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.     

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.     

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.     

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.     

Estimation of fracture flow considering the inhomogeneous structure of single rock fractures

Considering the safe, long-term isolation of energy byproducts, such as radioactive waste, one of the important parameters is the velocity of the groundwater flow through the void of rock masses and/or fractures. Although it is generally known that a natural rock fracture indicates a complex aperture distribution, the fracture is often ideally represented by a parallel plate model. The cubic law is applied to evaluate the hydraulic properties of fractured rock. From several previous research works, it is understood that the cubic law can be applied when the Reynolds number is less than 1.0 and that the inertia term can basically be ignored in such slow fracture flows. In this research work, two-dimensional seepage flow analyses, using the authors' proposed 2D model, in which the inertia term, the pressure term and the diffusion term are incorporated, are carried out for single fracture permeability tests under conditions which allow for the application of the cubic law. In comparing the results of the experiments with the results of the numerical simulation, the results of the simulation employing the 2D model show a good agreement with the experimental results; the 2D model can simulate the water flow in an inhomogeneous fracture more accurately than the simulation based on the local cubic law. From these simulation results, the fracture flow in an inhomogeneous structure is discussed, along with the local Reynolds number, and the resistance through the fracture geometry is considered. Consequently, under the condition of a mean Reynolds number of less than 1.0, the inertia terms do not affect the fracture flow, but the hydraulic resistance does affect the fracture flow.     

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.     

剪切条件下单裂隙渗流机制试验及三维数值分析研究

为研究裂隙内部接触面对其过流能力的影响,设计具有相同接触率、不同接触面分布方式的2组平行板裂隙以及1组具有天然特征的人工裂隙,分别进行渗流试验和剪切–渗流试验,并对试验过程进行有限元数值模拟。数值模拟结果与试验结果的对比表明,相对于一维的立方定律和二维的Reynolds方程,基于三维的Navier-Stokes方程的数值方法更能精确模拟出裂隙内过流的实际状态。裂隙的过流能力不仅受接触率和接触面分布方式影响,还受雷诺数的影响。雷诺数较大时,随着雷诺数的增大,裂隙的水力传导系数降低;同时,接触面的附近区域还会观察到回流,这被认为是导致裂隙水力传导系数降低的重要因素之一。     

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。     

Single fractures under normal stress: The relation between fracture specific stiffness and fluid flow

Fracture specific stiffness and fluid flow through a single fracture under normal stress are implicitly related through the geometry of the void space and contact area that comprise the fracture. Data from thirteen different rock samples, each containing a single fracture, show that relationships between fracture specific stiffness and fluid flow through a fracture fall into two general classes of behavior. Fractures either fall on a loosely-defined universal curve relating fluid flow to fracture specific stiffness, or else the flow is weakly dependent on fracture specific stiffness. The second relationship shows that flow decreases slowly with increasing fracture specific stiffness. The first relationship shows that flow decreases rapidly for increases in fracture specific stiffness. To understand this behavior, computer simulations on simulated single fractures were performed to calculate fluid flow, fracture displacement, and fracture specific stiffness as a function of normal stress. Simulated fractures with spatially correlated and uncorrelated aperture distributions were studied. Fractures with spatially uncorrelated aperture distributions tend to exhibit a weak dependence of fluid flow on fracture specific stiffness because these fractures tend to have multiple connected paths across the sample which can support flow with uniformly distributed contact area. Thus an increment in stress will increase the stiffness of the fracture without greatly reducing the amount of fluid flow. On the other hand, fractures with spatially correlated aperture distributions tend to belong to the universal relationship because correlated fractures tend to have only one or two dominant flow paths and the contact area is limited to a few regions resulting in a compliant fracture. Thus an increment in stress on a spatially correlated fracture will result in an increase in stiffness and rapid decrease in fluid flow. These spatial correlations in fracture void geometry can be differentiated in the laboratory based on the observed fracture specific stiffness–fluid flow relationship for a single fracture under normal loading.     

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。     

Fracture morphology and viscous transport

The morphology of a fracture in a granite block is sampled using a high resolution profiler providing a 3999×4000 pixel image of the roughness. We checked that a self-affine model is an accurate geometrical model of the fracture morphology on the basis of a spectral analysis. We also estimated the topothesy of the experimental surface to be and the roughness exponent to be ζ≈0.78. A finite difference scheme of the Stokes equation with a lubrication approximation was used to model the viscous flow through a fracture aperture defined as the gap between the experimental fracture surface and a flat plane. We finally compare our numerical results to experimental measurements of the flux through the fracture of a glycerol/water mixture (to be at sufficiently low Reynolds number where Stokes equations holds) changing the average aperture of the fracture. The comparison is successful despite a limited resolution of the experimental measurements. Interestingly we show that only long wavelengths of the fracture morphology control the fracture hydraulic conductivity.     

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.     

Uncertainty analysis of groundwater inflow into underground excavations by stochastic discontinuum method: Case study of Siah Bisheh pumped storage project,Iran

This paper presents a framework for the near-field stochastic discontinuum modeling and uncertainty analysis of groundwater inflow into underground excavations by direct utilization of discrete fracture network (DFN) concept. The sources of uncertainty in the groundwater inflow into underground excavations in fractured rocks were classified into two different groups including the geometrical and hydraulic properties of fractures. The main input data for stochastic discontinuum modeling of groundwater inflow were captured from site investigations in Siah Bisheh pumped storage project in Iran. Detailed measurements of groundwater inflow into powerhouse and transformer caverns provided the possibility to determine the hydraulic aperture through back calibration. The validity of calibrated hydraulic aperture was explored by simulation results of the groundwater inflow into transformer cavern, and shows high accuracy when compared with data obtained from field measurements. The statistical results of these groundwater flow simulations with constant calibrated hydraulic aperture reflected the uncertainty associated with geometrical properties of fractures. Finally, the role of hydraulic properties of fractures on the uncertainty of groundwater inflow was investigated by the variation of standard deviation of hydraulic aperture through the sensitivity analysis. The results of this study demonstrated that the geometrical properties of fractures did much greater uncertainty in the groundwater inflow into underground excavations than hydraulic properties. Moreover, it was found that both the mean and standard deviation of simulated groundwater inflow into underground excavations decrease non-linearly by increasing the standard deviation of hydraulic aperture even though it is generally anticipated that the uncertainty of hydrogeological systems increases by increasing the variance of hydraulic parameters.     

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.     

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.     

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.

     

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。     

Performance assessment of a nuclear waste repository: Upscaling coupled hydro-mechanical properties for far-field transport analysis

A methodology for addressing the DECOVALEX III Bench Mark Test 2 is presented. Hydro-mechanical (HM) modelling has been conducted on fracture networks generated from fracture length and density statistics, which have been described by a power law. For each rock formation in the test, effective hydraulic conductivity tensors have been derived for a range of mechanical parameters and depths below ground level. The upscaled hydraulic conductivities have been used in a site scale continuum model of groundwater flow and transport to assess performance indicators, including time of travel from repository to ground surface. Preliminary results indicate that interpretation of the fracture length and density data can have a significant effect on upscaling calculations, including the determination of a suitable hydraulic representative elementary volume. HM modelling shows that there is a non-linear decrease in the change of fracture aperture with depth, and that although large aperture fractures remain at depth, the majority of fractures tighten to almost the residual aperture at about 750 m below ground level. Consequently, anisotropy of the effective hydraulic conductivity also changes with depth. Flow and transport modelling at the field scale indicates that, of the controls investigated, mechanical properties of the rock have the greatest influence on solute travel times.     

岩石节理剪切过程中应力与渗流特性的数值模拟

 岩石节理剪切过程中应力与渗流特性受节理法向条件的影响很大。在岩石节理表面形状三维数值化表达的基础上,首先建立岩石节理剪切过程中力学与渗流的计算模型;接着,应用GIS技术,模拟分析不同法向条件(固定应力、固定刚度)下节理的剪切过程,获得节理剪切过程中应力与渗流特性的变化规律。结果表明,法向应力、裂隙张开度、渗透系数均随着剪切位移的增加而逐渐增加,整个剪切过程渗透系数增加了两个量级左右;而剪应力的变化却受法向条件的影响,剪应力在出现峰值后快速下降,而后固定应力条件下剪应力很快趋于一个稳定的值,而固定刚度条件下剪应力却又缓慢上升。