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

2

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 '

6

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)

14

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

16

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

20

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

21

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

25

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)