Preliminary Investigations on Post-earthquake Assessment of Damaged RC Structures Based on Residual Drift Jianze Wang Supervisor: Assoc. Prof. Kaoshan Dai State Key Laboratory of Disaster Reduction in Civil Engineering May 2015 The 5th Tongji-UBC Symposium on Earthquake Engineering

Outline Background and Motivations Seismic assessment methods based on residual drifts Application to E-Defense shaking table model Discussion and Conclusion

1.Background and motivations Performance-based Assessment Performance Indicators Element deformation Damage Indices (e.g. Park & Ang) ………….. Roof drift Interstory drift (GB. FEMA-356, ATC-58, Eurocode-8….)

1.Background and motivations Roof drift Interstory drift (GB. FEMA-356, ATC-58, Eurocode-8….) Maximum drift took place during earthquake Residual drift Unknown after main-shock Measurable Maximum displacement Residual displacement

2.Seismic assessment methods based on residual drifts a). Empirical Relations between Maximum and Residual drifts b). Probabilistic Estimation ………….

2.Seismic assessment methods based on residual drifts a). Empirical Relations C 𝑟 =[ 1 𝜃 1 + 1 41 𝑇 𝜃 2 ]𝛽 𝛽= 𝜃 3 [1−exp(− 𝜃 4 𝑅− 1) 𝜃 5 ]   (Garcia, 2006) 𝑢 𝑚𝑎𝑥 =( 𝑎 1 𝑇+ 𝑎 2 𝑢 𝑟𝑒𝑠 + 𝑎 3 𝑢 𝑟𝑒𝑠 2 + 𝑎 4 𝑇 𝑢 𝑟𝑒𝑠 )×(1+ 𝑎 5 𝐻+ 𝑎 6 𝐻 2 ) (Hatzigeorgiou et.al, 2011) 𝑑 𝑅 =( 0.019 𝑎 g 1 3 )( exp 10 1−𝑟 𝑑 𝑚 𝑑 𝑦 𝑑 𝑚 +(𝑟−1) 𝑑 𝑚 𝑑 𝑦 𝑑 𝑦 −1) (Takeda) 𝑑 𝑅 =( 0.000074 𝑎 g 5 6 )( exp 35 1−𝑟 𝑑 𝑚 𝑑 𝑦 𝑑 𝑚 +(𝑟−1) 𝑑 𝑚 𝑑 𝑦 𝑑 𝑦 −1) (Kinematic)  (Zhang et.al,2013) d 𝑅 = d 𝑇𝑃 −0.069 𝑎 g 2 +1.164 𝑎 g × 10 2 𝑟+3.58 (Gong et.al,2011) ………….

2.Seismic assessment methods based on residual drifts b). Probabilistic estimation (Yazgan and Dazio, 2012) Step 1: Modeling of the structure Step 2: Estimation the prior probabilistic distribution of the maximum drift ratio Step 3: Updating the maximum drift ratio distribution based on visible damage Step 4: Updating the maximum drift ratio distribution based on known residual drift

3.Application to E-Defense shaking table model A full-scale four-story RC structure model (Design and instrumentation of the 2010 E-Defense Four-Story Reinforced Concrete and Post-Tensioned Concrete Buildings, Peers, 2011) Longitudinal Direction (X) : Moment frame system Transverse Direction (Y): Frame-Shear wall system Story Height: 3m; Overall Height: 12m; All data were download from https://nees.org/warehouse/filebrowser/1005

3.Application to E-Defense shaking table model A full-scale four-story RC structure model Ground motions: JMA-Kobe motions (1995) , scaled by 25%, 50%, 100% Table. Roof displacements after each scenario Excitation Input X direction Displacements (mm) Drifts Maximum Residual KOBE-25% 22 0.2 0.184% 0.001% KOBE-50% 141 2.6 1.181% 0.022% KOBE-100% 272 9.6 2.269% 0.080%

2.Seismic assessment methods based on residual drifts Method: a) Empirical Relations C 𝑟 =[ 1 𝜃 1 + 1 41 𝑇 𝜃 2 ]𝛽 𝛽= 𝜃 3 [1−exp(− 𝜃 4 𝑅− 1) 𝜃 5 ]   Eq.1 (Garcia, 2006) Eq.2 𝑢 𝑚𝑎𝑥 =( 𝑎 1 𝑇+ 𝑎 2 𝑢 𝑟𝑒𝑠 + 𝑎 3 𝑢 𝑟𝑒𝑠 2 + 𝑎 4 𝑇 𝑢 𝑟𝑒𝑠 )×(1+ 𝑎 5 𝐻+ 𝑎 6 𝐻 2 ) (Hatzigeorgiou et.al, 2011) Eq.3 𝑑 𝑅 =( 0.019 𝑎 g 1 3 )( exp 10 1−𝑟 𝑑 𝑚 𝑑 𝑦 𝑑 𝑚 +(𝑟−1) 𝑑 𝑚 𝑑 𝑦 𝑑 𝑦 −1) (Takeda) 𝑑 𝑅 =( 0.000074 𝑎 g 5 6 )( exp 35 1−𝑟 𝑑 𝑚 𝑑 𝑦 𝑑 𝑚 +(𝑟−1) 𝑑 𝑚 𝑑 𝑦 𝑑 𝑦 −1) (Kinematic)  (Zhang et.al,2013) Eq.4 Eq.5 d 𝑅 = d 𝑇𝑃 −0.069 𝑎 g 2 +1.164 𝑎 g × 10 2 𝑟+3.58 (Gong et.al,2011) ………….

Calculation result (mm) 2.Seismic assessment methods based on residual drifts Method: a) Empirical Equtions In JMA-Kobe-100% test, the maximum roof displacement(drift) is 272mm(2.26%) in X direction With the equations, the results are: Calculation result (mm) Difference Eq.1 54.2 80% Eq.2 16.1 94% Eq.3 38.5 86% Eq.4 70.5 74% Eq.5 140 49%

3.Application to E-Defense shaking table model Method: b) Probabilistic Estimation Step 1:Modeling of the structure Comparisons between tests and simulations Perform-3D Nonlinear simulation: Beam: plastic hinges at member ends Column: fiber sections Actual material properties obtained from specimen in tests Cyclic degradation and strength loss were considered Kobe-25%-X Kobe-50%-X Kobe-100%-X

3.Application to E-Defense shaking table model Method: b) Probabilistic Estimation Step 2: Estimation the prior probabilistic distribution of the maximum drift ratio Assumption: Certainties: Structure properties Uncertainties: Ground motions Prior probabilistic distribution: Pr ( M 𝑖 )≈ 𝑛=1 𝑁 Pr M 𝑖 𝑆 𝑛 Pr ( S 𝑛 ) S 𝑛 −𝑛𝑡ℎ 𝑛𝑜𝑛𝑙𝑖𝑛𝑒𝑎𝑟 𝑡𝑖𝑚𝑒 ℎ𝑖𝑠𝑡𝑜𝑟𝑦 𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 One structure model A set of 50 ground motion records (PEER-NGA database, http://peer.berkeley.edu/nga/) Earthquake Name Year Station Name Mw Rjb (km) Rrup (km) Vs30 (m/sec) Kobe Japan 1995 KJMA 6.9 0.94 0.96 312

3.Application to E-Defense shaking table model Method: b) Probabilistic Estimation Step 2: Estimation the prior probabilistic distribution of the maximum drift ratio Uncertainties extent: Case 1: A reliable record is available. (JMA-Kobe) Sa(T1,ζ=0.05) of JMA-Kobe Sa(T1,ζ=0.05) of 50 records Case 2: MCE Response spectrum is available (USGS) Sa(T1,ζ=0.05) of spectrum Sa(T1,ζ=0.05) of 50 records Case 3: Just fundamental properties of the seismic event are known.(Mw, Rjb, Site….) GMPM model (Attenuation relationship) (Campbell and Bozorgnia, 2007) Median:0.82g σln(Sa)=0.58

3.Application to E-Defense shaking table model Method: b) Probabilistic Estimation Step 3: Updating the maximum drift ratio distribution based on visible damage Damage description: (After JMA-Kobe-100%) 2.5mm shear crack width in interior beam-column joints 1.1mm shear crack width in exterior beam-column joints 250mm height of cover concrete spalled in first story (Nagae et.al, 2012)

Structural Performance Levels 3.Application to E-Defense shaking table model Method: b) Probabilistic Estimation Step 3: Updating the maximum drift ratio distribution based on visible damage Performance levels taken from FEMA-356 Element Type Structural Performance Levels Collapse Prevention Life Safety Immediate Occupancy Primary Extensice cracking and hinge formation in ductile elements. Limited cracking and/or splice failure in some nonductile columns. Severe damage in short columns Extensive damage to beams. Spalling of cover and shear cracking (<0.32mm) for ductile columns. Minor spalling in nonductile columns. Joint cracks <0.32mm wide. Minor hairline cracking. Limited yielding possible at a few locations. No crushing (strains below 0.003). Secondary Extensive spallings in columns and beams. Severe joint damage. Some reinforcing buckled. Extensive cracking and hinge formation in ducttile elements. Limited cracking and/or splice failure in some nonductile columns. Severe damage in short columns. Minor spalling in a few places in ductile columns and beams. Flexural cracking in beams and columns. Shear cracking in joints<0.16mm. Drift 4% transient 2% transient 1% transient Assume uniform distribution : 𝐼= 𝐼 1 ∩ 𝐼 2 = 2%≤𝑀𝐴<4% Updated maximum drift ratio distribution: Pr 𝑀 𝑖 𝐼 1 ∩ 𝐼 2 = Pr 𝐼 2 𝑀 𝑖 ∩ 𝐼 1 Pr⁡ 𝑀 𝑖 𝐼 1 𝑗 Pr 𝐼 2 𝑀 𝑗 ∩ 𝐼 1 Pr⁡ 𝑀 𝑖 𝐼 1

Joint probability of max and residual drift given on visible damage: 3.Application to E-Defense shaking table model Method: b) Probabilistic Estimation Step 4: Updating the maximum drift ratio distribution based on known residual drift Pr M 𝑖 ∩ R 𝑗 𝐼 = Pr 𝐼 𝑀 𝑖 ∩ R 𝑗 Pr (M 𝑖 ∩ R 𝑗 ) 𝑖 𝑗 Pr 𝐼 𝑀 𝑖 ∩ R 𝑗 Pr (M 𝑖 ∩ R 𝑗 ) Joint probability of max and residual drift given on visible damage: Case 1: Case 3: Case 2:

3.Application to E-Defense shaking table model Method: b) Probabilistic Estimation Prior distribution Updated distribution based on visible damage Updated distribution based on residual drift Roof Drift After JMA-Kobe-100% X direction Test: 2.26% Estimation (Maximum Probability): Case 1: in the range 2.25%-2.5% Case 2: in the range 2%-2.25% Case 3: in the range 2.75%-3%

Post-earthquake assessment 3.Application to E-Defense shaking table model Post-earthquake assessment (Residual seismic capacity Sa,cap) Residual roof drift Maximum roof drift With the help of SPO2IDA spreadsheet tool, IDA curves could be derived. (Vamvatsikos amd Cornell, 2002.) IDA curves Pushover for intact and damaged structures

(considered residual drift) 3.Application to E-Defense shaking table model Seismic capacity Sa,cap(T1) (Median,50th) Structure Sa,cap(T1)(g) INTACT 2.93 DAMAGED 2.04 (considered residual drift) 2.86 Aleatory uncertainty (βR): 0.45 Epistemic uncertainty (βU): 0.40 16th Median(50th) 84th Fragility Curves：

4.Discussion and Conclusion Empirical relations between maximum and residual drift derived from simulations are unapplicable to result of the E-Defense shaking table test. The dispersion of residual drift should be considered. Probabilistic estimation could predict the maximum roof drift more accurately if residual roof drift and visible damage are available. In order to get better assessment results, the uncertainties of structure and ground shaking should be evaluated and quantified reasonably. The maximum drift distribution of structural damage used in step 3 of probabilistic estimation should be developed to a more accurate model.

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