Transient finite-element soil-structure interaction analysis of nuclear power plants Ushnish Basu, Livermore Software Tech. Corp. Anil K. Chopra, UC Berkeley
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