Site Response
Transcript of Site Response
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One-Dimensional Site Response AnalysisOne-Dimensional Site Response Analysis
What do we mean?
One-dimensional = Waves propagate in one direction only
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One-Dimensional Site Response AnalysisOne-Dimensional Site Response Analysis
What do we mean?
One-dimensional = waves propagate in one direction onlyMotion is identical on planes perpendicular to that motion
to infinityto infinity
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One-Dimensional Site Response AnalysisOne-Dimensional Site Response Analysis
What do we mean?
One-dimensional = waves propagate in one direction onlyMotion is identical on planes perpendicular to that motion
Can’t handle refraction so layer boundaries must be perpendicular to
direction of wave propagation
Usual assumption is vertically-propagating shear !"# waves
Horizontal input motion
Horizontal surface motion
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One-Dimensional Site Response AnalysisOne-Dimensional Site Response Analysis
When are one-dimensional analyses appropriate?
!tiffer
with
depth
Focus
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One-Dimensional Site Response AnalysisOne-Dimensional Site Response Analysis
When are one-dimensional analyses appropriate?
!tiffer
with
depth
Horizontal boundaries –waves tend to be refracted
toward vertical
Decreasing stiffness
causes refraction of waves
to increasingly vertical
pat
Focus
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One-Dimensional Site Response AnalysisOne-Dimensional Site Response Analysis
When are one-dimensional analyses appropriate?
!tiffer with
depth
!otappropriate
ere
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$etaining structures
%ams and
emban&ments
'unnels
One-Dimensional Site Response AnalysisOne-Dimensional Site Response Analysis
When are one-dimensional analyses appropriate?
(nclined ground surface and)or non-
hori*ontal boundaries can re+uire use
of two-dimensional analyses
!ot ere"!ot ere"
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Comple, soilconditions
%ams in
narrow
canyons
Multiple
structures
One-Dimensional Site Response AnalysisOne-Dimensional Site Response Analysis
When are one-dimensional analyses appropriate?
ocali*ed structures may re+uire
use of .-% response analyses
!ot ere"!ot ere"
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One-Dimensional Site Response AnalysisOne-Dimensional Site Response Analysis
"ow should ground motions be applied?
#ncoming motion
u i
Roc$outcropping
motion
2u i
%edroc$ motion
u i + u r
Free surface
motion
u s
!ot te same"!ot te same"
Soil
Rock
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One-Dimensional Site Response AnalysisOne-Dimensional Site Response Analysis
"ow should ground motions be applied?
Ob&ect motion
Free surface
motion
u s
(nput ob/ect# motion
(f recorded at roc& outcrop0 apply as
outcrop motion program will remove
free surface effect#1 2edroc& should
be modeled as an elastic half-space1
(f recorded in boring0 apply as within-
profile motion recording does notinclude free surface effect#1 2edroc&
should be modeled as rigid1
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Comple, $esponse Method
3pproach used in computer programs li&e !"345
'ransfer function is used with input motion to compute surface motion
convolution#
6or layered profiles0 transfer function is 7built8 layer-by-layer to go from input
motion to surface motion
Amplification
De-amplification
'etods of One-Dimensional Site Response Analysis'etods of One-Dimensional Site Response Analysis
Single
elastic
layer
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(ayer j )*
(ayer j
* 9
9
9
9
9
9
ξ
ξ
ξ
ξ
ξ
ξ
ρ
ρ
ρ
ρ
ρ
ρ
:
; < :
;
/ < :
/
=
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:
=
/
;
:
=
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:
=
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;
; < :
:
=
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;
; < :*
h
h
h
h
h
*
*
*
*Consider the soil deposit shown to the
right1 Within a given layer0 say ayer j 0 the hori*ontal displacements will be
given by
( ) ( ) j j j i k z
j ik z i t u z t A e B e e j j j j,
* *= +
− ω
3t the boundary between layer j and layer j <:0 compatibility of displacements
re+uires that
j j j i k h j i k h A B A e B e j j j j+ + −+ = +1 1* *
Continuity of shear stresses re+uires that
j j j j
j j
ik h j j
ik h A BG k
G k
A e B e s j s j+ ++ +
−− = −
1 1
1 1
* *
* *
* *
+omple, Response 'etod (inear analysis.+omple, Response 'etod (inear analysis.
Amplitudes of upward- anddownward-traveling waves in (ayer j
5+uilibrium satisfied
;o slip
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%efining α> / as the comple, impedance ratio at the boundary between layers
j and j <:0 the wave amplitudes for layer j <: can be obtained from the
amplitudes of layer j by solving the previous two e+uations simultaneously
( ) ( ) j j j i k h
j j i k h A A e B e j j j j+
−= + + −11
2 1
1
2 1* ** *
α α
( ) ( ) j j j
i k h j j
i k h B A e B e j j j j
+
−= − + +11
2 1
1
2 1* ** *
α α
Wave amplitudes in ayer j
Wave amplitudes in ayer j <:
!o0 if we can go from ayer j to ayer j <:0 we can go from j <: to j <0 etc1
'his means we can apply this relationship recursively and e,press the amplitudes in
any layer as functions of the amplitudes in any other layer1 We can therefore 7build8
a transfer function by repeated application of the above e+uations1
+omple, Response 'etod (inear analysis.+omple, Response 'etod (inear analysis.
ropagation of wave
energy from one layer to
another is controlled by
comple,# impedance ratio
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+omple, Response 'etod (inear analysis.+omple, Response 'etod (inear analysis.
!ingle layer on rigid base
H = :@@ ft
V s = A@@ ft)sec
ξ = :@B
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+omple, Response 'etod (inear analysis.+omple, Response 'etod (inear analysis.
!ingle layer on rigid base
H = A@ ft
V s = :0A@@ ft)sec
ξ = :@B
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+omple, Response 'etod (inear analysis.+omple, Response 'etod (inear analysis.
!ingle layer on rigid base
H = :@@ ft
V s = .@@ ft)sec
ξ = AB
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+omple, Response 'etod (inear analysis.+omple, Response 'etod (inear analysis.
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+omple, Response 'etod (inear analysis.+omple, Response 'etod (inear analysis.
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+omple, Response 'etod (inear analysis.+omple, Response 'etod (inear analysis.
%ifferent se+uence of soil layers
%ifferent transfer function
%ifferent response
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+omple, Response 'etod (inear analysis.+omple, Response 'etod (inear analysis.
3nother se+uence of soil layers
%ifferent transfer function
%ifferent response
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+omple, Response 'etod (inear analysis.+omple, Response 'etod (inear analysis.
Comple, response method operates in fre+uency domain
(nput motion represented as sum of series of sine waves!olution for each sine wave obtained
!olutions added together to get total response
rinciple of
superposition
τ
γ
inear
system
Can we capture important effects of nonlinearity with linear model?
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!oils e,hibit nonlinear0 inelastic behavior under cyclic loading conditions
!tiffness decreases and damping increases as cyclic strain amplitude increases
'he nonlinear0 inelastic stress-strain behavior of cyclically loaded soils can be
appro,imated by e+uivalent linear properties1
)log( eff γ )log( eff γ
ξ
5+uivalent shear modulus5+uivalent shear modulus 5+uivalent damping ratio5+uivalent damping ratio
max/ GG
/0uivalent (inear Approac/0uivalent (inear Approac
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)log( eff γ )log( eff γ
ξmax
/ GG
3ssume some initial strain and use to estimate 9 and ξ 3ssume some initial strain and use to estimate 9 and ξ
*. *.
!oils e,hibit nonlinear0 inelastic behavior under cyclic loading conditions
!tiffness decreases and damping increases as cyclic strain amplitude increases
'he nonlinear0 inelastic stress-strain behavior of cyclically loaded soils can be
appro,imated by e+uivalent linear properties1
/0uivalent (inear Approac/0uivalent (inear Approac
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)log( eff γ )log( eff γ
ξmax
/ GG
γ :# γ :#
Use these values to compute responseUse these values to compute response
!oils e,hibit nonlinear0 inelastic behavior under cyclic loading conditions
!tiffness decreases and damping increases as cyclic strain amplitude increases
'he nonlinear0 inelastic stress-strain behavior of cyclically loaded soils can be
appro,imated by e+uivalent linear properties1
/0uivalent (inear Approac/0uivalent (inear Approac
γ t #
t
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)log( eff γ )log( eff γ
ξmax
/ GG
γ :# γ :#
%etermine pea& strain and effective strain
γ eff
= $γ
γ ma,
%etermine pea& strain and effective strain
γ eff = $γ γ ma,
!oils e,hibit nonlinear0 inelastic behavior under cyclic loading conditions
!tiffness decreases and damping increases as cyclic strain amplitude increases
'he nonlinear0 inelastic stress-strain behavior of cyclically loaded soils can be
appro,imated by e+uivalent linear properties1
/0uivalent (inear Approac/0uivalent (inear Approac
γ t #
t
γ ma,γ eff
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)log( eff γ )log( eff γ
ξmax
/ GG
γ :# γ :#γ #
γ #
!elect properties based on updated strain level!elect properties based on updated strain level
!oils e,hibit nonlinear0 inelastic behavior under cyclic loading conditions
!tiffness decreases and damping increases as cyclic strain amplitude increases
'he nonlinear0 inelastic stress-strain behavior of cyclically loaded soils can be
appro,imated by e+uivalent linear properties1
/0uivalent (inear Approac/0uivalent (inear Approac
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)log( eff γ )log( eff γ
ξmax
/ GG
γ :# γ :#γ #
γ #γ .# γ .#
Compute response with new properties and determine
resulting effective shear strain
Compute response with new properties and determine
resulting effective shear strain
!oils e,hibit nonlinear0 inelastic behavior under cyclic loading conditions
!tiffness decreases and damping increases as cyclic strain amplitude increases
'he nonlinear0 inelastic stress-strain behavior of cyclically loaded soils can be
appro,imated by e+uivalent linear properties1
/0uivalent (inear Approac/0uivalent (inear Approac
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)log( eff γ )log( eff γ
ξmax
/ GG
$epeat until computed effective strains are
consistent with assumed effective strains
$epeat until computed effective strains are
consistent with assumed effective strains
γ eff γ eff
!oils e,hibit nonlinear0 inelastic behavior under cyclic loading conditions
!tiffness decreases and damping increases as cyclic strain amplitude increases
'he nonlinear0 inelastic stress-strain behavior of cyclically loaded soils can be
appro,imated by e+uivalent linear properties1
/0uivalent (inear Approac/0uivalent (inear Approac
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3dvantages
Can wor& in fre+uency domainCompute transfer function at relatively small number of fre+uencies
compared to doing calculations at all time steps#
(ncreased speed not that significant for :-% analyses
(ncreased speed can be significant for -%0 .-% analyses
5+uivalent linear properties readily available for many soils D familiarity
breeds comfort)confidence
Can ma&e first-order appro,imation to effects of nonlinearity and inelasticity
within framewor& of a linear model
/0uivalent (inear Approac/0uivalent (inear Approac
'he e+uivalent linear approach is an appro,imation1 ;onlinear analyses are
capable of representing the actual behavior of soils much more accurately1
E often0 a very good oneF
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!onlinear Analysis!onlinear Analysis
2 3
2 2
u u
z t z t
∂τ ∂ ∂= ρ + η∂ ∂ ∂ ∂
5+uation of motion must be integrated in time domain
Wave e+uation for
visco-elastic medium
*
%ivide profile
into series of
layers
%ivide time into series of time stepst
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!onlinear Analysis!onlinear Analysis
2 3
2 2
u u
z t z t
∂τ ∂ ∂= ρ + η∂ ∂ ∂ ∂
5+uation of motion must be integrated in time domain
Wave e+uation for
visco-elastic medium
*
%ivide profile
into series of
layers
%ivide time into series of time stepst
v i/ = v z = z i0 t = t /#
t /
z i
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!onlinear Analysis!onlinear Analysis
2 3
2 2
u u
z t z t
∂τ ∂ ∂= ρ + η∂ ∂ ∂ ∂
5+uation of motion must be integrated in time domain
Wave e+uation for
visco-elastic medium
*
t t /
z i
, 1/ 2 , ,
1
2i j i j i jv v a t + = + ∆%
, 1 , , 1/ 21
2i j i j i ju u v t + += + ∆%
, 1 , 1/ 2 , 11
2i j i j i jv v a t + + += + ∆%
More steps0 but basic process
involves using wave e+uation to
predict conditions at time j <: from
conditions at time j for all layers in
profile1
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!onlinear Analysis!onlinear Analysis
2 3
2 2
u u
z t z t
∂τ ∂ ∂= ρ + η∂ ∂ ∂ ∂
5+uation of motion must be integrated in time domain
Wave e+uation for
visco-elastic medium
*
t t /
z i
More steps0 but basic process
involves using wave e+uation to
predict conditions at time j <: from
conditions at time j for all layers in
profile1
Can change material properties
for use in ne,t time step1
Changing stiffness based on
strain level0 strain history0 etc1 can
allow prediction of nonlinear0
inelastic response1
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!onlinear Analysis!onlinear Analysis
2 3
2 2
u u
z t z t
∂τ ∂ ∂= ρ + η∂ ∂ ∂ ∂
5+uation of motion must be integrated in time domain
Wave e+uation for
visco-elastic medium
*
t t /
z i
More steps0 but basic process
involves using wave e+uation to
predict conditions at time j <: from
conditions at time j for all layers in
profile1
Can change material properties
for use in ne,t time step1
Changing stiffness based on
strain level0 strain history0 etc1 can
allow prediction of nonlinear0
inelastic response1
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!onlinear Analysis!onlinear Analysis
2 3
2 2
u u
z t z t
∂τ ∂ ∂= ρ + η∂ ∂ ∂ ∂
5+uation of motion must be integrated in time domain
Wave e+uation for
visco-elastic medium
*
t t /
z i
More steps0 but basic process
involves using wave e+uation to
predict conditions at time j <: from
conditions at time j for all layers in
profile1
Can change material properties
for use in ne,t time step1
Changing stiffness based on
strain level0 strain history0 etc1 can
allow prediction of nonlinear0
inelastic response1
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!onlinear Analysis!onlinear Analysis
2 3
2 2
u u
z t z t
∂τ ∂ ∂= ρ + η∂ ∂ ∂ ∂
5+uation of motion must be integrated in time domain
Wave e+uation for
visco-elastic medium
*
t t /
z i
More steps0 but basic process
involves using wave e+uation to
predict conditions at time j <: from
conditions at time j for all layers in
profile1
Can change material properties
for use in ne,t time step1
Changing stiffness based on
strain level0 strain history0 etc1 can
allow prediction of nonlinear0
inelastic response1
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!onlinear Analysis!onlinear Analysis
2 3
2 2
u u
z t z t
∂τ ∂ ∂= ρ + η∂ ∂ ∂ ∂
5+uation of motion must be integrated in time domain
Wave e+uation for
visco-elastic medium
*
t t /
z i
More steps0 but basic process
involves using wave e+uation to
predict conditions at time j <: from
conditions at time j for all layers in
profile1
Can change material properties
for use in ne,t time step1
Changing stiffness based on
strain level0 strain history0 etc1 can
allow prediction of nonlinear0
inelastic response1
rocedure steps through time from
beginning of earth+ua&e to end1
Step through time
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!onlinear %eavior !onlinear %eavior
τ
γ
τ
γ
Continuous inear
segments
3ctual 3ppro,imation
(n a nonlinear analysis0 we appro,imate the continuous actual
stress-strain behavior with an incrementally-linear model1 'he
finer our computational interval0 the better the appro,imation1
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3dvantages
Wor& in time domainCan change properties after each time step to model nonlinearity
Can formulate model in terms of effective stresses
Can compute pore pressure generation
Can compute pore pressure redistribution0 dissipation
3voids spurious resonances associated with linearity of 5 approach#
Can compute permanent strain permanent deformations
!onlinear Approac!onlinear Approac
i+uefaction
;onlinear analyses can produce results that are consistent with e+uivalent
linear analyses when strains are small to moderate0 and more accurate
results when strains are large1
'hey can also do important things that e+uivalent linear analyses can’t0 such
as compute pore pressures and permanent deformations1
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What are people using in practice?
/0uivalent (inear vs1 !onlinear Approaces/0uivalent (inear vs1 !onlinear Approaces
5+uivalent linear analysesOne-dimensional D
-% ) .-% D
;onlinear analyses
One-dimensional D
-% ) .-% D
!"345
GU3%H0 6U!"
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What are people using in practice?
/0uivalent (inear vs1 !onlinear Approaces/0uivalent (inear vs1 !onlinear Approaces
5+uivalent linear analysesOne-dimensional D
-% ) .-% D
;onlinear analyses
One-dimensional D
-% ) .-% D
!"345
GU3%H0 6U!"
%5!$3
'3$3
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Dimensions OS /0uivalent (inear !onlinear
:-%%O! %yne+0 !ha&eJ: 3M50 %5!$30 %MO%0
6(0 !UM%5!0 '5!!
Windows !ha&e5dit0 ro!ha&e0!ha&e@@@0 55$3
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Available +odes
!ince early :J@s0 numerous computer programs developed for site
response analysis
Can be categori*ed according to computational procedure0 number of
dimensions0 and operating system
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+urrent 2ractice
Method of 3nalysis
Method of
3nalysis
W;3 5;3 Overseas
rivate.A#
ublic.#
rivateN#
ublic:#
rivateA#
ublicA#
:-% 5+uivalent inear N A N A@ H A
:-% ;onlinear :: : : @ H A
-%).-% 5+uiv1 inear J : A N @
-%).-% ;onlinear : . : A . J@
Of the total number of site response analyses you perform, indicate theapproximate percentages that fall within each of the following categories:
[ ] a. One-dimensional equivalent linear
[ ] b. One-dimensional nonlinear
[ ] c. wo- or three-dimensional equivalent linear
[ ] d. wo- or three-dimensional nonlinear
One-dimensional e+uivalent linear analyses dominate ;orth 3merican
practiceP nonlinear analyses are more fre+uently performed overseas
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!onlinear %eavior !onlinear %eavior
5+uivalent linear vs nonlinear
analysis D how much difference
does it ma&e?
'opanga motion scaled to @1@A g
Wea& motion<stiff soil
ow strains
ow degree of nonlinearity
!imilar response
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'opanga motion scaled to @1@A g
Wea& motion<stiff soil
ow strains
ow degree of nonlinearity
!imilar response
!onlinear %eavior !onlinear %eavior
5+uivalent linear vs nonlinear
analysis D how much difference
does it ma&e?
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'opanga motion scaled to @1@A g
Wea& motion<stiff soil
ow strains
ow degree of nonlinearity
!imilar response
!onlinear %eavior !onlinear %eavior
5+uivalent linear vs nonlinear
analysis D how much difference
does it ma&e?
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'opanga motion scaled to @1@ g
Moderate motion<stiff soil
$elatively low strains
$elatively low degree of nonlinearity
!imilar response
!onlinear %eavior !onlinear %eavior
5+uivalent linear vs nonlinear
analysis D how much difference
does it ma&e?
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'opanga motion scaled to @1@ g
Moderate motion<stiff soil
$elatively low strains
$elatively low degree of nonlinearity
!imilar response
!onlinear %eavior !onlinear %eavior
5+uivalent linear vs nonlinear
analysis D how much difference
does it ma&e?
Stiffness starting to &ar#more significantl# o&er
course of ground motion
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'opanga motion scaled to @1A@ g
!trong motion<stiff soil
Moderate strains
ow D moderate degree of nonlinearity
;oticeably different response
!onlinear %eavior !onlinear %eavior
5+uivalent linear vs nonlinear
analysis D how much difference
does it ma&e? "cceleration
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'opanga motion scaled to @1A@ g
!trong motion<stiff soil
Moderate strains
ow D moderate degree of nonlinearity
;oticeably different response
!onlinear %eavior !onlinear %eavior
5+uivalent linear vs nonlinear
analysis D how much difference
does it ma&e?
! li % i
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'opanga motion scaled to :1@ g
Lery strong motion<stiff soil
Moderate strains
Moderate degree of nonlinearity
;oticeably different response
!onlinear %eavior !onlinear %eavior
5+uivalent linear vs nonlinear
analysis D how much difference
does it ma&e? "cceleration
Substantial softening by/( metod causes
underprediction of initial
portion of record(inearity inerent in /( metod
causes overprediction response in
strongest portion of record
Softening by /( metod
causes underprediction
! li % i
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'opanga motion scaled to @1A@ g
Lery strong motion<stiff soil
Moderate strains
Moderate degree of nonlinearity
;oticeably different response
!onlinear %eavior !onlinear %eavior
5+uivalent linear vs nonlinear
analysis D how much difference
does it ma&e?
! li % i! li % i
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!onlinear %eavior !onlinear %eavior
5+uivalent linear vs nonlinear analysis D how much difference does it ma&e?
14 m V s = .@@ m)sec
V s = N m)sec
16 m V s = :@@ m)sec
uH 0t #
u@0t #
: m
:A m
J m
! li % i! li % i
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!onlinear %eavior !onlinear %eavior
5+uivalent linear vs nonlinear
analysis D how much difference
does it ma&e?
arge strain levels QNB# near
bottom of upper layer
5 model converges to low 9
and high ξ
"igh-fre+uency componentscannot be transmitted through
over-softened 5 model
!( model? Stiffness stays relatively ig
e,cept for a few large-amplitude cycles
"cceleration
5 model predicts very soft behavior at beginning of earth+ua&e0
before any large strains have developed1
! li % i! li % i
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!onlinear %eavior !onlinear %eavior
5+uivalent linear vs nonlinear
analysis D how much difference
does it ma&e?
arge strain levels QNB# near
bottom of upper layer
5 model converges to low 9
and high ξ
"igh-fre+uency componentscannot be transmitted through
over-softened 5 model
!( model? Stiffness stays relatively ig
e,cept for a few large-amplitude cycles
"cceleration
More consistency0 but ; model can transmit high-fre+uencyoscillations superimposed on low-fre+uency cycles D too much?
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! li % i!onlinear %eavior
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!onlinear %eavior !onlinear %eavior
5+uivalent linear vs nonlinear
analysis D how much difference
does it ma&e?
arge strain levels QNB# near
bottom of upper layer
5 model converges to low 9
and high ξ
"igh-fre+uency componentscannot be transmitted through
over-softened 5 model
!( model? Stiffness stays relatively ig
e,cept for a few large-amplitude cycles
!onlinear Soil %ea ior!onlinear Soil %eavior
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T i m e
!onlinear Soil %eavior !onlinear Soil %eavior
!mall cycle
superimposed on large
cycle after 3ssima&i and4ausel0 @@#
(ow stiffness
Hig stiffness
/0uivalent linear modelmaintains constant
stiffness and damping –
iger stiffness
e,cursions associated
wit iger fre0uency
oscillations aren@t seen1
!onlinear Soil %eavior!onlinear Soil %eavior
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T i m e
!onlinear Soil %eavior !onlinear Soil %eavior
!mall cycle
superimposed on large
cycle after 3ssima&i and4ausel0 @@#
Hig damping
(ow damping
/0uivalent linear modelmaintains constant
stiffness and damping –
iger stiffness
e,cursions associated
wit iger fre0uency
oscillations aren@t seen1
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'odified /0uivalent (inear Approac'odified /0uivalent (inear Approac
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3ssima&i and 4ausel
'odified /0uivalent (inear Approac'odified /0uivalent (inear Approac
Fre0uency-dependent model +onventional model
"igh fre+uenciesoversoftened and
overdamped
5,cellent agreement
with nonlinear model
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!tewart and 4wo&
55$ study to determine proper manner in which to use nonlinear analyses
Wor&ed with five e,isting
nonlinear codesP hired
developers to run their codes
and comment on results
5stablished advisory
committee to oversee
analyses and assist with
interpretation
Met regularly with advisory
committee and developers
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!tewart and 4wo&
Considered codes
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%-MO%R Matasovic#
5nhanced version of %-MO%0 which is enhanced version of %5!$3
umped mass model
$ayleigh damping
% a m p i n g
r a t i o
6re+uency
Mass-proportional
!tiffness-proportionalRayleig
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%-MO%R Matasovic#
5nhanced version of %-MO%0 which is enhanced version of %5!$3
umped mass model
$ayleigh damping
;ewmar& β method for time integration
Lariable slice width D simulating response of dams0 emban&ments on roc&
%encmar$ing of !onlinear Analyses%encmar$ing of !onlinear Analyses
Decreasing stiffnessdue to geometry
%encmar$ing of !onlinear Analyses%encmar$ing of !onlinear Analyses
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%-MO%R Matasovic#
5nhanced version of %-MO%0 which is enhanced version of %5!$3
umped mass model
$ayleigh damping
;ewmar& β method for time integration
Lariable slice width D simulating response of dams0 emban&ments on roc&
Can simulate slip on wea& interfaces
Uses M4S soil model modified hyperbola D needs Gma,0 τma,0 α and s#
Can soften bac&bone curve to model cyclic degradation
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%-MO%R Matasovic#
5nhanced version of %-MO%0 which is enhanced version of %5!$3
umped mass model
$ayleigh damping
;ewmar& β method for time integration
Lariable slice width D simulating response of dams0 emban&ments on roc&
Can simulate slip on wea& interfaces
Uses M4S soil model modified hyperbola D needs Gma,0 τma,0 α and s#
Can soften bac&bone curve to model cyclic degradationUses Masing rules for unloading-reloading behavior
;eed input parameters for
M4S bac&bone curve H#
Cyclic degradation . for clay0 H for sand#
ore pressure generation H for clay0 H for sand#
ore pressure redistribution)dissipation at least #
$ayleigh damping coefficients #
2asic layer properties density0 shear wave velocity0 half-space properties#
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%55!O( "ashash#
!imilar to %MO%- lumped mass0 derives from %5!$3-#
More advanced $ayleigh damping scheme lower fre+uency dependence#
'5!! y&e#
6inite difference wave propagation analysis not lumped mass#
Cundall-y&e hypothesis for loading-unloading behavior
!imilar bac&bone curve to %MO%- and %55!O(
(nviscid sort of# low-strain damping scheme
Open!ees Kang0 5lgamal#
6inite element model :%0 %0 .% capabilities#
Multi-surface plasticity model von Mises yield surface0 &inematic
hardening0 non-associative flow rule#
6ull $ayleigh damping
!UM%5!
6inite element model
2ounding surface plasticity model ade-li&e yield surface0 &inematic
hardening0 non-associative flow rule#
!implified $ayleigh damping
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erformance
2ased on validations against vertical array data
T Models produce reasonable results
T !ome indication of overdamping at high fre+uencies0 overamplification at
site fre+uency
T Lariability of predictions due to bac&bone curves and damping models
most pronounced at T @1A sec and is significant only for relatively thic&
profiles1 Model-to-model variability most pronounced at low periods1
T ;onlinearity modeled well up to levels for which ade+uate data is
available generally up to about @1g#1 %ata for stronger sha&ing being
sought centrifuge tests0 recent ;igaata earth+ua&e#1
T %MO%-0 %55!O(0 and Open!ees generally produced similar
amplification factors and spectral shapesP '5!! produced differentresponse at high fre+uencies different damping formulation#0 !UM%5!
results were significantly different than all others for deep sites probably
due to simplified $ayleigh damping#1
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!onlinear %eavior – /ffective Stress Analyses!onlinear %eavior – /ffective Stress Analyses
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!onlinear %eavior /ffective Stress Analyses!onlinear %eavior /ffective Stress Analyses
Wildlife D !uperstition "ills recordings
!onlinear %eavior!onlinear %eavior – /ffective Stress Analyses – /ffective Stress Analyses
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!onlinear %eavior o ea e a o /ffective Stress Analysesect e St ess a yses
Wildlife D !uperstition "ills recordings
!onlinear %eavior!onlinear %eavior – /ffective Stress Analyses – /ffective Stress Analyses
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!onlinear %eavior /ffective Stress Analysesy
Wildlife D 5lmore $anch recordings
!onlinear %eavior !onlinear %eavior – /ffective Stress Analyses – /ffective Stress Analyses
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yy
Wildlife D !uperstition "ills recordings
ow
fre+uency
"igh
fre+uency
9round surface record
???
Site /ffectsSite /ffects
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5lmore $anch record D no li+uefaction
$atio of waveletamplitudes D variation
with fre+uency and time
ime sec.
F r e 0 u e n c y - H z .
Site /ffectsSite /ffects
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5lmore $anch record D no li+uefaction
$atio of waveletamplitudes D variation
with fre+uency and time
ime sec.
F r e 0 u e n c y - H z .
!onlinear %eavior !onlinear %eavior – /ffective Stress Analyses – /ffective Stress Analyses
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yy
Wildlife D !uperstition "ills recordings
!onlinear %eavior !onlinear %eavior – /ffective Stress Analyses – /ffective Stress Analyses
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yy
Wildlife D !uperstition "ills recordings