ABSTRACT: This paper aims to estimate the long-term evolution of hydraulic properties of the rock mass. Because the evaluation of the fracture interface change over time under various hydro-thermal conditions is insufficient, the long-term evolution of permeability in a rock fracture has been investigated in this research. Results indicated that the fracture surface roughness and the contact area were altered. However, the topography of the fracture surface and the aperture distribution could not be obtained directly from the permeability experiments. Therefore, a triaxial cell with heating capabilities was assembled, and a microfocus X-ray CT (µX-ray CT) was utilized to intermittently obtain the fracture structures. The fracture aperture and the contact area were then extracted through the µX-ray CT scanning results. The decrease of the aperture or the increase of the contact area is likely attributed to chemical processes such as pressure solution, and the mechanisms should be further examined.

ABSTRACT: In this study, an improved version of the Simplified 3D Displacement Discontinuity Method (S3D DDM) is introduced which can be used to simulate single and multiple fracture problems in a layered formation. The developed model is then used to predict the geometry of hydraulic fractures, and to characterize the stress shadowing effect between fractures with variable heights and vertical offsets. Similar to the original S3D DDM, 3D correction factors are used to calculate the normal and shear displacements along the fracture length. For this improved version, the original 3D correction factors are modified to account for fractures with nonuniform height along the length direction. A stress correction factor is employed to calculate the influence of stress contrast between layers on fracture opening. Static simulation results from the improved model compare favorably with reference analytical solutions for penny-shaped fractures and with fully 3D numerical solutions. While the fully 3D model requires discretization in both lateral and vertical directions, the simplified model requires only a single row of elements in height, resulting in considerably lower computation time and memory utilization without a loss of accuracy.

Abstract In this paper, we describe efforts to create a computationally efficient model that is accurate for multiple, three dimensional fracture problems. The accuracy of a fast pseudo-3D method (Olson, 2004) for describing fracture interaction is investigated through comparing with a fully 3D displacement discontinuity method (DDM). Results demonstrate that the pseudo- 3D solution underestimates the mechanical interaction between nearby fractures. The apertures of both interior and exterior fractures given by the pseudo-3D method are larger than the fully 3D solutions. However, 3D DDM is computationally far more expensive than the pseudo-3D method because a) more elements are required to describe a fracture in three dimensions and b) the computational cost per element is higher in 3D. We show that using 1 element in the fracture height direction with the standard 3D equations is unacceptably inaccurate, but by employing an analytically based correction factor, that accuracy can be significantly improved, eliminating the need for extra elements for height-contained hydraulic fracture problems. The higher per element computation cost in 3D is largely the result of the fact that the 3D displacement discontinuity method has three unknowns (opening, strike-slip shear and dip-slip shear). Further speed advantage is gained by dictating all fractures must be vertical, which allows elimination of equation components related to the dip-slip shear. We demonstrate how this model can be applied to problems of multiple hydraulic fracture propagation in horizontal wells. 1. INTRODUCTION In recent years, production of tight oil and shale gas has increased exponentially in the United States. Multiple fracture treatments in horizontal wellbores are becoming a prevalent approach to economically develop unconventional reservoirs. A better understanding of multiple fracture growth is essential for accurately predicting fracture geometry. Mechanical interaction between multiple fractures, also referred to as stress shadow effects, is a critical factor controlling fracture geometry and inducing complex fracture geometry. To better model fracture interaction, an efficient and accuracy method is required.

Abstract In order to estimate the changes in fracture aperture under various long-term confining and thermal conditions, measurements of the fracture aperture are conducted using microfocus X-ray CT (µX-ray CT). Through the imaging data, the height of the fracture surface and the contact points are evaluated, and contact ratios for the fracture, the JRC and the aperture distribution are estimated. On the other hand, measurements are also conducted using a laser scan profile sensor, and some parameters are estimated. In comparing these parameters, the validity of the µX-ray CT data and an analysis of the data will be discussed. In addition, a fracture flow simulation will be conducted using the surface roughness and aperture data obtained by the µX-ray CT. 1. INTRODUCTION It is well known that for a rock fracture under various thermal and stress conditions, a reduction in permeability occurs due to chemical and mechanical compaction. The chemical and mechanical compaction may include a pressure solution and a reduction in permeability could be explained by this pressure solution [1]-[5]. Yasuhara, et al. [6] conducted flow-through experiments on a single fracture in granite under controlled temperature and stress conditions. Specifically, two different experiments, short-term and long-term, were performed to examine the influence of the loading time on the evolution of fracture permeability. The measured changes in fracture permeability showed reversible and irreversible behaviors under short-term and long-term conditions, respectively. These results indicated that the surface roughness and the structure of a fracture may be changed by pressure solution. However, no change in the fracture structure could be directly obtained. A change in the hydraulic conductivity was indirectly obtained. The joint surface roughness is basically measured with a non-contact laser scan profiler or a CCD camera, and then, high quality profiling data can be obtained. On the other hand, the fracture roughness and the aperture distributions of a single rock fracture under certain confining stress conditions have not been evaluated, although it is very important that a measurement system is developed to measure these parameters under confining stress conditions. Measuring the joint surface roughness and the aperture distribution is not enough to obtain the height of surface roughness, the contact conditions and the aperture distribution under confining stress conditions.

Abstract Fracture intersections provide connectivity among fractures and fracture sets, yet few studies have focused on methods to characterize intersections and the response of intersections to changes in stress. An experimental investigation was performed to determine if distinct elastic-wave modes exist that propagate along fracture intersections. Ultrasonic waves propagated along the intersection between two orthogonal, synthetic fractures in aluminum were compared with waves that were propagated through the bulk and along single fractures as a function of stress. Intersections give rise to several elastic-wave modes not observed for a single fracture that are sensitive to contact points along an intersection, i.e., a linear non-welded contact. In addition, observation of the intersection waves is affected by the relationship between the applied external loading configuration and the polarization of the shear wave source. Intersection waves have the potential to provide a new method for monitoring the condition of fracture intersections.

ABSTRACT: A new 2D numerical simulation method for water flows in discrete fracture networks is proposed. Firstly, hydraulic analysis of a single fracture is carried out. Each fracture in a discrete fracture network is treated as a weighted branch with a start node and an end node in a directed network. Node and branch laws of water flow in discrete fracture networks are derived based on the conservation of mass and energy. The topology theory is applied in order to search the subways of water flow, and to calculate water pressures and flow rate in each branch of a weighted, directed and connected path. Identification of water flow pathways and tree cutting are considered in the developed method. An example is analyzed. It shows that the proposed topology analysis method (TAM) is effective in analyzing water flow in discrete fracture networks. The advantages of TAM include: 1) Boundaries and fractures are unified with the same form of governing equation, which makes it possible to obtain water flows in a network analytically; so TAM is actually an efficient analytical method for analyzing water flows in discrete fracture networks; 2) Solutions of water pressures and flow rates in discrete fracture networks are obtained by solving a system of nonhomogeneous linear equations; 3) Results demonstrate that the developed method is effective and promising for more complex applications and engineering purpose. 1. INTRODUCTION Rock masses consist of various structural planes or discontinuities which form up a discrete fracture network. The fluid flow laws in discrete fracture networks (DFN) in rock masses are also influential for repository of nuclear waste, CO2, petroleum and natural gas, for water supply reservoirs and hydraulic power station, for water inflow assessment in underground engineering and mining. Different conceptual and mathematical models have been established.

ABSTRACT: Fractures in rock masses influence strongly the mechanical and hydraulic properties of a rock mass. Thus, the detection and characterization of fractures using geophysical methods is of critical importance for maintaining the integrity of sub-surface infrastructure and subsurface waste or storage repositories. While the effects of single fractures or sets of parallel fractures on seismic wave propagation have been studied by many scientists and engineers, little research has been performed to determine the role of fracture intersections on seismic wave attenuation and velocity. A fundamental question is whether the specific stiffness or compliance of an intersection is the same or differs from the stiffness of any of the individual fractures within two intersecting sets of fractures. In this paper, we show from experimental and numerical studies that the stiffness of fracture intersections can be less than, equal to, or greater than the stiffness of the individual fractures depending on the applied bi-axial loading conditions. 1. INTRODUCTION Rock fractures often occur in sets, as networks, or singly on nearly all length scales. Although many fracture sets contain parallel fractures, sets with orthogonal intersecting fractures are also common. Orthogonal fractures are prevalent in many geologic formations found in Norway, the United States, the United Kingdom, and even on extraterrestrial bodies such as the Moon [1-4]. Extensive theoretical, computational and experimental research has examined the effect of single fractures and fracture sets in isotropic and anisotropic media on seismic wave propagation [5-13]. Hydraulic studies on similar fractures have also been conducted as well as for intersecting fractures [14-23]. It is surprising then, that so little work has been done on characterizing orthogonal fracture intersections seismically. From the aforementioned studies on single and parallel sets of fractures, fractures give rise to converted modes, guided modes, and anisotropy.

ABSTRACT: Laboratory experiments were performed to determine the spatial variability of seismic fracture specific stiffness and the dominant flow path within a single fracture subjected to normal stress. Two cylindrical granite specimens were used in the study: an intact sample and a fractured sample with the fracture oriented perpendicular to the load. Compressional and shear waves were measured for the samples in dry conditions and during fluid invasion. The normal fracture specific stiffness increased with increasing stress (0 – 18.9 MPa), while the shear fracture specific stiffness started to approach an asymptote at around 10 MPa. During fluid invasion, the amplitude of both the compressional and shear waves decreased as water filled the fracture while the velocity of the waves increased. By tracking the arrival time changes of the waves, the fluid invasion path was identified. The fluid first invaded portions of the fracture that had a relatively low fracture stiffness and then spread to the regions with higher stiffness. In conclusion, the fluid front can be detected seismically and the spatial variation of fracture stiffness is correlated to the fluid flow path. 1. INTRODUCTION A goal of geophysical characterization of rock is to detect fractures and characterize the hydraulic and mechanical properties of the fracture. Experimental data and numerical simulations have shown that fluid flow through a fracture and fracture specific stiffness are implicitly related through fracture geometry, i.e., aperture and contact area distributions [1-9]. This relationship is important because fracture specific stiffness can be determined from seismic wave attenuation and velocity [10]. In this study, we investigated, seismically, the spatial variability in fracture specific stiffness in single fractures subjected to normal stress and whether the variability in fracture specific stiffness is linked to the most conductive flow paths through a fracture.

Abstract Experimental studies have shown that fracture specific stiffness and fluid flow through a fracture are implicitly related through the geometry of the fracture. We investigated numerically the fundamental geometric lengths scales that affect fracture deformation and fluid flow with the goal of developing a scaling relationship between this two fracture properties. We examined the displacement-stress and flow-stress relationships as a function of scale. Though deformation-stress and fluid flowstress relationships differed for each simulated fracture or subset of a fracture, we were able to collapse the statistical fluctuations in these relationships by using zeroth order approach. 1. INTRODUCTION Understanding the mechanical and hydraulic properties of single fractures is important in many scientific and engineering fields, i.e, nuclear waste isolation, oil & gas production, and carbon sequestration among others. Single fractures are composed of two rough surfaces in contact that results in a complicated distribution of void spaces, through which fluids flow, and areas of contact that provide mechanical stability. Cook [9] noted that the geometry of a single fracture primarily determines its mechanical deformation and hydraulic properties. This geometry has many length scales associated with it; for example the size and spatial distribution of the apertures (distance between the two rough surfaces or size of the voids) and contact areas. From a computational study, Pyrak-Nolte & Morris [20] surmised that the spatial correlation length of the aperture distribution in a single fracture is the defining length scale that affects the interrelationship between the hydraulic and mechanical response of a fracture. However, they did not fully explore which correlation length associated with the void geometry or contact is the most relevant length scale. For example, there are spatial correlation lengths associated with the percolation cluster (largest cluster of connected void space) and also with the separation between clusters. Both of these correlation lengths will be affected by changes in stress on a fracture because the void geometry and contact area are affected by stress. In this paper, we perform a computational study of the effect of fracture void geometry on both fluid flow and displacement of single fractures to determine the relevant length scales for future work on scaling the fluid flow-fracture specific stiffness relationship. 2. FRACTURE MODEL There are many methods for generating fracture void geometry. Most numerical approaches for simulating synthetic fracture void geometry are based on generating two rough surfaces that are then brought into contact to form the void geometry [3, 4, 15, 25, 32]. For example, Brown [4] developed a method for simulating fracture roughness by specifying the fractal dimension of the roughness, the root mean square roughness and a length describing the mismatch between the two fracture surfaces. In our approach, we use the stratified continuum percolation method to directly generate the void geometry of a fracture (i.e. the contact area and variable apertures voids) without generating two independent rough surfaces. The stratified continuum percolation method [22-24] constructs a two-dimensional hierarchical aperture distribution with a tunable spatial correlation.

ABSTRACT: Modeling of fluid flow is important in geological, petroleum, environmental, civil and mining engineering. Fluid flow through jointed hard rock is very much dependent on the fracture network pattern in the rock mass and on the flow behavior through these fractures. Flow behavior through a single fracture depends on the spatial distribution of the aperture including their connectivity, the contact area distribution of the fracture and fluid properties. The aperture and the contact area distributions of a fracture depend on the stress system acting on the joint. This research deals with fluid flow behavior through single joints subjected to normal stresses. The features of the built equipment and various phases of the laboratory experimental program are described in the paper. The initial test results obtained between applied normal stress and fracture closure for a natural rock joint indicate the built equipment works very well in obtaining normal stress versus fracture closure measurements. Fluid flow tests performed for the same rock joint under different normal stresses proved that the built fluid flow experimental system performs very well. Spatial distribution of aperture calculated at different normal stresses using rock joint surface height measurements obtained through a laser profilometer with and without silicon rubber injection to the same rock joint showed that the experimental procedure developed to estimate the spatial distribution of aperture of a rock joint works well. INTRODUCTION Modeling of fluid flow through jointed rock is important in performing the following tasks associated with jointed rock masses: (a) characterization and development of fractured rock oil reservoirs, (b) geothermal energy development, (c) petroleum well design, (d) nuclear waste repository performance assessment studies, (e) interpretation of hydrologic tests, (f) design of in-situ hydrologic tests, (g) groundwater contamination studies, (h) in-situ mine leaching studies, and (i) stability studies of rock masses in the presence of groundwater flow. In general, fluid flow through jointed rock depends on the following factors: (a) stratigraphy, (b) fracture network pattern, (c) flow behavior through single fractures, (d) flow properties of matrix rock, (e) in-situ stressystem and (f) hydraulic boundary conditions. For sedimentary rocks, the matrix permeability is significant compared to the hydraulic conductivity of fractures. Therefore, all the aforementioned factors should be considered in modeling fluid flow through the rock mass. However, for most of the igneous and metamorphic rocks, the matrix permeability is negligible compared to the hydrauliconductivity of fractures. Therefore, for such rock masses, fluid flow through jointed rock is very much dependent on the fracture network pattern in the rock mass and on the flow behavior through these fractures. Discrete fracture flow models have been suggested in the literature (Schwartz et al., 1983; Robinson, 1984; Pruess, 1987; Karasaki, 1987; Kulatilake et al., 1999) to simulate fluid flow through jointed hard rock masses. To use these models, at present, a realistic model is not available to represent fluid flow through single joints. This study initiates research to overcome this shortcoming. Flow behavior through a single joint depends on the spatial distribution of the aperture including their connectivity, the contact area distribution of the joint and fluid properties. The aperture and contact area distributions of a joint depend on the type of the fracture (tensile, shear or mixed mode), the stress system acting on the joint, and the stress history of the joint. Stresses acting on a joint can be separated into normal and shear stresses. This

ABSTRACT A discussion on the interpretation of the water pressure tests (Lugeon test) is made by the authors. Laminar and turbulent flow regimens are considered in the analysis which is based on some results of laboratory tests using granite fractures with varying opening and roughness. INTRODUCTION The water pressure test as it is performed nowadays derives from the original proposal by M. Lugeon (1933) to characterize pervious regions into the rock mass volume being studied. In Brazil, these tests are often performed using five steps of pressure as following: minimum corresponds to the coefficient of pressure, Pmin=0.10 kg/c?2 ( used at the beginning and end of tests); maximum pressure, Pmax = 0.25 kg/cm2 per meter of packer depth and intermediary pressure, Pint = Pmax/2. The total pressure adopted in estimative of k, the water pressure test is a resultant also from the head losses occuring during the test which include that on the fracture entrance (Risslet, 1978). In recent years changes in the effective pressure during the test execution are often read in the centre of the test interval using electronic devices and pressure transducers .

INTRODUCTION ABSTRACT: A stratified continuum model is used to generate fracture void geometries to investigate the effect of trapping on immiscible flow through a fracture. For a wetting phase invading a fracture initially saturated with a non-wetting phase, trapping of the non- wetting phase occurs in local maxima that are surrounded by smaller apertures. Trapping of the non-wetting phase results in high residual saturation and low values of wetting phase relative permeability. An epoxy cast of a natural fracture was used to visually observe trapping in a fracture. Energy sources such as coalbed methane, geothermal springs, and oil fields often occur in fractured reservoirs and involve the flow of two phases in fractures. Multiphase flow through fractures is also a concern for contaminant transport and the isolation of radioactive waste. An underlying question of the movement of two fluids through a fracture is how the fracture geometry affects residual saturation and relative permeabilities. In reviewing the literature, few experimental measurements have been made of relative permeability in fractures (Barton, 1972; Merrill, 1975; Bawden & Rogiers, 1985). These experiments were performed on artificial fractures, or fractures represented by parallel glass plates. Several investigators have undertaken theoretical investigations of multiphase flow in fractures. Some models involve the use of capillary theory to study multiphase flow through fractures idealized as parallel plates (Evans, 1983; Evans & Huang, 1983; Rasmussen et al., 1985) or wedge-shaped fractures with continuously varying apertures [Rasmussen, 1987]. Pruess & Tsang (1990) numerically analyzed relative permeabilities of a rough-walled fracture for a lognormal aperture distribution and various spatial correlations. They found that relative permeabilities are sensitive to the nature and range of spatial correlation of the apertures. Pyrak-Noltet al. (1990) examined unsaturated flow in single fractures for the case of a non-wetting phase invading a wetting phase fluid (such as mercury injected into a fracture saturated with air in rock). Pruess & Tsang (1990) investigated numerically the effect of different aperture distributions on two-phase flow through a fracture using global accessibility. Accessibility determines which apertures will be occupied by which phase. For wetting- phase invasion, global accessibility allows all sites to be occupied even if they are not connected to the inlet. This paper will examine the effect of global accessibility compared with inlet accessibility with trapping for a wetting phase invading a fracture initially saturated with a non-wetting phase. Numerical and experimental results will be presented.

ABSTRACT: A numerical procedure is presented for the simultaneous inversion of hydraulic and electrical data describing the flow of fluid and electrical current through a single fracture. Application of the inversion procedure to hydraulic and electrical data computed for an arbitrary aperture distribution illustrates a number of aspects and advantages of the simultaneous inversion procedure. 1 INTRODUCTION Fracture aperture governs the rates of fluid flow and contaminant transport within single fractures and fracture systems. These transport processes are of interest to the various disciplines faced with the description of flow and transport within naturally fractured formations. Accurate interpretation or prediction of these processes therefore requires knowledge of the spatial distribution of aperture. Forward analysis of transport processes in fractured media requires, as input, a description of the spatial distribution of aperture. Theoretically, aperture may be inferred from fracture surface topography and shear and normal displacement magnitudes [Brown (1987), Wang et al. (1988), Brown (1989b)]. In many field and laboratory settings, a deterministic description of the distribution of aperture is not available. Statistical descriptions are more frequently available but, lacking a deterministic form, are limited in application. Inverse analysis of transport processes requires, as input, a description of the distribution of transport related parameters (hydraulic head, contaminant breakthrough times, etc.) which may be more readily measured in field and laboratory settings [Raven et al. (1988), Novakowski (1988), Piggott and Elsworth (1990)]. Application of inversion procedures leads to an estimate of the distribution of aperture which may then be used as the basis for forward modelling. This approach is particularly useful if apertures derived from data describing one transport process may be used to predict the progress of a second process; for example, if hydraulic test results are used to derive apertures which are then used to simulate tracer test results. This leads to spatial distributions of hydraulic head and electrical potential which differ in form with the electrical potential distribution exhibiting a subdued degree of spatial variability relative to the hydraulic head distribution. Experimental and numerical observations confirm this behavior [Brown (1989b), Piggott and Elsworth (1990)]. For the sake of clarification, it should be noted that the analogy between fluid and electrical current flow applies to current established by the application of a potential difference directly to the fluid and not to current induced within or by the fluid as the result of the physical motion of the fluid. The analogy also assumes that the electrical current is established by a DC potential difference. Experimental measurements of the electrical properties of fractures are performed using AC power and the resulting properties are not equivalent to DC properties in the presence of reactive behavior. The contrast between the hydraulic head and electrical potential distributions, and the fact that both are a consequence of the aperture distribution, is a means of adding additional constraints to inversion procedures for determining aperture if the data are represented in a simultaneous manner. Additional constraints generally improve the performance of inversion procedures.

ABSTRACT INTRODUCTION The upper part of the earth's crust is highly fractured on all scales ranging from microcracks to large-scale joints and faults. Joints are well known for their effects on the physical properties of a rock mass. Mechanical properties such as bulk elastic constants and shear strength are strongly affected by the presence of joints [e.g., Goodman, 1976; Gangi, 1978; Walsh and Grosenbaugh, 1979; Bandis et al., 1983; Brown and Scholz, 1986]. Joints also control the permeability of crystalline and tight sedimentary rocks [e.g., Iwai, 1976; Gangi, 1978; Brace, 1980; Tsang and Witherspoon, 1981; Brown, 1987a, 1989a; Pyrak-Nolte et al., 1988]. Fluid flow in fractured rocks is a subject of active research in petroleum engineering, engineering geology, and hydrogeology. Applications include oil and gas production from fractured reservoirs, reservoir stimulation by hydrofracturing, hazardous waste isolation, and geothermal energy extraction. For this reason considerable effort is being placed on characterization [Beydoun et al., 1985; Paillet, 1985] and modeling [Noorishad et al., 1982; Long et al., 1985] of fractures and fracture systenas. Of central importance to all applications is the hydromechanical behavior of a single fracture. The mechanical and transport properties of fractures in rock depend on the topography of the contacting surfaces and the degree of mismatch between them. Understanding this behavior in the earth requires knowledge of how fracture topography and aperture scales with or depends on surface size. In this paper I present a brief review of my previous work on the effect of surface roughness on the physical properties of fractures. This is not intended to be a comprehensive review of the subject.

ABSTRACT ABSTRACT: An analytical model that assumes variable height asperities and full interaction between them has been developed and implemented numerically to study the behavior of a single fracture under stress. The model has been used to calculate specific stiffness and aperture profiles for specified fracture geometries. The formulation takes account of the deformation of the half-planes defining the fracture which is shown to lead to changes in aperture geometry that are not predicted by other asperity models. A parameter sensitivity study shows that specific stiffness varies significantly depending on the size of the asperities, their height distribution, and their spatial orientation. Curves of stress vs. specific stiffness generated with the model are found to agree in shape and magnitude with those obtained in the laboratory for rock specimens. 1 INTRODUCTION Understanding the properties of fractures under stress is important in characterizing most geological sites and predicting the behavior of underground engineering structures. The purpose of the present study is to identify the parameters that play an important role in determining the mechanical response of a single fracture to applied loads. An important application of the work is the description of fracture closure as a function of stress. The ability to describe changes in aperture geometry with changes in stress is crucial to predicting fluid flow through fractured rock (see, e.g., Tsang, 1984 and Brown, 1987). Specific stiffness is property that defines the relationship between applied stress and fracture deformation. More formally, specific stiffness is defined as the average applied stress divided by the average displacement across the fracture interface in excess of the displacement that would occur if the fracture were not present. Laboratory experiments on single fractures in rock indicate that specific stiffness is initially a sharply rising function with stress that levels off and approaches a constant value (e.g., Goodman, 1976; Bandis et al., 1983; and Pyrak-Nolte et al., 1987). A common approach to modeling the mechanical deformation of fractures has been to represent the fracture surfaces as parallel planes separated by asperities of varying height. Greenwood and Williamson (1966) modeled the contact between a plane and a nominally fiat surface covered by a large number of asperities with heights described by a specified statistical distribution. The asperity tips were taken to be spherical and their deformation calculated from the Hertzian solution for an elastic sphere in contact with a plane. Their model was extended by Greenwood and Tripp (1971) to the case of two rough surfaces in contact. Gangi (1978) used what he termed a bed of nails model to describe the permeability of a fractured porous rock as a function of confining pressure. The asperities were modeled as rods with equal spring constants and heights following a power law distribution. Brown and Scholz (1985, 1986), like Greenwood and Williamson, assumed the asperity tips to be spherical and modeled their deformation using the Hertzjan solution. However, they also included a term for tangential stresses arising from the oblique contact of spheres so that the stresses at the contacts are not restricted to be normal.

ABSTRACT ABSTRACT Current research on fracture hydrology at Lawrence Berkeley Laboratory is focused on two scales: the single fracture and fracture networks. In the area of single fractures, we have established a research program aimed at characterizing the geometry of the void spaces. This involves the use of metal casts and mercury injection to elucidate details of the complex geometry that result as a fracture closes under stress. With this geometry, the flow regime is being examined using an approach based on Navier-Stokes equations. Three techniques are being used to investigate the geometry of fracture networks: (1) statistical analysis of observed field data, (2) geophysical techniques for seeing into the rock, and (3) prediction of fracture patterns through .the application of rock mechanics. Statistical analysis has centered on developing a parent-daughter model to represent fracture swarms. Techniques for comparing the results of seismic tomography with the fracture properties controlling flow are being investigated. Shear zones have become a major focus of our efforts because they appear to control the hydrology of many sites. New models for fluid flow include the development of codes to analyze flow and transport in a network of channelized fractures. 1 INTRODUCTION Modeling the behavior of fluid flow in fractured rock is largely a problem of defining the geometry of the fractures. The calculation of flow, once the geometry is known, is a far simpler problem. However, a major problem that must be faced is that of determining the location of all the fractures and describing their properties. We can at most hope to describe the fractures and derive the properties of the network in a stochastic sense. To create a stochastic model requires that one have a conceptual model that can reveal how the fractures are located in space and what relationship they have to each other. Given the conceptual model, the field data can be used to derive the parameters of the model, and the parameterized model can then be used to estimate the behavior of the field site. Recent research on fracture hydrology at Lawrence Berkeley Laboratory has been focused on two different scales: the single fracture and fracture networks. Investigations of single fractures have been concerned with the problem of identifying the details of the geometry of the flow spaces within the fracture. Once the geometry of the flow paths is known, one can examine the nature of this flow regime. The primary problem in dealing with fracture networks is characterizing the location of the fractures and this involves a statistical sample from which a stochastic model can be inferred. 2 SINGLE FRACTURES A variety of laboratory and analytical techniques are being developed to define the pore space in a fracture (Myer et al., 1985; Myer et al., 1986). Concurrently, a numerical method for solving the NavieroStokes equations in a complex, multiply connected domain is being developed by Muralidhar and Long (1987a, 1987b). This is an attempt to investigate the theoretical relationship between flow and fracture void geometry and will also be used to analyze flow in voids of a real fracture.