Probabilistic Performance-Based Optimum Design of Seismic Isolation for a California High-Speed Rail Prototype Bridge

Transcription

1 Probabilistic Performance-Based Optimum Design of Seismic Isolation for a California 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 Outline 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 2

3 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

4 CHSR Prototype Bridge Designed in collaboration with engineers at Parsons Brinckerhoff in San Fancisco.

5 Schematic View of CHSR Prototype Bridge Abutment Interior Expansion Expansion Joint Joint Elevation & Plan View Interior Expansion Abutment Joint Expansion Joint Z O X Y O X 42' Transversal Section Expansion Joint Continuous Joint 42' Interior Expansion Joint

6 3D Nonlinear Finite Element Modeling in OpenSees 6

7 Schematic View of Bridge Model 24 Quasi-rigid beams A A Stress [ksi] Single Pier of Prototype Bridge Strain [%] Stee rebar #11 (Steel02) Unconfined Concrete (Concrete01) Stress [ksi] Stress [ksi] Confined concrete (Concrete02) Section A-A Strain [%] Strain [%]

8 Schematic View of Bridge Model rails A A Quasi-rigid beams Bridge deck (box girder) Single Span Single Pier of Prototype Bridge Steel rebar #11 (Steel02) Unconfined Concrete (Concrete01) Confined Concrete (Concrete02) Section A-A Three Continuous Span Frame

9 Layout and Model of Seismic Isolators Axial Force Distribution Shear Force Yield Strength: F y D y 1 k k eff k 1 : Initial Stiffness Shear Displacement Bilinear Model for Seismic Isolators

10 Modeling of Bridge Abutments with Soil Backfills Maroney and Chai (1994) Scaled by 4.6 Megally et al. (2001) Scaled by 2.15 PYCAP (Mokwa et al. 2001) GHFD (Khalili Tehrani et al. 2010) Hyperbolic spring backbone curve F - D

11 Modeling of Pile Foundations including SFSI Gapping effect p-y behavior in upper soil layers (clay) pile p c closure drag p d p-y springs y y g g elastic plastic dashpot p y p p e y p r e y e p-y formulation by Boulanger et al. (1999) p-y behavior in lower soil layers (sand)

12 Modeling of Track with Track-Structure Interaction bollard Neoprene Pads Track slab Leveling Rail Track slab Direct fixation fastener (Longitudinal: EPP) Elastic rail elements Concrete Base Bridge Deck Bridge Deck Train Track Cross-section Modeling of Train Track

13 Comprehensive Bridge Model with SFSI and Rail-Structure Interaction R#1 R#37 R#80 R#123 R#166 R#203 F#1 F#37 F#38 F#80 F#81 F#123 F#124 F#166 F#167 F#204 Subgrade Pile supported left abutment Left rail extension (361 ft) I#1 I#3 I#5 I#11 I#13 I#19 I#7 I#9 I#15 I#17 I#21 S#1 S#3 P#1 P#2 P#3 P#4 P#5 P#6 P#7 P#8 Bridge (110 ft 9 = 990 ft) Elevation View of the FE Element Model I#23 Pile supported right abutment Foundation System Subgrade Right rail extension (361 ft) De-convolution analysis for depth-variation of ground displacement Response simulation for Multiple-support-excitation

14 Probabilistic Performance-Based Optimum Seismic Design Framework 14

15 Probabilistic Performance-Based Optimum Seismic Design Framework Site Location Structural System Seismic Hazards (IM) Design/Upgrade Alternatives (SP) SP: Structural Parameters hazard model P[IM] Load Hazard Analysis loads P[IM] IM: Intensity Measure structural model PEDP IM Demand Hazard Analysis demand P[EDP] EDP: Engr. Demand Par. Probabilistic Model Development fragility model PDM EDP Damage Hazard Analysis damage P[DM] DM: Damage Measure loss model PDV DM Loss Hazard Analysis loss P[DV] DV: Decision Variable Probabilistic Performance Evaluation PBEE YES NO No feasible design Final design Decision Analysis Update Design (SP) NO Optimal YES NO YES Decision making Performance Constraints YES Optimization? NO Performance Objectives Define Objectives Serviceability Life Safety Collapse Prevention Resilience Sustainability Robustness

16 Probabilistic Comparison of Bridge Seismic Response Behavior with and without Seismic Isolation 16

17 Seismic Demand Hazard Analysis Results for Bridge Structure Relative deck displacement over Pier #5 in transversal direction: P EDP edp IM im EDP edp PEDP edp IM im d im IM 77% 20% IM 7.0 Conditional statistics/pdf Unconditional demand hazard curves Column base moment (Pier #5) in transversal direction: M cr M y

18 Seismic Demand Hazard Analysis Results for Pile Foundation Maximum (normalized) pile cap rotation under Pier#5 in transv. dir.: Maximum rail stress due to axial force at interior expansion joint #2: EDP = Max. Stress due to Axial Force [Mpa]

19 Parametric Probabilistic Demand Hazard Analysis

20 Demand Hazard Based Risk Features/Metrics SI Beneficial SI Beneficial NIB: 35,468 NIB: 25,302 Max. Pier#5 Base Moment Max. Pier#5 Base Moment DV : K 1 [kips/in] DV : F [kips] y DV : K 1 [kips/in] DV : F [kips] y Mean demand conditional on MCE SI Detrimental NIB: 1.07 Max. Rel. Deck Displ. Unconditional mean demand SI Detrimental NIB: 0.5 Max. Rail Stress due to Axial Force DV : K 1 [kips/in] DV : F [kips] y DV : K 1 [kips/in] DV : F [kips] y Mean demand conditional on OBE Mean demand conditional on OBE 20

21 Probabilistic Performance-Based Design Optimization Problems for Seismic Isolation of CHSR Prototype Bridge 21

22 Optimum Probabilistic PBD Optimization problem formulated for PBD conditional on OBE TBS, all columns OBE Minimize conditional median demand (Total Base Shear): Ftransv. Subject to constraints : deck 1 E AAtransv. OBE 0.35 g deck 2 Pctl.95th AAtransv. OBE 0.5 g Pier #5 pier 4 3 Pctl.95th M transv. OBE M cr ( kips -ft ) piles, Pier #5 OBE M crpile ( kips -ft ) 4 Pctl.95th M transv. 5 Pctl.95th Prail, left abut. OBE 12.5ksi 6 Prail M, abut. OBE 42.5ksi (3) (1) (4) (6) (2) (5)

23 Optimum Probabilistic PBD Optimization problem formulated for PBD with constraints conditional on two hazard levels (OBE & MCE) TBS, all columns Minimize conditional mean: EFtransv. OBE Subject to: Constraints for OBE hazard level. deck 1 E AAtransv OBE 0.35 g th deck 2 Pctl. AAtransv. OBE 0.5g th Pier pier 3 Pctl. Mtransv. OBE M cr (1.510kips- ft) th piles P pile 4 Pctl. Mtransv. OBE M cr (5.310kips- ft) th rail left abut 5 Pctl. P OBE 12.5ksi 6 P M OBE 42.5ksi #5 4 95, #5 3 95,. rail, left abut. 95 th Rot. P #5 Pctl Constraints for MCE hazard level 7. transv. MCE 1.3% th Isolator 8 Pctl. Def. transv. MCE 20 in th Pier pier 9 Pctl. Mtransv. MCE M e (4.1510kips- ft) th piles P pile 10 Pctl. Mtransv. MCE M e (1.210 kips- ft) 95 #13 95 #5 4 95, #5 4 (9) (3) (2) (10) (1) (2) (7) (4) (6) (5) (8)

24 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). 25

26 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.

27 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)