[1] While permeability scaling of fractured media has been so far studied independently at the fracture-and network-scales, we propose a numerical analysis of the combined effect of fracture-scale heterogeneities and the network-scale topology. The analysis is based on 2Á10 6 discrete fracture network (DFNs) simulations performed with highly robust numerical methods. Fracture local apertures are distributed according to a truncated Gaussian law, and exhibit self-affine spatial correlations up to a cutoff scale L c . Network structures range widely over sparse and dense systems of short, long or widely distributed fracture sizes and display a large variety of fracture interconnections, flow bottlenecks and dead-ends. At the fracture scale, accounting for aperture heterogeneities leads to a reduction of the equivalent fracture transmissivity of up to a factor of 6 as compared to the parallel plate of identical mean aperture. At the network scale, a significant coupling is observed in most cases between flow heterogeneities at the fracture and at the network scale. The upscaling from the fracture to the network scale modifies the impact of fracture roughness on the measured permeability. This change can be quantified by the measure a 2, which is analogous to the more classical power-averaging exponent used with heterogeneous porous media, and whose magnitude results from the competition of two effects: (i) the permeability is enhanced by the highly transmissive zones within the fractures that can bridge fracture intersections within a fracture plane; (ii) it is reduced by the closed and low transmissive areas that break up connectivity and flow paths.

[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,

[1] We present a theoretical and numerical study of the connectivity of fracture networks with fractal correlations. In addition to length distribution, this spatial property observed on most fracture networks conveys long-range correlation that may be crucial on network connectivity. We especially focus on the model that comes out relevant to natural fracture network: a fractal density distribution for the fracture centers (dimension D) and a power law distribution for the fracture lengths (exponent a, n(l) $ l Àa ). Three different regimes of connectivity are identified depending on D and on a. For a < D + 1 the length distribution prevails against fractal correlation on network connectivity. In this case, global connectivity is mostly ruled by the largest fractures whose length is of the order of the system size, and thus the connectivity increases with scale. For a > D + 1 the connectivity is ruled by fractures much smaller than the system size with a strong control of spatial correlation; the connectivity now decreases with system scale. Finally, for the self-similar case (a = D + 1), which corresponds to the transition between the two previous regimes, connectivity properties are scale invariant: percolation threshold corresponds to a critical fractal density and the average number of intersections per fracture at threshold is a scale invariant as well.

[1] We investigate if a mean equivalent flow model can be defined to describe hydraulic head variations in a crystalline aquifer characterized by multiscale heterogeneity. We analyzed in particular the hydraulic response of a crystalline aquifer to pumping tests covering a large range of spatial and temporal scales. Pumping tests appear to be well designed to test the medium hydraulic properties and to track scaling effects, since the perturbation induced by pumping grows with time and samples increasingly large volumes. We tested well-test interpretation frameworks underpinned by equivalent media models that basically contain scaling information. Interpretations of drawdown time series, recorded in piezometers located at distances ranging from 2 to 400 m from the pumping well and of durations ranging from 5 to 90 days, show that the temporal evolutions of drawdown are well modeled by fractional flow models [Barker, 1988;Acuna and Yortsos, 1995]. Estimates of flow dimensions are consistent across the whole site and lie in the range [1.4-1.7]. To investigate the nature of diffusion, we defined a methodology based on the evolution of the characteristic time or amplitude of hydraulic head variations with the distance from the pumping well. For most of the piezometers, those aligned along the main fault, it is possible to define a scaling law for all piezometers with a unique set of parameters. The derived exponents imply that hydraulic head diffusion is anomalously slow, a characteristic that is taken into account only in the model of Acuna and Yortsos [1995], based on diffusion in fractals.

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.

The French critical zone initiative, called OZCAR (Observatoires de la Zone Critique-Application et Recherche or Critical Zone Observatories-Application and Research) is a National Research Infrastructure (RI). OZCAR-RI is a network of instrumented sites, bringing together 21 pre-existing research observatories monitoring different compartments of the zone situated between "the rock and the sky," the Earth's skin or critical zone (CZ), over the long term. These observatories are regionally based and have specific initial scientific questions, monitoring strategies, databases, and modeling activities. The diversity of OZCAR-RI observatories and sites is well representative of the heterogeneity of the CZ and of the scientific communities studying it. Despite this diversity, all OZCAR-RI sites share a main overarching mandate, which is to monitor, understand, and predict ("earthcast") the fluxes of water and matter of the Earth's near surface and how they will change in response to the "new climatic regime." The vision for OZCAR strategic development aims at designing an open infrastructure, building a national CZ community able to share a systemic representation of the CZ , and educating a new generation of scientists more apt to tackle the wicked problem of the Anthropocene. OZCAR articulates around: (i) a set of common scientific questions and cross-cutting scientific activities using the wealth of OZCAR-RI observatories, (ii) an ambitious instrumental development program, and (iii) a better interaction between data and models to integrate the different time and spatial scales. Internationally, OZCAR-RI aims at strengthening the CZ community by providing a model of organization for pre-existing observatories and by offering CZ instrumented sites. OZCAR is one of two French mirrors of the European Strategy Forum on Research Infrastructure (eLTER-ESFRI) project.

[1] Field observations have revealed that the diffusion properties of fractured materials are strongly influenced by the presence of fractures. Using power law fracture length and fracture permeability distributions currently observed on natural fractured networks, we model the equivalent permeability of two-dimensional (2D) discrete fracture networks by using numerical simulations and theoretical arguments. We first give the dependence of the network equivalent permeability, obtained at the scale of the network, on the characteristic power law exponents of the fracture length and fracture permeability distributions. We especially show that the equivalent permeability depends simply on the geometrical mean of the local fracture permeability distribution. Such networks are characterized by an increase of permeability with scale without limitations, provided that the fracture length and fracture permeability distributions are broad enough. Although a correlation length cannot be systematically defined, the flow structure is still characterized by simple properties. The flow is either extremely channeled in one dominant path or distributed in several separated structures. We show finally that the observed scale effects and flow structure are very different from the one obtained in the lognormal fracture permeability distribution case.

In fractured materials of very low matrix permeability, fracture connectivity is the first-order determinant of the occurrence of flow. For systems having a narrow distribution of object sizes (short-range percolation), a first-order percolation criterion is given by the total excluded volume which is almost constant at threshold. In the case of fractured media, recent observations have demonstrated that the fracture-length distribution is extremely large. Because of this widely scattered fracture-length distribution, the classical expression of the total excluded volume is no longer scale invariant at the percolation threshold and has no finite limit for infinitely large systems. Thus, the classical estimation method of the percolation threshold established in short-range percolation becomes useless for the connectivity determination of fractured media. In this study, we derive an expression for the total excluded volume that remains scale invariant at the percolation threshold and that can thus be used as the proper control parameter, called the parameter of percolation in percolation theory. We show that the scale-invariant expression of the total excluded volume is the geometrical union normalized by the system volume rather than the summation of the mutual excluded volumes normalized by the system volume. The summation of the mutual excluded volume (classical expression) remains linked to the number of intersections between fractures, whereas the normalized geometrical union of the mutual excluded volume (our expression) can be essentially identified with the percolation parameter. Moreover, fluctuations of this percolation parameter at threshold with length and eccentricity distributions remain limited within a range of less than one order of magnitude, giving in turn a rough percolation criterion. We finally show that the scale dependence of the percolation parameter causes the connectivity of fractured media to increase with scale, meaning especially that the hydraulic properties of fractured media can dramatically change with scale.