Multivariate Fragility Models for Earthquake Engineering

2016 ◽  
Vol 32 (1) ◽  
pp. 441-461 ◽  
Author(s):  
Abbas Javaherian Yazdi ◽  
Terje Haukaas ◽  
Tony Yang ◽  
Paolo Gardoni
Keyword(s):  
Logistic Regression ◽  
Earthquake Engineering ◽  
Shear Walls ◽  
Performance Assessments ◽  
Fragility Functions ◽  
Structural Components ◽  
Logistic Regression Models ◽  
Damage Models ◽  
Damage States ◽  
Performance Based Earthquake Engineering

This paper employs a logistic regression technique to develop multivariate damage models. The models are intended for performance assessments that require the probability that structural components are in one of several damage states. As such, the developments represent an extension of the univariate fragility functions that are omnipresent in contemporary performance-based earthquake engineering. The multivariate logistic regression models that are put forward here eliminate several of the limitations of univariate fragility functions. Furthermore, the new models are readily substituted for existing fragility functions without any modifications to the existing performance-based analysis methodologies. To demonstrate the proposed modeling approach, a large number of tests of reinforced concrete shear walls are employed to develop multivariate damage models. It is observed that the drift ratio and aspect ratio of concrete shear walls are among the parameters that are most influential on the damage probabilities.

Analysis of Seismic Fragility Functions of Highway Embankments

2020 ◽  
Author(s):  
Balázs Hübner ◽  
András Mahler
Keyword(s):  
Finite Element ◽  
Earthquake Engineering ◽  
Seismic Fragility ◽  
Response Analysis ◽  
Fragility Functions ◽  
Ground Response ◽  
Ground Response Analysis ◽  
Fragility Function ◽  
Damage States ◽  
Log Normal

Vulnerability assessment of structures is a vitally important topic among earthquake engineering researchers. Generally, their primary focus is on the seismic performance of buildings. Less attention is paid to geotechnical structures, even though information about the performance of these structures (e.g. road embankments, levees, cuts) during an earthquake is essential for planning remediation and rescue efforts after disasters. In this paper the seismic fragility functions of a highway embankment are defined following an analytical methodolgy. The technique is a displacement-based evaluation of seismic vulnerability. Displacements of an embankment during a seismic event are approximated by a 2-D nonlinear ground response analysis using the finite element method. The numerical model was calibrated based on the results of a 1-D nonlinear ground response analysis. The expected displacements were calculated for 3 different embankment heights and Peak Ground Acceleration (PGA) values between 0,05 and 0,35g. Based on the results of the 2-D finite element analysis, the relationship between displacements and different seismic intensity measures (PGA, Arias-intensity) was investigated. Different damage states were considered, and the probability of their exceedance was investigated. The seismic fragility functions of the embankments were developed based on probability of exceedance of these different damage states based on a log-normal fragility function. The legitimacy of using a log-normal fragility function is also examined.

Fragility of Mechanical, Electrical, and Plumbing Equipment

2010 ◽  
Vol 26 (2) ◽  
pp. 451-472 ◽  
Author(s):  
Keith Porter ◽  
Gayle Johnson ◽  
Robert Sheppard ◽  
Robert Bachman
Keyword(s):  
Professional Practice ◽  
Earthquake Engineering ◽  
Fragility Functions ◽  
Subsequent Work ◽  
Engineering Research ◽  
Modifying Factors ◽  
Industrial Buildings ◽  
Average Condition ◽  
Performance Based Earthquake Engineering ◽  
Level Performance

A study for the Multidisciplinary Center for Earthquake Engineering Research (MCEER) provides fragility functions for 52 varieties of mechanical, electrical, and plumbing (MEP) equipment commonly found in commercial and industrial buildings. For the majority of equipment categories, the MCEER study provides multiple fragility functions, reflecting important effects of bracing, anchorage, interaction, etc. The fragility functions express the probability that the component would be rendered inoperative as a function of floor acceleration. That work did not include the evidence underlying the fragility functions. As part of the ATC-58 effort to bring second-generation performance-based earthquake engineering to professional practice, we have compiled the original MCEER specimen-level performance data into a publicly accessible database and validate many of the original fragility functions. In some cases, new fragility functions derived by ATC-58 methods show somewhat closer agreement with the raw data. Average-condition fragility functions are developed here; we will address in subsequent work the effect of potentially important—arguably crucial—performance-modifying factors such as poor anchorage and interaction.

Fragility Functions for Steel Plate Shear Walls

2012 ◽  
Vol 28 (2) ◽  
pp. 405-426 ◽  
Author(s):  
Nicole M. Baldvins ◽  
Jeffery W. Berman ◽  
Laura N. Lowes ◽  
Todd M. Janes ◽  
Natalie A. Low
Keyword(s):  
Steel Plate ◽  
Probability Distributions ◽  
Experimental Studies ◽  
Shear Walls ◽  
Fragility Functions ◽  
Empirical Relationships ◽  
Steel Plate Shear Walls ◽  
Story Drift ◽  
Damage States ◽  
Lognormal Probability

Fragility functions are developed to predict the method of repair required for steel plate shear walls damaged due to earthquake loading. The results of previous experimental studies are used to develop empirical relationships between damage states and story drift. Damage states are proposed and linked deterministically with commonly employed methods of repair; these damage states are characterized by parameters such as yielding and tearing of the steel plate and yielding, buckling and fracture of frame members. Lognormal probability distributions are fit to the empirical data and evaluated using standard statistical methods. The results of this effort are families of fragility functions that predict the required method of repair for a damaged wall.

Story loss functions for seismic design and assessment: Development of tools and application

2021 ◽  
pp. 875529302110235
Author(s):  
Davit Shahnazaryan ◽  
Gerard J O’Reilly ◽  
Ricardo Monteiro
Keyword(s):  
Seismic Design ◽  
Earthquake Engineering ◽  
Academic Research ◽  
Loss Functions ◽  
Design Stage ◽  
Building Performance ◽  
Assessment Development ◽  
Damage States ◽  
Performance Based Earthquake Engineering

Performance-based earthquake engineering (PBEE) has become an important framework for quantifying seismic losses. However, due to its computationally expensive implementation through a typically detailed component-based approach (i.e. Federal Emergency Management Agency (FEMA) P-58), it has primarily been used within academic research and specific studies. A simplified alternative more desirable for practitioners is based on story loss functions (SLFs), which estimate a building’s expected monetary loss per story due to seismic demand. These simplified SLFs reduce the data required compared to a detailed study, which is especially true at a design stage, where detailed component information is likely yet to be defined. This article proposes a Python-based toolbox for the development of user-specific and customizable SLFs for use within seismic design and assessment of buildings. It outlines the implementation procedure alongside a comparative demonstration of its application where dependency and correlation of damage states between different components are considered. Finally, a comparison of SLF-based and component-based loss estimation approaches is carried out through the application to a real case study school building. The agreement and consistency of the attained loss metrics demonstrate the quality and ease of the SLF-based approach in achieving accurate results for a more expedite assessment of building performance.

Epistemic Uncertainties in Component Fragility Functions

2010 ◽  
Vol 26 (1) ◽  
pp. 41-62 ◽  
Author(s):  
Brendon A. Bradley
Keyword(s):  
Quality Assurance ◽  
Earthquake Engineering ◽  
Epistemic Uncertainty ◽  
Finite Size ◽  
Seismic Demand ◽  
Fragility Functions ◽  
Seismic Performance Assessment ◽  
Fragility Function ◽  
Documentation Quality ◽  
Performance Based Earthquake Engineering

This paper is concerned with the inclusion of epistemic uncertainties in component fragility functions used in performance-based earthquake engineering. Conventionally fragility functions, defining the probability of incurring at least a specified level of damage for a given level of seismic demand, are defined by a mean and standard deviation and assumed to have a lognormal distribution. However, there exist many uncertainties in the development of such fragility functions. The sources of epistemic uncertainty in fragility functions, their consideration, combination, and propagation are presented and discussed. Two empirical fragility functions presented in literature are used to illustrate the epistemic uncertainty in the fragility function parameters due to the finite size of the datasets. These examples and the associated discussions illustrate that the magnitude of epistemic uncertainties are significant and there are clear benefits of the consideration of epistemic uncertainties pertaining to the documentation, quality assurance, implementation, and updating of fragility functions. Epistemic uncertainties should therefore always be addressed in future fragility functions developed for use in seismic performance assessment.

scholarly journals Empirical fragility functions and loss curves for Italian business facilities based on the 2012 Emilia-Romagna earthquake official database

2019 ◽  
Vol 18 (4) ◽  
pp. 1693-1721 ◽  
Author(s):  
Leonardo Rossi ◽  
Marco Stupazzini ◽  
Davide Parisi ◽  
Britta Holtschoppen ◽  
Gabriella Ruggieri ◽  
...  
Keyword(s):  
Earthquake Engineering ◽  
Economic Losses ◽  
Seismic Events ◽  
Fragility Functions ◽  
Administrative Authority ◽  
Specific Data ◽  
Related Data ◽  
Long Span ◽  
Performance Based Earthquake Engineering ◽  
Source Of Information

AbstractThe 2012 Emilia-Romagna earthquake, that mainly struck the homonymous Italian region provoking 28 casualties and damage to thousands of structures and infrastructures, is an exceptional source of information to question, investigate, and challenge the validity of seismic fragility functions and loss curves from an empirical standpoint. Among the most recent seismic events taking place in Europe, that of Emilia-Romagna is quite likely one of the best documented, not only in terms of experienced damages, but also for what concerns occurred losses and necessary reconstruction costs. In fact, in order to manage the compensations in a fair way both to citizens and business owners, soon after the seismic sequence, the regional administrative authority started (1) collecting damage and consequence-related data, (2) evaluating information sources and (3) taking care of the cross-checking of various reports. A specific database—so-called Sistema Informativo Gestione Europa (SFINGE)—was devoted to damaged business activities. As a result, 7 years after the seismic events, scientists can rely on a one-of-a-kind, vast and consistent database, containing information about (among other things): (1) buildings’ location and dimensions, (2) occurred structural damages, (3) experienced direct economic losses and (4) related reconstruction costs. The present work is focused on a specific data subset of SFINGE, whose elements are Long-Span-Beam buildings (mostly precast) deployed for business activities in industry, trade or agriculture. With the available set of data, empirical fragility functions, cost and loss ratio curves are elaborated, that may be included within existing Performance Based Earthquake Engineering assessment toolkits.

Fragility Analysis of Reinforced Masonry Shear Walls

2012 ◽  
Vol 28 (4) ◽  
pp. 1523-1547 ◽  
Author(s):  
Juan Murcia-Delso ◽  
P. Benson Shing
Keyword(s):  
Shear Walls ◽  
Fragility Functions ◽  
Damage State ◽  
Shear Damage ◽  
Drift Ratio ◽  
Reinforced Masonry ◽  
Specific Loading ◽  
Story Drift ◽  
Damage States ◽  
Story Building

Fragility functions have been developed to evaluate the damageability of fully grouted and partially grouted reinforced masonry shear walls subjected to in-plane seismic loading. Six damage states are considered, representing different levels of flexure, diagonal shear, and sliding shear damage. For each damage state, two classes of fragility functions have been developed. One has the story-drift ratio as the demand parameter. The other uses normalized demand parameters that account for the specific loading condition and design details of a wall component. All the fragility functions are derived from experimental data except for those developed for partially grouted walls and the sliding shear damage state. With both classes of fragility functions, the seismic damageability of flexure-dominated cantilever reinforced masonry shear walls in a four-story building has been assessed. It has been shown that the normalized flexural demand parameter provides a better correlation to the degree of damage developed in a wall than the story-drift ratio.

scholarly journals Creating Fragility Functions for Performance-Based Earthquake Engineering

2007 ◽  
Vol 23 (2) ◽  
pp. 471-489 ◽  
Author(s):  
Keith Porter ◽  
Robert Kennedy ◽  
Robert Bachman
Keyword(s):  
Expert Opinion ◽  
Professional Practice ◽  
Earthquake Engineering ◽  
Damage Analysis ◽  
Fragility Functions ◽  
Fragility Function ◽  
Applied Technology ◽  
Engineering Demand Parameter ◽  
Performance Based Earthquake Engineering ◽  
First Time

The Applied Technology Council is adapting PEER's performance-based earthquake engineering methodology to professional practice. The methodology's damage-analysis stage uses fragility functions to calculate the probability of damage to facility components given the force, deformation, or other engineering demand parameter (EDP) to which each is subjected. This paper introduces a set of procedures for creating fragility functions from various kinds of data: (A) actual EDP at which each specimen failed; (B) bounding EDP, in which some specimens failed and one knows the EDP to which each specimen was subjected; (C) capable EDP, where specimen EDPs are known but no specimens failed; (D) derived, where fragility functions are produced analytically; (E) expert opinion; and (U) updating, in which one improves an existing fragility function using new observations. Methods C, E, and U are all introduced here for the first time. A companion document offers additional procedures and more examples.

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