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

International audienceIn 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

Which fractures are imaged with Ground Penetrating Radar? Results from an experiment in the Äspö Hardrock Laboratory, Sweden

Identifying fractures in the subsurface is crucial for many geomechanical and hydrogeological applications. Here, we assess the ability of the Ground Penetrating Radar (GPR) method to image open fractures with sub-mm apertures in the context of future deep disposal of radioactive waste. GPR experiments were conducted in a tunnel located 410 m below sea level within the Äspö Hard Rock Laboratory (Sweden) using 3-D surface-based acquisitions (3.4 m × 19 m) with 160 MHz, 450 MHz and 750 MHz antennas. The nature of 17 identified GPR reflections was analyzed by means of three new boreholes (BH1-BH3; 9–9.5 m deep). Out of 21 injection and outflow tests in packed-off 1-m sections, only five provided responses above the detection threshold with the maximum transmissivity reaching 7.0 × 10−10 m2/s. Most GPR reflections are situated in these permeable regions and their characteristics agree well with core and Optical Televiewer data. A 3-D statistical fracture model deduced from fracture traces on neighboring tunnel walls show that the GPR data mainly identify fractures with dips between 0 and 25°. Since the GPR data are mostly sensitive to open fractures, we deduce that the surface GPR method can identify 80% of open sub-horizontal fractures. We also find that the scaling of GPR fractures in the range of 1–10 m2 agrees well with the statistical model distribution indicating that fracture lengths are preserved by the GPR imaging (no measurement bias). Our results suggests that surface-GPR carries the resolution needed to identify the most permeable sub-horizontal fractures even in very low-permeability formations, thereby, suggesting that surface-GPR could play an important role in geotechnical workflows, for instance, for industrial-scale siting of waste canisters below tunnel floors in nuclear waste repositories

Scaling of fractured rock flow. Proposition of indicators for selection of DFN based flow models

International audienceThe objective of the paper is to better understand and quantify the flow structure in fractured rocks from flow logs, and to propose relevant indicators for validating, calibrating or even rejecting hydrogeological models. We first studied what the inflow distribution tells us about the permeability structure from a series of analyses: distribution of transmissivities as a function of depth, proportion of flowing sections as a function of section scale, and scaling of the arithmetically-averaged and geometrically-averaged permeability. We then define three indicators that describe few fundamental characteristics of the flow/permeability, whatever the scale: a percolation scale , the way permeability increases with scale above , and the variability of permeability. A 4th indicator on the representative elemental volume could in principle be defined but the data show that this volume/scale is beyond the 300 m investigated. We tested a series of numerical models built in three steps: the geo-DFN based on the observed fracture network, the open-DFN which is the part of the geo-DFN where fractures are open, and a transmissivity model applying on each fracture of the open-DFN (Discrete Fracture Network). The analysis of the models showed that the percolation scale is controlled by the open-DFN structure and that the percolation scale can be predicted from a scale analysis of the percolation parameter (basically, the third moment of the fracture size distribution that provides a measure of the network connectivity). The way permeability increases with scale above the percolation threshold is controlled by the transmissivity model and in particular by the dependence of the fracture transmissivity on either the orientation of the fractures via a stress-controlled transmissivity or their size or both. The comparison with data on the first two indicators shows that a model that matches the characteristics of the geo-DFN with an open fraction of 15% as measured adequately fits the data provided that the large fractures remain open and that the fracture transmissivity model is well selected. Most of the other models show unacceptable differences with data but other models or model combinations has still to be explored before rejecting them. The third indicator on model variability is still problematic since the natural data show a higher variability than the models but the open fraction is also much more variable in the data than in the models

Flow simulations in geology-based Discrete Fracture Networks

International audienceThe underground is a reservoir of natural resources (water, oil and gas, heat,...) and a potential warehouse storage solution. Using these resources and storage facilities in a sustainable way requires a good understanding of the physical, chemical and biological processes happening there. Also, the geometry of the subsurface couples these processes together. Here, numerical models are very useful: they reduce the costs and risks of in situ experiments and allow long-term predictions

Corrélations dans les réseaux de fractures : Caractérisation et conséquences sur les propriétés hydrauliques

Thèse publiée dans la collection des Mémoires de Géosciences Rennes (ISSN 1240-1498) : Mémoire n° 1 (ISBN 2-914375-07-7)forthcomingL'étude des propriétés hydrauliques des milieux fracturés s'inscrit dans le cadre général de la gestion de la ressource en eau et plus particulièrement dans le domaine de la gestion des déchets et de leur stockage dans des sites d'enfouissement. Les fractures, qui constituent les chemins d'écoulements préférentiels dans les milieux fissurés, sont distribuées sur une large gamme d'échelles et présentent une géométrie complexe. Le travail de la thèse est centré sur la caractérisation des corrélations spatiales dans les réseaux de fractures et sur l'étude de l'effet induit par ces corrélations sur les propriétés de connectivité et hydrauliques de ces milieux. De nombreuses études de terrain ont montré que la répartition des fractures n'est pas homogène dans l'espace. Cette évolution de la densité de fracturation suit un modèle fractal, qui, couplé avec une distribution des longueurs de fractures, constitue un modèle pertinent de réseau de fractures. L'organisation spatiale des réseaux se retrouve aussi à un degré supérieur dans une corrélation positive entre la position des fractures et leur longueur, telle qu'il existe en moyenne une zone d'écran autour des fractures dont l'aire est corrélée à la longueur. Le travail préliminaire de caractérisation de la géométrie des réseaux est complété par une analyse stéréologique permettant de relier les propriétés apparentes des réseaux, déterminées à partir d'observations 1D ou 2D (transects, puits, affleurements), à leurs propriétés intrinsèques (3D). Ainsi, on montre que la dimension fractale d'un réseau 3D peut être reliée à la dimension fractale apparente du réseau échantillonné sur un affleurement ou un transect. L'étude des propriétés hydrauliques est réalisée pour un modèle de réseau bidimensionnel présentant les caractéristiques principales associées aux réseaux de fractures, soit une densité de fracturation fractale (exposant D), et une distribution des longueurs de fractures en loi de puissance (exposant a). L'étude préalable de la connectivité montre qu'une corrélation fractale forte (D faible) tend à déconnecter les réseaux, alors que la présence de grandes fractures (a faible) induit une augmentation de la connectivité. Le modèle de comportement dépend donc des valeurs relatives de a et D. Les deux effets se compensent uniquement lorsque a=D+1 (cas self-similaire), et dans ce cas seulement l'état de connexion des réseaux ne dépend pas de l'échelle d'observation. Enfin, l'effet de la corrélation spatiale sur les propriétés hydrauliques des réseaux de fractures est soit de premier ordre lorsque a>D+1, puisque alors les réseaux sont déconnectés à grande échelle et par conséquent la perméabilité nulle, soit de second ordre lorsque a£D+1: dans ce cas l'effet des longueurs domine et l'évolution de la perméabilité avec l'échelle est peu sensible à la valeur de D, bien que les écoulements restent chenalisés aux fortes densités

Corrélations dans les réseaux de fractures (caractérisation et conséquences sur les propriétés hydrauliques )

Developments performed during the last decades in the domain of hydraulic and transport properties modeling of fractured media have been mainly motivated by the current problematic about nuclear repositories safety. The understanding of the complex hydraulic behavior of fractured media is tackled here through a direct representation of the fracture network geometry and through a discrete stochastic modeling process. In that context, our work is focused on the notion of spatial correlations. Firstly spatial correlations are identified. Then a model of discrete fracture network is developed and finally the consequences of spatial correlations on hydraulic properties of fractured media are determined.Natural fracture patterns often display an heterogeneous spatial density distribution which can be characterized by a fractal dimension D. In addition we show that fracture lengths and positions are also organized such that around each fracture there exists on average a shield (empty of other fractures) whose area is correlated to the fracture length. A stereological analysis shows that the fractal dimension of a 3D fracture pattern is simply related to the apparent fractal dimension measured on a lower dimensional sample of the fracture network.The model of fracture network considered is fractal (D) and its fracture length distribution is a power law (a). For 2D fracture networks, the type of global behavior depends on the relative values of a and D. Indeed, a strong fractal correlation (D low) induces a decrease of the global network connectivity when the observation scale increases. On the contrary, a decrease of a induces an increase of the connectivity with scale. When a=D+1 (self-similar case), both effects exactly compensate and the connection state is independent of the observation scale. In that case, we show that, although the flow remains channeled at high densities as long as D<2, the evolution of the permeability with scale is weakly dependent on D.At last, we show that the fractal dimension associated with 2D fracture networks tends to decrease the connectivity with increasing scale. When the deconnexion effect is compensated by the length distribution, the evolution of the permeability with scale is weakly sensible to variations of D, although flow is channeled. On the contrary we expect a stronger influence of the parameter D on the transport properties.RENNES1-BU Sciences Philo (352382102) / SudocPARIS-BIUSJ-Sci.Terre recherche (751052114) / SudocSudocFranceF

Scaling effects on elastic properties of jointed rock mass

International audienc

Statistical Fracture Domain methodology for DFN modeling applied to site characterization

International audienceFractures in rock masses strongly influence the underground mechanical and hydrogeological behavior. Understanding the relation between fracturing properties and rock properties is essential and still is a research area. In parallel, it is as much important to be able to characterize the fracturing properties into DFN models whose mean estimates and estimate accuracy are well defined. Fracturing properties indeed combine multi-scale range of sizes together with sharp variations of densities and orientation organization, which prevents from any simple characterization. In this paper we focus on the notion of variability: how it can be assessed, what is its importance and how it is transmitted in the modeling, from local scale to largest site scale. The DFN characterization is only based on depth core logging data and the DFN models relate to densities and orientation distributions. We describe a method recently developed, called SFD (Statistical Fracture Domain), which is used to first appraise the uncertainty of density estimates due to local variability, next to quantify and compute differences (statistical distance) between any number of dataset density estimates and finally to group datasets into classes of compatible statistical properties. The method is applied to some data from the SKB Forsmark site