Hierarchical geometric-mechanical models attempt to capture the relations between the geometry of rock fracture systems and the underlying geologic mechanisms of fracturing. The two-dimensional enhanced hierarchical model can represent complex fracture trace patterns. Since two-dimensional representations of fracture patterns are insufficient for many applications, a three-dimensional hierarchical model is being developed. The model generates hierarchically related sets of fractures using a sequence of three stochastic processes: Poisson plane process, Poisson line process, and a combined translation-rotation process. The modeling that is presented in this paper is still geometric but relations to the underlying mechanisms are discussed as well.


Modeling of fracture systems for use in a number of engineering applications ranging from slope reliability analysis to analysis and design of foundations and tunnels on and in rock masses, to flow and transport in fractured rock masses has been the objective of many research efforts. In the opinion of the authors of this paper, one can group the fracture system models in three categories: 1. Mechanical Models; 2. Geometric Models; and 3. Combined GeometricMechanical Models.

From the point of view of engineers and scientists, mechanical modeling is the most desirable approach in that one tries to duplicate the actual fracture nucleation and propagation mechanisms which have acted throughout the geologic history, under varying applied stress conditions. However, so far, only relatively simple fracture patterns can be replicated by the mechanical models, be they experimentally or numerically based. In particular, the three dimensional characteristics and the often pervasive clustering can be modeled to a limited extent only. Further development is likely to lift some of these limitations. Prime examples of mechanical models are the models developed by the Stanford Group (see e.g. Wu and Pollard 1992).

Purely geometric models, often called conceptual models, are the most widely used category. Geometric modeling started with statistical evaluation of pole diagrams for orientation on the one hand, and the development of simple deterministic block or wedge models on the other hand. Today a wide variety of stochastic models exist. Many of them are threedimensional and capture, at least to a certain extent, the clustering of geometric fracture characteristics. Since they simulate what is observed rather than what caused the fracture pattern, it is not easy to produce complete representations from the usually available information such as boreholes and outcrops. Examples of advanced geometric models are the conceptual models incorporated in the commercially available software package FracMan (Dershowitz et al. 1993).

Combined geometric-mechanical models consist of geometric modeling procedures which attempt to duplicate typical. 'mechanical processes. Examples are the model by Martel et al. (1991) in which fractal-like objects are created in two dimensions using so called Iterated Function Systems conditioned on geologic information, and the two-dimensional Hierarchical Model developed at MIT (see e.g. Lee et al. 1990). In the latter, the hierarchy of fracture genesis is modeled by creating fracture sets in sequence and by incorporating dependencies (or independencies if applicable) between different fracture sets in this process.

In our developments at MIT we worked originally on purely geometric models (e.g. Baecher et al. 1977; Veneziano 1978) and simultaneously looked into the mechanical aspects of fracture behavior (Einstein et al. 1983). However, the latter involved engineering application rather than an inv

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