The 31th U.S. Symposium on Rock Mechanics (USRMS),
1990. A. A. Balkema, Rotterdam. Permission to Distribute - American Rock Mechanics Association
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Rock fracture parameters such as size, attitude, spacing and shape vary in space in a way that can be practically described only in probabilistic terms. Stochastic fracture geometry models have been developed by Baecher, et al. (1977), Veneziano, (1979), Dershowitz, (1985), Long et al. (1985, 1987), Hestir et al., (1987) and La Pointe and Hudson (1985) among others. These models are not completely satisfactory because:
-They do not account for spatial nonhomogeneities such as fracture clustering (An exception is the parent/daughter model of Long et al., 1987).
-The models are only loosely tied to the geologic genesis of the fractures. In particular, most models assume independence among fracture sets. From a physical viewpoint, this assumption is often incorrect.
-Only in a few cases have the models been validated using actual fracture data.
A way to address these concerns is proposed here. The main features of our model are that fracture sets are described in a hierarchical order and dependencies among fractures of the same set or of different sets are accounted for. The sequential generation and correlation of fracture sets correspond to what happens in nature. Equally important as the modelling principle is the availability of statistical procedures to estimate parameters and validate the model. In its present form, the model is two-dimensional, i.e. it can be used to describe fracture trace patterns on outcrops. Some comments will be made at the end of the paper how to extend the hierarchical model. The model will be presented by first introducing the basic ideas and then developing the details, the latter simultaneously with showing an application to actual data.
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