Fluid flow in rock fractures is significantly influenced by cyclic shear. This phenomenon arises due to seismic activity or repeated stress changes resulting from excavation, blasting, and operational loads. In this study, experiments are carried out to investigate non-Darcian flow in single rough fractures after cyclic shearing. The evolution of inertial and viscous permeability is analyzed, and a predictive model for non-Darcian flow is established. Cyclic shearing experiments are first conducted to examine shear characteristics and geometric variations, using four groups comprising 24 rough rock fractures. Subsequently, 360 non-Darcian flow experiments are performed to study the evolution of inertial and viscous permeability under cyclic shearing. It is observed that both types of permeability tend to decrease with an increasing number of shearing cycles. The most significant reduction occurs during the first cycle, followed by a slower decline that eventually stabilizes. A predictive model for non-Darcian flow is then developed, considering the geometry before shearing, rock properties, and cyclic shear characteristics. This model is validated against experimental data. Based on the proposed predictive model, a method for determining the critical number of shear cycles is also proposed. These findings contribute to understanding the evolution of non-Darcian flow in fractures subjected to seismic activity or repeated stress changes.

Significant differences in non-Darcian flow between different directions (i.e., forward and reverse flow directions) exist in rock fractures, and understanding of these differences holds crucial implications for evaluating and characterizing flow within fractured rocks. This study proposes a directional aperture parameter to quantitatively characterize the differences in flow between different directions. Firstly, a directional aperture parameter capable of quantitatively distinguishing geometric information of fractures in different directions is proposed. Then, 900 sets of linear and nonlinear flow numerical experiments based on 90 rough fractures are conducted. The results reveal that the differences between forward and reverse flow are shown in the nonlinear flow regime, with equal viscous permeability but significant differences in inertial permeability between the two flow directions. The main reason for the differences lies in the variations of aperture along the two flow directions. A dual-parameter model characterizing the inertial permeability is established by using the directional aperture parameter based on the numerical experimental data from the 90 rough fractures. The critical condition where the significant differences between the forward and reverse flow starting to appear are identified. The quantitative characterization of differences in three-dimensional rough fractures between different directional flows is discussed. The findings from this study could be helpful in advancing our understanding of fluid flow behaviors in natural rock fractures.

Inertial permeability is a critical parameter that quantifies the pressure loss caused by inertia in fluid flow through rough-walled fractures, described by the Forchheimer equation. This study investigates the size effect on the inertial permeability of rough-walled fractures and establishes a characterization model for fractures of varying sizes. Numerical simulations are conducted on five large-scale fracture models (1 m x 1 m) by resolving the Navier-Stokes equations. Smaller models are extracted from these large-scale fracture models for detailed size-dependent analysis. The results show that the peak asperity height (xi), asperity height variation coefficient (eta), and the fitting coefficient of the aperture cumulative distribution curve

Obtaining a comprehensive understanding of solute transport in fractured rocks is crucial for various geoengineering applications, including waste disposal and construction of geo-energy infrastructure. It was realized that solute transport in fractured rocks is controlled by stochastic discrete fracture-matrix systems. However, the impacts and specific uncertainty caused by fracture network structures on solute transport in discrete fracture-matrix systems have yet not been fully understood. In this article, we aim to investigate the influence of fracture network structure on solute transport in stochastic discrete fracture-matrix systems. The fluid flow and solute transport are simulated using a three-dimensional discrete fracture matrix model with considering various values of fracture density and size (i.e., radius). The obtained results reveal that as the fracture density or minimum fracture radius increases, the corresponding fluid flow and solute transport channels increase, and the solute concentration distribution range expands in the matrix. This phenomenon, attributed to the enhanced connectivity of the fracture network, leads to a rise in the effluent solute concentration mean value from 0.422 to 0.704, or from 0.496 to 0.689. Furthermore, when solute transport reached a steady state, the coefficient of variation of effluent concentration decreases with the increasing fracture density or minimum fracture radius in different scenarios, indicating an improvement in the homogeneity of solute transport results. The presented analysis results of solute transport in stochastic discrete fracture-matrix systems can be helpful for uncertainty management in the geological disposal of high-level radioactive waste.

Cement grouting has been widely used in rock tunneling to reduce groundwater inflow by sealing rock fractures. However, the injected cement grout often encounters hydraulic erosion that affects the safety and sustainability of rock tunnels in the long term. Analysis of the long-term hydraulic erosion effect on cement grout in rock fractures is therefore important for the safety and sustainability development of rock tunnel engineering. In this work, a hydraulic erosion model for analyzing cement grout erosion in a homogeneous fracture is established and used to theoretically investigate the transmissivity evolution of the grouted fracture under longterm hydraulic erosion. In the present model, the fracture seepage characteristics, solid erosion theory and mass conversation for water-solid two-phase flow are considered, and the mathematical model as a set of partial differential equations is established. Based on laboratory tests, the key parameters (e.g., erosion coefficient) are calibrated and the erosion model is validated. Numerical simulations are conducted by numerically resolving the mathematical model. The results show that the erosion phenomenon first occurs in the edge areas of the grouted area near the fracture boundary; the erosion area gradually expands toward the center of the grouted area. The porosity and flow velocity significantly increase in the area with relatively strong erosion effects. During the erosion process, the concentration of cement grout gradually increases along the seepage path until a more uniform distribution of cement particle concentration is achieved. Due to the erosion process, the spatial distribution of hydraulic pressure along the fracture direction transforms from a linear distribution to a nonlinear distribution. The effective fracture transmissivity increases nonlinearly along the erosion process. The presented erosion model and analysis results are potentially useful for the safety and durability assessment of rock tunnels.

Cement grouting is widely used in rock tunnelling to control groundwater inflow by sealing rock fractures. Accurately predicting grout propagation in rock fractures is crucial for the design, execution, and monitoring of rock grouting in engineering applications. Current methods rely on theoretical models, such as the real-time grouting control (RTGC) method, which is derived based on simplified fracture geometries like smooth parallel plates/disks. However, real rock fractures consist of rough surfaces with variable apertures. In this study, we present a computational model for theoretically predicting the propagation of non-Newtonian cement grout in variable fracture apertures. This model is validated with laboratory test data on grout propagation in a one-dimensional varying aperture long slot (VALS). We also analysed the impact of varying aperture on cement grout propagation processes. Our findings demonstrate that the presented computational model predicts the grout propagation process in this geometry with good accuracy. Moreover, we observed that varying aperture significantly affects the grout propagation process in fractures. The insights provided by our model and analysis results are potentially useful in rock tunnelling projects, specifically for the theoretical analysis of cement grout propagation in rock fractures.

Understanding the shear strength characteristics of rock fractures is crucial for a wide range of rock engineering applications. The strength of rock fractures is significantly dependent on fracture geometry that can be altered during historical shearing process. This study presents a brief analysis of repeated direct shear of a mated fracture. We conducted five repeated shear test simulations under constant normal load conditions using a predictive shear model presented in our previous work. The fracture surface used in the first round of shear simulation is scanned from a natural granite fracture surface. After shearing, the fracture surfaces are repeatedly used for the next rounds of shear simulations. The results generally show that the repeated shear induces irreversible surface degradation, which reduces the shear strength and normal displacement. The findings of this study are helpful for understanding the shear behavior of rock fractures.

Rock grouting is a common measure to reduce the seepage through conductive fractures in the rock mass around tunnels. Two types of grouting are normally carried, pre-excavation grouting and postexcavation grouting. Pre-grouting, commonly applied in Scandinavian tunnels, is used to seal the conductive fractures around the tunnel before the excavation of tunnel sections. In post-excavation grouting, which is dedicated to seal the remaining leakage in the excavated tunnel sections, the injected grout often encounters large seepage in rock fractures. Previous experiments have shown that the grout can be washed out easily when the grout is fresh even though the injected grout has initially sealed the fracture. One of the most significant phenomena for the water to “break up” the grout is viscous fingering. Viscous fingering occurs when certain conditions enable interface instability between the water and the cement-based grout. In this paper, the authors aim to evaluate if viscous fingering can be avoided under pre- and post-grouting conditions. For this purpose, computational fluid dynamics (CFD) simulations using the software Ansys Fluent is carried out. The simulation results demonstrating viscous fingering between water and cement-based grout are analyzed and discussed. Based on the results, suggestions on the grouting strategy with respect to pre- and post-grouting are provided to deal with the potential issues related to viscous fingering.

Flow of typical non-Newtonian fluids such as cement grouts can experience different regimes as the Reynolds number (Re) changes, understanding of which is important for design and operation of rock grouting in various rock engineering applications. Here, flow regimes of representative non-Newtonian fluids, i.e., Bingham and Herschel–Bulkley (H–B) fluids, are numerically investigated with experimental validations. Three tensile rock fracture surfaces originated from a fine-grained sandstone, a medium-grained sandstone and a medium-grained granite samples are used to create rough-walled fracture models with variable aperture structures. Flow of groundwater, Bingham and H–B fluids through these fractures is numerically simulated respectively, by solving the full mass and momentum conservation equations with the Re ranging from 0.01 to 1000. The regimes for these fluids flowing through the fractures are characterized. Laboratory flow tests are conducted in a cylindrical granite fracture sample to verify the characterized flow regimes. The results reveal important differences of flow regimes between Newtonian and non-Newtonian fluids. Specifically, the transmissivity for water flow is constant when Re is relatively small until the Re reaches certain critical values; the transmissivity for Bingham and H–B fluids flow increases with increasing Re until asymptotically reaches certain peak values, followed by a descending stage when Re is relatively large. The critical (water) and peak (Bingham and H–B fluids) values are affected by surface roughness, that is, a rougher surface results in smaller critical and peak values as well as greater discrepancies compared to the analytical solutions based on the smoothed parallel plates model. These results show that a peak or optimum transmissivity is achievable in a specific range of Re (Re = 10–100 for the fractures studied). This new finding can potentially help optimize the injection pressure or flow rate in rock grouting practices.

Co-exploitation of coal and geothermal energy through water-conducting structures is one of the most promising methods for harnessing renewable energy in some coal mines. A rock compression-erosion coupling test system is built to investigate the extraction efficiency of geothermal wells in the co-exploitation scheme. Compression-erosion tests are carried out to analyze the evolution of mechanics and hydraulic characteristics of broken rocks. The testing results show that the hydrothermal flow erodes the fine rock particles, and compressive deformation can be observed during the erosion process. The erosion effect in broken rocks intensifies with the decrease of axial stress and the increase of fractal dimension, water pressure, and inner radius. Meanwhile, the rock sample shows more significant deformation. Two permeability forecasting models are adopted to forecast permeability evolution during geothermal extraction. The forecasting results indicate that the Brinkman model is better than the Hazen model, and the accuracy of the Brinkman model is lower for the samples with stronger compression-erosion effects. In addition, strategies to improve the extraction efficiency are proposed, i.e., reinforcing the broken rocks above the geothermal well, locating geothermal wells in rocks with higher fragmentation, increasing pumping pressure, and expanding the geothermal well size.