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

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 e