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.     

岩石节理剪切渗流耦合试验及分析

节理岩体内渗流的发生主要是通过断裂节理网络产生,节理面的几何特性和受力特征决定和影响着节理裂隙的渗透性质,从而极大地影响着水下隧道及地下硐室中的渗流。应用自行研制开发的试验设备(岩石节理单一剪切-渗流试验机(SMT-E-4010)),在恒定法向荷载和恒定法向刚度的边界条件下,对不同接触状态下的岩石断裂节理试件分别进行一系列节理的剪切渗流耦合试验,研究剪切过程中力学性质、水力学性质的变化情况;同时,结合立方准则对试验数据进行分析讨论。试验结果表明:节理力学性质,水力开度和透过率在剪切过程中呈现出两阶段的变化性质。     

Effect of shear displacement on the aperture and permeability of a rock fracture

The results of experiments using radial and unidirectional flow in a carefully described single rough aperture are reported and compared with numerical predictions. Aperture replicas of a natural sandstone fracture were made at 0, 1 and 2 mm shear displacements using silicone rubber, with a reproducibility of better than 2%. The experimental arrangement permitted shear displacement to be obtained without causing damage to the two displaced surfaces, which thus retained their original (and essentially matching) geometry. Both the number of contact points and the fractional contact area decreased with increasing shear displacement. With increasing shear displacement, mean aperture and standard deviation increased and the ratio of standard deviation to mean aperture increased slightly. Semivariogram studies indicated that as shear displacement increased in the direction normal to the roughness ridges, the aperture distribution became more closely correlated in the direction parallel to the roughness ridges than in the shear direction. Flow tests showed that with increasing shear displacement, the fracture became heterogeneous and anisotropic and became more permeable in the direction perpendicular to the shear displacement than in the direction parallel to the displacement. Simulations were made of flow through the fracture using the Reynolds equation and the actual aperture distribution; the measured hydraulic apertures were generally about 20% lower than those measured numerically.     

Effect of shear displacement on the hydraulic conductivity of a fracture

The effect of shear displacement inclined relative to macroscopic water flow on the hydraulic conductivity of a rock fracture was estimated, using synthetic fractures that reproduce a tensile fracture in granite. The results showed that the hydraulic aperture normalized by the mean aperture increased with the angle between the directions of shear displacement and macroscopic water flow, according to a sinusoidal function of twice the angle. Formulae were established to estimate the hydraulic aperture of the fracture as a function of the mean aperture, the standard deviation of the initial aperture, the shear displacement, and the angle between the shear displacement and macroscopic water flow, based on results obtained in both this work and previous work, but neglecting scale effects. By assuming the mechanical properties of the fracture based on experimental results for granite, but neglecting scale effects, the hydraulic conductivity of the fracture with an arbitrary direction under a given state of stress (σ₁=29 MPa, σ₂=25 MPa and σ₃=13.5 MPa) was estimated for macroscopic water flow in the directions of both σ₁ and σ₂. When the contour map of the transmissivity of the fracture is plotted on a stereonet of the normal direction of the fracture in the principal axes of stress, there is a ridge (line of the local maximum) of transmissivity in the circumferential direction, and the inclination angle of the ridge from the σ₃-axis decreases with shear displacement, since shear dilation increases with both a decrease in normal stress and an increase in shear displacement. Furthermore, for the condition of stress given in this study, the transmissivity for macroscopic water flow in the direction of σ₁ is maximum for a fracture with a normal direction within the σ₂–σ₃ plane, while that in the direction of σ₂ is maximum for a fracture with a normal direction within the σ₁–σ₃ plane.     

Coupled hydro-mechanical model for fractured rock masses using the discontinuous deformation analysis

A coupling analysis model is proposed to study the hydro-mechanical response of the fluid flow in fractured rock mass with the method of discontinuous deformation analysis (DDA). The DDA coupled hydro-mechanical model is interpreted in details by expressing the fracture fluid flow equations, the coupling process and the global coupled equations. For the mechanical response, the hydraulic pressure is determined first, followed by the coupled motion equations expressed under the DDA framework, to study the interaction between the fluid flow along the fractures and the movement of the rock blocks. In the fluid flow analysis, the cubic law is applied to study the steady flow along the fractures using the finite difference method (FDM). A real case of cavern excavation is analyzed by the proposed DDA coupled 2D hydro-mechanical model, to study the influence of fluid flow on the rock cavern stability during the excavation phase. The results show that the DDA coupled hydro-mechanical model is suitable for the stability and seepage analysis of practical engineering problems.     

A numerical study on differences in using Navier–Stokes and Reynolds equations for modeling the fluid flow and particle transport in single rock fractures with shear

The study on fluid flow and transport processes of rock fractures in most practical applications involves two fundamental issues: the validity of Reynolds equation for fluid flow (as most often assumed) and the effects of shear displacements on the magnitudes and anisotropy of the fluid flow velocity field. The reason for such concerns is that the impact of the surface roughness of rock fractures is still an unresolved challenging issue. The later has been systematically investigated with results showing that shear displacement plays a dominant role on evolutions of fluid velocity fields, for both magnitudes and anisotropy, but the former has not received examinations in details due to the numerical complexities involving solution of the Navier–Stokes (NS) equations and the representations of fracture geometry during shear. The objective of this paper aims to solve this problem through a FEM modeling effort.Applying the COMSOL Multiphysics code (FEM) and assuming a 2D problem, we consider the coupled hydromechanical effect of fracture geometry change due to shear on fluid flow (velocity patterns) and particle transport (streamline/velocity dispersion), using measured topographical data of natural rock fracture surfaces. The fluid flow in the vertical 2D cross-sections of single rock fractures was simulated by solving both the Navier–Stokes and the Reynolds equation, and the particle transport was predicted by the streamline particle tracking method with calculated flow velocity fields (vectors) from the flow simulations, obtaining results such as flow velocity profiles, total flow rates, particle travel time, breakthrough curves and the Péclet number, Pe, respectively.The results obtained using NS and Reynolds equations were compared to illustrate the degree of the validity of the Reynolds equation for general applications in practice since the later is mush more computationally efficient for solving large-scale problems.The flow simulation results show that both the total flow rate and the flow velocity fields in a rough rock fracture predicted by the NS equation were quite different from those predicted by the Reynolds equation. The results show that a roughly 5–10% overestimation on the flow rate is produced when the Reynolds equation is used, and the ideal parabolic velocity profiles defined by the local cubic law, when Reynolds equation is used, is no longer valid, especially when the roughness feature of the fracture surfaces changes with shear. These deviations of flow rate and flow velocity profiles across the fracture aperture have a significant impact on the particle transport behavior and the associated properties, such as the travel time and Péclet number. The deviations increase with increasing flow velocity and become more significant when fracture aperture geometry changes with shear.     

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.     

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.     

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.     

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.     

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.     

岩体非连续裂隙网络三维面状渗流模型

模拟了一个野外实际入渗试验的岩体裂隙网络及其中的渗流。通过逆方法建立岩体三维裂隙网络模型,其指导原则是使模型能够再现野外通过露头和钻孔所观察到的裂隙现象。逆方法由于可以对模拟和实测裂隙进行相同条件统计抽样,因此避免了实测数据统计分析中复杂的误差矫正。裂隙面状渗流分析采用了任意多边形有限差分法。讨论了通过模型校正确定裂隙导水系数的方法,进行了随机模型重复实现,验证了模型的稳定性。     

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.     

Using the migration of the induced seismicity as a constraint for fractured Hot Dry Rock reservoir modelling

The challenge for Hot Dry Rock technology is to develop a heat exchanger in deep hot rock masses and to circulate a fluid in order to extract its energy to be used at the ground surface. The present day strategy is to take advantage of natural fractures that pre-exist at these depths and to improve their hydraulic properties. The extension of the area with enhanced properties must then be evaluated so that the best locations for further boreholes can be proposed. To date, this development procedure is based on fluid injection at high rates, forcing hydro-mechanical interactions to take place along pressurised fractures. These pore-pressure-driven mechanisms are accompanied by seismic activity. Assuming the validity of poro-elastic theory in the fractured host rock, some authors have derived the virgin hydraulic diffusivity of the fractured reservoir from the analysis of the spatio-temporal growth of the induced seismicity. The present work is aimed at verifying this approach using a numerical code to solve directly for hydro-mechanical interactions in random fracture networks. Our approach assumes that the seismic activity is controlled by a Coulomb shear criterion and we show how the interpretation of spreading rate of the modelled shear activity in a given network coincides with the upscaled virgin hydraulic diffusivity of the same fracture network, calculated from an independent numerical procedure at the reservoir scale. Therefore, it is shown that the direct analysis of the seismicity migration is appropriate to give reliable estimates of virgin hydraulic and mechanic parameters. These parameters can then be used for performing any further quantitative analysis of a reservoir open to the far field. This is of importance, as fluid mass-balance in multi-well exploitation systems will include the contribution from areas surrounding the stimulated zone.     

应变敏感的裂隙及裂隙岩体水力传导特性研究

通过将岩体单裂隙视为非关联理想弹塑性体，导出单裂隙在压剪荷载作用下，其机械开度和水力传导度的解析模型，并采用已有相关试验研究成果对解析模型进行验证。在此基础上，通过将岩体概化为含一组或多组优势裂隙的等效连续介质，给出一种描述裂隙岩体在复杂加载条件下考虑非线性变形特征及滑动剪胀特性的等效非关联理想弹塑性本构模型。基于该模型，给出裂隙岩体在扰动条件下应变敏感的渗透张量的计算方法，该计算方法不仅考虑裂隙的法向压缩变形，而且反映材料非线性及峰后剪胀效应对裂隙岩体渗透特性的影响。该模型通过引入滑动剪胀角和非关联理想塑性，较为逼真地反映了真实裂隙及裂隙岩体峰后的剪胀特性、变形行为和水力传导度变化特征。通过数值算例，研究了裂隙岩体在力学加载及开挖条件下渗透特性的演化规律。     

Estimation of fracture normal stiffness using a transmissivity-depth correlation

A new method for determination of fracture normal stiffness is developed in this paper. From the point of hydro-mechanical coupling, the relationship between transmissivity and depth is utilized to calculate fracture normal stiffness of large-scale rock masses, which is an important but difficult-to-obtain parameter. The basic idea is that flow in fractured media is very sensitive to aperture of discontinuity, and the aperture of the discontinuity is mainly determined by the normal stress and normal stiffness. A decrease in transmissivity of fractured rock masses with increasing depth, as indicated in hydraulic tests, is due to closure of the joints caused by an increase in the normal stress that is nearly proportional to depth. Consequently, it is possible to estimate in-situ fracture normal stiffness by using information of depth-dependent transmissivity. An equation is derived to achieve the purpose. In our preliminary case study at the fractured sandstone on the left bank of the Xiaolangdi Reservoir in China, the variable fracture normal stiffness is estimated. It satisfies the fact that normal stiffness will increase with increasing stress, i.e. with increasing depth. The value obtained by our method is of the same order of magnitude as the normal stiffness values obtained from laboratory tests reported in the literature. Furthermore, the estimated deformation modulus of the rock mass is close enough to that obtained from in-situ tests or inverse analysis.     

基于Barton剪胀模型的粗糙节理渗流分析

 为研究粗糙节理在剪切过程中的渗流规律,首先,采用Barton剪胀模型分析节理在剪切过程中的剪胀效应,计算节理在不同剪切位移下的剪胀位移,采用Brown-Scholz(B-S)理论模型分析法向应力作用下的节理闭合变形;通过初始隙宽、法向闭合变形和剪胀位移建立剪切过程中的节理隙宽与法向应力和剪切位移之间的关系,在此基础上得到剪切过程中的节理渗流计算公式;然后,在对节理试件进行渗流试验的基础上,分别采用基于Barton剪胀模型的节理渗流计算公式和Barton经验公式计算通过节理试件的理论渗流流量,并将预测结果与实测值进行比较,比较结果表明,基于Barton剪胀模型的节理渗流计算公式的预测结果与实测值较为一致,而Barton经验公式预测值与实测值偏差较大,从而验证了该公式在计算节理剪切过程中的渗流情况的正确性。     

充填砂裂隙在剪切位移作用下渗流规律的实验研究

对充填砂裂隙进行控制位移的剪切渗流实验，结合充填砂的物性，揭示了岩体裂隙发生剪切位移时的渗流规律，并对剪切位移与隙宽、剪切位移与流量、隙宽与流量的关系进行了探讨，提出了砂粒的微小扰动与孔隙比（隙宽）的增加是影响裂隙流量的主要因素。     

破断岩体裂隙的流体流动特性分析

 讨论立方定律成立的前提条件,指出立方定律只有在裂隙隙宽波动极小的情况下才能近似成立,对于岩体粗糙裂隙来说,此种状态只会出现在裂隙的局部区域,即局部立方定律;而在裂隙隙宽波动较大的区域,则需准确表述裂隙粗糙对流体流动的影响作用。提出天然粗糙裂隙的多平行板离散等效模型,可以有效地适用局部立方定律,推导粗糙裂隙的隙宽表示和流量计算公式;借助数值软件分析隙宽波动对等效模型单元体内部流体压力的作用规律,并定义一个过量压力降损耗系数,基于该系数对粗糙裂隙的流量计算方法进行修正。     

An experimental investigation of hydraulic behaviour of fractures and joints in granitic rock

A method of measuring mean mechanical aperture of fractures based on gas volume balance is introduced. The effects of shear displacement and normal stress on mechanical and hydraulic behaviour of fractures are also investigated. The results obtained from tests conducted on granite samples from Olympic Dam (Central Australia) are compared with those calculated from existing shear dilation theories. It is found that hydraulic aperture is considerably narrower than the measured mean mechanical aperture. This highlights the need to consider tortuosity and surface roughness of fractures in the calculation of hydraulic aperture. It is also found that shear dilation angle decreases linearly with increases in confining pressure, as opposed to more rapid decreases predicted by existing empirical models. From the results of this study, a range of data describing the relationships between confining pressure, shear displacements, hydraulic aperture and permeability are presented, which could help to develop stimulation programs for geothermal reservoirs.