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. 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

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.

Deterministic example

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

In general

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.

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

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

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

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.

The damage will be categorized in different levels (normally four) 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

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

Concrete fc (MPa) epsc fu (MPa) epsu Cover Concrete 21 0.002 0.01 0.015 Sec1 Core 24.2 2.98x10-3 21.3 6.89 x10-3 Sec2 Core 26.3 3.83 x10-3 23.8 8.88 x10-3

Longitudinal Reinforcement Steel fy (MPa) E0 (MPa) B Longitudinal Reinforcement Steel 420 2x105 0.00225

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)

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.

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