1. 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

2. 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

3. 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)

4. 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)

5. 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

6. Schematic view of the applied approaches

7. 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

8. 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)

9. 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

10. 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

11. 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

12. 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 g g

13. 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

14. 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

15. 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)

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

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

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

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

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

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

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

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

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

25. Fragility curves
Percentage increase in vulnerability due to soil compliance

26. Fragility curves
Percentage decrease in vulnerability due soil-structure interaction

27. 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.

28. 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