Post-earthquake residual deformations and seismic performance assessment of buildings

Transcription

1 Post-earthquake residual deformations and seismic performance assessment of buildings Ufuk Yazgan and Alessandro Dazio Group of Earthquake Engineering and Structural Dynamics Institute of Structural Engineering, ETH-Zurich ETH Zürich 29.August.26

2 Motivation Management of Earthqauke Risks using Condition Indicators The need to reduce the uncertainties in the assessment of seismic performance after an earthquake The need for a direct consideration of post-earthquake residual displacements in the seismic design of structures 29.August.26 2

3 Post-Earthquake Residual Displacements Displacement (m).6 Maximum Displacement 16 Force (kn).4 Residual Displacement Time (s) Displacement (m) August.26 3

4 Residual Deformations at the Component Level Courtesy National Information Service for Earthquake Engineering, University of California, Berkeley. 29.August.26 (Source: Lestuzzi P., Wenk. T & Bachmann T., (1999), Dynamische Versuche an Stahlbetontragwänden auf dem ETH-Erdbebensimulator, IBK IBK Bericht Nr. 24, April 1999 ) 4

5 Residual Displacements at the Structural Level 29.August.26 Courtesy National Information Service for Earthquake Engineering, University of California, Berkeley. 5

6 Residual Displacements due to Ground Deformations Courtesy National Information Service for Earthquake Engineering, University of California, Berkeley. 29.August.26 6

7 Post-Earthquake Assessment Reconnaissance Survey Recorded Ground Motion FEM Model Damaged Building Measured Residual Displacements Estimates of Maximum Displacements A Seismic Performance Assessment Method for buildings based on residual displacements is is being developed. P(D>DCi) Post-Earthquake Vulnerability P(D>DC) P(D>DC1) P(D>DC2) P(D>DC3) P(D>DC4) Spectral Displacment - S d (cm) 29.August.26 7

8 Performance-Based Design Se [m/s2] A B C D E T [s] FE Model PSH Model Seismic Performance Estimates of Maximum Displacements Estimates of Residual Displacements Known to be well correlated with the attained damage Provide essential information about the the post-earthquake: - Reparability/Usability - Vulnerability 29.August.26 8

9 Difficulties related to simulation of response Lumped Plasticity Models: φ 8 / 1 25 Moment, M (knm) 2 Ruaumoko, DRAIN-2DX, OpenSees, SeismoStruct Simulated large-cycle responses 4 8 φ Curvature, 8 (m -1 ) Force (kn) N n = =.2 ρ g = 1% A g f c Displacement (m) Ruaumoko SeismoStruct (Lump.Plast.) DRAIN-2DX OpenSees (Lump.Plast.) 27 are practically the same. 29.August.26 9

10 Practically, the maxima are the same Results: Lumped Plasticity Models.6 Maximum Displacement, u m (m) Ground Motion Maximum Displacement, u m (m) However, the residual displacements are significantly different T =.5 [s] R y = 4 ζ = 5% Mean Standard Deviation Ruaumoko(26/1/4) SeismoStruct(v.3.9.5) DRAIN-2DX(v.1.1) OpenSees (1.6.2e)! Residual Displacment, u r (m) Residual Displacement, u r (m) Ground Motion Mean Standard Deviation 29.August.26 1

11 Fiber Models: OpenSees, SeismoStruct, Rechenbrett-2D Reinforcement: Stress (MPa) 2 Strain OpenSees(Steel2) SeismoStruct(stl_mp) Concrete: Strain Stress (MPa) OpenSees (Concrete2) SeismoStruct(con_cc) Simulated large-cycle responses 15 1 Force (kn) Displacement (m) -5-1 SeismoStruct (Fiber) OpenSees (Fiber) -15 practically the same Rechenbrett-2D 29.August.26 11

12 Again Practically, the maxima are the same Results: Fiber Models Maximum Displacement, u m (m) Maximum Displacement, u m (m) OpenSees (1.6.2e) SeismoStruct(v.3.9.5) Rechenbrett-2D Ground Motion Again the residual displacements are significantly different Mean Standard Deviation! Residual Displacement, u r (m).6 Residual Displacement, u r (m) Ground Motion Mean Standard Deviation 29.August.26 12

13 Results: Fiber vs Lumped Plasticity Maximum Displacements Residual Displacements.6 Maximum Displacement, u m (m).2 Residual Displacement, u r (m).5 Model with fiber elemnts Model with fiber elements Model with lumped plasticity elements Model with lumped plasticity elements Residual displacements are significantly influenced by the! adopted modeling approach 29.August.26 13

14 Comparison with the experimental data Description of the shake table test Lestuzzi, P., T.Wenk, H. Bachmann (1999), Dynamische Versuche an Stahlbetontragwänden auf dem ETH-Erdbebensimulator, IBK Bericht Nr.24, Institut für Baustatik und Konstruktion, ETH Zürich 29.August.26 14

15 Rotation - z =.25 [m].15 Bending Moment [knm] Time [s] Response history Peak deformations Points of unloading Rotation - z=.25 [m] Residual deformation 29.August.26 15

16 FE model is subjected to the measured rotation history 15 Moment [knm] 1 5 Measured Simulated Time [s ] Moment [knm] Rotation 29.August.26 16

17 6 4 Experiment OpenSees Top displacement(mm) Time(s) 29.August.26 17

18 Example application Adapazari, Turkey Located in a region of high seismicity M w 7.4 Kocaeli, Turkey 1999 Earthquake Around ~7 buildings - mostly RC - MRF Three decision alternatives: strengthening the frame by structural walls no action preventing liquefaction by stone columns Performance of the structural stock subjected to a range of seismic events needs to be assessed. Number of Stories [m] (Bayraktarli Y., U. Yazgan, A. Dazio A. and M. Faber, 26) 29.August.26 18

19 Example application Set of representative RC frame buildings N story =1,2,3,,7 h story = 2.4 [m] L bay = 6 [m] ε sy = 2.1 [%] A story =3 [m 2 ] M story =.6 [t/m 2 ] Yield ground story drift, θ y Priestley (1998) Fundamental mode shape, φ 1 Yield displacement at roof, Δ y,roof Modal participation factor, Γ 1 Dazio(2) Modal Analysis TEC-98, ζ=5%, Z1, R= Sa [g] Elastic spectrum Design spectrum T [s] Yield Yield displacement, displacement, Δ* Δ* y y Base Base shear shear capacity, capacity, V* V* y y V [kn ] Equivalent SDOF Systems for RC - MRF's N story D [m ] August.26 19

20 Example application Representative models for retrofitted buildings Added Structural Walls H/L 4 ρ = 1% Yield curvature, φ y Yield displacement at the top, Δ y,w Flexural yield strength, M y Base shear at yielding V y Wall +Frame System Yield displacement, Δ y,roof Base shear at yielding V y Dazio(2) V [kn] 25 Equivalent SDOF Systems for RC MRF + Wall N story D [m] August.26 2

21 Example application Ground Motions Substitute SDOF System Simulated Response T, ζ, R y Maximum Displacement, Δ max Residual Displacement, Δ res P(PS>PS i ) n story =4 FO O LS NC C Which Δ res? Performance State Vision2(1995) u res [m] Δ res [m] 29.August.26 21

22 Conclusions Residual displacements are significantly influenced by the adopted modeling approach It is possible to establish a performance assessment strategy taking into account residual displacements to update the uncertainties Further study is needed to identify: - Which deformations would provide an effective measure? - Which are feasible to measure? 29.August.26 22

23 Outlook / Open Questions RC frame and structural wall systems are being studied Effective intensity measures related to residual displacements are being investigated Efficient ways to relate the seismic performance to structural response parameters needs to be identified Methods to include nonlinear soil deformation in the seismic performance assessment needs to be investigated Effect of ground motion record processing schemes on the simulated residual displacements needs to be studied 29.August.26 23

24 Thank you Any Questions? 29.August.26 24

25 Force (kn) Displacement (m) August Displacement [m] Time [s] Lumped-plasticity model (Ruaumoko) Fiber-element model (OpenSees) 25

26 Imprtance of time integration step size and proper updating of stiffness 16 Force (kn) 16 Force (kn) Displacement (m) dt=.1 dt=.5 dt=.2 dt=.5 dt= Displacement (m) Stiffness is updated at the end of each step -8 Stiffness is updated within each step 29.August.26 26

27 Maximum Displacement, u m (m) Residual Displacement, u r (m).8.2 With proper stiffness updating With proper stiffness updating With late stiffness updating With late stiffness updating Properly updating stiffness is crucial for estimating the residual displacements! 29.August.26 27

28 Effect of mesh density Effect of element formulation 2 Force (kn) 15 Force (kn) 1-element 3-elements 5-elements 7-elements Displacement (m) Displacement (m) Stiffness-based approach Flexibilty-based approach August.26 28

29 Limited memory problem of the steel hysteresis: without partial reloading with partial reloading Force - Displacement Force (kn) Partial reloading % increase in the displacement at the unloaded state Displacement (m) Steel Stress-Strain Strain Partial reloading Stress (MPa) without partial reloading with partial reloading Strain % increase in strain at the unloaded state Properly simulating the response of steel is critical for estimating the residual displacements! 29.August.26 29

30 Residual displacements are significantly influenced by the adopted modeling approach Differences in the small-cycle response leads to notably different residual displacement estimates Time integration step size can have a strong effect on the computed residual displacements Meshing of the system may have a significant influence on the computed residual displacements Memory limitation problem related to steel hysteresis response results inappropriate unloading paths 29.August.26 3

31 Limit State Drifts Calculation of limit state displacements Maximum Displacements H story = 2.4 [m] - Height of a story MRF H N FO O LS NC C FO O LS NC C φ 1,1 Γ FO O LS NC C n story [m] < > <[m] [m] [m] [m] [m]> n story <[m] [m] [m] [m] [m]> E-3 1.2E-2 3.6E-2 6.E-2 6.E E E E E E E E E E E E E E E E E E-2 1.1E E E E E E E E E E E E E-1 Vision 2 (1995) Dazio(2) Dazio(2) Residual Displacements MRF + SW φ 1,1 Γ FO O LS NC C n story <[m] [m] [m] [m] [m]> E-3 1.2E-2 3.6E-2 6.E-2 6.E E E E E E E E E E E E E E E E E E E-1 7.1E-1 7.1E E E E-1 9.8E-1 9.8E E E E-1 1.3E+ 1.3E+ H N FO O LS NC C FO O LS NC C φ 1,1 Γ FO O LS NC C n story [m] < > <[m] [m] [m] [m] [m]> n story <[m] [m] [m] [m] [m]> E-3 4.8E-3 1.2E-2 6.E-2 6.E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-1 Vision 2 (1995) θ 1st Story θ 1st Story Δ 1st Story Δ 1st Story Dazio(2) MRF Dazio(2) MRF + SW Δ * =Δ 1stStory / ( Γφ 1,1 ) Δ * =Δ 1stStory / ( Γφ 1,1 ) Δ * =Δ 1stStory / ( Γφ 1,1 ) 29.August.26 φ 1,1 Γ FO O LS NC C n story <[m] [m] [m] [m] [m]> E-3 4.8E-3 1.2E-2 6.E-2 6.E E E E E E E E E E E E E E E E E E E-1 7.1E-1 7.1E E E E-1 9.8E-1 9.8E E-2 1.4E E-1 1.3E+ 1.3E+ Dazio(2) Dazio(2) 31