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 Incremental Dynamic Analysis (IDA) model Preliminary results of IDA  Maximum drift  Instability limits of rocking and hinging systems  Residual drift Conclusions

Damaged columns in past earthquakes

Centrifuge test matrix

Rocking Foundation Centrifuge Tests 5 Gazli earthquake, pga= 0.88 g

Hinging Column Centrifuge Test 6 Gazli earthquake, pga= 0.88 g

Photos of hinging column after 0.88g Gazli shake 7

8 CHY024, pga=0.23 g Hinging Column Centrifuge Test

Collapse of hinging column 9 SDOF bridges on rocking foundation survived after 20 scaled GM’s, but the one on fixed foundation and hinging column collapsed

OpenSees model for IDA and parametric study Moment Rotation Column hinge spring Foundation: zerolength elements Column: Stiff elasticBeamColumn xixi kiki LfLf KθKθ Mass = m Footing mass = m*r m Footing center Fixed ground center HcHc

Validate model through centrifuge data Centrifuge model (Cy/Cr=5, T_sys=1 s, FSv=11.0)

Input parameters in IDA model C y, C r : base shear coefficients for column or rocking footing Two yielding mechanisms:  C r > C y  Hinging column system;  C y > C r  Rocking foundation system A c /A=0.2, r m =0.2 (Footing length) (Column hinge strength) Equally spaced foundation elements (Column hinge stiffness) (Foundation element stiffness) (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) T_sys (sec)CyCr# GM# Scale factors pulse-like0.2, broad-band0.6, , , ,

IDA results: Sa(T=T_sys) vs. max drift Elastic zone Nonlinear zone Failure zone Instability limit ~=2.2 m Elastic zone Nonlinear zone 0.2 g Instability limit ~=2 m Rocking Footing (C y =0.5, C r =0.2, T_sys=0.85 s) 0.2 g Hinging column (C y =0.2, C r =0.5, T_sys=0.85 s) Failure zone

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 Collapse mechanisms P  P 

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) On-verge-of-collapse case Collapse caseOn-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 50% Median

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-  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

Panagiotou CODE DEVELOPERS Collaborators Kutter Browning Moore Martin Jeremic Mar Comartin McBride Mahan Desalvatore Khojasteh Shantz BRIDGES BUILDINGS Mejia BOTH GEOTECHNICAL STRUCTURAL Mahin Kunnath Ashheim Stewart Hutchinson THEORYDESIGNCONSTRUCTION

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 (C y =0.5, C r =0.2, T_sys=0.85 s) Hinging column (C y =0.2, C r =0.5, T_sys=0.85 s) Equivalent Static Analysis (ESA) commonly used in codes may underestimate the displacement.