1. NUMERICAL SEISMIC SAFETY ASSESSMENT OF RC BRIDGES WITH HOLLOW PIERS
Pedro Delgado1, António Arêde2, Nelson Vila Pouca2, Aníbal Costa3
1: Instituto Politécnico de Viana do Castelo, Portugal
2: Faculdade de Engenharia da Universidade do Porto, Portugal
3: Departamento de Engenharia Civil, Universidade de Aveiro, Portugal

2. OBJECTIVES
Several options for structural simulation to assess the seismic response of bridges: (i) plastic hinge model, (ii) fiber model and (iii) damage model.
Evaluation of seismic vulnerability through the failure probability quantification.
The applicability of the proposed methodologies is then illustrated in the seismic analysis of two reinforced concrete bridges, involving a series of experimental tests and numerical analysis, providing an excellent set of results for comparison and global calibration.

3. OUTLINE 1 - Seismic behaviour of bridges
2 - Methodologies for non-linear analysis
3 - Seismic safety assessment
4 - Application to the Talubergang Warth bridge
5 - Application to the PREC8 bridge
6 - Conclusions

4. 1 – SEISMIC BEHAVIOR OF BRIDGES
Past earthquakes:
Loma Prieta, 1989 (USA)
Northridge, 1994 (USA)
Kobe, 1995 (Japan)
Chi-Chi, 1999 (Taiwan)
Wenchuan, 2008 (China)
1 – Seismic behaviour of bridges
2 – Methodologies for non-linear analysis
3 – Seismic safety assessment
4 – Application to the Talubergang Warth bridge
5 – Application to the PREC8 bridge
6 - Conclusions
Significant damage was observed in these earthquakes, been illustrated the most important structural fails

5. 1 – SEISMIC BEHAVIOR OF BRIDGES
Loma Prieta : - 17/10/1989
- magnitude = 7,1
joint failures

6. 1 – SEISMIC BEHAVIOR OF BRIDGES
Northridge : - 17/01/1994
- magnitude = 6,6
Insufficient bending ductility Shear failure with hoops slips

7. 1 – SEISMIC BEHAVIOR OF BRIDGES
Kobe : - 17/01/1995
- magnitude = 7,2
Premature interruption of piers longitudinal reinforcement

8. 1 – SEISMIC BEHAVIOR OF BRIDGES
Taiwan : - 20/09/1999
- magnitude = 7,6
Seismic fault located under the bridge have caused significant damages in the piers

9. 1 – SEISMIC BEHAVIOR OF BRIDGES
Wenchuan : - 12/05/2008
- magnitude = 7,9
Piers failure leads to the bridge collapse

10. 1 – SEISMIC BEHAVIOR OF BRIDGES
The most important damages results from:
- insufficient ductility
- insufficient shear capacity
- wrong reinforcement detail
Need to use non-linear models with the accurate consideration of the cyclic behaviour aspects

11. 2 - METHODOLOGIES FOR NON-LINEAR ANALYSIS
Plastic Hinge Model
Cyclic behavior based on the Takeda model:
a – stiffness degradation
b – pinching effect
g – strength degradation
1 – Seismic behaviour of bridges
2 – Methodologies for non-linear analysis
3 – Seismic safety assessment
4 – Application to the Talubergang Warth bridge
5 – Application to the PREC8 bridge
6 - Conclusions

12. 2 - METHODOLOGIES FOR NON-LINEAR ANALYSIS
Fiber Model
finite element discretization and based on a modeling section fibers (for concrete and steel fibers), where the non-linear behavior is distributed along the element length and cross-sectional area.

13. 2 - METHODOLOGIES FOR NON-LINEAR ANALYSIS
Damage Model
Two independent scalar damage variables (d+ e d-), operating on the effective stress tensor (s):
supported on refined finite element (FE) meshes - 2D or 3D
Steel reinforcement modelled with uniaxial bar elements
Half pier with symmetry conditions
Cross section

14. 2 - METHODOLOGIES FOR NON-LINEAR ANALYSIS
Bridge modelling with plane models
The tri-dimensional dynamic analyses (transverse direction) was translated by a simplified structural 2D model
Links between piers and deck are simulated through ties that insure compatibility of displacements.
Piers are oriented to have their larger dimension in the plane direction.
Axial load equal to the vertical action of the deck must be considered.

15. 3 - SEISMIC SAFETY ASSESSMENT
Probabilistic methodology through vulnerability functions
1 – Seismic behaviour of bridges
2 – Methodologies for non-linear analysis
3 – Seismic safety assessment
4 – Application to the Talubergang Warth bridge
5 – Application to the PREC8 bridge
6 - Conclusions
With the seismic action distribution (1) and the vulnerability function (3)
probability distribution of maximum ductility demand (4)
collapse probability of the bridge (5)

16. 3 - SEISMIC SAFETY ASSESSMENT
Probabilistic methodology through fragility curves
Demand ductilities for the intensity level agi

17. 4 - APPLICATION TO THE TALÜBERGANG WARTH'S BRIDGE
Bridge geometry, main study purpose on the scope of a European project, Vulnerability Assessment of Motorway Bridges (VAB)
1 – Seismic behaviour of bridges
2 – Methodologies for non-linear analysis
3 – Seismic safety assessment
4 – Application to the Talubergang Warth bridge
5 – Application to the PREC8 bridge
6 - Conclusions
Deck section Piers section

18. 4 - APPLICATION TO THE TALÜBERGANG WARTH'S BRIDGE
Bridge geometry, main study purpose on the scope of a European project, Vulnerability Assessment of Motorway Bridges (VAB)
1 – Seismic behaviour of bridges
2 – Methodologies for non-linear analysis
3 – Seismic safety assessment
4 – Application to the Talubergang Warth bridge
5 – Application to the PREC8 bridge
6 - Conclusions
Piers height
Piers
P1 (A20)
P2 (A30)
P3 (A40)
P4 (A50)
P5 (A60)
P6 (A70)
L (m)
29.8
38.9
37.8
36.0
30.0
16.9
Axial load (kN)
26460
28633
28473
28218
27353
24610

19. 4 – WARTH BRIDGE Non-linear material behavior of the piers sections
Moment-curvature curves at the base of piers P3 (left) e P6 (right)

20. 4 - WARTH BRIDGE Pier response to imposed top displacements
Comparison between the numerical models and the experimental results (obtained at JRC lab., Italy)
Cyclic force-displacement curves for piers P3 (left) and P6 (right)

21. 4 - WARTH BRIDGE Time history response of pier P3
475 years return period
2000 years return period

22. 4 - WARTH BRIDGE
Vulnerability functions of piers P3 (left) and P6 (right)
Pier
PNL
Seismostruct
µd = 2.2
µd = 4.4 P3
Collapse probabilities

23. 5 - APPLICATION TO THE PREC8 BRIDGE
Bridge geometry, experimentally studied at the JRC, in the scope of PREC8 (Prenormative Research in support of EuroCode 8)
1 – Seismic behaviour of bridges
2 – Methodologies for non-linear analysis
3 – Seismic safety assessment
4 – Application to the Talubergang Warth bridge
5 – Application to the PREC8 bridge
6 - Conclusions

24. 5 - APPLICATION TO THE PREC8 BRIDGE
Bridge geometry, experimentally studied at the JRC, in the scope of PREC8 (Prenormative Research in support of EuroCode 8)
1 – Seismic behaviour of bridges
2 – Methodologies for non-linear analysis
3 – Seismic safety assessment
4 – Application to the Talubergang Warth bridge
5 – Application to the PREC8 bridge
6 - Conclusions
Piers section – reinforcement details

25. 5 - PREC8 BRIDGE Pier response to imposed top displacements
Comparison between the numerical model (plastic hinge) and the experimental results (obtained at JRC lab., Italy)
Cyclic force-displacement curves for tall pier (left) and short pier (right)

26. 5 - PREC8 BRIDGE Time history response Numerical – plastic hinge model
Numerical MG – fiber model
Medium pier
Short pier
Tall pier

27. 5 - PREC8 BRIDGE Vulnerability functions of the piers
VC = 0.05
VC = 0.20
µd = 4
µd = 8
µd = 12
Short
Medium
Tall
Collapse probabilities

28. 5 - PREC8 BRIDGE
Influence of the piers height irregularity on the seismic safety of PREC8 bridge
regularity parameter (R) proposed by Calvi et al. (1993)
Exponential relation between the collapse probability and the regularity parameter

29. CONCLUSIONS
Several numerical models were suggested for the cyclic and seismic responses of RC bridges, involving different approaches for the simulation of the non-linear behavior. One methodology for seismic safety assessment of bridges was also presented.
For comparison and calibration of the methodologies, two applications were carried out, showing good accuracy for the structural assessment of bridges subjected to cyclic and seismic loading.
The first application (Warth bridge) was mainly focus on the bridge piers static and cyclic analysis, allowing the comparison of results and evidencing the potentiality of the numerical models.
An irregular bridge (PREC8) was used for seismic analysis, with numerical simulations performed with plastic hinge model and fiber model. The numerical responses obtained compares quite well with the experimental results, both in the maximum displacement values and frequencies.
The safety evaluation performed to this bridge only presents a collapse probability below an acceptable level for µd = 12 and VC = 0.05, demonstrating the total inability of this irregular bridge in dealing with earthquake loadings.

30. ACKNOWLEDGEMENTS
This study was performed with the financial support of the “FCT- Fundação para a Ciência e Tecnologia" through the Project PTDC/ECM/72596/2006, ”Seismic Safety Assessment and Retrofitting of Bridges”.