University of Washington

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University of Washington Seattle
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Pedro Arduino
Computational GeoMechanics Geotechnical
Engineering University of Washington
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Outline

• Behavioral characteristics of coarse materials
  under general loading conditions
• 3-D contact elements
• A demonstration of the NEES system for studying
  soil-foundation-structure interaction
• Introduction to performance based design

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Behavioral Characteristics of Coarse Materials
under General Loading Conditions

• ChangHo Choi, Michael Harney, and Pedro Arduino

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Need for robust constitutive models

• Numerical Simulation

(Shin, 2003)
(Petek, 2003)
Constitutive

• Require robust implementation scheme
• Appropriate representation of mathematical
  expressions for material behavior

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True Triaxial Apparatus

• Add one more degree of freedom
• Able to simulate general 3-D stress conditions
• Type of TTAs

?1
?2
?3
Cylindrical triaxial test
Truly triaxial device
Rigid Boundary TTA (Pearce 1971) Strain Control
Flexible Boundary TTA (Sture and Desai 1979)
Stress Control
Mixed Boundary TTA (Green 1971, Lade and Duncan
1973)
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Various TTAs developed worldwide
Inherited from
Specimen size (inches)
Material
Location
Designer
Rigid boundary type
N/A
4.0 ? 4.0 ? 4.0
Kaolin clay
Cambridge University (England)
Pearce(1971)
Pearce(1971)
4.0 ? 4.0 ? 4.0
Kaolin clay
Cambridge University (England)
Airey and Wood(1988)
Pearce(1971)
3.9 ? 3.9 ? 3.9
Dry sand
Institute de Mecanique de Genoble (France)
Lanier(1988)
Pearce(1971)
2.8 ? 2.8 ? 2.8
Clay and air-pluviated sand
Aalborg University (Denmark)
Ibsen and Praastrup(2002)
Fexible boundary type
N/A N/A
2.4 ? 4.0 ? 4.0 4.0 ? 4.0 ? 4.0
German standard sand Ottawa sand
Vattenbyggnadsbyran (Sweden) University of
Boulder (US)
Kjellman(1936) Ko and Scott(1967)
Ko and Scott(1967)
3.9 ? 3.9 ? 3.9
Leighton Buzzard sand
University College (England)
Arthur and Menzies(1972)
N/A
3.9 ? 3.9 ? 3.9
Fuji river sand
University of Tokyo (Japan)
Yamada and Ishihara(1979)
Ko and Scott(1967)
4.0 ? 4.0 ? 4.0
Crushed basalt and clay
Virginia Polytechnic Institute (US)
Sture and Desai(1979)
Sture and Desai(1979)
1.75 ?1.75?1.75
Clay
University of Boulder (US)
Brends and Ko(1980)
N/A
4.0 ? 4.0 ? 4.0
Balast and rock
University of Arizona (US)
Desai, et al.(1982)
Sture and Desai(1979)
4.0 ? 4.0 ? 4.0
Railroad ballast
Virginia Polytechnic Institute (US)
Janardhanam and Desai (1983)
Sture and Desai(1979)
4.0 ? 4.0 ? 4.0
Kaolinite/silt mixture
Purdue University (US)
Sivakugan, et al(1988)
Ko and Scott(1967)
4.0 ? 4.0 ? 4.0
Cemented sand
Illinois Institute of Technology (US)
Reddy, et al(1992)
N/A
3.9 ? 3.9 ? 3.9
Silty sand
Georgia Institute of Technology (US)
Hoyos and Macari(2000)
Sture and Desai(1979)
9.5 ? 9.5 ? 9.5
Sand and gravel
University of Washington (US)
Anderson(1993) and Choi(2003)
Mixed boundary type
N/A
3.3 ? 3.2 ? 2.1
Ham river sand
Imperial College (England)
Green(1971)
N/A
3.0 ? 3.0 ? 3.0
Air-dry sand
University of California, Los Angeles (US)
Lade and Duncan(1973)
N/A
2.0 ? 3.1 ? 3.9
Undisturbed clay
Queens University (Canand)
Mitchell(1973)
N/A
2.8 ? 3.8 ? 2.8
Toyora sand
Kyoto University (Japan)
Matsuoka(1974)
Lade and Duncan(1973)
3.0 ? 3.0 ? 3.0
Sand and clay
University of California, Los Angeles (US)
Lade(1978)
N/A
2.0 ? 2.0 ? 3.9
Rock
National Technical University of Athens (Greece)
Michelis(1985)
N/A.
2.0 ? 1.5 ? 3.9
Natural and artificial clays
McGill University (Canada)
Sivestri, et al.(1988)
N/A.
2.5 ? 1.6 ? 3.1
Seto sand
Osaka City University (Japan)
Mochizuki, et al.(1988)
...
Sydney sand
University of New South Wales (Australia)
Lo. et al.(1994)
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UW-TTA Setup (Components)
Main Frame
Bottom Plate
Side Wall Parts
Control Box
Side Wall Assembly
During Testing
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UW-TTA Control System
Driving Variables
Response Variables
LVDT SS-107
Three Principal Stresses
Displacement
Digital Computer LabView
Back Pressure
Field Point
Pressure Transducer PT-302/150
Pore Pressure
Sample
E-P Transducer T7800
Pressure Transducer PT-302/150
Principal Stresses
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Materials Tested
GSD UNIMIN 4060
3/4"
4
10
40
200
3"
100
UNIMIN 4060 Pea Gravel
USGS SP GP
Gs 2.65 2.72
D50(in) 0.021 0.26
Cu 1.4 1.6
Cc 1.1 1.0
90
80
70
Percent Passing ()
60
50
40
30
20
10
0
0.001
0.010
0.100
1.000
10.000
100.000
Grain Size (mm)
Pea Gravel
3/4"
4
10
40
200
3"
100
90
80
70
60
Percent Passing ()
50
40
30
20
10
0
0.001
0.010
0.100
1.000
10.000
100.000
Grain Size (mm)
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Stress Paths in the Deviatoric Plane
?A
Specimen preparation direction
?A
TC0 (?0?)
CCT (?0360?)
SS30 (? 30?)
?
?C
TC240 (?240?)
TC120 (?120?)
TE180 (?180?)
?B
?B
?C
DT and DR stress paths
CCT stress path
Specimen Preparation Direction
?A
SS
? 30?
? 0?
UCTC (?0, 180?)
UCSS30 (?30, 210?)
UCSS90 (?90, 270?)
?B
?C
UCTC stress path
UCSS30 stress path
UCSS90 stress path
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Monotonic Test Result 1
Undrained TC, TE, and SS at p010 psi
Effect of Stress Path direction

• Effect of Stress path direction (?)
• Different volumetric response
• Willam-Warnke approxiamtion

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Monotonic Test Result 2
Phase Transformation Lines from Monotonic tests

• State of Phase Transformation

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Undrained Unidirectional Cyclic Test
UCSS90
UCTC
UCSS30

• Understand the mechanism of pore-water and volume
  change response
• Identify cyclic mobility, or liquefaction behavior

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Unidirectional Cyclic Test Result 1
CT9, UCSS90
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Unidirectional Cyclic Test Result 2
Effect of CSR (Cyclic Stress Ratio)
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• Rotational Stress Path Test Example

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• Rotational Stress Path Test Example

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• Rotational Stress Path Test Example

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• Rotational Stress Path Test Example

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Manzari-Dafalias Model (1997)
Surface in ? plane
Yield surface
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Dr Constitutive
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Manzari-Dafalias Model Parameters
Elastic parameters value
4691
0.25
0.86
Critical state parameters
1.62/1.13
0.018
0.59
148 psi
Model parameters
4.3/2.3
6.0/3.8
1500
0.0
0.05
0.25
330
150
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Monotonic Test Model Simulation
Undrained monotonic test p0 10 psi (DT1, 2, 3)

• Experiment

• Simulation

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UCSS Model Simulation
Unidirectional cyclic SS test UCSS90, CT9

• Experiment

• Simulation

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CCT Model Simulation
Circular cyclic test

• Experiment

• Simulation

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CCT Model Simulation 2
Circular cyclic test strain vectors at 1st and
7th cycles

• Experiment

• Simulation

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UW-TTA Experimental Results
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3-D Contact Elements

• Kathy Petek, Peter MacKenzie, Pedro Arduino

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Contact Problem using 3D Full Continuum Element
Models
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Contact Element Formulation

• Contact element applies a geometric constraint to
  the system that relates a slave node to a master
  contact line segment or surface.

• Using the method of Lagrange Multipliers, the
  element utilizes the Hertz-Signori-Moreau
  conditions for contact

g
tn
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Example 2 Friction Pile
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Example 2 Friction Pile
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Example 2 Pushover Analysis with Plastic Soil
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Example 3 Pushover Analysis with Plastic Soil
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Objective 2 Program3D Mixed Beam-Column Element
Models
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Beam-to- Soil Contact Element
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Beam-to- Soil Contact Element
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Collaborative Research Demonstration of NEES for
Studying SFSI

• Numerical Analysis of Seismic Soil-Pile-Structure
  Interaction Problem Using OpenSees
• HyungSuk Shin, Tyler Ranf
• Marc Eberhard, Steve Kramer, Pedro Arduino
• Lanka, Bruce Kutter

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Collaborative research A demonstration of the
NEES system for studying soil-foundation-structure
interaction
Perdue University
University of California, Davis
University of Nevada, Reno
University of Texas, Austin (Vibration mobile)
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Centrifuge Test 1
1 / 52 scale
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NEES Project (Centrifuge Test )
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Centrifuge Test
Shaking direction
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Centrifuge Test
Shaking direction
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Soil
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Pile
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Input motion
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Interaction model
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OpenSees - Pressure Dependent MultiYield Material
Const. Model
Requires definition of 10 material parameters
Correletions to N1(60) Or Dr have been proposed
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Experimental Numerical Results(freefield
response - 0.25g event)
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Experimental Numerical Results(freefield
response 0.25g event)
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Bent Model Simplification
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Experimental Numerical Results(A single bridge
bent 0.25g event)
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Single Pile Model Results (0.25g event)
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Bridge Model Simplification
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Bridge Model Simplification
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Bridge Model Simplification
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Experimental Numerical Results(A bridge)
1(S)
2(L)
3(M)
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Experimental Numerical Results(A bridge)
1(S)
2(L)
3(M)
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Experimental Numerical Results(A bridge)
0.25g event
bent 3
bent 2
bent 1
1(S)
2(L)
3(M)
0.74g event
bent 3
bent 2
bent 1
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Experimental Numerical Results(A bridge)
(a) bent 1 short
(b) bent 2 long
(c) bent 3 medium
0.25g event
0.74g event
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Centrifuge Test 2
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Oriented Bent Model Simplification
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3D Bent Structure Soil
axbase cos(?)
axbase sin(?)
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Experimental Numerical Results(free field
motion)
2.6 m depth
0.5 m depth
21.1 m depth
5.9 m depth
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Experimental Numerical Results(Oriented Bents
0o, 30o, 60o, 90o)
0o
30o
ax
ay1
60o
90o
y
x
z
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Experimental Numerical Results(Oriented Bents
0o, 30o, 60o, 90o)
0o
30o
ax
60o
90o
y
x
z
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Experimental Numerical Results(Oriented Bents
0o, 30o, 60o, 90o)
0o
30o
ay1
60o
90o
y
x
z
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Experimental Numerical Results(Oriented Bents
0o, 30o, 60o, 90o)
-z
0.78g event
?zz
?xx
?yy
y
x
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Experimental Numerical Results(Oriented Bents
0o, 30o, 60o, 90o)
0o
30o
60o
90o
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Centrifuge Test 3
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Performance Based Eq. Eng. Motivation

• General
• State/federal agency wants to optimize use of
  resources in structural design retrofitting
  (e.g. buildings/bridges).
• Addresses the problem from a performance based
  approach (priority to retrofit related to
  likelihood a certain level of response/damage
  will be achieved)
• Which bridge must be retrofitted first?
• Case Specific
• A bridge needs earthquake retrofitting
• Total estimated cost is 80 million dollars
• Only 20 million available
• Which structural aspects should be considered??
  Where to put the money?

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Performance Based Eq. Eng. Must evaluate
performance
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Performance Based Eq. Eng. Earthquake Intensity
? Damage
Need to understand physical processes
Develop terminology for phenomena of interest
RESPONSE OF SYSTEM OF INTEREST
DAMAGE TO SYSTEM OF INTEREST
GROUND MOTION
EARTHQUAKE
PGA PGV PGD Sa(T0) Ia CAV
Cracks, fracture, collapse Flow slide, lateral
spreading, settlement Slope movement, ground
cracking, structural distress
Ductility, m Settlement, dv Lateral displacement,
dh Pore pressure ratio, ru
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Performance Based Eq. Eng. PEER Framework

• Performance Based Earthquake Engineering (PBEE)
  framework developed by PEER to describe this
  process

Intensity Measure (IM) measure of ground
motion Engineering Demand Parameter (EDP) -
measure of system response Damage Measure (DM)
measure of physical damage
RESPONSE OF SYSTEM OF INTEREST
DAMAGE TO SYSTEM OF INTEREST
GROUND MOTION
IM
EDP
DM
EARTHQUAKE
PGA PGV PGD Sa(T0) Ia CAV
Cracks, fracture, collapse Flow slide, lateral
spreading, settlement Slope movement, ground
cracking, structural distress
Ductility, m Settlement, dv Lateral displacement,
dh Pore pressure ratio, ru
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Performance-Based Earthquake Engineering
Covers range of hazard (ground motion)
levels Accounts for uncertainty in parameters,
relationships
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Hazard Curves
Annual rate of exceedance
hazard curve for IM
f
1/T
1/Return Period
event
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Performance-Based Earthquake Engineering
Covers range of hazard (ground motion)
levels Accounts for uncertainty in parameters,
relationships
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Fragility Curves
Cumulative probability a certain EDP value will
be reached given a IM
CDF disp
IM
Fragility curve permanent displacement given IM
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Performance-Based Earthquake Engineering
Covers range of hazard (ground motion)
levels Accounts for uncertainty in parameters,
relationships
PEER extends analysis to include decision
variables (DV) related to loss, downtime,
fatalities, etc.
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Relation between ground motion and damage
Response Model
EDP
DM
IM
What is a good IM?
-- An efficient parameter
What is efficiency?
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Relation between ground motion and damage
Response Model
EDP
DM
IM
What is a good IM?
-- An efficient parameter
What is efficiency?
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Relation between ground motion and damage
Response Model
EDP
DM
IM
What is a good IM?
-- An efficient parameter
What is efficiency?
An efficient IM predicts response accurately
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Relation between ground motion and damage
Damage Model
Response Model
EDP
DM
IM
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Performance-Based Evaluation
PEER PBEE framework Modular approach from
ground motion to cost Recognizes different
participants, stakeholders
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Performance-Based Liquefaction Evaluation
1.0
PEDPgtEDP IM
lEDP proportional to sum of thick red lines
Fragility curve
0.0
IM
lIM
Hazard curve
IM
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Fragility Curves
IM-EDP fragility curve Conditional
Probability Probability a certain EDP
value will be reached
IM-EDP fragility curves must be created for
general and specific situations
Development of fragility curves for earthquake
engineering problems require the use of advanced
numerical tools
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OpenSees

• Open System for Earthquake Engineering Research
  Simulation by Pacific Earthquake Engineering
  (PEER) Center
• OpenSees is a software framework (FEM) for
  developing applications to simulate the
  performance of structural and geotechnical
  systems subjected to earthquakes.
• The goal of the OpenSees development is to
  improve the modeling and computational simulation
  in earthquake engineering through open-source
  development.

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OpenSees
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OpenSees
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OpenSees - Pressure Dependent MultiYield Material
Const. Model
Requires definition of 10 material parameters
Correletions to N1(60) Or Dr have been proposed
97

• Lets go back to the problem of fragility curves.
• Caltrans (California State Department of
  Transportation) is very interested in fragility
  curves for bridges
• Using OpenSees it is possible to develop them.
• Must consider full bidge including structure and
  soil.

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Bridge System on Liquefiable Soils
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Bridge and soil geometry

• Five-span bridge
• Approach embankments
• Variable thickness of liquefiable soil

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Soil Conditions
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GiD-OpenSees - Soil Layers
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Loose Sand N1(60) Proposed vs. OpenSees
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Clay - Undrained Strength
53.9
46.7
surface clay
39.5
57.5
Su (kPa)
57.5
35.9
55.7
50.3
44.9
deeper clay
58.4
Su (kPa)
39.7
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reinforce conc column (column A 4 ft)
prestressed reinforced conc bridge (type 1
22ft)
spring connection
abutment
3 x 2 pile group (3 ft diameter)
simplified abutment (roller or spring)
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OpenSees Bridge Idealization
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P-y curve Pult
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P-y curve y50
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Spring Abutment (Mackie et al.)
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Soil deformation measurement
Soil 1
Right toe
Soil 2
Soil 3
Soil 4
Left toe
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Soil deformation profiles
50 in 50 years
Small shaking
2 in 50 years
10 in 50 years
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Preliminary Comparison of IMs
40 input motions, four hazard levels
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Preliminary Comparison of IMs
40 input motions, four hazard levels
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Preliminary Comparison of IMs
40 input motions, four hazard levels
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EDP vs. IM (max. bridge column drift)
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EDP vs. IM (max. soil surface horizontal movement)
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EDP vs. IM (max. bridge column bending moment)
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EDP vs. IM (max. pile bending moment)
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Summary Conclusions

• The performance based design methodology provides
  an excellent framework to consider hazards in
  earthquake engineering.
• OpenSees provides a good tool for the development
  of fragility curves.
• Preliminary results show the framework could be
  applied for the performance based design of
  typical bridges.

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Acknowledgements

• Korea Water Resources Corporation
• Dong-Hoon Shin
• Hyung-Suk Shin
• Wookuen Shin
• Changho Choi
• NSF, PEER, NEES

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Thanks You!!