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Performance-based Evaluation of the Seismic Response of Bridges with Foundations Designed to Uplift Marios Panagiotou Assistant Professor, University of California, Berkeley Bruce Kutter Professor , University of California, Davis.

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3 Questions

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  1. Performance-based Evaluation of the Seismic Response of Bridges with Foundations Designed to UpliftMariosPanagiotouAssistant Professor, University of California, Berkeley Bruce KutterProfessor , University of California, Davis

  2. AcknowledgmentsPacific Earthquake Engineering Research (PEER) Center for funding this work through the Transportation Research ProgramAntonellisGrigoriosGraduate Student Researcher, UC Berkeley Lu YuanGraduate Student Researcher, UC Berkeley

  3. 3 Questions • Can foundation rocking be considered as an alternative seismic design method of bridges resulting in reduced: i) post-earthquakedamage, ii) required repairs, and iii) loss of function ? • What are the ground motion characteristics that can lead to overturn of a pier supported on a rocking foundation? • Probabilistic performance-based earthquake evaluation ?

  4. “Fixed” Base Design • Susceptible to significant post-earthquake damage and permanent lateral deformations that: • Impair traffic flow • Necessitate costly and time consuming repairs flexural plastic hinge

  5. Design Using Rocking Shallow Foundations Pier on rocking shallow foundation “Fixed” base pier

  6. Design Using Rocking Pile Caps “Fixed” base pier Pier on rocking pile-cap

  7. Design Using Rocking Pile-Caps Pile-cap simply supported on piles Pile-cap with sockets Mild steel for energy dissipation ?

  8. Rocking Foundations - Nonlinear Behavior Moment, M Infinitely strong soil Elastic soil N M Θ Inelastic soil B NB NB Rotation, Θ 6 2

  9. Nonlinear Behavior Characteristics Force, F Displacement, Δ Shallow foundation with limited soil inelasticity Rocking pile-cap or shallow foundation on elastic soil Fixed-base or shallow foundation with extensivesoil inelasticity

  10. SDOF Nonlinear Displacement Response Mean results of 40 near-fault ground motions

  11. An archetype bridge is considered and is designed with: fixed base piers with piers supported on rocking foundations Numerical Case Study of a Bridge Archetype bridge considered – Tall Overpass 56 ft 150 ft 150 ft 120 ft 120 ft 150 ft Analysis using 40 near-fault ground motions

  12. Computed Response of a Bridge System Archetype bridge considered – Tall Overpass 56 ft 150 ft 150 ft 120 ft 120 ft 150 ft • 5 Spans • Single column bents • Cast in place box girder 39 ft 6 ft D = 6ft 50 ft • Column axial load ratio N / fc’Ag = 0.1 • Longitudinal steel ratio ρl = 2% B

  13. Designs Using Rocking Foundations Shallow foundation Rocking Pile-Cap 39 ft 39 ft 6 ft 6 ft D = 6ft 50 ft 50 ft D = 6ft B = 24 ft (4D) Soil ultimate stress σu = 0.08 ksi FSv = Aσu/ N = 5.4 B = 18 ft (3D)

  14. Modeling of Bridge OPENSEES 3-dimensional model Abutment , shear keys: nonlinear springs Columns, deck : nonlinear fiber beam element Soil-foundation : nonlinear Winkler model

  15. Bridge Model - Dynamic Characteristics Fixed - base B = 4D Rocking Pile Cap B=3D 1.9 1.8 1st mode, T1 (sec) 2nd mode, T2 (sec) 2.1 1.9 1.1 0.8

  16. Monotonic Behavior – Individual Pier

  17. Ground Motions Considered – Response Spectra , 2% Damping

  18. Computed Response of Bridge Δ Δ: total drift Δf Δf: drift due to pier bending z: soil settlement at foundation edge z

  19. Computed Bridge Response - Total drift, Δ

  20. Computed Bridge Response Drift due to pier bending Δf

  21. Computed Bridge Response

  22. Ground motion characteristics that may lead to overturn ? Ground motions with strong pulses (especially low frequency) that result in significant nonlinear displacement demand Pulse A Pulse B ap ap Acceleration Tp Tp Velocity Rocking response of rigid block on rigid base to pulse-type excitation Zhang and Makris (2001) Displacement Time Time

  23. Near Fault Ground Motions and their representation using Trigonometric Pulses Tp = 0.8 sec Tp = 5.0 sec ap = 0.13 g ap = 0.7 g

  24. Conditions that may lead to overturn 39 ft 6 ft WD = 1350 kips Pulse A Pulse B 50 ft ap ap D = 6ft Acceleration Tp Tp WF = 300 kips Velocity B = 18 ft Displacement Minimum ap at different Tpthat results in overturn ? Time Time

  25. Conditions that may lead to overturn

  26. Conditions that may lead to overturn

  27. The PEER methodology and the framework of Mackie et al. (2008) was used for the PBEE comparison of the fixed base and the rocking designs. Probabilistic Performance Based Earthquake Evaluation (PBEE) • Ground Motion Intensity Measures [Sa ( T1 )] • Engineering Demand Parameters (e.g. Pier Drift ) • Damage in Bridge Components • Repair Cost of Bridge System

  28. PBEE Evaluation – Damage Models (Mackie et al. 2008)

  29. PBEE Evaluation Foundation Damage Model

  30. PBEE – Median Total Repair Cost

  31. PBEE – Disaggregation of Cost Fixed Base Bridge

  32. PBEE – Disaggregation of Cost Bridge with Shallow Foundations B=4D

  33. END

  34. Response of Individual Pier on Rocking Pile Cap

  35. Response of Individual Pier on Rocking Pile Cap

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