Soil–Foundation–Structure Interaction Simulations: Static...

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

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.


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


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


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


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


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


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.


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)


Static (Kinematic) SFSI

• Computational geomechanics for large scale problems

• Single pile behavior in elastic–plastic soils, effects of layers

• Pile group behavior


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)


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


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)


Pile Group Simulations

• 4x3 pile group model and plastic zones


Out of Plane Effects

• Out-of-loading-plane bending moment diagram,

• Out-of-loading-plane deformation.


Pile Spreading Stress Path


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


Piles Interaction at -2.0m

• Note the difference in response curves (cannot scale single pile

response for multiple piles)


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


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


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.


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


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


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


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


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


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


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

)


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


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


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

)


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


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


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


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)


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


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


Geologic and Soil Conditions


Local Site Conditions

• Adjacency of foundations in soft and stiff soil

• Spatial distribution of soil materials


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


I–880: Hierarchy of Models


I–880: Seismic Input

• Coupling free field motions to SFSI system (Domain Reduction

Method)

• Wave propagation over the

bridge length

Fault


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


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)


Thank you


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