Discrete Fracture Network Model Research Articles

Predicting fluid flow in reservoirs: analysis of fracture clustering in outcrop analogues

Researchers have used lacunarity, a parameter that quantifies scale-dependent clustering in patterns, to differentiate fracture networks that belong to the same fractal system. In a previous study, the authors showed that lacunarity is efficient in representing connectivity and fluid flow in fractal-fracture models with the same fractal dimension. The objective of this research is to investigate if the concepts thus developed are applicable to outcrop analogues that are representative of subsurface fractured reservoirs. A set of nested fracture networks belonging to a single fractal system but mapped at different scales and resolutions is considered in this study. Lacunarity and connectivity values of these maps are evaluated using geospatial data analysis techniques. Fracture continuum (FC) models are built from these fracture maps and a streamline simulator, TRACE3D, is used to flow simulate these maps. Results show that although the fractal dimension of these maps is same, differences exist in the values of lacunarity, percolation connectivity and also fluid recovery values. It is further noted that the clustering, connectivity and fluid recovery values can be pairwise correlated very well for these natural fracture maps. Thus, the overall results indicate that connectivity in fracture maps, and hence their flow properties, are controlled by lacunarity or scale-dependent clustering attributes. Therefore, there could be novel applicability of the lacunarity parameter in calibrating discrete fracture network (DFN) models with respect to connectivity in natural fracture maps and the prediction of flow behaviour in fractured reservoirs. Thematic collection: This article is part of the Digitally enabled geoscience workflows: unlocking the power of our data collection available at: https://www.lyellcollection.org/topic/collections/digitally-enabled-geoscience-workflows

Data-driven hydraulic property analysis and prediction of two-dimensional random fracture networks

The large parameter space and uncertainty of the discrete fracture networks (DFNs) make the hydraulic characteristics have multiple possibilities. Statistical analysis of hydraulic characteristics based on a large amount of data is a standard practice and central to DFN methodology. The present study developed a two-dimensional (2D) DFN numerical seepage model based on Matlab and Comsol from modeling and parameter calculation to simulation to investigate the influence of parameters involved fracture network on seepage characteristics of DFNs. In total, 1728 2D DFN models were generated with increasing fracture density, fracture length, power-law exponent, fracture orientations, and fracture included angles, and 1728 × 3 = 5184 numerical simulations of fluid flow along the x-axis, y-axis, and center through the DFN models are conducted using a self-developed numerical code. The influence of fracture geometric features on connectivity and permeability are estimated, respectively. And to realize the prediction of permeability tensor by known geological data, a theoretical model based on the Snow model and a data mining model based on the back-propagation model are discussed. The analysis helps researchers and engineers can make informed decisions and develop effective strategies for addressing the challenges posed by uncertainty hydraulic property of the fractured rock masses.

Effects of Geo-Stress and Natural Fracture Strength on Hydraulic Fracture Propagation in a Deep Fractured Tight Sandstone Reservoir.

Hydraulic fracturing technology has been widely used in the tight reservoir reconstruction. Unfortunately, with the deepening of mining depth and the increase of geo-stress, the propagation mechanism of medium-pressure fractures in the reservoir is significantly different from that of conventional shallow reservoirs. Based on the combined finite discrete element method, this paper conducts numerical simulation research on deep tight sandstone reservoirs in the west. The discrete fracture network modeling method is used to establish a tight sandstone reservoir model with natural bedding, and the influence of geo-stress difference and natural fracture strength on hydraulic fracture propagation law in a high geo-stress environment is discussed in detail. The results show that the difference between geo-stress and the strength of natural fractures has a significant effect on the shape and expansion of hydraulic fractures under the high geo-stress conditions. The greater the difference in ground stress, the more obvious the tendency of the main fractures of the reservoir, and the shorter the branch fractures. With the increase of natural fracture strength, the changes in propagation pressure, fracture length, area, and width, which can be fitted with a linear function with a goodness of fit as high as 0.99. In addition, the morphological results of hydraulic fractures in the simulation are not only affected by the constitutive parameters of the model but also may be affected by the randomness of the natural fracture network, thus, showing a certain degree of dispersion. Therefore, it is extremely necessary to build a reservoir fracturing model in a specific area based on more detailed geological monitoring data to guide actual construction. The above achievements have certain reference significance for the field operation of deep tight sandstone reservoirs.

A comparative study on the influences of fracture intersections on the prediction of rock mass permeability

Geometric predictive methods are efficient for determining the permeability of fractured rock masses, which evaluate the contribution of each fracture to the flow. However, the influences of fracture intersections are ignored during the calculation. In this study, influences of fracture intersections on the permeability prediction are studied. The result shows that the predicted flow rate can only have a good accuracy when there is an infinite-length fracture with a larger aperture. Based on this conclusion, three inferences for the applicability of geometric predictive methods are proposed: (a) for fracture networks where all fractures have infinite length, the predicted permeability can have a good accuracy; (b) for fracture networks containing both infinite-length and finite-length fractures, the predicted permeability is only accurate when the infinite-length fracture have a larger aperture; and (c) for fracture networks where all the fractures have finite length, the error rates of predicted permeability increase as the aperture ratios of fracture sets increase. Sixty-three sets of discrete fracture network models are generated for verification, and these numerical results validated our proposed inferences.

Numerical insight into hydraulic fracture propagation in hot dry rock with complex natural fracture networks via fluid-solid coupling grain-based modeling

Abundant natural fractures (NFs) in hot dry rock (HDR) reservoirs serve as a crucial element in hydraulic fracturing technology and reservoir production. Nevertheless, the interaction mechanism between hydraulic fractures (HFs) and natural fracture networks (NFNs) remains poorly understood. This study combines the novel hydro-grain-based model (hydro-GBM) and discrete fracture network (DFN) model to investigate the effects of in-situ stress, fracture number, and fracture length on hydraulic fracturing behaviors in mineral-scale granite with NFNs. Results indicate that as the complexity of NFs increases, the stress shadow effect is amplified during HF propagation, while the spatial arrangement of NFs governs the propagation of secondary paths. Additionally, a downward trend is observed in average activity levels of acoustic emission (AE) events and proportions of large events within NFs and matrix. Damage and activation degrees in both NFs and matrix decrease with an increase in the number of NFs. The inability of main hydraulic paths to propagate over long distances can be attributed to the dispersion of fracturing fluid and the rapid decay of pressure within densely distributed, short NFs. These numerical findings shed light on the process of HFs activating NFNs and provide valuable insights for enhancing heat extraction efficiency in HDR reservoirs.

Experimental and numerical analysis of flow through a natural rough fracture subject to normal loading

Fractured crystalline rocks have been chosen or are under consideration by several countries as host rock formations for deep geological repositories for spent nuclear fuel. In such geological formations, flow and solute transport are mostly controlled by a network of connected natural fractures, each of them being characterised by internal heterogeneity, also denoted as roughness. Fractures are, in turn, subject to variable load caused by various factors, such as the presence of thick ice sheets formed during glaciation periods. Understanding how coupled hydro-mechanical (HM) processes affect flow and transport at the scale of a single natural fracture is crucial for a robust parameterisation of large-scale discrete fracture network models, which are not only used for nuclear waste disposal applications but are also of interest to problems related to geothermics, oil and gas production or groundwater remediation. In this work, we analyse and model an HM experiment carried out in a single natural fracture and use the results of both, the experimental and the modelling work, to get insights into fundamental questions such as the applicability of local cubic law or the effect of normal load on channeling. The initial fracture aperture was obtained from laser scanning of the two fracture surfaces and an equivalent initial aperture was then defined by moving the two fracture surfaces together and comparing the results obtained using a Navier–Stokes based computational fluid dynamics (CFD) model with the experimental flowrate obtained for unloaded conditions. The mechanical effect of the different loading stages was simulated using a high-resolution contact model. The different computed fracture apertures were then used to run groundwater flow simulations using a modified Reynolds equation. The results show that, without correction, local cubic law largely overestimates flowrates. Instead, we show that by explicitly acknowledging the difference between the mechanical aperture and the hydraulic aperture and setting the latter equal to 1/5 of the former, cubic law provides a very reasonable approximation of the experimental flowrates over the entire loading cycle. A positive correlation between fluid flow channeling and normal load is also found.

A precise modeling method of three‐dimensional discrete fracture network based on rectangular joint model

AbstractAs the weak structure and main seepage channel of rock mass, the discrete fracture network (DFN) has a significant influence on the physical and mechanical properties of rock mass. In this paper, based on the rectangular joint model, two algorithms are proposed to realize the precise modeling of the DFN in any polyhedron. First, the equivalence of DFN modeling with the rectangular joint model and the elliptical joint model is theoretically deduced. On this basis, the chain splicing algorithm suitable for the rectangular joint model is proposed, which can generate the DFN model according to the actual distribution of joint spacing, trace, and bridge length. Aiming at the concave boundary in the model domain, the segmentation‐stitching operation is put forward, and the continuity of the joint when passing through the interface is ensured. Finally, the effectiveness of the above algorithm is verified by several simple cases, and the relationship between the size of the geometrical representative elementary volume (REV) and discontinuity parameters is discussed. The results show that when the mean values of the joint distribution parameters are the same, even if the distribution rules are different, the number of joints generated in the same spatial region is approximately equal. The size of the geometrical REV is independent of the spacing and bridge length and is approximately three to five times the mean of the trace. The relevant algorithms and conclusions in this paper can be used as the basis for subsequent rock mass stability analysis and seepage calculation.

Characterization and reconstruction of rough fractures based on vector statistics

The characteristics of fracture networks are of great significance for unconventional geo-energy exploitation such as shale oil, shale gas and geo-thermal extraction. Natural fractures and induced fractures after reservoir stimulation control the mechanical properties and fluid flow of the reservoirs. The quantitative characterization and reconstruction of rough fractures are essential for studying the fluid flow and mechanical properties of the reservoirs with complicated fracture networks. Based on vector statistics, a vector statistical method (VSM) for quantitative characterization of rough fractures is proposed and tested using 10 standard joint profiles. Furthermore, the growth vector counting method (counting method) and growth vector probability method (probability method) for single rough fractures in two-dimensional (2D) and three-dimensional (3D) models are proposed. Afterward, a morphology comparison and quantitative evaluation of single rough fractures before and after reconstruction are conducted. When the counting and probability methods are used to reconstruct single rough fractures, the difference in the tortuosity and fractal dimensions of the original and reconstructed fractures are less than 5% and 2.5%, respectively. It implies the counting and probability methods proposed herein can reconstruct rough fractures with approximate statistical characteristics and quantitative characterization parameters. Subsequently, the counting and probability methods for single rough fractures are further developed for 2D and 3D modeling of conventional and rough discrete fracture networks. The results indicate that the growth vector counting and probability methods proposed in this study have significant potential for rough discrete fracture network modeling. In addition, the merits and limitations of the proposed algorithms in modeling discrete fracture network models are discussed.

A CLUSTERED FRACTAL DISCRETE FRACTURE NETWORK MODEL FOR FRACTURED COAL

The fracture network in fractured coal is the main channel of coal seam gas flow. Not only the geometric topology properties (such as fractal characteristics) of a single fracture but also the connection topology properties (interconnection characteristics between fractures) of the fracture network have an important impact on the fluid flow in fracture networks. In this study, the connection topology properties of the fracture network in the fractured coal are explored based on the complex network theory for the first time. The property parameters such as the fracture node degree, the clustering coefficient, and the average path length are analyzed. It shows that the average clustering coefficient of the fracture network in fractured coal is larger, and the average path length is smaller. The connection property of the fracture network in the fractured coal presents a typical “small-world” clustering model. Further, by considering the fractal characteristics of the single fracture and the clustering characteristics of the fracture network, an improved clustered fractal discrete fracture network (DFN) model is developed. Then, based on the lattice Boltzmann method, the permeability properties of the generated clustered fractal DFNs are analyzed. The results show that the permeability of DFNs is positively correlated with the average clustering coefficient of fracture network, and negatively correlated with the fractal dimension of fracture. Therefore, the topological clustering characteristics of fracture networks and the fractal characteristics of fractures cannot be ignored in describing the fluid flow in the fracture network, and our clustered fractal DFN model provides a new idea for guiding the optimization design in DFN engineering.

Assessing Stress Variability in Fractured Rock Masses with Frictional Properties and Power Law Fracture Size Distributions

AbstractThe presence of fractures in rock masses plays a major role in its stress state and its variability. Each fracture potentially induces a stress perturbation, which is correlated to its geometrical and mechanical properties. This work aims to understand and quantitatively predict the relationship between fractured systems and the associated stress fluctuations distribution, considering any regional stress conditions. The approach considers the rock mass as an elastic rock matrix into which a population of discrete fractures is embedded—known as a Discrete Fracture Network (DFN) modeling approach. We develop relevant indicators and analytical solutions to quantify stress perturbations at the fracture network scale, supported by 3D numerical simulations, using various fracture size distributions. We show that stress fluctuations increase with fracture density and decrease as a function of the so-called stiffness length, a characteristic length that can be defined as the ratio between Young’s modulus of the matrix and fracture stiffness. Based on these considerations we discuss, depending on DFN parameters, which range of fractures should be modeled explicitly to account for major stress perturbations in fractured rock masses.

Heat Extraction Evaluation of CO2 and Water Flow through Different Fracture Networks for Enhanced Geothermal Systems

Enhanced geothermal system (EGS) technologies have been developed to improve geothermal energy production from hot dry rock (HDR). In this study, discrete fracture network models for geometric topological networks that consider different parameters (the fracture density and the fracture length index) were built on the basis of fractal geometry theory. The heat extraction processes of CO2 and water as the working fluid through different discrete fracture networks were simulated with the application of the thermal–hydraulic–mechanical (THM) coupled method. A series of sensitivity analyses were carried out to reveal the influences of fracture parameters on heat transfer processes. Based on the simulation results, heat extraction efficiencies and temperature distributions in the reservoir of CO2 and water as the working fluid were compared, which showed that CO2 as the working fluid can bring a faster thermal breakthrough. It was found that the fracture length index a = 2.5 and the fracture density I = 5.0 can provide the highest heat extraction rate compared with other cases. This study provides a detailed analysis of fracture parameters and working fluids, which will contribute to the optimized management of geothermal energy production.

Review of discrete fracture network characterization for geothermal energy extraction

Geothermal reservoirs are highly anisotropic and heterogeneous, and thus require a variety of structural geology, geomechanical, remote sensing, geophysical and hydraulic techniques to inform Discrete Fracture Network flow models. Following the Paris Agreement on reduction of carbon emissions, such reservoirs have received more attention and new techniques that support Discrete Fracture Network models were developed. A comprehensive review is therefore needed to merge innovative and traditional technical approaches into a coherent framework to enhance the extraction of geothermal energy from the deep subsurface. Traditionally, statistics extracted from structural scanlines and unmanned aerial vehicle surveys on analogues represent optimum ways to constrain the length of joints, bedding planes, and faults, thereby generating a model of the network of fractures. Combining borehole images with seismic attributes has also proven to be an excellent approach that supports the stochastic generation of Discrete Fracture Network models by detecting the orientation, density, and dominant trends of the fractures in the reservoirs. However, to move forward to flow modelling, computation of transmissivities from pumping tests, and the determination of hydraulically active fractures allow the computation of the hydraulic aperture in permeable sedimentary rocks. The latter parameter is fundamental to simulating flow in a network of discrete fractures. The mechanical aperture can also be estimated based on the characterization of geomechanical parameters (Poisson’s ratio, and Young’s modulus) in Hot Dry Rocks of igneous-metamorphic origin. Compared with previous review studies, this paper will be the first to describe all the geological and hydro-geophysical techniques that inform Discrete Fracture Network development in geothermal frameworks. We therefore envisage that this paper represents a useful and holistic guide for future projects on preparing DFN models.

Differences in the permeability assessment of the fractured reservoir rocks using the conventional and the rough discrete fracture network modeling

Permeability assessment of naturally fractured rocks and fractured rocks after fracturing is critical to the development of oil and gas resources. In this paper, based on the discrete fracture network (DFN) modeling method, the conventional discrete fracture network (C-DFN) and the rough discrete fracture network (R-DFN) models are established. Through the seepage numerical simulation of the fractured rocks under different DFN, the differences in permeability of the fractured rocks under different parameters and their parameter sensitivity are analyzed and discussed. The results show that unconnected and independent fractures in the fracture network may weaken the seepage capacity of the fractured rocks. The fractured rock permeability increases with increase in connectivity and porosity and decreases with increase in maximum branch length and fracture dip. The use of C-DFN to equate the fracture network in the fractured rocks may underestimate the connectivity of the fracture network. For the more realistic R-DFN, the promotion of gas flow by connectivity is dominant when connectivity is high, and the hindrance of gas flow by fracture roughness is dominant when connectivity is low or when it is a single fracture. The permeability of the fractured rocks with R-DFN is more sensitive to the parameters than that of the fractured rocks with C-DFN. The higher the connectivity and porosity of the fractured rocks, the more obvious the difference between the permeability of the fractured rocks evaluated by C-DFN and R-DFN.

Performance evaluation of enhanced geothermal systems with intermittent thermal extraction for sustainable energy production

Efficient extraction of thermal energy from deep geothermal reservoirs using Enhanced Geothermal Systems (EGS) is fundamental for sustainable clean energy generation. This study presents the Intermittent Thermal Extraction (ITE) method, addressing thermal breakthrough challenges encountered during continuous thermal extraction (CTE) within EGS reservoirs. Employing a thermal-hydraulic coupled approach and discrete fracture network modeling, the ITE process for EGS reservoirs is assessed, omitting considerations of stress-induced deformation. The research evaluates the ITE and CTE methods within a typical high-temperature geothermal reservoir in the Himalayan geothermal belt. Analysis includes variations in reservoir temperatures and pressures, alongside an examination of rock matrix permeability and injection fluid temperature impacts on EGS thermal extraction performance. Results demonstrate the ITE method's efficacy in prolonging the EGS reservoir lifespan by preventing thermal breakthroughs and maintaining pressure equilibrium. Under studied conditions, ITE extends the EGS reservoir lifespan by a minimum of 17.7 years, amplifying clean power generation by 13.1% compared to CTE. Additionally, ITE implementation substantially reduces greenhouse gas emissions by an estimated 1.46–5.03 million tons. The rock matrix permeability and injection fluid temperature significantly affect the EGS thermal extraction performance when the fracture aperture is constant. These findings highlight the ITE method's potential to optimize thermal extraction from EGS reservoirs, particularly in remote regions. This study contributes essential insights into advancing geothermal energy extraction techniques, emphasizing ITE as a promising approach for sustainable energy production.

Effect of fracture characteristics on groundwater flow adjacent to high-level radioactive waste repository

In the study, a 2-D numerical model-delineating the high-level radioactive waste repository surrounded by hosting granite-rock was designed to evaluate pressure build-up, elevated temperature, and fracture flow caused by heat generation at the repository. During the early stage (0.1 years), build-up pressure at the repository induced radial groundwater flow. On the other hand, buoyancy-driven vertical flow was dominant during the late stage (2,000 years). The pressure build-up and elevated temperature varied significantly in bentonite, excavation-damaged zone and granite, resulting in different groundwater velocity. Fracture flow in both single and intersecting fractures were also influenced by the pressure and temperature, but their impact varied depending on the geometrical properties (e.g. orientation, elevation, lateral position) of the fracture. In complex discrete fracture network models, build-up pressure in the early stage mainly generated preferential fracture flow through few pathways, while in the late stage, convection-circulating flow induced by the buoyancy was distinct. In the early stage, higher density and connectivity of fracture network did not lead to an increase in average fracture flow, whereas the circulating flow in the late stage became more frequent and larger. Especially, long fractures served as both preferential flow pathways in the early stage and conduits for circulating flow in the late stage. The circulating flow was highly dependent on the spatial distribution of the long fractures, causing a significant uncertainty of average fracture flow in the late stage. The low angle of intersection between fractures resulted in low connectivity that decelerated the average fracture flow in both stages.

Development of an improved three-dimensional rough discrete fracture network model: Method and application

Structure plane is one of the important factors affecting the stability and failure mode of rock mass engineering. Rock mass structure characterization is the basic work of rock mechanics research and the important content of numerical simulation. A new 3-dimensional rough discrete fracture network (RDFN3D) model and its modeling method based on the Weierstrass-Mandelbrot (W-M) function were presented in this paper. The RDFN3D model, which improves and unifies the modelling methods for the complex structural planes, has been realized. The influence of fractal dimension, amplitude, and surface precision on the modeling parameters of RDFN3D was discussed. The reasonable W-M parameters suitable for the roughness coefficient of JRC were proposed, and the relationship between the mathematical model and the joint characterization was established. The RDFN3D together with the smooth 3-dimensional discrete fracture network (DFN3D) models were successfully exported to the drawing exchange format, which will provide a wide application in numerous numerical simulation codes including both the continuous and discontinuous methods. The numerical models were discussed using the COMSOL Multiphysics code and the 3-dimensional particle flow code, respectively. The reliability of the RDFN3D model was preliminarily discussed and analyzed. The roughness and spatial connectivity of the fracture networks have a dominant effect on the fluid flow patterns. The research results can provide a new geological model and analysis model for numerical simulation and engineering analysis of jointed rock mass.

The Criteria for Transition of Fluid to Nonlinear Flow for Fractured Rocks: The Role of Fracture Intersection and Aperture

Understanding the fluid pattern is of special significance for estimating the hydraulic conductivity of fractured rock masses. The nonlinearity of fluid flow in discrete fracture networks (DFNs) originates from inertial effects and is enhanced by complex geometric topologies, which produces additional viscous friction and is subject to inertia effects, consequently transitioning the fluid to the nonlinear flow regime. Therefore, it is important to obtain the critical conditions for the transition of a fluid from laminar to turbulent flow. To investigate the role of fracture aperture and fracture intersection on the onset of the transition of a fluid to nonlinear flow in fractured rocks, the fluid dynamic computation was performed by solving Navier–Stokes (N–S) equations in DFN models. The results show that the flow flux initially linearly correlates with the hydraulic gradient (J) and the permeability of DFNs initially remains constant. As the hydraulic gradient increases, the flow flux presents a strong nonlinear relationship with the hydraulic gradient, and the permeability decreases dramatically. In particular, significant inertial effects appear earlier with a large fracture aperture or a dense fracture intersection. A critical hydraulic gradient (Jc) is proposed to judge the onset of nonlinear flow. The mathematical expression of Jc and Forchheimer coefficients A and B involving the fracture aperture and fracture intersection density is established through a multiple regression algorithm. Finally, the reliability of the predictive model was verified by comparing the results of the prediction and fluid dynamic computation of a series of DFN models with well-known geometric distributions. The consistency of the fitted equations and a correlation coefficient greater than 0.9 between them indicate that the predictive model proposed in this study is reliable.

Spatial Characterization of Shallow Structures in the Revell Batholith Integrating Seismic Imaging Techniques

The Revell Site, located in Northwestern Ontario within the Canadian Shield, is being assessed as a potential Deep Geological Repository (DGR) for Canada’s used nuclear fuel. Effective DGR establishment requires comprehensive subsurface assessment, particularly in evaluating structural stability, hydrogeological attributes, geological composition, and geochemical properties. Key among these considerations is understanding the three-dimensional characteristics of structural features to ensure the site’s suitability for long-term containment of radioactive materials. This case study focuses on imaging and characterizing structures within the predominantly intact biotite granodiorite-tonalite host rock at the Revell Site. Borehole data reveals these structures as mostly sub-horizontal mafic intrusions, with thicknesses of up to 3.5 m. They appear either as separate, discrete entities or in stacked configurations. Despite their limited thickness, most of these intrusions exhibit discernible attributes in surface seismic images due to their distinct physical properties. Some, however, exhibit velocity variations that decrease their overall reflectivity properties. An integrative approach employing surface seismic, Vertical Seismic Profiles (VSP), and borehole data facilitates the spatial identification of over 30 of these mafic structures. This comprehensive characterization not only lays the foundational framework for future discrete fracture network models but also provides important support for simulations related to fluid flow dynamics, groundwater behavior, contaminant dispersion, and heat transport mechanisms within the Revell Site. This study underscores the critical role of in-depth subsurface characterization in ensuring the secure, long-term management of radioactive materials in DGRs.

A Numerical Method for Evaluating the Collapse of High-Steep Scarp Slopes Based on the Bonded Block Model–Discrete Fracture Network Model

Geotechnical engineering works in deep-incised valleys or open-pit mining areas often encounter high-steep scarp slopes with a slope angle greater than 75°. This type of slope directly threatens the safety of construction personnel, so assessing their stability is essential to ensure construction safety. The natural geometry of high-steep scarp slopes possesses complexity in terms of geometric morphology, structural features of rock mass, and occurrence mechanisms of collapse. There is little research and less emphasis on the evaluation of the collapse risk of high-steep scarp slopes. In particular, the fracture of intact rock or rock bridges is generally ignored in the analysis of collapse processes. A bonded block model (BBM)–discrete fracture network (DFN) coupling characterization model for the high-steep scarp slope is proposed based on a high-steep scarp slope containing dominant joint sets on the left bank of the dam site of the Huangzangsi Water Conservancy Project (Qinghai Province, China). By using the model, the complex geometric forms of the surface of the high-steep scarp slope are quantified, and the fracture process of falling rock masses as well as the controlling effect of dominant joints on the collapse of the scarp slope are revealed. A strength reduction method based on the BBM–DFN model is constructed, and the safety factor of the collapse-prone scarp slope is evaluated. The research results show that (1) the BBM–DFN model can be used to describe the local collapse process; (2) the occurrence of dominant joints plays an important part in controlling the collapse process; (3) there are differences in the safety factor of the scarp slope with different coupling methods; the collapse and failure modes also differ. For safety considerations, the safety factor of the scarp slope on the left bank of the dam site area is determined to be 1.85. The research findings can be used to guide the safety assessment of high-steep scarp slopes and the formulation of both collapse risk prevention and control measures to ensure construction safety in high-steep scarp slope areas.

Study on the influence of statistical geometrical characteristics on the permeability tensor of fractured rock masses by the equivalent pipe network method

The permeability of the host rock of the nuclear waste underground repository is one of the most keys for estimating the potential risk for nuclide waste to escape. Therefore, a three-dimensional discrete fracture network (DFN) model using the Monte Carlo method is generated based on the statistical geometrical characteristics of fracture network in Beishan I area which is selected as the site for constructing the nuclear waste repository in China. And the permeability of Beishan I fractured rock masses is calculated through the equivalent pipe network (EPN) method and representative elementary volume (REV) of it is determined. A rotating algorithm is developed to calculate different direction permeability. Furthermore, the influence of fracture statistical geometrical characteristics on REV size is explored by creating a series of DFN models with varying log-normal distribution of side lengths. The results show that the REV size of the Beishan Ⅰ area is 1.66 × 105 m3 and the corresponding principal permeability direction is 111.29°/75.36°. The REV size and permeability both increase with the increment of the mean and variance of the log-normal distribution increases. And with the increase of mean and variance, the growth rate gradually accelerated.