Performance-based earthquake resistant design of concrete bridges

Transcription

1 City University London Civil Engineering Department Research Centre for Civil Engineering Structures Research in progress at the Research Centre for Civil Engineering Structures Performance-based earthquake resistant design of concrete bridges Konstantinos I. Gkatzogias (PhD student) Prof. A. J. Kappos (supervisor) December, 2014

2 Overview of PBD/DBD methods for bridges DDBD procedure by Kowalsky (2002), Dwairi, Kowalsky (2006): Applicable to multi-degree-of-freedom (MDOF) continuous concrete bridges with flexible or rigid superstructures (target displacement profile based on modal analysis: EMS) Similar version of the method included in the Priestley et al. book (2007): Design in longitudinal direction, approximate method for higher mode effects focusing on deck forces only) Adhikari, Petrini, Calvi (2010): Long-span bridges with tall piers (approximate procedure for higher mode effects on flexural strength of hinges) Suarez-Kowalsky ( ): SSI in drilled shaft bents, skewed configurations of piers and/or abutments, conditions for applying DDBD using predefined displacement patterns, target displacements that account for P-Δ Kappos-Gkatzogias-Gidaris ( ): Modal DDBD (proper consideration of higher mode effects + additional design criteria) Bardakis, Fardis (2011): Indirect displacement-based design of bridges based on calculating inelastic rotations from elastic analysis Kappos and co-workers ( ): Deformation-based design (Def-BD) procedure focusing on buildings

3 Steps of the deformation-based procedure for bridges Type of analysis Linear Start Step 1: Flexural design of dissipating zones based on serviceability criteria Earthquake level <ν 0 EQII Selection of seismic actions for PBD Set-up of the partial inelastic model (PIM) Nonlinear Step2: Serviceability/operationality verifications EQII Nonlinear Step 3: Flexural design of non-dissipating zones on the basis of life safety criteria EQIII Implicitly consid. Implicitly consid. Step 4: Design and detailing for shear Step 5: Detailing for confinement, anchorages and lap splices End EQIV EQIV

4 Steps of the deformation-based procedure for bridges Type of analysis Linear Start Step 1: Flexural design of dissipating zones based on serviceability criteria Earthquake level <ν 0 EQII Selection of seismic actions for PBD Set-up of the partial inelastic model (PIM) Nonlinear Step2: Serviceability/operationality verifications EQII Nonlinear Step 3: Flexural design of non-dissipating zones on the basis of life safety criteria EQIII Implicitly consid. Implicitly consid. Step 4: Design and detailing for shear Step 5: Detailing for confinement, anchorages and lap splices End EQIV EQIV

5 Steps of the deformation-based procedure for bridges Step 1: Flexural design of plastic hinge zones based on operationality criteria Establishes basic level of strength for the bridge to remain operational during and after the selected level of earthquake (Τ r =40 110yrs-ordinary bridges): yielding zones (pier ends) in PIM have strength determined from an initial elastic analysis (dynamic or, if permitted, static); pier stiffness (EI ef M y /φ y ) estimated from simplified procedures (preferably the Caltrans charts)

6 Steps of the deformation-based procedure for bridges Step 1: Flexural design of plastic hinge zones based on operationality criteria Establishes basic level of strength for the bridge to remain operational during and after the selected level of earthquake (Τ r =40 110yrs-ordinary bridges): yielding zones (pier ends) in PIM have strength determined from an initial elastic analysis (dynamic or, if permitted, static); pier stiffness (EI ef M y /φ y ) estimated from simplified procedures (preferably the Caltrans charts) allowable damage expressed explicitly as rotational ductility factor (μ θ ) R/C pier design typically based on f cd, f yd, but damage verification typically based on inelastic analysis using mean values (f cm, f ym ); also, overstrength is present in some zones, due to detailing and practical requirements elastic analysis run for a fraction (ν ) of EQII: pier strength elastic analysis run for EQII: bearing deformations the goal is to reach the target μ θ in the piers and γ v in the el. bearings during the operationality earthquake (not to be much lower than it!)

7 Steps of the deformation-based procedure for bridges inelastic pier rotations are estimated from elastic ones Step 1 contnd M el Elastic Inelastic M el, θ el (analysis) M y θ inel β θ el θ y = θ inel / μ θ,ls θ y simple approach, assume : θ el elastic-perfectly-plastic M θ θ inel M tot θ tot & M E θ E have identical slope (typically applies in bridge piers) Μ y from θ y (M y M G ) β-values from Bardakis & Fardis (2011), ls 3 L pl, ls 1 1 h ls y pl y y eq

8 Steps of the deformation-based procedure for bridges Type of analysis Linear Start Step 1: Flexural design of dissipating zones based on serviceability criteria Earthquake level <ν 0 EQII Selection of seismic actions for PBD Set-up of the partial inelastic model (PIM) Nonlinear Step2: Serviceability/operationality verifications EQII Nonlinear Step 3: Flexural design of non-dissipating zones on the basis of life safety criteria EQIII Implicitly consid. Implicitly consid. Step 4: Design and detailing for shear Step 5: Detailing for confinement, anchorages and lap splices End EQIV EQIV

9 Steps of the deformation-based procedure for bridges Step 2: Serviceability/operationality verifications Set-up of the partially inelastic model PIM for bridges: piers modelled as yielding elements (strength from Step 1, stiffness: M-φ analysis, e.g RCCOLA.net (AUTh)) all other parts of the bridge modelled as elastic members (including common bearings; but LRBs should be modelled inelastically) Selection of seismic actions Pairs of records are required for 3D analysis (or triplets, if vertical motion is influential) Recommended selection criteria: M, R (from deaggregation of hazard analysis), PGA (e.g. 0.1g), similarity of spectra, accepted variability of response Modern tools (like ISSARS, Sextos-Katsanos (2013)) select sets of e.g. 7 records based on such multi-criteria, also including the EC8 procedure Scaling procedures: EC8-Part 1/2 (based on considered earthq. components)

10 Steps of the deformation-based procedure for bridges Serviceability/operationality verifications Step 2 contnd PIM analysed for set of records ( 7) scaled to the seismic action associated with operationality requirement verifications include specific limits for pier drifts, ductility factors (μ θ ) and plastic hinge rotations (θ p ); ideally μ θ,an μ θ,ls =f(ε c, ε s ) recommended values of μ θ and/or θ p vary significantly, e.g. proposals by Eastern (DesRoches et al.) and Western (Priestley et al.) US teams ε c, ε y are good basis for estimating damage to R/C piers damage to bearings (γ b < ) should also be checked, might be critical joint widths should be such as to prevent damage to backwalls

11 Steps of the deformation-based procedure for bridges Type of analysis Linear Start Step 1: Flexural design of dissipating zones based on serviceability criteria Earthquake level <ν 0 EQII Selection of seismic actions for PBD Set-up of the partial inelastic model (PIM) Nonlinear Step2: Serviceability/operationality verifications EQII Nonlinear Step 3: Flexural design of non-dissipating zones on the basis of life safety criteria EQIII Implicitly consid. Implicitly consid. Step 4: Design and detailing for shear Step 5: Detailing for confinement, anchorages and lap splices End EQIV EQIV

12 Steps of the deformation-based procedure for bridges Step 3: Verifications for the life safety or damage limitation limit state PIM is now analysed for records scaled to the seismic action associated with damage limitation or life safety requirement (T r yrs) elastomeric bearings γ b verifications of pier drifts, ductility factors (μ θ ) and plastic hinge rotations (θ p ) based on allowable ε c, ε s verifications that members assumed elastic do not yield (except for continuity slabs)

13 Steps of the deformation-based procedure for bridges Type of analysis Linear Start Step 1: Flexural design of dissipating zones based on serviceability criteria Earthquake level <ν 0 EQII Selection of seismic actions for PBD Set-up of the partial inelastic model (PIM) Nonlinear Step2: Serviceability/operationality verifications EQII Nonlinear Step 3: Flexural design of non-dissipating zones on the basis of life safety criteria EQIII Implicitly consid. Implicitly consid. Step 4: Design and detailing for shear Step 5: Detailing for confinement, anchorages and lap splices End EQIV EQIV

14 Steps of the deformation-based procedure for bridges Step 4: Design for shear Less ductile failure mode V E should be calculated for higher seismic actions (T r 2500yrs) associated with collapse prevention to avoid 3 rd set of response-history analyses, V E from Step 3 could be empirically scaled; recommended γ v no need for code-type conservative capacity design, since inelastic analysis is used! Step 5: Detailing of critical members Detailing of R/C piers for: confinement, anchorages, lap splices the actual μ φ values from Step 3 can be used, implicitly associated with collapse prevention (e.g. γ ω 2.00) bearings should be verified based on stability considerations N ' cr G S r ' t r A r Constantinou et al. (2011)

15 Def-BD: Implementation & Verification Description of the studied bridge (T7 Overpass) 3-span structure ( m)

16 Def-BD: Implementation & Verification Description of the studied bridge (T7 Overpass) 3-span structure ( m) Prestressed concrete box girder section (variable geometry)

17 Def-BD: Implementation & Verification Description of the studied bridge (T7 Overpass) 3-span structure ( m) Prestressed concrete box girder section (variable geometry) Deck monolithically connected to the (circular single-column) piers Unrestrained transverse displacement at the abutments (elastom. bearings)

18 Def-BD: Implementation & Verification Description of the studied bridge (T7 Overpass) 3-span structure ( m) Prestressed concrete box girder section (variable geometry) Deck monolithically connected to the (circular single-column) piers Unrestrained transverse displacement at the abutments (elastom. bearings) Different pier heights (longitudinal deck slope of 7%) Surface foundations

19 Software used: Ruaumoko3D Def-BD: Implementation & Verification Analysis of the bridge

20 M (knm) Research in progress at the RCCES Def-BD: Implementation & Verification PE (%) in 50/100/200 yrs T r (yrs) Earthquake level Negligible damage No repair Full service Minimal damage Minimal repair Limited service Moderate damage Feasible repair Disruption of service Severe damage Replacement ** * * * * EQI EQII EQIII EQIV * Implicit definition according to Step 1 ** Partial or complete replacement may be required Performance criteria N=10.4 MN 4000 Bilin. Buckling 3000 Hoop fracture 2000 Bar fracture Ultimate φ (m -1 ) M-φ for column section EQII: Columns: ε c or ε s 15.0, elastom. bearings: γ b 1.0 EQIII: Columns: ε c 18.0 or ε s 60.0, elastom. bearings: γ b 2.0 EQIV: Columns: ε c ε cc,u or ε s ε s,u, elastom. bearings: toppling Limit-state (ls) deformations: Based on allowable strains and section analysis e.g., ls 3 L pl, ls 1 1 h ls y pl y y eq

21 S a (g) S a (g) Research in progress at the RCCES Def-BD: Implementation & Verification Implementation: Selection of input motions (ISSARS) No. Name Region Date Station Magnitude Distance (km) PGA(g) Hor. Component 1 (HC1) Hor. Component 2 (HC2) 1 Imperial Valley-02 USA El Centro Array # IMPVALL_I-ELC180 IMPVALL_I-ELC270 3 Imperial Valley-06 USA Chihuahua IMPVALL_H-CHI012 IMPVALL_H-CHI282 5 Imperial Valley-06 USA Holtville Post Office IMPVALL_H-HVP225 IMPVALL_H-HVP315 6 Imperial Valley-06 USA SAHOP Casa Flores IMPVALL_H-SHP000 IMPVALL_H-SHP270 8 Corinth, Greece Greece Corinth CORINTH_COR--L CORINTH_COR--T 10 Northridge-01 USA Arleta - Nordhoff Fire St NORTHR_ARL090 NORTHR_ARL Northridge-01 USA LA - Hollywood Stor FF NORTHR_PEL090 NORTHR_PEL Northridge-01 USA LA - N Faring Rd NORTHR_FAR000 NORTHR_FAR Kobe, Japan Japan Kakogawa KOBE_KAK000 KOBE_KAK090 Zone Suite of records Scaling factor (SF) Spectral deviation δ P 1 SEE (%) P 2 SEE (%) II III IMPVALL_I-ELC270.AT2 IMPVALL_H-CHI282.AT2 IMPVALL_H-HVP315.AT2 IMPVALL_H-SHP270.AT2 NORTHR_PEL360.AT2 NORTHR_FAR090.AT2 KOBE_KAK090.AT2 Average-T Sc. EC8-2 (T =4.0s) (Unsc.) D IMPVALL_I-ELC270.AT2 IMPVALL_H-HVP315.AT2 IMPVALL_H-SHP270.AT2 CORINTH_COR--T.AT2 NORTHR_ARL360.AT2 NORTHR_FAR090.AT2 KOBE_KAK090.AT2 Average-T Sc. EC8-2 (T =4.0s) (Unsc.) D T (sec) T (sec)

22 Sa (g) Sd (cm) Research in progress at the RCCES Assessment using inelastic response-history analysis (RHA) Refined limit-states : Analysis of column sections based on final detailing Inelastic modelling of all yielding members, using standard point-hinge approach (with Takeda model) Verification of design for Ζone ΙΙ & ΙΙΙ Def-BD: Implementation & Verification Verification Use of spectrum-compatible synthetic records (ASING code), i.e. a different set from that used in the Def-BD procedure T (sec) SIM1 SIM2 SIM3 SIM4 SIM5 Average EC8-2 (T =4.0s) D SIM1 SIM2 SIM3 SIM4 SIM5 Average EC8-2 (T =4.0s) D T (sec)

23 Displacement (m) Displacement (m) Research in progress at the RCCES Def-BD: Implementation & Verification Position (m) EQII-D-L EQII-D-NL EQII-A-NL EQIII-D-NL EQIII-A-NL EQIV-D-NL EQIV-A-NL MDDBD-D MDDBD-A Position (m) EQII-D-L EQII-D-NL EQII-A-NL EQIII-D-NL EQIII-A-NL EQIV-D-NL EQIV-A-NL MDDBD-D MDDBD-A EQII: Excellent agreement of design and assessment (for critical performance level), despite the different input motions used in each case EQIII & EQIV: Differences in the area of Abt1 and Pier1 (differences could be attributed to the fact that the structure-specific ground motion selection was based on linear analysis and was different from assessment set P-D effects are not critical (EQIII-A-NL and MDDBD-A(EIass) result in similar displacements and drifts)

24 Moment (knm) Moment (knm) Research in progress at the RCCES Def-BD: Implementation & Verification ΖΙΙI ΖΙΙI ΖΙΙ 4000 ΖΙΙ EQII Chord rotation (10 3 rad) EQII Chord rotation (10 3 rad) EQII: Controls the design SA (section analysis): refers to the limit-state deformations (design values) Slight exceedance of P 1 limit-state deformation Ζone ΙΙ, D =1.20m ρ l,req,col1 =ρ l,req,col2 = 10.4 Zone III, D =1.20m ρ l,req,col1 =12.5, ρ l,req,col2 = 9.5 Design was found to be safe during assessment

25 Moment (knm) Moment (knm) Research in progress at the RCCES Def-BD: Implementation & Verification ΖΙΙI ΖΙΙI ΖΙΙ 4000 ΖΙΙ EQIII Chord rotation (10 3 rad) Chord rotation (10 3 rad) EQIII EQIII: Not critical (although bearing strains were close to the def. limits) All pier limit-state deformations were easily satisfied Pier deformation demand were close to deformation limits corresponding to minimum transverse reinf. ratio.

26 Moment (knm) Moment (knm) Research in progress at the RCCES Def-BD: Implementation & Verification ΖΙΙI D-L D-NL-SA D-NL-RHA A-NL-SA A-NL-RHA ΖΙΙI ΖΙΙ 4000 ΖΙΙ EQIV Chord rotation (10 3 rad) Chord rotation (10 3 rad) EQIV EQIV: Implicitly checked (also checked explicitly for verification reasons) Critical for the transverse reinforcement (based on curvature ductility demand) D-SA shown is based on transverse steel ρ w,min Ζone ΙΙ: ρ w,req,col1 =12.4, ρ w,req,col2 = 10.6 Zone III: ρ w,req,col1 =13.2, ρ w,req,col2 = 10.4

27 Conclusions Operationality PL: governs the design Damage-limitation PL: not critical Collapse-prevention PL: critical (with respect to stability) for bearings deformations Very good prediction of structural response while resulting in safe design Applicable to most common concrete bridge configurations without practical limitations related to the irregularity of the structural system considered Increased adaptability: Different performance objectives accounting for the importance of the bridge can be met (inclusion in future codes) Further research is required with investigate the effectiveness of the suggested procedure for complex bridge configurations (e.g. curved in plan bridges) and /or under challenging loading conditions (e.g. asynchronous pier excitation)

28 Relevant publications Kappos AJ, Gidaris IG, Gkatzogias KI (2012) "Problems associated with direct displacement-based design of concrete bridges with single-column piers, and some suggested improvements, Bulletin of Earthquake Engineering, 10(4): Kappos AJ, Gkatzogias KI, Gidaris IG (2013) "Extension of direct displacement-based design methodology for bridges to account for higher mode effects, Earthquake Engineering and Structural Dynamics, 42(4), Kappos AJ (2014) Performance-based seismic design and assessment of bridges, in Ansal, A. (ed.) Perspectives on European Earthquake Engineering and Seismology (Vol.2), Springer, (in press) Gkatzogias KI, Kappos AJ (2015) Deformation-based seismic design of concrete bridges Earthquakes and Structures, (submitted)