Hydromechanical response of a fracture undergoing compression and shear

Int. J. RockMech. Min. Sci. & Geomech. Abstr, Vol.30, No.7, pp. 845-851, 1993

0148-9062/93 $6.00 + 0.00 Pergamon Press Ltd

Printed in Great Britain

Hydromeclhanical Response of a Fracture Undergoing Compression and Shear W.A. O L S S O N t S.R. B R O W N I The normal compliance and fluid flow rates through a natural fracture in Austin Chalk were measured as a function of shear offset. We compare the experimental data on the effects of normal stress and shear offset on fluid flow rates to predictions from a microscopic theory of surface contact constrained by surface roughness measurements.

NORMAL LOAD

INTRODUCTION Coupled fluid flow-rock deformation processes can be important in several engineered and natural phenomena. Water may flow through rock joints or faults into mined openings or around dams, stress sensitive fractures may affect hydrocarbon reservoir management, or radionuclides may migrate along joints away from underground nuclear waste repositories. The effect of normal stress and closure on fracture flow rates has been much studied [1], but little has been reported on the effect of fracture slip. The effect of slip on fracture flow was estimated theoretically [2-4] but there has been little experimental work done [5,6] on this effect. Mukarat et al. [5] measured flow across a rectangular fracture, and Esaki et al. [6] measured flow from a central hole in a rectangular fracture surface; both fractures were slid in direct shear. Olsson [7] combined the rotary shear test with the radial flow geometry to study the effect of joint shear on fracture flow rates for a sawed and ground surface in tuff (Fig. 1). This technique has the advantages of well-known stress and fluid flow fields, uniform normal stress, and fewer problems with boundary conditions. In this study, we extend the experimental work of Olsson [7] to the study of a natural fracture from drill core. We evaluate the effects of normal stress and shear offset on fluid flow rates with predictions from a microscopic theory of surface contact constrained by surface roughness measurements. EXPERIMENTAL PROCEDURES Sample Material and Mounting The natural fracture used in this investigation was found in a core taken from an oil well drilled in Austin Chalk. The fracture surfaces were clean and undamaged, and without apparent mineralization. Sample halves could be closely mated, or interlocked, by hand. A short core with diameter of 60.3 mm was taken perpendicular to the fracture so as to contain the fracture in the center of its length. Into one surface of the fracture, a blind hole was bored to a depth of about 10 mm so that when the two halves were pressed ?Geomechanics Departraent 6117, Sandia National Laboratories, Albuquerque, New Mexico 87185 845

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Fig. 1. Sketch of rotary shear sample combined with radial flow test on left, and a cross-sectionof the experimental set up on right. The white area is the sample, the light gray is the aluminum holder, and the dark gray is the plaster of paris potting material. The LVDT mounting arrangement, inlet hole and internal cavity a r e also indicated. Sketch not to scale. together, the area of contact was washer-shaped with outside diameter of 60.3 mm and inside diameter of 24.0 mm. An access hole of 8 mm diameter was bored from the side of the sample into the central cavity to allow the introduction of fluid. Each sample half was potted with plaster of paris into aluminum mounting fixtures leaving the fracture surfaces about 3 mm above the plaster (Fig 1). These fixtures were then bolted to the platens of an axial/torsion load frame where angle of platen rotation and axial load and displacement were servo-controlled. A pair of LVDT's measured the distance between the aluminum fixture holding one sample half and the opposite platen holding the second sample half. This arrangement has the same problem common to samples potted into shear boxes in direct shear machines: the apparent change in displacement is the sum of distortions of the intact rock, the joint, the potting compound, and any mounting fixture included in the gauge length. An approximation to the joint closure was obtained by assuming that the mated aperture was zero in the compression test (see G below) at 20 MPa. The unloading slope for this test was multiplied by stress and subtracted from the displacement at any stress for all the other tests. The term "offset" denotes change in relative position effected during periods of separation, and "slip" denotes change in relative position effected during periods of contact at non-zero normal stress. Both offset and slip are computed as 27r x(mean radius). In the figures, dp is the gauge pressure of the fluid in the central cavity driving fluid flow at constant pressure.

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R O C K M E C H A N I C S tN T H E 1990s

The overall test sequence was as follows: A. A normal compression cycle to 8 MPa was applied, followed by another cycle to 8 MPa with flow measurements made at selected normal stress levels during loading and unloading. B. The fracture was separated and the walls offset 1 mm, then compressed to 8 MPa with flow measurements made during loading and unloading. C. The fracture was separated and the walls offset 3 mm, then compressed to 8 MPa with flow measurements made during loading and unloading. D. Repeat C. E. The fracture walls were returned to mated condition, i.e., 0 mm offset, then compressed to 8 MPa. F. In the mated position, a normal stress of 4.3 MPa applied and held constant, then sheared to 3.5 mm of slip. Dilation was recorded continuously, and flow measuremerits were made at selected amounts of slip. G. The sample walls were separated and returned to 0 mm offset, then compressed to 20 MPa with flow measurements made during loading and unloading. Any time multiple tests are made on a given fracture, damage accumulation at asperity contacts can increasingly influence successive measurements. This was minimized by keeping the normal stress low until late in the sequence, and in the compression tests (A through E) by applying different offsets only while the fracture surfaces were separated. No surface damage was visually evident until the fracture was slid at constant normal stress, test F; however, every cycle showed some hysteresis in both the stress-displacement and flow rate-stress curves. Becanse of the lubricating properties of the silicone oil used as a permeant, the shear stiffness and the shear strength da_!ahave only qualitative value. Fluid Flow Measurements Steady-state fluid flow measurements were made at selected stress or slip levels with silicone oil having a kinematic viscosity of 50 centistokes and a specific gravity of 0.98. The fluid was moved at constant pressure by a sliding-piston dilatometer with a capacity of 352.9 cm3. The 4ilatometer displacement and pressure transducer outputs at the input side of the dilatometer and at the entrance port to the central hole in the sample were digitally recorded as were normal load, torque, and relative rotation of the fracture walls. Fracture Surface Topography Prior to the experiments, the topography of the fracture surfaces was measured with a non-contacting laser profilometer. This instrument consists of a precision three-axis positioning system which moves a laser distance meaaa~merit probe over the surface, recording surface height. The probe is moved along parallel straight lines to record a series of one-dimensional surface profiles. The principle of operation of the laser sensor of this instrument is described in detail by Huang et al. [8].

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Hm/z~lD ~ (ram) Fig. 2. Typicalmatchedprofilesand resulting aperturedistribution. The prolilometer can sample a 15 x 15 cm area on a minimum grid spacing of 25 #m. The maximum peak to valley height range is 10 cm. The theoretical height resolution is 3.8 #m, but the rms noise level dueto mechanical vibration is 5 #m with a maximum peak to valley value of 20 #m (this peak to valley value is the maximum uncertainty oftbe height measurement). The contacting portion of the fracture forms an annular region on the sample surfaces. Eleven pairs of linear profiles 30.5 mm in length and sampled at 0.0254 mm were taken from this region. Six of the profiles were taken parallel to one another from one side of the annulus tangent to the circumference of the sample. Five additional profiles were taken parallel to these from the region located directlyacross the diameter of the sample from the first profiles. Tbe sample was mounted in the profilometer in such a way as to allow matched pairs of profiles from each surface to be closely refitted in the subsequent analysis. Several preliminary data processing steps were done once the profiles are taken. First each pair of profiles from the two halves of the fracture were fitted together and the standard deviation of the aperture distribution (local distance between the surfaces) was computed. Then the two profiles were repeatedly shifted relative to one another and the aperture distribution was computed until the best match was obtained as indicated by the minimum standard deviation of the aperture. The two resulting matched profiles were then tnmcated to the same length and the D.C. level and the linear slope were removed from both profiles. A typical example of the best fit of two profiles from this fracture and the resulting aperture distribution is shown in Figure 2.

EXPKRIMENTAL OBSF~VATIONS Normal Stiffness,Closure and Flow Rates Figure 3 shows the results of test A and indicates that the fracture was stifferand less hystereticon the second cycle. Also shown, is the effect of subtracting stross×un!oading modulus of the 20-MPa-compression testfrom the measured platen closure. The sires-closure curve is nearly vertical above 5 or 6 M P a suggesting that the fracturehas closed,

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The computed value of n is plotted as a function of offset, 6, in Figure 5. At any given stress, the stiffness appears to fall rapidly with increasing offset; at 1 mm offset (B, Fig. 5 ), it is less than 50% of its value in the mated condition. Increasing the offset to 3 mm causes only a small additional decrease in stiffness (C, Fig. 5). At 3 mm, the second compression cycle (D, Fig. 5) yielded a higher stiffness than the first cycle, and when the fracture walls were returned to the mated condition, the stiffness was about 10% lower than the original value (E, Fig. 5). After the shear test, discussed next, the fracture was compressed to 20 MPa at zero offset and this gave an n-value about 10% greater than the original (G, Fig. 5). The effect of normal stress and amount of offset on flow rates are shown by the solid lines in Figure 6. In this figure,

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where a is the joint normal stress and 6 is the joint closure. Constants m and n are fitting parameters that, as shown below, may have certain physical interpretation. The goodness of fit indicated in Figure 3 is typical of all the other experiments. The next two compression cycles were applied after the fracture had been separated and offset to 1 mm and 3 ram, respectively. The effect of offsetting the fracture walls is shown in Figure 4. The compression curve at 0 mm offset suggests that the fracture comes very near to closing, i.e., the slope is asymptotic to the vertical and there is very little hysteresis. Increasing the offset from 0 to 1 mm causes a much larger change in the response than increasing offset from 1 to 3 ram. Differentiating (1) gives the normal stiffness Knn as da

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Fig. 3. Results of two cycles of normal compression to 8 MPa on a mated natural fracture in Austin Chalk. In the top two plots, the dotted lines are total normal displacement measured across the fracture, and the solid lines show joint closure computed as discussed in the text. For the second cycle, the bottom two plots show the best fit of In(stress) to closure and its fidelity to the data.

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Fig. 5. The stiffness parameter n plotted against fracture shear offset. The letters correspond to the tests identified in the text, performed in alphabetical order. A model fit discussed in the text is shown by the dotted line. The shear test was run between E and G. the offset and test sequence is indicated by the letters to the right of each curve. As expected, increasing normal stress causes the flow rate to decrease and there is hysteresis in the response. The most striking aspect of the plot (Fig. 6) is that tangential movements of the fracture walls cause orderof-magnitude changes, whereas only factors of 2 or 3 occur due to change in normal stress of the magnitudes applied here. Similar results were reported in [6]. Shear Displacement, Dilatancy, and Flow Rates The effect of sliding at constant normal stress on the flow rate is indicated in Figure 7. The sample halves were mated and a normal stress of of 4.3 MPa was applied. The fracture was then slid to about 3.5 mm. After reaching peak shear stress at about 0.2 ram, the curve descends gradually with increasing slip to about 2 mm where the stress becomes approximately constant. The fracture opens (shown by closure increasing negatively) steadily with increasing slip after

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fracture walls were displaced at a constant normal stress of 4.3 MPa. peak stress. In a similar way, the flow rate changes little until peak stress, at which time it begins a steady increase with increasing aperture past peak stress. At the termination of the shear test, the surface had several obvious damaged areas resembling slickensides in that the patches were shiny and appeared to represent areas of plastic deformation. ANALYSIS AND DISCUSSION

At this point we consider the role of s u r f ~ roughness in determining the normal stress and shear-offset dependent properties meawaed in the laboratory. A microscopic model of contact of rough surfaces based on the studies of Hertz has been shown to successfully describe the elastic properties o f a single fracture including both normal and shear sfif~ess [9,10,12,13]. This model has a long history in the engineering studies of friction and wear, and

was first presented in its present form by Greenwood and Wdliamson [14] and applied to rock fractures by Walsh and Grosenbaugh [15]. Variations of this model have been studied by others [ 16,17]. In this model a fracture is composed of two contacting rough surfaces. This model shows that the mechanical properties are largely determined by the "composite topography" of the fracture. If the topographic heights of each surface are h i ( z , y) and h2(x, y) measured relative to the mean level of each surface with positive values facing outward from the solid, then the composite topography is defined as h c ( z , V) = h ~( z , V) + h 2 ( x , V ) . T h e composite topography is simply the negative of the aperture distribution and contains only the mismatched part of the surface roughness. The normal contact of two rough surfaces is equivalent to the contact of the composite topography with a fiat surface. The surface topography parameters appearing in the model are things such as the number of contacts per unit area, the standard deviation of asperity heights, the probability density function for asperity heights, and the mean radius of curvature of the contacting asperities. This model has two major deficiencies: (1) plastic or brittle failure of asperities is not included, and (2) nearby asperities do not interact elastically. Brown and Scholz [10] showed that the amount of permanent deformation due to plastic and brittle processes decreases rapidly with the number of load cycles. Therefore. this is not considered to be a major source of error in the following analysis. The possibility and consequences of asperity interaction have been extensively studied by Hopkins et al. [ 18]. Clearly this problem is more pronounced when the contact area becomes large at high normal loads. Considering the previous successes of the non-interacting asperity model at describing experimental data in both normal compression and shear [9,10,12,13], we feel that under the low normal loads reached here asperity interaction can be neglected. In the following, we use these ideas to analyze the three major normal stress and shear offset dependent properties of single fractures observed in the experiments. Dependence o f N o r m a l Stiffness on Shear Offset

The properties of the microscopic model of elastic contact of rough surfaces can be shown by assuming that the upper tail of the probability density function of the composite topography can be fit by a negative exponential distribution: 1

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Fig. 8. Composite topography and its probability density function at 0 mm offset. The best fit of a decaying exponential distribution to the upper tail of the probability density function is shown by the smooth solid curve on the right. ponential. Only the upper portion of the probability density function (above the upper inflection point in the bell) can be expected to fit an exponential form. Secondly the exponential distribution is a best fit, where both the standard deviation and the mean are free parameters. The mean of the exponential distribution does not equal the actual mean and, in fact, has no physical significance in this theory. Considering this simple elastic theory, we have used the surface profiles to simulate the evolution of normal stiffness of this fracture with shear offset. The matched profiles taken from this fracture were offset in shear from one another by 0, 1, and 3 mm. At each offset the composite topography was computed and analyzed. Figures 8-10 show the evolution of the composite topography and its probability density function with shear offset. The upper tail of the probability density function for the composite topography was fit by an exponential distribution (Figs. 8-10). The dashed curve in Figure 5 is the stiffness parameter n derived from the surface topography. We see that at zero offset the topography predicts that the fracture is almost twice as stiff as really observed, but the agreement improves dramatically with shear offset. There are at least three possible sources for this discrepancy: (1) The surface roughness measurements are limited in coverage and may have missed some high amplitude, shon wavelength compliant asperities. (2) The amplitude of the composite topography at zero offset is only a few times the non-repeatability of the topography measurements. This low signal-to-noise ratio may give a false picture of the actual contacting asperities. (3) There could be a slight non-parallelism in the sample fixture preventing the surfaces from coming uniformly into contact making the fractrue appear more compliant than predicted by the surface topography. All three of these problems would diminish in importance with shear offset.

Dependence of Fluid Permeability on Normal Stress and Shear Offset By adding some additional information, we can extend this simple idea on normal stiffness to evaluate the dependence of fluid permeability on both normal stress and shear offset. The closure as a function of normal stress ~(~r) measured in the laboratory is the change in aperture. If we know the initial aperture do then the aperture at at any normal stress is given by d(~r) = do - 6(or). To a first approximation

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Fig. 10. Composite topography and its probability density function at 3 mm offset. the volumetric fluid flow rate through a fracture Q depends on the aperture d through the cubic law, where Q o c d 3. Substituting d(~r) in this relation gives the volumetric flow rate as a function of normal stress. Due to the influence of surface roughness, the closure is not the same as the change in aperture for flow. However, Brown [19] showed that this error should be less than 20% for moderate amounts of contact area. The initial aperture can be estimated from the surface topography as the distance between the mean levels of the surfaces when they just touch. Since this assumes that there is absolutely zero normal stress and that surfaces can just touch at one point, then perhaps a better way of estimating this is to take the initial aperture as some multiple of the standard deviation of the composite topography (say in the range 3so - 4so). This is a reasonable statistical approach, since for a Gaussian distribution greater than 99% of the surface is less than three standard deviations from the mean. Note, we are referring to the true standard deviation of the composite topography here, not the standard deviation of the exponential fit used to determine stiffness. Besides knowing the true standard deviation of the composite topography sc (to determine the initial aperture) and the standard deviation of the exponential fit s~ (to determine stiffness), we also need to know the parameter m in (1). Since this parameter depends on myriad roughness properties and on the elastic constants it is significantly more difficult to obtain. However, we have noticed from this work and that by Brown and Scholz [9] that when ~r is in MPa and 6 is in microns, then typically -1.5 < m < -0.5. For each of the three shear offsets (0,1,3 mm) Sc and s~ were measured. The normal stiffness parameter in (1) was then estimated as n = 1/s~. The cubic law was then combined with the simple elastic closure theory and used to

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Fig. I 1. Volumetric flow rate calculated from the elastic closure model and the cubic law (dashed lines) compared to the laboratory data of Figure 6 (open circles). With the values of the initial aperture indicated (do = fsc), each experiment for which the normal stress stayed below 10 MPa has three curves plotted, the top for ra = -0.5, the middle for m = -1, and the bottom for m = -1.5. The bottommost curve where the normal stress reached 20 MPa has one curve corresponding to m = - 1. calc-l_a_!ethe fluid flow rate over a range of normal stresses (Fig. 11). First we assumed that m = - 1 and found the factor f in the relation do = fs~ which gave a reasonable fit to the laboratory dam Then keeping this factor constant, we calculated two additional curves for the cases rn = - 0 . 5 and rn = - 1.5 to check the sensitivity to this parameter. In all cases, the normal stress dependence of the fluid flow rate can be fit reasonably well by the simple elastic model and the cubic law. For an offset of 3 nun, the best fitting initial aperture has a reasonable value. However, as the offset is reduced, the initial aperture required to give the right flow rates grows significantly and is too high by about a factor of 2 when the offset is 0 nun. The final experiment run at an offset of 0 mm after considerable "working in" of the surfaces shows a somewhat smaller initial aperture. A reasonable explanation of this discrepancy is that there was either (1) a slight non-parallelism in the sample fixture preventing the surfaces from coming uniformly in contact allowing the a fluid flow to be more profound and channelized on one side of the sample and making the aperture estimates from surface topography invalid or (2) there are natural features or channels on the fracture surfaces which were missed by the limited profile coverage. Both problems would become less important as shear offset progressed and the sample surfaces are worn in. Later examination of the pattern o f flow from the sample, where (1) was eliminated, shows that flow tends to be chanuelized preferentially on one side of the sample giving some support to the second explanation. Dependence of Normal Dilation on Shear Offset or Slip A close look at the shear stress and dilation curves as a function of shear slip (Fig. 7) shows that approximately

the first 0.2 mm slip results in zero dilation. Also, it is over this same slip distance that the peak in the shear stress curve develops completely. Since the dilation and shear stress result from the interaction of two rough surfaces riding over one another, we suggest that there is an underlying geometric feature of the surface roughness controlling this behavior. When the Fourier spectrum is computed, individual fracture surfaces tend to have the property that the long wavelength features tend to have much higher amplitude than the shorter wavelength features [11]. This is manifested in the decaying power-law power spectrum, where the inverse of wavelength is plotted against the square o f the amplitude. Natural fractures are composed of two surfaces which are often closely matched with one another at large wavelengths and mismatched at small wavelengths [20]. When the two surfaces are pressed together, the liner scale mismatched part gives rise to a net open space between the surfaces known as the aperture. In terms of the power spectrum, the aperture tends to have a constant amplitnde at the longer wavelengths, and then the amplitude decays as a power-law at shorter wavelengths. The transition between these two behaviors occurs at a characteristic length scale, which can be used as a measure of the degree of mismatch of the surfaces. Since the standard deviation of the aperture distribution is related directly to the integral of the power spectrum, it is determined largely by this mismatch length scale. This mismatch length scale is essentially the largest wavelength present in the composite topography with any significant amplitude, and defines the dominant roughness component affecting the fracture properties. In this light, the aperture of a fracture depends on two geometric quantifies (1) the intrinsic mismatch length scale between the surfaces due to processes during formation of the fracture and later corrosion or mineral infilling, and (2) the amount shear offset or slip between the surfaces tending to bring the surfaces away from their best fitting position. The second effect is due to the tendency of two surfaces to over ride one another and thus dilate under shear motion. In fact, the mismatch length scale just described tends to increase roughly in proportion to the amount of shear offset or slip applied. A quantitative relationship between the power spectrum of the aperture and the relative shear offset of two mirror-image fractal surfaces has been presented by Wang et al. [21]. Following Brown et al. [20] we have analyzed the mismatch length scale at zero offset by comparing the power spectrum of the composite topography to that of the surfaces (Fig. 12). We find that the mismatch length scale is in the range 0.2-0.4 mm based on the departure of the spectral ratio from its asymptotic value at high frequency. The lower limit of this range is the same as the slip distance required to develop the peak in shear stress and to begin significant dilation. The intrinsic mismatch length defined in this way describes the sloppiness in the fit of the two surfaces. Apparently the surfaces can slide over this distance before the larger scale asperities interact enough to cause dilation.

SUMMARY The normal compliance and fluid flow rates through a

ROCK MECHANICS IN THE 1990s

851

REFERENCES O.18mm

1. Cook N. G. W. Natural joints in rock: mechanical, hydraulic and seismic behavior and properties under normal stress. Int. J. Rock Mech. Min. Sci. & Geomech.Abstr. 29, 198-223 (1992). 2. Gale J. E. and Witherspoon P. A. Effects of fracture deformation on fluid pressure distribution-an indicator of slope instability. Can. Geotech. J. 14, 302-309 (1977). 3. Bawden W. F., Curran J. H. and Roegiers J.-C. Influence of fracture deformation on secondary permeability-a numerical approach.Int. J. Rock Mech. Min. Sci. & Geomech.Abstr. 17, 265-279 (1980). 4. BartonN., Bandis, S., and Bakhtar, K., Strength, deformation and conductivity coupling of rock joint. Int. J. Rock Mech. Min. Sci. & Geomech.Abstr. 22, 121-140 (1985). 5. Makurat A., Barton N. and Rad N. S. Joint conductivity variation due to normal and shear deformation. Rock Joints (Barton N. and Stephansson O., Eds.), 535-540, A. A. Balkema, Brookfield, 1990. 6. Esaki T., Hojo H., Kimura T. and Kameda N. Shear-flow coupling test on rock joints. Proc. 7 th ]nl. Cong. Rock Mech. (W. Wittke, Ed.) 389-392, A. A. Balkema, Rotterdam (1991). 7. Olsson W. A. The effect of slip on the flow of fluid through a fracture. Geophys. Res. Lett. 19, 541-543 (1992). 8. C. Huang, I. White, E.G. Thwaite, and A. Bendeli, A noncontact laser system for measuring soil surface topography. J. Soil Science Society of America 52, 350-355 (1988). 9. Brown S. R. and Scholz C. H. Closure of random elastic surfaces in contact. J. Geophys. Res. 90, 5531-5545 (1985). 10. Brown S. R. and Scholz C. H. Closure of rock joints. J. Geophys. Res. 91, 4939-4948 (1986). 11. Brown, S. R., and Scholz, C. H., Broad bandwidth study of the topography of natural rock surfaces. J. Geophys. Res. 90, 575-582 (1985). 12. Yoshioka, N. and Scholz, C. H., Elastic properties of contacting surfaces under normal and shear loads 1. Theory. J. Geophys.Res. 94, 17681-17690 (1989). 13. Yoshioka, N. and Scholz, C. H., Elastic properties of contacting surfaces under normal and shear loads 2. Comparison of theory with experiment. J. Geophys. Res. 94, 17691-17700 (1989). 14. Greenwood J. A. and Williamson J. B. P. Contact of nominally flat surfaces. Proc. RoyalSoc. London, A 295,300-319 (1966). 15. Walsh J. B. and Grosenbaugh M. A. A new model for analyzing the effect of fractures on compressibility. J. Geophys. Res. 84, 3532-3536 (1979). 16. Swan, G., Tribology and the characterization of rock joints. Proc. U.S. Symp. Rock Mech. 22nd, 402-407 (1981). 17. Swan, G. andZongqi, S., Prediction ofshearbehaviorofjoints using profiles. RockMech. Rock Eng. 18, 183-212 (1985). 18. Hopkins, D.L., N.G.W. Cook, and L.R. Myer, Normal stiffness as a function of spatial geometry and surface roughness. In Rock Joints (Edited by N. Barton and O. Stephansson), pp 203-210. Balkema, Rotterdam (1990). 19. Brown S. R. Fluid flow through rock joints: the effect of surface roughness. J. Geophys. Res. 92, 1337-1347 (1987). 20. Brown, S. R., R. L. Kranz, and B. P. Bonnet, Correlation between the surfaces of natural rock joints. Geophys. Res. Lett. 13, 1430-1433 (1986). 21. J.S.Y, Wang, T.N. Narasimhan, and C. H. Scholz, Aperture correlation of a fractal fracture. J. Geophys. Res. 93, 22162224 (1988).

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Fig. 12. Ratio of the power spectrum of the composite topography to that of the individual surfaces. The high frequency plateau where the ratio = 2.0 represents complete mismatch of features with wavelengths smaller than 0.2 mm. The spectrum of the composite topography and that of the surfaces are equal at a wavelength of 0.4 mm.

natural fracture in Austin Chalk were measured as a function of shear offset and slip. We find that tangential movements of the fracture walls cause order-of-magnitude changes in the fluid flow rate through the fracture, whereas only factors of 2 or 3 occur due to changes in normal stress. We have compared this experimental data to predictions from a microscopic theory of surface contact constrained by surface roughness measurements. The theory predicts both the effects of normal stress and shear offset on fracture flow and lends some insight into the effects of surface roughness on the dilation and development of the peak she~ stress characteristic of sliding of interlocked fracture surfaces. This work demonstrates that in any engineering activity wherein shear stress is sufficient to cause slip on discrete fractures one can expect significant changes in the fluid permeability. For example, during water injection or hydrofracturing in an oil reservoir to enhance production, the effective normal stress on existing fractures may decrease enough to cause frictional sliding. If the fracture surfaces are initially well matched, then there may be a significant and permanent permeability increase associated with the fluid injection. If, however, the surfaces are initially poorly matched or misaligned then the opposite effect may be observed [7].

Acknowledgements--T.V. Tormey and R.D. Hardy provided able assistance in the laboratory. The core was provided by Oryx Energy Co. The work was supported by DOE's Oil Recovery Technology Partnership through the Bartlesville Project Office. This work performed at Sandia National Laboratories supported by the U.S. Department of Energy under contract number DE-AC04-76DP00789.