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Publication# Approche mathématique de l'impact des sites contaminés sur les eaux souterraines dans un contexte d'analyse de risque

Abstract

The primary objectives of this thesis are, firstly, to develop analytical solutions for estimating the impact of contaminated sites (in particular landfills, and to a lesser extent accidentally contaminated soils) on groundwater, and secondly to evaluate methods for taking into account the uncertainty relative to the different relevant parameters. These developments are performed with particular reference to a risk analysis framework. One of the distinctive features of such a framework is the incomplete and uncertain nature of the information that is generally available in practice. This has a direct influence on the choice of tools and approaches. It is proposed, in the introductory chapter, to define risk as the likelihood that a damage may occur, thus avoiding the more frequently used term probability. The latter refers to a strictly statistical description of the uncertainty, and assumes a degree of knowledge with respect to the various relevant parameters that is not necessarily available in practice. A presentation of several risk analysis models underlines their respective areas of application. Chapter 2 presents analytical solutions for estimating the impact of contaminated sites on groundwater, several of which are original. The mathematical development of the original solutions is presented in detail in the appendix. The succession of proposed solutions goes from the simpler to the more complex, starting with solutions for a one-layer domain and one-, two- and three-dimensional contaminant migration, and then passing to solutions for a multi-layer domain. These solutions are presented in terms of dimensionless variables that allow the equations to be written in a compact fashion, and independently of any system of units. The dimensionless variables serve to construct type curves that provide a visual analysis of solution behaviour with respect to variations of input parameter values. The proposed original solutions are of particular interest for estimating the potential impact of waste disposal sites, as they take into account the effect of the diffusive-dispersive flux on the impact on groundwater. This component of the mass flux is generally either omitted by existing risk analysis tools, or else it is not truly coupled with the mass balance in the groundwater (via the boundary conditions). The proposed solutions are applied to several practical examples. The example involving the original solution developed for estimating the impact of a stabilized waste-disposal site, illustrates the solution's usefulness as an aid for site conception and design. The example also shows how, by providing a picture of the site's global performance with respect to its potential impact, the model can bring the designer to question some of his choices. Another example helps to clarify the concept of "equivalence" between different barrier systems. An original solution is also proposed for the problem of early contaminant detection using inorganic trace elements. A comparison with another approach proposed in the literature illustrates the limits of the latter. Chapter 3 addresses the question of how to take imperfection of knowledge into account in the calculations. Two methods for accounting for uncertainty with respect to input parameter values are described and compared. The first method is the Monte Carlo method, which relates to a statistical and probabilistic framework. The second method is based on the theory of possibilities and on so-called fuzzy calculus. The representation of the main model parameters (hydraulic conductivity, porosity, etc.) using fuzzy numbers rather than probability distributions, is often more consistent with the basic nature of the information that is available in practice. The comparison between the two methods, underlines the conservative character of the fuzzy approach. This is related to the fact that the calculation based on fuzzy numbers considers all possible combinations of fuzzy input parameter values, but does not transmit (through multiplication) the degrees of unlikelihood of the different values. In the Monte Carlo calculation, on the other hand, a scenario that combines low-probability values of the input parameters, has all the less chance of being randomly selected. Nevertheless, when the mere possibility that an unfavourable scenario may occur becomes an element of decision, the fuzzy approach may seem preferable. This situation can appear in an environmental context, where human health is often at stake. The examples presented herein contribute to introducing an "impact framework" to the management of contaminated sites. Such a framework tends to define the acceptability of choices with respect to the management of these sites, on the basis of a comparison between emitted pollutant fluxes and fluxes considered acceptable for the local environment. They also underline the usefulness of having a certain degree of freedom with respect to the choice of the conceptual model underlying the mathematical model, in order to provide reasonable appropriateness between the calculation tool and the various situations that might appear in practice. Existing risk analysis models are often difficult to apply to specific sites, due to the rigidity of their conceptual models. In some cases, these models are better described as tools for ranking chemical substances as a function of their contamination potential. Some of the original analytical solutions proposed herein can be readily incorporated into the "vector" module of a risk analysis tool.

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Related concepts (8)

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Risk management is the identification, evaluation, and prioritization of risks (defined in ISO 31000 as the effect of uncertainty on objectives) followed by coordinated and economical application of resources to minimize, monitor, and control the probability or impact of unfortunate events or to maximize the realization of opportunities.

Conceptual model

A conceptual model is a representation of a system. It consists of concepts used to help people know, understand, or simulate a subject the model represents. In contrast, a physical model focuses on a physical object such as a toy model that may be assembled and made to work like the object it represents. The term may refer to models that are formed after a conceptualization or generalization process. Conceptual models are often abstractions of things in the real world, whether physical or social.

Mathematical model

A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).