A model of fracture nucleation, growth and arrest, and consequences for fracture density and scaling

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Abstract
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.

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