Thèse de doctorat en Sciences de la Terre
Sous la direction de Philippe Davy.
Soutenue en 2002
à Rennes 1 .
Developments performed during the last decades in the domain of hydraulic and transport properties modeling of fractured media have been mainly motivated by the current problematic about nuclear repositories safety. The understanding of the complex hydraulic behavior of fractured media is tackled here through a direct representation of the fracture network geometry and through a discrete stochastic modeling process. In that context, our work is focused on the notion of spatial correlations. Firstly spatial correlations are identified. Then a model of discrete fracture network is developed and finally the consequences of spatial correlations on hydraulic properties of fractured media are determined. Natural fracture patterns often display an heterogeneous spatial density distribution which can be characterized by a fractal dimension D. In addition we show that fracture lengths and positions are also organized such that around each fracture there exists on average a shield (empty of other fractures) whose area is correlated to the fracture length. A stereological analysis shows that the fractal dimension of a 3D fracture pattern is simply related to the apparent fractal dimension measured on a lower dimensional sample of the fracture network. The model of fracture network considered is fractal (D) and its fracture length distribution is a power law (a). For 2D fracture networks, the type of global behavior depends on the relative values of a and D. Indeed, a strong fractal correlation (D low) induces a decrease of the global network connectivity when the observation scale increases. On the contrary, a decrease of a induces an increase of the connectivity with scale. When a=D+1 (self-similar case), both effects exactly compensate and the connection state is independent of the observation scale. In that case, we show that, although the flow remains channeled at high densities as long as D<2, the evolution of the permeability with scale is weakly dependent on D. At last, we show that the fractal dimension associated with 2D fracture networks tends to decrease the connectivity with increasing scale. When the deconnexion effect is compensated by the length distribution, the evolution of the permeability with scale is weakly sensible to variations of D, although flow is channeled. On the contrary we expect a stronger influence of the parameter D on the transport properties.
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