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Jens Ulfkjaer

Management of Earthquake Risk using Condition Indicators Determination of vulnerability functions. Jens Ulfkjaer. Outline. What is the project MERCI about What is a vulnerability function? Six steps for determination of the vulnerability function for a structural class.

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Jens Ulfkjaer

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  1. Management of Earthquake Risk using Condition IndicatorsDetermination of vulnerability functions Jens Ulfkjaer

  2. Outline • What is the project MERCI about • What is a vulnerability function? • Six steps for determination of the vulnerability function for a structural class. • Choice of the Attenuation function and intensity of the load • Simulation of a set of time histories • Simulation of a set of materials parameters • Structural analysis • Determination of the structural damage • Calculations of the damage probabilities and the vulnerability function • Example

  3. What is a vulnerability function? • A vulnerability function is a function that describes the probability of obtaining a certain level of damage dependent on the intensity of the load.

  4. Deterministic example

  5. Stochastic problem • The load in it self is stochastic • The structure class will compromise many structures with different sizes, irregularities, and material parameters • Even at the single house level the strength parameters are only known with a certain probability

  6. In general

  7. 1) Choice of the Attenuation function and intensity of the load • The are many different available attenuation relationships in the literature and particular attention should be paid to the choice. • For the moment, as a rough choice, we have chosen Boore et al. 1997.

  8. 2) Set of acceleration time histories • Basically two types exist: real records and simulated records

  9. 3) Simulation of a set of materials parameters • The material and the structural parameters should be simulated with certain statistical parameters.

  10. 4) Structural analysis • The structural response can be calculated in many different ways: analytically and numerically • We are at the moment using the Finite Element Method and the program openSees

  11. 5) Determination of the structural damage • The damage should be determined from the response calculated by openSees. • Many possibilities could be imagined but as a beginning we will use the maximal drift during the earthquake.

  12. 6) Calculations of the damage probabilities and the vulnerability function • The damage will be categorized in different levels (normally four) • The vulnerability is then the probability of having a certain level of damage

  13. 6m A mass1 Sec1 A mass1 4m Sec2 Sec2 B B y x Section A-A: Section B-B: All rebars 16 (201mm2) 2.5cmmm As = 493mm2 2.5cmmm 2.5cmmm y z 45cmmm 35cmmm z x 2.5cmmm 2.5cmmm A’s = 226mm2 35cmmm 2.5cmmm 2.5cmmm 25cmmm 2.5cmmm Example • The following house is used Mass 1 Mass x-direction : 1.53 tons

  14. Concrete

  15. Steel

  16. Material properties variation • The steel yielding strength been assumed to be normal distributed and 250 displacement time series has been calculated (with example3.3 from openSees manual)

  17. Load • 3 intensities and 3 distances are used • Intensities: M1=5.5 M2=6.5 M3=7.5 • Distances:R1=20 km R2=40 km R3=80 km • For each of these nine combinations 10 time series has been generated.

  18. Conclusions • The software PreOpenSeesPost developed for calculating vulnerability functions in 2D and 3D is almost finished. • More functions to interact with the user needs to be developed. • More complex structures should be tested • More structural element types as masonry has to be implemented

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