Report

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 Acknowledgments Pacific Earthquake Engineering Research (PEER) Center for funding this work through the Transportation Research Program Antonellis Grigorios Graduate Student Researcher, UC Berkeley Lu Yuan Graduate Student Researcher, UC Berkeley 3 Questions 1. Can foundation rocking be considered as an alternative seismic design method of bridges resulting in reduced: i) post-earthquake damage, ii) required repairs, and iii) loss of function ? 2. What are the ground motion characteristics that can lead to overturn of a pier supported on a rocking foundation? 3. Probabilistic performance-based earthquake evaluation ? “Fixed” Base Design Susceptible to significant postearthquake damage and permanent lateral deformations that: • Impair traffic flow flexural plastic hinge • Necessitate costly and time consuming repairs Design Using Rocking Shallow Foundations “Fixed” base pier Pier on rocking shallow foundation Design Using Rocking Pile Caps “Fixed” base pier Pier on rocking pile-cap Design Using Rocking Pile-Caps Pile-cap simply supported on piles Pile-cap with sockets Mild steel for energy dissipation ? Rocking Foundations - Nonlinear Behavior Moment, M Elastic soil N Infinitely strong soil NB 2 M Θ B Inelastic soil NB 6 Rotation, Θ Nonlinear Behavior Characteristics Force, F Displacement, Δ Fixed-base or shallow foundation with extensive soil inelasticity Shallow foundation with limited soil inelasticity Rocking pile-cap or shallow foundation on elastic soil Mean results of 40 near-fault ground motions R=2 R=4 R=6 40 40 40 30 30 30 20 20 20 10 R=2 10 40 0 0 30 1 2 T (sec) Sd (in) d SDOF Nonlinear Displacement Response 10 40 0 0 30 3 20 1 2 T (sec) 3 0 0 Nonlinear Elastic R=6 40 1 2 T (sec) 3 Clough Flag 20 10 1 2 T (sec) Flag 0 030 3 20 10 0 0 R=4 Clough Nonlinear Elastic 10 1 2 T (sec) 3 0 0 1 2 T (sec) 3 Numerical Case Study of a Bridge An archetype bridge is considered and is designed with: i) fixed base piers ii) with piers supported on rocking foundations Analysis using 40 near-fault ground motions Archetype bridge considered – Tall Overpass 56 ft 120 ft 150 ft 150 ft 150 ft 120 ft Computed Response of a Bridge System Archetype bridge considered – Tall Overpass 56 ft 150 ft 120 ft 150 ft • • • 39 ft 6 ft D = 6ft 50 ft B 150 ft 120 ft 5 Spans Single column bents Cast in place box girder • Column axial load ratio N / fc’Ag = 0.1 • Longitudinal steel ratio ρl = 2% Designs Using Rocking Foundations Shallow foundation Rocking Pile-Cap 39 ft 39 ft 6 ft 6 ft 50 ft 50 ft D = 6ft D = 6ft B = 24 ft (4D) Soil ultimate stress σu = 0.08 ksi FSv = Aσu / N = 5.4 B = 18 ft (3D) Modeling of Bridge OPENSEES 3-dimensional model Abutment , shear keys: nonlinear springs Columns, deck : nonlinear fiber beam element Force Soil-foundation : nonlinear Winkler model Deformation Bridge Model - Dynamic Characteristics Fixed - base 1st mode, T1 (sec) 2nd mode, T2 (sec) 1.1 0.8 B = 4D 2.1 1.9 Rocking Pile Cap B=3D 1.9 1.8 Monotonic Behavior – Individual Pier 20000 Moment, (kips-ft) 15000 10000 Fixed base B=5D, FSv=8.4 5000 B=4D, FSv=5.4 Pile cap, B=3D 0 0 0.5 1 1.5 2 2.5 3 Drift Ratio, / H, (%) 3.5 4 4.5 5 4 4 3 2 2 1 0.5 1 1.5 2 2.5 0 3 75 2 4 6 8 10 2 4 6 8 10 400 300 50 Sd (in) Sd (in) 3 25 Sd (in) 0 Sa (g) 5 1 10 10 5 Sa (g) Sa (g) Ground Motions Considered – Response Spectra , 2% Damping 200 100 0 0.5 1 1.5 T (sec) 2 2.5 3 0 T (sec) Computed Response of Bridge Δ Δ: total drift Δf Δf: drift due to pier bending z: soil settlement at foundation edge z Computed Bridge Response - Total drift, Δ Drift Ratio / H, (%) 15 10 5 0 0 5 10 15 20 25 30 Ground Motion Number 35 40 f Flexural Drift Ratio, / H, (%) f Flexural Drift Ratio, / H, (%) Computed Bridge Response Drift due to pier bending Δf 8 6 4 2 0 0 5 10 15 20 25 Ground Motion Number Ground Motion Number 30 35 40 Computed Bridge Response Settlement Z, (in) 10 8 6 4 2 0 0 5 10 15 20 25 30 Ground Motion Number 35 40 Ground motion characteristics that may lead to overturn ? Ground motions with strong pulses (especially low frequency) that result in significant nonlinear displacement demand Accel. Pulse PulseAA Pulse PulseBB ap ap Tp Time Time Time Time Rocking response of rigid block on rigid base to pulse-type excitation Zhang and Makris (2001) Displ. Vel. Tp Near Fault Ground Motions and their representation using Trigonometric Pulses Ground acceleration, ag ( g ) Northridge 1994, Rinaldi (FN) 1 Landers 1999, Lucerne Valley (FN) 1 Tp = 0.8 sec 0.5 0.5 0 0 -0.5 -0.5 Ground velocity vg ( in / s ) -1 0 ap = 0.7 g 5 10 -1 0 80 80 40 40 0 0 -40 -40 -80 0 5 time (sec) 10 -80 0 Tp = 5.0 sec ap = 0.13 g 10 20 30 10 20 time ( sec ) 30 Conditions that may lead to overturn 39 ft 6 ft WD = 1350 kips 50 ft Accel. Pulse PulseAA B = 18 ft ap Tp Tp Time Time Time Time Displ. WF = 300 kips ap Vel. D = 6ft Pulse PulseBB Minimum ap at different Tp that results in overturn ? Conditions that may lead to overturn 14 12 Pulse A Pulse B 8 p a (g) 10 6 4 2 0 0 2 4 Tp (sec) 6 8 Conditions that may lead to overturn 1 Pulse A Pulse B ap (g) 0.75 0.5 0.25 0 0 2 4 Tp (sec) 6 8 Probabilistic Performance Based Earthquake Evaluation (PBEE) 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. • • • • Ground Motion Intensity Measures [Sa ( T1 )] Engineering Demand Parameters (e.g. Pier Drift ) Damage in Bridge Components Repair Cost of Bridge System PBEE Evaluation – Damage Models (Mackie et al. 2008) P[dm>DM LS] Column Abutment 1 1 0.8 0.8 0.6 0.6 0.4 0 0 0.4 Cracking Spalling Bar Buckling Failure 0.2 5 10 Onset of Damage Joint Seal Assembly BackWall Approach Slab 0.2 15 0 0 4 P[dm>DM LS] Shear Key Bearing 1 1 0.8 0.8 0.6 0.6 Elastic Limit Concrete Spalling Failure 0.2 0 0 120 240 Shear force (kips) 12 Long. Displacement (in.) Drift Ratio (%) 0.4 8 360 0.4 Yield Failure 0.2 0 0 4 8 12 Displacement (in.) 16 PBEE Evaluation Foundation Damage Model Column Foundation 1 P [ dm > DM LS] 0.8 0.6 Elastic First Yield Limited Yielding Extensive Yielding 0.4 0.2 0 0 1 2 Normalized Edge Settlement z / z 3 yield PBEE – Median Total Repair Cost Total Repair Cost ( million of $) 1.0 Fixed Base 0.8 B=4D, Fsv=5.4 Pile Cap, B=3D 0.6 0.4 0.2 0 0 0.5 1 Sa ( T = 1 sec ), (g) 1.5 2 PBEE – Disaggregation of Cost Fixed Base Bridge Repair Cost (million of $) 0.3 EDGE COLUMNS MIDDLE COLUMNS BEARINGS SHEAR KEYS 0.2 0.1 0 0 0.5 1 Sa (T=1sec), (g) 1.5 2 PBEE – Disaggregation of Cost Bridge with Shallow Foundations B=4D Disaggregation of Cost - B=4D, Fsv=5.4 EDGE COLUMNS 0.3 MIDDLE COLUMNS BEARINGS Repair Cost (million of $) SHEAR KEYS EDGE COLUMNS FOUNDATIONS MIDDLE COLUMNS FOUNDATIONS 0.2 0.1 0 0 0.5 1 Sa(T=1sec), (g) 1.5 2 END Response of Individual Pier on Rocking Pile Cap Base rotation ( radians ) Northridge, Rinaldi - FN Landers, Lucerne Valley - FN 0.04 0.04 0.02 0.02 0 0 -0.02 -0.02 -0.04 0 20 time ( sec ) 40 -0.04 0 50 time ( sec ) 100 Response of Individual Pier on Rocking Pile Cap 1.6 LCN 1.3xLCN base rotation ( radians ) 1.2 0.8 0.4 0 -0.4 -0.8 -1.2 -1.6 0 5 10 15 time ( sec ) 20 25 30