^VETENSKAP» K.UNGL
- TEKNISKA
KONST
APERTURE DISTRIBUTION OF
ROCK FRACTURES
Eva Hakami
Stockholm 1995 sa, Doctoral Thesis
Division of Engineering Geology
Department of Civil and Environmental Engineering Royal Institute of Technology
VOL 2 7 Ns 0 6.
Doctoral Thesis
Aperture Distribution of Rock Fractures
by
Eva Hakami
Division of Engineering Geology
Department of Civil and Environmental Engineering Royal Institute of Technology
Stockholm, Sweden
June 1995
APERTURE DISTRIBUTION OF ROCK FRACTURES
by
Eva Hakami
AKADEMISK AVHANDLING
Som med tillstånd av Kungliga Tekniska Högskolan i Stockholm framläggs till offentlig granskning för avläggande av teknisk doktorsexamen fredagen den 15:e september 1995, kl. 10.00, i kollegiesalen, Valhallavägen 79, Stockholm (pga ombyggnad ev. i annan sal, vänligen kontakta KTH's växel 790 6000 för besked). Avhandlingen försvaras på engelska.
Fakultetsopponent: Professor John E Gale
Memorial University, St John's, Canada Examinator: Professor Ove Stephansson
Avd för Teknisk geologi
TRITA-AMI PHD 1003, ISSN 1400-1284, ISRN KTH/AMI/PHD 1003-SE, ISBN 91-7170-835-9
Stockholm 1995
ABSTRACT
Ground water flow in crystalline rock masses is governed by the conductivity of the fractures in the rock. The void geometry has a major influence on the hydromechanical properties of fractures, and this thesis concerns the properties of the fracture void geometry of single rock
fractures. It is suggested that the parameter aperture be used to describe the fracture void geometry and a definition of the aperture is proposed. The relation between void geometry and other fracture properties such as roughness, conductivity, stiffness and channelling are discussed.
The spatial correlation of the aperture distribution over a fracture surface influences both the mechanical and the hydraulic properties of the fracture. Therefore, a parameter defining the spatial correlation should be included in the description of the aperture distribution. It is proposed that the geostatistical parameters range and sill be used for this purpose.
Aperture measurement methods may be divided into three groups depending on the basic principle of the method: surface topography measurements, grout or resin injection and casting techniques. Different experimental techniques have been developed within the thesis work. The methods are applicable to fractures of different nature and size.
A compilation of measurement results indicates that the spatial correlation (range) of fracture apertures increases with increasing mean aperture and that the range is correlated with the coefficient of variation.
The existing data from aperture measurements and fracture flow experiments are still very scarce, in particular for fractures with large apertures. For future research, additional aperture measurements from fractures of different types is recommended. A further development of aperture measurement techniques suitable for field investigations is also suggested.
Key words: Rock fractures, aperture, void geometry, aperture
measurements, flow experiements, statistical analysis, spatial correlation.
FOREWORD
The research work presented in this thesis was conducted during the period 1985- 1988 at Luleå University of Technology (LuTH) and during 1992-1995 at the Royal Institute of Technology (KTH).
Professor Ove Stephansson was my supervisor during both periods and I am deeply grateful to him for his continuous support, trust and enthusiasm. I would also like to thank DrNick Barton who was my assistant supervisor during the beginning of my studies and made me share his interest in the mechanics of rock fractures.
Financial support provided by Swedish Nuclear Fuel and Waste Management Co.
(8KB) is gratefully acknowledged and I wish to thank Dr Lars O Eriksson at 8KB for his interest and personal engagement in the work.
Parts of this thesis were carried out together with the Department of Geology at Chalmers University of Technology. I would like to express my sincere thanks to Erik Larsson for his careful work with the flow experiments and to Professor Gunnar Gustafson for valuable co-operation during the last three years.
The efforts of Elis Svensson and Per Delin, at the Division of Soil and Rock
Mechanics, KTH, was an important contribution to the experimental part of the work for which I give my warmest thanks. I would also like to acknowledge the assistance of Tobias Eklind who helped me with the use of the image analysis system.
I would also like to thank all the personnel at the Department of Civil and Environmental Engineering, KTH, and my former colleagues at LuTH and Vattenfall HydroPower AB, for giving me a friendly and stimulating atmosphere to work in. In particular my fellow graduate students at the division of Engineering Geology all contributed in different ways to the thesis with assistance, advice, and friendship.
Finally, I wish to thank my husband Dr Hossein Hakami for his review work and for his help and encouragement during the course of my studies.
Stockholm, June 1995
Eva Hakami
ABSTRACT
Ground water flow in crystalline rock masses is governed by the conductivity of the fractures in the rock. The void geometry has a major influence on the hydromechanical properties of fractures, and this thesis concerns the properties of the fracture void geometry of single rock fractures. It is suggested that the parameter aperture be used to describe the fracture void geometry and a definition of the aperture is proposed. The relation between void geometry and other fracture properties such as rouglmess, conductivity, stiffness and channelling are discussed.
The spatial correlation of the aperture distribution over a fracture surface influences both the mechanical and the hydraulic properties of the fracture. Therefore, a parameter defining the spatial correlation should be included in the description of the aperture distribution. It is proposed that the geostatistical parameters range and sill be used for this purpose.
Aperture measurement methods may be divided into three groups depending on the basic principle of the method: surface topography measurements, grout or resin injection and casting techniques. Different experimental techniques have been developed within the thesis work. The methods are applicable to fractures of different nature and size.
A compilation of measurement results indicates that the spatial correlation (range) of fracture apertures increases with increasing mean aperture and that the range is correlated with the coefficient of variation.
The existing data from aperture measurements and fracture flow experiments are still very scarce, in particular for fractures with large apertures. For future research, additional aperture measurements from fractures of different types is recommended. A further development of aperture measurement techniques suitable for field investigations is also suggested.
Key words: Rock fractures, aperture, void geometry, aperture measurements, flow experiments, statistical analysis, spatial correlation.
SAMMANFATTNING
Grundvattenflödet i hårda kristallina bergmassor bestäms av konduktiviteten hos sprickorna i berget. Spricköppningens geometri har en avgörande betydelse för de hydromekaniska egenskaperna hos bergsprickor. Denna avhandling behandlar spricköppningsgeometrin hos enskilda sprickplan i granitiska bergarter.
För att beskriva spricköppningsgeometrin förslås att parametern sprickvidd (aperture) används. Sambandet mellan sprickvidd och andra sprickegenskaper, såsom råhet, konduktivitet, styvhet och kanaleffekter, behandlas.
Den spatiella korrelationen hos sprickviddsfördelningen på en sprickyta har betydelse både för de mekaniska och de hydrauliska egenskaperna hos sprickan. Därför behövs en parameter som bestämmer spatiell korrelation i beskrivningen av
sprickviddsfördelningen. Parametrarna range och sill föreslås till detta.
Metoderna för mätning av sprickvidd kan delas in i tre grupper: metoder med mätning av sprickytans topografi, metoder med injicering av resin eller bruk och
avgjutningsmetoder. Flera metoder för sprickviddsmätning har utvecklats och presenteras i avhandlingen. Metoderna kan appliceras på sprickor av olika typ och storlek.
En sammanställning av mätresultat visar att sprickviddens spatiella korrelation ökar med ökad medelsprickvidd och att det finns ett samband mellan korrelationsavståndet och variationskoefficienten.
Det finns idag en mycket begränsad mängd data från sprickviddsmätningar och flödesexperiment, i synnerhet från sprickor med stor sprickvidd. För framtida studier rekommenderas fortsatta mätningar på sprickor av olika typ. Fortsatt utveckling förslås också av mätmetoder lämpliga för sprickviddsundersökningar i fält.
111
TABLE OF CONTENTS
Page FOREWORD i ABSTRACT ii SAMMANFATTNING iii 1 INTRODUCTION 1 2 APERTURE AND RELATED PROPERTIES 2 2.1 Aperture 2 2.2 Roughness 4 2.3 Contact area 4 2.4 Matedness and spatial correlation 5 2.5 Tortuosity 6 2.6 Channelling 7 2.7 Stiffness 7 3 METHODS FOR APERTURE MEASUREMENT 9 4 MEASUREMENT RESULTS 12
4.1 Aperture distribution of fractures of different nature 12 4.2 Compilation of results 16 4.3 Conceptual models 17 4.4 Flow experiments 17 5 CONCLUSIONS 18 6 RECOMMENDATIONS FOR FUTURE RESEARCH 19 7 REFERENCES 20
IV
Page APPENDIX
Paper A: Aperture measurements and flow experiments using
transparent replicas of rock joints A1-A8 Paper B: Joint aperture measurements - An experimental technique B1-B5 Paper C: Experimental technique for aperture studies of
intersecting joints C1-C8 Paper D: Characterisation of fracture apertures - Methods and parameters D l -D4 Paper E: Aperture distribution of a highly conductive single fracture E l -E 19 Paper F: Aperture measurements and flow experiments on a single
natural fracture F1-F20
l
INTRODUCTIONRock masses consist of intact rock and rock fractures of different sizes. The
hydromechanical rock mass properties are to a large extent determined by the properties of the rock fractures, as the fractures are weaker and more permeable than the intact rock.
Therefore, much research in the field of rock mechanics is directed to towards studying the properties of rock fractures. One of the research aims is to be able to understand and predict flow and transport processes which take place in the bedrock. This issue has attracted increasing interest, in particular in connection with assessing the safety of storing hazardous waste underground. The conductivity of a rock mass depends on the entire fracture network within the particular rock mass in question and is thus governed by both the connectivity of the network and the conductivity of the single fractures. In this work, geometrical and hydraulic properties of single fractures are addressed.
To predict flow in a single fracture, three factors must be known: the fluid property, the fracture void geometry and the fluid pressure at the boundaries of the fracture (Figure 1). The fracture void geometry is governed by the geological history of the fracture and may be modified by changes in the prevailing geological conditions. This thesis will deal with the geometrical parameters for description of the fracture void geometry - how to define these parameters and which methods to use to determine the geometry.
PREDICTION OF FLUID FLOW IN SINGLE FRACTURE (overall objective)
FLUID PRESSURE AT BOUNDARIES
Determined by I 'APERTURE.!;:•?#;'.
.MEASUREMENTS;
Figure 1. Flow chart showing the context of the thesis work (shaded).
The thesis begins with an introduction to the different aspects of fracture apertures referring to the previous work in this field. This is followed by a brief description of the different methods developed for aperture measurements. These methods are presented and discussed in more detail in the appended papers. Finally, the results obtained from aperture measurements are summarized and the conclusions of the thesis work are drawn.
2 APERTURE AND RELATED PROPERTIES
A fracture can be said to consist of two rock surfaces, with irregular shape, and being more or less in contact with each other. The volume between the surfaces is the fracture void. The fracture void geometry is related in various ways to several properties and variables which often appear in the literature about rock fractures (Figure 2).
Aperture is used to describe the void geometry and roughness to describe the shape of the rock surfaces. The percentage contact area is used as a measure of the separation of the fracture surfaces and matedness or spatial correlation describes how well they match.
The fracture void geometry determines the tortuosity of the fracture flow and the variation in aperture also causes channelling. The void geometry also governs the fracture stiffness. In the following, the relation between fracture void geometry and the different fracture properties depicted in Figure 2 will be discussed in more detail.
2.1 Aperture
The parameter fracture aperture is here defined as illustrated in Figure 3. The two fracture surfaces are assumed to be parallel with a reference x-y-plane and the aperture, b, is the separation between the surfaces in the z-direction at each point. The aperture thus varies from point to point on the fracture surface. The aperture distribution of a fracture is only valid at a certain state of stress and if the stress changes the distribution will be altered.
Having defined the parameter aperture it may be worth analysing the reasons for the existence of apertures. If we assume that a fracture is originally created when a block of rock is divided into two pieces, the fracture is formed from two opposing surfaces. When the two surfaces are put together, there are principally two reasons why the aperture is not zero: 1) the surfaces do not have an equal (mirror) shape and/or 2) the surfaces are displaced relative to each other. The difference in the shape of the surfaces may be due to the stress release of the mineral grains, damage and crushing of asperities or be caused by chemical processes over time, such as alteration, precipitation and leaching. Relative movement of the surfaces is caused by the stresses in the surrounding rock giving rise to separation, shearing, rotation and deformation of the rock blocks. For most natural fractures a combination of these mechanisms is the explanation for the existing aperture.
The hydromechanical properties can therefore be expected to differ between artificial and natural fractures. This has also been observed experimentally [Gale, 1982]. The work in this thesis aims at studies of natural fractures.
Fracture void geometry
Figure 2. Fracture properties determined by fracture void geometry.
/
fracture surfaces
reference plane
Figure 3. Definition of fracture aperture, b(x,y).
2.2 Roughness
To characterise the shape of the individual fracture surfaces the term roughness is often used. The parameter studied is normally the surface height distribution defined analogous to the aperture (see Figure 2). Roughness can be fairly conveniently measured with automatic profilometers [Iwano & Einstein, 1993], but can also be recorded with a simple mechanical profilometer and compared to standard roughness profiles [Barton &
Chobey, 1977]. Roughness has mainly been used to predict fracture shear strength, but attempts have also been made to correlate roughness with the aperture and to use roughness parameters to simulate fracture apertures [Gentier, 1986; Brown 1985a,b and
1987]. However, the aperture depends on the shape and correlation of the two surfaces as they are put together and thus roughness parameters alone cannot be used to describe the fracture void geometry, in particular not for fractures at greateer depths in the crust where compressive stresses are high.
2.3 Contact area
Normally, fracture surfaces are at some points in contact with each other. At these points the compressive and shear stresses are transferred through the fracture. It is difficult to define the term contact areas because there is no sharp border between contact and non-contact points even at microscopic level. Therefore, in this thesis, the contact area is defined as the areas with an aperture smaller than a certain threshold value [Paper D]. This definition is convenient and implies that the aperture also includes the contact areas, i.e. the aperture can be any small value including zero. When required, the contact area may be determined from the aperture distribution. A relevant aperture threshold can be chosen depending on the quality of aperture data and the purpose of the study.
2.4 Matedness and spatial correlation
When the fracture surfaces are displaced due to shear movement the fracture is called unmated. The unmated fracture exhibits clearly different properties as compared to the mated fracture. The permeability increases and the strength and stiffness decrease dramatically with shear displacement [e.g. Makurat, 1985; Esaki et al, 1995; Boulon, 1995]. The expression matedness has also been used for the general match between the two opposing fracture surfaces. In the following the term spatial correlation will be used as a purely geometrical property depending on the matedness of the fracture, irrespective of the mechanism creating the aperture.
The spatial correlation tells how abruptly or slowly the aperture changes from one point on the fracture surface to another. A (semi-)variogram is a geostatistical tool for analyses of spatial variables [Isaacs & Srivastava, 1990] and has been applied to the aperture distribution [Paper E; Paper F]. Figure 4 illustrates how different spatial correlations are manifested in sections of the fracture void and in the corresponding variograms. The curve of the variogram will have a shape reflecting the correlation of tlie aperture and the parameters range and sill are used to describe the characteristics of the curve. Note that ordinary non-spatial statistical parameters such as the mean and standard deviation may be the same for fractures that have different spatial correlation.
FRACTURE 1 Hiqh correlation
FRACTURE II Low correlation
X-Z-section of 3D fracture void space
X-Y-seotlon of 3D fracture void space
Total contact jrea AI = As
Seml-variogram
S B Sill
RsRango Ihl = Lag distance
Y(h) S--
Y(h)
s -4-
I h l
f
IhlR! > RI |
Figure 4. The influence of different spatial correlation on the aperture distribution.
To be able to analyse spatial correlation it is necessary that the aperture is measured at known locations and that the measurement points are close to each other. If
measurements are taken along sections in different directions on the fracture surface, anisotropy in the spatial correlation may be revealed [Paper E].
2.5 Tortuosity
The flow pattern through a fracture is evidently influenced by the geometry of the fracture void space. The forced bending of the stream lines in the flow field of a fracture is called tortuosity and is often quantified by comparing the bent length of stream lines with straight flow lines [Paper A]. Figure 5a shows experimentally determined stream lines for a fracture that have a large spread in the aperture distribution.
To visualise or predict the tortuosity of a fracture having a known aperture distribution, the fracture flow can be calculated by numerical methods (Figure 5b), [Hakami & Larsson, 1993]. The direction ..ad magnitude of the water gradient must then also be known (boundary conditions). If the fracture void geometry is anisotropic the flow tortuosity may well become different for flow in different directions.
a)
Go
b)
o I
Figure 5. Illustration of flow tortuosity in a single fracture; a) Experimentally observed stream lines of a specmien with large variation in aperture values, [Hakami, 1988];
b) Calculated flow pattern for the same specimen [Hakami and Larsson, 1993].
2.6 Channelling
The aperture variation over a fracture surface causes a variation of the ground water pressure and flow velocity over the surface. In some cases the void geometry is such that the flow along some paths is much faster than along others. This difference in flow velocity is called channelling. All fractures exhibit channelling to some extent. The reason for having strong channelling effects in a single fracture is that the apertures are very well correlated. The reason for the high correlation may, for example, be that the fracture is extensively sheared or that the fracture fill is not distributed uniformly.
Major channelling has been observed in chemical transport tests in the field [Abelin et al., 1991]. Flow in field test, with several fractures involved, is expected to display more pronounced channelling because of the influence of the connectivity between the single fracture planes. Also, flow may take place in large apertures along the
intersections [Paper C]. The difference in aperture distribution between individual fractures is another factor that further increases the expected channelling effect on the rock mass scale compared to the channelling of single fractures.
2.7 Stiffness
A way of studying the mechanical properties of a rock fracture is to perform a normal stiffness test. The result of such a test is often shown as the closure, or normal deformation (AV) of the fracture, plotted against the applied normal stress (Figure 6a).
Stiffness curves have been used by Goodman [1976] and Bandis et al. [1983] to define parameters related to the fracture aperture. Both authors use the term maximum closure Vm determined from the fracture position at a certain "initial" stress level. The initial stress cannot be put at zero because at this stress the position of the fracture surfaces can not be defined. Also a very low initial stress, as used by Bandis et al. [1983], may give experimental problems since the stiffness orthe fracture is extremely low at these stress levels and the curve of stress versus deformation will be unreliable (Figure 6a). It is therefore suggested that a rather high reference stress level be chosen for characterisation and prediction of fracture stiffness behaviour [Paper B].
A coupling between parameters related to fracture stiffness and those related to fracture conductivity has been very desirable because it enables calculation of coupled hydromechanical processes. A linear function relating the hydraulic aperture and the closure (AV) has been proposed by e.g. Witherspoon et al. [1980] and Elliot et al. [1985].
A non-linear function relating hydraulic aperture and the closure was proposed by Barton et al. [1985]. These functions contain the closure parameters, AV or AE and Vm> which are determined from fracture stiffness curves (these should not be confused with the geometrical aperture parameter, b, defined in Figure 3). The hydraulic aperture (often denoted e, 2b or bh) is the equivalent width of a fracture consisting of two parallel plates.
The hydraulic aperture is calculated through the well known "cubic law" for laminar flow between parallel plates, by using results from flow experiments.
The only study known to the author that deals directly with the relation between fracture stiffness and fracture void geometry is the study by Hopkins et al. [1990 and 1992]. They used a numerical model to analyse the effect of different patterns of contact area on the fracture stiffness and found that fractures with a few but large contact areas were less stiff than fractures with many small contact areas. Expressed in terms of spatial correlation, this relation would imply that a fracture with a high correlation of apertures has a lower stiffness compared to a fracture with a low correlation of apertures.
a)
Closure [ urn
b) Aa
1/2 Abj
1/2 AV t
^s^~^-~ Aperture change
Closure
Figure 6. a) Fracture parameters determined from a normal stiffness test, b) Deformation of fracture void geometry during normal compression.
When the normal stress across a fracture is increased, the aperture will change at all points except for the contact points (Figure 6b). The larger aperture changes occur when the contact points are far from each other and it may thus be expected that the aperture distribution of a fracture becomes more peaked as the normal stress across the fracture increases. This has also been confirmed by experimental results (Figure 7).
a)
12,-
b) '5
100 200 300 400 500 600 Aperture, urn
ZOO 300 400 Aportura C*lcron«]
Figure 7. Aperture measurement results showing the change in fracture aperture distribution with normal stress; a) [Paper B]; b) [Hakami, 1988].
The relation between fracture void geometry and shear stiffness has not been investigated to any great extent. Experimental results from [Yoshinaka et al, 1993]
demonstrate that the shear strength increases, as expected, with the sheared contact area.
The void geometry, in terms of the percentage of contact areas, is therefore one factor defining the shear properties. The shear stiffness is, however, governed by the surface roughness to a large extent, since the roughness determines the dilation angle [e.g.
Bartonetal., 1985].
3 METHODS FOR APERTURE MEASUREMENT
Several different techniques have been used to measure fracture aperture. The measurement methods can be grouped with regard to the measurement procedures (Figure 8) and are described in Paper D. One procedure (I) is to measure the topography of the two fracture surfaces forming the void space and to define the aperture as the space between the surfaces. Another procedure (II) is to inject resin into a fracture to fill up the void space. The specimen containing the fracture can then be cut into slices and the aperture be measured as the resin thickness along the fracture on each slice. A third procedure (III) is to make a replica of the void space between the surfaces of a fracture, or to make replicas of the fracture surfaces.
Ill
Surface topography
Injection
Casting
Figure 8. Different approaches to measure fracture void geometry.
This thesis presents aperture measurements carried out with several different methods. Paper A describes a technique using transparent replicas of fracture surfaces. A simple principle for measuring the aperture is applied which is explained in Figure 9. A small known volume, V, of water is placed between the fracture surface. The water drop covers a small area, A, that is recorded and the average aperture over the small area can be calculated. Paper B presents a technique applying the same principle. In this case small volumes of silicon rubber are placed inside a natural fracture. After compression of the fracture it is opened and the areal extent of the silicon rubber at different points can be recorded. This method has the advantage that it does not damage the fracture specimen, which may later be used in further testing [Hakami, 1992].
Figure 9. Principle for aperture determination using a small known volume of water or silicon rubber placed behveen the fracture surfaces [Paper A; Paper BJ.
Aperture measurements applying the injection approach have been carried out using different injection materials. Paper C describes a technique in which fractures are injected in-situ with polyurethane and cylindrical specimens containing fracture intersections have been obtained by core drilling. In this way, the aperture distribution along fracture intersections may also be studied. The disadvantage of using polyurethane is that it has an uneven colour and texture, which makes digital image analysis difficult.
The measurements described in Paper E concern a fracture filled with red-coloured cement grout. This was a suitable material for the very conductive fracture studied. Also in this case close-up pictures of the fracture profile were recorded on a video film and the apertures were measured manually on the computer screen. This cumbersome procedure could be overcome by developing the method further. Paper F presents a technique using fluorescent epoxy and an image analysis system for aperture measurements (Figures 10 and 11). The fracture was first used in flow experiments and thereafter filled with fluorescent epoxy while still placed in the loading cell. After hardening of the epoxy the specimen was cut into slices and the aperture of the fracture profile measured.
10
Natural fracture
Concrete casting
x-y-table
X j h
1
t»
Y, -H_
t
M *Statistical analysis
Figure 10. Experimental technique for aperture measurements using fluorescent epoxy injection and image analysis [Paper FJ.
Figure J1. Close-up photograph of a fracture filled with fluorescent epoxy using the image analysis system. The aperture, b, is measured as the distances marked out in the image [Paper FJ.
11
All of the different techniques have advantages and drawbacks and should be chosen depending on the aim and the scale of the study. For fractures with very large apertures an in-situ injection technique must be appJied, and the fracture surface area studied should be large [Paper E; Hakami, 1994]. Therefore, if it is possible to drill boreholes parallel to the fracture plane, a technique using photographs taken from inside the boreholes is recommended. This technique may also be applicable when the quality of the rock is poor and good core recovery is not possible. For fractures with smaller apertures in fairly competent rocks, the technique using sectioned cores is recommended.
The fracture could be injected in-situ or in the laboratory and a high contrast in colour between the rock and injected material is very helpful.
The method using small volumes of rubber is less accurate but may provide a quick estimate of the aperture without destroying the fracture specimen. The use of transparent replicas is recommended when the fracture models are to be used in flow experiments where advantage is taken of the transparency for the study of tortuosity and channelling.
4 MEASUREMENT RESULTS
4.1 Aperture distribution of fractures of different nature
The results of aperture measurements on a 410x190 mm fracture specimen in granite are presented in Paper F. The surface area studied is divided into eight subareas and the frequency histograms of the subareas are given in Figure 12. This fracture is a well mated joint and has little spread in the aperture. The mean aperture is 360 urn and the coefficient of variation CV = o/b) is only 0.4. The fracture described in Paper E is a minor fault and has a much different character. For comparison, the aperture distribution of the sample J2 (360x190 mm) of this fracture is given in Figure 14. The apertures are in this sample generally large but there is also a large percentage of zero-apertures and the spread in aperture is thus considerable. The mean aperture is 2.3 mm and the coefficient of variation is 1.3.
The difference in the character of these two fractures is also reflected in the spatial correlation of apertures. The range of the variograms is, as expected, much larger for the sheared fault than for the joint with well correlated surfaces (Figures 13 and 15).
These two aperture distributions are the extreme cases among the distributions encountered in measurements performed within this thesis work. The character of other fractures falls somewhere in between these two. Without claiming that the fracture aperture follows any standard distribution function, a general observation is that aperture distributions with a small spread have best fit to normal functions while distributions with a large spread have better fit to log-normal functions (contact areas not included).
The measurement results suggest that if the aperture distribution were to be generated with a stochastic model, the contact areas would have to be treated separately from the other areas
12
•§ s > If * 5
ro >-~ p Nj =, aI I
55 8Frequency [%] •^ CD ro 01
f i l i Is
§••8 S §
a a- I! ra
f i f s
J. og
O) S m
t O SFT
*s Is
-c -g 3.8U) S S CD
Subaroa A Subarea B
0 10 20 30 40 50 60 70 Lag distance [mm]
O 10 20 30 40 50 60 70 Lag distance [mm]
Subarea C Subarea 0
10 20 30 40 50 60 70 Lag distance [mm]
10 20 30 40 50 60 70 Lag distance [mm]
Subarea E Subarea F
10 20 30 40 50 60 70 Lag distance [mm]
10 20 30 40 50 60 70 Lag distance [mm]
Subarea G
Subarea H
10 20 30 40 50 60 70 Lag distance [mm]
10 20 30 40 50 60 70 Lag distance [mm]
Figure 13. Variograms calculated for subsets of the aperture data in Figure 12, [Paper FJ.
14
co 400
300
200
100
Sample J2
4 6 8
aperture [mm]
10 12
Figure 14. Minor fault with large variation in aperture. Frequency histogram of apertures. Sample J2, [Paper EJ.
10 15 20 lag distance [cm]
Figure 15. Variogram of the aperture data of a highly conductive minor fault, [Paper EJ.
15
4.2 Compilation of results
A compilation has been made of results from aperture measurements presented in this thesis and the results reported in the literature. The coefficient of variation (CV=a/b) is plotted versus the mean aperture in Figure 17 and the range versus CV in Figure 18.
Although the available data are limited, these graphs indicate that the spread increases with mean aperture and that the spatial correlation increases with the spread in apertures.
The correlation between CV and mean aperture is less strong than the correlation between range and CV because of the difference in stress level for the fractures compared. As discussed earlier, the mean aperture is sensitive to the stress level while the parameters CV and R are more stable (cf. Figure 7), [Paper C]. The range is not expected to change very much with stress as long as the contact area is small. This is because the range is determined by the difference in shape of the fracture surfaces.
Therefore, both the CV and the range may be fairly robust parameters suitable for comparisons and the classification of fracture void geometry.
The mean aperture must be determined or estimated for a specific state of stress. The change in mean aperture with normal stress may then be estimated through the results of normal stiffness tests. The aperture change due to shear stress can be addressed by using theoretical models describing fracture dilation caused by shear displacement.
O 1.4, 1.2-
1 •
0.8 •
0.6 -
0.4 -
0.2- 0 .
o o
DO
0 O O
9 A
a A 'it
D [Gentler, 1990]
o[Hakami, 1988]
• [Hakami, 1993]
ofHakami, 1995]
A[Hakami&Larsson, 1995]
A [Iwano&Einstein, 1993]
» [Iwano&Einstein, 1995]
0 0.5 1 1.5 2 2.5
Mean aperture [mm]
Figure 16. Compilation of fracture aperture data: Coefficient of variation (CV) versus mean aperture.
16
100 T
E
7 10-
D)
1
1
•
* A D
• A*
A
D [Gentler, 1990]
• [Hakami, 1993]
o[Hakami, 1995]
A [Hakami&Larsson, 1995]
A [Iwano&Einstein, 1993]
* [Iwano&Einstein, 1995]
0.5 1.5 2.5
CV
Figure 17. Compilation of fracture aperture data: Range (correlation length) versus Coefficient of variation (CV).
4.3 Conceptual models
A conceptual model of the aperture distribution can be constructed based on experimental data. One example of this kind of conceptual model is given in Figure 16 [Paper E]. Here anisotropy is anticipated in the distribution owing to both the inferred shear displacement of the fault and the results of the statistical analysis of measured apertures.
The conceptual models can serve either as general descriptions or classifications of the fracture aperture characteristics or they can constitute a basis for synthetic generation of aperture distributions in theoretical studies [e.g. Moreno, 1988]. Measurement results from Paper F have been used in numerical calculations of flow and transport by [Larsson
& Hakami, 1995]. In these studies, comparisons made between calculated flow and measured flow showed good agreement.
4.4 Flow experiments
Results from the flow experiments performed in combination with aperture measurements, show that the ratio between mean aperture and hydraulic aperture lies in the interval 1.1-1.7, for fractures with a mean aperture of 0.1 - 0.5 mm [Paper A, Paper B, Paper F]. This result is in accordance with results reported in the literature, both from experimental studies [Witherspoon, 1980; Barton et al., 1985; Gale, 1990; Sundaram, 1987; Iwano, 1995] and numerical studies [Brown 1987; Zimmermann, 1991]. This means that the mean aperture can be used as a rough estimate of the hydraulic aperture
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and vice versa, for fractures in the aperture interval mentioned. The hydraulic aperture or the mean aperture can be used to predict the total flow through this type of fracture.
However, for predicting the flow distribution of a fracture some other parameters characterising the correlation of the fracture must be included in the conceptual model used for the prediction.
strike 010°
vertical
fault plane
contact area
5cm shear displacement
horizontal 3cm
Figure 18. Conceptual model for the aperture distribution of a highly conductive minor fault, [Paper EJ.
5 CONCLUSIONS
Fracture void geometry has a major influence on the hydromechanical properties of single fractures and rock masses. To increase our knowledge of single fracture
properties, further studies of fracture void geometry are needed. Ways of describing a fracture void geometry and measurement methods to obtain the appropriate parameters must be established. This thesis emphasizes the need for spatial correlation parameters to be included in fracture aperture characterisation.
It is proposed that the parameter "aperture" be defined as the pointwise distance between the opposing fracture surfaces, measured perpendicular to a reference plane parallel to the fracture. Clearly, the aperture distribution changes with changes in the state of stress. Measurements of the aperture may be used for the geometrical description of the fracture void space.
If the contact area is defined as the subareas with apertures smaller than a threshold value, it can be assessed from the aperture distribution. The spatial distribution of the
18
contact areas within a fracture, likewise the entire aperture distribution, is determined by the geological history of the fracture and the present state of stress.
The different methods of measuring aperture, which were developed within the thesis, have been successfully applied to fractures of different types. One method is based on measurements taken on close-up pictures from sections sawn along a resin- or grout-filled fracture. Fractures may be injected in-situ or in the laboratory, and pictures may be taken via a microscope, by a video camera or with a camera from inside a borehole, depending on the scale and the scope of the study. Another method is based on placing small known volumes of silicon rubber between fracture surfaces. This method has the advantage that it does not damage the fracture specimen, which may later be used in further testing. In the third method presented, transparent replicas of fracture surfaces are used. Such replicas are used to measure the aperture and to perform flow tests in which stream lines are visible.
Statistical methods have been used to analyse the aperture distribution of a fracture and statistical parameters are proposed that enable quantitative comparisons to be made between fractures of different kind. The aperture frequency distribution is generally bell- shaped, with a certain percentage of very small apertures in the contact areas. Apart from the contact areas, the aperture frequency may be fairly well approximated with normal or log-normal distributions. The distribution is more skewed for fractures with large apertures. The few existing experimental results indicate that the coefficient of variation increases with increasing mean aperture and that the range (spatial correlation) is
correlated with the coefficient of variation. Results of flow experiments on fractures with known aperture distribution show that the ratio between mean aperture and hydraulic aperture is 1.1 - 1.7, for O.K b < 0.5 mm.
6 RECOMMENDATIONS FOR FUTURE RESEARCH
In future research, more measurements of fracture apertures taken on fractures of different character and from different rock types are recommended. In particular there is a lack of data collected from fractures with a mean aperture larger than about 0.5 millimetres. Aperture measurement extended to include fracture intersections is also desirable. At present, aperture data from fracture intersections are very limited.
It is further recommended that fracture aperture characterisation, carried out in the field and/or in the laboratory, should become an integrated part of fracture flow and transport experiments. A better understanding of the fracture void geometry will undoubtedly make it possible to interprete the experimental results more correctly. In particular, the coupling between different disciplines dealing with rock fractures will be facilitated by clearly defined terms and improved conceptual models of the fracture void geometry. Conceptual models of the fracture void geometry, based on measurement results, may be utilised in calculations of fracture deformation, fracture flow and nuclide transport in fractures.
For future development of aperture measurements, use of advanced borehole equipment appears promising. The recent improvement of drilling techniques together
19
with video scanners and digital cameras may provide the means for such development.
Borehole measurement techniques will be specially desired for field investigations, including flow and migration experiments, in which fractures are studied at a large scale.
There is also a need for further laborator}' experiments investigating fluid flow and two-phase flow in rock fractures. In such experiments the geometrical properties of the fracture should be an indispensable part of the investigation.
Consequently, it is recommended that future research be directed partly towards aperture measurement methods which are quick and robust, and can be used for the characterisation of a large number of fractures, and partly towards methods which are adapted to specific multi-discipline experiments.
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