Performance-based Evaluation of the Seismic Response of Bridges with Foundations Designed to Uplift

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

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 N NB Elastic soil Infinitely strong soil M 2 B NB 6 Inelastic soil Rotation,

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

SDOF Nonlinear Displacement Response Mean results of 4 near-fault ground motions Clough Flag 4 R = 2 4 R = 4 4 R = 6 Nonlinear Elastic 3 3 3 S d (in) 2 2 2 1 1 1 1 2 3 T (sec) 1 2 3 T (sec) 1 2 3 T (sec)

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 4 near-fault ground motions Archetype bridge considered Tall Overpass 56 ft 12 ft 15 ft 15 ft 15 ft 12 ft

Computed Response of a Bridge System Archetype bridge considered Tall Overpass 56 ft 12 ft 15 ft 15 ft 15 ft 12 ft 6 ft 39 ft 5 Spans Single column bents Cast in place box girder 5 ft D = 6ft Column axial load ratio N / f c A g =.1 Longitudinal steel ratio l = 2% B

Designs Using Rocking Foundations Shallow foundation 39 ft Rocking Pile-Cap 39 ft 6 ft 6 ft 5 ft D = 6ft 5 ft D = 6ft B = 24 ft (4D) Soil ultimate stress u =.8 ksi B = 18 ft (3D) FS v = A u / N = 5.4

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

Bridge Model - Dynamic Characteristics Fixed - base B = 4D Rocking Pile Cap B=3D 1 st mode, T1 (sec) 2 nd mode, T2 (sec) 1.1.8 2.1 1.9 1.9 1.8

Monotonic Behavior Individual Pier 2 15 Moment, (kips-ft) 1 5 Fixed base B=5D, FS v =8.4 B=4D, FS v =5.4 Pile cap, B=3D.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Drift Ratio, / H, (%)

Ground Motions Considered Response Spectra, 2% Damping 5 5 4 4 Sa (g) 3 2 Sa (g) 3 2 1 1.5 1 1.5 2 2.5 3 2 4 6 8 1 75 4 Sd (in) 5 25 Sd (in) 3 2 1.5 1 1.5 2 2.5 3 T (sec) 2 4 6 8 1 T (sec)

Computed Response of Bridge : total drift f f : drift due to pier bending z: soil settlement at foundation edge z

Computed Bridge Response - Total drift, 15 Drift Ratio / H, (%) 1 5 5 1 15 2 25 3 35 4 Ground Motion Number

Computed Bridge Response Drift due to pier bending f Flexural Drift Ratio, / H, (%) f 8 6 4 2 5 1 15 2 25 3 35 4 Ground Motion Number

Computed Bridge Response 1 Settlement Z, (in) 8 6 4 2 5 1 15 2 25 3 35 4 Ground Motion Number

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 Accel. a p a p T p T p Vel. Rocking response of rigid block on rigid base to pulse-type excitation Zhang and Makris (21) Displ. Time Time

Near Fault Ground Motions and their representation using Trigonometric Pulses Ground acceleration, a g ( g ).5 -.5 Northridge 1994, Rinaldi (FN) 1-1 5 1 8 T p =.8 sec a p =.7 g Landers 1999, Lucerne Valley (FN) 1.5 -.5-1 1 2 3 8 T p = 5. sec a p =.13 g Ground velocity v g ( in / s ) 4-4 4-4 -8 5 1 time (sec) -8 1 2 3 time ( sec )

Conditions that may lead to overturn 39 ft 6 ft Pulse A Pulse B W D = 135 kips Accel. a p a p 5 ft D = 6ft T p T p W F = 3 kips Vel. B = 18 ft Displ. Time Time Minimum a p at different T p that results in overturn?

Conditions that may lead to overturn 14 12 1 Pulse A Pulse B a p (g) 8 6 4 2 2 4 6 8 T p (sec)

Conditions that may lead to overturn 1.75 Pulse A Pulse B a p (g).5.25 2 4 6 8 T p (sec)

Probabilistic Performance Based Earthquake Evaluation (PBEE) The PEER methodology and the framework of Mackie et al. (28) was used for the PBEE comparison of the fixed base and the rocking designs. Ground Motion Intensity Measures [Sa ( T 1 )] Engineering Demand Parameters (e.g. Pier Drift ) Damage in Bridge Components Repair Cost of Bridge System

PBEE Evaluation Damage Models (Mackie et al. 28) 1 Column 1 Abutment.8.8 P[dm>DM LS].6.4.2 Cracking Spalling Bar Buckling Failure.6.4.2 Onset of Damage Joint Seal Assembly BackWall Approach Slab 5 1 15 Drift Ratio (%) 4 8 12 Long. Displacement (in.) 1 Shear Key 1 Bearing.8.8 P[dm>DM LS].6.4.2 Elastic Limit Concrete Spalling Failure.6.4.2 Yield Failure 12 24 36 Shear force (kips) 4 8 12 16 Displacement (in.)

PBEE Evaluation Foundation Damage Model 1 Column Foundation P [ dm > DM LS].8.6.4.2 Elastic First Yield Limited Yielding Extensive Yielding 1 2 3 Normalized Edge Settlement z / z yield

PBEE Median Total Repair Cost Total Repair Cost ( million of $) 1..8.6.4.2 Fixed Base B=4D, Fsv=5.4 Pile Cap, B=3D.5 1 1.5 2 Sa ( T = 1 sec ), (g)

Repair Cost (million of $).3.2.1 PBEE Disaggregation of Cost EDGE COLUMNS MIDDLE COLUMNS BEARINGS SHEAR KEYS Fixed Base Bridge.5 1 1.5 2 Sa (T=1sec), (g)

PBEE Disaggregation of Cost Repair Cost (million of $).3.2.1 Bridge with Shallow Foundations B=4D Disaggregation of Cost - B=4D, Fsv=5.4 EDGE COLUMNS MIDDLE COLUMNS BEARINGS SHEAR KEYS EDGE COLUMNS FOUNDATIONS MIDDLE COLUMNS FOUNDATIONS.5 1 1.5 2 Sa(T=1sec), (g)

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