Flow in multiscale fractal fracture networks
The paper aims at defining the flow models, including equivalent permeability, that are appropriate for multiscale fracture networks. As a prerequisite of the flow analysis, we define the scaling nature of fracture networks that is likely quantified by power-law length distributions whose exponent fixes the contribution of large fractures versus small ones. Despite the absence of any characteristic length scale of the power-law model, the flow structure appears to contain three length scales at the very maximum: the connecting scale, the channelling scale, and the homogenization scale, above which the equivalent permeability tends to a constant value. These scales, including their existence, depend on the fracture length distribution and on the transmissivity distribution per fracture. They are basic in defining the flow properties of fracture networks.
Figures & Tables
Fractal Analysis for Natural Hazards
In the Earth sciences, the concept of fractals and scale invariance is well recognized in many natural objects. However, the use of fractals for spatial and temporal analyses of natural hazards has been less used (and accepted) in the Earth sciences. This book brings together 12 contributions that emphasize the role of fractal analyses in natural hazard research, including andslides, wildfires, floods, catastrophic rock fractures and earthquakes. A wide variety of spatial and temporal fractal-related approaches and techniques are applied to ‘natural’ data, experimental data and computer simulations. These approaches include probabilistic hazard analysis, cellular-automata models, spatial analyses, temporal variability, prediction and self-organizing behaviour. The main aims of this volume are (a) to present current research on fractal analyses as applied to natural hazards and (b) to stimulate the curiosity of advanced Earth science students and researchers in the use of fractals analyses for the better understanding of natural hazards.