A technique for estimating permeability of a randomly fractured rock mass

Extensive field and laboratory testing programs were performed to develop a relationship between the permeability of a fractured limestone and the core recovery values. The studied limestone does not encompass any jointing system but is consistently and randomly fractured. Nineteen in situ falling head permeability tests were carried out to measure permeability of the fractured rock mass at a representative study area. Analysis of test results has led to the formulation of an empirical equation that estimates the permeability of the rock mass in terms of its solid core recovery value and the permeability of the fractures filling material. Unlike the existing equations for estimating the permeability of rock masses, the proposed equation is simple and utilizes parameters that can be easily determined in regular geotechnical field and laboratory investigations. A technique is also presented to estimate the permeability of a rock layer, the quality of which significantly changes with depth, using the proposed equation that utilizes a single value of core recovery. Analysis of well-documented pumping test results supported the validity of the proposed equation and technique.     

Flow–stress coupled permeability tensor for fractured rock masses

In this paper a new analytical model is proposed to determine the permeability tensor for fractured rock masses based on the superposition principle of liquid dissipation energy. This model relies on the geometrical characteristics of rock fractures and the corresponding fracture network, and demonstrates the coupling effect between fluid flow and stress/deformation. This model empirically considers the effect of pre‐peak shear dilation and shear contraction on the hydraulic behavior of rock fractures and can be used to determine the applicability of the continuum approach to hydro‐mechanical coupling analysis. Results of numerical analysis presented in this paper show that the new model can effectively describe the permeability of fractured rock masses, and can be applied to the coupling analysis of seepage and stress fields. Copyright © 2008 John Wiley & Sons, Ltd.     

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。     

Modelling three-dimensional stress-dependent failure of hard rocks

Acta Geotechnica - Hard rocks exhibit three-dimensional (3D) stress-dependent failure under true triaxial compression. The deformability and strength of hard rocks under true triaxial compression...     

Upscaling permeability for three-dimensional fractured porous rocks with the multiple boundary method

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.     

FDEM-TH3D: A three-dimensional coupled hydrothermal model for fractured rock

This paper proposes a three-dimensional coupled hydrothermal model for fractured rock based on the finite-discrete element method to simulate fluid flow and heat transport. The 3D coupled hydrothermal model is composed of three main parts: a heat conduction model for the rock matrix, a heat transfer model for the fluid in the fractures (including heat conduction and heat convection), and a heat exchange model between the rock matrix and the fluid in the fractures. Four examples with analytical solutions are provided to verify the model. A heat exchange experiment of circulating water in a cylindrical granite sample with one fracture is simulated. The simulation results agree well with the experimental results. The effects of the fracture aperture, fluid viscosity, and pressure difference on the heat exchange between the fluid and rock are studied. Finally, an application concerned with heat transport and fluid flow in fractured rock is presented. The simulation results indicate that the 3D fully coupled hydrothermal model can capture the fluid flow and temperature evolution of rocks and fluids.     

裂隙岩体三维柔度张量的数值试验方法

在裂隙岩体二维柔度张量数值试验的基础上,建立了裂隙岩体三维柔度张量及其表征单元体积（REV）尺度研究的简化数值试验方法。首先根据岩体裂隙的统计参数及分布规律,运用蒙特卡罗方法在研究域内获得与实际岩体裂隙同分布的三维随机裂隙网络,提取位于不同方位的岩体试件,运用二维柔度张量的数值试验方法求出各个平面方向上的二维柔度张量,然后根据二维与三维柔度张量的拓扑关系,用数学方法求解裂隙岩体的三维柔度张量。对于含3组正交全贯通裂隙的岩体,通过数值试验获得的柔度张量与理论解相比,其主对角线上各参数的误差在5%以内,表明该数值试验方法较为可靠。最后将此方法运用到小湾水电站工程中,确定左岸坝区裂隙岩体的应力REV为11 m×11 m×11 m,并获得该区域裂隙岩体的三维柔度张量。     

一种基于地质指标的裂隙岩体渗透系数估算模型

裂隙岩体的渗透特性受控于裂隙的发育特征、连通特性和充填情况,并与岩体的地应力水平具有显著的相关性。基于裂隙岩体渗透性的影响因素,并考虑现有渗透系数估算模型的不足,利用钻孔压水试验和钻孔电视图像资料,建立考虑埋深(Z)、岩石质量指标(RQD)以及充填物指标(FSD)等3个指标的渗透系数估算ZRF模型,并应用到牙根二级水电站及其他工程区的渗透系数估算中。结果表明,与已有的渗透系数估算模型相比,ZRF模型较好地反映了岩体渗透性的影响因素,且模型参数物理意义明确,便于获取,对分析裂隙岩体渗透性具有一定的工程参考价值。     

蒲石河抽水蓄能电站上水库裂隙岩体渗透张量的确定

本文提出了一种既能反映裂隙岩体的渗透特性,又相对准确的确定裂隙岩体渗透张量的方法。首先通过裂隙在空间展布状况的测量,用统计学方法初步确定裂隙岩体的渗透张量,获得渗透主值及主方向,然后根据野外压水试验得到的岩体透水率,利用巴布什金公式计算各试段岩体的渗透系数,求出修正系数,从而得到研究区裂隙岩体的修正渗透张量。并运用上述方法对蒲石河抽水蓄能电站上水库坝址区裂隙岩体的渗透张量进行了计算。结果表明,该方法能较好地刻画裂隙岩体渗透性的各向异性特征,可为岩体渗透性分区及防渗帷幕的优化提供科学依据。     

裂隙岩体高压压水试验水-岩耦合过程数值模拟

为了解高压水渗流作用对裂隙岩体应力和变形的影响,结合黑麋峰抽水蓄能电站岩体高压压水试验的渗压及变形测试成果,采用多孔连续介质全耦合理论,研究了试验区岩体测点在压水孔加压和卸压过程中的孔隙压力和位移变化过程。通过对测点位移和渗压随时间变化过程的计算值和实测值对比研究,验证了所采用的水-岩耦合数值模型的合理性。研究表明：在压水孔内的水压力和岩体孔隙压力的共同作用下,岩体内的应力大幅度增加;压水过程中,岩体因渗流作用产生了较大的位移,停止压水后的一段时间内,由于岩体中还存在一定的孔隙水压力和水压力梯度,从而导致岩体内仍存在部分变形值,且该部分变形值并非是压水孔卸载后岩体内的塑性残余变形;高压水渗流作用下的岩体耦合效应对工程应力和围岩变形有重大影响,考虑水-岩耦合效应的岩体稳定性评价结果对工程设计更具指导意义     

Numerical estimation of REV and permeability tensor for fractured rock masses by composite element method

The Monte Carlo method is used to generate parent stochastic discrete fracture network, from which a series of fractured rock samples of different sizes and orientations are extracted. The fracture network combined with a regular grid forms composite element mesh of the fractured rock sample, in which each composite element is composed of sub‐elements incised by fracture segments. The composite element method (CEM) for the seepage is implemented to obtain the nodal hydraulic potential as well as the seepage flow rates through the fractured rock samples. The application of CEM enables a large quantity of stochastic tests for the fractured rock samples because the pre‐process is facilitated greatly. By changing the sizes and orientations of the samples, the analysis of the seepage characteristics is realized to evaluate the variation of the permeability components, the existence of the permeability tensor and the representative element volume. The feasibility and effectiveness are illustrated in a numerical example. Copyright © 2008 John Wiley & Sons, Ltd.     

Modeling of subsidence and stress-dependent hydraulic conductivity for intact and fractured porous media

Summary This study investigates the changes in deformation and stress dependent hydraulic conductivities that occur as a result of underground mining in intact and fractured porous media. The intact porous medium is assumed to be comprised of regularly packed spherical grains of uniform size. The variation in grain size or pore space due to the effect of changing intergranular stresses results in a change in rock hydraulic conductivity. A model is developed to describe the sensitivity of hydraulic conductivity to effective stresses through Hertzian contact of spherical grains. The fractured porous medium is approximated as an equivalent fracture network in which a single fracture is idealized as a planar opening having a constant equivalent thickness or aperture. Changes in fracture aperture as a result of changes in elastic deformation control the variation of hydraulic conductivity. A model is presented to illustrate the coupling between strain and hydraulic conductivity. Subsidence induced deformations that result from mining induced changes in hydraulic conductivity in both intact and fractured media. These changes are examined and compared with results from a mining case study.     

Elastic moduli for fractured rock mass

Summary The presence of joint discontinuities has long been recognized as an important factor influencing the mechanical behavior of rock masses. This paper proposes a stress-strain model for an assemblage of intact rock blocks separated by joint planes. The stress-strain relationship accounts for spacings and orientations of the joint sets. Closed-form expressions of elastic moduli for a rock mass with three intersecting sets of joints are derived explicitly in terms of properties of joints and intact rock. Applicability of the derived expressions are evaluated by comparing the predicted results with experimental results from physical model tests.     

辐射流条件下裂隙岩体渗透性表征单元体尺寸与等效渗透系数

一般情况下,随着尺寸的增大,裂隙岩体的性质参数也会发生变化,当尺寸增大到某一临界状态时,该参数会保持不变,这一临界尺寸称为裂隙岩体表征单元体(REV)。依托国家某地下水封石洞油库项目,基于辐射流的REV尺寸确定方法,研究了该库址区的渗透性REV尺寸及渗透系数,得到了该库址区辐射流情况的REV尺寸为37.5 m,是迹长的1.3倍;研究了迹长、间距、岩桥长度对REV尺寸及渗透系数的影响,得到了迹长、间距对REV尺寸和渗透系数有一定的影响,而岩桥长度对REV尺寸的影响不明显;对比分析了平行流和辐射流情况下REV尺寸与渗透系数的异同,得到了采用辐射流得到的REV尺寸和渗透系数更加符合实际,并且计算较为方便。     

A comparative simulation study of coupled THM processes and their effect on fractured rock permeability around nuclear waste repositories

This paper presents an international, multiple-code, simulation study of coupled thermal, hydrological, and mechanical (THM) processes and their effect on permeability and fluid flow in fractured rock around heated underground nuclear waste emplacement drifts. Simulations were conducted considering two types of repository settings (1) open emplacement drifts in relatively shallow unsaturated volcanic rock, and (2) backfilled emplacement drifts in deeper saturated crystalline rock. The results showed that for the two assumed repository settings, the dominant mechanism of changes in rock permeability was thermal–mechanically induced closure (reduced aperture) of vertical fractures, caused by thermal stress resulting from repository-wide heating of the rock mass. The magnitude of thermal–mechanically induced changes in permeability was more substantial in the case of an emplacement drift located in a relatively shallow, low-stress environment where the rock is more compliant, allowing more substantial fracture closure during thermal stressing. However, in both of the assumed repository settings in this study, the thermal–mechanically induced changes in permeability caused relatively small changes in the flow field, with most changes occurring in the vicinity of the emplacement drifts.     

Retention properties of flow paths in fractured rock

There is no straightforward way to extrapolate solute retention properties from typical site characterisation scales to typical scales in the performance assessment of the geological disposal of nuclear wastes. Solutes diffuse much deeper into the rock matrix under performance assessment flow conditions than under site characterisation flow conditions. The modelling approach applied in this study, associated with the Äspö Task Force, enables evaluation of the contribution of the individual immobile layers to the overall retention. This makes it possible to determine the influence of the immobile zone heterogeneity on solute retention under different flow conditions. It appears that there is a significant difference between the dominating immobile retention zones on site characterisation and performance assessment scales. Fractured rock is characterised by heterogeneity and in particular a large spread of hydraulic properties. This favours formation of the preferential flow paths by leading to a few dominating transport paths. Large hydraulic features are, on average, better hydraulic conductors than smaller ones. This causes spatial scale effects for the solute retention properties. In particular, the hydraulic properties at the early parts of flow paths are more favourable to retention than those at the later parts of the flow paths.     

Risk analysis of fractured rock mass underground structures

Recent accidents in underground structures have raised the risk awareness of the geotechnical engineering community. Geotechnical design is subject to significant uncertainties in load and strength parameters as well as in engineering models. However, engineering models which objectively address such uncertainties in design are still scarce. This paper presents an objective framework for the quantification of the risks involved in underground structures excavated in fractured rock masses, where structural failures may occur due to block falls. The framework considers the structure as a distributed system, where falling block probabilities are integrated over the main structural dimension. Random block size and geometry, arising from random joint orientation, are taken into account, as well as uncertainties in joint strength and geometrical parameters. A cost function is used to quantify failure consequences in terms of the block size. The framework is demonstrated in an application to a case study involving a real structure: the Paulo Afonso IV power station cavern. Results of the case study show that the studied cavern presents high reliability and very low risk. The framework proposed herein is shown to be a practical tool for the risk evaluation of underground structures constructed in rock masses, such as caverns and tunnels.