Fracture patterns observed in the field are not completely random and not completely ordered. Geostatistical techniques can be used to estimate the statistical parameters which describe the spatial variability of the fracturing. Data from the Fansy-Augères mine in France has been used as an example in developing these techniques.
Les distributions de fractures observees dans la nature ne sont ni complètement aleatoires ni complètement ordonnees. Les paramètres statistiques qui rendent compte de la variabilite spatiale de la fracturation peuvent être estimes en utilisant les techniques de la geostatistique. Cette approche a ete experimentee sur des donnees provenant de la mine de Fanay-Augères, en France.
Die in der Natur beobachteten Kloeftestukturen sind weder voellig zufaellignoch geordnet. Die Geostatistik-Methoden koennen benutzt werden, um die statistische Parametern abzuschaetzen, die die rauemliche variabilitaet der Kloefte beschreiben. Diese Methoden sind benutzt worden, um die Beobachtungen aus dem Bergwerk bei Fanay-Augères zu studieren.
To model the behavior of a fracture system, for example the flow through a fracture network, we first develop a conceptual model for the system. The conceptual model then forms the basis of a numerical model used to calculate the flow. A fracture network model may be stochastic in that we create a random realization of a fracture system which is conceptually and statistically similar to that observed in the field. A stochastic model is not a model of the specific fractures which actually exist. However, a stochastic model may be a conditional model where we adjust the stochastic process such that features we can observe are reproduced in the model and features we cannot observe are randomly generated. To make a stochastic model, we general1yspecify rules for generating fractures, rules for truncating fractures and distributions for the random parameters. The rules are derived from the conceptual model, the distributions are derived from field data. For example, a rule for generating fractures in two dimensions might be that fractures are randomly located. Thus, locating fractures in space is a Poisson process with a strength, λ A where λ A is the areal density of the fractures (number of fractures per unit area). Thus we pick A λ A points with random coordinates in the area, A. Now we provide an orientation distribution, f (θ) for choosing the lines through the center coordinates and a rule for truncating the lines. For instance, we might truncate the fractures where they intersect another fracture (Conrad and Jacquin, 1973; Dershowitz, 1984)or we might truncate the fractures such that they have some specified distribution of length, g(l) (Baecher et al. 1977). Fracture networks are often conceptualized as some type of Poisson process. That is, the fractures are said to occur randomly in space. However, real systems are not usually completely random. Often we are able to identify "swarms" of closely spaced subparallel fractures, or that fracture density varies from location to location. These and other non-Poisson characteristics comprise the spatial structure of fracture networks. The conceptual model chosen for a particular site should reflect the spatial structure of the site. For instance, one would model polygonal fracture patterns in the colonade of a basalt (Smalley, 1966). Many other conceptual-stochastic models have been proposed in the literature including Beecher (1977), Dershowitz (1984), Veneziano (1979), Conrad and Jaquin (1973) and LaPointe and Hudson (1981). The work described here is an attempt to develop a conceptual model for the fractures at Fanay-Augeres, a mine in the Massif Central in France, and determine the parameters of the appropriate statistical distributions from the field data. The final goal is to model the hydrologic behavior of the fracture network.
Fanay-Augeres is a uranium mine owned by Cogema Co. and located in Limousin, France in the granite massif of Saint-Sylvestre. For the past 7 years this mine has been used as a test facility to develop methods and tools for investigating mass and heat transfer in granitic rocks (Barbreau et al, 1985; Lassagne, 1983). In particular we have focused on the data collected in a long section of a drift, about 3m in diameter at the 320m level. In this section fractures on the East wall have been mapped over two sections, SI and S2, totaling 180m in length. For any fracture trace which intersected the 2m high rectangle the visible trace length, number of visible endpoints, orientation and morphology were recorded.
