基于DDA方法一种流-固耦合模型的建立及裂隙体渗流场分析和应用

以非连续变形分析方法（DDA）为基础并采用稳态流体计算方法将二者结合进行裂隙岩体流-固耦合分析。利用DDA方法生成裂隙岩体模型,在此基础上采用矩阵搜索等方法形成新的裂隙水通网络模型。采用稳态迭代算法和立方定律求得裂隙水压力,并把裂隙水压力作为线载荷施加到块体边界,在DDA算法中每个迭代步完成后更新裂隙开度和水压值,与DDA算法结合研究裂隙水与块体之间相互作用关系。利用以上裂隙岩体流-固耦合计算方法研究了某水封油库开挖和运行过程洞室围岩流量和密封性,为该工程预测水封效果提供了有益的主要依据,也是国内首次采用DDA方法做大型工程的流-固耦合模型分析。     

离散裂隙渗流方法与裂隙化渗透介质建模

流体渗流模拟的连续介质方法通常适用于多孔地质体，并不一定适用于裂隙岩体，由于裂隙分布及其特征与孔隙差异较大。若流体渗流主要受裂隙的控制，对于一定尺寸的裂隙岩体，多孔介质假设则较难刻划裂隙岩体的渗流特征。离散裂隙渗流方法不但可直接用于模拟裂隙岩体非均质性和各向异性等渗流特征，而且可用其确定所研究的裂隙岩体典型单元体及其水力传导（渗透）张量大小。主要讨论了以下问题：（1）饱和裂隙介质中一般的离散流体渗流模拟；（2）裂隙岩体中的REV（典型单元体）及其水力传导（渗透）张量的确定；（3）利用离散裂隙网络流体渗流模型研究裂隙方向几何参数对水力传导系数和REV的影响；（4）在二维和三维离散裂隙流体渗流模型中对区域大裂隙和局部小裂隙的处理方法。调查结果显示离散裂隙流体渗流数学模型可用来评价不同尺度上的裂隙岩体的水力特征，以及裂隙方向对裂隙化岩体的水力特征有着不可忽视的影响。同时，局部小裂隙、区域大裂隙应当区别对待，以便据其所起的作用及水力特征，建立裂隙化岩体相应的流体渗流模型。     

Fully coupled hydro-mechanical numerical manifold modeling of porous rock with dominant fractures

Coupled hydro-mechanical (HM) processes are significant in geological engineering such as oil and gas extraction, geothermal energy, nuclear waste disposal and for the safety assessment of dam foundations and rock slopes, where the geological media usually consist of fractured rock masses. In this study, we developed a model for the analysis of coupled hydro-mechanical processes in porous rock containing dominant fractures, by using the numerical manifold method (NMM). In the current model, the fractures are regarded as different material domains from surrounding rock, i.e., finite-thickness fracture zones as porous media. Compared with the rock matrix, these fractured porous media are characterized with nonlinear behavior of hydraulic and mechanical properties, involving not only direct (poroelastic) coupling but also indirect (property change) coupling. By combining the potential energy associated with mechanical responses, fluid flow and solid–fluid interactions, a new formulation for direct HM coupling in porous media is established. For indirect coupling associated with fracture opening/closure, we developed a new approach implicitly considering the nonlinear properties by directly assembling the corresponding strain energy. Compared with traditional methods with approximation of the nonlinear constitutive equations, this new formulation achieves a more accurate representation of the nonlinear behavior. We implemented the new model for coupled HM analysis in NMM, which has fixed mathematical grid and accurate integration, and developed a new computer code. We tested the code for direct coupling on two classical poroelastic problems with coarse mesh and compared the results with the analytical solutions, achieving excellent agreement, respectively. Finally, we tested for indirect coupling on models with a single dominant fracture and obtained reasonable results. The current poroelastic NNM model with a continuous finite-thickness fracture zone will be further developed considering thin fractures in a discontinuous approach for a comprehensive model for HM analysis in fractured porous rock masses.     

Parametric study of factors affecting fluid flow through a fracture

Understanding the flow behavior through fractures is critically important in a wide variety of applications. In many situations, the fluid flow can be highly irregular and non-linear in nature. Numerical simulation can be employed to simulate such conditions which are difficult to replicate in laboratory experiments. Therefore, a parametric study has been conducted on the fluid flow through micro-fracture over a large range of inlet pressure, fluid density, fluid viscosity, temperature, joint roughness coefficient (JRC), and fracture using finite element analysis. Irregular fracture profiles were created using Barton’s joint roughness coefficient. The Navier-Stokes (NS) equation was used to simulate the flow of water in those micro-fractures. The result showed that the fracture, fluid, and ambient conditions have a wide and varied effect on the fluid flow behavior. The interrelationship between these parameters was also studied. The model simulation provided result in the form of velocity and pressure drop profile, which can be used to determine the behavior of flow under different condition. The volumetric flow was calculated for each condition and has been plotted against the corresponding parameter to study the interrelationship.     

低应力与覆水环境下单裂隙粉砂质泥岩渗流特性

为探究不同外部环境因素影响下浅层粉砂质泥岩边坡裂隙渗流特性,采用自主研发的岩体裂隙渗流试验装置,对含6种不同裂隙面粗糙度（JRC）的粉砂质泥岩裂隙试样进行渗流试验,研究了不同低围压和覆水深度下粉砂质泥岩裂隙渗流特性。结果表明：不同覆水深度及JRC下围压与粉砂质泥岩裂隙渗透系数均呈反相关,两者之间关系可用幂函数表征,且渗透系数的降低过程可分为快速降低（围压为0～30 kPa）和缓慢降低（围压为30～50 kPa）两个阶段,CT扫描结果验证了围压增大使得粉砂质泥岩裂隙开度减小是渗透系数随围压增大而减小的主要原因。随围压的增大或覆水深度的减小,不同JRC粉砂质泥岩裂隙渗透系数的离散程度逐渐减小。当围压增至最大,同时覆水深度最小时,JRC对裂隙渗透系数的影响将会被消除。不同围压下,粉砂质泥岩裂隙渗透系数与覆水深度呈正相关,且两者关系可用指数函数表征。推导出了粉砂质泥岩裂隙渗流非线性Izabsh模型,该模型能较好地反映低应力及低流速下粉砂质泥岩裂隙渗流量与压力梯度之间的非线性变化关系,但随围压的增大,该模型的相关性有一定程度的减小。     

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。     

Effect of different wall roughness on the frictional behavior of rock joints

Rock discontinuities play a crucial and critical role on the deformational and failure behavior of the rock mass. In most investigations, both the surfaces of the rock joints are considered to have same roughness. But, in nature, the walls of a fresh joint is only expected to be complimentary and to have same roughness. Weathered and water percolating rock joint is most likely to develop different surface roughness on the two opposite walls. So, the shear strength and frictional response behavior derived from the single joint roughness coefficient (JRC) assumption cannot be used in such a condition. To address this shortcoming, we have prepared sandstone blocks with different surface roughness and conducted experiments in a tribometer. The static friction, shear stiffness and coefficient-of-friction of the joint surfaces were calculated and their changes with increasing normal load were noted. One of the major findings of this paper is that, shear strength of the joints may not have a direct correlation with the increasing JRC value of the individual joint walls. Hence, some of the joint walls having higher cumulative JRCs were found to show lower shear strength than those with lowers roughness. This is because, the opposing walls of such joints are not anymore complementary and the frictional resistance is completely controlled by the height and contact area of the asperites.     

Natural fracture profiles,fractal dimension and joint roughness coefficients

Summary Thirteen natural rock profiles (Barton and Choubey, 1977) are analyzed for their fractal properties. Most of the profiles were found to approximate fractal curves but some also showed features of specific wavelengths and amplitudes superimposed on fractal characteristics. The profiles showed fractal dimensions from 1.1 to 1.5 covering a range of selfsimilar and self-affine curves. The analysis results suggest a negative correlation between fractal dimension,D, and amplitude,A. Joint roughness coefficients (JRC) show a positive correlation with amplitude,A, and a negative correlation with fractal dimension,D. A numerical model of fracture closure is used to investigate the effects of different profile characteristics (D, A and sample size) on the nature of dilation and contact area, using the natural profiles and synthetic fractional Brownian motion profiles. Smooth profiles (low JRC, highD, lowA) display many small contact regions whereas rough fractures (high JRC, lowD, highA) display few large contact areas. The agreement with published experimental data supports the suggested correlations between JRC and the fractal parameters,A andD. It is suggested that observed scale effects in JRC and joint dilation can be explained by small differential strain discontinuities across fractures, which originate at the time of fracture formation.     

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.     

Linear flow behaviour of matched joints – case study on standard JRC profiles

Roughness on rock joints produces a variable aperture across the joints and increases the flow path length. These conditions should be taken into account for a good approximation from cubic law. In this paper, the concept of local true aperture and tortuosity is applied to assumed joints where surfaces are matched to each other and correspond with standard Joint Roughness Coefficient (JRC) profiles. Furthermore, the hydraulic behaviour of JRC profiles is studied by a new laboratory experiment setup. The analytical approach provides new insights into the effects of roughness on hydraulic properties of rock joints. The results indicate that for a constant mechanical aperture, both the minimum local aperture and hydraulic aperture decrease with increasing JRC. Furthermore, tortuosity and standard deviation of local true aperture increase with JRC increment. The trend obtained between different parameters and JRC shows an obvious fluctuation for JRC lower than 10. On one hand, the results of this study along with a critical review of previous studies demonstrate that JRC profiles cannot present a precise roughness increment when JRC is less than 10. A new laboratory setup was designed to study the flow behaviour of JRC profiles. The results obtained from laboratory experiments under linear flow conditions validate the accuracy of the applied analytical method.     

Application of Stochastic Fracture Network with Numerical Fluid Flow Simulations to Groundwater Flow Modeling in Fractured Rocks

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Modified governing equation and numerical simulation of seepage flow in a single fracture with three-dimensional roughness

Roughness and tortuosity influence groundwater flow through a fracture. Steady flow through a single fracture can be described primitively by the well-known Cubic Law and Reynolds equation with the assumption that the fracture is made of smooth parallel plates. However, ignoring the roughness and tortuosity of the fracture will lead to inaccurate estimations of the flow rate. To obtain a more accurate flow rate through a rough fracture, this paper has derived a modified governing equation, taking into account the three-dimensional effect of the roughness. The equation modifies the Reynolds equation by adding correction coefficients to the terms of the flow rates, which are relative to the roughness angles in both the longitudinal and transverse directions. Experiments of steady seepage flow through sawtooth fractures were conducted. The accuracy of the modified equation has been verified by comparing the experimental data and the theoretical computational data. Furthermore, three-dimensional numerical models were established to simulate the steady flow in rough fractures with the triangular, sinusoidal surfaces and the typical joint roughness coefficient (JRC) profiles. The simulation results were compared with the calculation results of the modified equation and the current equations. The comparison indicates that the flow rate calculated by the modified equation is the closest to the numerical result.     

考虑应力历史的岩石单裂隙渗流特性试验研究

通过开展单裂隙花岗岩不同围压加、卸载和不同水力梯度作用下的渗透试验,研究应力历史对裂隙渗透性能演化的影响。试验结果表明：在围压加载过程中,渗流流量与渗透压差大致呈线性关系;在渗透压差相同的条件下,围压越小,流量越大,随着围压上升,裂隙渗流流量持续减小,但随着围压的进一步增大,流量的减小有减缓的趋势。在围压相同以及渗透压差相同的条件下,单裂隙花岗岩在卸载条件下的渗流特性与加载条件下相比,其渗流流量明显降低,且卸载过程中渗流流量与渗透压差开始偏离线性关系。从试验前、后裂隙面粗糙度系数值的对比可以看出,由于法向应力挤压以及渗流流体的冲蚀作用,试验后裂隙面粗糙度系数明显降低。卸载的过程中,裂隙渗透性能的恢复具有明显的滞后效应,表明在法向应力和流体冲蚀的共同作用下,裂隙产生了不可恢复的非弹性变形。     

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.     

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.     

岩石裂隙的非饱和渗透特性及其演化规律研究

岩石裂隙的非饱和渗透特性是岩土、能源和环境等领域科学研究中的热点问题。采用三维激光扫描获取花岗岩裂隙的表面形貌特征,分析裂隙微观形貌特征对非饱和渗透特性的影响。研究在张拉、压缩、剪切等复杂荷载作用下裂隙开度分布的演化规律,建立复杂荷载作用下岩石裂隙非饱和毛细压力曲线演化模型。基于裂隙的微观形貌特征推导了岩石裂隙非饱和相对渗透系数模型,通过与试验数据对比,验证了模型的准确性和有效性,并在此基础上建立了复杂荷载作用下岩石裂隙非饱和相对渗透系数演化模型。研究成果对非饱和条件下裂隙岩体的水-力耦合机制研究具有一定指导意义。     

Simulations of hydro-fracking in rock mass at meso-scale using fully coupled DEM/CFD approach

The paper deals with two-dimensional (2D) numerical modelling of hydro-fracking (hydraulic fracturing) in rocks at the meso-scale. A numerical model was developed to characterize the properties of fluid-driven fractures in rocks by combining the discrete element method (DEM) with computational fluid dynamics (CFD). The mechanical behaviour of the rock matrix was simulated with DEM and the behaviour of the fracturing fluid flow in newly developed and pre-existing fractures with CFD. The changes in the void geometry in the rock matrix were taken into account. The initial 2D hydro-fracking simulation tests were carried out for a rock segment under biaxial compression with one injection slot in order to validate the numerical model. The qualitative effect of several parameters on the propagation of a hydraulic fracture was studied: initial porosity of the rock matrix, dynamic viscosity of the fracking fluid, rock strength and pre-existing fracture. The characteristic features of a fractured rock mass due to a high-pressure injection of fluid were realistically modelled by the proposed coupled approach.

     

Analysis of a deformable fracture in permeable material

The response of deformable fractures to changes in fluid pressure controls phenomena ranging from the flow of fluids near wells to the propagation of hydraulic fractures. We developed an analysis designed to simulate fluid flows in the vicinity of asperity‐supported fractures at rest, or fully open fractures that might be propagating. Transitions between at‐rest and propagating fractures can also be simulated. This is accomplished by defining contact aperture as the aperture when asperities on a closing fracture first make contact. Locations on a fracture where the aperture is less than the contact aperture are loaded by both fluid pressure and effective stress, whereas locations where the aperture exceeds the contact aperture are loaded only by fluid pressure. Fluid pressure and effective stress on the fracture are determined as functions of time by solving equations of continuity in the fracture and matrix, and by matching the global displacements of the fracture walls to the local deformation of asperities. The resulting analysis is implemented in a numerical code that can simulate well tests or hydraulic fracturing operations. Aperture changes during hydraulic well tests can be measured in the field, and the results predicted using this analysis are similar to field observations. The hydraulic fracturing process can be simulated from the inflation of a pre‐existing crack, to the propagation of a fracture, and the closure of the fracture to rest on asperities or proppant. Two‐dimensional, multi‐phase fluid flow in the matrix is included to provide details that are obscured by simplifications of the leakoff process (Carter‐type assumptions) used in many hydraulic fracture models. Execution times are relatively short, so it is practical to implement this code with parameter estimation algorithms to facilitate interpretation of field data. Copyright © 2006 John Wiley & Sons, Ltd.     

剪胀对复杂裂隙岩体渗透性影响的离散元分析

裂隙岩体流固耦合问题是目前国内外研究热点之一,采用离散元软件UDEC对裂隙岩体发生节理剪胀的渗透性变化规律进行了模拟分析。基于现场调查的裂隙信息统计生成裂隙网络岩体模型。 通过固定垂直应力、不断增加应力比RS(RS=水平应力/垂直应力)使岩体出现剪胀,采用库伦滑移节理模式对岩体在剪胀过程中的渗透性变化情况进行模拟。结果发现:当应力比较小(RS3.1)时,节理水力隙宽、流速、渗透系数等参数都随着应力比的增加表现出明显的降低; 而当岩体出现剪胀现象之后(应力比大于3.1),发生剪切滑移和剪胀现象的节理控制着裂隙岩体的总体渗流行为,与不考虑节理剪胀的计算结果相比,岩体渗透能力出现了显著增长。这一结果表明,剪胀对裂隙岩体渗透性的影响是显著而不可忽视的。     

Cubic law with aperture-length correlation: implications for network scale fluid flow

Previous studies have computed and modeled fluid flow through fractured rock with the parallel plate approach where the volumetric flow per unit width normal to the direction of flow is proportional to the cubed aperture between the plates, referred to as the traditional cubic law. When combined with the square root relationship of displacement to length scaling of opening-mode fractures, total flow rates through natural opening-mode fractures are found to be proportional to apertures to the fifth power. This new relationship was explored by examining a suite of flow simulations through fracture networks using the discrete fracture network model (DFN). Flow was modeled through fracture networks with the same spatial distribution of fractures for both correlated and uncorrelated fracture length-to-aperture relationships. Results indicate that flow rates are significantly higher for correlated DFNs. Furthermore, the length-to-aperture relations lead to power-law distributions of network hydraulic conductivity which greatly influence equivalent permeability tensor values. These results confirm the importance of the correlated square root relationship of displacement to length scaling for total flow through natural opening-mode fractures and, hence, emphasize the role of these correlations for flow modeling.