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Soil–Foundation–StructureInteraction Simulations:
Static and Dynamic Issues
Boris Jeremic
Department of Civil and Environmental Engineering
University of California, Davis
Jeremic, UCLA Seminar Series, May 2004 1 JB
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Leitmotiv
• Create high fidelity models of constructed facilities (bridges, build-
ings, port structures, dams...).
• Models will live concurrently with the physical system they represent.
• Models to provide owners and operators with the capabilities to
assess operations and future performance.
• Use observed performance to update and validate models through
simulations.
Jeremic, UCLA Seminar Series, May 2004 2 JB
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Presentation Overview
• Role of numerical simulations
• Static (kinematic) behavior
– Layered soils
– Pile groups
• Dynamic behavior
– Application of seismic loads (motions)
– Site response analysis
– From large scale geophysical simulations to large scale soil–
structure simulations
– Application to long bridges
Jeremic, UCLA Seminar Series, May 2004 3 JB
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Goal
• Develop and use computational models in order to
– Design physical tests
– Use observed behavior to validate and improve models
– Use validated models to predict behavior of realistic bridge sys-
tems
• Educate users about new, exciting simulation tools that are now
available
Jeremic, UCLA Seminar Series, May 2004 4 JB
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Goals of Validation
Quantification of uncertainties and errors in the computational
model and the experimental measurements
• Goals on validation
– Tactical goal: Identification and minimization of uncertainties and
errors in the computational model
– Strategic goal: Increase confidence in the quantitative predictive
capability of the computational model
• Strategy is to reduce as much as possible the following:
– Computational model uncertainties and errors
– Random (precision) errors and bias (systematic) errors in the
experiments
– Incomplete physical characterization of the experiment
Jeremic, UCLA Seminar Series, May 2004 5 JB
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Validation Procedure Uncertainty
• Aleatory uncertainty → inherent variation associated with the phys-
ical system of the environment (variation in external excitation,
material properties...). Also know known as irreducible uncertainty,
variability and stochastic uncertainty.
• Epistemic uncertainty → potential deficiency in any phase of the
modeling process that is due to lack of knowledge (poor understand-
ing of mechanics...). Also known as reducible uncertainty, model
form uncertainty and subjective uncertainty
Deterministic Epistemicuncertainty
Aleatoryuncertainty
Heise
nber
gpr
incip
le
Jeremic, UCLA Seminar Series, May 2004 6 JB
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Validation Experiments
• A validation experiment should be jointly designed and executed by
experimentalist and computationalist
– Need for close working relationship from inception to documenta-
tion
– Elimination of typical competition between each
– Complete honesty concerning strengths and weaknesses of both
experimental and computational simulations
• A validation Experiment should be designed to capture the relevant
physics
– Measure all important modeling data in the experiment
– Characteristics and imperfections of the experimental facility
should be included in the model
Jeremic, UCLA Seminar Series, May 2004 7 JB
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Application Domain
DomainApplication
System Parameter
Sys
tem
com
plex
ity
System Parameter
Sys
tem
com
plex
ity
System Parameter
Sys
tem
com
plex
ity
DomainValidation
DomainApplication
DomainValidation
ApplicationDomain
DomainValidation
Inference
Complete Overlap Partial Overlap No Overlap
• Inference ⇒ Based on physics or statistics
• Validation domain is actually an aggregation of tests (points) and
might not be convex (bifurcation of behavior)
• NEES research provides for validation domain (experimental facili-
ties) that are mostly (if not exclusively) non–overlapping with the
application domain.
Jeremic, UCLA Seminar Series, May 2004 8 JB
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Computability
Physical Problem Computability : (von Neumann computability)
how well a mathematical model can predict the response of a
mechanical system (related to validation)
Computational computability : (Turing computability) discretized
problem is computable if there exists an algorithm that can solve
the problem in a finite number of steps (related to verification)
Jeremic, UCLA Seminar Series, May 2004 9 JB
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Static (Kinematic) SFSI
• Computational geomechanics for large scale problems
• Single pile behavior in elastic–plastic soils, effects of layers
• Pile group behavior
Jeremic, UCLA Seminar Series, May 2004 10 JB
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Single Pile in Layered Soils
−1000 0 1000 2000−10
−8
−6
−4
−2
0
2
SAND
φ = 37.1o
−1.718
SOFT CLAY
Cu = 21.7 kPa
−3.436
SAND
φ = 37.1o
Bending Moment (kN.m)
Dep
th (
m)
SAND
φ = 37.1o
−1.718
SOFT CLAY
Cu = 21.7 kPa
−3.436
SAND
φ = 37.1o
SAND
φ = 37.1o
−1.718
SOFT CLAY
Cu = 21.7 kPa
−3.436
SAND
φ = 37.1o
−400 −200 0 200 400 600−10
−8
−6
−4
−2
0
2
Shear Force (kN)−100 0 100 200 300
−10
−8
−6
−4
−2
0
2
Lateral Resistance (kN/m)−1000 0 1000 2000
−10
−8
−6
−4
−2
0
2
SAND
φ = 37.1o
−1.718
SOFT CLAY
Cu = 21.7 kPa
−3.436
SAND
φ = 37.1o
Bending Moment (kN.m)
Dep
th (
m)
−400 −200 0 200 400 600−10
−8
−6
−4
−2
0
2
Shear Force (kN)−100 0 100 200 300
−10
−8
−6
−4
−2
0
2
Lateral Resistance (kN/m)
Jeremic, UCLA Seminar Series, May 2004 11 JB
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p− y Response for Single Pile inLayered Soils
0 2 4 6 8 10 120
50
100
150
200
250
300
Lateral Displacement y (cm)
Late
ral P
ress
ure
p (k
N/m
)
Depth −0.322Depth −0.537Depth −0.752Depth −0.966Depth −1.181Depth −1.396Depth −1.611Depth −1.825Depth −2.040Depth −2.255Depth −2.470Depth −2.684
0 2 4 6 8 10 120
50
100
150
200
250
300
Lateral Displacement y (cm)La
tera
l Pre
ssur
e p
(kN
/m)
Depth −0.322Depth −0.537Depth −0.752Depth −0.966Depth −1.181Depth −1.396Depth −1.611Depth −1.825Depth −2.040Depth −2.255Depth −2.470Depth −2.684
• Influence of soft layers propagates to stiff layers and vice versa
• Can have significant effects in soils with many layers
Jeremic, UCLA Seminar Series, May 2004 12 JB
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Lateral Resistance RatioDistributions
0.5 0.6 0.7 0.8 0.9 1−6
−5
−4
−3
−2
−1
0
Z / D
p / phomog. case
y/D = 0.050
SANDγ=14.5kN/m3
CLAY, γ=11.8kN/m3
Cu=13.0kPa,Eo=11000kPaCu=21.7kPa,Eo=11000kPaCu=30.3kPa,Eo=11000kPa
0.5 0.6 0.7 0.8 0.9 1−6
−5
−4
−3
−2
−1
0
p / phomog. case
y/D = 0.065
SANDγ=14.5kN/m3
CLAY, γ=11.8kN/m3
Cu=13.0kPa,Eo=11000kPaCu=21.7kPa,Eo=11000kPaCu=30.3kPa,Eo=11000kPa
• Influence increases as the shear strength of soft layer decreases
(think of cyclic mobility of liquefaction)
Jeremic, UCLA Seminar Series, May 2004 13 JB
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Pile Group Simulations
• 4x3 pile group model and plastic zones
Jeremic, UCLA Seminar Series, May 2004 14 JB
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Out of Plane Effects
• Out-of-loading-plane bending moment diagram,
• Out-of-loading-plane deformation.
Jeremic, UCLA Seminar Series, May 2004 15 JB
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Pile Spreading Stress Path
Jeremic, UCLA Seminar Series, May 2004 16 JB
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Load Distribution per Pile
0 1 2 3 4 5 6 7 8 9 10 115
6
7
8
9
10
11
12
13
14
15
Late
ral L
oad
Dis
trib
utio
n in
Eac
h P
ile (
%)
Displacement at Pile Group Cap (cm)
Trail Row, Side PileThird Row, Side PileSecond Row, Side PileLead Row, Side PileTrail Row, Middle PileThird Row, Middle PileSecond Row, Middle PileLead Row, Middle Pile
Jeremic, UCLA Seminar Series, May 2004 17 JB
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Piles Interaction at -2.0m
• Note the difference in response curves (cannot scale single pile
response for multiple piles)
Jeremic, UCLA Seminar Series, May 2004 18 JB
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Comparison with Centrifuge Tests
0 1 2 3 4 5 6 7 8 9 1015
20
25
30
35
40
45La
tera
l Loa
d di
strib
utio
n in
eac
h ro
w (
%)
Lateral Displacement at Pile Group Cap (cm)
FEM − Trail RowFEM − Third RowFEM − Second RowFEM − Lead RowCentrifuge − Trail RowCentrifuge − Third RowCentrifuge − Second RowCentrifuge − Lead Row
Jeremic, UCLA Seminar Series, May 2004 19 JB
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Dynamic SFSI
• Application of seismic loads (motions)
• Site response analysis
• From large scale geophysical simulations to large scale soil–structure
simulations
• Application to long bridges
Jeremic, UCLA Seminar Series, May 2004 20 JB
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Domain Reduction Method (DRM)
• Work by Bielak et al. (2003, Bulletin of the Seismological Society
of America) at CMU.
• Modular, two step procedure for large 3D dynamics problems.
• Primary unknowns:
– Total wave field within the local domain,
– Scattered wave field in the exterior domain,
• Free field wave field from the background structure only act on a
single concave surface.
Jeremic, UCLA Seminar Series, May 2004 21 JB
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DRM: Background Wave Field
• Determination using any available numerical or measurement tech-
nique,
• Need displacement and acceleration field
• Green’s functions solutions, Quake system, SCEC database,
SHAKE...
• 3D downhole arrays,
Fault
GeologicLayers
FeatureLocal
Jeremic, UCLA Seminar Series, May 2004 22 JB
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DRM: Idea
• Simplified original model
• Local geological feature
u
u
uFault
Γ
Γ
Ω
Ω+
+
0b
0e
0i0
ePu
u
Pe
e0
b0
Fault
Γ
Ω
Γ
+
+
Pb−
u
u
P
b0
i0
b
Γ
Ω0
u
P
b
b
Γ
Ω
ui
Jeremic, UCLA Seminar Series, May 2004 23 JB
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DRM: Dynamics
[MΩ
ii MΩib
MΩbi MΩ
bb
]ui
ub
+
[KΩ
ii KΩib
KΩbi KΩ
bb
]ui
ub
=
0Pb
, in Ω
[MΩ+
bb MΩ+be
MΩ+eb MΩ+
ee
]ub
ue
+
[KΩ+
bb KΩ+be
KΩ+eb KΩ+
ee
]ub
ue
=
−Pb
Pe
, in Ω+
MΩii MΩ
ib 0MΩ
bi MΩbb + MΩ+
bb MΩ+be
0 MΩ+eb MΩ+
ee
ui
ub
ue
+
KΩii KΩ
ib 0KΩ
bi KΩbb + KΩ+
bb KΩ+be
0 KΩ+eb KΩ+
ee
ui
ub
ue
=
00Pe
u
u
uFault
Γ
Γ
Ω
Ω+
+
0b
0e
0i0
eP
Jeremic, UCLA Seminar Series, May 2004 24 JB
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DRM: Change of Variables
Equations of motion in Ω+ for changed model[MΩ+
bb MΩ+be
MΩ+eb MΩ+
ee
]u0
b
u0e
+
[KΩ+
bb KΩ+be
KΩ+eb KΩ+
ee
]u0
b
u0e
=
−P 0
b
Pe
⇒
Pe = MΩ+eb u0
b + MΩ+ee u0
e + KΩ+eb u0
b + KΩ+ee u0
e
Change of variables: ue = u0e + we
• total displacement ue
• free field, background structure u0e
• residual field, relative displacement field with respect to the reference free,background field we MΩ
ii MΩib 0
MΩbi MΩ
bb + MΩ+bb
MΩ+be
0 MΩ+eb
MΩ+ee
uiubwe
+
KΩii KΩ
ib 0
KΩbi KΩ
bb + KΩ+bb
KΩ+be
0 KΩ+eb
KΩ+ee
uiubwe
=
P
effi
Peffb
P effe
Jeremic, UCLA Seminar Series, May 2004 25 JB
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DRM: Dynamic (Seismic) Forces
P eff
i
P effb
P effe
=
0
−MΩ+be u0
e −KΩ+be u0
e
MΩ+eb u0
b + KΩ+eb u0
b
u
uFault
Γ
Ω
Ω+
+
e
i
eP
uube
ΓΓe
• Seismic forces Pe replaced by the effective nodal forces P eff ,
• P eff involve only submatrices, Mbe,Kbe,Meb,Keb
• They vanish everywhere except in the single layer of elements in Ω+
adjacent to Γ.
• The material inside Ω does not have to be linear elastic
Jeremic, UCLA Seminar Series, May 2004 26 JB
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Application Examples
• Seismic wave propagation
– Effects of elastic plastic soils on free field motions
• Soil–Structure interaction
– Effects of elastic–plastic soils on dynamic response of pile–column
system
Jeremic, UCLA Seminar Series, May 2004 27 JB
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Wave Propagation Model
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
−27.3
−23.3
−21.8
−18.3
−14.8
−11.8
−8.8
−6.3
−3.3
−1.8
0.0
Time (s)
Acc
eler
atio
n (m
/s2 )
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−27.3
−23.3
−21.8
−18.3
−14.8
−11.8
−8.8
−6.3
−3.3
−1.8
0.0
Time (s)
Dis
plac
emen
t (m
)
Jeremic, UCLA Seminar Series, May 2004 28 JB
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Wave PropagationSoft Soil
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.0625−27.3
0.0633−23.3
0.0678−21.8
0.0749−18.3
0.0846−14.8
0.0960−11.8
0.1076 −8.8
0.1160 −6.3
0.1208 −3.3
0.1207 −1.8
0.1181 0.0
Max
Time (s)
Dis
plac
emen
t (m
)
Z
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.0622−25.0
0.0779−21.0
0.0837−19.5
0.0982−15.0
0.1069−11.0
0.1123 −7.0
0.1169 −4.3
0.1174 −3.6
0.1179 −1.8
0.1181 0.0
0.1183 1.8
0.1178 3.6
0.1173 4.3
0.1129 7.0
0.1075 11.0
0.0984 15.0
0.0837 19.5
0.0779 21.0
0.0622 25.0
Max
Time (s)
Dis
pala
cem
ent (
m)
Y
Jeremic, UCLA Seminar Series, May 2004 29 JB
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Wave PropagationStiff Soil
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.0625−27.3
0.0658−23.3
0.0724−21.8
0.0735−18.3
0.0745−14.8
0.0753−11.8
0.0758 −8.8
0.0761 −6.3
0.0762 −3.3
0.0762 −1.8
0.0760 0.0
Max
Time (s)
Dis
plac
emen
t (m
)
Z
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.0622−25.0
0.0715−21.0
0.0727−19.5
0.0737−15.0
0.0746−11.0
0.0754 −7.0
0.0759 −4.3
0.0759 −3.6
0.0760 −1.8
0.0760 0.0
0.0760 1.8
0.0759 3.6
0.0758 4.3
0.0754 7.0
0.0746 11.0
0.0737 15.0
0.0726 19.5
0.0715 21.0
0.0622 25.0
Max
Time (s)
Dis
plac
emen
t (m
)
Y
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SSI Model
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
−38.0
−30.0−28.0
−20.0
−16.0
−12.0
−8.0
−4.0
0.0
Time (s)
Acc
eler
atio
n (m
/s2 )
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−38.0−30.0
−28.0
−20.0
−16.0
−12.0
−8.0
−4.0
0.0
Time (s)
Dis
plac
emen
t (m
)
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SSI Model Free FieldStiff Elastic–Plastic Soil
0 1 2 3 4 5 6 7 8 9 10
0.0000−38.0
0.0052−30.00.1055−28.0
0.1142−20.0
0.1183−16.0
0.1219−12.0
0.1576 −8.0
0.1947 −4.0
0.2002 0.0
Time (s)
Dis
plac
emen
t (m
)
Z(m) Max
0 1 2 3 4 5 6 7 8 9 10
0.2002 0.0
0.1937 4.0
0.1749 8.0
0.1261 12.0
0.1231 16.0
0.1139 24.0
0.0124 26.0
0.0000 34.0
Time (s)
Dis
plac
emen
t (m
)
Z(m) Max
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SSI Model: Pile–ColumnStiff Elastic–Plastic Soil
0 1 2 3 4 5 6 7 8 9 10
0.0000−38.0
0.0052−30.00.1055−28.0
0.1142−20.0
0.1183−16.0
0.1222−12.0
0.1496 −8.0
0.1899 −4.0
0.2091 0.0
Time (s)
Dis
plac
emen
t (m
)
Z(m) Max
0 1 2 3 4 5 6 7 8 9 10
0.2091 0.0
0.1935 4.0
0.1751 8.0
0.1262 12.0
0.1232 16.0
0.1139 24.0
0.0124 26.0
0.0000 34.0
Time (s)
Dis
plac
emen
t (m
)
Y(m) Max
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SSI Model Free FieldSoft Elastic–Plastic Soil
0 1 2 3 4 5 6 7 8 9 10
0.0000−38.0
0.0140−30.00.0971−28.0
0.1096−20.0
0.1190−16.0
0.1261−12.0
0.1622 −8.0
0.2823 −4.0
0.3158 0.0
Time (s)
Dis
plac
emen
t (m
)
Z(m)
0 1 2 3 4 5 6 7 8 9 10
0.3158 0.0
0.2890 4.0
0.2545 8.0
0.1567 12.0
0.1512 16.0
0.1338 24.0
0.0362 26.0
0.0000 34.0
Time (s)
Dis
plac
emen
t (m
)
Y(m) Max
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SSI Model: Pile–ColumnSoft Elastic–Plastic Soil
0 1 2 3 4 5 6 7 8 9 10
0.0000−38.0
0.0140−30.00.0976−28.0
0.1094−20.0
0.1207−16.0
0.1227−12.0
0.1328 −8.0
0.2448 −4.0
0.3680 0.0
Time (s)
Dis
plac
emen
t (m
)
Z(m) Max
0 1 2 3 4 5 6 7 8 9 10
0.3680 0.0
0.2896 4.0
0.2536
8.0
0.1549
12.0
0.1497
16.0
0.1331
24.0 0.0356
26.0
0.0000 34.0
Time (s)
Jeremic, UCLA Seminar Series, May 2004 35 JB
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SSI Model: Pile–Column Behavior
0 1 2 3 4 5 6 7 8 9 10−0.03
−0.02
−0.01
0
0.01
0.02
0.03
0.04
Dis
plac
emnt
(m
)
Time (s)0 1 2 3 4 5 6 7 8 9 10
−0.25
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
0.25
Dis
plac
emen
t (m
)
Time (s)
Stiff soil Soft soil
Jeremic, UCLA Seminar Series, May 2004 36 JB
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I–880 Bridge SFSI Issues
• Seismic response of I–880 viaduct using performance based engi-
neering
• Hierarchical set of SFSI simulations models developed to represent
engineering demand parameters (EDP)
• Local site conditions (inelastic SFSI interaction problem)
• Wave propagation over the bridge length (scale problem)
• Single point (spatial) far field input motions
• Stochastic distribution of materials (properties) over spatial scales
Jeremic, UCLA Seminar Series, May 2004 37 JB
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Geologic and Soil Conditions
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Local Site Conditions
• Adjacency of foundations in soft and stiff soil
• Spatial distribution of soil materials
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Soil–Foundation System Models
• Hierarchical set of models used to estimate performance
• Reducing epistemic uncertainty as much as possible
7.2
0.6 1.5 1.5 1.5 1.5 0.6
7.2
21.2
1.5
0.60.60.60.60.6
Jeremic, UCLA Seminar Series, May 2004 40 JB
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I–880: Hierarchy of Models
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I–880: Seismic Input
• Coupling free field motions to SFSI system (Domain Reduction
Method)
• Wave propagation over the
bridge length
Fault
Jeremic, UCLA Seminar Series, May 2004 42 JB
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Seismic Amplification
• Adjacent bents
• Foundation will survive but the superstructure or joints might not
0 5 10 15 20 25 30 35 40
0.0000−38.0
0.0077−30.0
0.0783−28.0
0.0791−20.0
0.0844−16.0
0.0878−12.0
0.1248 −8.0
0.1800 −4.0
0.1946 0.0
Time (s)
Dis
plac
emen
t (m
)
Z(m) Max
0 5 10 15 20 25 30 35 40
0.0000−38.0
0.0224−30.0
0.0879−28.0
0.1102−20.0
0.1161−16.0
0.1227−12.0
0.3961 −8.0
0.6258 −4.0
0.6928 0.0
Time (s)
Dis
plac
emen
t (m
)
Z(m) Max
Stiff soil Soft soil
Jeremic, UCLA Seminar Series, May 2004 43 JB
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Concluding Remarks
• Static (kinematic) SFSI issues
– Layered soils
– Piles in liquefied soils (layers)
• Dynamic (seismic) SFSI issues
– Free field vs. SFSI motions
– Very large scale coupling (with geophysical simulations)
Jeremic, UCLA Seminar Series, May 2004 44 JB
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Thank you
Jeremic, UCLA Seminar Series, May 2004 45 JB