Hazard Identification
A hazard is a set of circumstances, possibly occurring within a given system, with the potential for causing events with undesirable consequences. For instance the hazard of a civil engineering system may be a set of circumstances with the potential to an abnormal action (e.g. fire, explosion) or environmental influence (flooding, tornado) and/or insufficient strength or resistance or excessive deviation from intended dimensions. In the case of a chemical substance, the hazard may be a set of circumstances likely to cause its exposure [2].
Hazard identification and modelling is a process to recognize the hazard and to define its characteristics in time and space. In the case of civil engineering systems the hazards Hi may be linked to various design situations of the building (as defined in [7]) including persistent, transient and accidental design situation. As a rule Hi are mutually exclusive situations (e.g. persistent and accidental design situations of a building). Then if the situation Hi occurs with the probability P{Hi}, it holds EP(Hi} = 1. If the situations Hi are not mutually exclusive, then the analysis becomes more complicated.
- Figure 2. Flowchart of iterative procedure for the risk assessment (adopted from [9]).
Note that in some documents (for example in the recent European document EN 1990 [10]) the hazard is defined as an event, while in risk analysis [2] it is usually considered as a condition with the potential for causing event, thus as a synonym to danger.
3 DEFINITION AND MODELLING OF RELEVANT SCENARIOS
Hazard scenario is a sequence of possible events for a given hazard leading to undesired consequences. To identify what might go wrong with the system or its subsystem is the crucial task to risk analysis. It requires detail examination and understanding of the system [6]. Nevertheless, a given system is often a part of a larger system. Consequently, modelling and subsequent analysis of the system is a conditional analysis.
The modelling of relevant scenarios may be dependent on specific characteristics of the system. For this reason a variety of techniques have been developed for the identification of hazards (e.g. PHA HAZOP) and for the modelling of relevant scenarios (fault tree, event tree/decision trees, causal networks). Detail description of these techniques is beyond the scope of this contribution, may be however found in [6, 9] and other literature.
4 ESTIMATION OF PROBABILITIES
Probability is generally the likelihood or degree of certainty of a particular event occurring during a specified period of time. In particular, reliability of a structure is often expressed as probability related to a specific requirement and a given period of time, for example 50 years [3,10].
Assuming that a system may be found in mutually exclusive situations Hu and the failure F of the system (e.g. of the structure or its element) given a particular situation Hi occurs with the conditional probability P{F|Hi}, then the total probability of failurepF is given by the law of total probability (see for example [11]) as:
Equation (1) can be used for the modification of the partial probabilities P{Hi}P{F|Hi} (appropriate to the situations Hi) with the aim to comply with the design condition pF < pt, where pt is a specified target probability of failure. The target value pt may be determined using the probabilistic optimisation of an objective function describing, for example, the total cost.
The conditional probabilities P{F|H;} must be determined by a detail probabilistic analysis of the respective situations Hi under relevant scenarios. The traditional reliability methods [8] assume that the failure F of the system can be well defined in the domain of the vector of basic variables X. For example, it is assumed that a system failure may be defined by the inequality g(x) < 0, where g(x) is the so called limit state function, where x is a realisation of the vector X. Note that g(x) = 0 describes the boundary of the limit state, and the inequality g(x) > 0 the safe state of a structure.
If the joint probability density fX(x|Hi) of basic variables Xgiven situation Hi is known, the conditional probability of failure P{F|H;} can be then determined [6] using the integral
It should be mentioned that the probability P{F|HJ calculated using equation (2) suffers generally from two essential deficiencies:
- uncertainty in the definition of the limit state function g(x),
- uncertainty in the theoretical model for the density function fX(x|Hi) of basic variables X [8].
These deficiencies are most likely the causes of the observed discrepancy between the determined probability pF and actual frequency of failures; this problem is particularly disturbing in case of fire. Yet, the probability requirement pF < pt is generally accepted as a basic criterion for design of structures.
In a risk analysis we need to know not only probability of the structural failure F but probabilities of all events having unfavourable consequences. In general, the situations Hi may cause a number of events Eij (e.g. excessive deformations, full development of the fire). The required conditional probabilities P{Eij\Hi} must be estimated by a separate analysis using various methods, for example the fault tree method or causal networks.
5 ESTIMATION OF CONSEQUENCES
Consequences are possible outcomes of a desired or undesired event that may be expressed verbally or numerically to define the extent of human fatalities and injuries or environmental damage and economic loss [1]. A systematic procedure to describe and/or calculate consequences is called consequence analysis. Obviously, consequences are generally not one-dimensional. However in specific cases they may be simplified and described by several components only, e.g. by human fatalities, environmental damage and costs. At present various costs are usually included only. It is assumed that adverse consequences of the events Ey can be normally expressed by several components Cy,k, where the subscript k denotes the individual components (for example the number of lost lives, number of human injuries and damage expressed in a certain currency).
6 ESTIMATION OF RISK
Risk is a measure of the danger that undesired events represent for humans, environment or economic values. Risk is commonly expressed in the probability and consequences of the undesired events. It is often estimated by the mathematical expectation of the consequences of an undesired event. Then it is the product "probability x consequences". However, a more general interpretation of the risk involves probability and consequences in a non-product form. This presentation is sometimes useful, particularly when a spectrum of consequences, with each magnitude having its own probability of occurrence, is considered [2].
The estimation of risk is the process used to produce an estimate of a measure of risk. As already stated above the risk estimation is based on the hazard identification and generally contains the following steps: scope definition, frequency analysis, consequence analysis, and their integration [2]. If there is one-to-one mapping between the consequences Cy,k and the events Ey, then the risk component Rk related to the considered situations Hi is the sum
If the dependence of consequences on events is more complicated than just one-to-one mapping, then equation (3) will have to be modified. A practical example of equation (3) can be found in [10], where an attempt to estimate the risk due to persistent and fire design situation is presented.
In some cases it is possible to deal with one-component risk R only. Then the subscript k in equation (2.3) may be omitted. Moreover, probability of undesired events may depend on the vector of basic variables X. Then the total risk R may be formally written as where R(x) denotes the degree of risk as a function of basic variables X, and fX(x) denotes joint probability density function X.
7 LOGIC TREES
A number of different logic (decision) trees (fault tree, event tree, cause/consequence chart) have been developed to analyse the risk of a system [11] to [13]. Applications of logic trees significantly improve the completeness and clarity of the engineering work. The use of this kind of tool is widespread in risk analysis and implies some important advantages. Influences of the environment and of human activities can easily be considered simultaneously. Logic trees can also enable the detection of the most effective countermeasures. Furthermore, they can be easily understood by inexperienced persons and therefore can provide very effective communication means between experts and public authorities.
The fault tree can be defined as a logical diagram for the representation of combinations of influences that can lead to an undesired event. When establishing a fault tree, the undesired
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