Impact of normal stress-induced closure on laboratory-scale solute transport in a natural rock fracture

The impact of normal stress-induced closure on fluid flow and solute transport in a single rock fracture is demonstrated in this study.The fracture is created from a measured surface of a granite rock sample.The Bandis model is used to calculate the fracture closure due to normal stress,and the fluid flow is simulated by solving the Reynold equation.The Lagrangian particle tracking method is applied to modeling the advective transport in the fracture.The results show that the normal stress significantly affects fluid flow and solute transport in rock fractures.It causes fracture closure and creates asperity contact areas,which significantly reduces the effective hydraulic aperture and enhances flow channeling.Consequently,the reduced aperture and enhanced channeling affect travel time distributions.In particular,the enhanced channeling results in enhanced first arriving and tailing behaviors for solute transport.The fracture normal stiffness correlates linearly with the 5 th and 95 th percentiles of the normalized travel time.The finding from this study may help to better understand the stress-dependent solute transport processes in natural rock fractures.     

Nonlinear fluid flow through three-dimensional rough fracture networks:Insights from 3D-printing,CT-scanning,and high-resolution numerical simulations

Nonlinear flow behavior of fluids through three-dimensional(3 D) discrete fracture networks(DFNs)considering effects of fracture number, surface roughness and fracture aperture was experimentally and numerically investigated. Three physical models of DFNs were 3 D-printed and then computed tomography(CT)-scanned to obtain the specific geometry of fractures. The validity of numerically simulating the fluid flow through DFNs was verified via comparison with flow tests on the 3 D-printed models. A parametric study was then implemented to establish quantitative relations between the coefficients/parameters in Forchheimer's law and geometrical parameters. The results showed that the 3 D-printing technique can well reproduce the geometry of single fractures with less precision when preparing complex fracture networks, numerical modeling precision of which can be improved via CT-scanning as evidenced by the well fitted results between fluid flow tests and numerical simulations using CT-scanned digital models. Streamlines in DFNs become increasingly tortuous as the fracture number and roughness increase, resulting in stronger inertial effects and greater curvatures of hydraulic pressure-low rate relations, which can be well characterized by the Forchheimer's law. The critical hydraulic gradient for the onset of nonlinear flow decreases with the increasing aperture, fracture number and roughness,following a power function. The increases in fracture aperture and number provide more paths for fluid flow, increasing both the viscous and inertial permeabilities. The value of the inertial permeability is approximately four orders of magnitude greater than the viscous permeability, following a power function with an exponent a of 3, and a proportional coefficient β mathematically correlated with the geometrical parameters.     

Experimental and numerical study of the geometrical and hydraulic characteristics of a single rock fracture during shear

Coupled shear-flow tests were conducted on two artificial rock fractures with natural rock fracture characteristics under constant normal loading boundary conditions. Numerical simulations using the 3-D Navier–Stokes equations taking account of the inertial effects of fluid were conducted using the void space geometry models obtained from the coupled shear-flow tests. The test and numerical simulation results show that the evolutions of geometrical and hydraulic characteristics of rock fracture exhibit a three-stage behavior. Transmissivity of a certain void space geometry within a fracture is related to the Reynolds number of fluid flow due to the inertial effects of fluid, which can be represented by the Navier–Stokes equations, but cannot be represented by some simplified equations, such as the cubic law, the Reynolds equation or the Stokes equations. The mechanical aperture is usually larger than the hydraulic aperture back-calculated from measured flow rate, and the difference between them is found strongly related to the geometrical characteristics of the fractures. A mathematical equation is proposed to describe the relation between hydraulic aperture and mechanical aperture by means of the ratio of the standard deviation of local mechanical aperture to its mean value, the standard deviation of local slope of fracture surface and Reynolds number.     

Experimental study of the hydro-mechanical behavior of rock joints using a parallel-plate model containing contact areas and artificial fractures

In recent years, geological disposal of radioactive wastes is considered to be the most promising option, which requires the understanding of the coupled mechanical, hydraulic and thermal properties of the host rock masses and rock fractures. The hydro-mechanical behavior and properties of rock fractures are usually determined by laboratory experiments on fracture specimens that serve as the basic building block of the constitutive models of fractured rock masses.Laboratory testing of rock fractures involve a number of technical issues that may have significant impacts on the reliability and applicability of the testing results, chief among them are the quantitative estimation of the evolutions of hydraulic transmissivity fields of fractures during shear under different normal constraint conditions, and the sealing techniques when fluid flow during shear is involved. In this study, a new shear-flow testing apparatus with specially designed fluid sealing techniques for rock fractures were developed, under constant normal load (CNL) or constant normal stiffness (CNS) constraint. The topographical data of all fracture specimens were measured before testing to constitute the geometrical models for simulating the change of mechanical aperture distributions during shearing. A number of shear-flow coupling tests were carried out on three kinds of rock fracture specimens to evaluate the influence of morphological properties of rock fractures on their hydro-mechanical behaviour. Some empirical relations were proposed to evaluate the effects of contact area and surface roughness on the behavior of fluid flow through rock fractures.     

Effect of shear-induced contact area and aperture variations on nonlinear flow behaviors in fractal rock fractures

This study experimentally analyzes the nonlinear flow characteristics and channelization of fluid through rough-walled fractures during the shear process using a shear-flow-visualization apparatus. A series of fluid flow and visualization tests is performed on four transparent fracture specimens with various shear displacements of 1 mm, 3 mm, 5 mm, 7 mm and 10 mm under a normal stress of 0.5 MPa. Four granite fractures with different roughnesses are selected and quantified using variogram fractal dimensions. The obtained results show that the critical Reynolds number tends to increase with increasing shear displacement but decrease with increasing roughness of fracture surface. The flow paths are more tortuous at the beginning of shear because of the wide distribution of small contact spots. As the shear displacement continues to increase, preferential flow paths are more distinctly observed due to the decrease in the number of contact spots caused by shear dilation; yet the area of single contacts increases. Based on the experimental results, an empirical mathematical equation is proposed to quantify the critical Reynolds number using the contact area ratio and fractal dimension.     

Numerical simulation of shear-induced flow anisotropy and scale-dependent aperture and transmissivity evolution of rock fracture replicas

Fluid flow anisotropy in a single rock fracture during a shear process is an important issue in rock mechanics and is investigated in this paper using FEM modelling, considering evolutions of aperture and transmissivity with shear displacement history. The distributions of fracture aperture during shearing with large shear displacements were obtained by numerically manipulating relative translational movements between two digitalized surfaces of a rock fracture replica, with changing sample sizes. The scale dependence of the fluid behaviour and properties were also investigated using a fractal approach.The results show that the fracture aperture increases anisotropically during shear with a more pronounced increase in the direction perpendicular to the shear displacement, causing significant fluid flow channelling effect, as also observed by other researchers. This finding may have important impacts on the interpretation of the results of coupled hydro-mechanical experiments for measurements of hydraulic properties of rock fractures because the hydraulic properties are usually calculated from flow test results along the shear directions while ignoring the more significant anisotropic flow perpendicular to the shear direction. This finding indicates that the coupled stress-flow tests of rough rock fractures should be conducted in true three-dimensions if possible. Significant change in fracture aperture/transmissivity in the out-of-plane direction should be properly evaluated if two-dimensional tests are conducted. Results obtained from numerical simulations also show that fluid flow through a single rough fracture changes with increasing sample size and shear displacements, indicating that representative hydro-mechanical properties of the fractures in the field can only be more reliably determined using samples of large enough sizes beyond the stationarity threshold and tested with larger shear displacements.     

Hydro-mechanical interaction effects and channelling in three-dimensional fracture networks undergoing growth and nucleation

The flow properties of geo mechanically generated discrete fracture networks are examined in the context of channelling.Fracture networks are generated by growing fractures in tension,modelling the low permeability rock as a linear elastic material.Fractures are modelled as discrete surfaces which grow quasi-statically within a three-dimensional(3 D) volume.Fractures may have their locations specified as a simulation input,or be generated as a function of damage,quantified using the local variation in equivalent strain.The properties of the grown networks are shown to be a product of in situ stress,relative orientation of initial flaws,and competitive process of fracture interaction and growth.Fractures grow preferentially in the direction perpendicular to the direction of maximum tension and may deviate from this path due to mechanical fracture interaction.Flow is significantly channelled through a subset of the fractures in the full domain,consiste nt with observations of other real and simulated fractures.As the fracture networks grow,small changes in the geometry of the fractures lead to large changes in the locations and scale of primary flow channels.The flow variability and formation of channels are examined for two growing networks,one with a fixed amount of fractures,and another with nucleating fractures.The interaction between fractures is shown to modify the local stress field,and in turn the aperture of the fractures.Pathways for single-phase flow are the results of hydro-mechanical effects in fracture networks during growth.These are the results of changes to the topology of the network as well as the result of mechanical self-organisation which occurs during interaction leading to growth and intersection.     

考虑三维形貌特征的粗糙节理渗流空腔模型研究

 为研究粗糙节理中的渗流,建立节理渗流空腔模型。将节理平面离散成1 mm×1 mm的单元格,单元格节点处的隙宽值由节理三维空腔组合形貌确定,假设单元格内渗流服从立方定理,逐一对单元格进行分析,用连续性方程求解整个节理面渗流,编制MATLAB程序进行计算。用大理岩人工节理试件沿节理长度方向将同一节理上表面相对下表面分别错开1,2,3,4,5和6 mm,形成节理不同的接触状态,计算这6种情况下的节理三维空腔组合形貌,得到不同接触状态下节理的隙宽分布和平均隙宽值。将节理渗流空腔模型和立方定理在不同接触状态下的渗流计算结果与节理试件在不同接触状态下的室内试验结果进行比较。分析结果表明：节理渗流空腔模型计算结果比立方定理更接近室内渗流试验结果,但是空腔模型计算结果和试验结果还有一定的差距,并对其误差存在的原因进行分析。     

Three-dimensional double-rough-walled modeling of fluid flow through self-affine shear fractures

This study proposes a double-rough-walled fracture model to represent the natural geometries of rough fractures.The rough surface is generated using a modified successive random additions(SRA) algorithm and the aperture distribution during shearing is calculated using a mechanistic model.The shear-flow simulations are performed by directly solving the Navier-Stokes(NS) equations.The results show that the double-rough-walled fracture model can improve the accuracy of fluid flow simulations by approximately 14.99%-19.77%,compared with the commonly used single-rough-walled fracture model.The ratio of flow rate to hydraulic gradient increases by one order of magnitude for fluids in a linear flow regime with increment of shear displacement from 2.2 mm to 2.6 mm.By solving the NS equations,the inertial effect is taken into account and the significant eddies are simulated and numerically visualized,which are not easy to be captured in conventional experiments.The anisotropy of fluid flow in the linear regime during shearing is robustly enhanced as the shearing advances;however,it is either increased or decreased for fluids in the nonlinear flow regime,depending on the geometry of shear-induced void spaces between the two rough walls of the fracture.The present study provides a method to represent the real geometry of fractures during shearing and to simulate fluid flow by directly solving the NS equations,which can be potentially utilized in many applications such as heat and mass transfer,contaminant transport,and coupled hydro-thermo-mechanical processes within rock fractures/fracture networks.     

变饱和裂隙多孔介质的双渗透率数值模型与参数分析

针对裂隙多孔介质中的变饱和流动与运移,分析了双渗透率数值模型的参数构成与计算特征。双渗透率模型由分别代表裂隙等效连续介质和孔隙介质的两组并列体积单元集合构成,用平均裂隙宽度和平均裂隙间距表达裂隙等效连续介质的参数,用裂隙单元与孔隙单元之间的有效作用面积、有效作用距离和有效渗透系数描述裂隙-孔隙相对流动和运移。裂隙-孔隙相互作用参数取决于概念模型,并与流体动态相关。计算分析表明,裂隙单元与孔隙单元之间的毛细力梯度与重力的共同作用决定裂隙流动、孔隙流动和裂隙-孔隙相对流动的相对大小,流体和溶质的动态受到裂隙宽度变化的显著影响。     

Interactive roles of geometrical distribution and geomechanical deformation of fracture networks in fluid flow through fractured geological media

In this study,the combined effects of geometrical distribution and geomechanical deformation of fracture networks on fluid flow through fractured geological media are investigated numerically.We consider a finite-sized model domain in which the geometry of fracture systems follows a power-law length scaling.The geomechanical response of the fractured rock is simulated using a hybrid finitediscrete element model,which can capture the deformation of intact rocks,the interaction of matrix blocks,the displacement of discrete fractures and the propagation of new cracks.Under far-field stress loading,the locally variable stress distribution in the fractured rock leads to a stress-dependent variable aperture field controlled by compression-induced closure and shear-induced dilatancy of rough fractures.The equivalent permeability of the deformed fractured rock is calculated by solving for the fracture-matrix flow considering the cubic relationship between fracture aperture and flow rate at each local fracture segment.We report that the geometrical connectivity of fracture networks plays a critical role in the hydromechanical processes in fractured rocks.A well-connected fracture system under a high stress ratio condition exhibits intense frictional sliding and large fracture dilation/opening,leading to greater rock mass permeability.However,a disconnected fracture network accommodates much less fracture shearing and opening,and has much lower bulk permeability.We further propose an analytical solution for the relationship between the equivalent permeability of fractured rocks and the connectivity metric(i.e.percolation parameter) of fracture networks,which yields an excellent match to the numerical results.We infer that fluid flow through a well-connected system is governed by traversing channels(forming an"in parallel" architecture) and thus equivalent permeability is sensitive to stress loading(due to stress-dependent fracture permeability),whilst fluid flow through a disconnected system is more ruled by matrix(linking isolated clusters"in series") and has much less stress dependency.     

多级加载下岩石裂隙渗流分段特性试验研究

利用自行研制的岩石裂隙辐射型渗流系统,试验研究室温下粗晶大理岩、中砂岩、灰岩和细晶大理岩4个岩石张裂隙在法向闭合过程中的渗流分段特性及加载历史的影响。根据闭合裂隙的接触状态及流域分布特征,裂隙渗流可分为群岛流、过渡流、沟槽流3个阶段;单位水头流量与法向应力呈指数函数关系,随法向应力增加而降低,后次加载中相同法向应力下单位水头流量明显较低;单位水头流量与力学隙宽呈幂函数关系,幂指数范围为1.93～2.60,可认为接触型粗糙岩石裂隙渗流量与力学隙宽呈次立方关系;后次加载时,相同力学隙宽下单位水头流量也明显较低;水力等效隙宽与力学隙宽呈分段的线性关系,修正的立方定律在相应分段内成立。研究结果对岩体裂隙渗流计算有一定的理论意义。     

Numerical simulations examining the relationship between wall-roughness and fluid flow in rock fractures

Understanding how fracture wall-roughness affects fluid flow is important when modeling many subsurface transport problems. Computed tomography scanning provides a unique view of rock fractures, allowing the measurement of fracture wall-roughness, without destroying the initial rock sample. For this computational fluid dynamics study, we used several different methods to obtain three-dimensional meshes of a computed tomography scanned fracture in Berea sandstone. These volumetric meshes had different wall-roughnesses, which we characterized using the Joint Roughness Coefficient and the fractal dimension of the fracture profiles. We then related these macroscopic roughness parameters to the effective flow through the fractures, as determined from Navier–Stokes numerical models. Thus, we used our fracture meshes to develop relationships between the observed roughness properties of the fracture geometries and flow parameters that are of importance for modeling flow through fractures in field scale models. Fractures with high Joint Roughness Coefficients and fractal dimensions were shown to exhibit tortuous flow paths, be poorly characterized by the mean geometric aperture, and have a fracture transmissivity 35 times smaller than the smoother modeled fracture flows.     

三轴压应力–化学溶液渗透作用下单裂隙花岗岩裂隙开度演化

 为研究单裂隙花岗岩在应力–化学溶液渗透条件下的开度演化规律,开展单裂隙花岗岩在恒定三轴压应力及化学溶液渗透作用下的试验。对试验过程中渗透溶液离子浓度进行分析,结果表明,压应力作用下,裂隙接触面矿物溶解、自由面矿物溶解以及矿物沉淀3个过程影响裂隙开度的演化规律。通过裂隙面三维扫描数据获取裂隙开度变化与接触面积率的关系,并基于此在已有研究基础上分别建立酸性溶液和碱性溶液渗透作用下花岗岩裂隙开度演化模型。模拟结果表明,模型计算结果与试验结果符合较好,能够很好地描述裂隙在化学溶液渗透和应力作用下的演化规律;酸性溶液渗透作用下,接触面矿物溶解过程的强弱控制着裂隙开度的演化,而碱性溶液渗透作用下,矿物的沉淀过程也发挥着重要作用。     

Size effect on aperture and permeability of a fracture as estimated in large synthetic fractures

Synthetic fractures of from 0.2 to 12.8 m in size were created on a computer by a new spectral method to reproduce the ratio of the power spectral density of the initial aperture (the aperture when the surfaces are in contact at a single point) to that of the surface height determined for a tensile fracture of 1 m. First, the size effect on the standard deviation of the initial aperture was analyzed for fractures with and without shearing. Next, by taking aperture data at constant intervals to establish a flow area, water flow was simulated for fractures during both normal closure and closure after shearing, by solving Reynolds equation to determine the hydraulic aperture. When the fracture is closed without shearing and has the same mean aperture, the effect of the fracture size on the hydraulic aperture disappears if the fracture is larger than about 0.2 m, since beyond this size the standard deviation of the initial aperture is almost independent of the fracture size. When the fracture is closed after shearing, the hydraulic conductivity shows remarkable anisotropy, which becomes more significant with both shear displacement and closure. However, the relation between the hydraulic aperture normalized by the mean aperture and the mean aperture normalized by the standard deviation of the initial aperture is almost independent of both the fracture size and shear displacement when the shear displacement is less than about 3.1% of the fracture size, at which point the standard deviation of the initial aperture of the sheared fracture is almost independent of the fracture size.     

岩石单裂隙稳态渗流研究进展

 从3个方面介绍目前单裂隙渗流研究的最新成果：(1) 单裂隙内的流体运动规律,主要研究裂隙渗流模型和流速分布规律等;(2) 裂隙过流能力的影响因素,包括应力、隙宽、粗糙度、充填物以及多场耦合等;(3) 单裂隙渗流的数值模拟方法,包括裂隙的数值生成方法和模拟技术。系统总结和分析目前最新的研究成果,对渗流研究理论和方法中存在的问题进行深入探讨：裂隙内渗流的流动规律复杂,裂隙渗流模型和机制仍有很多不明之处;剪应力影响是目前裂隙渗流研究的热点,三维应力和拉应力对裂隙渗流的影响也是未来研究的方向,但模拟复杂应力状态下的渗流试验装置仍是研究的“瓶颈”;评价裂隙面粗糙程度仍是一个复杂的问题;数值模拟裂隙渗流与试验方法相辅相成,正确选择合理的数值方法非常重要。     

Aperture measurements and seepage properties of typical single natural fractures

Fractures play an important role in controlling the hydraulic conductivity of rock masses, and the aperture significantly influences the magnitude of fracture seepage. In this study, field measurements and experiments were conducted at a well-exposed granite fracture site in the Beishan area, China. Several types of single natural fractures were selected to remove the weathered surface and expose the fresh fractures. Subsequently, measuring ruler dispersion-tangent middle axis (MRD-TMA) method was developed to measure the fracture aperture and capture fracture geometry. Then, electrical resistivity tomography (ERT) technique was employed to investigate the seepage properties of these fractures. The results reveal that MRD-TMA method achieved good flexibility and accuracy in the current measurement of fracture aperture, and ERT is a useful tool for detecting the seepage properties of fractures in hard rock masses. Combined with field observations, the filling form of fractures can be categorized according to the ERT inversion results, as follows: open-weak filling, open filling, loose filling, and fully cemented-closed form, whose seepage properties decrease as the filling density increases. Generally, the open-weak filling is the main water channel in a fracture network, while the fully cemented-closed type is a water-blocking fracture and typically exhibits a pseudo-fracture with a large surface opening. In summary, the method for obtaining the morphological characteristics of the aperture can provide a low-cost and time-efficient approach for fracture logging in the field, and ERT technique provides a reference for the detection of potential hazards caused by connected water-conducting fractures in rock engineering.

     

Hydraulic properties of fractured rock masses with correlated fracture length and aperture

Permeability of fractured rocks is investigated considering the correlation between distributed fracture aperture and trace length, based on a newly developed correlation equation. The influence of the second moment of the lognormal distribution of apertures on the existence of representative elementary volume (REV), and the possibility of equivalent permeability tensor of the fractured rock mass, is examined by simulating flow through a large number of stochastic discrete fracture network (DFN) models of varying sizes and varying fracture properties.The REV size of the DFN models increases with the increase of the second moment of the lognormal distribution, for both the correlated and uncorrelated cases. The variation of overall permeability between different stochastic realizations is an order of magnitude larger when the aperture and length are correlated than when they are uncorrelated. The mean square error of the directional permeability increases with increasing value of the second moment of the lognormal distribution function, and good fitting to an ellipsis of permeability tensor can only be reached with very large sizes of DFN models, compared with the case of constant fracture aperture, regardless of fracture trace length.     

岩石单节理面剪切与渗流特性的试验研究 与数值分析

 基于几组具有自然岩石节理表面特征的试件在高性能直接剪切–渗流装置上进行不同荷载边界条件下的剪切–渗流试验。利用新开发的渗流可视化系统对其中一组试验进行可视化研究。考虑节理面上的接触领域的非透水性,用有限元法对节理中的渗流进行数值模拟。试验和数值模拟的结果揭示了节理剪切过程中接触领域中透水系数及流路的一些变化规律,以及节理表面粗糙度对剪胀效应和流路分布特征的重要影响。