MODEL VULNERABILITY Author: Mohammad Zolfaghari CatRisk Solutions

Transcription

1 BACKGROUND A catastrophe hazard module provides probabilistic distribution of hazard intensity measure (IM) for each location. Buildings exposed to catastrophe hazards behave differently based on their structural characteristics. In probabilistic terms such dependencies are formulated in the following form: Risk = Hazard x Asset_Value x Asset_Vulnerability All the terms in this relationship are in fact probabilistic variables. Risk is defined as adverse consequences; in insurance terms, represented by severity and frequency of financial losses. Hazard is also represented by severity and frequency of potentially damaging forces on the structure and therefore probabilistic. There are various sources of uncertainties which result in variation of buildings response to hazard. VULNERABILITY VS. FRAGILITY FUNCTIONS Structural behavior to catastrophe hazards are described by either Fragility or Vulnerability terms. The differences between these two terms are on the definitions used to describe degree of damage suffered by building; vulnerability looks at financial consequences and fragility looks at percentage of loss. One of the first systematic attempts of developing building vulnerability was carried out by ATC- 13, in which qualitative levels where used to represent damage levels to buildings, called damage stages (e.g. Slight Damage, Moderate Damage, to Collapse). The results were presented as a series of Damage Probability Matrix (DPM) for various building taxonomies in California. The matrixes were presenting probability distribution of damage stages for each intensity measure. Further empirical and analytical studies on seismic damage followed the same classifications of damages stages. Fragility functions were defined as cumulative probability functions of intensity measure (e.g. MMI) for each damage stage. On the other hand vulnerability functions used for assessment of monetary losses to buildings, represent continues dependency of damage ratio vs. intensity measures. As a measure of damage level in vulnerability functions, damage ratio in quantitative nature and directly related to monetary loss are used. Fragility functions at best provide CDF of Intensity for each qualitative physical damage to the building, however, to use such curves for loss estimation, one needs to assign monetary losses to each damage stage. This in turn highlights a big gap between all empirical/analytical researches on the fragility study and what catastrophe model require which is vulnerability functions. Development and application of fragility curves for the purpose of qualitative risk assessment or for measuring efficiency of structural retrofitting are well established in the engineering community. However, for insurance loss estimation, vulnerability functions are required. There are many studies and guidelines on converting fragility functions to vulnerability curves (e.g. ). For seismic risk assessment, building response to natural hazard should be expressed in terms of monetary losses which could be due to physical damage to the building, content damage, downtime, injuries and fatalities. 1

2 (a) Fragility curves corresponding to n =4 damage states (b) Column of a damage probability for intensity im ds 0 = No Damage; ds 1 = Slight Damage; ds 2 = Moderate Damage; ds 3 = Near Collapse; ds 4 = Collapse DEVELOPMENT METHODOLOGY In the early stage, very limited earthquake loss data were available and there was no acceptable analytical approach available for estimating building damages. However, with advanced structural analytical approach and fast computing power, numerous studies carried out on the estimation of building behavior to seismic loading. Incorporating uncertainties associated with seismic load or/and material behavior, many researchers have developed structural fragility curves for various type of buildings, all such studies provided structural response, usually measured by structural variables such as inter-story drift. Damages stages were then associated to structural response in order to develop fragility curves. In general, the following approaches are used to estimate response of building to seismic hazard. 1)expert-opinion- Although the information generated from these approaches may not be very reliable, it is the only viable option for developing loss models when information or resources are limited. ATC-13 (1985) is an example of such method. 2) observation-based on building damage data- The most direct approach of developing both fragility and vulnerability functions, based on building damage data observed in historical events. This approach requires damage data of large number of buildings for different construction classes, height, age and other characteristics. On the other hand, in countries were earthquake insurance premiums are in use, insurance claims data can provide large quantity of damage data, which can be used to develop new functions or calibrate existing functions. However, in order to develop fragility or vulnerability functions using observed damage data, it is also necessary to have information about hazard levels at each observed damage building to allow for further correlation. Such information is not always available and further assumptions of a proxy are involve which contribute to uncertainties of this approach. 3) analytical approach- The analytical approach involve use of structural analytical approach to assess performance of building subject to seismic load. These approaches provide fragility curve by the convolution of damage state given a demand parameter (EDP) and EDP given a hazard intensity. To derive vulnerability functions further convolution is needed to assess the repair cost of different building components associated with a damage state. 4) A combination of all above methods 2

3 CHOICE OF INTENSITY MEASURE Parameter selection representing an intensity measure is another factor in developing fragility/vulnerability functions regardless of the approaches taken to develop such functions. MMI, PGA and spectral acceleration are the most common parameters used as intensity measures for earthquake for example. For vulnerability functions based on expert opinion or observed data mostly MMI and PGA are used, while for those developed by analytical approaches, spectral acceleration is used as an intensity measure. COVERAGE CORRELATION Insurance losses in reality are driven not only by building damages but also due to damage to contents and those due to business interruption. There are also numerous studies on analytical approaches backed with experimental tests to develop vulnerability functions for contents. Similarly claim data and system engineering analyses are performed to assess BI vulnerability functions. Loss estimation to insurance policies with multi coverage (e.g. building and contents) requires aggregation of losses caused by all coverage which in turn highlight the issue of correlation between different coverage. There are approaches to implement coverage correlation in loss models, however, the real issues is how to identify and measure real correlation between different coverage which is quite a complex issue and in most cases specific to building type and even hazard levels. The next area to address in the practical use of catastrophe models is the link between the modelled hazard and its real-world effects, described as losses, on the assets exposed to the hazardous event. Vulnerability is the propensity of these assets to incur losses due to the assets' fragility, according to the following relationship: Vulnerability =F( FRAGILITY, LOSS Model) Vulnerability = Fragility = Loss Model = Equation 1: The components of vulnerability. Such relationships can be established in different ways: Empirically, using statistical regressions and models on the basis of data collected in previous events, which allow to determine a direct of correlation between the intensity of the event and the damage or losses incurred. Analytically, by developing numerical simulations able to provide a reliable physical description of the response of the assets to the hazardous event, also modelled 3

4 numerically. The physical damage, described in terms of engineering response indicators, is then converted into losses using probabilistic loss models. Heuristically, by relying on correlations between hazard intensity and damage or loss, based on observation and the direct experience of experts or a combination of the above. The type, volume and detail of the input data necessary to produce vulnerability and risk functions is highly dependent on the derivation method highlighted above, while the reliability of the function is dependent on the quality, extent and compatibility of the data collected. VULNERABILITY INPUT DATA The likely amount of catastrophic damage at a specific site can be estimated if we are in possession of certain facts. In the case of buildings, construction information such as design, materials, quality of construction and inspection, etc. will give approximate figures depending on the severity of the catastrophe. This information is often limited, however, and therefore assumptions become a necessity. There are also many other random variables to consider, such as whether the building has had a change of use. An office or industrial property may have been retrofitted for use as a residential building. Load-bearing walls may have been interfered with and the contents will certainly be different, all of which change the behaviour of a building. DATA TYPES Three types of information are considered in combination when assessing vulnerability: 1. Empirical information. For a considerable number of years now the scientific and catastrophe modelling community has collected detailed data following catastrophic events. To be of use, information about factors such as wind load or intensity, and detailed information on damage and building type must be collated. This level of data gathering has considerable value as it reduces some of the uncertainty shown in the more theoretical approaches. Empirical information, however, often consists of claims data contaminated by the application of limits and deductibles, and it can therefore prove difficult to adequately extract the actual damage values. 2. Engineering consensus. Expert opinion is a mainstay in the production of vulnerability functions. For example one main source for the derivation of earthquake vulnerability curves is the non-profit research organisation the Applied Technology Council, established by the Structural Engineers Association, in California which is one of the few organisations to provide generic information on this type of damage. 3. Engineering reliability analysis. Computer-aided design (CAD) models analyse the exact components of buildings in order to ascertain the probabilities of various failure modes under specific circumstances. From the theoretical perspective this analysis is the most sound; however, the resulting fragility curves still have to be calibrated using actual loss data, which in many cases is insufficient. Another drawback is that it estimates the damage of an average structure, which does not account for the construction of the buildings in question being potentially better or worse than average. This is a relatively expensive method and so is mostly used for complex commercial or industrial buildings. 4

5 VARIATIONS BY HAZARD In exposure databases buildings are generally classified according to two principal criteria: the physical structural features that determine the response to the action of the specific hazard, and hence correlate to the physical level of damage experienced by the asset given a level of intensity of the hazardous event at the site, the physical and non physical features that determine the use and value of the asset, and hence correlate directly with the economic and non-economic losses linked to a given level of damage. It is important to note that the significance of some specific physical structural features of an asset will relate primarily or even exclusively to a particular hazard. For instance, the lateral load-resisting system of an asset would be a significant element in assessing the likely damage sustained during a seismic event, but of less interest when considering the effects of a flood. Similarly, when considering the second criterion, the type of building occupancy (i.e. residential, commercial, industrial, etc.) is crucial for seismic risk due to the sudden nature of the earthquake event, which usually prevents the timely evacuation of occupants and contents from buildings. When considering hazard events with a more gradual onset or higher likelihood of an advance warning, such as a tsunami or flood, some losses may be prevented or mitigated by proper evacuation procedures, reducing the significance of the exact nature of these potential losses. Whether both of these classes of parameters are available in a given database and for a given hazard depends to a large extent on the objectives of the risk analysis carried out, and on the method used (empirical/analytical). LIMITATIONS There are practical limitations on the resolution of data required by each model to ensure a reasonable assessment of the risk. In practice, CRESTA zone data (an internationally accepted method of accumulating exposures - generally along recognised political boundaries) is a practical minimum ex-usa, and county or zip code a minimum within the USA. Data that is coarser than this will cause the uncertainty of the results to be considerably increased, possibly to a level that might be considered unusable. Industry accord that location data should be kept at zip/postcode level has led to commensurate improvements in results. It is also important to note that it is not only the construction value of a risk that insurers and reinsurers need to know in order to accurately assess vulnerability, but also the replacement value. The rebuild costs can, and often do, increase following a disaster. Some policies include business interruption alongside contents and the structure itself and it is possible that, even if a building has no actual structural damage, the loss due to business interruption or contingency business interruption could be a total loss. This vulnerability - the unknown unknowns - has to be taken into account by the modeller and assumptions made to cover them as comprehensively as possible. 5

6 VULNERABILITY MODULE The likely amount of catastrophic damage at a specific site can be estimated if we are in possession of certain facts. In the case of buildings, construction information such as design, materials, quality of construction and inspection etc. will give approximate figures depending on the severity of the catastrophe. This information is often limited however and therefore assumptions become a necessity. There are also many other random variables to consider, such as whether the building has had a change of use. An office or industrial property may have been retrofitted for use as a residential building. Load-bearing walls may have been interfered with and the contents will certainly be different, all of which change the behaviour of a building. There are practical limitations however on the resolution of data required by each model to ensure a reasonable assessment of the risk. In practice, CRESTA zone data (an internationally recognised method of accumulating exposures - generally along recognised political boundaries) is a practical minimum ex-usa and county or zip code a minimum within the USA. Data that is coarser than this will cause the uncertainty of the results to be considerably increased, possibly to a level that might be considered unusable. Industry accord that location data should be kept at zip/postcode level has led to commensurate improvements in results. It is not only the construction value of a risk however that insurers and reinsurers need to know in the event of a catastrophe, but also the replacement value. The rebuild costs can, and often do, increase following a disaster. Some policies include business interruption alongside contents and the structure itself and it is possible that, even if a building has no actual structural damage, the loss due to business interruption or contingency business interruption could be a total loss. This vulnerability - the unknown unknowns - has to be taken into account by the modeller and assumptions made to cover them as comprehensively as possible. Three types of information in combination are considered: 1. Empirical information. For a considerable number of years now the scientific and catastrophe modelling community has collected detailed data following catastrophic events. To be of use, information about factors such as wind load or intensity, and detailed information on damage and building type must be collated. This level of data gathering has considerable value as reduces some of the uncertainty shown in the more theoretical approaches. Empirical information however often unfortunately consists of claims data contaminated by the application of limits and deductibles and it can be difficult therefore to adequately extract the damage values. 2. Engineering consensus. Expert opinion is a mainstay in the production of vulnerability functions. One main source for the derivation of earthquake vulnerability curves is the non-profit research organisation the Applied Technology Council, established by the Structural Engineers Association, in California which is one of the few organisations to provide generic information on this type of damage. 3. Engineering reliability analysis. Computer-aided design (CAD) models analyse the exact components of buildings in order to ascertain the probabilities of various failure modes under specific circumstances. From the theoretical perspective this analysis is the most sound; however, the resulting fragility curves still have to be calibrated using actual loss data, which in many cases is insufficient. Another drawback is that it estimates the damage of an average structure and the construction of the buildings in question may be better or worse than average. This is a relatively expensive method and so is mostly used for complex commercial or industrial buildings. 6

7 VULNERABILITY FOR INDUSTRIAL FACILITIES In the last years, vulnerability curves have become popular for assessing the structural capability of industrial structures with the best current practises being the use of non- linear dynamic, incremental dynamic and pushover analyses. In industrial risks, indirect losses are usually much greater when compared to direct losses and hence sometimes building characteristics can be ignored. The derivation of industrial vulnerability curves entails the classification of main production elements, the identification of dependencies and the elaboration of measurable variables. Available production data is subject to standardisation for consistency reasons, weighting which sets the relative importance of data to the overall vulnerability and aggregation which defines the final vulnerability data or range. Developed vulnerability functions are always subject to sensitivity checks and visualisation analysis and they are sources of epistemic uncertainty and expert judgement. MEMORANDUM Vulnerability for industrial facilities Authors: Alkis Daskaloudis / Barnali Ghosh A vulnerability curve expresses the likelihood of damage when a risk (buildings/ infrastructure) is subjected to natural (floods, storms, earthquakes) or man-made (terrorism, political risk) disasters. Vulnerability curves are in general specific to risk, location, coverage type and building characteristics. They can be derived through analytical, empirical or hybrid processes and they define damage states in which certain failures are likely to be observed under specific ranges of loads. Vulnerability is a function of direct losses (physical damage to buildings and contents) and indirect losses (due to production disruption). The outcome of vulnerability functions can be used for a variety of business or academic purposes such as emergency response planning, risk mitigation and disaster management. In the last years, vulnerability curves have become popular for assessing the structural capability of industrial structures with the best current practises being the use of non- linear dynamic, incremental dynamic and pushover analyses. In industrial risks, indirect losses are usually much greater when compared to direct losses and hence sometimes building characteristics can be ignored. The derivation of industrial vulnerability curves entails the classification of main production elements, the identification of dependencies and the elaboration of measurable variables. Available production data is subject to standardisation for consistency reasons, weighting which sets the relative importance of data to the overall vulnerability and aggregation which defines the final vulnerability data or range. Developed vulnerability functions are always subject to sensitivity checks and visualisation analysis and they are sources of epistemic uncertainty and expert judgement. 7