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Incremental Dynamic Analyses on Bridges on various Shallow Foundations. Lijun Deng PI’s: Bruce Kutter , Sashi Kunnath University of California, Davis. NEES & PEER annual meeting San Francisco October 9, 2010. Outline. Introduction and centrifuge model tests
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Incremental Dynamic Analyses on Bridges on various Shallow Foundations Lijun Deng PI’s: Bruce Kutter, SashiKunnath University of California, Davis NEES & PEER annual meeting San Francisco October 9, 2010
Outline • Introduction and centrifuge model tests • Incremental Dynamic Analysis (IDA) model • Preliminary results of IDA • Maximum drift • Instability limits of rocking and hinging systems • Residual drift • Conclusions
Rocking Foundation Centrifuge Tests Gazli earthquake, pga= 0.88 g
Hinging Column Centrifuge Test Gazli earthquake, pga= 0.88 g
Hinging Column Centrifuge Test CHY024, pga=0.23 g
Collapse of hinging column • SDOF bridges on rocking foundation survived after 20 scaled GM’s, but the one on fixed foundation and hinging column collapsed
OpenSeesmodel for IDA and parametric study Mass = m Column hinge spring Column: Stiff elasticBeamColumn Kθ Hc Foundation: zerolength elements Moment Fixed ground center Rotation Footing center Footing mass = m*rm ki xi Lf
Validate model through centrifuge data Centrifuge model (Cy/Cr=5, T_sys=1 s, FSv=11.0)
Input parameters in IDA model • Cy, Cr: base shear coefficients for column or rocking footing • Two yielding mechanisms: • Cr > Cy Hinging column system; • Cy > Cr Rocking foundation system (Column hinge strength) (Foundation element stiffness) Equally spaced foundation elements (Column hinge stiffness) Ac/A=0.2, rm=0.2 (Footing length) (Foundation element strength)
Input parameters in IDA model • Input ground motions from PEER database Forty pulse-like ground motions at soil sites(Baker et al. 2010)
IDA results: Sa(T=T_sys) vs. max drift Rocking Footing (Cy=0.5, Cr=0.2, T_sys=0.85 s) Hinging column (Cy=0.2, Cr=0.5, T_sys=0.85 s) 0.2 g Failure zone 0.2 g Failure zone Nonlinear zone Nonlinear zone Elastic zone Elastic zone Instability limit ~=2 m Instability limit ~=2.2 m
Collapse mechanisms • A hinge is a hinge • Hinges can be engineered at either position • A hinge forms at the edge when rocking occurs • P-delta is in your favor for rocking – recentering • Instability limits are related to Cy and Cr values P P D D
Selected animations • Cy=0.2, Cr=0.5, T=0.85 s (Hinging column) • Cy=0.5, Cr=0.2, T=0.85 s (Rocking foundation) Collapse case On-verge-of-collapse case On-verge-of-collapse case Collapse case
IDA results: Sa(T=T_sys) vs. max drift • 50% median of Sa vs. max drift and +/-σ 50% Median
Compare medians of Sa vs. max drift for various T_sys • Longer periods lead to higher drift • The max drift is not sensitive to Cy/Cr ratio • The max might rely on min{Cy, Cr}, to be confirmed with further study
IDA results: Sa (T_sys) vs. Residual rotation • Bridge with rocking foundation have smaller rotation than hinging column re-confirm the recentering benefits
Conclusions • Rocking foundations provide recentering effect that limits the accumulation of P-D demand (i.e., much smaller residual rotation) • Experiments and IDA simulations show column with rocking footing is more stable than hinging column (i.e., fewer collapse cases) • ESA approach is not conservative for highly nonlinear cases • Analysis is ongoing, and fragility functions are being developed from the results. We are also evaluating the adequacy of Sa(T_sys) as an Intensity Measure of ground motions
Collaborators CONSTRUCTION DESIGN THEORY Khojasteh Shantz GEOTECHNICAL Kutter Martin Mejia Desalvatore Stewart Jeremic CODE DEVELOPERS Hutchinson Panagiotou Browning Kunnath Comartin Mahin Moore McBride Ashheim Mar Mahan BRIDGES STRUCTURAL BOTH BUILDINGS
Acknowledgments • Current financial support of California Department of Transportation (Caltrans). • Network for Earthquake Engineering Simulation (NEES) for using the Centrifuge of UC Davis. • Other student assistants: T. Algie (Auckland Univ., NZ), E. Erduran (USU), J. Allmond (UCD), M. Hakhamaneshi (UCD).
IDA results: Sa(T=T_sys) vs. max drift Rocking Footing (Cy=0.5, Cr=0.2, T_sys=0.85 s) Hinging column (Cy=0.2, Cr=0.5, T_sys=0.85 s) • Equivalent Static Analysis (ESA) commonly used in codes may underestimate the displacement.