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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.

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.

This repository contains an executable of the Riverlab model. If you use this model, please cite the appropriate references., {"references":["Davy, P., Croissant, T., & Lague, D. (2017). A precipiton method to calculate river hydrodynamics, with applications to flood prediction, landscape evolution models, and braiding instabilities. Journal of geophysical research: earth surface, 122(8), 1491-1512.","Davy, P. and Lague, D. (2009). Fluvial erosion/transport equation of landscape evolution models revisited. Journal of Geophysical Research : Earth Surface (2003–2012), 114(F3).","Crave, A. and Davy, P. (2001). A stochastic precipiton model for simulating erosion/sedimentation dynamics. Computers & Geosciences, 27(7) :815–827.","Davy, P. and Crave, A. (2000). Upscaling local-scale transport processes in large-scale relief dynamics. Physics and Chemistry of the Earth, Part A : Solid Earth and Geodesy, 25(6) :533–541."]}

International audience; Due to flow variability and sediment heterogeneity, different modes of transport are observed, either successively or simultaneously, in natural rivers. All these modes contribute to the total sediment transport and thus should be considered in the context of fluvial sediment transport and morphodynamic modeling. However, a universal sediment transport law from bed load to suspended load applicable to the full range of hydraulic conditions and to sediment mixtures is lacking despite numerous published transport capacity laws. Similarly, morphodynamic fluvial models typically assume transport-limited conditions that can not capture under-capacity conditions occurring potentially for a certain range of grain sizes and flow conditions. Thus, we aim at building a self-consistent theory by gathering widely accepted concepts of sediment transport in the framework of erosion-deposition models using a disequilibrium transport length. First, we develop a new transport length model that takes into account the different transport modes as a physical continuum. Second, we combine this continuous model of transport length with the erosion-deposition model that we adapt to account for multi-grain sizes. All these steps use existing, tested elementary ingredients that do not require further calibration parameters. Predicted transport lengths range over several orders of magnitude and, for the same hydraulic conditions, the transport length increases with finer grain sizes. Modeled stream capacities obtained at saturation are in agreement with flume observations for both single-grain and multi-grain approaches with at least 70% of the experimental data predicted within a factor 10. The main result is, to our knowledge, the first Multi-Grain Size Sediment Transport model encompassing the diversity of transport modes in non-stationary regimes and predicting how stream capacities scale with bed shear stress. We illustrate how this universal theory of sediment transport can be used to better understand the relationship between grain sizes and transport distances. And we develop long-term transport laws that include the effects of water discharge variability and sediment heterogeneity on fluvial morphodynamic instabilities and deposit stratigraphy, e.g., armor layer and downstream fining.

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; 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.

Flash floods observed in headwater catchments often cause catastrophic material and human damage worldwide. Considering the large number of small watercourses possibly affected, the use of automated methods for flood inundation mapping at a regional scale can be of great help for the identification of threatened areas and the prediction of potential impacts of these floods. An application of three mapping methods of increasing level of complexity is presented herein, including a digital terrain model (DTM) filling approach (height above nearest drainage/Manning–Strickler or HAND/MS) and two hydrodynamic methods (caRtino 1D and Floodos 2D). These methods are used to estimate the flooded areas of three major flash floods observed during the last 10 years in southeastern France, i.e., the 15 June 2010 flooding of the Argens river and its tributaries (585 km of river reaches), the 3 October 2015 flooding of small coastal rivers of the French Riviera (131 km of river reaches) and the 15 October 2018 flooding of the Aude river and its tributaries (561 km of river reaches). The common features of the three mapping approaches are their high level of automation, their application based on a high-resolution (5 m) DTM, and their reasonable computation times. Hydraulic simulations are run in steady-state regime, based on peak discharges estimated using a rainfall–runoff model preliminarily adjusted for each event. The simulation results are compared with the reported flood extent maps and the high water level marks. A clear grading of the tested methods is revealed, illustrating some limits of the HAND/MS approach and an overall better performance of hydraulic models which solve the shallow water equations. With these methods, a good retrieval of the inundated areas is illustrated by critical success index (CSI) median values close to 80 %, and the errors on water levels remain mostly below 80 cm for the 2D Floodos approach. The most important remaining errors are related to limits of the DTM, such as the lack of bathymetric information, uncertainties on embankment elevation, and possible bridge blockages not accounted for in the models.

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).