Formulation of strain-dependent hydraulic conductivity for a fractured rock mass

By characterizing rock masses as anisotropic continua with one or multiple sets of critically oriented fractures, a methodology is developed in this paper to address the change in hydraulic conductivity resulted from engineering disturbance, material nonlinearity and anisotropy. An equivalent elastic–perfectly plastic constitutive model with non-associated flow rule and mobilized dilatancy is developed to describe the global nonlinear response of the rockmass under complex loading conditions. By separating the deformation of fractures from that of the equivalent medium, a strain-dependent hydraulic conductivity tensor is formulated. This not only considers the normal compressive deformation of the fractures, but also and more importantly, integrates the effect of material nonlinearity and post-peak shear dilatancy. Using this methodology, a closed-form solution is derived to describe the hydraulic behavior of a single fracture during combined normal and shear loading processes. The closed-form solution is validated by an existing coupled shear-flow test under wide ranges of normal and shear loads. Numerical simulations are performed to investigate the changes in hydraulic conductivities of a cubic block of fractured rock mass under triaxial compression and shear loading, as well as a circular underground excavation in a biaxial stress field at the Stripa mine, Sweden. The simulation results agree well with the in-situ experimental observations and an existing elastic strain-dependent analytical solution, respectively. The evaluation results clearly demonstrate that the proposed model is capable of predicting the changes in hydraulic properties of fractured rock masses under loading or excavation.     

矿山岩体破坏突水非达西流模型及数值求解

 为模拟突水流体瞬态流动全过程并揭示突水流体流动机制,针对矿山岩体破坏突水过程中流体的高速非达西流特征和流场动力学统一性特征,基于流体质量守恒和压力平衡原理建立耦合Darcy方程、Forchheimer方程和Navier-Stokes方程的矿山岩体破坏突水非达西流模型,将含水层水源、破碎岩体突水通道和采场巷道出口整个水流路径有机联系在统一流动场中;并基于有限元弱形式和有限体积法耦合积分方程,提出有限元和有限体积法相结合的数值计算方法,应用FEPG有限元软件编译FORTRAN源程序,模拟突水瞬态流动全过程。通过算例对比达西和非达西流结果表明,对于矿山岩体破坏突水问题采用非达西流模型计算十分必要,破碎岩体作为导水通道沟通含水层和巷道的水力联系,导水通道内高速水流的惯性作用是含水层充足的补给水量沿破碎带进入巷道形成突水的主要原因。     

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.     

A three-dimensional numerical model for thermohydromechanical deformation with hysteresis in a fractured rock mass

A three-dimensional finite-element solution to the problem of coupled thermohydromechanical deformation, groundwater flow, and heat transport in deformable fractured porous media is presented in this paper. The governing equations are based on Biot’s consolidation theory for poroelastic materials, extended to the non-isothermal environment. The normal and lateral deformations in joints are simulated by a new joint element. The new joint element is based on the Bandis–Barton models and is capable of simulating normal and lateral deformations with dilatancy, contractancy, and hysteresis due to irrecoverable damages/rubblization. A three-dimensional finite-element code Model Of Transport In Fractured porous media (MOTIF) has been developed based on the theoretical framework presented herein. Verification results with experimental data and analytical solutions are presented in this paper. An application example with flow of fluid through a non-isothermally deforming joint is also presented. Results indicate that non-isothermal deformation could play a major role in the transport of fluid and water-borne substances in fractured rocks.     

裂隙岩体温度场数值流形方法初步研究

基于三角形有限覆盖数值流形理论，提出了裂隙岩体二维不稳定温度场求解的数值流形方法(NMM)，并推导了第一类温度边界条件处理的罚方法，给出了计算格式。数值流形方法采用两套覆盖，其中数学覆盖独立于求解区域，生成数学覆盖时不用考虑裂隙数量、位置和方向，避免了常规方法处理裂隙处网格划分的不便。对于裂隙岩体，裂隙两侧对应不同流形单元，可以实现温度的不连续模拟。裂隙作为内部流形单元或外部边界条件叠加进入到温度场的总体求解矩阵中，实现了裂隙岩体温度场的数值流形求解。该方法具有较高精度，且能求解任意多条裂隙的岩体温度场问题。最后对部分文献算例进行计算，结果具有较好的一致性。     

裂隙岩体在单轴加载过程中变形、破裂规律的PFC2D数值模拟研究

运用离散元软件PFC2D模拟裂隙岩体,建立一个包含不同倾角、不同组数,宽度5cm、厚度1mm裂隙的10cm×10cm模型,分析单轴加载情况下岩体的变形、破裂规律。结果显示,在单轴加载情况下,随着倾角的增加,岩体的单轴抗压强度出现先减后增的趋势,且裂纹不断增多;随着裂隙的增多,单轴抗压强度逐渐减小。岩体的破裂区集中在裂隙的尖端点部位,以翼裂纹、次生共面裂纹和次生倾斜斜纹为主。通过分析破裂后岩体的颗粒速度分布,从微观层面发现岩体破坏的主要形式及破裂原因。     

Determination of hydraulic conductivity of fractured rock masses:A case study for a rock cavern project in Singapore

In order to reduce the risk associated with water seepage in an underground rock cavern project in Singapore,a reliable hydro-geological model should be established based on the in situ investigation data.The key challenging issue in the hydro-geological model building is how to integrate limited geological and hydro-geological data to determine the hydraulic conductivity of the fractured rock masses.Based on the data obtained from different stages(feasibility investigation stage,construction stage,and post-construction stage),suitable models and methods are proposed to determine the hydraulic conductivities at different locations and depths,which will be used at other locations in the future.     

深部隧洞裂隙围岩渗透特性及衬砌外水压力变化规律

高外水压岩是影响隧道开挖过岩围岩稳定及衬砌结构安全的关键因素之一,基于裂隙介质渗流经典理论,给出围岩、衬砌不同渗透系数下的外水压岩解析解,采用数值方法对隧洞二次衬砌后的外水压岩作用特性进行仿真模拟,探讨裂隙围岩岩衬砌渗透系数对渗流场的影响,围岩、衬砌渗透和排水措施岩外水压岩的相关性。研究表明岩体和衬砌渗透系数之比是影响衬砌外水压岩的关键,正确的灌浆、排水设计对外水压岩折减系数影响较大,是减小衬砌外水压岩的有效措施。结论对高压水作用下裂隙岩体渗流及衬砌外水压岩研究具有重要理论意义,对高水压下围岩注浆及衬砌结构材料选型、参数选择等具有重要岩岩实用价值。     

Continuous approach for coupled mechanical and hydraulic behavior of a fractured rock mass during hypothetical shaft sinking at Sellafield, UK

An indicator simulation technique was used to infer the continuous hydraulic conductivity distribution in the BVG for Task 1A of DECOVALEX II. Young's modulus from the wireline geophysical survey was used as soft data. To calibrate the model with measured data in Task 1B, a back analysis with Bayesian estimate was applied to determine the hydraulic conductivity of all the elements of the finite element mesh. To avoid the ill-posed problem, a geostatistically kriged hydraulic conductivity distribution was used as mean a priori information. While there are some remaining problems, the solution was improved in comparison with the ordinary analysis. For the shaft sinking problem defined as Task 1C, the continuous approach to coupled mechanical and hydraulic behavior was used by combining crack tensor theory and the Barton and Bandis model for rock joints. The mechanical and hydraulic properties were derived with resultant anisotropy and heterogeneity during the simulated shaft excavation. It is found that the calculated hydraulic conductivity becomes larger than measured one as a consequence of excavation.     

Multiscale hierarchical analysis of rock mass and prediction of its mechanical and hydraulic properties

Engineering geological and hydro-geological characteristics of foundation rock and surrounding rock mass are the main factors that affect the stability of underground engineering. This paper presents the concept of multiscale hierarchical digital rock mass models to describe the rock mass, including its structures in different scales and corresponding scale dependence. Four scales including regional scale, engineering scale, laboratory scale and microscale are determined, and the corresponding scale-dependent geological structures and their characterization methods are provided. Image analysis and processing method, geostatistics and Monte Carlo simulation technique are used to establish the multiscale hierarchical digital rock mass models, in which the main micro- and macro-structures of rock mass in different geological units and scales are reflected and connected. A computer code is developed for numerically analyzing the strength, fracture behavior and hydraulic conductivity of rock mass using the multiscale hierarchical digital models. Using the models and methods provided in this paper, the geological information of rock mass in different geological units and scales can be considered sufficiently, and the influence of downscale characteristics (such as meso-scale) on the upscale characteristics (such as engineering scale) can be calculated by considering the discrete geological structures in the downscale model as equivalent continuous media in the upscale model. Thus the mechanical and hydraulic properties of rock mass may be evaluated rationally and precisely. The multiscale hierarchical digital rock mass models and the corresponding methods proposed in this paper provide a unified and simple solution for determining the mechanical and hydraulic properties of rock mass in different scales.     

Coupled hydro-mechanical effect of a fractured rock mass under high water pressure

To explore the variation of permeability and deformation behaviors of a fractured rock mass in high water pressure,a high pressure permeability test(HPPT),including measuring sensors of pore water pressure and displacement of the rock mass,was designed according to the hydrogeological condition of Heimifeng pumped storage power station.With the assumption of radial water flow pattern in the rock mass during the HPPT,a theoretical formula was presented to estimate the coefficient of permeability of the rock mass using water pressures in injection and measuring boreholes.The variation in permeability of the rock mass with the injected water pressure was studied according to the suggested formula.By fitting the relationship between the coefficient of permeability and the injected water pressure,a mathematical expression was obtained and used in the numerical simulations.For a better understanding of the relationship between the pore water pressure and the displacement of the rock mass,a 3D numerical method based on a coupled hydro-mechanical theory was employed to simulate the response of the rock mass during the test.By comparison of the calculated and measured data of pore water pressure and displacement,the deformation behaviors of the rock mass were analyzed.It is shown that the variation of displacement in the fractured rock mass is caused by water flow passing through it under high water pressure,and the rock deformation during the test could be calculated by using the coupled hydro-mechanical model.     

Stochastic analysis of flow response in a three-dimensional fractured rock mass block

The pressure variations observed during an interference test performed in a fractured volcanic tuff are modeled using a stochastic continuum approach. Two sets of spatially heterogeneous conductivity fields are generated. The first one is only conditioned to hard and soft data on conductivities, whereas the second one is also conditioned to transient pressure information. Conditioning to the interference tests introduces an important modification in the conductivity fields, reducing the presumed contrast between the faulted blocks and those that represent the background fracturing. It was possible to reproduce most of the pressure responses simply using a heterogeneous distribution of conductivities without the need to resort to a hydro-mechanical process coupling.     

Quantifying fractured rock hydraulic heterogeneity and groundwater inflow prediction in underground excavations: the heterogeneity index

This paper presents an approach to quantify the degree of heterogeneity of a fracture network starting from the information that is collected for a geomechanical classification of rock masses. Six synthetic experiments have been used to prove the existence of a correspondence between the variability in fracture properties and in the direction and magnitude of flow. Statistical analyses conducted using fracture data collected at a tunnel crossing the north-western Italian Alps have also shown that variability in fracture characteristics is indeed related to the magnitude of inflows. These findings have proved that it is reasonable to estimate the degree of heterogeneity of a fracture network by combining the variance of those fracture characteristics that regulate both flow and the geomechanical behavior of a rock mass. An index comprising a combination of variances of fracture parameters at different scales is presented. Its dependence on scale showed that the heterogeneity of fractured rock increases with scale up to a certain scale and then gradually decreases at large scales.     

一种模拟节理岩体破坏的新方法:单元劈裂法

在有限单元法中,三结点三角单元在几何上具有独特的优点,即当一条裂纹贯穿单元(单元劈裂)时,总有一结点位于裂纹的一侧,而另外两个结点位于裂纹的另一侧。位于一侧的两个结点与位于另外一侧的一个结点可以潜在地构成两个接触点对,从而可以利用这两个接触点对来推导劈裂单元的刚度矩阵,以再现裂纹面之间的接触和摩擦效应。利用该三角单元的几何特点,提出了单元劈裂法,用于模拟节理或其它裂纹的扩展问题。由于劈裂单元刚度矩阵与原三角单元享有共同的结点,因而在模拟裂纹扩展过程中无需为设置节理单元而改变原网格划分方案,这为节理扩展的数值模拟提供了很大方便,提高了计算效率。在劈裂单元刚度矩阵推导过程中,没有考虑单元劈裂后所形成两个块体自身的弹塑性变形,所以该方法只是一种近似方法。对相应试验进行了数值模拟,结果表明该方法是有效的。     

深部裂隙岩体锚固机制研究进展与思考

 高地应力、高地温、高渗透压以及强时间效应使得深部裂隙岩体表现出一定的延性、蠕变性等软岩力学特性,现有锚固理论落后于工程实践的现状,导致许多锚固工程设计多采用经验、半经验方法。几十年来,国内外诸多学者对深部岩体锚固机制开展了大量现场、室内试验及数值计算工作,岩体锚杆锚固作用机制方面的理论研究取得了丰硕成果,但由于深部岩体所处地质条件的复杂性,这些成果普适性和准确性较低。结合已有的锚固理论,运用合理的数值模拟方法与现场、室内试验对岩土锚固机制进行深入研究,进而指导锚固工程设计施工具有重大意义。对深部裂隙岩体锚固机制研究现状进行了系统全面的总结,归纳分析了该研究领域存在的关键科学问题,主要包括：选择合理的锚固力学传递计算模型、正确描述锚固体应力分布规律、建立合理的锚固界面力学模型。深部裂隙岩体锚固机制研究应综合考虑工程应用效果和加锚岩体形态、加锚构件效应等因素。     

裂隙岩体渗流–断裂耦合机制及应用

将断裂力学引入裂隙岩体流固耦合分析,建立裂隙岩体渗流–断裂耦合机制,在 FLAC ^3D 现有计算模块的基础上,通过 FISH 研制了裂隙岩体渗流–断裂耦合分析程序。该模型的耦合机制体现在：渗透水力梯度作为渗透体积力作用于应力计算单元,裂隙渗透压作为面力作用于裂纹张开部分引起断续岩体裂纹的劈裂扩展;岩体裂纹的扩展引起岩体渗透系数的增加导致渗流场的改变。将渗流 – 断裂耦合理论应用于高水头不衬砌压力隧洞工程中,系统地研究高水头不衬砌压力隧洞在运行期间的水力劈裂、渗流场和内水外渗渗漏情况,得到：①处于水力劈裂的高水头压力隧洞周边向外延伸依次为拉剪劈裂区、压剪劈裂区、未劈裂区;②由于渗流体积力作用,高水头压力隧洞内水外渗过程中洞周产生径向向外变形;③高水头压力隧洞内水外渗过程中渗漏率先增加后平稳减少最终稳定。首次提出陡倾地表下不衬砌压力隧洞与裂纹几何特性、力学特性和岩石断裂韧度高度相关的水力劈裂系数的概念 。 建议在水工隧洞设计规范中建立与水力劈裂系数相匹配的安全控制标准,可为我国不衬砌压力隧洞工程的设计提供理论基础。     

Estimation of REV size and three-dimensional hydraulic conductivity tensor for a fractured rock mass through a single well packer test and discrete fracture fluid flow modeling

A new methodology is presented to determine the representative elementary volume (REV) size and three-dimensional (3-D) hydraulic conductivity tensor for a fractured rock mass. First, a 3-D stochastic fracture network model was built and validated for a gneissic rock mass based on the fracture data mapped from scanline surveys at the site. This validated fracture network model was combined with the fracture data observed on a borehole to generate a stochastic-deterministic fracture network system in a cubic block around each packer test conducted at a different depth region in the same borehole. Each packer test was simulated numerically applying a developed discrete fracture fluid flow model to estimate the influenced region or effective range for the packer test. A cubic block of size 18 m, with the packer test interval of length about 6.5 m located at the centre of this block, was found to be suitable to represent the influenced region. Using this block size, the average flow rate per unit hydraulic gradient (defined as the transmissivity multiplied by mean width of flow paths) field for fractures was calibrated at different depth regions around the borehole by numerically simulating the packer tests conducted at different depth regions. The average flow rate per unit hydraulic gradient of the fractures that intersect the borehole was considered to be quite different to the average flow rate per unit hydraulic gradient of the fractures that do not intersect the borehole. A relation was developed to quantify the ratio between these two parameters. By studying the directional hydraulic conductivity behaviour of different cubic block sizes having the validated stochastic fracture network and calibrated hydraulic parameters, a REV for the hydraulic behaviour of the rock mass was estimated to be a block size of 15 m. The hydraulic conductivity tensor in 3-D computed through regression analysis using the calculated directional hydraulic conductivity values in many directions was found to be significantly anisotropic. The principal directions of the hydraulic conductivity tensor were found to be agreeable with the existing fracture system of the site. Further, the geometric hydraulic conductivity calculated was found to be comparable to the hydraulic conductivity estimated through the radial flow assumption in continuum porous media.     

Characterization of fractured rock in the vicinity of tunnels by the swept impact seismic technique

The diversity of the applications of high-resolution seismics requires investigations in the range of hundreds of meters to be performed in very diverse conditions. We found the swept impact seismic technique (SIST) to be a viable solution for high-resolution surveys in hard rocks. Swept impact seismic technique combines the Vibroseis swept frequency and the Mini-Sosie multi-impact ideas. Several variations of the method have been studied leading to improved resolution and efficiency. The development was partly funded by the Finnish Center for Technical Development (TEKES) and partly by the French National Agency for the Management of Radioactive Waste—ANDRA. A test programme was carried out at the Grimsel test site, operated by NAGRA—the Swiss National Cooperative for the Disposal of Radioactive Waste. Measurements were also carried out with single-pulse sources, but data of acceptable quality could not be obtained. Surface and tunnel-wall, as well as borehole SIST sources have been developed and tested. The ability of the seismic techniques to detect and characterize rock discontinuities was proven by investigating a rock block delimited by two parallel boreholes and a tunnel perpendicular to them, involving source–detector distances of 100–200 m. The characterization included the determination of the 3-D positions and orientations of rock features and the tomographic mapping of seismic velocities.     

The behavior of mass migration and loss in fractured rock during seepage

Bulletin of Engineering Geology and the Environment - Mass migration and loss in fractured rock during seepage processes are considered to cause seepage instabilities, which can lead to seepage...