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。     

Spatial statistics for predicting fluid flow through a single rock fracture

Steady-state laminar flow through single rock fractures is predicted in terms of spatial statistics computed from the arrangement of voids and contact areas within the fracture. Within the voids, aperture is assumed to be constant. One statistic measures how often pixels alternate from void to contact area in the rows parallel to the flow direction. Two others measure the dispersion of voids in the rows and columns of the pattern. Fractures with complexity typical of observed data are simulated. Flow through patterns with 80% voids is predicted in terms of a linear combination of the three statistics. Using an extended model involving one of the three statistics, flow through patterns with other void fractions is predicted.The author did this work at the Earth Sciences Division at Lawrence Berkeley Laboratory, Berkeley, California. It is part of a Ph.D. thesis which was submitted at Stanford University.     

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.     

爆炸气体驱动下岩体破裂的有限元-离散元模拟

在原有有限元/离散元（FEM/DEM）耦合分析方法中,实现了一种新的爆破计算模型。该模型考虑了在爆生气体的作用下,随着裂隙的扩展,气体占据的体积不断增大,气体压力逐渐减小这一问题。同时考虑了气体嵌入与爆腔联通的裂隙对裂隙的作用力。克服了原有FEM/DEM方法中的爆破模型仅仅将压力施加于爆腔四周的岩壁上,无法考虑爆生气体嵌入生成的裂隙对裂隙的作用。提出了一种新颖的贯通裂隙网络形成的递归搜索算法,只需通过编写一个简单的递归函数,即可实现复杂裂隙网络的搜索,采用一种简洁的方法完成了对复杂问题的处理。最后通过一个爆破算例,结果表明FEM/DEM方法可以对爆炸过程中应力波的传播及岩体中裂纹的萌生、扩展进行全程捕捉,展现了该方法用于爆破模拟的潜力。     

A pore-scale numerical model for non-Darcy fluid flow through rough-walled fractures

This paper aims at developing a pore-scale numerical model for non-Darcy fluid flow through rough-walled fractures. A simple general relationship between the local hydraulic conductivity and the flow velocity is proposed. A new governing equation for non-Darcy fluid flow through rough-walled fractures is then derived by introducing this relationship into the Reynolds equation. Based on the non-linear finite element method, a self-developed code is used to simulate the non-Darcy fluid flow through fractures. It is found that the macroscopic results obtained by the numerical simulation agree well with the experimental results. Furthermore, some interesting experimental observations can be reproduced.     

Analysis of fracture network connectivity using percolation theory

Connectivity aspects of fracture networks are analyzed in terms of percolation theory. These aspects are of fundamental importance in characterization, exploitation, and management of fractured formations. General connectivity and power law relationships are determined that characterize the density of fractures and average number of intersections per fracture necessary to ensure network connectivity, the likelihood of a fractured formation being hydraulically connected, and the probability that any specific fracture is connected to the conducting portion of the network. Monte Carlo experiments with a two-dimensional fracture network model confirm the percolation theory predictions. These relationships may prove useful in formulating theoretically tractable approximations of fracture nerworks that capture the essential system properties.     

Electromagnetic emissions during dilating fracture of a rock

A lot of experiments on electromagnetic emissions (EMEs) have been reported under axial compressive fracture, shear fracture, indentation fracture and stick–slip (friction) in lab and blasting in situ, but there are rare reports on the in-lab experimental work on EMEs during dilating fracture of a rock which is helpful in studying and understanding EMEs related to slow earthquakes and the earthquakes due to volcanic activities and water level changes of reservoirs. Therefore, in the present paper in order to check whether there are detectable EMEs during dilating fracture of a rock in lab, dilating fracture experiments were conducted. The dry cuboid specimens of initially intact granodiorite and limestone were tested inside magnetic field free space (MFFS) at room temperature. We arranged evenly 20 EME antennas whose resonance frequencies range from 2.5 kHz to 540 kHz close to rock specimens. Our experimental results strongly indicate that detectable EMEs could generate during dilating fracture of a rock. They were recorded only associated with some but not all phases of fracture. Their waveforms often took on the trend that a peak arrived at first and then attenuated sharply and followed by a series of low-amplitude oscillations. The electromagnetic (EM) signals after eliminating the effects of EME antennae via deconvolution had the maximum peak-to-peak amplitudes of about 80.0 mV and 40.5 mV for granodiorite and limestone, respectively. Their main spectral components often concentrated in the band of several kHz to ∼60 kHz and of several kHz to ∼280 kHz. The emission of electrons and charged particles from fracture surfaces and/or micro-fracture electrification could be possible mechanisms for our experimental results.     

Size effect on the hydraulic behavior of fluid flow through rough-walled fractures: a case of radial flow

Hydrogeology Journal - This study provides a numerical approach to investigate radial flow through a single rough-walled fracture. To facilitate the size-dependency investigation, rough-walled...     

Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock

The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution.     

Experimental study of fracture processes in rock

Summary The Fracture process zone in compact tension specimens of Indiana limestone was investigated to study its effect on the fracture mechanics parameters in such materials. Specimens were tested up to the peak load, and propagation of the crack from a preexisting notch was monitored. Experiments were designed to study the two features of the fracture process zone in rocks: ligament connections and microcracking.To observe this zone with high sensitivity and accuracy, laser interferometry methods were adopted. Holographic Interferometry was used to observe initial crack propagation. To obtain more quantitative measurements of the displacement field, in realtime, the recently developed technique of electronic speckle pattern interferometry was applied. This technique can provide continuous video recording of the interferometric fringe pattern, depict the evolution of the fracture process, and measure profiles of crack opening displacements.The macroscopic observations of full-field displacement by the laser techniques were supplemented by post mortem observation of the fracture region under a scanning electron microscope. Regions around the crack were studied after the test for possible presence of microcracks.An interactive finite element code was used to compute the stress intensity factors of the propagating crack-tip and displacements. Finite element computations were used to evaluate the effect of the process zone on crack propagation.     

基于逾渗模型的盐岩损伤与破坏研究

逾渗是一种分形模型,利用声发射点定位盐岩内部破坏网格来建立逾渗模型,可以分析三轴压缩条件下盐岩逾渗特征以及损伤演变发展。研究发现,各试样逾渗模型团簇(cluster)数与最大团簇占有率关系曲线斜率在70%应力峰值后基本相等,利用最大团簇沿试样轴向的延伸来描述裂缝的扩展规律,并通过最大团簇在轴向的延伸终点得到了各试样逾渗的临界破坏比率,它对于研究渗透陡增点非常重要。提出利用逾渗关联长度(关联长度?代表处于同一团簇中的两个点的平均距离)确定试样损伤起始点,并通过计算逾渗模型破坏比率得到损伤变量,它和基于AE振铃计数以及AE能量计算得到的损伤变量结果相近。研究结果表明,逾渗可以形象地表述岩石内部破裂过程和损伤情况,为研究岩石破坏失效及裂缝衍生发展提供了新的思路。     

Compaction-driven fluid flow in viscoelastic rock

Abstract

Compaction driven fluid flow is inherently unstable such that an obstruction to upward fluid flow (i.e. a shock) may induce fluid-filled waves of porosity, propagated by dilational deformation due to an effective pressure gradient within the wave. Viscous porosity waves have attracted attention as a mechanism for melt transport, but are also a mechanism for both the transport and trapping of fluids released by diagenetic and metamorphic reactions. We introduce a mathematical formulation applicable to compaction driven flow for the entire range of rheological behaviors realized in the lithosphere. We then examine three first-order factors that influence the character of fluid flow: (1) thermally activated creep, (2) dependence of bulk viscosity on porosity, and (3) fluid flow in the limit of zero initial connected porosity. For normal geothermal gradients, thermally activated creep stabilizes horizontal waves, a geometry that was thought to be unstable on the basis of constant viscosity models. Implications of this stabilization are that: (1) the vertical length scale for compaction driven flow is generally constrained by the activation energy for viscous deformation rather than the viscous compaction length, and (2) lateral fluid flow in viscous regimes may occur on greater length scales than anticipated from earlier estimates of compaction length scales. In viscous rock, inverted geothermal gradients stabilize vertically elongated waves or vertical channels. Decreasing temperature toward the earth’s surface can induce an abrupt transition from viscous to elastic deformation-propagated fluid flow. Below the transition, fluid flow is accomplished by short wavelength, large amplitude waves; above the transition flow is by high velocity, low amplitude surges. The resulting transient flow patterns vary strongly in space and time. Solitary porosity waves may nucleate in viscous, viscoplastic, and viscoelastic rheologies. The amplitude of these waves is effectively unlimited for physically realistic models with dependence of bulk viscosity on porosity. In the limit of zero initial connected porosity, arguably the only model relevant for melt extraction, travelling waves are only possible in a viscoelastic matrix. Such waves are truly self-propagating in that the fluid and the wave phase velocities are identical; thus, if no chemical processes occur during propagation, the waves have the capacity to transmit geochemical signatures indefinitely. In addition to solitary waves, we find that periodic solutions to the compaction equations are common though previously unrecognized. The transition between the solutions depends on the pore volume carried by the wave and the Darcyian velocity of the background fluid flux. Periodic solutions are possible for all velocities, whereas solitary solutions require large volumes and low velocities. © Elsevier, Paris     

Blast‐induced rock fracture near a tunnel

Damage in the form of cracks is predicted to assess the susceptibility of a tunnel to failure due to a blast. The material‐point method is used in conjunction with a decohesive failure model as the basis for the numerical simulations. The assumption of a cylindrical charge as the source for the blast allows the restriction of plane strain and two‐dimensional analyses. In the simulation, a further restriction of a single pressure pulse is used as the source of stress waves that are reflected and refracted after reaching the free surface of the tunnel wall. Three critical zones of significant cracking in the vicinity of a tunnel are identified as potential contributors to tunnel failure. Copyright © 2014 John Wiley & Sons, Ltd.     

地下空间逾渗与裂缝属性的关系分析

裂缝连通性评价是地下空间研究的重要内容。逾渗分析是研究裂缝网络连通性的一种有效手段。裂缝网络逾渗临界值多使用裂缝间接表征参数(如分形维数)来确定,但存在裂缝网络连通性不同却有相同间接表征参数的情况,这降低了预测的可靠性。为避免此类问题并更加准确快速地表征裂缝网络的连通性,文章在构建逾渗临界值方程时,摒弃了间接参数简化的方式,使用裂缝直接表征参数(如裂缝数量、长度等)进行非线性拟合。通过二维数值模拟建立不同参数的离散裂缝网络模型,分析逾渗低、中、高概率临界条件与裂缝直接表征参数的关系,建立逾渗临界条件预测方程,并对方程在不同尺度研究区的应用进行了讨论和验证。结果表明：预测方程可有效地预测不同概率的逾渗临界值。同时文章在预测方程的基础上,建立了裂缝网络连通性评价标准,这对于裂缝发育地区的地下空间评价工作具有一定的指导和借鉴意义。     

Characterization and reconstruction of a rock fracture surface by geostatistics

It is well understood that, in studying the mechanical and hydromechanical behaviour of rock joints, their morphology must be taken into account. A geostatistical approach has been developed for characterizing the morphology of fracture surfaces at a decimetre scale. This allows the analysis of the spatial variability of elevations, and their first and second derivatives, with the intention of producing a model that gives a numerical three‐dimensional (3D) representation of the lower and upper surfaces of the fracture. Two samples (I and II) located close together were cored across a natural fracture. The experimental data are the elevations recorded along profiles (using recording steps of 0.5 and 0.02 mm, respectively, for the samples I and II). The goal of this study is to model the surface topography of sample I, so getting estimates for elevations at each node of a square grid whose mesh size will be, for mechanical purposes, no larger than the recording step. Since the fracture surface within the sample core is not strictly horizontal, geostatistical methods are applied to residuals of elevations of sample I. Further, since structural information is necessary at very low scale, theoretical models of variograms of elevations, first and second derivatives are fitted using data of both that sample I and sample II. The geostatistical reconstructions are computed using kriging and conditional simulation methods. In order to validate these reconstructions, variograms and distributions of experimental data are compared with variograms and distributions of the fitted data. Copyright © 2002 John Wiley & Sons, Ltd.     

岩石断裂表面的分形模拟

根据岩石断裂表面粗糙度所具有的统计自仿射分形的特征,提出了改进的自仿射分形插值的概念。运用改进的自仿射分形插值方法,根据实测岩石断裂表面粗糙度数据,对岩石断裂表面粗糙形态进行了分形模拟,给出了二元分形插值数学模型。将以不同数量的观测数据模拟出的插值曲面与实际测量的岩石断裂表面相比较,得出了不同数量信息点的模拟精度,它们之间的关系曲线显示为幂函数关系的规律。这就意味着不仅可以得到模拟结果,还可以得到模拟结果的估计精度。运用少量已知数据值,模拟出未知曲面,给出了由局部模拟整体的方法这对于根据少量数据研究、模拟和直观显示复杂物体的几何形态,如地形地貌、断层表面和材料裂隙表面,具有重要的应用意义。     

Stability concept of brittle fracture propagation in rock

The results of brittle fracture propagation studies in rock are presented. Stable and unstable fracture propagation is discussed and it is shown that the transition between these two processes in rock is determined by the critical energy release during fracturing, a concept originally introduced for brittle fracture in metals.The concept of critical energy release is now applied to rock and experimental determination of the critical energy release rate,G_e, for quartzite and norite is reported.The significance ofG_e in rock fracture processes is dealt with and its practical applications in mining are outlined.     

Modeling spatial fracture intensity as a control on flow in fractured rock

Spatial fracture intensity (P ₃₂, fracture area by volume) is an important characteristic of a jointed rock mass. Although it can hardly ever be measured, P ₃₂ can be modeled based on available geological information such as spatial data of the fracture network. Flow in a mass composed of low-permeability hard rock is controlled by joints and fractures. In this article, models were developed from a geological data set of fractured andesite in LanYu Island (Taiwan) where a site is investigated for possible disposal of low-level and intermediate-level radionuclide waste. Three different types of conceptual models of spatial fracture intensity distribution were generated, an Enhanced Baecher’s model (EBM), a Levy–Lee Fractal model (LLFM) and a Nearest Neighborhood model (NNM). Modeling was conducted on a 10 × 10 × 10 m synthetic fractured block. Simulated flow was forced by a 1% hydraulic gradient between two vertical x–z faces of the cube (from North to South) with other boundaries set to no-flow conditions. Resulting flow vectors are very sensitive to spatial fracture intensity (P ₃₂). Flow velocity increases with higher fracture intensity (P ₃₂). R-squared values of regression analysis for the variables velocity (V/V _max) and fracture intensity (P ₃₂) are 0.293, 0.353, and 0.408 in linear fit and 0.028, 0.08, and 0.084 in power fit. Higher R ² values are positively linked with structural features but the relation between velocity and fracture intensity is non-linear. Possible flow channels are identified by stream-traces in the Levy–LeeFractal model.