J.K. Vrijling

An overview of quantitative risk measures for loss of life and economic damage.

A comprehensive overview of methods to quantify and limit risks arising from different sources is still missing in literature. Therefore, a study of risk literature was carried out by the authors. This article summarises about 25 quantitative risk measures. A risk measure is defined as a mathematical function of the probability of an event and the consequences of that event. The article focuses mainly on risk measures for loss of life (individual and societal risk) and economic risk, concentrating on risk measurement experiences in The Netherlands. Other types of consequences and some international practices are also considered. For every risk measure the most important characteristics are given: the mathematical formulation, the field of application and the standard set in this field. Some of the measures have been used in a case study to calculate the flood risks for an area in The Netherlands.

Acceptable risk as a basis for design

Abstract Historically, human civilisations have striven to protect themselves against natural and man-made hazards. The degree of protection is a matter of political choice. Today this choice should be expressed in terms of risk and acceptable probability of failure to form the basis of the probabilistic design of the protection. It is additionally argued that the choice for a certain technology and the connected risk is made in a cost-benefit framework. The benefits and the costs including risk are weighed in the decision process. A set of rules for the evaluation of risk is proposed and tested in cases. The set of rules leads to technical advice in a question that has to be decided politically.

Probabilistic design of water defense systems in The Netherlands

Abstract After the disaster in 1953, a statistical approach to the storm surge levels was chosen and an extrapolated storm surge level would be the basis for dike design. In recent decades, the development of reliability theory made it possible to assess the flooding risks taking into account the multiple failure mechanisms of a dike section and the length effect. It is pointed out that economic activity in the protected areas has grown considerably since the 1950s and that even more ambitious private and public investments, particularly in infrastructure, are planned. Moreover, the safety of a growing population is at stake. These considerations justify a fundamental reassessment of the acceptability of the flood risks.

A framework for risk evaluation

Human civilizations are threatened by natural hazards and by risks connected to technological progress in civil, chemical and nuclear engineering. The notion of acceptable risk forms the basis for the design of many engineering structures ranging from simple river levees to nuclear reactors, that contribute to human welfare. A frame work is developed to judge the acceptability of risks from an individual and a societal point of view.

Flood Risk Assessment in the Netherlands: A Case Study for Dike Ring South Holland

Large parts of The Netherlands are below sea level. Therefore, it is important to have insight into the possible consequences and risks of flooding. In this article, an analysis of the risks due to flooding of the dike ring area South Holland in The Netherlands is presented. For different flood scenarios the potential number of fatalities is estimated. Results indicate that a flood event in this area can expose large and densely populated areas and result in hundreds to thousands of fatalities. Evacuation of South Holland before a coastal flood will be difficult due to the large amount of time required for evacuation and the limited time available. By combination with available information regarding the probability of occurrence of different flood scenarios, the flood risks have been quantified. The probability of death for a person in South Holland due to flooding, the so-called individual risk, is small. The probability of a flood disaster with many fatalities, the so-called societal risk, is relatively large in comparison with the societal risks in other sectors in The Netherlands, such as the chemical sector and aviation. The societal risk of flooding appears to be unacceptable according to some of the existing risk limits that have been proposed in literature. These results indicate the necessity of a further societal discussion on the acceptable level of flood risk in The Netherlands and the need for additional risk reducing measures.

The estimation of extreme quantiles of wind velocity using L-moments in the peaks-over-threshold approach

Abstract The paper evaluates the effectiveness of the method of L-moments for estimating parameters of the Pareto distribution model of peaks over a sufficiently high threshold, and compares its performance against a widely used method of de Haan (de Haan L. Extreme value statistics. In: Galambos J, Lechner J, Simin E, editor. Extreme value theory and applications, vol. 1. 1994. p. 93–122). Monte Carlo simulations and actual wind speed data collected at various stations in the United States have been utilized in this study. In the de Haan method, the first two moments of peaks of log-transformed data are used for the parameter estimation, whereas the L-moment method utilizes linear combinations of expectations of order statistics of peaks in the original data. Despite the procedural differences, the paper shows that the de Haan and two L-moments based estimates of the tail shape parameter are in fairly close agreement in simulated data as well as in the US wind speed data. Furthermore, higher order estimates of the shape parameter are obtained using the L-skewness of peaks data. Such estimates appear to provide a more stable upper bound, which can be useful in identifying meaningful values of design quantiles.

Societal Risk and the Concept of Risk Aversion

It seems generally accepted that the FN-curve is a fairly accurate description of the societal risk. However in the communication with the public and representative decisionmakers a schematisation of the FN-curve to one or two numbers may bring certain advantages. Various measures like Potential loss of Life, the area under the FN-curve, the Risk Integral etc. are proposed in the literature. Although the formulae look distinctly different at first sight a more thorough inspection reveals, that all schematisations contain as building blocks the two familiar statistical moments of the FN-curve, the expected value of the number of deaths E(N) and the standard deviation σ(N). In the paper the linear combination E(N) + k.σ(N) is proposed as a simple risk averse measure of the societal risk.

Evaluation of tunnel safety: towards an economic safety optimum

The aim of this paper is to propose a method for the evaluation of tunnel safety using probabilistic risk assessment. The framework includes three criteria; personal-, societal- and economic risk. The use of personal and societal risk is becoming more and more widespread. There are however, still some difficulties in using the economic risk criterion. As a first step towards economic risk optimisation, the cost effectiveness of addition and removal of safety measures in tunnels is investigated. Finally, the application of the three proposed criteria is further discussed for some tunnelling projects currently underway in the Netherlands.

Probabilistic coastline position computations

The classical deterministic approach of the simulation of coastline development often gives unreliable results due to the uncertainty in the values of the coastal variables; in the input data of simulation models, and in the models themselves. With the probabilistic approach of the simulation, using probability distributions of the coastal variables and the model factors, it is possible to forecast coastline development with a chosen degree of certainty. In a design context one can calculate the failure probability of the planned coastal defence systems. Probabilistic methods have the additional advantage that the insight in the influence of coastal processes and of changes in variable values on intermediate coastline development will be enhanced. It is stressed that the existence of correlation between coastal variables influences the results considerably.

A general approach for the estimation of loss of life due to natural and technological disasters

Abstract In assessing the safety of engineering systems in the context of quantitative risk analysis one of the most important consequence types concerns the loss of life due to accidents and disasters. In this paper, a general approach for loss of life estimation is proposed which includes three elements: (1) the assessment of physical effects associated with the event; (2) determination of the number of exposed persons (taking into account warning and evacuation); and (3) determination of mortality amongst the population exposed. The typical characteristics of and modelling approaches for these three elements are discussed. This paper focuses on “small probability–large consequences” events within the engineering domain. It is demonstrated how the proposed approach can be applied to various case studies, such as tunnel fires, earthquakes and flood events.