Assessment of an equivalent porous medium for coupled stress and fluid flow in fractured rock

The equivalent porous medium (EPM) for coupled stress and fluid flow in fractured rock was assessed. The assessment was focused on the contributions of the seepage-induced force to the system's equilibrium and deformation as well as fluid flux through the fractures, with the special emphasis on the inter-relations among these three aspects. Seepage-induced average stress was calculated for the EPM. And it was proved, with respect to the fluid flow system (FFS) proposed by Long et al. [Long JCS, Remer JC, Wilson CR, Witherspoon PA. Porous medium equivalents for networks of discontinuous fractures. Water Resour Res 1982;18:645–658], that the equivalence of the equilibrium contribution of the seepage-induced force is unconditionally satisfied in the EPM. The equivalence of fluid flux and seepage-induced deformation was evaluated using numerical techniques based on the FFS, in which the seepage-induced deformation was considered as ‘tensile’ deformation under fluid pressures. The numerical simulation results of the two cases suggest that the EPM established in terms of fluid flux based on the FFS guarantees equivalence of coupled stress and fluid flow. Also, the numerical simulation results indicate that the percolation theory can not be applied to a system with fractures of remarkably different size and hydraulic conductivity.     

Stress-dependent shear wave splitting and permeability in fractured porous rock

It is well known that shear wave propagates slower across than parallel to a fracture, and as a result, a travelling shear wave splits into two directions when it encounters a fracture. Shear wave splitting and permeability of porous rock core samples having single fracture were experimentally investigated using a high-pressure triaxial cell, which can measure seismic shear wave velocities in two directions mutually perpendicular to the sample axis in addition to the longitudinal compressive wave velocity. A single fracture was created in the samples using a modified Brazilian split test device, where the cylindrical sample edges were loaded on two diametrically opposite lines by sharp guillotines along the sample length. Based on tilt tests and fracture surface profilometry, the method of artificially induced tensile fracture in the sample was found to create repeatable fracture surfaces and morphologies. Seismic velocities of the fractured samples were determined under different levels of stress confinement and fracture shear displacement or mismatch. The effective confining stress was varied from 0.5 MPa to 55 MPa, while the fractures were mismatched by 0 mm, 0.45 mm and 1 mm. The degree of matching of the fracture surfaces in the core samples was evaluated using the joint matching coefficient (JMC). Shear wave splitting, as measured by the difference in the magnitudes of shear wave velocities parallel (V_S1) and perpendicular (V_S2) to the fracture, is found to be insensitive to the degree of mismatching of the fracture joint surfaces at 2 MPa, and decreased and approached zero as the effective stress was increased. Simple models for the stress- and JMC-dependent shear wave splitting and fractured rock permeability were developed based on the experimental observations. The effects of the joint wall compressive strength (JCS), JMC and stress on the stress dependency of joint aperture were discussed in terms of hydro-mechanical response. Finally, a useful relationship between fractured rock permeability and shear wave splitting was found after normalization by using JMC.     

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.     

土体应力应变关系的影响因素分析

土体与岩体作为岩土工程研究的重点对象广泛受到关注,地球表面的岩体经过不断的风化形成土体。土体作为一种三相介质,其应力应变关系非常的复杂,它的关系受到很多因素的影响。为了保障工程的顺利实施,土体的应力应变关系的研究一直备受重视。在总结分析现有研究的基础上,对影响土体本构关系的因素进行了归纳总结,其结果表明土体的结构性、应力条件是影响土体应力应变关系的主要因素。     

Numerical determination of the equivalent elastic compliance tensor for fractured rock masses using the distinct element method

The purpose of this paper is to establish a methodology to determine the equivalent elastic properties of fractured rock masses by explicit representations of stochastic fracture systems, and to investigate the conditions for the application of the equivalent continuum approach for representing mechanical behavior of the fractured rock masses. A series of numerical simulations of mechanical deformation of fractured rock masses at different scales were conducted with a large number of realizations of discrete fracture networks (DFN), based on realistic fracture system information and using the two-dimensional distinct element program, UDEC. General theory of anisotropic elasticity was used for describing the macroscopic mechanical behavior of fractured rock masses as equivalent elastic continua. Verification of the methodology for determining the elastic compliance tensor was conducted against closed-form solutions for regularly fractured rock mass, leading to very good agreements. The main advantage of the developed methodology using the distinct element method is that it can consider complex fracture system geometry and various constitutive relations of fractures and rock matrix, and their interactions. Two criteria for the applicability of equivalent continuum approach were adopted from the investigations: (i) the existence of a properly defined REV (representative elementary volume) and (ii) the existence of an elastic compliance tensor. For the problems with in situ conditions studied in this paper, the results show that a REV can be defined and the elastic properties of the fractured rock mass can be represented approximately by the elastic compliance tensor through numerical simulations.     

考虑松动圈影响的引水隧洞应力及位移弹性分析

采用弹性力学理论,推导出圆形隧洞衬砌和围岩松动圈的应力及位移解析解,并以新疆某引水隧洞工程为背景,分析了平面应变、弹性情况下,衬砌及松动圈支护体内应力之差与位移分布规律,最终得出了一些有价值的结论。     

基于浆液–岩体耦合效应的微裂隙岩体注浆理论研究

在微裂隙岩体注浆工程中,浆液–岩体耦合效应对注浆扩散过程影响显著。基于宾汉流体浆液本构模型并引入两阶段裂隙变形控制方程,建立考虑浆–岩耦合效应的裂隙注浆扩散理论模型。利用质量守恒条件实现浆液扩散锋面追踪与注浆流量分配,通过试错法实现压力场与速度场的迭代求解,建立可完整描述注浆扩散过程的步进式算法。利用所创建的理论模型及步进式算法,分析浆液压力场及裂隙开度的分布规律,并从浆液扩散半径、裂隙变形所吸收的浆液量两个方面分析不同裂隙开度条件下浆–岩耦合效应对裂隙注浆扩散过程的影响程度。研究结果表明:在微裂隙岩体注浆工程中,裂隙宽度越小,浆–岩耦合效应对注浆扩散过程的影响越显著,注浆压力取代裂隙初始隙宽成为影响浆液扩散半径的主控因素。最后结合青岛地铁花岗岩微裂隙注浆工程实例验证了理论模型及步进式算法的正确性。     

含排水孔裂隙岩体渗流与法向应力耦合的复合单元算法

提出了含排水孔裂隙岩体的渗流与法向应力耦合的复合单元算法。基于“空气单元”和“充填模型”,提出的复合单元耦合模型视排水孔和裂隙为虚拟的具有高空隙率的“充填介质”,采用复合单元前处理程序,排水孔和裂隙依据其具体位置和方位可自动离散模拟在复合单元内部,计算网格生成时无需考虑排水孔和裂隙的存在,网格划分不受限制。基于复合单元法,采用两场交叉迭代算法,建立了含排水孔裂隙岩体的渗流与法向应力耦合算法。此耦合算法不仅考虑了排水孔和裂隙中的渗流,而且考虑了排水孔和裂隙与相邻岩块之间的流量交换。通过复合单元和传统有限元两种数值模型进行简单算例分析,可知两种算法结果基本一致,进一步验证了提出的含排水孔裂隙岩体的渗流与法向应力耦合算法的有效性,同时可看出复合单元耦合模型的前处理简便快捷。     

The relationship between porosity and strength for porous concrete

As for many porous media, the strength of porous concrete is significantly affected by the porosity of its internal structure. This paper describes the development of a mathematical model to characterize the relationship between compressive strength and porosity for porous concrete by analyzing empirical results and theoretical derivations. The suitability of existing equations for porous concrete is assessed and a new model is then proposed. The new model, which was derived from Griffith’s theory, presents a better agreement with the experimental data for porous concrete. It is demonstrated that the proposed model could provide a better prediction of porous concrete compressive strength based on the material porosity.     

Effects of fracture distribution and length scale on the equivalent continuum elastic compliance of fractured rock masses

fracture systems have strong influence on the overall mechanical behavior of fractured rock masses due to their relatively lower stiffness and shear strength than those of the rock matrix.Understanding the effects of fracture geometrical distribution,such as length,spacing,persistence and orientation,is important for quantifying the mechanical behavior of fractured rock masses.The relation between fracture geometry and the mechanical characteristics of the fractured rock mass is complicated due to the fact that the fracture geometry and mechanical behaviors of fractured rock mass are strongly dependent on the length scale.In this paper,a comprehensive study was conducted to determine the effects of fracture distribution on the equivalent continuum elastic compliance of fractured rock masses over a wide range of fracture lengths.To account for the stochastic nature of fracture distributions,three different simulation techniques involving Oda's elastic compliance tensor,Monte Carlo simulation(MCS),and suitable probability density functions(PDFs) were employed to represent the elastic compliance of fractured rock masses.To yield geologically realistic results,parameters for defining fracture distributions were obtained from different geological fields.The influence of the key fracture parameters and their relations to the overall elastic behavior of the fractured rock mass were studied and discussed.A detailed study was also carried out to investigate the validity of the use of a representative element volume(REV) in the equivalent continuum representation of fractured rock masses.A criterion was also proposed to determine the appropriate REV given the fracture distribution of the rock mass.     

Correlations between jointing and seismic velocities in highly fractured rock masses

The paper presents the results of a study of heavily fractured calcareous rock masses outcropping in southern Italy based on both the unidimensional joint frequency (Nl) and rock quality designation (RQD) of rock cores and seismic velocity data from laboratory and down-hole tests. The in situ longitudinal wave velocities (v) were always very low and were correlated with both Nl and RQD. Between 1 and 2 km/s, small increases in velocity were associated with a considerable decrease in Nl and significant increase in RQD value. A velocity of 1.22 km/s corresponded to an RQD value of 0. The study indicated that the simple correlation proposed by the International Society for Rock Mechanics to evaluate the RQD from the unidimensional joint frequency can underestimate the results for heavily fractured rock masses, but that good correlations can be obtained between RQD and seismic velocity. Electronic Publication     

A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock

This paper presents the methodology in which two computer codes—TOUGH2 and FLAC3D—are linked and jointly executed for coupled thermal–hydrologic–mechanical (THM) analysis of multiphase fluid flow, heat transfer, and deformation in fractured and porous rock. TOUGH2 is a well-established code for geohydrological analysis with multiphase, multicomponent fluid flow and heat transport, while FLAC3D is a widely used commercial code that is designed for rock and soil mechanics with thermomechanical and hydromechanical interactions. In this study, the codes are sequentially executed and linked through external coupling modules: one that dictates changes in effective stress as a function of multi-phase pore pressure and thermal expansion, and one that corrects porosity, permeability, and capillary pressure for changes in stress. The capability of a linked TOUGH-FLAC simulator is demonstrated on two complex coupled problems related to injection and storage of carbon dioxide in aquifers and to disposal of nuclear waste in unsaturated fractured porous media.     

裂隙岩体透水率与其完整性指数及BQ值的关系初探

岩体的渗透系数是评价岩体渗透性,进行裂隙岩体渗流模拟的必备参数,在工程实际应用中亦具有重大意义。研究发现:岩体的完整性系数和基本质量指标(BQ值)的算术平均值与裂隙岩体透水率的几何平均值相关性较好,故利用岩体的完整性系数和基本质量指标(BQ值)的算术平均值估算裂隙岩体的渗透系数是可行的。根据金堆城杨家湾尾矿库初期坝的岩体压水试验结果,初步探索了岩体的基本质量指标及岩体完整性指数与其透水率的关系。     

Review of permeability evolution model for fractured porous media

The ability to capture permeability of fractured porous media plays a significant role in several engineering applications, including reservoir, mining, petroleum and geotechnical engineering. In order to solve fluid flow and coupled flow-deformation problems encountered in these engineering applications,both empirical and theoretical models had been proposed in the past few decades. Some of them are simple but still work in certain circumstances; others are complex but also need some modifications to be applicable. Thus, the understanding of state-of-the-art permeability evolution model would help researchers and engineers solve engineering problems through an appropriate approach. This paper summarizes permeability evolution models proposed by earlier and recent researchers with emphasis on their characteristics and limitations.     

裂隙岩体渗流场与应力场耦合研究进展与展望

在分析岩体多介质渗透特性的基础上，提出了岩体多介质渗透类型，综述了裂隙岩体渗流场与应力场耦合模型的研究进展，并提出耦合模型进一步研究的方向。     

Stress and water flow relation in fractured rock

Bulletin of Engineering Geology and the Environment - A field test was performed to investigate the relation between rock stresses and the hydraulic properties of a fractured rock mass. In thisin...     

多孔混凝土孔隙的表征及其与渗透性的关系研究

分别研究了单掺粉煤灰、矿渣和硅灰3种矿物掺合料的多孔混凝土有效孔隙率与目标孔隙率之间的关系,并探讨了掺有矿物掺合料时多孔混凝土有效孔隙率、透水系数、平面孔隙率、等效孔径和抗压强度之间的关系以及等效孔径大小的分布情况.试验结果表明:采用绝对体积法能有效控制多孔混凝土的孔隙率,不同掺合料的多孔混凝土有效孔隙率与透水系数之间存在相关性良好的二次甬数关系,与抗压强度基本成反比例关系,并据此得出对应关系式.等效孔径的大小和孔隙的个数影响着平面孔隙率变化.分别单掺粉煤灰、矿渣和硅灰且有效孔隙率在20%～30%的多孔混凝土,其等效孔径大小在10～20 mm之间,其中主要范围集中在13～16 mm.在此范围内,多孔混凝土的透水系数增幅最大.