岩体裂隙中渗流场有限元随机模拟分析

采用有限元方法数值,模拟了开度随机分布裂隙中的渗流场问题。根据给定的裂隙开度均值和标准差,随机分布生成有限元模型中的单元裂隙开度,模型中的材料参数和单元属性用ANSYS中的APDL参数化语言赋值。根据有限元随机模拟断面的流量分布和稳态渗流问题的达西定律,计算在不同裂隙开度标准差条件下的等效导水系数,研究等效导水系数与裂隙粗糙度之间的关系。数值模拟结果表明,与光滑平直的裂隙相对比,在裂隙平均开度为常数、开度随机正态分布的条件下,表面粗糙裂隙的等效导水系数略有降低;对于裂隙平均开度为0.5 mm的裂隙模型,裂隙开度标准差从0.01 mm变化到 0.2 mm,其等效导水系数变化小于5 %。传统的渗流控制方程无法精确描述地下水在粗糙裂隙中的流动特征,因为在压力水头的定义中忽略了速度项。     

Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

Fracture networks play a more significant role in conducting fluid flow and solute transport in fractured rock masses, comparing with that of the rock matrix. Accurate estimation of the permeability of fracture networks would help researchers and engineers better assess the performance of projects associated with fluid flow in fractured rock masses. This study provides a review of previous works that have focused on the estimation of equivalent permeability of two-dimensional (2-D) discrete fracture networks (DFNs) considering the influences of geometric properties of fractured rock masses. Mathematical expressions for the effects of nine important parameters that significantly impact on the equivalent permeability of DFNs are summarized, including (1) fracture-length distribution, (2) aperture distribution, (3) fracture surface roughness, (4) fracture dead-end, (5) number of intersections, (6) hydraulic gradient, (7) boundary stress, (8) anisotropy, and (9) scale. Recent developments of 3-D fracture networks are briefly reviewed to underline the importance of utilizing 3-D models in future research.     

岩石节理表面几何特性的三维统计分析

在利用三维非接触式高精度激光表面形状测定仪精确测量岩石节理的表面粗糙形状并进行数值化表达的基础上,应用地理信息系统(GIS)技术,实现了岩石节理粗糙面的三维可视化。再对岩石节理粗糙面的三维几何特性参数（诸如表面粗糙度、裂隙张开度和粗糙高度等）进行统计分析并计算频数分布的特征数字。最后,根据频率直方图的分布趋势和频数分布的特征数字研究各几何特性参数的分布规律。结果表明,花岗岩节理粗糙表面起伏比砂岩大,但二者几何特性参数的分布规律相似,节理粗糙高度和裂隙张开度分布近似于正态分布规律,而节理粗糙面倾斜角分布近似于Γ分布规律。     

节理粗糙度对岩块体积的影响规律研究

岩体结构直接控制着岩体力学、水力学特性,岩块体积分布规律可直接反映岩体结构特征。目前研究多将节理面简化为平面,忽略了粗糙度对岩块体积的影响。利用Hurst指数H和高度均方根R_q表征节理粗糙度,研究了节理粗糙度对岩块数量和体积分布规律的影响。结果表明：(1)H、R_q控制节理的粗糙起伏形态,粗糙度随着R_q的增大而增大、随着H的增大而减小;(2)块体的数量总体上与节理粗糙度正相关,即随着粗糙度的增大而增加;(3)R_q和H对岩块体积分布的影响,主要通过改变小体积块体所占比例实现,块体的平均体积和中位体积随着粗糙度的增大而减小;(4)当节理正交且间距相近时,块体数量随粗糙度的变化可以分为3个阶段,即稳定阶段、初始增长阶段和快速增长阶段,R_q和H共同控制着各区间的相对分布范围。最后,基于摄影测量采集的数据建立了岩体节理模型,对大连某公路边坡的岩块体积分布进行了研究,验证了上述结论的准确性。     

裂隙特征对岩石渗流特性的影响规律研究

裂隙是油气储层主要的储集空间及流体渗流通道,影响油气的运移规律,是油气勘探开发的重要指标。以冀中坳陷任丘油田任10井为例,运用数值模拟方法研究了裂隙开展宽度和裂隙面粗糙度对岩石渗流特性的影响规律。研究结果表明,(1)裂隙开展宽度较小时,孔隙内流体压力仅在入口处小范围内呈扇形分布,裂隙中压力分布曲线呈正切函数型,流体流速在裂隙和孔隙中都较小;随着裂缝开展宽度的增加,孔隙内流体压力逐渐增大,裂隙中压力分布曲线逐渐向直线型转变,流体流速在入口处先减小后稳定,在裂隙中先增加后稳定;(2)裂隙面粗糙度对裂隙岩石渗流特性的影响与裂隙开展宽度有关,在裂隙开展宽度较大时,裂隙面粗糙度对流体压力的分布影响较大;随着裂隙面粗糙度增大,孔隙内流速逐渐增大,而裂隙中流速逐渐减小;(3)随着裂隙开展宽度的增大,影响裂隙流体流动的主控因素逐渐由裂隙开展宽度转变为裂隙面粗糙度。     

粗糙岩石裂隙低速非线性渗流模型及试验验证

岩体粗糙裂隙非线性渗透特性是岩体渗流研究的重要课题。针对Javadi所提T模型中亚裂隙中速度恒定这一假设的不足,将其修正为速度与开度成正比的经验关系,考虑黏性压降和局部压降,提出了新的低速下粗糙裂隙非线性渗流模型（MT模型）。为了验证MT模型的正确性,对5种不同粗糙裂隙进行了低流量的饱和渗流试验,将现有模型及MT模型的预测值与试验结果进行对比,分析表明MT模型与试验结果更为吻合,且模型适用于粗糙性系数JRC≤10的低粗糙度裂隙,雷诺数小于1 000的低流速情况。对MT模型进行分析,初步揭露了粗糙裂隙的非线性渗流机制,即小雷诺数下的Darcy流和大雷诺数下的Forchheimer流,并用临界雷诺数区分两种流动行为。分析了裂隙的粗糙度和开度对非线性渗流特性的影响,表明裂隙越粗糙或开度越小,则临界雷诺数越小,非线性作用将越强。提出了临界雷诺数与水力开度和绝对粗糙度的经验关系式,同时指出该关系式适用于JRC≤10的低粗糙度裂隙。     

Friction Factor of Water Flow Through Rough Rock Fractures

Fluid flow through rock joints occurs in many rock engineering applications. As the fluid flows through rough-walled rock fractures, pressure head loss occurs due to friction drag of the wall and local aperture changes. In this study, the friction factor was experimentally investigated by performing flow tests through sandstone fractures with joint roughness coefficient ranging from 5.5 to 15.4 under changing normal stress from 0.5 to 3.5 MPa. According to the experimental results, the friction factor was formulated as a function of two-independent variables—Reynolds number and relative roughness. Relative roughness is defined as the ratio of maximum asperity height to equivalent hydraulic aperture. The experimental results show that the proposed predictor of the friction factor fits the data with a coefficient of determination R ² > 0.93. Sensitivity analyses indicate that in general, the proposed friction factor increases with the relative roughness of confined fractures. The large difference of friction factor induced by relative roughness occurs when the Reynolds number is lower than unity, especially for Re < 0.2. For Reynolds numbers greater than unity, the difference of friction factor induced by relative roughness is smaller. Inclusion of joint roughness in calculating the friction resistance to fluid flow in rough rock joints and the influence of normal stress to the joints is a major step towards more accurate predictions for fluid flow in underground joint networks. This study provides a significant improvement in fundamental understanding of fluid flow in the jointed strata.     

A numerical model simulating reactive transport and evolution of fracture permeability

A numerical model is presented to describe the evolution of fracture aperture (and related permeability) mediated by the competing chemical processes of pressure solution and free‐face dissolution/precipitation; pressure (dis)solution and precipitation effect net‐reduction in aperture and free‐face dissolution effects net‐increase. These processes are incorporated to examine coupled thermo‐hydro‐mechano‐chemo responses during a flow‐through experiment, and applied to reckon the effect of forced fluid injection within rock fractures at geothermal and petroleum sites. The model accommodates advection‐dominant transport systems by employing the Lagrangian–Eulerian method. This enables changes in aperture and solute concentration within a fracture to be followed with time for arbitrary driving effective stresses, fluid and rock temperatures, and fluid flow rates. This allows a systematic evaluation of evolving linked mechanical and chemical processes. Changes in fracture aperture and solute concentration tracked within a well‐constrained flow‐through test completed on a natural fracture in novaculite (Earth Planet. Sci. Lett. 2006, in press) are compared with the distributed parameter model. These results show relatively good agreement, excepting an enigmatic abrupt reduction in fracture aperture in the early experimental period, suggesting that other mechanisms such as mechanical creep and clogging induced by unanticipated local precipitation need to be quantified and incorporated. The model is applied to examine the evolution in fracture permeability for different inlet conditions, including localized (rather than distributed) injection. Predictions show the evolution of preferential flow paths driven by dissolution, and also define the sense of permeability evolution at field scale. Copyright © 2006 John Wiley & Sons, Ltd.     

壁面局部接触裂隙岩体水流-传热的一种理论模型及计算分析

核废物地质处置、地热开发、石油开采等工程领域都可能涉及稀疏裂隙岩体中的水流-传热过程。现有的裂隙岩体水流-传热理论模型和计算方法基本上都是以平行光滑壁面裂隙模型为基础的,没有考虑裂隙的壁面局部接触对水流、水-岩热交换以及岩体传热的影响。针对粗糙壁面裂隙水流过程,阐述了基于Stokes方程的Reynolds润滑方程及Hele-Shaw裂隙模型,采用MATLAB软件中的PDE工具求解,并与Walsh的等效水力开度公式进行对比;分析壁面局部接触裂隙水流-传热与填充裂隙水流-传热的相似性,提出了瞬时局部热平衡假设的适用条件,并在裂隙局部接触体传热满足Biot数条件的前提下,计算分析裂隙局部接触体与水流之间的局部热平衡时间及其影响因素;在裂隙局部接触体与水流之间满足瞬时热平衡假设的前提下,利用填充裂隙水流-传热的解析解,计算了壁面局部接触裂隙水及两侧岩石的温度分布,并分析了裂隙局部接触面积率、裂隙开度、裂隙水平均流速对岩石温度和裂隙水温度的影响特征,结果表明：（1）在设定条件下,由于裂隙局部接触体与裂隙水流之间的热交换,裂隙水流对其两侧岩石温度的影响范围随接触面积率的增大而减小,裂隙两侧岩石对裂隙水流温度的影响程度随接触面积率的增大而增大;（2）裂隙开度和裂隙水流速对岩石温度和裂隙水温度的影响方式的影响是一致的,即由于裂隙水流量随裂隙开度和裂隙水流速的增大而增大,裂隙水流对其两侧岩石温度的影响范围随裂隙开度和裂隙水流速的增大而增大,裂隙两侧岩石对裂隙水流温度的影响程度随裂隙开度和裂隙水流速的增大而减小。     

岩体裂隙网络等效渗透系数方向性的数值计算

采用渗流力学理论并结合Monte Carlo方法描述岩体裂隙的随机分布,研究渗流模型的尺寸效应并确定表征单元体积（REV）,得到了3种开口度分布形式的等效渗透系数椭圆曲线,建立了等效渗透系数方向性的判别标准。离散裂隙网络（DFN）模型假定流体只在岩体裂隙内部流动,而不通过岩体本身渗流。基于二维离散元程序UDEC并进行二次开发,建立DFN模型,通过改变流体的流动方向,得到不同流动方向下岩体裂隙网络的等效渗透系数,并分析不同的开口度分布形式对岩体裂隙网络等效渗透系数方向性的影响。计算结果表明,表征单元体积存在的条件是等效渗透系数保持稳定且渗透椭圆比较光滑。等效渗透系数的方向性受开口度分布形式的影响很大：当开口度-长度关联分布时,等效渗透系数各向异性;当开口度对数正态分布时,等效渗透系数各向同性;当开口度恒定分布时,等效渗透系数的特性介于二者之间。变化系数（CV）是否大于5%是判定岩体裂隙网络渗透系数是否具有方向性的判别标准。     

Influence of three-dimensional roughness of rock fracture on seepage characteristics based on the digital image technology

Digital image processing technology can objectively reflect the surface roughness of coal and rock mass fractures and turn physical properties such as fluctuation height to physical data of the rock fracture surface to be used for numerical analyses; thus, it can effectively be applied to the seepage flow analysis of rock fractures. First, clear digital images of the fracture surface height are obtained under the same camera conditions, and then characteristic function values specific to various structure are normalized. Subsequently, the fluctuation height distribution of the rock surface is restored according to the measured fluctuation heights of local points. Finally, according to the surface fluctuation of fractures, invasive restructuring is carried out for three-dimensional fractures in the same coordinate system. Obtained physical parameters on the three-dimensional fractures of the rock are inputted into the COMSOL Multiphysics software to obtain the characteristic three-dimensional model of the rock fracture surface. The numerical analysis results are compared with experimental data on fracture seepage obtained from a seepage coupling true triaxial test system, and the relevance between the simulated result and the physical experiment is higher than 90%, which confirms that the integration of the digital image technology and the numerical analysis method can effectively simulate seepage in rough fractures. The hydraulic gradient of rough fractures and seepage velocity are also consistent with Forchheimer flow characteristics.     

Fracture roughness and thermal exchange: A case study at Soultz-sous-Forêts

Heat exchange during laminar flow in an open fracture is studied numerically on the basis of the Stokes equation in the limit of hydrothermal lubrication. We examine the influence of fracture roughness on hydraulic permeability and heat flux through the fracture sides when a cold fluid is injected into a homogeneous hot host rock. Spatial temperature fluctuations inside the fluid are studied assuming the temperature of the rock to be constant and the fracture aperture to be self-affine. An application to the case study at the deep geothermal reservoir of Soultz-sous-Forêts, France, is presented. Finally, a thermal model based on sparse spatial information of the geometrical aperture is successfully proposed to reproduce the response of the fracture.     

Hydraulic Characteristics of Rough Fractures in Linear Flow under Normal and Shear Load

Summary A hydro-mechanical testing system, which is capable of measuring both the flow rates and the normal and shear displacement of a rock fracture, was built to investigate the hydraulic behaviour of rough tension fractures. Laboratory hydraulic tests in linear flow were conducted on rough rock fractures, artificially created using a splitter under various normal and shear loading. Prior to the tests, aperture distributions were determined by measuring the topography of upper and lower fracture surfaces using a laser profilometer. Experimental variograms of the initial aperture distributions were classified into four groups of geostatistical model, though the overall experimental variograms could be well fitted to the exponential model. The permeability of the rough rock fractures decayed exponentially with respect to the normal stress increase up to 5 MPa. Hydraulic behaviours during monotonic shear loading were significantly affected by the dilation occurring until the shear stress reached the peak strength. With the further dilation, the permeability of the rough fracture specimens increased more. However, beyond shear displacement of about 7 to 8 mm, permeability gradually reached a maximum threshold value. The combined effects of both asperity degradation and gouge production, which prohibited the subsequent enlargement of mean fracture aperture, mainly caused this phenomenon. Permeability changes during cyclic shear loading showed somewhat irregular variations, especially after the first shear loading cycle, due to the complex interaction from asperity degradations and production of gouge materials. The relation between hydraulic and mechanical apertures was analyzed to investigate the valid range of mechanical apertures to be applied to the cubic law. Received June 12, 2001; accepted February 26, 2002 Published online September 2, 2002     

考虑三维形貌特征粗糙裂隙加卸载渗流规律研究

裂隙岩体在天然地质因素和人工扰动作用下处于加卸载环境是普遍存在的,裂隙面的几何特征和加卸载环境对裂隙渗流特性的影响在实际工程中不可忽视。采用试验和数值模拟相结合的方法,利用热-流-固三场耦合渗流试验系统,开展了应力加卸载作用下不同粗糙度裂隙岩芯试件的渗透试验,自主开发程序将激光扫描裂隙面的三维形貌信息导入到ABAQUS软件,模拟应力作用下的粗糙裂隙渗流。试验和数值模拟一致表明,粗糙裂隙的宽度和渗透率都随载荷的增加而减小,随着载荷的增加,裂隙接触刚度增大,裂隙的宽度和渗透率对载荷变化的敏感性降低;由于点接触产生的塑性变形不可恢复,卸载阶段的裂隙宽度和渗透率增加幅度减小,且小于加载阶段同载荷条件下的宽度和渗透率;裂隙渗透率、宽度与粗糙度呈正相关关系,且粗糙度越大,接触应力分布越不均匀;裂隙内流场符合群岛流,粗糙度越大群岛流现象越明显。     

Rockfall Hazard Analysis From Discrete Fracture Network Modelling with Finite Persistence Discontinuities

Developing an accurate representation of the rock mass fabric is a key element in rock fall hazard analysis. The orientation, persistence and density of fractures control the volume and shape of unstable blocks or compartments. In this study, the discrete fracture modelling technique and digital photogrammetry were used to accurately depict the fabric. A volume distribution of unstable blocks was derived combining polyhedral modelling and kinematic analyses. For each block size, probabilities of failure and probabilities of propagation were calculated. A complete energy distribution was obtained by considering, for each block size, its occurrence in the rock mass, its probability of falling, its probability to reach a given location, and the resulting distribution of energies at each location. This distribution was then used with an energy–frequency diagram to assess the hazard.     

Fracture networks and fluid transport in active fault zones

Field measurements were made of 1717 mineral-filled veins in the damage zone of an active dextral strike-slip fault zone in Iceland. Most veins are composed of quartz, chalcedony and zeolites, strike roughly parallel or perpendicular to the fault zone, and are members of dense palaeo-fluid transporting networks. A common vein frequency in these networks is 10 veins per metre. Cross-cutting relationships indicate that 79% of the veins are extension (mode I) cracks and 21% are shear cracks. The apertures of most veins, measured as mineral-fill thicknesses, are from 0.1 to 85 mm, and the aperture frequency distribution is a power law. The outcrop trace lengths of 384 veins (of the 1717) could be measured accurately. These 384 veins are mostly small and range in length from 2.5 to 400 cm, in aperture from 0.01 to 0.9 cm, and have an average length/aperture ratio of about 400. Simple analytical models are derived and used to make rough estimates of the volumetric flow rates in hydrofractures of dimensions equal to those of typical veins. The results indicate that volumetric flow rates for a horizontal fracture and a vertical fracture in a rigid (non-deforming) host rock would be around 1.5×10⁻⁴ and 8.9×10⁻⁴ m³s⁻¹, respectively. The volumetric flow rate in a vertical fracture of equal size but in a deforming host rock, with buoyancy added to the pressure gradient, is around 1.3×10⁻³ m³s⁻¹. Thus, vertical fluid transport is favoured under these conditions.     

The role of in situ stress in determining hydraulic connectivity in a fractured rock aquifer (Australia)

Fracture network connectivity is a spatially variable property that is difficult to quantify from standard hydrogeological datasets. This critical property is related to the distributions of fracture density, orientation, dimensions, intersections, apertures and roughness. These features that determine the inherent connectivity of a fracture network can be modified by secondary processes including weathering, uplift and unloading and other mechanisms that lead to fracture deformation in response to in situ stress. This study focussed on a fractured rock aquifer in the Clare Valley, South Australia, and found that fracture network connectivity could be discriminated from several geological, geophysical and hydrogeological field datasets at various scales including single well and local- to regional-scale data. Representative hydromechanical models of the field site were not only consistent with field observations but also highlighted the strong influence of in situ stress in determining the distribution of fracture hydraulic apertures and the formation of hydraulic chokes that impede fluid flow. The results of this multi-disciplinary investigation support the notion that the hydraulic conductivity of a fracture network is limited to the least hydraulically conductive interconnected fractures, which imposes a physical limit on the bulk hydraulic conductivity of a fractured rock aquifer.     

Hydromechanical properties and alteration of natural fracture surfaces in the Soultz granite (Bas-Rhin, France)

Natural fractures are characterized by rough surfaces and complex fluid flows. A large distribution of apertures (residual voids) within their walls and the presence of contact points (in situ normal loads) produce heterogeneous flows (channeling). The resulting permeabilities, porosities or fluid–rock exchange surfaces cannot be realistically modeled by parallel and smooth plate models. Four natural fractures are sampled at different depths and degrees of alteration in the Soultz sandstone and granite (EPS1 drillhole, Soultz-sous-Forêts, Bas-Rhin, France). The fracture surfaces are measured with mechanical profilometry and maps of asperity heights (XYZ). Resulting local apertures (XYe) are then calculated. A statistical study of the surface profiles (XZ) show that the fractures are more or less rough and tortuous according to the types of alteration. Altered samples are characterized by smoother surfaces of fractures. Such differences imply that (i) the average fracture aperture is not representative for the whole fracture and that (ii) the different local apertures should be integrated in hydraulic and mechanical models. A hydraulic model (finite difference calculations) of fluid flow, taking into account the elastic closure (Hertz contact theory) of fractures with depth, is used. Maps of contact points and relative local loads within the fracture planes are compared to flow maps. They show different channeling of fluid flows. Strongly altered fractures are characterized by homogeneous fluxes despite the presence of numerous contact zones during the closure of fracture. By contrast, fresh fractures develop, increasing fluid flow channels with depth.Fracture closure (increasing normal stress) does not systematically increase the channeling of fluid flow. There is evidence for a general smoothing out of the irregularities of the fracture walls due to precipitation of secondary minerals, indicating that the cubic law can be commonly valid, also at great crustal depth but this validity depends on the degree of fracture alteration. Mineralogical and geochemical observations, thus, should be taken into account to perform more accurate permeability calculations and models of fluid circulation in fracture networks.     

Numerical modelling of fluid flow tests in a rock fracture with a special algorithm for contact areas

The fluid flow in rock fractures during shear processes has been an important issue in rock mechanics and is investigated in this paper using finite element method (FEM), considering evolutions of aperture and transmissivity with shear displacement histories under different normal stress and normal stiffness conditions as measured during laboratory coupled shear-flow tests. The distributions of fracture aperture and its evolution during shearing were calculated from the initial aperture, based on the laser-scanned sample surface roughness results, and shear dilations measured in the laboratory tests. Three normal loading conditions were adopted in the tests: simple normal stress and mixed normal stress and normal stiffness to reflect more realistic in situ conditions. A special algorithm for treatment of the contact areas as zero-aperture elements was used to produce more accurate flow field simulations, which is important for continued simulations of particle transport but often not properly treated in literature. The simulation results agree well with the measured hydraulic apertures and flow rate data obtained from the laboratory tests, showing that complex histories of fracture aperture and tortuous flow fields with changing normal loading conditions and increasing shear displacements. With the new algorithm for contact areas, the tortuous flow fields and channeling effects under normal stress/stiffness conditions during shearing were more realistically captured, which is not possible if traditional techniques by assuming very small aperture values for the contact areas were used. These findings have an important impact on the interpretation of the results of coupled hydro-mechanical experiments of rock fractures, and on more realistic simulations of particle transport processes in fractured rocks.     

裂隙岩体渗透性影响因素的研究

采用UDEC离散单元法中关于裂隙岩体开挖模拟及水力全耦合分析模型,分析裂隙岩体洞室开挖后,因围岩应力与水力耦合作用导致裂隙隙宽变化及渗流变化的过程。为了更直观地了解耦合作用对裂隙岩体渗透特性的影响,以隧洞开挖为例,用开挖后隧洞内总涌水量来表征岩体的渗透特性。利用数值试验的方法,研究了块体边界大小、初始应力比、裂隙隙宽和裂隙夹角对开挖后隧洞内涌水量变化的影响,进而可以看出它们对裂隙岩体渗透性的影响。并得出如下结论：随着块体尺寸和初始应力比的增大,隧洞内总涌水量减少;随初始隙宽的增大涌水量增加并当达到某一固定值时保持不变;隧洞涌水量在θ2/θ1=3.5,其中θ1=30°,即两组节理的夹角为75°处达到最大。