[1] We argue that most fracture systems are spatially organized according to two main regimes: a "dilute" regime for the smallest fractures, where they can grow independently of each other, and a "dense" regime for which the density distribution is controlled by the mechanical interactions between fractures. We derive a density distribution for the dense regime by acknowledging that, statistically, fractures do not cross a larger one. This very crude rule, which expresses the inhibiting role of large fractures against smaller ones but not the reverse, actually appears be a very strong control on the eventual fracture density distribution since it results in a self-similar distribution whose exponents and density term are fully determined by the fractal dimension D and a dimensionless parameter g that encompasses the details of fracture correlations and orientations. The range of values for D and g appears to be extremely limited, which makes this model quite universal. This theory is supported by quantitative data on either fault or joint networks. The transition between the dilute and dense regimes occurs at about a few tenths of a kilometer for faults systems and a few meters for joints. This remarkable difference between both processes is likely due to a large-scale control (localization) of the fracture growth for faulting that does not exist for jointing. Finally, we discuss the consequences of this model on the flow properties and show that these networks are in a critical state, with a large number of nodes carrying a large amount of flow.Citation: Davy, P., R. Le Goc, C. Darcel, O. Bour, J. R. de Dreuzy, and R. Munier (2010), A likely universal model of fracture scaling and its consequence for crustal hydromechanics,

A major use of DFN models for industrial applications is to evaluate permeability and flow structure in hardrock aquifers from geological observations of fracture networks. The relationship between the statistical fracture density distributions and permeability has been extensively studied, but there has been little interest in the spatial structure of DFN models, which is generally assumed to be spatially random (i.e., Poisson). In this paper, we compare the predictions of Poisson DFNs to new DFN models where fractures result from a growth process defined by simplified kinematic rules for nucleation, growth, and fracture arrest. This so‐called “kinematic fracture model” is characterized by a large proportion of T intersections, and a smaller number of intersections per fracture. Several kinematic models were tested and compared with Poisson DFN models with the same density, length, and orientation distributions. Connectivity, permeability, and flow distribution were calculated for 3‐D networks with a self‐similar power law fracture length distribution. For the same statistical properties in orientation and density, the permeability is systematically and significantly smaller by a factor of 1.5–10 for kinematic than for Poisson models. In both cases, the permeability is well described by a linear relationship with the areal density p32, but the threshold of kinematic models is 50% larger than of Poisson models. Flow channeling is also enhanced in kinematic DFN models. This analysis demonstrates the importance of choosing an appropriate DFN organization for predicting flow properties from fracture network parameters.

[1] In order to improve discrete fracture network (DFN) models, which are increasingly required into groundwater and rock mechanics applications, we propose a new DFN modeling based on the evolution of fracture network formation-nucleation, growth, and arrest-with simplified mechanical rules. The central idea of the model relies on the mechanical role played by large fractures in stopping the growth of smaller ones. The modeling framework combines, in a time-wise approach, fracture nucleation, growth, and arrest. It yields two main regimes. Below a certain critical scale, the density distribution of fracture sizes is a power law with a scaling exponent directly derived from the growth law and nuclei properties; above the critical scale, a quasi-universal self-similar regime establishes with a self-similar scaling. The density term of the dense regime is related to the details of arrest rule and to the orientation distribution of the fractures. The DFN model, so defined, is fully consistent with field cases former studied. Unlike more usual stochastic DFN models, ours is based on a simplified description of fracture interactions, which eventually reproduces the multiscale self-similar fracture size distribution often observed and reported in the literature. The model is a potential significant step forward for further applications to groundwater flow and rock mechanical issues.Citation: Davy, P., R. Le Goc, and C. Darcel (2013), A model of fracture nucleation, growth and arrest, and consequences for fracture density and scaling,

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The topology of two discrete fracture network models is compared to investigate the impact of constrained fracture growth. In the Poissonian discrete fracture network model the fractures are assigned length, position and orientation independent of all other fractures, while in the mechanical discrete fracture network model the fractures grow and the growth can be limited by the presence of other fractures. The topology is found to be impacted by both the choice of model, as well as the choice of rules for the mechanical model. A significant difference is the degree mixing. In two dimensions the Poissonian model results in assortative networks, while the mechanical model results in disassortative networks. In three dimensions both models produce disassortative networks, but the disassortative mixing is strongest for the mechanical model.