Physical Vulnerability

How are the products of relevance?

Seismic vulnerability functions represent the probabilistic relationship between seismic shaking intensity and cost of repair for a particular asset (building) or asset class (category of buildings). Seismic fragility functions on the other hand represent the relation between shaking intensity and the probability of reaching or exceeding a certain limit state – a condition beyond which a structure no longer fulfills the relevant design criteria – such as collapse.

Both are of key importance in estimating the probability of damage or loss caused in the event of an earthquake. Bringing all functions together in a single dataset, with guidelines for applications, as well as present methods for creation of new functions where they are currently lacking, has not yet been done before on a global scale.

In a nutshell

The following will become available to facilitate both direct application of fragility and vulnerability functions throughout the globe, as well as development of additional functions for use in local contexts.

  • Empirical vulnerability compendium; a global dataset of 23 empirical vulnerability and 135 empirical fragility functions
  • Empirical guidelines on how to derive vulnerability functions based on empirical data (for example post-earthquake damage data)
  • Damage scales; analysis of damage scales and harmonized damage scale that can be applied globally
  • Analytical vulnerability compendium; a dataset consisting of 5000 HAZUS-based vulnerability functions for 128 building types and 33 occupancy classes
  • Analytical fragility compendium; a global dataset that contains 154 sets of analytical fragility functions
  • Analytical structural guidelines on how to derive vulnerability functions using analytical methods for damage related to the structure itself
  • Analytical content guidelines on how to derivevulnerability functions using analytical methods for damage to structures that feature a contents with a higher value than the structure itself, such as hospitals and research labs
  • Analytical nonstructural guidelines on how to derive vulnerability functions using analytical methods for damage related to non-structural elements of a building, for example electrical installations, ceilings, etc.
  • Expert opinion procedures on rating expert’s ability to estimate past seismic performance of buildings
  • Casualty guidelines on estimation of earthquake-induced fatalities and non-fatal injuries that includes a proposed set of fatality rates for 31 ‘global’ building types
  • Empirical National Vulnerability; renewed earthquake fatality rate models and the first economic loss estimation model for global application, accompanied by guideline documents
  • Various uncertainty white papers that facilitate proper treatment of uncertainty and feature methods for Bayesian updating of existing vulnerability functions with new empirical information

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Who are developing the functions and methods?

The project features many experts from around the globe. Coordinated by Keith Porter, the project features as co principal investigators Anne Kiremidjian, Emily So, Dina D’Ayala, Tiziana Rossetto and Kishor Jaiswal. The following presents a complete overview of project collaborators:

Innovations in methods and approaches


GA, Standford, UCL

  • Systematic method for determining mean empirical curves; quantifying uncertainty
  • Incorporating uncertainty in intensity measure(s) into vulnerability



  • Treat brittle & ductile systems; flexible structural analysis procedures
  • PEER/ATC 58 “light” method with 3 levels of uncertainty propagation

Expert opinion, empirical-national


  • Cooke’s method to weight experts
  • Casualties (USGS & Cambridge)
  • Rates for 30 building types from 25 earthquakes since 1972



  • Kernel smoothing for uncertain intensity measure and loss
  • Bayesian updating method


Empirical vulnerability compendium

The compendium contains 23 vulnerability and 135 fragility relationships constructed mainly from sing-event databases for reinforced concrete and masonry buildings located in Japan, Southern Europe, Turkey and the United States.

Empirical Guidelines

  • 2 levels of detail in data, 3 levels of complexity for the curve derivation
  • Incorporate uncertainty in the shaking intensity, the spatial correlation of data
  • Include procedures for the combination of different databases
  • Propose a range of parametric and non-parametric regression techniques, which can be selected according to the nature of the damage or loss data
  • Include diagnostic procedures that can identify the optimum regression model for these data
  • Example applications include Irpinia 1980 (by UCLa), two Australian Earthquakes (by Geoscience  Australia) and the 2011 Christchurch Earthquake NZ (nonstructural vulnerability by University of Adelaide)

Damage Scale

Guide for conversion from damage to loss in indirect vulnerability curve. The guide includes a full review of damage scales, a damage scale rating system, review and summary of existing damage factors.


Compendium of (existing) analytical vulnerability curves

5000 HAZUS-based vulnerability functions for 128 building types and 33 occupancy classes

Compendium of (existing) analytical fragility curves

  • 154 sets of fragility curves
  • 20 earthquake prone countries
  • 7 broad material types
  • 3 height ranges

The dataset has undergone extensive review: building characteristics have been quality-checked, material and geometry are reviewed on representativeness, classification according to GEM Building Taxonomy has been reviewed from a rationality viewpoint and the document quality of the various fragility parameters has been investigated.

Collected fragility curves by country

Collected fragility curves by country

Material Types

Material Types


Analytical structural guidelines

The guideline provide support for the different approaches to modelling of structures and the subsequent derivation of fragility functions.

These 3 approaches are explained in detail, guidance is provided on how to apply them and what factors to take into account, considering also effort and uncertainty. One approach is proposed as the default.

Further guidance is provided on different options for modelling of structures:

Analytical content guidelines

  • Simplified version of PEER/ATC-58 PBEE-2
  • 8 categories, all acceleration-sensitive (analyst can add more)

In further detail:

  1. Define asset class with 1 or 3 index buildings
  • Stories, structural material, LLRS
  • Quantities of 8 categories (analyst can add categories)
  • 3 restraint categories
  1. Story-level vulnerability function
  • Lognormal fragility functions, default params provided
  • Damage state: replace
  • Integrate damage-state pmf and unit costs for story-level vulnerability
  1. Building-level vulnerability
  • Structural analysis per D’Ayala or defaults a la FEMA 695, ASCE 7
  • Includes non-collapse and collapse
  1. Mean vulnerability function and uncertainty
  • 2 levels of uncertainty treatment

Analytical nonstructural guidelines

  • Simplified version of PEER/ATC-58 PBEE-2
  • Hundreds of categories, drift or acceleration-sensitive (analyst can add more)

In further detail:

  1. Define asset class with 1, 3, or 7 index buildings
  • Stories, structural material, LLRS…
  • Quantities of up to 6 top categories
  • Vulnerability function factored up later to account for partial inventory
  1. Story-level vulnerability function
  • Lognormal fragility functions, default parameters provided
  • Fragility functions and repair costs per ATC-58 with local adjustment
  • Integrate damage-state PMF and unit costs for story-level vulnerability
  1. Building-level vulnerability
  • Combine story functions using structural response per defaults using FEMA 695, ASCE 7 and generalized mode shape; or by 2D or 3D
  1. Mean vulnerability function and uncertainty
  • 3 options for uncertainty propagation up to moment matching and MCS

Expert Opinion Procedures

The Collapse Fragility Modeling Process consists of 3 phases:

  1. Analyze responses to seed questions
  2. Analyze responses to target questions
  3. Generate fragility functions

To develop the process, USGS and EERI successfully conducted a structured expert elicitation workshop in September 2012, featuring 13 leading experts from around the globe that offered judgments on collapse fragility of six masonry and six reinforced concrete building types. Cooke’s method was applied to first solicit and then combine multiple judgments to produce seismic fragility models. The outcome was as follows:

Casualty and Fatality

Casualty Guidelines

  • Empirical fatality data related to predominant structural class, population, occurrence time, and well-documented building collapses from 25* significant earthquakes since 1972 (*account for > 70% of earthquake deaths during this period)
  • Detailed investigations relating collapse and volume reduction yielded important clues related to the lethality of different failure mechanisms in modern and older construction types
  • Presents a set of judgment-based rates for 30 global building types; which represents a significant advancement 

Empirical National Vulnerability

  • Updated empirical-national earthquake fatality models for the globe, based on USGS/PAGER work
  • First, globally applicable, direct shaking-induced economic loss estimation model, with the help of Munich Re’s NatCAT economic loss database
  • Improvement of existing models in terms of incorporating recent well-studied earthquakes, modelling hazard uncertainties through calibration, and improving ad-hoc regionalization schemes