### Abstract

This article presents a method for the development of vector-valued fragility functions, which are a function of more than one intensity measure (IM, also known as ground-motion parameters) for use within seismic risk evaluation of buildings. As an example, a simple unreinforced masonry structure is modelled using state-of-the-art software and hundreds of nonlinear time-history analyses are conducted to compute the response of this structure to earthquake loading. Dozens of different IMs (e. g. peak ground acceleration and velocity, response spectral accelerations at various periods, Arias intensity and various duration and number of cycle measures) are considered to characterize the earthquake shaking. It is demonstrated through various statistical techniques (including Receiver Operating Characteristic analysis) that the use of more than one IM leads to a better prediction of the damage state of the building than just a single IM, which is the current practice. In addition, it is shown that the assumption of the lognormal distribution for the derivation of fragility functions leads to more robust functions than logistic, log-logistic or kernel regression. Finally, actual fragility surfaces using two pairs of IMs (one pair are uncorrelated while the other are correlated) are derived and compared to scalar-based fragility curves using only a single IM and a significant reduction in the uncertainty of the predicted damage level is observed. This type of fragility surface would be a key component of future risk evaluations that take account of recent developments in seismic hazard assessment, such as vector-valued probabilistic seismic hazard assessments.

Language | English |
---|---|

Pages | 365-384 |

Number of pages | 20 |

Journal | Bulletin of Earthquake Engineering |

Volume | 11 |

Issue number | 2 |

Early online date | 25 Nov 2012 |

DOIs | |

Publication status | Published - Apr 2013 |

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### Keywords

- earthquake risk evaluation
- fragility functions
- ground-motion parameters
- intensity measures
- uncertainties
- unreinforced masonry

### Cite this

*Bulletin of Earthquake Engineering*,

*11*(2), 365-384. https://doi.org/10.1007/s10518-012-9402-7

}

*Bulletin of Earthquake Engineering*, vol. 11, no. 2, pp. 365-384. https://doi.org/10.1007/s10518-012-9402-7

**Vector-valued fragility functions for seismic risk evaluation.** / Gehl, Pierre; Seyedi, Darius M.; Douglas, John.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Vector-valued fragility functions for seismic risk evaluation

AU - Gehl, Pierre

AU - Seyedi, Darius M.

AU - Douglas, John

PY - 2013/4

Y1 - 2013/4

N2 - This article presents a method for the development of vector-valued fragility functions, which are a function of more than one intensity measure (IM, also known as ground-motion parameters) for use within seismic risk evaluation of buildings. As an example, a simple unreinforced masonry structure is modelled using state-of-the-art software and hundreds of nonlinear time-history analyses are conducted to compute the response of this structure to earthquake loading. Dozens of different IMs (e. g. peak ground acceleration and velocity, response spectral accelerations at various periods, Arias intensity and various duration and number of cycle measures) are considered to characterize the earthquake shaking. It is demonstrated through various statistical techniques (including Receiver Operating Characteristic analysis) that the use of more than one IM leads to a better prediction of the damage state of the building than just a single IM, which is the current practice. In addition, it is shown that the assumption of the lognormal distribution for the derivation of fragility functions leads to more robust functions than logistic, log-logistic or kernel regression. Finally, actual fragility surfaces using two pairs of IMs (one pair are uncorrelated while the other are correlated) are derived and compared to scalar-based fragility curves using only a single IM and a significant reduction in the uncertainty of the predicted damage level is observed. This type of fragility surface would be a key component of future risk evaluations that take account of recent developments in seismic hazard assessment, such as vector-valued probabilistic seismic hazard assessments.

AB - This article presents a method for the development of vector-valued fragility functions, which are a function of more than one intensity measure (IM, also known as ground-motion parameters) for use within seismic risk evaluation of buildings. As an example, a simple unreinforced masonry structure is modelled using state-of-the-art software and hundreds of nonlinear time-history analyses are conducted to compute the response of this structure to earthquake loading. Dozens of different IMs (e. g. peak ground acceleration and velocity, response spectral accelerations at various periods, Arias intensity and various duration and number of cycle measures) are considered to characterize the earthquake shaking. It is demonstrated through various statistical techniques (including Receiver Operating Characteristic analysis) that the use of more than one IM leads to a better prediction of the damage state of the building than just a single IM, which is the current practice. In addition, it is shown that the assumption of the lognormal distribution for the derivation of fragility functions leads to more robust functions than logistic, log-logistic or kernel regression. Finally, actual fragility surfaces using two pairs of IMs (one pair are uncorrelated while the other are correlated) are derived and compared to scalar-based fragility curves using only a single IM and a significant reduction in the uncertainty of the predicted damage level is observed. This type of fragility surface would be a key component of future risk evaluations that take account of recent developments in seismic hazard assessment, such as vector-valued probabilistic seismic hazard assessments.

KW - earthquake risk evaluation

KW - fragility functions

KW - ground-motion parameters

KW - intensity measures

KW - uncertainties

KW - unreinforced masonry

UR - http://www.scopus.com/inward/record.url?scp=84874947489&partnerID=8YFLogxK

U2 - 10.1007/s10518-012-9402-7

DO - 10.1007/s10518-012-9402-7

M3 - Article

VL - 11

SP - 365

EP - 384

JO - Bulletin of Earthquake Engineering

T2 - Bulletin of Earthquake Engineering

JF - Bulletin of Earthquake Engineering

SN - 1570-761X

IS - 2

ER -