Probabilistic Performance-Based Optimum Design of Seismic ...
Transcript of Probabilistic Performance-Based Optimum Design of Seismic ...
Probabilistic Performance-Based Optimum Design
of Seismic Isolation for aCalifornia High-Speed Rail Prototype Bridge
Joel P. Conte(1) and Yong Li (2)
(1) Department of Structural Engineering, University of California at San Diego, La Jolla, California
(2) Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Canada
2018 PEER Annual Meeting January 18-19, Berkeley, CA
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Introduction and Motivation
California High-Speed Rail (CHSR) Prototype Bridge
3D Nonlinear FE Model in OpenSees
Probabilistic Performance-Based Optimum Seismic Design (PPBOSD) Framework
Comparison of CHSR Prototype Bridge with and without Seismic Isolation in Terms of Demand Hazard
Optimum Performance-Based Design of Seismic Isolation System
Concluding Remarks
Outline
Testbed Application: Seismic Isolation for CHSR Bridges
California High-Speed Train Project (CHST)
Arial/Bridge Structure Supporting System
Potential Seismic Risk in California
CHST Alignment Promising Application
of Seismic Isolation
CHSR Prototype Bridge
• Designed in collaboration with engineers at Parsons Brinckerhoff in San Fancisco.
Schematic View of CHSR Prototype BridgeElevation & Plan View
O XZ
O XY
Abutment Expansion Joint
Abutment Expansion Joint
Interior Expansion Joint
Interior Expansion Joint
Interior Expansion
Joint
Transversal Section Expansion Joint Continuous Joint42 '
42 '
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3D Nonlinear Finite Element Modelingin OpenSees
Section A-A
Schematic View of Bridge Model 24
Confined concrete
(Concrete02)
Unconfined Concrete
(Concrete01)
Stee rebar #11 (Steel02)
Single Pier of Prototype Bridge
Quasi-rigid beams
A A
Stre
ss [k
si]
Strain [%]
Stre
ss [k
si]
Strain [%] Strain [%]
Stre
ss [k
si]
Single Span
rails
Bridge deck (box girder)
Three Continuous Span Frame
Confined Concrete
(Concrete02)
Unconfined Concrete
(Concrete01)
Steel rebar #11 (Steel02)
Section A-A
Single Pier of Prototype Bridge
Quasi-rigid beams
A A
Schematic View of Bridge Model
Layout and Model of Seismic Isolators
Bilinear Model for Seismic Isolators
Axial Force Distribution
1
Shear Displacement
Shear Force
1 k1: Initial StiffnessYield Strength: Fy
keff1
Dy
k2
Modeling of Bridge Abutments with Soil Backfills
F - DHyperbolic spring backbone curve
PYCAP (Mokwa et al. 2001)
GHFD (Khalili‐Tehrani et al. 2010)
Maroney and Chai (1994)
Scaled by 2.15
Scal
ed b
y 4.
6 Megally et al. (2001)
Modeling of Pile Foundations including SFSI
p-y formulation by Boulanger et al. (1999)
closure
drag
elastic
plastic dashpotpile
c gp y
d gp y pp y
e ep y
r ep y
p-y springs
p-y behavior in lower soil layers (sand)
Gapping effect
p-y behavior in upper soil layers (clay)
Modeling of Track with Track-Structure Interaction
Direct fixation fastener(Longitudinal: EPP)Track slab
Bridge Deck – Train Track Cross-section
Leveling
Neoprene Pads Fasteners @27”
Bridge DeckConcrete
Base
Track slab
Modeling of Train Track
RailElastic rail elements
bollard
Comprehensive Bridge Model with SFSI and Rail-Structure Interaction
Elevation View of the FE Element Model
De-convolution analysis for depth-variation of ground displacement
Response simulation for Multiple-support-excitation
Foundation System
Pile supported left abutment
Pile supported right abutment
Subgrade Subgrade
S#1 S#3
P#1 P#2 P#3 P#4 P#5 P#6 P#7 P#8
I#3
Left rail extension (361 ft)
I#5 I#11 I#13 I#19I#21
I#1I#7 I#9 I#15 I#17
I#23
F#1 F#37 F#38 F#80 F#81 F#123 F#124 F#166 F#167 F#204R#1 R#80R#37 R#123 R#166 R#203
Bridge (110 ft × 9 = 990 ft)Right rail extension
(361 ft)
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Probabilistic Performance-Based Optimum Seismic Design Framework
Site Location
Seismic Hazards(IM)
Structural System
Design/Upgrade Alternatives
(SP)SP: Structural
Parameters
hazardmodelP[IM]
Probabilistic Model Development
LoadHazard
Analysis
IM: IntensityMeasure
loadsP[IM]
DemandHazard
Analysis
demandP[EDP]
EDP: Engr.Demand Par.
damageP[DM]
DM: DamageMeasure
DamageHazard
Analysis
lossP[DV]
DV: DecisionVariable
LossHazard
Analysis
Probabilistic Performance Evaluation
PerformanceConstraints
Decision Analysis
Update Design (SP)
Final design
NO
YES
OptimalYES
NO
Decision making
NO
Optimization?
YES
NO
No feasible design
YES
Define Objectives
ServiceabilityLife Safety
Collapse PreventionResilience
SustainabilityRobustness
Performance Objectives
Probabilistic Performance-Based Optimum Seismic Design Framework
PBEE
structural model P EDP|IM
fragility model
P DM | EDP
loss model P DV | DM
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Probabilistic Comparison of Bridge Seismic Response Behavior with and without Seismic Isolation
Seismic Demand Hazard Analysis Results for Bridge Structure• Relative deck displacement over Pier #5 in transversal direction:
Conditional statistics/PDF Unconditional demand hazard curves
• Column base moment (Pier #5) in transversal direction:
|EDP IMIM
edp P EDP edp IM im d im
7.0
77%
20%
|P EDP edp IM im
Mcr My
Seismic Demand Hazard Analysis Results for Pile Foundation
• Maximum (normalized) pile cap rotation under Pier#5 in transv. dir.:
EDP = Max. Stress due to Axial Force [Mpa]
• Maximum rail stress due to axial force at interior expansion joint #2:
Parametric Probabilistic Demand Hazard Analysis
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Demand Hazard Based Risk Features/Metrics
NIB: 35,468
SI Beneficial
1DV : K [kips/in] DV : F [kips]y
Max. Pier#5 Base Moment
NIB: 25,302
SI Beneficial
1DV : K [kips/in] DV : F [kips]y
Max. Pier#5 Base Moment
SI DetrimentalNIB: 1.07
1DV : K [kips/in] DV : F [kips]y
Max. Rel. Deck Displ.
NIB: 0.5SI Detrimental
1DV : K [kips/in] DV : F [kips]y
Max. Rail Stress due toAxial Force
Unconditional mean demandMean demand conditional on MCE
Mean demand conditional on OBE Mean demand conditional on OBE
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Probabilistic Performance-Based Design Optimization Problems
for Seismic Isolation of CHSR Prototype Bridge
Optimum Probabilistic PBD • Optimization problem formulated for PBD conditional on OBE
(1)
(2)
(3)
(4)
(6)(5)
:Subject to constraints
95.2 . | 0.5th deck
transvPctl AA OBE g 95 #5 4
.3 . | (1.5 10 - ) th Pier piertransv crPctl M OBE M kips ft
95 , #5 3.4 . | (5.3 10 - )th piles Pier pile
transv crPctl M OBE M kips ft 95 , left abut .5 . | 12.5th rail
PPctl OBE ksi , abut.6 | 42.5rail
P M OBE ksi
.1 | 0.35 decktransvE AA OBE g
TBS, . conditional median demand (Total Base Shear): |all columns
transvF OBE Minimize
Optimum Probabilistic PBD • Optimization problem formulated for PBD with constraints
conditional on two hazard levels (OBE & MCE)
Constraints for OBE hazard level
Constraints for MCE hazard level
(1)(2)
(3)
(4)
(6)(5)
(2)(7)
(8)
(9)
(10)
TBS, . conditional mean: |
:
all columnstransvE F OBE
MinimizeSubject to
, .6 | 42.5rail left abutP M OBE ksi
95 , .5 . | 12.5th rail left abutPPctl OBE ksi
95 , #5 3.4 . | (5.3 10 - )th piles P pile
transv crPctl M OBE M kips ft
95 #5 4.3 . | (1.5 10 - ) th Pier pier
transv crPctl M OBE M kips ft
95.2 . | 0.5th deck
transvPctl AA OBE g
.1 | 0.35 decktransvE AA OBE g
95 . #5.7 . | 1.3% th Rot P
transvPctl MCE 95 #13
.8 . . | 20 th IsolatortransvPctl Def MCE in
95 #5 4.9 . | (4.15 10 - ) th Pier pier
transv ePctl M MCE M kips ft 95 , #5 4
.10 . | (1.2 10 - ) th piles P piletransv ePctl M MCE M kips ft
Conclusions & Future Research Needs
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Concluding Remarks
• Probabilistic Performance-based Optimum Seismic Design (PPBOSD) framework Provides an integrated and scientific approach for optimum seismic design of civil
infrastructure systems in the face of uncertainty, with objective and constraint functions defined in terms of risk features/metrics defined at different stages of the PBEE assessment methodology (i.e., demand, damage, and/or loss hazard).
Provides the proper tool to develop, calibrate and validate simplified probabilistic PBD methods for engineering practice (i.e., development of PBD code procedures).
Can be extended to other natural and man-made hazards (e.g., tsunami, wind/hurricane/tornadoes, blast, fire), as well as multi-hazard design problems.
• Investigation of seismic isolation for California high-speed rail bridges in high seismic risk areas Seismic isolation decreases the seismic demand (e.g., displacements,
deformations, internal forces) on the bridge substructure (piers and foundations) as well as the absolute deck acceleration.
Seismic isolation increases the seismic demand on deck displacement and thus on rail stress (especially at the interior expansion joints).
Concluding Remarks
• Design optimization in the context of Probabilistic Performance-Based Design (PBD)
Optimization of seismic isolation for CHSR prototype bridge achieved using a grid-based brute force approach taking advantage of cloud-based computing for parallel instead of sequential evaluation of multiple design alternatives and multiple time history analyses.
The proposed PPBOSD framework allows to find:• Initial feasible design satisfying the target risk-based design criteria.• Improved design• Optimum design
The proposed PPBOSD framework provides high flexibility in the formulation of risk-based design criteria (at the demand, damage and/or loss hazard level) in support of Probabilistic PBD.
Acknowledgements
Funding Support:Pacific Earthquake Engineering Research (PEER) Center• Transportation Systems Research Program
Technical Support and Insightful Discussions: Jack Baker (Stanford)Ross W. Boulanger (UC Davis)Scott J. Brandenberg (UC Los Angeles)Roy Imbsen (Earthquake Protection Systems, Inc., Vallejo, California)Thomas B. Jackson (Parsons Brinckerhoff, San Francisco)Pang Yen Lin (Parsons Brinckerhoff, San Francisco)Steve Mahin (UC Berkeley)Frank McKenna (UC Berkeley)Kongsak Pugasap (Parsons Brinkerhoff, San Francisco)Jose I. Restrepo (UC San Diego)Ertugrul Taciroglu (UC Los Angeles)