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Ph.D. Thesis project of Paolo E. Sebastiani PBEE - Mala Rijeka Viaduct

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The case study bridge "Mala Rijeka" is one of the most important bridges on the Belgrade - Bar International Line. The bridge was built in 1973 as the highest railway bridge in the World (Worlds Record Lists) and it is a continuous fivespan steel frame carried by six piers of which the middle ones have heights ranging from 50 to 137.5 m measured from the foundation interface. The main steel truss bridge structure consists in a continuous girder with a total length L=498.80 m. Static truss height is 12.50 m, and the main beams are not parallel, but are radially spread, in order to adjust to the route line.

Performance-based earthquake engineering (PBEE) consists of the evaluation, design and construction of structures to meet seismic performance objectives (expressed in terms of repair costs, downtime, and casualties) that are specified by stakeholders (owners, society, etc.).

It is based on the premise that performance can be predicted and evaluated with quantifiable confidence to make, together with the client, intelligent and informed trade-offs based on life-cycle considerations rather than
construction costs alone.

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Ph.D. Thesis project of Paolo E. Sebastiani PBEE - Mala Rijeka Viaduct

  1. 1. 1 P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org 1. PERFORMANCE-BASED EARTHQUAKE ENGINEERING CONDITIONAL PROBABILISTIC APPROACH (IM-BASED METHODS) APPROACHES UNCONDITIONAL PROBABILISTIC APPROACH SEMI-PROBABILISTICAPPROACH (DM2008) PHILOSOPHY PBEE DETERMINISTICAPPROACH EVALUATION, DESIGN AND CONSTRUCTION OF STRUCTURESTO MEET SEISMIC PERFORMANCE OBJECTIVES 1.1 – PBEE Outline
  2. 2. 2 1.2 – Definition Performance-based earthquake engineering (PBEE) consists of the evaluation, design and construction of structures to meet seismic performance objectives (expressed in terms of repair costs, downtime, and casualties) that are specified by stakeholders (owners, society, etc.) It is based on the premise that performance can be predicted and evaluated with quantifiable confidence to make, together with the client, intelligent and informed trade-offs based on life-cycle considerations rather than construction costs alone. Krawinkler, H. and Miranda, E. (2004). “Performance-Based Earthquake Engineering”. Chapter 9 of Earthquake Engineering: From engineering seismology to performance-based engineering, edited by Y. Bozorgnia, andV. Bertero, CRC press. 1. PERFORMANCE-BASED EARTHQUAKE ENGINEERING 1.3 – Assumptions P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  3. 3. 3 1.4 – Development of PBEE Most of the concepts that are implemented in the context of PBEE are not new. In various forms they have been explored, tried and partially implemented in past design/evaluation guidelines and standards of various countries and industries In the United States various efforts were initiated during the early 1990s which faced up to the many challenges of performance-based seismic design. The most widely known ones are Vision 2000 (SEAOC, 1995), FEMA 273 and FEMA 274 (1996) and ATC-40 (1996) 1. PERFORMANCE-BASED EARTHQUAKE ENGINEERING Krawinkler, H. and Miranda, E. (2004). “Performance-Based Earthquake Engineering”. Chapter 9 of Earthquake Engineering: From engineering seismology to performance-based engineering, edited by Y. Bozorgnia, andV. Bertero, CRC press. 1.5 – PBEE concepts in the Codes P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  4. 4. 4 1.6 –Vision 2000 report (SEAOC 1995) 1. PERFORMANCE-BASED EARTHQUAKE ENGINEERING One of the many strong points of theVision 2000 document is that it proposes a comprehensive design/assessment/build process that incorporates important aspects of: • Selection of a suitable site • Selection of suitable structural materials and systems • Configuration and continuity of load path • Quality of detailing • Strength and stiffness • Consideration of nonstructural and content systems • Quality and consistency of design • Quality of design review • Quality of construction • Quality of inspection P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  5. 5. 5 1. PERFORMANCE-BASED EARTHQUAKE ENGINEERING Performance objectives for buildings, recommended in SEAOC (1995). P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  6. 6. 6 1. PERFORMANCE-BASED EARTHQUAKE ENGINEERING CONDITIONAL PROBABILISTIC APPROACHES PEER METHOD It is not in closed form but it allows more flexibility and generality in the evaluation of the desired so- called “decision variable”, not necessarily coinciding with Pf. SAC/FEMA It has the advantage of providing a closed-form expression for the failure probability (Pf), that can also be put in a partial factor format. 1.7 – Conditional Probabilistic Approaches In the middle of the 90’s very promising results started to materialize (i.e. Bazzurro and Cornell 1994, Cornell 1996). The problem was posed in terms of a direct (probabilistic) comparison between demand and capacity, with the demand being the maximum of the dynamic response of the system to a seismic action characterized in terms of a chosen return period Fib (2012) Probabilistic performance-based seismic design. Bulletin n°68, Fédération internationale du béton, Lausanne, Switzerland P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  7. 7. 7 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE 2.1 – Definition The Pacific Earthquake Engineering Research (PEER) Center has focused for several years on the development of procedures, knowledge and tools for a comprehensive seismic performance assessment of buildings and bridges In the approach, decision variables are identified whose quantification, together with an assessment of important uncertainties, will make it feasible to characterize and manage economic and societal risks associated with direct losses, downtime and collapse and life safety. Krawinkler, H. and Miranda, E. (2004). “Performance-Based Earthquake Engineering”. Chapter 9 of Earthquake Engineering: From engineering seismology to performance-based engineering, edited by Y. Bozorgnia, andV. Bertero, CRC press. P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  8. 8. 8 2.2 – Components of PEER method: PerformanceTargets 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE It is assumed that a performance target can be expressed in terms of a quantifiable entity and, for instance, its annual probability of exceedance. For instance, l$(y), the mean annual frequency (MAF) of the loss exceeding y dollars, could be the basis for a performance target P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  9. 9. 9 2.3 – Components of PEER method: DecisionVariables 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE The quantifiable entities, on which performance assessment is based, are referred to as decision variables (DVs). Examples of DVs of primary interest are the existence of collapse, the number of casualties, dollar losses and the length of downtime P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  10. 10. 10 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE To compute DVs and their uncertainties, other variables have to be evaluated to define: 1. The seismic hazard 2. The demands imposed on the structural systems by the hazard 3. The state of damage P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  11. 11. 11 2.4 – Components of PEER method: Seismic Hazard 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE The seismic hazard is quantified in terms of a vector of intensity measures (IMs), which should define the seismic input to the structure. This vector could have a single component, such as spectral acceleration at the first mode period of the structure, Sa(T1), or could have several. If a single component is used, such as Sa(T1), the hazard is usually defined in terms of a hazard curve. The outcome of hazard analysis, which forms the input to demand evaluation, is usually expressed in terms of an MAF of IMs, i.e., l(IM), P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  12. 12. 12 2.5 – Components of PEER method: Engineering Demands Parameters 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE Given the ground motion hazard, a vector of engineering demand parameters (EDPs) needs to be evaluated, which defines the response of the structure in terms of parameters that can be related to DVs. Interstory drift is an example of a relevant EDP for buildings P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  13. 13. 13 2.6 – Components of PEER method: Damage Measures DM 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE In most cases an intermittent variable, called a damage measure (DM), has to be inserted between the EDP and the DV simply to facilitate the computation of DVs from EDPs. A DM describes the damage and consequences of damage to a structure or to a component of the structural, nonstructural or content system, and the term G (DM|EDP) can be viewed as a fragility function for a specific damage (failure) state (probability of being in or exceeding a specific damage state, given a value of EDP). P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  14. 14. 14 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE The assessment problem has been “de-constructed” into the four basic elements of 1. hazard analysis 2. demand prediction 3. modeling of damage states 4. failure or loss estimation by introducing the three intermediate variables, IM, EDP and DM To close the loop… 1. EDPs have to be related to IMs (Probabilistic Seismic Demand Analysis PSDA) 2. DMs have to be related to EDPs (Damage Analysis) P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  15. 15. 15 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE Relationships between EDPs and IMs (also called Probabilistic Seismic Demand Models PSDM) can be obtained through simulations, which should incorporate the complete structural, geotechnical and SFSI (soil–foundation–structure interaction) systems 2.7 – Probabilistic Seismic Demand Analysis in the PEER method So the first step is the evaluation of a PSDM The outcome of this process, which may be referred to PSDA, can be expressed as G(EDP|IM) or more specifically as G[EDP ≥ y | IM = x], which is the probability that the EDP exceeds a specified value y, given (i.e., conditional) that the IM is equal to a particular value x P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  16. 16. 16 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE Synthetic or recorded accelerograms SEISMIC LOADS STRUCTURE Geometry Meterials Method of design Ductility Isolation system INPUTS Type Range of values Scalar or vector One or more EDP IM SETTINGS Type Range of values Scalar or vector One or more COMMON APPROACHES BIN APPROACH CLOUD METHOD STRIPE METHOD IDA SIMPLIFIED METHOD IMPROVED CLOUD METHOD MCS - LHS EMPIRICAL METHOD PSDM 2.8 – PSDM in the PSDA Two values for each level of IM: - mIM , Median of EDP - z, Standard deviation of EDP P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  17. 17. 17 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE A regression analysis can be used to obtain the mean (mIM) and the standard deviation (z) by assuming the logarithmic correlation between median EDP and an appropriately selected IM: where the parameters "a" and "b" are regression coefficients obtained for example by the nonlinear time history analyses ln⁡(𝐸𝐷𝑃) = ln 𝑎 + 𝑏 𝑙𝑛(𝐼𝑀) P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  18. 18. 18 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE Assuming a log-normal distribution of EDP at a given IM, the probability that the EDP exceeds a specified value y, given (i.e., conditional) the IM, can be written as: where F is the standard normal distribution function 𝐺 𝐸𝐷𝑃 ≥ 𝑦|𝐼𝑀 = 1 − Φ ln 𝑦 − ln⁡(𝑎 𝐼𝑀 𝑏 ) 𝜁 The remaining variability in ln(EDP) at a given IM is assumed to have a constant variance for all IM range, and the standard deviation can be estimated: 𝜁 = ln 𝐸𝐷𝑃𝑖 − (ln 𝑎 + 𝑏 ln 𝐼𝑀𝑖) 2𝑛 𝑖=1 𝑛 − 2 P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  19. 19. 19 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE 2.9 – Damage analysis and fragility functions in the PSDA The specified value y of EDP, defined previously, can be related to a Damage Measure DM. Consequently it is possible to define some Limit States LS according to different damaging. STRUCTURAL CAPACITY (DAMAGEANALYSIS) P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  20. 20. 20 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE Nielson, B. G. (2005). “Analytical fragility curves for highway bridges in moderate seismic zones.” PhDThesis, Georgia Institute ofTechnology,Atlanta, Georgia. P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  21. 21. 21 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE Therefore G (DM|EDP) can be viewed as a fragility function for three different damage states P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  22. 22. 22 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE 2.10 – Loss analysis The seismic fragility can be convolved with the seismic hazard in order to assess the annual probability PAi of exceeding the ith damage state: where H(a) is the hazard curve that quantifies the annual probability of exceeding a specific level of IM at a site. Additionally, under the assumption of time-invariant structural resistance, it is possible to evaluate the T-year probability PTfi of exceeding the damage state ith, estimated as: 𝑃𝐴𝑖 = 𝑃 𝐷𝐼 ≥ 𝐿𝑆|𝐼𝑀 𝑑𝐻(𝑎) 𝑑𝑎 𝑑𝑎 PTf 𝑖 = 1 − 1 − PA𝑖 T P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  23. 23. 23 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE 2.10 – Loss analysis For each damage state it is possible to define a nominal cost of restoration which depends on the repair strategy. So the probability of exceeding a damage state can be related to the probability of exceeding a “cost” to close the loop of PEER method Fib (2012) Probabilistic performance-based seismic design. Bulletin n°68, Fédération internationale du béton, Lausanne, Switzerland P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  24. 24. 24 2. PEER METHOD: A PROBABILISTIC DESIGN/ASSESSMENT APPROACH TO PBEE 2.10 – Loss analysis At the same time it is possible to calculate the expected value of the life-cycle costs due to seismic damage in present day dollars can be expressed as follow: where i is the damage state, T=50 years is the remaining service life of the bridge, Ci is the cost associated with damage state i. An inflation adjusted discount ratio, a=0.03, is used for converting future costs into present values Wen,Y. K., and Kang,Y. J. (2001a). “Minimum Building Life-Cycle Cost Design Criteria. I: Methodology.” Journal of Structural Engineering, 127(3), 330–337. E LCC = 1 αT 1 − e−αT −C𝑖 3 𝑖=1 ln 1 − PTf𝑖 − ln⁡1 − PTf𝑖+1 P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  25. 25. 25 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT 3.1 –The case study P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  26. 26. 26 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  27. 27. 27 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT 3.2 –The case study: geometry The case study bridge "Mala Rijeka" is one of the most important bridges on the Belgrade - Bar International Line. The bridge was built in 1973 as the highest railway bridge in the World (Worlds Record Lists) and it is a continuous five- span steel frame carried by six piers of which the middle ones have heights ranging from 50 to 137.5 m measured from the foundation interface. The main steel truss bridge structure consists in a continuous girder with a total length L=498.80 m. Static truss height is 12.50 m, and the main beams are not parallel, but are radially spread, in order to adjust to the route line P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  28. 28. 28 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT 3.3 – Uncertainties AVAILABLE DATA •Geometry •Site Characteristics* •Damage inspection made in the 2007 NOT AVAILABLE DATA •Pier’s section •Materials •Devices Z. Radosavljevid and O, Markovic. (1976) Some Foundation Stability Problems of the Railway Bridge over the Mala Rijeka. Rock Mechanics 9, 55--64 P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  29. 29. 29 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT 3.4 – Modeling of the highest pier The response of the pier III in figure 1 is evaluated via non-linear dynamic analyses run in OpenSees 2.2.2 (McKenna, 1997).The column is modelled with a nonlinear element with fiber-section distributed plasticity P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  30. 30. 30 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT 3.5 – Material assumptions Deck (120 m for the 3th pier) : 870 kNs2/m Pier (distributed along the pier) : 7166 kNs2/m 3.6 – Mass assumptions P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  31. 31. 31 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT 3.7 – Section assumptions •Tube 6.5 16.5 m x 6.516.5 m (variable) •0.5 m of thickness •Rebar F26 / 0.2 m SECTION A P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  32. 32. 32 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT 3.8 – Pushover analysis to define limit states First Cracking st = 5.2 N/mm2 is the concrete tensile strength SEC 107 SEC 105 SEC 103 SEC 101P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org 32
  33. 33. 33 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT 3.9 – Pushover analysis to define limit states SEC 107 SEC 105 SEC 103 SEC 101 Yielding ss = 440 N/mm2 is the steel yield strength P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org 33
  34. 34. 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT 3.10 – Pushover analysis to define limit states Three damage states DS namely slight, moderate and complete damage are adopted in this study and their concerning limit values are shown in tab. 6. Through the pushover analysis presented previously, the slight damage has been associated to the achievement of maximum tensile strength of concrete, while the moderate one to the yielding of the steel rebar. A comparison between the values adopted by Choi et al. (2004) and the ductility factor defined in the EC8 for piers, has allowed us to define also limit values referred to the collapse. P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org 34
  35. 35. 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT 3.11 – PSDM results with different type of retrofit NOT ISOLATED ISOLATED (FRICTION-PEDULUM SYSTEM) ISOLATED (ELASTOMERIC BEARINGS) Using the curvature ductility at the pier base mc and displacement ductility dc as EDPs, for different type of IMs and type of retrofit, the PDSM results are the following: Sebastiani P.E., Padgett J.E., Petrini F., Bontempi F. (2014). Effectiveness Evaluation of Seismic Protection Devices for Bridges in the PBEE Framework. In proceeding of: ASCE-ICVRAM-ISUMA 2014 - second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) Liverpool, 13th-17th July 2014 P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  36. 36. 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT 3.12 – PSDM results with different type of retrofit Sebastiani P.E., Padgett J.E., Petrini F., Bontempi F. (2014). Effectiveness Evaluation of Seismic Protection Devices for Bridges in the PBEE Framework. In proceeding of: ASCE-ICVRAM-ISUMA 2014 - second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) Liverpool, 13th-17th July 2014 P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org
  37. 37. 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT 3.12 – Fragility results P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org 37
  38. 38. 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT 3.12 – Fragility results In terms of damage probability, choosing the example of slight damage and referring to the curvature ductility as EDP, the probability of damage during a period of 50 years is: 23% for the structure without isolation, 7% for the structure equipped with ERB, and 3% for the structure equipped with FPS isolation. Sebastiani P.E., Padgett J.E., Petrini F., Bontempi F. (2014). Effectiveness Evaluation of Seismic Protection Devices for Bridges in the PBEE Framework. In proceeding of: ASCE-ICVRAM-ISUMA 2014 - second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) Liverpool, 13th-17th July 2014 P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org 38
  39. 39. 3. APPLICATIONTO THE “MALA RIJEKA”VIADUCT 3.12 – Example of expected cost calculation P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org 39
  40. 40. 4. FUTURE WORK 1) Full 3D model of the Mala Rijeka Bridge 2) Loss estimation taking into account aging effects 3) Effectiveness Evaluation of different Seismic Protection Devices 4) Application to two representative categories of Highway bridges: - Most common bridge type, i.e. short span, simply supported deck - Less common bridge type, i.e. high piers, long span, continuous deck DEMAND CAPACITY FRAGILITY COMPONENT SYSTEM NETWORK LOSS ? P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org 40
  41. 41. KEYWORDS PBEE PRACTICE-ORIENTED TARGET OPENSEES SEISMIC ADJUSTMENTAGING LIMIT STATES ISOLATION (MFPS, ERB) LCC 4. FUTURE WORK P. E. Sebastiani – Ph.D. Student Sapienza University of Rome - a.a. 2013/2014 paolo.sebastiani@uniroma1.it francesco.petrini@uniroma1.it franco.bontempi@uniroma1.it www.francobontempi.org 41

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