An OpenSees material model for the cyclic behaviour of corroded steel bar in RC structures
- 1. OpenSees Days Europe 2017 1st European Conference on OpenSees Porto, Portugal, 19–20 June 2017 AN OPENSEES MATERIAL MODEL FOR THE CYCLIC BEHAVIOUR OF CORRODED STEEL BAR IN RC STRUCTURES Davide Lavorato1(*), Riccardo Tartaro1, Alessandro V. Bergami1, Camillo Nuti1,2 1 Dept. of Architecture University of Roma Tre, Rome, Italy 2 Visiting Prof. of College of Civil Engineering of Fuzhou University, Fuzhou, China (*) davide.lavorato@uniroma3.it 1 Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy
- 2. 2 Outline of the presentation Problem definition: corrosion of steel rebar in RC elements Numerical model to describe the cyclic behaviour of corroded rebar including buckling in compression, anisotropic behaviour Implementation of the proposed model in OPENSEES - uniaxial material model for fiber section analysis Test on the implemented Material Conclusions and future development Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy
- 3. 3 Problem: corrosion of rebar in concrete structures No sufficient cover Aggressive environment Corroded Steel expansion (rebar diameter increases) Concrete spalling Rebar diameter reduction for distributed and/or pitting corrosion Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy For effect of corrosion there is a “new” RC section with: (i) reduced rebar (uniform corrosion); (ii) reduced steel properties (pitting local corrosion); (iii) new concrete geometry (iv); bad quality of concrete in zones near rebar It is a well-known problem … Local corrosion and distributed Local corrosion
- 4. 4 Problem: corroded rebar behaviour Reduction of the Yielding and Maximum Stresses Different Yielding Stress in tension and in compression Reduction of the maximum deformation Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy Researchers and dates Y. G. Du et al. (2001) Maslehuddin et al. (1990) Andrade et al. (1991) Leeet al. (1996) Palssom and Mirza (2002) Zhang et al. (1995) Testingspecimen Barebars Bars in concrete Singlebarebars Singlebare bars Bars in concrete Bars in concrete Bars in concrete Reinforcement type (diameter) Plain (8, 16) Ribbed (8, 16, 32) Plain (8–32) Ribbed (8–32) Ribbed (12) Ribbed (10) Not stated Plain (8–14) Ribbed (10—25) Corrosion condition Accelerated 0.5–2.0 mA/cm2 Marineexposure Accelerated 1.0 mA/cm2 Accelerated 13.0 mA/cm2 Servicechloride Service carbonation Amount (%) 0–25% 0–0.5% 0–11% 0–25% 0–>30% 0–67% Yield strength β 0.0049 0.0012 0.00 0.0045 0.0021 0.00 0.0004 Xcorr=Xnoncorr∙(1- Ψ ∙ β ) Xcorr = Corroded rebar Stress, force o deformation Xnoncorr=NON Corroded rebar Stress, force o deformation Ψ =corrosion percentage β = Coefficient for local corrosion corroded Non corroded The change in the stress-strain response is due to non-uniform distribution of pits along the length of corroded bars Kashiani et al 2013
- 5. 5 Effects of corrosion on rc sections Section Strength Capacity decreases because: Longitudinal rebar diameter is reduced (distributed corrosion) Corrosion of stirrups can change the slenderness of the rebar in compression; buckling can arise also in case of rebar with slenderness smaller than the critical value before the corrosion effects (local corrosion) Section Ductility Capacity reduces because corrosion reduces the maximum rebar deformation (local corrosion) Concrete geometry change for spalling There is Cracked Concrete with bad quality near the corroded rebar Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy N
- 6. 6 Aims of this research: to study seismic behaviour of rc section with corroded rebar By RC fiber section model in OPENSEES Performing cyclic analysis Implementing in OPENSEES new uniaxial material models to define the behavior of the corroded rebar Defining a proper Fiber section with a new geometry after corrosion action (spalling concrete; zone with bad concrete quality, etc.) Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy N F STEEL MODEL FOR CORRODED REBAR CONCRETE MODEL HOW???
- 7. 7 Cyclic model for corroded rebars A Menegotto-Pinto curve Cyclic behavior evolution by definition of parameters (yielding stress on skeleton curve σy, Curvature radious R, b hardening ratio) after each inversion of deformation history (Monti-Nuti) Buckling phenomena in compression (Monti-Nuti 1992) Possibility to consider different yielding stresses, R and b factors in tension (t) and compression (c); (Lavorato-Nuti-Zhihao) and new calibration of model parameters Input parameters defined by the previous expression: Xcorr=Xnoncorr∙(1- Ψ ∙ β ) (local corrosion; common for rebar in concrete) Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy 𝜎𝜎𝑠𝑠 ∗ = 𝑏𝑏 ∗ 𝜀𝜀∗ + 1 − 𝑏𝑏 𝜀𝜀∗ 1 + 𝜀𝜀∗ 𝑅𝑅 1 𝑅𝑅 We introduce a model: Monti G, Nuti C. (1992). “Nonlinear cyclic behaviour of reinforcing bars including buckling.” Journal of Structural Engineering, ASCE, 118 (12), 3268-3284
- 8. 8 Material model implementation in OPENSEES Proposed Cyclic model was implemented in OPENSEES as uniaxial material Steel06 Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy uniaxialMaterial Steel06 $matTag fyt fyc b0 E0 L D Fconst R0 A6 P matTag : material tag fyt: yield stress in tension fyc: yield stress in compression b0: hardening ratio E0: elastic modulus L: stirrup spacing D: diameter of longitudinal rebars Fconst: yield stress of Feb44 R0: initial value of parameter R A6: the parameter to update elastic modulus when reversal from compression P: weight factor to decider the contribution from kinematic hardening rule.
- 9. 9 Material test on simple element Procedure matTest.tcl by OPENSEES site to test Steel 06 model Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy Steel06 $matTag $fyt $fyc $b0 $E0 $L $D $Fconst $R0 $A6 $P Element element truss 1 1 2 1.0 1 loads pattern Plain 1 "Series -dt $dt -filePath $filename -factor $factor" { ##Set reference displacement value ##node dof value sp 2 1 1.0} Analysis definition system UmfPack constraints Penalty 1.0e12 1.0e12 # Set increment in load factor used for integration # Does not have to be the same as dt used to read in displacement pattern set dl $dt integrator LoadControl $dl 1 $dl $dl test NormDispIncr 1.0e-6 10 algorithm Newton numberer RCM
- 10. 10 Material test on simple element Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy Steel06: comparison between Opensees and Matlab outputs for the same deformation history Story of deformation Valueofdeformation Comparison between Opensees-matlab Comparison between Opensees-matlab the same deformation history; different parametres for the Steel06 model (case 1 - softening in compression due to buckling ; case 2 - no softening in compression) case 1 case 2
- 11. 11 Material test on simple element Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy Comparison between Steel06 Opensees-Matlab Comparison between Opensees-matlab Comparison between Opensees-matlab Story of deformation Valueofdeformation case 1 case 2 the same deformation history; different parameters for the Steel06 model (case 1 - softening in compression due to buckling ; case 2 - no softening in compression)
- 12. 12 Conclusion and future development Material Steel06 implementation in OPENSEES is a work in progress This material works well by mattes.tcl function considering different material properties and deformation histories (also much complicated) however there are some numerical problems running in OPENSEES fiber section analysis using this new steel material model we want to calibrate the analyses parameters or modify the numerical model to assure convergence Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy
- 13. 13 Future development We have implemented in MATLAB a program CYRUS 2.0 to perform RC fiber section analysis We have implemented the OPENSEES material models Concrete02 and Steel01 in this program For a selected case of study we have compared the results of CYRUS 2.0 with the ones of OPENSEES using the same load and displacement histories Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy
- 14. Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy The comparison between OPENSEES and cyrus results is very good 14 Future development
- 15. results of test2 on rc fiber section framework of functions in MATLAB (cyrus) Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy 15 Future development
- 16. results of test 3 on rc fiber section framework of functions in MATLAB (cyrus) Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy 16 Future development
- 17. FUTURE DEVELOPMENT: CYRUS WORKS USING Steel06 MATERIAL Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy • Core section with diameter of 280 mm. • Cover section with diameter of 420 mm, so with a thickness of 70 mm. • 14 bare ɸ18 mm, area 254 mm², with a concrete cover of 30 mm • MATLAB this rc section to • obtain moment –curvature curves using: concret02 and steel06 material models 17
- 18. davide.lavorato@uniroma3.it Lavorato D. et al. davide.lavorato@uniroma3.it Dept. of Architecture University of Roma Tre, Rome, Italy 18 COMPDYN 2017 15-17 June 2017, Rhodes Island, Greece 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering Thank you OpenSees Days Europe 2017 1st European Conference on OpenSees Porto, Portugal, 19–20 June 2017