Fragility curves

The fragility is the failure probability of a component conditioned on parameters, such as Stress, moment, or spectral acceleration. 

A fragility curve for a component is calculated by knowing the conditions that will fail it. These conditions are calculated, deterministically by a structure analyst. The PSA specialist determines the variability of the conditions which together gives the probability of failure vs acceleration forces for given operating conditions, A separate fragility curve is needed for each mode that must to be considered. 

For example, Table 5.1-3. shows that a motor-operated valve can fail in several ways. 

Failure of power or controls to the valve (generally related to the seismic capacity of the cable trays, control room, and emergency power). These failure modes are analyzed as failures of separate systems linked to the equipment since they are not related to the specific piece of equipment (i.e., a motor-operated valve) and are common to all active equipment. 

Analysis may show one mode of failure to be most likely in which case further analysis conteiunilcs on ihat mode thereby considerably reducing the scope of the analysis. If there are several etiiiallv likely modes, they must all be analyzed. 

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The entire fragility curve and its uncertainty can be expressed by only three parameters , ... 

P R, and p u. With the limited data available on component fragility, it is neces.sary to estimate these parameters rather than the entire shape of the fragility curve and its uncertainty. 

Using fire models, locations of equipment, heat transfer calculations, and environmental qualifications of the equipment, it is possible to estimate the time to failure. Fragility cuives that relate fire durations and equipment damage while considering the probability of fire suppre.ssion are produced to relate to the overall PSA. These fragility curves and their use is simitar the methods ised for seismic analysis. 

Figure 6-2. Osmotic fragility test (Parpart method). A typical osmotic fragility curve of fresh (left) or 24-hour incubated (right) erythrocytes from a patient with HS is shown. The hatched area represents the normal range.

Determine the fracture probability of structures and components. This is rather conventionally undertaken using fragility curves which relate the conditioned probability of fracture with the maximum acceleration of the component/struc-ture. The simplification introduced by the fragility curves consists in the fact that they are supposed to depend on three parameters only a median rupture acceleration, /, and two logarithmic standard deviations (log-normal distribution), Par and Pav, related to the intrinsic variability of the component behaviour and to the variability... 

Mosleh, A. Apostolakis, G. 1986. The Assessment of probability distributions from expert opinions with an application to Seismic Fragility Curves. Risk Analysis, 6, No. 4 447 61. 

Figure 6. Fragility curves for windows, slider, entry door and exterior wall for a given apartment type. 

Erberik MA (2008) Generation of fragility curves for Turkish masonry buildings considering in-plane failure modes. Earthq Eng Struct Dyn 37 387-405... 

Empirical fragility curves for European-type RC building populations are derived in their study based on a data bank of 99 post-earthquake damage distributions observed in 19 earthquakes and concerning a total of 340,000 RC stmctures. The heterogeneous observational data are reinterpreted in terms of a damage scale. 

In a post-event situation, one of the most important problems that intervention teams face is finding not necessarily the shortest path, but the quickest or the safest path between locations, for example between the conunand centres such as the Prefecture or the Fire Department headquarters and the affected areas, and from there to the hospitals or to other similar facilities. In the inunediate circumstances after an earthquake, there are not enough data to precisely know the damage state of buildings or lifeline systems from an existing infrastructure, but one can estimate the damage probabilities based on fragility curves. 

Fragility curves of different structures or structural elements, also known as damage functions, are used to approximate structural damage from natural hazards. They represent a measure of vulnerability or an estimate of overall seismic risk, developed so far by using different methods such as heuristic, empirical, analytical ones or a combination of these. 

Immediately after an earthquake, there could be not enough data to help the intervention teams, therefore the probabilities from the fragility curves can be used... 

In a previous work (Leon and Atanasiu 2(X)7), we noticed that many fragility curves have a typical shape, similar to a sigmoid function. Through regression, we estimated them with this simplified analytical model which takes into account only one coefficient ... 

For the same value of PGA (in this case 0.2g), one can see that the results are different. The overall aspect of the two trials is similar most buildings are not affected. However, there are some changes buildings that are not affected in one trial can have minor or moderate damage in the other trial, depending on the fragility curves. 

Additional dotted sdsmic assessments of the IMsassembly Basin were not performed. Rather, a sheening was performed to detemime what stnietures and components would be inq>ortant in preventing or mitigatiDg the accident conditions considered in the basin risk assessment A qualitative assessment was then made as to the vulnerability of those structures and components. Based on similarities to structures and components considered in the reactor seismic PRA, fragility curves were assigned to those components (Ref 8-33). 

Examples include containment failure modes (early versus late), fragility curves, and failure mechanisms... 

Figure 5 Fragility curves (a) Slight, (b) Moderate, (c) Extensive and (d) Complete structural damage states.

The definition of the fragility curve for containment of a Nuclear Power Plant (NPP) generally represents a crucial step for the level 2 probabilistic safety assessment (PSA L2), where the probability of containment failure can be evaluated as the convolution of the fragility curve with the load curve (SSG-4). The assessment of the structural strength of the containment of a nuclear power plant has acquired even a greater importance in the framework of post-Fukushima stress tests where the assessment of the safety margin and off-design conditions. 

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