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Field monitoring programs (e.g., convergence measurements and stress measurements in the support system) play an important role in following the response of the ground and of the support s...

International audience; A squeezing Carboniferous formation was met at a depth of 300 m during the excavation of the Saint-Martin-la-Porte access gallery (SMP2) in France within the Lyon-Turin railway link project. Large, time-dependent and anisotropic deformation was observed around the tunnel wall during and after excavation, and difficulties related to tunneling in squeezing ground have been encountered. An anisotropic visco-elastic plastic constitutive law (Tran- Manh et al. 2015) has been proposed in order to model the ground behavior. This model was validated by field auscultation carried out in SMP2. As a part of the base tunnel, a new survey gallery (SMP4) began to be excavated in the recent years across the same squeezing rock formation at a depth of about 600 m. A yield control support system was adopted in the zones of large deformation, which contains highly deformable concrete elements to stabilize the high convergence (Bonini and Barla 2012). In the present work, the studies of SMP2 are extended to SMP4 by considering the constitutive model developed for SMP2. The innovative excavation and support method is taken into account. Numerical modeling is performed using FLAC3D to analyze the tunnel response. A good agreement can be obtained between the field measurements and the numerical results.

International audience; The 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.

In crystalline bedrock, the open fraction of the fracture network constitutes the main pathways for fluids. Many observations point out that the state of stress influences the open fraction, likely indicating recent reactivation. But how this occurs is still unresolved. We analyse the conditions for fracture reactivation from fracture data collected in the uppermost 1 km of bedrock in Forsmark, Sweden. The open fraction is mainly correlated to the stress acting normally on the fracture but even away from critical failure, leading us to analyse the potential fluid pressure required for reactivation, $${P}_{c}$$ P c . We observe that 100% of the fractures are open when $${P}_{c}$$ P c is hydrostatic, and the ratio decreases exponentially to a plateau of ~ 17% when $${P}_{c}$$ P c is lithostatic and above. Exceptions are the oldest fractures, having a low open fraction independent of $${P}_{c}$$ P c . We suggest that these results reflect past pressure build-ups, potentially related to recent glaciations, and developing only if the preexisting open fraction is large enough.

International audience; Biot coefficient and Skempton coefficient are key descriptors of the coupled hydro-mechanical (HM) behavior of fluid-saturated porous materials. Biot coefficient defines a relationship between an applied load, fluid pressure and the stress that effectively acts on the solid skeleton. Skempton coefficient defines the temporary pore pressure variation caused by the application of a load in undrained conditions. The product of the two coefficients establishes the impact of an applied load on the solid skeleton, and thus the material deformation, under undrained conditions. The two coefficients are generally estimated through analytical expressions valid for isotropic homogeneous materials, or they are experimentally estimated at the laboratory sample-scale.In this work, we define a framework for the evaluation of equivalent Biot coefficient and Skempton coefficient at the scale of a fractured rock mass. We derive theoretical expressions that estimate the two equivalent coefficients from the properties of both the porous intact rock and the discrete fracture network (DFN), including fractures with different orientation, size, and mechanical properties. These formal expressions are validated against results from fully coupled hydro-mechanical simulations on systems with explicit representation of deformable fractures and rock blocks. We show that the coefficients largely vary with the fracture orientation and density, which implies that disregarding the presence of fractures may incur an incorrect evaluation of the HM response. We also discuss the variability of the coefficients under different settings of DFN properties, including realistic scaling conditions of size-dependent and stress-dependent fracture properties.

International audience; ost of the viscoplastic models used to describe the constitutive behavior of squeezing grounds assume isotropic deformation. However, it is commonly observed that squeezing behavior is characterized not only by large time-dependent but also often by anisotropic deformations. This study uses a semi-empirical approach based on the analysis of convergence measurements and a numerical model that takes into account the time-dependent and the anisotropic response of the rock mass to investigate the squeezing behavior of the Saint-Martin-la-Porte access gallery, excavated within the Lyon–Turin railway project. We first show how the semi-empirical convergence law of Sulem et al. (Int J Rock Mech Min Sci Geomech Abstr 24(3):155–164, 1987a; Int J Rock Mech Min Sci Geomech Abstr 24(3):145–154, 1987b) can be extended to anisotropic tunnel closure by considering an elliptical deformation of the rock mass and by fitting the convergence data along the principal axes of deformation. A new anisotropic time-dependent constitutive model is then proposed. This model includes ubiquitous joints of specific orientation embedded in an isotropic viscoplastic medium. This model is implemented in FLAC3D and numerical simulations are performed to back-analyze the anisotropic closure of the Saint-Martin-la-Porte access gallery. An efficient two-step procedure for calibrating the model parameters is proposed: the parameters of the isotropic solid matrix are first estimated by performing axisymmetric numerical simulations. The parameters of the ubiquitous joints are then calibrated by performing 3D computations. It is shown that the numerical results reproduce very well the convergence measurements of the studied sections of Saint-Martin-la-Porte gallery.

Abstract This paper focuses on the understanding of the controlling factors of breakthrough curves in fractured systems. DFN.lab is used to define DFN models derived from the characteristics of a sub-part of the Forsmark repository and to perform simulations of flow and of inert transport with a particle tracking algorithm. We show that particles potentially follow two kind of paths: fast paths, composed by a limited number of highly transmissive, well oriented fractures, and slow paths, where particles go through a larger number of fractures. These paths have different characteristics: fast paths are controlled by the transmissivity structure of some large fractures and produce “peak” arrival times while slow paths are controlled by the network organization and the transmissivity structure, resulting in arrival times obeying an inverse gamma distribution. In addition, those late arrival times are controlled by the presence of "traps" where the velocity is significantly slower.

Geothermal energy applications involve heat circulation in naturally fractured reservoirs, which are in general difficult to characterize due to the multiscale complexity of the fracture network and therefore the flow. In this context, numerical modeling is key to forecast the performance of geothermal energy applications under a number of scenarios. Numerical modeling is challenging because fractures represent the main pathway for flow and advective transport, but diffusive thermal exchange with the host rock controls the geothermal performance - the two processes occurring on very different length and time scales. Moreover, the host rock cooling provokes thermal contraction which tends to increase the fracture aperture, with direct effects on the flow and the advective transport. Quantify these processes is crucial but in general computational demanding when dealing with large reservoirs with hundreds of thousands of fractures.In this study we present a novel methodology to simulate thermo-mechanical (TM) heat transport. The method is based on the particle tracking approach in Discrete Fracture Networks (DFN) and it has been implemented in the DFN.Lab software platform. The contribution of the host rock matrix in terms of diffusive heat exchange and thermal contraction/expansion is analytically evaluated, which directly impacts the fracture aperture and therefore the advective heat transfer. The methodology enables investigating the reservoir behavior and optimizing the geothermal performance while keeping the computational effort within reasonable values. Results from simulations of cold fluid injection show that rock contraction accelerates the advective transport resulting in a faster recovery of cold fluid at the outlet. We analyze systems of fractures with different characteristics (density, aperture, geometrical patterns, ...) and we identify the parameters that mostly impact the TM response.

International audience; The dependency of permeability with depth, its sensitivity to injection pressure and earthquakes are all evidence that permeability depends on stress. Since stresses vary both vertically (lithostatic pressure) and horizontally (tectonic stresses) in the Earth’s crust, permeability is likely both depth dependent and anisotropic with potential consequences on flow that depend on the magnitude of the permeability variation with stress. In addition, the permeability is no longer a rock mass intrinsic property, but becomes a constitutive relationship between permeability and stress that we here refer to as “permecability”. The proposed analysis of the permeability dependency with stress is carried out for fractured rocks under conditions representative of deep storage of nuclear waste. It relies on a Discrete Fracture Network approach, where each fracture is assigned a stress dependent transmissivity.First, at single fracture scale, a literature review allows us to assume a simplified 3-parameter stress-transmissivity relationship, for which experiment based parameter estimates are available.At the network scale, each fracture experiences specific stress conditions that depend on the remote stress conditions, the fracture orientation and the stress fluctuations induced by surrounding fractures. Numerical simulations show that the latter cannot be neglected under the conditions under study, hence emphasizing the need to develop numerical methods able to both calculate the stress fluctuations in DFN models with hundreds of thousands of fractures of any size, and the DFN flow simulations to determine network scale equivalent permeabilities.We then analyze the relationship between the DFN structure, the stress-transmissivity relation, and the resulting permeability tensor. The anisotropy and magnitude of the permeability tensor highly depend on the intensity and directions of both fractures and remote stress. A complete sensitivity analysis is carried out to quantify this effect for a wide range of DFN models with varying hydraulic and mechanical (stiffness) parameters.Finally, we address the issue of defining as simply as possible the permecability constitutive relationship, which determines the rock mass permeability from DFN models and in-situ stress conditions.

International audience; Discrete Fracture Network (DFN) is a modeling framework for fractured rocks. The core element is the description of geological medium as a network of discrete fractures that can be either generated from statistical distributions or imported as deterministic surfaces. It is an alternative to continuum methods with both advantages of easily integrating the statistical properties of fracture networks, and of not assuming any homogenization scale. DFN has been extensively used to describe fracture network flow properties supported by the fact that connectivity, which is a constitutive element of the network organization, is a key element of fluid percolation. Application of the DFN modeling framework to geomechanics is also promising and, conversely, DFN models will benefit from rock mechanics integration.Integration between DFN and rock mechanics modeling is in expansion in many fields and broad contexts. This includes prediction of mechanical effective properties, increased understanding of the fracture scales and indicators that control these properties, distribution of block sizes and shapes for block fall risk analysis, potential wave attenuation effect and fracture shear displacements caused by and within the fracture network induced by an earthquake, or hydromechanical effects for flow and transport predictions.These applications are relevant only if DFN models involve the right complexity and provide a reliable description of the fracture networks. DFN models also benefit from rock mechanics concepts to improve their realism as it is done with genetic models that mimic the growth and arrest of fractures according to stress conditions prevailing at the time of their formation.

International audience; Modeling heat transfer in complex heterogeneous fractured system is key for geothermal energy applications. Discrete fracture network (DFN) modeling is the ideal framework to reproduce the advective part of the transport, which is determined by the fracture connectivity and heterogeneity. This approach in general sacrifices the representation of the rock matrix, disregarding both its diffusive heat exchange with the fractures and the effects of its thermo-mechanical deformation on the fracture aperture. Here we propose a new semi-analytic formulation that can be implemented in a DFN simulator with particle tracking approach. The contribution of the rock matrix in terms of diffusive heat exchange and thermal contraction/expansion is analytically evaluated, which respectively impact the advective heat transfer and the fracture aperture variation. The methodology enables investigating the reservoir behavior and optimizing the geothermal performance while keeping the computational effort within reasonable values. This allows exploring the uncertainty in cases when the characterization is poor, which is the spirit of the DFN modeling.

International audience; evaluate the use of graphs as a fast and relevant substitute to DFNs. Graphs reduce the DFNs’ complexity to their connectivity structure by forming an assembly of nodes connected by edges, to which physical properties, like a conductance, can be assigned. Both the graph architecture (either fracture- or intersection- based) and the edge conductance definition, have an impact on the estimation of flow and transport parameters. The intersection graph brings a reliable description of the flow connectivity but with edge redundancy in fractures with a large number of intersections. As a consequence, the expression of the edge conductances should depend on the number of intersections in the fracture plane. We first introduce some of our previous work which propose a reliable expression of the edge conductance in the case of a pair of intersections. For the intersection graph, a correction on the conductance expression is proposed for fractures with a large number of intersections. Both graphs provide very good estimate of the bulk permeability although they tend to slightly overestimate it when the DFN connectivity increases (~×2) certainly due to fractures with large intersection numbers. We address this issue by analyzing flow simulations on a fracture with multiple intersections. We also propose another way to correct the intersection graph, which consists in removing redundant edges. The method drastically simplifies the intersection graph, which is promising in term of computational time. The bulk permeability is overestimated by a factor of 2.3 but independently of the DFN density and connectivity.

International audience; The United States and countries around the world face an increasing demand for energy at the same time that carbon emissions and other environmental issues are facing greater scrutiny. Geothermal energy, generating electricity using the temperature difference between the surface and the sub-surface, is an active topic of research by the US Department of Energy and other agencies around the world. Much of the existing geothermal power generation is based on existing natural hydrothermal system. These hydrothermal schemes rely on abnormally high heat flow and an existing ground water system. The concept of enhanced geothermal systems (EGS) allows geothermal energy to be produced in nearly any land location. EGS reservoirs are often below 3 km in depth and rely on some engineered permeability enhancement to be economical. This paper describes a numerical modeling capability to help better understand the interactive thermal, hydrological, and mechanical effects that control the behavior of an EGS system. A 3D discrete fracture network is explicitly represented and a combination of specialized meshing and explicit solution techniques is used make predictions of the stimulation and production of EGS reservoirs. A comparison is made between a fully-coupled model using the 3DEC software and a complimentary approach using the DFN.lab software.

International audience; Intersections between the fractures of a network defines its connectivity and constitute a key component both for the hydrogeological and mechanical behavior of fractured rock masses. Existing analyses of 2D field trace maps provide a framework for analyzing 2D fracture intersection distributions. In this paper, we perform a complete analysis of 3D fracture intersections distribution of various DFN models and investigate how it can be related to the 2D distribution of intersecting virtual outcrops. The DFN models are either fully random (with no correlation between fractures) or defined from a genetic process (named UFM model). By comparing with natural 2D field trace maps, we show that, unlike the fully random DFN model which produces only X intersections, the UFM model is quantitatively consistent with the intersection distribution observed on field trace maps. The analysis framework developed here can be used as a relevant metric to select DFN models in terms of connectivity and give insights on the 3D topology of fracture networks.

This paper presents analytical solutions to estimate at any scale the fracture density variability associated to stochastic Discrete Fracture Networks. These analytical solutions are based upon the assumption that each fracture in the network is an independent event. Analytical solutions are developed for any kind of fracture density indicators. Those analytical solutions are verified by numerical computing of the fracture density variability in three-dimensional stochastic Discrete Fracture Network (DFN) models following various orientation and size distributions, including the heavy-tailed power-law fracture size distribution. We show that this variability is dependent on the fracture size distribution and the measurement scale, but not on the orientation distribution. We also show that for networks following power-law size distribution, the scaling of the three-dimensional fracture density variability clearly depends on the power-law exponent.

International audience; Lahars (volcanic debris flows) are natural phenomena that can generate severe damage and wreak havoc in densely populated urban areas. The evaluation of the forces and pressures generated by these mass flows on constructions (e.g., buildings, bridges and other infrastructure) is crucial for civil protection, assessment of physical vulnerability and risk management. The current tools developed to model the spread of flows at large scale in densely populated urban areas remain inaccurate in the evaluation of mechanical efforts. Here, we developed a discrete numerical model for evaluating debris-flow (DF) impact forces at the local scale of one structure (pillar or column) like a building, a bridge and other infrastructure. In this model, the large-sized solid particles that damage infrastructures and edifices are explicitly modelled using Distinct Element Method (DEM). We considered the fluid and fine-grained solid particles not only in the frame of the pressure exerted on structures, but also through their effects on the movement of particles, i.e. buoyancy and drag. The fluid velocity field and the fluid free surface obtained from Computational Fluid Dynamics (CFD) calculation based on Navier–Stokes equations are imported in the DEM simulation. This model is able to reproduce a range of magnitudes of DFs in terms of volumes, velocities and flow heights. Finally, the model provides insights on impact forces generated by particles on structures and on hydrostatic and/or dynamic pressure due to the combined effect of fluid and solid phases. The model provides results consistent with existing empirical models.

International audience; Modeling heat transfer in complex heterogeneous fractured system is key for geothermal energy applications. Discrete fracture network (DFN) modeling is the classical framework to reproduce the advective part of the transport, which is determined by the fracture connectivity and heterogeneity. This approach in general sacrifices the representation of the rock matrix, disregarding both its diffusive heat exchange with the fractures and the effects of its thermo-mechanical deformation on the fracture aperture. Here we propose a new semi-analytic formulation that can be implemented in a DFN simulator with particle tracking approach. The contribution of the rock matrix in terms of diffusive heat exchange and thermal contraction/expansion is analytically evaluated, which respectively impact the advective heat transfer and the fracture aperture variation. The method is proved to be accurate and robust. Results from simulations of cold fluid injection show that rock contraction affects the transmissivity, which accelerates the advective transport resulting in a faster recovery of cold fluid at the outlet. The methodology enables investigating the reservoir behavior and optimizing the geothermal performance while keeping the computational effort within reasonable values. This allows exploring the uncertainty in cases when the in-situ characterization is poor, which is the spirit of the DFN modeling.

The objective is to significantly reduce the rock mass mechanical modeling uncertainties, which are above all related to the geometrical and mechanical properties of the fracture network, especially relative to scaling and anisotropy issues. It is also to better address, in the numerical models, the issues raised by the complex nature of the rock fractured system (e.g. discrete/continuous representation).

International audience; We assess the performance of the Ground Penetrating Radar (GPR) method in fractured rock formations of very low transmissivity (e.g. T ≈ 10−9–10−10 m2/s for sub-mm apertures) and, more specifically, to image fracture widening induced by high-pressure injections. A field-scale experiment was conducted at the Äspö Hard Rock Laboratory (Sweden) in a tunnel situated at 410 m depth. The tracer test was performed within the most transmissive sections of two boreholes separated by 4.2 m. The electrically resistive tracer solution composed of deionized water and Uranine was expected to lead to decreasing GPR reflections with respect to the saline in situ formation water. The injection pressure was 5000 kPa leading to an injection rate of 8.6 mL/min (at steady state) that was maintained during 25 h, which resulted in a total injected volume of 13 L. To evaluate the fracture pathways between the boreholes, we conducted 3-D surface-based GPR surveys before and at the end of the tracer tests, using 160 MHz and 450 MHz antennas. Difference GPR data between the two acquisitions highlight an increasing fracture reflectivity in-between the boreholes at depths corresponding to the injection interval. GPR-based modeling suggests that the observed increasing reflectivity is not due to the tracer solution, but rather to a 50% widening of the fracture. Considering prevailing uncertainties in material properties, a hydromechanical analysis suggests that such a degree of widening is feasible. This research demonstrates that field-scale in situ GPR experiments may provide constraints on fracture widening by high-pressure injection and could help to constrain field-scale elastic parameters in fractured rock.

International audience; Debris flows (DFs) are dangerous events that can cause the complete destruction of buildings and infrastructure, such as bridges; DFs therefore represent a high risk to public safety in exposed areas. The impact pressures due to these flows are essentially determined by the flow height, velocity and density, but other parameters that are less often considered are also involved. We developed a numerical model to evaluate the impact pressure of mass flows, focusing on a better description of the influence of the blocks transported in these flows: the block size strongly influences the impact pressure, which has a strong effect on structural damage. The numerical model proposed considers a staggered, loosely one-way granular–fluid coupling based on a distinct-element-method code, using the separate simulation results of a computing fluid dynamics code used to model the fluid phase. This model estimates the impact pressure distribution due to blocks at the local scale of the obstacle; the pressure due to the fluid phase can be added afterwards. The pressure applied by the DF increased with the maximum block size for a given set of DF characteristics: velocity, height and apparent density. The vulnerability of a given structure depends on the intensity of DFs: the pressure applied on the structure is one of considerable intensity. The existing vulnerability functions are interpreted in the light of the results obtained with the numerical model. This interpretation highlights the need to integrate new parameters in the intensity to better evaluate structures’ vulnerability to debris flows.

International audience; Fractured rocks are often modeled as multiscale populations of interconnected discrete fractures (discrete fracture network, DFN). Graph representations of DFNs reduce their complexity to their connectivity structure by forming an assembly of nodes connected by links (edges) to which physical properties, like a conductance, can be assigned. In this study, we address the issue of using graphs to predict flow as a fast and relevant substitute to classical DFNs. We consider two types of graphs, whether the nodes represent the fractures (fracture graph) or the intersections between fractures (intersection graph). We introduce an edge conductance expression that accounts for both the portion of the fracture surface that carries flow and fracture transmissivity. We find that including the fracture size in the expression improves the prediction of flow compared to expressions used in previous studies that did not. The two graph types yield very different results. The fracture graph systematically underestimates local flow values. In contrast, the intersection graph overestimates the flow in each fracture because of the connectivity redundancy in fractures with multiple intersections. We address the latter issue by introducing a correction factor into the conductances based on the number of intersections on each fracture. We test the robustness of the proposed conductance model by comparing flow properties of the graph with high-fidelity DFN simulations over a wide range of network types. The good agreement found between the intersection graph and test suite indicates that this representation could be useful for predictive purposes.

International audience; 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.

International audience

International audience; The realism of Discrete Fracture Network (DFN) models relies on the spatial organization of fractures, which is not issued by purely stochastic DFN models. In this study, we introduce correlations between fractures by enhancing the genetic model (UFM) of Davy et al. [1] based on simplified concepts of nucleation, growth and arrest with hierarchical rules. To do so, the nucleation of new fractures is correlated with the elastic strain energy of distortion stored in the matrix, which is a function of preexisting fractures. Discrete Fracture Networks so generated show multi-scale clustering effects with fractal dimensions below the topological dimension over a broad range of scales. The fractal dimension depends on the way one correlates the nucleation occurrence to the strain energy. Fracture clustering entails a spatial variability of the fracture density, which increases with the intensity of the coupling between stress and nucleation. The analysis of connected clusters density and of fracture intersections also highlights the differences between the UFM models and its equivalent Poisson model. We show that our stress-dependent nucleation model introduces some new fracture size-positions correlations, with small fractures tending to connect to the largest ones.

International audience; Non-isothermal fluid flow in fractured media is a complex process because both pressure and temperature variations deform the rock, thus modifying the aperture of the fractures. This in turn affects the pressure diffusion and the heat transfer, creating the so-called Thermo-Hydro-Mechanical (THM) coupling. The complexity is particularly great because the hydraulic process and the thermal process occur at different time scales and the fracture heterogeneity happen at different length scales. This means that strains are different if observed at the small scale. The numerical simulation of such coupled problems is challenging. An additional difficulty resides in relating these models to the large scale response, to get a characterization of the aquifer.In this paper, we simulate the THM coupling by adopting a Discrete Fracture Network (DFN) approach with a Lagrangian method for the transport. We assume that the heat transfer occurs by means of advection within the fractures and diffusion toward the matrix. Thus, we adopt a particle tracking method to model heat transfer along streamlines with steady state flow, and we introduce a temperature decay to mimic the heat loss due to diffusion to the matrix. The methodology has been implemented within the DFN.lab platform, which allows for the generation and management of three-dimensional fracture networks with millions of fractures. The software allows for including heterogeneity within each fracture, which makes it possible to represent the presence of heterogeneity at small scale. At each fracture patch we calculate the variation of the fracture aperture in response to the thermal perturbation by means of simple elasticity laws. This small scale THM behavior is translated into a large scale behavior by observing at the variation of the heat transfer regime due to the mechanical response. In fact, the aperture variation is related to the hydraulic conductivity, which affects the flow regime and thus the heat transfer.Future developments will include the comparison of numerical results with field experimental data of non-isothermal injection into a fractured aquifer. This would allow us to calibrate the model parameters, in order to get a more physically-based model. Another future extension is aimed at including thermal effects in the prediction of fracture growth

International audience; The identification of (open) fractures in the subsurface is critical for evaluating potential routes for contaminant transport from deep disposal sites. Ground Penetrating Radar (GPR) is suitable for this task and its detection capacity depends on fracture characteristics (orientation, aperture and size) and on the dielectrical and electrical contrast between the fluid or material filling the fractures and the surrounding bedrock. A GPR experiment was performed in the Äspö Hard Rock Laboratory (Sweden) in a tunnel located 410 m below the sea level with a length of 20 m long, a width of 4 m and a height of 4.5 m. The geological formations are fractured granite, diorite and granodiorite with negligible matrix permeability and very low transmissive fractures (10E-9 to 10E-10 m2/s for most permeable zones). We used 160 MHz, 450 MHz and 750 MHz antennas, pulled along the clean and flat tunnel floor along parallel lines separated by 0.10 m for 160 MHz and by 0.05 m for 450 and 750 MHz antennas. This measurement set-up and antenna choices allow for a 3D identification of fractures from GPR diffractions and reflections, with different image resolutions and investigation depths reaching 10m, 8m and 5m for 160, 450 and 750 MHz, respectively. Based on the data, we identify 15 reflections that could correspond to larger fractures with dimensions of 2 to 5 m. We compare the GPR-inferred fractures with the corelogging of three 9.5 m deep boreholes that were drilled after the GPR campaign. The strong GPR reflections in the borehole area largely correspond to the depth and orientation to the fractures identified by the Optical Televiewer (OPTV) data. Additionally, pumping and injection tests in each borehole showed that the GPR-inferred fractures are situated in the most permeable regions. The occurrence of GPR fractures was then compared with a statistical description of the fracture network built from the intersection of boreholes and 2D trace maps from tunnel walls. Given the average size of the GPR-inferred fractures, we demonstrate that they are overall consistent with the expected fracture density below the tunnel.

International audience; DFN.lab is a modular computational suite to deal with three-dimensional discrete fracture networks (DFN) models from DFN generation to simulation and analysis of connectivity, flow, mechanical and transport properties. DFN.lab is developed by the Fractory, a joint laboratory between the French institute for scientific research (CNRS), the university of Rennes and Itasca Consultants s.a.s., to study the behavior of multiscale fractured media for various research topics including safety assessment for long-term nuclear waste storage, geothermal applications, mining, etc. DFN.lab can generate and compute flow and solute or heat transport on large DFNs containing millions of fractures. Core modules are developed in C++ for high performances and a Python API is provided for easy use.The main originality of DFN.lab is in its capacity to deal with multiscale heterogeneities at both the fracture and network scales. For each fracture, the hydraulic properties (transmissivity and aperture) can vary locally either deterministically, or statistically according to correlated random fields. A “sealing” algorithm was developed to model fracture patches that are clogged by mineralization. A graph algorithm was developed to derive the connectivity of open patches at the network scale. At the network scale, thanks to its computing capacities, DFN.lab can deal with fracture sizes ranging over more than 3 orders of magnitude.Another originality of DFN.lab is in its DFN generation modules, where genetic generation models [Davy et al., 2013; Davy et al., 2010] have been developed as an alternative to the classical Poisson (e.g., randomly distributed) models bootstrapped on statistical descriptions of the fracture properties (size, position, orientation). For the same distribution of fracture sizes, orientations and transmissivities, genetic models behave significantly differently from Poisson’s models [Maillot et al., 2016].Example applications of this suite for nuclear waste repository, solute transport and heat transport will be presented.Davy, P., R. Le Goc, and C. Darcel (2013), JGR, 118(4), 1393-1407.Davy, P., R. Le Goc, C. Darcel, O. Bour, J. R. de Dreuzy, and R. Munier (2010), JGR, 115(B10).Maillot, J., P. Davy, R. Le Goc, C. Darcel, and J.-R. De Dreuzy (2016), WRR, 52(11).

International audience; Fractures have a significant impact on rock mass mechanical and hydraulic properties, which is a concern for rock engineering applications like excavation or repository design, support design, slope stability and caving in mines. To address this issue, a sound description of the fracturing pattern is required. DFN models are statistical models which define the density of fractures having given geometrical properties (size and orientation) and which include an intrinsic variability term. One of the main challenging task is to combine all available data. Data remain sparse and scarce and are acquired at different scales and from different support shapes and dimension (1D, 2D). We present a 3D modelling approach combining data from borehole logs, outcrop trace maps and tunnel walls mapping. It is applied to the Äspö site in Sweden, for which a large database is available, containing tens of thousands of records. Using stereological rules and assumptions about the underlying DFN scaling model, we are able to integrate all data to define the fracturing properties from the borehole scale (ten centimeters) to the repository scale (several kilometers). An advanced DFN modeling framework is applied, accounting for fractures mechanical interactions. This model has proved to be almost universal in crystalline rocks and reproduces, with very few parameters, the scaling properties of fractures. We show that this modelling framework better reproduces observations at all available scales and yields DFN, which structure and associated properties have a better consistency with natural cases than for simple DFN approaches.

International audience; We are interested in solving flow in large trimensional Discrete Fracture Networks (DFN) with the hybrid high-order (HHO) method. The objectives of this paper are: (1) to demonstrate the benefit of using a high-order method for computing macroscopic quantities, like the equivalent permeability of fracture rocks; (2) to present the computational efficiency of our C++ software, NEF++, which implements the solving of flow in fractures based on the HHO method.

International audience; In crystalline rocks, flow takes place within the network of open fractures. Predicting flow paths is a basic requirement for groundwater management or environmental risk assessment. A major issue is that a large amount of fractures (up to 80%) is completely sealed by mineral precipitations and rock weathering with potentially important consequences on large-scale connectivity and flow paths. This study aims at characterizing the distribution of sealing in the fracture network. It is part of a risk assessment project related to the deep storage of nuclear waste in Sweden. The first part of this study relies on the analysis of 23 drilled boreholes (from 200 to 1000 meters deep) from the site of Forsmark (Sweden). The proportion of sealed fractures in boreholes gives an estimate of the total sealed surface regardless of the fracture size. We analyze the repartition of the total sealed surface as a function of fracture density, fracture trace orientation, depth and lithology. At shallow depth (

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International audience; 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 (Davy et al, 2010, 2013). 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 3D 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 to 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.

International audience; We start this presentation by assuming that a model and a mesh of the DFNs have been computed *. We focus here on the numerical methods to solve efficiently single-phase flow problems. We will present the software NEF-Flow dedicated to solving single phase flow in large scale DFNs. NEF stands for Numerical Experiments involving Fractures. The software NEF-Flow is written in Matlab and implements the mixed-hybrid finite element method in an optimized way, using vectorization to decrease the computational time. It handles either matching or non-matching meshes at the intersection between fractures, sink/source terms and contrasts in transmissivities. A large set of benchmark test cases will be presented. Typically, we extended those proposed in [1, 2] to DFNs generated with the UFM framework [3, 4]. These DFNs are large scale DFNs where the fracture size distribution matches the observations and where fractures are organized so that large fractures inhibit the smaller ones, creating T-termination configurations. They may contain hundreds of thousands of fractures. Hydraulic properties will be computed efficiently on these networks. * See Laug et al. MASCOT 2018 abstract, Simulations in large tridimensional Discrete Fracture Networks (DFN): I. Geometric modeling and mesh generation.

International audience; The 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.

International audience; We derive the relationships that link the general elastic properties of rock masses to the geometrical properties of fracture networks, with a special emphasis to the case of frictional crack surfaces. We extend the well-known elastic solutions for free-slipping cracks to fractures whose plane resistance is defined by an elastic fracture (shear) stiffness k s and a stick-slip Coulomb threshold. A complete set of analytical solutions have been derived for (i) the shear displacement in the fracture plane for stresses below the slip threshold and above, (ii) the partitioning between the resistances of the fracture plane on the one hand and of the elastic matrix on the other hand, and (iii) the stress conditions to trigger slip. All the expressions have been checked with numerical simulations. The Young's modulus and Poisson's ratio were also derived for a population of fractures. They are controlled both by the total fracture surface for fractures larger than the stiffness length l S (defined by k s and the intact matrix elastic properties) and by the percolation parameter of smaller fractures. These results were applied to power law fracture size distributions, which are likely relevant to geological cases. We show that if the fracture size exponent is in the range -3 to -4, which corresponds to a wide range of geological fracture networks, the elastic properties of the bulk rock are almost exclusively controlled by k s and the stiffness length, meaning that the fractures of size l S play a major role in the definition of the elastic properties.

International audience; Discrete Fracture Network – is primarily a modeling framework for fractured geological systems that aims to integrate field data into simulations of flow and/or deformation. It is complementary to, or competing with, continuum methods with both advantages of easily integrating the statistical properties of fracture networks, and of not assuming any homogenization scale. The core element is the DFN conceptual model, which makes a functional link between data from different sources, prior knowledge and medium models. We discuss some fundamental issues about this conceptual model, namely (i) the upscaling of small-scale measurements to site-scale relationships, (ii) intrinsic variability versus geological determinism, (iii) the way to incorporate a priori knowledge, (iv) the transformation of a statistical description into a medium model, (v) the critical characteristics (length scales, scaling laws or physical properties) of fractures for a given DFN application. The main product of the DFN conceptual model is medium models, whose role is to extrapolate/interpolate data with a faithful representation of the geological system. The way in which fracture correlations are taken into account, or not, in the generation process plays an important control on the connectivity and flow properties of medium models.

International audience; Fractures play a key role in many physical phenomena and have characteristics specific different from the surrounding rock matrix. Thus, computing the hydraulic properties of large scale fractured media raises many challenges, both in terms of mesh generation accurately representing the fracture geometry and in terms of numerical method to accurately solve the flow equations. The main novelty of this presentation is to combine different strategies to compute the flow properties at a moderate cost. Typically we combine advanced methods to generate high quality meshes together with robust methods based on mortar techniques to solve the flow. First, we will present the two steps software BLSURF FRAC [1]. In a first phase, it builds a geometric model including fracture intersections. The main difficulty is to build valid curve discretizations. To do so, BLSURF FRAC implements automatic corrections. In a second phase, it generates a mesh of the geometric model by calling a user-selected planar mesher. As planar meshers, we propose to consider the two followings, BAMG and BL2D. We will use the ability of BL2D to adaptively refine the mesh, for more accurate and less expensive flow computations. Then we will present Geofracflow, a software for the simulation of flow in large scale DFNs. Geofracflow is interfaced with BLSURF FRAC. It implements the Mixed-Hybrid Finite Element method in an optimized way, using vectorization, to decrease the computational time. It handles either matching or non-matching meshes at the intersection between fractures, sink/source terms and contrasts in transmissivities from one fracture to another. Finally, as a set of benchmark test cases, we extend those proposed in [2, 3] to DFNs generated with the UFM framework [4, 5]. They are large scale DFNs where the fracture size distribution matches the observations and where fractures are organized so that large fractures inhibit the smaller ones, creating T-termination configurations. Hydraulic properties will be computed on these networks.

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International audience; During a mine-by experiment performed at the Mont Terri Underground Research Laboratory located at the transition between the sandy and the shaly facies of the Opalinus Clay formation, excavation induced micro-acoustic events were recorded in the so-called Gallery 08 (the EZ-G experiment). A first cluster of events occurred in the vicinity of the eastern sidewall of Gallery 08, and a second cluster was observed ahead of the advancing tunnel face. For each recorded micro-acoustic event (AE), all located in the sandy facies of the Opalinus Clay formation, the total stresses associated with the onset of inelastic deformations were estimated using a three-dimensional numerical model. The numerical analysis is based on the assumption that the rock mass behavior in the vicinity of the excavation is essentially elastic before the stress redistribution causes damage evidenced by the triggered AE activity. For the cluster located at the tunnel sidewall, the source mechanism analysis reveals the predominance of extensional failure (tensile) events. The numerical analysis of each individual micro-acoustic event suggests that the differential stresses at the onset of damage range between 3 and 10 MPa. These values are in reasonable agreement with crack initiation thresholds obtained in the laboratory from samples of the various sub-facies types of the sandy facies in the Opalinus Clay formation, which range between 2 and 18 MPa. For the cluster located ahead of the tunnel face, the source mechanism analysis indicates the predominance of local shear failure events. This is consistent with observed shear dislocations on bedding planes within weak beds in the sandy facies that have similar strength properties as the shaly facies. Thus, the modelled shear and total normal stresses acting across the average bedding plane orientation at each event location were modelled and used to estimate the in situ shear strength along the bedding planes. The model suggests a friction angle of 33.4° and a cohesion of 0.43 MPa. The results are overall consistent with the bedding plane strength obtained through undrained direct shear tests on specimens of the shaly facies, suggesting that the observed weak beds with a strength similar to the shaly facies govern the behavior at the tunnel face.

International audience; This poster present a new method for DFN generation with stress-driven nucleation and growth, in a time-wise process

International audience; Fractures are key elements governing permeability and flow paths in crystalline rocks and sedimentary layers with low matrix porosity. The ability to properly predict those properties, which is crucial for some industrial applications, such as the risk assessment in nuclear waste management, strongly relies on our ability to properly describe the fracture network characteristics. A usual method is to define discrete fracture network (DFN) models, where a set of 3D fractures represents the geological environment. It primarily consists in combining various data, thanks to stereological relationships, on the fracture properties (geometry, transmissivity) and on hydraulic properties (e.g. borehole flow logs), in order to produce 3D statistical distributions and upscaling functions. However, this approach is not univocal and various DFN models can match the observations. We present the results of a study made for the Swedish Nuclear Fuel and Waste Management Company (SKB) through an application to the Forsmark site in Sweden. We perform an analysis of structural data and flow logging based on the PFL tool [1] to characterize the geological environment in terms of fracture density, permeability, and flow channeling by focusing on their scaling and variability. Then, we define candidate DFN models. A critical component of the DFN is the fracture size distribution, which is the upscaling function required to extrapolate fracture densities between data gaps, from borehole cores up to site scale. Another important feature of DFN models lays in the spatial correlations between fractures, which is neglected by the commonly used Poissonian (i.e. spatially random) models. We recently developed a new DFN modelling approach (further referenced as UFM for Ubiquitous Fracture Model), which mimics the geological processes of fracturing [2, 3]. For the same distribution of fracture size and orientations, networks from the UFM model are much less connected than their random equivalent [4]. Assigning fracture transmissivities is also an important issue in the modeling process, especially because only 20-25% of the total fracture surface is considered open (the rest is clogged). In addition, the transmissivity of permeable fractures is likely dependent on size and stress conditions. We perform flow simulations on these DFN models and reproduce the flow data. We compare the hydraulic properties of the synthetic (DFN) media to those of the natural environment to assess their prediction capabilities. Our conclusions are that networks produced by the UFM model are capable to properly reproduce the scaling behavior of the natural flow without any specific calibration, unlike Poissonian models. We also point out the importance of defining the dependency of fracture transmissivity on fracture size and orientation (including the role of the applied stress on fracture transmissivity). Indeed, such a dependency changes the scaling of hydraulic properties, their spatial variability and increases the channeling. [1] A. Öhberg, P. Rouhiainen, "Posiva Groundwater flow Measuring Techniques," (Posiva, 2000). [2] P. Davy, R. Le Goc, C. Darcel, A model of fracture nucleation, growth and arrest, and consequences for fracture density and scaling. Journal of Geophysical Research: Solid Earth 118, 1393-1407 (2013). [3] P. Davy et al., A likely universal model of fracture scaling and its consequence for crustal hydromechanics. J. Geophys. Res. 115, 1-13 (2010). [4] J. Maillot, P. Davy, R. L. Goc, C. Darcel, J. R. d. Dreuzy, Connectivity, permeability, and channeling in randomly distributed and kinematically defined discrete fracture network models. Water Resour. Res. 52, 8526-8545 (2016).

International audience; The realism of Discrete Fracture Network (DFN) models, beyond the bulk statistical properties, relies on the spatial organization of fractures, which is not issued by classical stochastic DFN models. This can be improved by injecting prior information in DFN from a better knowledge of the geological fracturing processes. We first develop a model using simple kinematic rules for mimicking the growth of fractures from nucleation to stop, in order to evaluate the consequences of realistic DFN on the network connectivity and flow structure. The model generates fracture networks with power-law scaling distributions and a percentage of T-intersections that are consistent with field observations. Nevertheless, a larger complexityrelying on the spatial variability of natural fractures positions cannot be explained by the random nucleation process. We propose to introduce a stress-driven nucleation in the timewise process of this kinematic model to study the correlations between nucleation, growth and existing fracture patterns. The method uses the stress field generated by existing fractures and remote stress as an input for a Monte-Carlo sampling of nuclei centers at each time step. Networks so generated are found to have fractal correlations over a large range of scales, with a dimension that varies with time and with the function that relates the nucleation probability to stress. A sensibility analysis of input parameters has been performed in 3D to quantify the influence of fractures and remote stress field orientations.

International audience; We present progress on Discrete Fracture Network (DFN) flow modeling, including realistic advanced DFN spatial structures and local fracture transmissivity properties, through an application to the Forsmark site in Sweden.DFN models are a framework to combine fracture datasets from different sources and scales and to interpolate them in combining statistical distributions and stereological relations. The resulting DFN upscaling function – size density distribution - is a model component key to extrapolating fracture size densities between data gaps, from borehole core up to site scale. Another important feature of DFN models lays in the spatial correlations between fractures, with still unevaluated consequences on flow predictions. Indeed, although common Poisson (i.e. spatially random) models are widely used, they do not reflect these geological evidences for more complex structures. To model them, we define a DFN growth process from kinematic rules for nucleation, growth and stopping conditions. It mimics in a simplified way the geological fracturing processes and produces DFN characteristics -both upscaling function and spatial correlations- fully consistent with field observations.DFN structures are first compared for constant transmissivities. Flow simulations for the kinematic and equivalent Poisson DFN models show striking differences: with the kinematic DFN, connectivity and permeability are significantly smaller, down to a difference of one order of magnitude, and flow is much more channelized. Further flow analyses are performed with more realistic transmissivity distribution conditions (sealed parts, relations to fracture sizes, orientations and in-situ stress field). The relative importance of the overall DFN structure in the final flow predictions is discussed.

International audience; We analyze the spatial fluctuations of stress in a simple tridimensional model constituted by a population of disc-shaped fractures embedded in an elastic matrix with uniform and isotropic properties. The fluctuations arise from the classical stress enhancement at fracture tips and stress shadowing around fracture centers that are amplified or decreased by the interactions between close-by fractures. The distribution of local stresses is calculated at the elementary mesh scale with the 3DEC numerical program based on the distinct element method.As expected, the stress distributions vary with fracture density, the larger is the density, the wider is the distribution. For freely slipping fractures, it is mainly controlled by the percolation parameter $p$ (i.e., the total volume of spheres surrounding fractures). For stresses smaller than the remote deviatoric stress, the distribution depends only on for the range of density that has been studied. For large stresses, the distribution decreases exponentially when increasing stress, with a characteristic stress that increases with entailing a widening of the stress distribution.We extend the analysis to fractures with plane resistance defined by an elastic shear stiffness $k_s$ and a slip Coulomb threshold. A consequence of the fracture plane resistance is to lower the stress perturbation in the surrounding matrix by a factor that depends on the ratio between $k_s$ and a fracture-matrix stiffness $k_m$ mainly dependent on the ratio between Young modulus and fracture size. $k_m$ is also the ratio between the remote shear stress and the displacement across the fracture plane in the case of freely slipping fractures. A complete analytical derivation of the expressions of the stress perturbations and of the fracture displacements is obtained and checked with numerical simulations. In the limit $k_s >> k_m$, the stress perturbation tends to 0 and the stress state is spatially uniform.The analysis allows us to quantify the intensity of the stress fluctuations in fractured rocks as a function of both the fracture network characteristics (density and size distribution), and the mechanical properties (fracture shear stiffness vs matrix elastic properties).

Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence discuss nucleation of a critical defect. The computation of the toughness allows for drawing a simple connection with crack front propagation (depinning) models., Comment: The European Physical Journal Special Topics Special Topics, 2014

International audience; In a lot of geological environments, permeability is dominated by the existence of fractures and bytheir degree of interconnections. Models have shown that flow properties depends mainly on thestatistical properties of the fracture population (length, apertures, orientation) and of intersections,on the topological properties of the network, as well as on some detailed properties within fractureplanes. None of them can be a priori discarded as fracture networks are potentially close to somepercolation threshold. Still, most of the details of the fracture and network structures are stronglyhomogenized by the inherent diffusive nature of flows. It should thus be possible to upscalepermeability on the basis of a limited number of descriptors.Based on an extensive analysis of 2D and 3D Discrete Fracture Networks (DFNs) as well as onreference connectivity structures, we investigate the relation between the local fracture structuresand the effective permeability. On the one hand, poor connectivity, small intersections, andfracture closures act as bottlenecks and obstacles limit permeability. If these patterns controlledthe flow, permeability would derive from an ensemble of fracture in series dominated by itsweakest element. Effective permeability could then be approached by the harmonic mean of thelocal permeabilities. On the other hand, extended fractures, locally higher fracture densities, andpreferential orthogonal fracture orientations enhance permeability. If these patterns controlled theflow, all fractures would contribute to flow equally, and effective permeability would tend to thearithmetic mean of the local permeabilities.Defined as the relative weight between the two extreme harmonic and arithmetic means, thepower-law averaging exponent provids a compact way of comparing fracture network hydraulics.It may further lead to some comprehensive upscaling rules. To this end, we determinenumerically the power-law averaging exponent for a wide range of 2D and 3D DFNs [de Dreuzyet al., 2012; de Dreuzy et al., 2001] and compare them to reference connectivity structures andpermeability fields [de Dreuzy et al., 2010]. Permeability is not only determined by globalconnectivity but also by more local effects. We measure them by defining a local connectivityindex equal to the number of fracture connections at some reference local scale. Knowledge ofthe relative importance of local vs. global effects should help optimizing characterizationstrategies.

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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. © 2015 Hope, Davy, Maillot, Le Goc and Hansen. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

International audience; We perform site scale DFN modeling using a geometrical and quantitative approach. The DFN model is a statistical model which defines the density of fractures having given geometrical properties (size and orientation) and which includes an intrinsic variability term. The density variability term is defined from a scaling analysis. Density terms are calculated in 3D using stereological rules and assumptions about the underlying DFN scaling model. This allows combining data acquired at different scales and from different support shapes.Local datasets and related models are first characterized and then clustered into statistically identical models. This classification process determines the minimum number of Statistical Fracture Models (SFMs, density distribution functions) which describes a database and relative site. It aims at providing, up to site scale, the best possible division into SFMs such that (i) within a SFM fracturing properties are statistically compatible with a single parent DFN model and (ii) DFN models associated to distinct SFMs are different (statistical parameters can be distinguished).The method is applied to the SKB Forsmark and Äspö sites in Sweden. The selected databases encompass up to hundreds of thousands records of fractures from various supports (cored boreholes, tunnel and surface outcrops). We discuss the classification process and the resulting fracture network description.

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