Quantitative assessment of the flow properties and mechanical stability of naturally fractured rock is frequently practised across the mining, petroleum, geothermal, geological disposal, construction and environmental remediation industries. These fluid and mechanical behaviours are strongly influenced by the connectivity of the fracture system and the size of the intact rock blocks. However, these are amongst the more difficult fracture system properties to characterize and honour in numerical simulations. Nonetheless, they are still the product of interactions between fractures that can be conceptualized as a series of deformation events following geomechanical principles. Generating numerical models of fracture networks by simulating this deformation with a coupled and evolving rock mass and stress field is a significant undertaking. Instead, large-scale fracture network models can be 'grown' dynamically according to rules that mimic the underlying mechanical processes and deformation history. This paper explores a computationally efficient rules-based method to generate fracture networks, demonstrates how different types of fracture patterns can be simulated, and illustrates how inclusion of fracture interactions can affect flow and mechanical properties. Relative to methods without fracture interaction and in contrast to some other rules-based approaches, the method described here regularizes and increases fracture connectivity and decreases flow channelling.

Natural fractures are characterized by high internal heterogeneity. This internal variability is the cause of flow channeling, which in turn leads to contaminant transport taking place primarily along the high-velocity channels. Mass exchange between the high-velocity channels and the low-velocity zones has the potential to enhance contaminant retention, due to solute diffusion into the low-velocity zones and subsequent exposure to additional surface area for diffusion into the bordering rock matrix. Here, we derive a random walk particle tracking method for heterogeneous fractures, which includes an additional term to account for the aperture gradient. The method takes into account advection, diffusion in the fracture and matrix diffusion. The developed numerical framework is applied to assess the effect of low-velocity zones in rough self-affine fractures. The results show that diffusion into low-velocity zones has a visible but modest impact on contaminant retention. The magnitude of this impact does not change considerably, regardless of whether diffusion into the rock matrix is considered in the model, and increases for a decreasing average Peclet number of the fracture. Natural fractures are highly heterogeneous, comprising flowing channels and lower-velocity zones We study the effects that diffusion into low-velocity zones has in contaminant transport through rough fractures Accounting for diffusion in low-velocity zones has a relatively modest impact on contaminant retention

Fracture networks are preferential flow paths playing a critical role in a wide range of environmental and industrial problems. Their complex multiscale structure leads to broad distributions of fluid travel times, affecting many biogeochemical processes. Yet, the relationship between the fracture network structures, their hydrodynamic properties, and the resulting anomalous transport dynamics remains unclear. We use a large database of fracture network models to investigate the factors controlling fluid velocity and travel-time distributions across a wide range of networks, from synthetic to field-calibrated models, with aperture variability at both fracture and network scales. Analysis reveals that transport statistics have generic properties across investigated networks, including notably heavy-tailed travel time distributions. Networks of increasing complexity and heterogeneity lead to broader velocity distributions and more channeled velocity fields, where flow concentrates in a narrow channel web in the three-dimensional (3D) fracture structure. While heterogeneity in point-velocity statistics increases travel-time variability, channeling tends to reduce it. This counterintuitive phenomenon challenges current theories, which assume that long travel time power law exponents are determined solely by point-velocity statistics. By analyzing velocity and travel time statistics for different flow structures, we develop a coupled Continuous Time Random Walk framework capturing the unexpected control of the velocity field's spatial structure on anomalous transport in fracture networks. This leads to a unique class of random walk models capturing the respective roles of velocity heterogeneity and spatial structure on transport in networks. These findings open a prospective for characterizing, modeling, and predicting transport dynamics in complex networks, with potential applications to geological, biological, and engineered networks.

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. We observe that 100% of the fractures are open when P-c is hydrostatic, and the ratio decreases exponentially to a plateau of similar to 17% when P-c is lithostatic and above. Exceptions are the oldest fractures, having a low open fraction independent of 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.

In the present paper, we discuss various aspects of the SKB Task Force on Modeling of Groundwater Flow and Transport of Solutes (TFGWFTS). The TFGWTS is a multi-lateral forum for modeling of groundwater flow and solute transport, focusing on issues of relevance for disposal of nuclear waste. We discuss the objectives and set-up of the different tasks performed during the last 30 years, and specifically how the results of the modeling have informed performance and safety assessment applications within SKB (Swedish Nuclear Fuel and Waste Management Company, Solna, Sweden). We conclude that the TFGWFTS has been instrumental in developing modeling methodologies and tools, and in training and fostering modelers. While the early tasks were related to the construction of the Äspö Hard Rock Laboratory in Sweden and developed general modeling competence, the later tasks have served performance and safety assessment purposes in a more substantial manner.

Groundwater flow in sparsely fractured crystalline rocks is highly channelized due to the existing complex hydrogeological heterogeneity in fracture networks. The impacts of multiscale hydraulic heterogeneity on channelized flow in a block of fractured rock under the unidirectional flow condition are investigated by three-dimensional (3D) discrete fracture network (DFN) modeling. A channel network (CN) model generated from DFN is used to model the channelized groundwater flow in fractured crystalline rock. An approach for parameterizing the channel conductance is proposed which uses information from the hydrogeological characterization data. The results show that the network scale hydrogeological heterogeneity dominates the distribution variability of flowrates. The proposed parameterization approach for the channel conductance is effective and robust. Based on the available hydrogeological characterization data, it is possible to compensate for the neglected heterogeneity in the CN model by enhancing the variability of assigned channel conductance. The findings from this work are useful for model simplification from 3D DFN to CN, and for overcoming the difficulty in the parameterization of CN models in applications.

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 ls, the way permeability increases with scale above ls, 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 beforerejecting 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.

The impact of shear displacement under different mechanical boundary conditions on fluid flow and advective transport in a single fracture at the laboratory scale is demonstrated in the present study. The shear-induced changes of fracture aperture structures are determined by using the measured normal displacements and digitalized fracture surfaces from laboratory shear tests. Five shear tests on concrete replicas of the same fracture under different mechanical boundary conditions, including constant normal loading (CNL) and constant normal stiffness (CNS), are conducted to analyse the influence of mechanical boundary conditions on the shear-flow-transport processes. Fluid flow in the fracture with different shear displacements are simulated by solving the Reynolds equation. The Lagrangian particle tracking method is applied to model the advective transport in the fracture after shearing. The results generally show that the shear displacements and the normal loading conditions can significantly affect flow patterns and advective travel time distributions in the fracture. For mated fractures, the flow and transport will be enhanced by the increasing shear displacement because of shear dilation. For cases with the same shear displacement, the median advective travel time increases with the increasing boundary normal stiffness. The median advective travel time under the CNS boundary condition is generally longer than that under the CNL boundary condition. The results from this study can help to improve our understanding of stress-dependent solute transport processes in natural rock fractures. 

SKB and several other waste management organizations have established the international SKB Task Force on Modeling of Groundwater Flow and Transport of Solutes (TF GWFTS) to support and interpret field experiments. Objectives of the task force are to develop, test and improve tools for conceptual understanding and simulating groundwater flow and transport of solutes in fractured rocks. Work is organized in collaborative modeling tasks. Task 9 focuses on realistic modeling of coupled matrix diffusion and sorption in heterogeneous crystalline rock matrix at depth, e.g. by inverse and predictive modeling of in-situ transport experiments. Posiva’s REPRO (rock matrix REtention PROperties) experimental campaign has been performed at the ONKALO rock characterization facility in Finland. The two REPRO experiments considered were the Water Phase Diffusion Experiment (WPDE), addressing matrix diffusion in gneiss around a single borehole interval (modeled in Task 9A), and the Through Diffusion Experiment, which is performed between sections of three boreholes and addressed by modeling in Task 9C. The Long-Term Diffusion and Sorption Experiment (LTDE-SD) was an in-situ radionuclide tracer test performed at the Swedish Äspö Hard Rock Laboratory at a depth of about 410 m below sea level. The experimental results indicated a possible deeper penetration of sorbing tracers into the rock matrix than expected. The shape of these tracer penetration profiles was difficult to reproduce. This experiment was modeled and interpreted in Task 9B. Task 9D is addressing the possible benefits of detailed models of the in-situ experiments in safety assessment calculations. The task is performed by upscaling of the WPDE models to conditions applicable for nuclear waste repositories. As Task 9 is now in a finalization process, a number of lessons learned from the 4 sub-tasks have been identified. These include: • field tracer experiments can provide surprises even when well designed and executed, • interaction between the experimentalists and modelers is important and mutually beneficial when investigating anomalous results, • differences in conceptual models have the greatest impact on model outcomes, • it is not trivial to go from modeling of field experiments to safety assessment modeling without making substantial simplifications.

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.