Transient finite-element soil-structureinteraction analysis of nuclear power plants

Ushnish Basu, Livermore Software Tech. Corp.

Anil K. Chopra, UC Berkeley

Intro

duction

State-of-th

e-art

practice

Often

use

legacycodes

such

asSASSI,FLUSH

etc.

Draw

backs:

1.freq

.-dom

ainanalysis

uses

equivalen

tlinear

models

2.surface

free-field

motion

isdecon

volved

⇒plan

ewave

approxim

ation

3.approxim

atetreatm

entof

unbounded

dom

ain

ORrestricted

geometry.

Weneed

aration

alapproach

!

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Earth

quakes

andinteraction

Earth

quake

freefieldwith

absorbingboundary

EQFa

ult

Un

bo

un

de

d d

om

ain

Stru

cture

scattersearth

quake

motion

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Earth

quakes

andinteraction

Stru

cture

inearth

quake

with

absorbingboundary

Un

bo

un

de

d d

om

ain

EQFa

ult

Sca

ttere

d w

ave

Stru

cture

interacts

with

andscatters

earthquake

motion

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Earth

quakes

andinteraction

Sca

tteredwave

fieldwith

absorbingboundary

Un

bo

un

de

d d

om

ain

Sca

ttere

d w

ave

(ou

tgo

ing

)

Subtract

free-field

motion

toelim

inate

EQ

source

quake

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Earth

quakes

andinteraction

Bounded-domain

approxim

atio

nwith

absorbingboundary

Bo

un

de

d d

om

ain

Ou

tgo

ing

wa

ve

Cannot

modelunbounded

dom

ainquake

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Earth

quakes

andinteraction

Bounded-domain

approxim

atio

nwith

absorbingboundary

refle

cte

db

ack

Bo

un

de

d d

om

ain

Ou

tgo

ing

wa

ve

Cannot

toleratelarge

reflection

s

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Earth

quakes

andinteraction

Stru

cture

onboundedsoilwith

absorbingboundary

Ou

tgo

ing

wa

veA

bso

rbin

g b

ou

nd

ary

red

uce

s re

flectio

n

Absorb

ingboundary

simulates

unbounded

soil

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Review

ofearth

quake

analysis

REVIEW

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Review

ofearth

quake

analysis

Step1:Getfre

e-field

groundmotio

ns

EQFa

ult

Un

bo

un

de

d d

om

ain

Earth

quake

generates

free-field

groundmotion

s

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Review

ofearth

quake

analysis

Step2:Modelstru

cture-so

ilinteractio

n

Un

bo

un

de

d d

om

ain

EQFa

ult

Sca

ttere

d w

ave

Stru

cture

interacts

with

andscatters

earthquake

motion

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Review

ofearth

quake

analysis

Step3:Absorb

outgoingsca

tteredwave

s

Ou

tgo

ing

wa

veA

bso

rbin

g b

ou

nd

ary

red

uce

s re

flectio

n

Absorb

ingboundary

foroutgoin

gwaves

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Review

ofearth

quake

analysis

Alltogether

Step

1:Get

free-field

groundmotion

s

Step

2:Modelstru

cture-soil

interaction

Step

3:Absorb

outgoin

gscattered

waves

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Review

ofearth

quake

analysis

Alltogether

Step

1:Get

free-field

groundmotion

s[later]

Step

2:Modelstru

cture-soil

interaction

3

Step

3:Absorb

outgoin

gscattered

waves

3

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PMLabsorb

ingboundary

Choice

ofabsorbingboundary

Practical

choice:

perfectly

match

edlayer

(PML)

Atte

nu

ate

dw

ave

Re

flecte

d w

ave

Ou

tgo

ing

wa

ve

PM

LE

lastic

mediu

m

Norefl

ectionfrom

interface

⇒perfectly

match

ed

Reflected

wave

canbemadeinsign

ifican

t

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PMLabsorb

ingboundary

Perfe

ctlymatch

edlaye

r(P

ML)

Origin

allydevelop

edfor

electromagn

eticwaves

[Beren

ger(1994);

Chew

-Weed

on(1994)]

Later

develop

edfor

elasticwaves

with

•disp

lacement-b

asedFEim

plem

entation

•exp

licittim

e-integration

[Basu

-Chopra

(2003,2004),Basu

(2009)]

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

Elastic

rod:aone-dim

ensio

nalsyste

m(P

MM)

Sem

i-infinite

rod:sim

plemodelof

unbounded

half-sp

ace8

Only

rightward

waves

allowed

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

Elastic

rod:Perfe

ctlymatch

edmedium

(PMM)

Math

ematically

design

edto

dam

poutwaves

8

Uses

adam

pingfunction

f(x)

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

Elastic

rodwith

PMM(P

ML)

f(x)

8

Reflection

atinterface?

No,

medium

ismath

ematically

design

edto

not

reflect

⇒Perfect

match

ingproperty

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

Elastic

rodwith

PML(P

MM)

LP

8

Truncate

toget

theperfectly

match

edlayer

Effect

oftru

ncation

?Wave

isrefl

ected

Reflected

wave

amplitu

de

|R|=

exp[−2F(L

P)],

F=

∫

fdx

controllab

leby

fandL

P

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PMLpara

meters

Goodchoice

ofatten

uation

function

anddepth

oflayer?

Typically,

choose

f(x)=

f0

(

xLP

)

m

Typically,

m=

2works

best

forfinite-elem

entanalysis

f0may

bechosen

fromsim

plified

discrete

analysis

[Bindel-G

ovindjee

(2005),Basu

(2009)]

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PML:3D

exa

mple

Applied

verticalforce

oversquare

areaon

ahalf-sp

ace

b

8

Fo

rce

Ha

lf−sp

ace

time

Benchmark

modelClassical

absorb

ingboundary

model

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PML:3D

exa

mple

PMLmodel(quarter

mesh

)

PM

L

6b

b/2

5.5

b

b/2

Ela

stic

fixe

d b

ou

nd

ary

Fo

rce

≈12

elements

per

shortest

wavelen

gth;5-elem

entPML

(mesh

density

inPMLsam

eas

inelastic

medium)

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PML:3D

exa

mple

Reduce

thedom

ainsize

PM

L

Fo

rce

Main

tainmesh

density

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PML:3D

exa

mple

PMLmodel(cross-section

)

CLA

tten

ua

tion

fun

ctio

ns

PM

L

V

b/5

b/5

b4b/5

4b/5

PMLplaced

veryclose

tosou

rce(8-elem

entPML)

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PML:3D

exa

mple

Dash

pot

model(cross-section

)

CL

Ela

stic

Da

sh

po

ts

b

V

b

b

Classical

model(sam

esize

asPMLmodel)

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PML:3D

exa

mple

Exten

ded-m

eshmodel(cross-section

)

CL

Ela

stic

V

25b

20b

b

Benchmark

model(≈

12elem

s/wavelen

gth)

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PML:3D

exa

mple

Excitation

andresp

onse

Apply

verticalforce:

-1 0 1

30

20

10

force

time

Com

pute

verticaldisp

lacementat

center

andcorn

er

Retu

rntim

eof

extd.mesh

>30

(norm

alisedtim

e)

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PML:3D

exa

mple

Center

disp

lacement

-0.5 0

0.5

0 1

0 2

0 3

0

displacement

time

PM

LE

xtd

. mesh

Dashpots

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PML:3D

exa

mple

Center

disp

lacement

-0.5 0

0.5

0 1

0 2

0 3

0

displacement

time

PM

LE

xtd

. mesh

Dashpots

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PML:3D

exa

mple

Center

disp

lacement

-0.5 0

0.5

0 1

0 2

0 3

0

displacement

time

PM

LE

xtd

. mesh

Dashpots

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PML:3D

exa

mple

Corn

erdisp

lacement

-0.5 0

0.5

0 1

0 2

0 3

0

displacement

time

PM

LE

xtd

. mesh

Dashpots

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PML:3D

exa

mple

Error:%

error=

max|u

PML−

uEXT|

max|u

EXT|

×100

Model

Center

disp

lacement

Corn

erdisp

lacement

PML

5%6%

Dash

pots

46%85%

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PML:3D

exa

mple

Com

putation

alcosts:

Model

Elem

ents

Tim

estep

sWall-clo

cktim

e

PML

4thousan

d600

30secs

Dash

pots

4thousan

d900

15secs

Extd

.mesh

10million

90035

proc-h

rs

PMLanddash

pot

results

computed

ondesktop

workstation

Extd

.mesh

results

required

asupercom

puter

and

parallelised

andspecially-op

timised

code

àPMLguaran

teesaccu

rateresu

ltsat

lowcost

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

PML:elastic

rod

PML:3D

exa

mple

Som

erem

arks:

1.Long-tim

estab

ilityverifi

ednumerically

2.Tim

e-stepwith

PMLsam

eas

with

elasticelem

ent

3.In

lastexam

ple,

results

for5-elem

entPMLclose

to

exact,butnot

perfect

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

GO

BACK

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Earth

quake

freefieldwith

absorbingboundary

EQFa

ult

Un

bo

un

de

d d

om

ain

Stru

cture

scattersearth

quake

motion

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Stru

cture

inearth

quake

with

absorbingboundary

Un

bo

un

de

d d

om

ain

EQFa

ult

Sca

ttere

d w

ave

Stru

cture

interacts

with

andscatters

earthquake

motion

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Sca

tteredwave

fieldwith

absorbingboundary

Un

bo

un

de

d d

om

ain

Sca

ttere

d w

ave

(ou

tgo

ing

)

Subtract

free-field

motion

toelim

inate

EQ

source

quake

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Stru

cture

onboundedsoilwith

absorbingboundary

Ou

tgo

ing

wa

veA

bso

rbin

g b

ou

nd

ary

red

uce

s re

flectio

n

Absorb

ingboundary

simulates

unbounded

soil

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Twoquestio

ns

How

dowe:

1.apply

thegrou

ndmotion

?

2.start

fromastatic

stateof

thestru

cture?

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Applyin

gthegroundmotio

n

Scatte

red

mo

tion

Dis

co

ntin

uity

To

tal m

otio

n

Stru

cture

onbounded

soilwith

absorb

ingboundary

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Applyin

gthegroundmotio

n

Scatte

red

mo

tion

Dis

co

ntin

uity

To

tal m

otio

n

Soil

has

scatteredmotion

...absorb

ingboundary

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Applyin

gthegroundmotio

n

Scatte

red

mo

tion

Dis

co

ntin

uity

To

tal m

otio

n

butstru

cture

has

totalmotion

absorb

ingboundary

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Applyin

gthegroundmotio

n

Scatte

red

mo

tion

Dis

co

ntin

uity

To

tal m

otio

n

Discon

tinuity

atinterface

createseff

ectiveforces

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Applyin

gthegroundmotio

n

Discon

tinuity

isexactly

thefree-fi

eldgrou

ndmotion

⇒eff

ectiveforces

dependonly

on

free-field

groundmotion

attheinterface

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Applyin

gthegroundmotio

n

Discon

tinuity

isexactly

thefree-fi

eldgrou

ndmotion

⇒eff

ectiveforces

dependonly

on

free-field

groundmotion

attheinterface

Effective

seism

icinputmethod

[Herrera,

Bielak

(1977);Bielak,

Christian

o(1984)]

compute

effective

seismicforces

attheinterface

usin

gonly

free-field

groundmotion

sat

theinterface

⇒nodecon

volution

isnecessary

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Startin

gfro

masta

ticsta

te

Intran

sientanalysis,

soilcan

not

carryanystatic

load,

becau

se

•PMLcan

not

carryanystatic

load

•Static

stateiselim

inated

inscattered

-motion

formulation

So:

1.Doastatic

analysis

ofthestru

cture

andsoil

2.Start

thetran

sientanalysis

with

thestresses

inthe

structu

reinitialized

tothestatic

state

3.Apply

staticreaction

sat

thebase

ofthestru

cture

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Transie

ntanalysis

procedure

•Equivalen

tto

propagatin

gearth

quake

fromfau

ltto

site

•Fully

finite-elem

entpro

cedure

•Uses

PMLfor

soil

Numerical

validation

:

•Com

plete

fortwo-d

imension

alanalysis,

against

EAGD-84

•Ongoin

gfor

three-d

imension

alanalysis,

against

EACD-3D

-2008

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Valid

atio

nforMorro

wPointDam

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Interaction

analysis

Valid

atio

nforMorro

wPointDam

0

4.0

E-3

0 5

10

center-crest, upstream direction displacement amplitude, ft

freq

ue

ncy, H

z

Fo

urie

r tran

sfo

rm

EA

CD

LS

-DY

NA

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Generatin

gfree-fi

eldgrou

ndmotion

sat

interface

Alltogether

Step

1:Get

free-field

groundmotion

s(now

!)

Step

2:Modelstru

cture-soil

interaction

3

Step

3:Absorb

outgoin

gscattered

waves

3

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu

Generatin

gfree-fi

eldgrou

ndmotion

sat

interface

Spectru

mofoptio

ns

1.Use

PSHAmotion

sdirectly

atinterface

2.Use

decon

volvedmotion

sto

generate

motion

s

3.Dom

ainred

uction

meth

od

4.Fullregion

modelin

g

Transie

ntfinite

-elementSSIanalysis

Ushnish

Basu