Stress-dependent permeability of fractured rock masses: a numerical study

We investigate the stress-dependent permeability issue in fractured rock masses considering the effects of nonlinear normal deformation and shear dilation of fractures using a two-dimensional distinct element method program, UDEC, based on a realistic discrete fracture network realization. A series of “numerical” experiments were conducted to calculate changes in the permeability of simulated fractured rock masses under various loading conditions. Numerical experiments were conducted in two ways: (1) increasing the overall stresses with a fixed ratio of horizontal to vertical stresses components; and (2) increasing the differential stresses (i.e., the difference between the horizontal and vertical stresses) while keeping the magnitude of vertical stress constant.These numerical experiments show that the permeability of fractured rocks decreases with increased stress magnitudes when the stress ratio is not large enough to cause shear dilation of fractures, whereas permeability increases with increased stress when the stress ratio is large enough. Permeability changes at low stress levels are more sensitive than at high stress levels due to the nonlinear fracture normal stress-displacement relation. Significant stress-induced channeling is observed as the shear dilation causes the concentration of fluid flow along connected shear fractures. Anisotropy of permeability emerges with the increase of differential stresses, and this anisotropy can become more prominent with the influence of shear dilation and localized flow paths. A set of empirical equations in closed-form, accounting for both normal closure and shear dilation of the fractures, is proposed to model the stress-dependent permeability. These equations prove to be in good agreement with the results obtained from our numerical experiments.     

Fracture permeability normal to bedding in layered rock masses

A two-dimensional model of fracture permeability normal to bedding in layered rock with orthogonal, bed-delimited fractures is investigated. Steady-state, saturated laminar flow is assumed. Permeability is assumed to be a function of apertures and flow path lengths in an otherwise impermeable matrix. Bedding planes or other separations between layers are modeled as fictitious interlayers to render a layered fractured rock mass equivalent to a layered porous medium. Layer, or bed-normal permeability is quantified in terms of readily available field data, using a probability model to represent fracture connectivity between layers. The bed-normal permeability is shown to depend on fracture spacing and aperture, layer spacing and bedding plane aperture, and to be scale-dependent. Numerical investigation and comparison with field data indicates that the derived expression is useful for estimating layer-normal permeability.     

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.     

二维裂隙岩体渗流传热的离散裂隙网络模型数值计算方法

 针对裂隙岩体渗流传热问题,用解析方法,比较2种不同岩石基质与裂隙水界面热交换假设下的计算结果,对一般裂隙岩体,2种假设下的计算结果相同。基于离散裂隙网络模型的思想,在商业有限元软件COMSOL中实现一种计算已知裂隙网络的裂隙岩体渗流和传热过程的数值方法,该方法可以同时计算岩石基质与裂隙中的渗流和传热过程及二者间的交换,并与解析解比较进行验证。用该方法对一随机生成的二维裂隙岩体进行计算,得到的出口温度曲线,可以反映裂隙岩体渗流传热的早期热突破和长尾效应等特点,并分析岩石基质渗透率、热传导系数的不同取值对裂隙岩体渗流和传热过程的影响。     

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.     

裂隙岩体渗透张量计算及其表征单元体积初步研究

基于三维节理网络模拟技术,应用渗流能量叠加原理,推导节理岩体渗透张量的理论计算公式,在此基础上提出裂隙岩体渗透表征单元体积的确定方法。该方法考虑空间节理的具体分布和连通情况,同时根据节理的开度变化和立方定理又可分析应力场对渗透张量的影响,可方便、有效地进行裂隙岩体渗透特性的分析。随后讨论节理迹长、间距、开度、产状和组数等结构面几何特征对岩体渗透特性及表征单元体积的影响。最后采用上述方法,以拉西瓦水电站右岸岩体为例,计算工程岩体的渗透张量,并分析渗透表征单元体积大小及地应力对其渗透特性的影响。研究结果在工程设计中具有应用价值。     

裂隙单元修正等效渗透率模型及其验证

 采用裂隙单元表征裂隙网络,引入裂隙单元等效渗透率的概念,按照流量等效的原则计算其大小,然而阶梯状裂隙单元造成渗流流程的增加,同时压差不变导致流量的减少,为解决这一问题,用裂隙在网格中的实际流程长度与裂隙迹长之比来修正裂隙单元等效渗透率,并且针对复杂裂隙网络,对其进行预处理--删除孤立裂隙、死端裂隙、孤立裂隙簇等非连通裂隙。用此修正模型对单裂隙、相交裂隙、复杂裂隙网络进行渗流数值模拟,并与理论解及离散裂隙网络模型方法渗流结果进行比较,结果显示：研究区域下游出口总流量及出口处流量分布均取得较好一致性;同时,此裂隙单元修正等效渗透率模型也能反映出裂隙岩体渗流的非均质和各向异性。     

复合温度条件下石灰岩多场耦合裂隙渗透侵蚀试验研究

深部岩石工程处在高应力、高水压力、高地热等复杂地质环境中,这些因素相互作用将对岩石的渗透特性产生重要影响,进而影响深部岩石工程的安全和生产效率。通过开展不同温度(25℃~90℃)条件下的同一块石灰岩裂隙多场耦合渗透特性变化试验,得到了温度因素对石灰岩裂隙渗透特性的影响规律。试验结果表明:在恒定有效压力作用下,升温阶段的初始时刻有一个流量峰值过程,温度恒定时,流量缓慢减小并最终趋于稳定状态;温度升高使得岩石裂隙渗透率单调下降,裂隙开度进一步减小;此外,温度越高,初始阶段裂隙开度闭合速度快,趋于稳定开度值历时越短且最终稳定开度值越小。石灰岩的侵蚀溶解速度随温度的升高而加快,裂隙面溶解出的矿物质增多,因此,渗出液中各离子的浓度随温度的升高变大。     

考虑渗流特性的岩体结构面分形特性研究

 裂隙的连通性和密度是影响岩体渗流特性的重要因素。从岩体渗流研究的需要出发,对计算机模拟的岩体裂隙网络,应用分形几何理论,提出考虑裂隙连通性和密度影响的岩体结构面信息维数的计算方法,建立信息维数与岩体渗透系数的关系,进而可以用信息维数和岩体结构面几何参数来直接推求各向异性裂隙岩体的渗透系数张量。工程算例表明：(1) 考虑渗流应力耦合作用时,用容量维数计算的渗透系数比用信息维数计算的值高出2倍多,说明用容量维数计算岩体渗透系数会夸大裂隙岩体的渗透能力;(2) 信息维数能较好地反映裂隙密度对渗流的影响。信息维数越大,表明岩体内连通裂隙数量越多,因而岩体的渗透性就更大一些。     

Flow of groundwater in fractured rocks

A pervasive problem in dealing with fractured rocks is the importance of the flow of ground water through the discontinuities. This paper describes the results of recent work in this laboratory to investigate this problem. A much better understanding of the physics of fluid flow in a natural fracture from a sample of granite has been obtained from metal casts of the complex topography of the surfaces of the fracture as it is subjected to normal stresses up to 85 MPa. Contact area within the deforming aperture increases up to 30 percent and produces a flow regime that cannot be described by the cubic law. An investigation of flow in a network of fractures using a new numerical technique has been carried out to determine the effect of length and density of fractures on permeability. Networks with shorter fracture lengths and higher density will have lower permeabilities and will behave less like porous media than networks with longer fracture lengths and lower density. As fracture length increases, permeability approaches a maximum that can be predicted on the basis of infinite length fractures. A new analytical solution for transient flow to a borehole that penetrates a fracture dominated rock mass is summarized. A new derivative method of analyzing pressure transients from this solution is discussed and enables one to distinguish a fracture dominated system from one that exhibits double-porosity behavior.     

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.     

Impact of stress on solute transport in a fracture network: A comparison study

This paper compares numerical modeling of the effect of stress on solute transport (advection and matrix diffusion) in fractured rocks in which fracture apertures are correlated with fracture lengths. It is mainly motivated by the performance and safety assessments of underground radioactive waste repositories. Five research teams used different approaches to model stress/deformation, flow and transport processes, based on either discrete fracture network or equivalent continuum models. The simulation results derived by various teams generally demonstrated that rock stresses could significantly influence solute transport processes through stress-induced changes in fracture apertures and associated changes in permeability. Reasonably good agreement was achieved regarding advection and matrix diffusion given the same fracture network, while some observed discrepancies could be explained by different mechanical or transport modeling approaches.     

渗流–应力–化学耦合作用下岩石裂隙渗透特性试验研究

 为研究渗流–应力–化学耦合作用下岩石裂隙渗透特性变化规律,设计3组试验工况,在改变渗透压以及化学溶液的条件下,分别测定每种工况下的渗出水流量、渗出水离子浓度值以及渗出水pH值变化情况,进而得出裂隙渗透特性变化情况。通过处理试验数据,总结分析各因素对裂隙渗透特性的影响,并建立裂隙开度变化率与渗出水中钙离子浓度值之间的关系式。试验结果表明,渗出水流量、裂隙开度总体趋势是随着时间逐渐减小的,最终趋于稳定状态;增大渗透压,稳定状态会被打破,裂隙的流量和开度都会增大,但最终趋于另一个稳定状态;化学溶液对岩体裂隙的侵蚀性大,对岩体渗透性的影响更明显。通过分析和提炼渗出水流量、裂隙开度、渗出水的离子浓度值以及渗出水的pH值等随时间变化的数据,及它们之间的内部关系,在理论上描述岩体裂隙在渗流–应力–化学耦合作用下的渗透特性,进一步揭示渗流–应力–化学耦合作用机制。     

Rôle des fluides dans le comportement hydromécanique des roches fracturées hétérogènes: Caractérisation in situ et modélisation numérique

Hydromechanical coupled processes in a shallow fractured rock mass were investigated in situ through field experiments and numerical simulations. The experimental approach consists of performing simultaneous and multi-frequency measurements of fluid pressures and displacements at different points and on different fracture types within a carbonate reservoir. Two kinds of experiments were conducted at the Coaraze Laboratory Site (France):

1. At the fracture network scale, a global hydraulic loading by groundwater level change shows that the coupling between fluid flow and deformation is simultaneously governed by a dual-permeability hydraulic behaviour and a dual-stiffness mechanical behaviour. The following fluid flow and hydromechanical conceptual scheme was established: first, a transient flow only occurs in faults with high permeability; second, when a steady-state flow is reached in faults, water flows from faults into lower permeability bedding planes. The intact rock matrix is practically impervious but the connectivity between the discontinuities is high. When fluid pressure changes occur within the fracture network, the hydromechanical coupling is direct in the highly permeable faults where a pressure change induces a deformation change. No direct hydromechanical coupling occurs within the lower permeability zones where deformation is not directly correlated with pressure changes. This means that the mechanical deformation of the bedding planes and rock matrix is induced by the fault deformation.
2. At the single fracture scale, the hydromechanical behaviour was evaluated by performing hydraulic pulse injection testing. This test was monitored using high-frequency (f = 120 Hz) hydromechanical measurements conducted with innovative fiber-optic borehole equipment. The hydromechanical response is simultaneously monitored at two measuring points spaced about 1 m apart within the plane of the sub-vertical fracture. Observed fluid pressure versus normal displacement curves shows a characteristic loop-shaped evolution in which the paths for loading (pressure increase) and unloading (pressure decrease) are different. The test was evaluated by coupled hydromechanical modelling using a distinct element technique. By matching the loop behaviour, modelling indicates that the pulse pressure increase portion allows the fracture hydromechanical properties to be determined while the pulse pressure decrease portion is strongly influenced by the hydromechanical effects within the surrounding fractured rock mass. A sensitivity study shows that the key parameters to coupled hydromechanical processes in such fracture systems are the initial hydraulic aperture and normal stiffness of the fracture, the stiffness of the rock matrix and the geometry of the surrounding fracture network.

     

应力对裂隙岩体渗流影响的研究

研究了应力变化对裂隙岩体渗流特征的影响。假设裂隙网络由等效隙宽相等的相互平行的一组裂隙组成，由于应力变化而导致的隙宽变化控制了裂隙岩体渗流的变化，据此得出了裂隙岩体渗透系数及渗流量与应力的关系式。通过裂隙岩体渗流试验，证实了关系式的正确性。利用此关系式及有限元方法计算，得出了裂隙岩体渗透系数随应力的变化值。     

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.     

Some aspects of unsaturated flow in jointed rock

The applicability of Darcy's Law to two-phase flow has been discussed. Specialised triaxial equipment has been employed to separately inject two pore fluid components (air and water) into fractured rock specimens, so that two-phase flow behaviour can be studied at high axial and confining stresses. Improvements to recently developed two-phase high-pressure triaxial apparatus have enabled the authors to continue their study of air–water (i.e. unsaturated) flow in intact and fractured rock specimens under a wide range of stress conditions, similar to those encountered in underground mining operations. In this paper, a simplified stratified two-phase flow model is also presented that satisfactorily predicts flow behaviour in an inclined rock fracture over a range of linear laminar flow for particular capillary pressure relationships. The mathematical model is based upon the principles of conservation of mass and momentum, and relates the fracture aperture (e_t) to phase permeability (k_i) using Poiseuille's law and the proposed ‘phase height’, h_i(t), for water and air phases. The experimental approach used to verify the model predictions is described and the predicted results compared with the measurements. The experimental data confirmed the relationship between relative permeability and flow rate, with respect to two-phase flow conditions.     

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。     

裂隙岩体水力学特性研究

 基于裂隙中的水流运动规律,通过现场压水试验,研究裂隙岩体的渗透特性及其高压渗透特性,重点分析其水力学特性的应力相关性。试验研究表明,裂隙岩体的渗透性与应力赋存环境密切相关,且对应力十分敏感;裂隙岩体的应力环境、水力劈裂压力及裂隙充填情况不同,其高压渗透特性有较大差异。同时,通过总结前人的研究成果并结合数值试验分析,从裂隙岩体渗流的非连续性、非均质性、各向异性、优势水力特性及尺寸效应等多方位描述裂隙岩体的水力学特性,对其水力学特性及其成因进行综合评述。     

An analytical solution of equivalent elastic modulus considering confining stress and its variables sensitivity analysis for fractured rock masses

The equivalent elastic modulus is a parameter for controlling the deformation behavior of fractured rock masses in the equivalent continuum approach. The confining stress, whose effect on the equivalent elastic modulus is of great importance, is the fundamental stress environment of natural rock masses. This paper employs an analytical approach to obtain the equivalent elastic modulus of fractured rock masses containing random discrete fractures (RDFs) or regular fracture sets (RFSs) while considering the confining stress. The proposed analytical solution considers not only the elastic properties of the intact rocks and fractures, but also the geometrical structure of the fractures and the confining stress. The performance of the analytical solution is verified by comparing it with the results of numerical tests obtained using the three-dimensional distinct element code (3DEC), leading to a reasonably good agreement. The analytical solution quantitatively demonstrates that the equivalent elastic modulus increases substantially with an increase in confining stress, i.e. it is characterized by stress-dependency. Further, a sensitivity analysis of the variables in the analytical solution is conducted using a global sensitivity analysis approach, i.e. the extended Fourier amplitude sensitivity test (EFAST). The variations in the sensitivity indices for different ranges and distribution types of the variables are investigated. The results provide an in-depth understanding of the influence of the variables on the equivalent elastic modulus from different perspectives.