Performance Modeling Strategies for Modern Reinforced Concrete Bridge Columns

Transcription

1 Performance Modeling Strategies for Modern Reinforced Concrete Bridge Columns Michael P. Berry Marc O. Eberhard University of Washington Project funded by the Pacific Earthquake Engineering Research Center (PEER)

2 UW-PEER Structural Performance Database Nearly 500 Columns spiral or circular hoop-reinforced columns (~180) rectangular reinforced columns (~300) Column geometry, material properties, reinforcing details, loading Digital Force-Displacement Histories Observations of column damage User s Manual (Berry and Eberhard, 2004)

3 Objective of Research Develop, calibrate, and evaluate column modeling strategies that are capable of accurately modeling bridge column behavior under seismic loading. Global deformations Local deformations (strains and rotations) Progression of damage

4 Advanced Modeling Strategies Distributed- Plasticity Lumped- Plasticity F F B ( Force-Based Fiber Beam Column Element (Flexure) Elastic Portion of Beam (A, EI ) eff Fiber Section at each integration point with Aggregated Elastic Shear Zero Length Section (Bond Slip) Lp to Plastic Hinge

5 Cross-Section Modeling

6 Cross-Section Modeling Components Concrete Material Model Reinforcing Steel Material Model Cross-Section Discretization Strategy

7 Concrete Material Model Popovic s Curve with Mander et. al. Constants and Added Tension Component (Concrete04)

8 Reinforcing Steel Material Models E s * b 1 1 σ/f y σ/f y, Bilinear Measured ε s Giufre-Menegotto-Pinto (Steel02) Measured Kunnath ε s Mohle and Kunnath (ReinforcingSteel)

9 Section Fiber Discretization Objective: Use as few fibers as possible to eliminate the effects of discretization 8 x M 5 εy Ratio M 10 εy Ratio Longitudinal Steel Fibers Cover-Concrete Fibers Moment (KN-mm) φ y Ratio Core-Concrete Fibers 2 1 Radial Unilateral φ (1/mm) 3 4 x 10-4

10 Cross-Section Fiber Discretization Uniform (220 Fibers) Confined n n r c t c = 10 = 20 Unconfined r nu = 1 n t u = 20

11 Reduced Fiber Discretization Uniform (220 Fibers) Nonuniform Strategies

12 Cross-Section Fiber Discretization Uniform (220 Fibers) Reduced (140 Fibers) r/2 Confined n n r c t c = 10 = 20 Unconfined n n r u t u = 1 = 20 Confined n n n r fine t fine r coarse = 5 = 20 = 2 Unconfined r nu = 1 n t u = 20 n t coarse = 10

13 Modeling with Distributed- Plasticity Element

14 Model Components Force-Based Fiber Beam Column Element (Flexure) Fiber Section at each integration point with Aggregated Elastic Shear Zero Length Section (Bond Slip) Flexure Model (Force-Based Beam-Column) nonlinearbeamcolumn Fiber section Popovics Curve (Mander constants) Giufre-Menegotto-Pinto (b) Number of Integration Points (Np) Anchorage-Slip Model zerolengthsection Fiber section Reinforcement tensile stressdeformation response from Lehman et. al. (1998) bond model (λ) Effective depth in compression (d comp ) Shear Model section Aggregator Elastic Shear (γ)

15 Model Optimization Objective: Determine model parameters such that the error between measured and calculated global and local responses are minimized. E push 2 n ( F ) 1 meas Fcalc = 2 ( max ( Fmeas )) n ( ε ) 1 meas εcalc n Estrain = 2 max ( ε ) n ( meas ) 2

16 Model Evaluation Optimized Model: Strain Hardening Ratio, b = 0.01 Number of Integration Points, N p = 5 Bond-Strength Ratio, λ = Bond-Compression Depth, d comp =1/2 N.A. Depth at comp strain Shear Stiffness γ = 0.4 Kmeas S. R. = K calc M. R. = M M meas _ 4% calc _ 4% E total (0 D / 2) E push E ( D / 2 D) strain E strain S. R. M. R. mean cov (%) 15 8

17 Modeling with Lumped- Plasticity Element

18 Lumped-Plasticity Model Elastic Portion of Beam (A, EI ) eff Hinge Model Formulation: beamwithhinges3 Force Based Beam Column Element with Integration Scheme Proposed by Scott and Fenves, Fiber Section Elastic Section Properties Elastic Area, A Lp Fiber Section assigned to Plastic Hinge Effective Section Stiffness, EI eff Calculated Plastic-Hinge Length L p

19 Section Stiffness Calibration eff Stiffness Ratio Stats calc EI = α E I α calc sec EIsec g c g mean cov (%) 19 16

20 Plastic-Hinge Length Calibration

21 Cyclic Response

22 Cyclic Material Response Cyclic response of the fiber-column model depends on the cyclic response of the material models. Reinforcing Steel Confined and Unconfined Concrete Giufre-Menegotto-Pinto (with Bauschinger Effect) Steel02 Current Methodologies Karsan and Jirsa with Added Tension Component Concrete04 Do not account for cyclic degradation steel Do not account for imperfect crack closure

23 Evaluation of Response Lumped-Plasticity Distributed- Plasticity E f orce (%) E f orce (%) mean min max Lehman No Force (KN) Measured OpenSees / y

24 Kunnath and Mohle Steel Material Model Cyclic degradation according to Coffin and Manson Fatigue. Model parameters: Ductility Constant, C f Strength Reduction Constant, C d

25 Preliminary Study with Kunnath Steel Model Ductility Constant, C f =0.4 Strength Reduction Constant, C d =0.4 Giufre-Menegotto- Pinto Kunnath and Mohle E f orce (%) E f orce (%) mean min max Lehman No Lehman No Force (KN) 0 Force (KN) Measured OpenSees Measured OpenSees / y / y Giufre-Menegotto-Pinto (with Bauschinger Effect) Kunnath and Mohle (2006)

26 Continuing Work

27 Imperfect Crack Closure

28 Prediction of Flexural Damage Drift Ratio Equations Distributed-Plasticity Modeling Strategy Lumped-Plasticity Modeling Strategy Key Statistics Fragility Curves Design Recommendations

29 Evaluation of Modeling-Strategies for Complex Loading Bridge Bent (Purdue, 2006) Unidirectional and Bi-directional Shake Table (Hachem, 2003)

30 Thank you