The critical (governing) failure mode was the shear failure of anchor bolt steel;

concrete breakout strength in tension and shear were calculated to be much

higher.

§

Separation of Variables Method

- HCLPF Capacity = 0.32g

- Randomness β

_R

= 0.19

- Uncertainty in median capacity β

_U

= 0.21

- Median capacity A

_m

= 0.62g

§

Hybrid Method

- CDFM Calculated HCLPF Capacity = 0.30g

- Randomness β

_R

= 0.24

- Uncertainty in median capacity β

_U

= 0.26

(30)

(31)

Seismic Walkdowns

§

Seismic walkdowns are an important element in the seismic PRA

process. The primary purpose of walkdowns is:

–

Verify that the seismic fragilities / margins / HCLPFs are realistic and plant

specific, and

–

To find any as-designed, as-built and as-operated seismic vulnerabilities

in the plant.

–

Ensure that no other adverse issues (corrosion, cracking or degraded

(32)

Screening and Evaluation Work Sheets (SEWS)

§

Record location of SSC

–

Screening tables are originally applicable for components mounted less than about 40 feet above

effective grade

–

Updated to compare the ISRS with 1.5 times screening levels of Table 2-4

§

Equipment caveats evaluation

–

When all caveats developed from earthquake experience data base are met, equipment itself can be