Time-dependent vulnerability assessment of RC buildings considering Aristotle University of Thessaloniki Department of Civil Engineering Laboratory of Soil Mechanics, Foundations & Geotechnical Earthquake Engineering Research Unit of Geotechnical Earthquake Engineering and Soil Dynamics Time-dependent vulnerability assessment of RC buildings considering SSI and aging effects Sotiria Karapetrou Argyro Filippa Stavroula Fotopoulou Kyriazis Pitilakis COMPDYN 2013, Kos Island, Greece June 2013

Methodological framework Selection of reference structures Low and medium rise RC frame buildings Modern seismic code design Simulation of the structural models under study Fiber based approach SSI Corrosion probabilistic models Non-linear dynamic analysis 8 different outcropping real records Response parameter: maxISD(%) Time-dependent fragility curves IM: PGA LS in terms of maxISD(%) Incorporation of uncertainties

Structural models Low-rise structural model 2-storey, 1-bay RC MRF building Designed based on Greek modern seismic code Material properties: Concrete C20/25 Steel B500C Fundamental period: T1=0.3936sec Gelagoti (2010)

Structural models Mid-rise structural model 4-storey, 3-bay RC MRF building Designed based on modern seismic code of Portugal Material properties: Concrete fc=28MPa Steel fy=460MPa Fundamental period: T2=0.5018sec Abo El Ezz (2008)

Numerical modeling Finite element code OpenSees Material inelasticity Distributed material plasticity (fiber based approach) Confined concrete: Modified Kent and Park model (Scott et al 1982) Unconfined concrete: Kent and Park model (1971) Steel: uniaxial bilinear steel material object with kinematic hardening

Schematic view of the applied approaches

Soil-structure interaction (SSI) modeling SSI two-step analysis (Fotopoulou et al. 2012) 1st step: 1D equivalent linear analysis of the soil column 2nd step: Impedance function by Mylonakis et al. (2006) Vs,30=300m/sec CyberQuake G-γ-D by Darendeli (2001) → free field surface motion → effective shear strain of the surface layer γeff

Soil-structure interaction (SSI) modeling SSI two-step analysis (Fotopoulou et al. 2012) 1st step: 1D equivalent linear analysis of the soil column 2nd step: Impedance function by Mylonakis et al. (2006)

Elastic soil layers Vs,30=300m/sec Soil-structure interaction (SSI) modeling SSI one-step analysis OpenSees Calibration of the soil parameters in terms of G = f(γ) και D(%) = f(γ) based on1D equivalent linear analysis conducted in Cyberquake for the SSI two-step analysis Soil profile 120m x 30m,  3600 four node quadrilateral elements Soil quad element 1m x 1m Rigid beam-column element Free field Common nodes-Apropriate constraints 30.0m Elastic soil layers Vs,30=300m/sec 30.0m Input Motion Elastic Bedrock Vs=1000m/sec 120.0m Lysmer-Kuhlemeyer (1969) dashpot

Soil-structure interaction (SSI) modeling SSI one-step analysis Soil profile 120m x 30m,  3600 four node quadrilateral elements Soil quad element 1m x 1m Lysmer-Kuhlemeyer dashpot at the base Elastic soil layers 30.0m Elastic bedrock Vs=1000m/sec Calibration of the soil parameters in terms of G = f(γ) και D(%) = f(γ) based on1D equivalent linear analysis conducted in Cyberquake for the SSI two-step analysis Soil – structure: common nodes, appropriate constraints

Corrosion modeling Corrosion scenario for the t=50 years Main parameters: W/C, Ccrit, Tini, icorr, Di, n Probabilistic modeling of corrosion initiation time due to chloride ingress according to FIB-CEB Task Group 5.6 (2006) Time-dependent loss of cross sectional area of reinforced bars based on Gosh και Padgett (2010) Distribution of Chloride corrosion initiation time Tini mean = 2.96 years Standard Deviation = 2.16 years

Nonlinear Dynamic Analysis 2D nonlinear time-history analysis for t=0 and 50 years 8 outcropping records corresponding to sites classified as rock or stiff soil according to EC8 3 scaling levels in terms of PGA: 0.1g 0.3g 0.5g

Definition of Damage States Ghobarah (2004) : max ISD(%) for ductile and non-ductile MRF systems Damage states Ductile MRF Non-ductile MRF Light damage 0.4 0.2 Moderate damage 1.0 0.5 Severe damage 1.8 0.8 Collapse > 3.0 > 1.0 Scenario t=0 years: damage states for MRF – ductile structures Scenario t=50 years: damage states for MRF – non-ductile structures

Definition of Damage States Ghobarah (2004) : max ISD(%) for ductile and non-ductile MRF systems Damage states Ductile MRF Non-ductile MRF Light damage 0.4 0.2 Moderate damage 1.0 0.5 Severe damage 1.8 0.8 Collapse > 3.0 > 1.0 Scenario t=0 years: damage states for MRF – ductile structures Scenario t=50 years: damage states for MRF – non-ductile structures

Time-dependent fragility curves Lognormal distribution t : reference time m(t), β(t): PGA median values and logarithmic standard deviations at different points in time t along the service life (t=0 and 50 years)

Time-dependent fragility curves Uncertainties βD: demand (variability in the numerical results) βC: capacity (HAZUS) βds: definition of damage state (HAZUS)

Fragility curves PGA-ISDmax (%) for the low rise structures considering fixed and compliant condition for t=0 and 50 years

Fragility curves Comparison with literature Low rise strucural model designed based on modern seismic codes (t=0 έτη)

Fragility curves Comparison with literature Mid rise strucural model designed based on modern seismic codes (t=0 έτη)

Fragility curves Low rise structural model Aging effects→ Increase in vulnerability

Fragility curves Mid rise structural model Aging effects→ Increase in vulnerability

Fragility curves Fixed and compliant (Vs=300m/sec) foundation conditions for t=0years SSI and foundation compliance → Increase in vulnerability

Fragility curves Fixed and compliant (Vs=300m/sec) foundation conditions for t=0years SSI → Decrease in vulnerability

Fragility curves Substructure (two-step) and direct (one-step) methods for SSI modeling

Fragility curves Percentage increase in vulnerability due to soil compliance

Fragility curves Percentage decrease in vulnerability due soil-structure interaction

Conclusions aging effects :  affect the dynamic response and the seismic vulnerability of the structures corrosion of reinforcement :  is considered as a loss of cross sectional area of reinforced bars  leads to significant increase of structure vulnerability due to the considered “worst case scenario” soil deformability and soil compliance :  modify the structural response of the analyzed structures resulting to higher vulnerability values.  depends on: the characteristics of the building, the input motion and the soil properties.

Conclusions soil-foundation-structure interaction (SFSI): leads to decrease in structural vulnerability the uncoupled two-step approach (substructure method) leads to higher vulnerability (overestimation due to uncertainties related, among others, to the evaluation of the impedance function) further research in:  definition of limit states for corroded structures based on adequate analytical, experimental and empirical data  incorporation of the fully probabilistic models within the dynamic analysis