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Anisotropic crack damage and stress-memory effects in rocks under triaxial loading
Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol.30, No.7, pp. 937-941, 1993
1/148-9062/93 $6.00 + 0.00 Pergamon Press Ltd
Printed in Great Britain
Anisotropic Crack Damage and Stress-Memory Effects in Rocks under Triaxial Loading C.E. S T U A R T * P.G. M E R E D I T H * S.A.F. M U R R E L L * J.G. van M U N S T E R #
O V E R V I E W OF PREVIOUS W O R K INTRODUCTION It is well-known that microcracks change the velocities of We present and analyse the results from tests performed
acoustic P and S waves in rocks, and that hydrostatic
on sandstone cubes in which the bulk acoustic emission
compression increases these velocities as cracks are closed
(AE) and the ultrasonic P and S wave velocity changes in
[1].
the three principal directions were monitored and measured
becomes anisotropic and the changes in acoustic wave
simultaneously with the stress and strain as samples were
velocity caused by stress, especially compressive stress,
deformed in three orthogonal directions independently.
are also anisotropic [2-7].
This combination of measurements has enabled us to
close under compression and new dilatant cracks which
directly link AE to the formation of new crack damage.
open under deviatoric or tensile stress will contribute to
From uniaxial cyclic stressing experiments the existence
Where deviatoric stresses are applied crack closure
Both pre-existing cracks which
changes in the acoustic wave velocities in rocks under
of the Kaiser stress-memory effect was confirmed based on
stress.
the AE data and the velocity data from directions normal
these effects was carried out at University College London
to the uniaxial stress direction.
by Jones [8].
Furthermore, the effect
A comprehensive experimental investigation of In the course of Jones's investigation AE
was found to occur in each principal stress direction
was also measured simultaneously with the acoustic wave
independently, regardless of whether or not stresses were
velocities during triaxial deformation experiments.
applied along orthogonal axes. This suggests that the crack
used the classical triaxial testing method with a cylindrical
damage formed during stressing is highly anisotropic, with
specimen geometry in which two principal stresses are
the new microcracks formed during each stress cycle
equal.
having minor
to the minor principal
fluid and temperature conditions can readily be applied,
axes parallel
compressive stress direction.
Jones
This method has the advantage that controlled pore
The observed effects have
but the special case of triaxial loading that is used has a
been modelled in terms of the elastic closure of pre-
limitation in the investigation of the anisotropy of the crack
existing cracks and the formation of new highly-oriented
damage.
dilatant cracks.
By
study in which cubic samples were loaded, using servo-
have
control, along the axes normal to the three pairs of
modelling
these
The dilatant cracks produce AE. two
separate
processes
we
demonstrated a clear quantitative correlation between the AE output and the new dilatant crack damage formed during deviatoric stressing.
The latter limitation was removed in the present
orthogonal cube faces independently [9]. AE of rocks has been investigated for some years [1015].
Holcomb and Costin have made an interpretation of
We believe our results confirm the potential of the use of
the Kaiser effect in a damage mechanics context [11-15],
the Kaiser effect to determine crustal stresses from
based on the idea that AE is predominantly the result of
measurements on oriented core plugs taken from borehole cores.
stress-induced damage due
* Rock & Ice Physics Research Group, Research School of Geological & Geophysical Sciences, Birkbeck College & University College London, Gower Street, London WC1E 6BT, UK. # K.S.E.P.L., Shell Research BV, Rijswijk, The Netherlands. 937
to microcrack
growth.
Observation of AE may discriminate between stress states where damage is constant and states where it is increasing. Both acoustic wave velocity and AE measurements can in principle provide information about the quantity of damage. Holcomb and Costin [14] demonstrated the anisotropy of crack damage by observing the Kaiser effect in samples which were re-loaded at different orientations, but the
938
ROCK MECHANICS IN THE 1990s
method did not provide quantitative information on this anisotropy, whereas acoustic wave velocity measurements made in orthogonal directions do provide such information. We conclude therefore that the combination of AE with acoustic wave velocity measurements is a good method for quantitatively studying crack damage in rocks as a function of stress-state. APPARATUS, EXPERIMENTAL METHOD, AND SAMPLE PREPARATION The apparatus used in the present study is based at K.S.E.P.L. at Risjwijk. Cubic rock samples (50mm edge length) were deformed in a three-axis stressing frame constructed of flanged steel beams, one of which is removable to allow the insertion of the sample. Three pairs of serve-controlled hydraulic jacks (loading capacity 300kN) are used to provide the loads along orthogonal axes normal to the faces of the samples. There are hemispherical seatings and aluminium platens immediately adjacent to the sample, and acoustic transducers are mounted in the platens. A data acquisition and control computer was used both to control the loading cycle and to record the data as a function of elapsed time. Load (stress), displacement (strain), and compressional (P) and shear (S) wave travel times measured in the three orthogonal directions were logged contemporaneously (5s logging time) at predetermined intervals (50s) throughout each test, and AE was recorded continuously between the logging periods. The P and S wave transducers had a nominal frequency of 1MHz, giving a dominant wavelength of -3.5ram, several times larger than the maximum grain size ( - 0 . 8 m m ) and smaller than the sample size as recommended by the ASTM [16]. The nominal resonant frequency of the AE transducer was 0.SMHz. Fuller details of the logging and reduction of the AE data are given in the next section. The sandstone used in these tests is from The Darley Dale quarry in the U.K. [17]. It is a felspathic sandstone with a grain size of 0.08 to 0.8mm, and a porosity of ~0.13. From two large rectangular blocks the 50mm (+/-0.03mm) cubic samples were cut, with opposite faces ground parallel to within +/-O.01mm. The bedding plane, observed visually and ultrasonically, was used to define the 1 direction in subsequent tests (the 2 and 3 directions being orthogonal to this). AE DATA RECORDING AND REDUCTION
Each AE event produces a signal which is observed as a wave packet due to source and path effects. An AE :hit is defined by a signal threshold and a hit definition time (HDT), and various characteristics of each hit can be recorded. In the present tests the recorded data were used to determine the hit rate per second, the cumulative number of hits as a function of time, and the seismic bvalue (determined from the hit amplitudes). EXPERIMENTAL RESULTS Results from a uniaxial test with loading to a maximum stress of 80MPa in the 1-direction are shown in Figures la (AE data) and lb (acoustic wave velocity data). The wave type nomenclature, based on the set of orthogonal cube axes 1, 2, and 3, employs two suffixes i and j (as in Vii) where i refers to the propagation direction of the wave, and j refers to the particle motion (polarisation) direction. During the early part of the loading cycle (to ~40MPa) the AE is negligible, but further loading produces an exponential increase in cumulative AE hits up to the maximum load reached followed by a rapid reduction to background noise level. The onset of AE we associate with dilatant crack initiation [8]. Up to that point the most important process consists of the closure of preexisting cracks, which causes an increase in the velocity of all the observed acoustic waves. Following the initiation of dilatant crack growth, dilatancy predominates over the crack closure effect in the case of V22, V33 , and V23(=V32), so for these waves the velocity reaches a peak. However, in the case of VII, V12(=V13), and V3t(=V21) crack closure continues to dominate and dilatancy is seen only in a downwards inflection of the velocity as a function of stress. In Figure 2 we show the results of an experiment using cyclic uniaxial stressing to increasingly higher loads. The AE results clearly show the Kaiser effect. Further AE occurs only once the previous maximum stress (PMS) in the given direction (the 1-direction in this experiment) is exceeded. The effect of dilatant crack growth which produces the AE responsible for the Kaiser effect is also very clearly seen in the measurements of V22, V33, and V23, where a sharp velocity reduction is observed. These results, taken together, show that the dilatant crack growth produces new cracks whose minor axes are mostly normal to the loading axis (the 1-direction). This is confirmed by measurements in which a sample was loaded sequentially to a maximum stress of 80MPa in the 3-, 2-, and 1-directions respectively. This experiment
ROCK MECHANICS IN THE 1990s
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Fig. 2. (a) Variation of cumulative AE hits during cyclic uniaxial compression. Construction lines indicate PMS levels.
r
~
lo so ~o ,o so 60 70 eo 90 -Direction Stress (MPo)
Fig. 3. Deduced crack density change for dilatant cracks (normals in 3-direction).
Fig. 1. (b) Corresponding percentage changes in P and S wave velocities in the same test.
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Fig. 2. (b) Corresponding percentage changes in P and S wave velocities in the same test. PMS lines shown.
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Fig. 1. (a) AE as a function of stress or time (at constant stress-rate) showing hit-rate, cumulative AE hits, and log of cumulative AE hits (showing exponential rise) in a uniaxial test.
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ROCK MECHANICS IN THE 1990s
demonstrates that the dilatant crack growth produced by stressing in one particular direction, for example (1-), is largely unaffected by previous stressing in orthogonal directions (2- and 3-). Remembering that the 1-direction is normal to the bedding it is not surprising that the results of compression in the 2- and 3- directions are closely similar, but that there are slightly larger velocity changes due to compression in the 1-direction. (Space limitations preclude the inclusion of a Figure showing the AE data for this experimen0. In all the above experiments the intermediate principal stress was equal to the least compressive principal stress, and the damage produced was charaeterised by cylindrical transverse isotropy [18]. Further experiments in which truly triaxial stresses were employed showed that the new dilatant cracks formed with their minor axes parallel to the least compressive principal stress, and that the intermediate principal stress lay in the plane of these cracks as predicted by Murrell & Digby [19]. In this case the new damage produced was charaeterised by planar transverse isotropy [18]. The anisotropy due to the new damage was of course superimposed on a small degree of planar transverse isotropy due to the bedding. MODELLING THE RESULTS Hudson [20] obtained expressions for the velocities of compressional and shear waves impinging on an array of paraUel penny-shaped cracks at an arbitrary angle. Using Hudson's expressions we have modelled the pre-existing cracks by three orthogonal arrays of such parallel cracks oriented normal to the principal stress directions, and the new dilatant cracks as separate arrays of parallel cracks oriented with their minor axes parallel to the least compressive principal stress direction. Obviously this model does not allow for non-crack porosity or for cracks in other orientations. We illustrate this from the first cycle of a multi-cycle experiment in which the stress in the l-direction was raised to 81MPa while the stress in the 2-direction was raised to 41MPa, with the stress in the 3-direction maintained constant at 4MPa. The changes of crack density were calculated from Hudson's equations for cracks with normals in the 1- and 2-directions (these are pre-existing cracks which closed under the application of the 1-direction stress). The crack density decreases continuously as the compressive stress normal to the cracks increases. The change of crack density calculated for cracks with normals in the 3-
direction, shows an initial reduction in crack density due to crack closure, followed by an increase as dilatant cracks with normals parallel to the 3-direction (the least compressive principal stress direction) open up. According to our model there should be no decrease in crack density of cracks with normals in the 3-direction. The observed decrease is due to the fact that the preexisting cracks are actually randomly oriented. In order to allow for this fact we assume that the form of the decrease of crack density due to crack closure under compression is the same in all directions but we scale the actual changes using constant scaling factors of 0.19 and 0.30 in the 1- and 2- directions respectively in order to bring the crack density changes in all three directions into coincidence. Then by subtracting the crack density change due to crack closure from the observed crack density change in the 3-direction we obtain the crack density change due to the opening of new dilatant cracks with normals parallel to the 3-direction (Figure 3). Comparison of the curve in Figure 3 with the curve representing the cumulative AE hits in the same experiment (see Figure la for a comparable experiment) demonstrates proportionality between the dilatant crack density increase and the AE as the stress increases above the threshold value (-40MPa) at which dilatancy begins. DISCUSSION In the general case in which there is a distinct intermediate principal stress our results show that crack damage caused by stressing of rocks is marked by the development of planar transverse isotropy determined by the major and minor principal stresses. This suggests a possible strategy for investigating crustal stresses by measurements on borehole rock cores, in which information about stress directions might be obtained from measurements of acoustic wave velocity as a function of orientation, and information about stress magnitudes might be obtained from measurements of AE as a function of the orientation of re-stressing directions. Such an experiment might be calibrated by independently determining principal stress directions using borehole breakout data, and principal stress magnitudes using hydrofracturing data. CONCLUSIONS Our experiments on a sandstone have confirmed that AE is primarily due to the growth of new dilatant cracks at deviatoric stresses above a threshold value, and that this
ROCK MECHANICS IN THE 1990s correlates with a reduction in acoustic wave velocity which is particularly apparent in directions normal to the planes o f the dilatant cracks.
This process is superimposed on a
separate process o f closure of pre-existing cracks by compressive stresses
normal
to their planes.
An
elementary model has been produced which gives an estimate of the increase or decrease of crack density as cracks open or close based on the acoustic wave velocity measurements.
The observed cumulative AE is shown to
correlate with the increase in crack density due to the growth o f new dilatant cracks at deviatoric stresses above some threshold value.
The experiments have confirmed
the existence of the Kaiser stress-memory effect in AE, where the AE depends on the difference between the major and minor principal stress.
If the principal stress
directions remain fixed then a reduction in the stress difference causes the AE to cease, and renewed AE only occurs when the stress difference exceeds the previous maximum value for fixed values of the minor and intermediate principal stresses.
However, because the
dilatant crack damage is highly anisotropic (in general producing planar transverse isotropy parallel to the plane containing the major and intermediate principal stresses), if the orientation o f the principal stresses is changed then AE will be observed at a different stress difference (this will be fully addressed in another paper).
These results
suggest a strategy for measuring crustal stresses based on borehole and borehole core measurements. REFERENCES 1. Paterson M.S. Experimental Rock Deformation-The Brittle Field. Ch.7,p. 112. Springer-Verlag,Berlin (1978). 2. O'Connell R. and Budiansky B. Seismic velocities in dry and saturated craeked solids.J. Geophys.Res.79, 5412-5426 (1974). 3. Hadley K. Comparison of calculated and observed crack densities and seismic velocities in Westerly granite. J. Geophys.Res.81, 3484-3494 (1976). 4. Soga N., Mizutani H., Spetzler H. and Martin R.J. The effect of dilatancy on velocity anisotropy in Westerly granite. J. Geophys.Res. 83,4451-4456 (1978). 5. Sayers C.M. Stress-induced ultrasonic wave velocity anisotropy in fractured rock. Ultrasonics.26, 311-317 (1988). 6. Sayers C.M., Munster J.G. and King M.S. Stress induced ultrasonic anisotropy in Berea sandstone, lnt.J.Rock Mech. Min.Sci. & Geomech. Abstr.27, 429-436 (1990). 7. Sayers C.M. and Munster J.G. Micro-crack induced seismic anisotropy of sedimentary rocks. J.Geophys.Res.96, 1652916533 (1991). 8. Jones C. and Murrell S.A.F. Acoustic compressional wave veloeity and dilatancy in triaxially stressed rock. In Rock At Great Depth, Proc. 1SRM/SPE International Symp. Pau, 1989. Eds. V.Maury & D.Fourrnaintraux.1,241-248. A.A.Balkema, Rotterdam (1989). 9. Stuart C.E. Evolution Of Anisotropic Microcrack Damage in
941
Cyclically Stressed Rock, Characterized By Contemporaneous Acoustic Emission and Elastic Wave Velocity Measurements. Ph.D. Thesis, University of London (1992). 10.Fonseka G.M., Murrell S.A.F. and Barnes P. Scanning electron microscope and acoustic emission studies of crack development in rocks. Int.J. Rock Mech. Min. Sci. & Geomech. Abstr.22, 273-289 (1985). 11.Holeomb D.J. Memory, relaxation and mierofraeturing in dilatant rock. J. Geophys.Res. 86, 6235-6248 (1981). 12.Holcomb D.J. Using acoustic emissions to determine in-situ stress: problems and promise. Proc. ASME Symp. Mech. Rocks, Soils And Ice, Houston TX. 11-21. ASME, New York (1983). 13.Holeomb D.J. and Martin R.J. Determining peak stress history using acoustic emissions. Proc. 26th US Syrup. on Rock Mech., Rapid City, Nevada. 715-722. A.A.Balkema, Boston (1985). 14.Holcomb D.J. and Costin L.S. Detecting damage surfaces in brittle materials using acoustic emissions. J.AppLMech.108, (1986). 15.Costin L.S. Time-dependent deformation and failure. In Fracture Mechanics Of Rock, Ed. B.K.Atkinson, 167-215. Academic Press, London (1987). 16. ASTM. Standard method for laboratory determination o f pulse velocities and ultrasonic elastic constants of rock. In Vol. 04.08 Std.D, 2845-2883 (1988). 17.Murrell S.A.F. The effect of triaxial stress systems on the strength of rocks at atmospheric temperatures. Geophys.J.R.Astr.Soc.lO, 231-281 (1965). 18.Hoenig A. Elastic moduli of a non-randomly cracked body. lnt.J. Solids Structures. 15, 137-154 (1979). 19.Murrell S.A.F. and Digby P.J. The theory of brittle fracturer initation under triaxial stress conditions. Geophys.J.R.Astron.Soc.19. 1. 309-334. II. 499-512 (1970). 20.Hudson J.A. Wave speeds and attenuation of elastic waves in a material containing cracks. Geophys.J. R.Astron. Soc. 64, 133150 (1981).
1/148-9062/93 $6.00 + 0.00 Pergamon Press Ltd
Printed in Great Britain
Anisotropic Crack Damage and Stress-Memory Effects in Rocks under Triaxial Loading C.E. S T U A R T * P.G. M E R E D I T H * S.A.F. M U R R E L L * J.G. van M U N S T E R #
O V E R V I E W OF PREVIOUS W O R K INTRODUCTION It is well-known that microcracks change the velocities of We present and analyse the results from tests performed
acoustic P and S waves in rocks, and that hydrostatic
on sandstone cubes in which the bulk acoustic emission
compression increases these velocities as cracks are closed
(AE) and the ultrasonic P and S wave velocity changes in
[1].
the three principal directions were monitored and measured
becomes anisotropic and the changes in acoustic wave
simultaneously with the stress and strain as samples were
velocity caused by stress, especially compressive stress,
deformed in three orthogonal directions independently.
are also anisotropic [2-7].
This combination of measurements has enabled us to
close under compression and new dilatant cracks which
directly link AE to the formation of new crack damage.
open under deviatoric or tensile stress will contribute to
From uniaxial cyclic stressing experiments the existence
Where deviatoric stresses are applied crack closure
Both pre-existing cracks which
changes in the acoustic wave velocities in rocks under
of the Kaiser stress-memory effect was confirmed based on
stress.
the AE data and the velocity data from directions normal
these effects was carried out at University College London
to the uniaxial stress direction.
by Jones [8].
Furthermore, the effect
A comprehensive experimental investigation of In the course of Jones's investigation AE
was found to occur in each principal stress direction
was also measured simultaneously with the acoustic wave
independently, regardless of whether or not stresses were
velocities during triaxial deformation experiments.
applied along orthogonal axes. This suggests that the crack
used the classical triaxial testing method with a cylindrical
damage formed during stressing is highly anisotropic, with
specimen geometry in which two principal stresses are
the new microcracks formed during each stress cycle
equal.
having minor
to the minor principal
fluid and temperature conditions can readily be applied,
axes parallel
compressive stress direction.
Jones
This method has the advantage that controlled pore
The observed effects have
but the special case of triaxial loading that is used has a
been modelled in terms of the elastic closure of pre-
limitation in the investigation of the anisotropy of the crack
existing cracks and the formation of new highly-oriented
damage.
dilatant cracks.
By
study in which cubic samples were loaded, using servo-
have
control, along the axes normal to the three pairs of
modelling
these
The dilatant cracks produce AE. two
separate
processes
we
demonstrated a clear quantitative correlation between the AE output and the new dilatant crack damage formed during deviatoric stressing.
The latter limitation was removed in the present
orthogonal cube faces independently [9]. AE of rocks has been investigated for some years [1015].
Holcomb and Costin have made an interpretation of
We believe our results confirm the potential of the use of
the Kaiser effect in a damage mechanics context [11-15],
the Kaiser effect to determine crustal stresses from
based on the idea that AE is predominantly the result of
measurements on oriented core plugs taken from borehole cores.
stress-induced damage due
* Rock & Ice Physics Research Group, Research School of Geological & Geophysical Sciences, Birkbeck College & University College London, Gower Street, London WC1E 6BT, UK. # K.S.E.P.L., Shell Research BV, Rijswijk, The Netherlands. 937
to microcrack
growth.
Observation of AE may discriminate between stress states where damage is constant and states where it is increasing. Both acoustic wave velocity and AE measurements can in principle provide information about the quantity of damage. Holcomb and Costin [14] demonstrated the anisotropy of crack damage by observing the Kaiser effect in samples which were re-loaded at different orientations, but the
938
ROCK MECHANICS IN THE 1990s
method did not provide quantitative information on this anisotropy, whereas acoustic wave velocity measurements made in orthogonal directions do provide such information. We conclude therefore that the combination of AE with acoustic wave velocity measurements is a good method for quantitatively studying crack damage in rocks as a function of stress-state. APPARATUS, EXPERIMENTAL METHOD, AND SAMPLE PREPARATION The apparatus used in the present study is based at K.S.E.P.L. at Risjwijk. Cubic rock samples (50mm edge length) were deformed in a three-axis stressing frame constructed of flanged steel beams, one of which is removable to allow the insertion of the sample. Three pairs of serve-controlled hydraulic jacks (loading capacity 300kN) are used to provide the loads along orthogonal axes normal to the faces of the samples. There are hemispherical seatings and aluminium platens immediately adjacent to the sample, and acoustic transducers are mounted in the platens. A data acquisition and control computer was used both to control the loading cycle and to record the data as a function of elapsed time. Load (stress), displacement (strain), and compressional (P) and shear (S) wave travel times measured in the three orthogonal directions were logged contemporaneously (5s logging time) at predetermined intervals (50s) throughout each test, and AE was recorded continuously between the logging periods. The P and S wave transducers had a nominal frequency of 1MHz, giving a dominant wavelength of -3.5ram, several times larger than the maximum grain size ( - 0 . 8 m m ) and smaller than the sample size as recommended by the ASTM [16]. The nominal resonant frequency of the AE transducer was 0.SMHz. Fuller details of the logging and reduction of the AE data are given in the next section. The sandstone used in these tests is from The Darley Dale quarry in the U.K. [17]. It is a felspathic sandstone with a grain size of 0.08 to 0.8mm, and a porosity of ~0.13. From two large rectangular blocks the 50mm (+/-0.03mm) cubic samples were cut, with opposite faces ground parallel to within +/-O.01mm. The bedding plane, observed visually and ultrasonically, was used to define the 1 direction in subsequent tests (the 2 and 3 directions being orthogonal to this). AE DATA RECORDING AND REDUCTION
Each AE event produces a signal which is observed as a wave packet due to source and path effects. An AE :hit is defined by a signal threshold and a hit definition time (HDT), and various characteristics of each hit can be recorded. In the present tests the recorded data were used to determine the hit rate per second, the cumulative number of hits as a function of time, and the seismic bvalue (determined from the hit amplitudes). EXPERIMENTAL RESULTS Results from a uniaxial test with loading to a maximum stress of 80MPa in the 1-direction are shown in Figures la (AE data) and lb (acoustic wave velocity data). The wave type nomenclature, based on the set of orthogonal cube axes 1, 2, and 3, employs two suffixes i and j (as in Vii) where i refers to the propagation direction of the wave, and j refers to the particle motion (polarisation) direction. During the early part of the loading cycle (to ~40MPa) the AE is negligible, but further loading produces an exponential increase in cumulative AE hits up to the maximum load reached followed by a rapid reduction to background noise level. The onset of AE we associate with dilatant crack initiation [8]. Up to that point the most important process consists of the closure of preexisting cracks, which causes an increase in the velocity of all the observed acoustic waves. Following the initiation of dilatant crack growth, dilatancy predominates over the crack closure effect in the case of V22, V33 , and V23(=V32), so for these waves the velocity reaches a peak. However, in the case of VII, V12(=V13), and V3t(=V21) crack closure continues to dominate and dilatancy is seen only in a downwards inflection of the velocity as a function of stress. In Figure 2 we show the results of an experiment using cyclic uniaxial stressing to increasingly higher loads. The AE results clearly show the Kaiser effect. Further AE occurs only once the previous maximum stress (PMS) in the given direction (the 1-direction in this experiment) is exceeded. The effect of dilatant crack growth which produces the AE responsible for the Kaiser effect is also very clearly seen in the measurements of V22, V33, and V23, where a sharp velocity reduction is observed. These results, taken together, show that the dilatant crack growth produces new cracks whose minor axes are mostly normal to the loading axis (the 1-direction). This is confirmed by measurements in which a sample was loaded sequentially to a maximum stress of 80MPa in the 3-, 2-, and 1-directions respectively. This experiment
ROCK MECHANICS IN THE 1990s
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Fig. 2. (a) Variation of cumulative AE hits during cyclic uniaxial compression. Construction lines indicate PMS levels.
r
~
lo so ~o ,o so 60 70 eo 90 -Direction Stress (MPo)
Fig. 3. Deduced crack density change for dilatant cracks (normals in 3-direction).
Fig. 1. (b) Corresponding percentage changes in P and S wave velocities in the same test.
4 0 0 0 0 -1
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Fig. 2. (b) Corresponding percentage changes in P and S wave velocities in the same test. PMS lines shown.
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940
ROCK MECHANICS IN THE 1990s
demonstrates that the dilatant crack growth produced by stressing in one particular direction, for example (1-), is largely unaffected by previous stressing in orthogonal directions (2- and 3-). Remembering that the 1-direction is normal to the bedding it is not surprising that the results of compression in the 2- and 3- directions are closely similar, but that there are slightly larger velocity changes due to compression in the 1-direction. (Space limitations preclude the inclusion of a Figure showing the AE data for this experimen0. In all the above experiments the intermediate principal stress was equal to the least compressive principal stress, and the damage produced was charaeterised by cylindrical transverse isotropy [18]. Further experiments in which truly triaxial stresses were employed showed that the new dilatant cracks formed with their minor axes parallel to the least compressive principal stress, and that the intermediate principal stress lay in the plane of these cracks as predicted by Murrell & Digby [19]. In this case the new damage produced was charaeterised by planar transverse isotropy [18]. The anisotropy due to the new damage was of course superimposed on a small degree of planar transverse isotropy due to the bedding. MODELLING THE RESULTS Hudson [20] obtained expressions for the velocities of compressional and shear waves impinging on an array of paraUel penny-shaped cracks at an arbitrary angle. Using Hudson's expressions we have modelled the pre-existing cracks by three orthogonal arrays of such parallel cracks oriented normal to the principal stress directions, and the new dilatant cracks as separate arrays of parallel cracks oriented with their minor axes parallel to the least compressive principal stress direction. Obviously this model does not allow for non-crack porosity or for cracks in other orientations. We illustrate this from the first cycle of a multi-cycle experiment in which the stress in the l-direction was raised to 81MPa while the stress in the 2-direction was raised to 41MPa, with the stress in the 3-direction maintained constant at 4MPa. The changes of crack density were calculated from Hudson's equations for cracks with normals in the 1- and 2-directions (these are pre-existing cracks which closed under the application of the 1-direction stress). The crack density decreases continuously as the compressive stress normal to the cracks increases. The change of crack density calculated for cracks with normals in the 3-
direction, shows an initial reduction in crack density due to crack closure, followed by an increase as dilatant cracks with normals parallel to the 3-direction (the least compressive principal stress direction) open up. According to our model there should be no decrease in crack density of cracks with normals in the 3-direction. The observed decrease is due to the fact that the preexisting cracks are actually randomly oriented. In order to allow for this fact we assume that the form of the decrease of crack density due to crack closure under compression is the same in all directions but we scale the actual changes using constant scaling factors of 0.19 and 0.30 in the 1- and 2- directions respectively in order to bring the crack density changes in all three directions into coincidence. Then by subtracting the crack density change due to crack closure from the observed crack density change in the 3-direction we obtain the crack density change due to the opening of new dilatant cracks with normals parallel to the 3-direction (Figure 3). Comparison of the curve in Figure 3 with the curve representing the cumulative AE hits in the same experiment (see Figure la for a comparable experiment) demonstrates proportionality between the dilatant crack density increase and the AE as the stress increases above the threshold value (-40MPa) at which dilatancy begins. DISCUSSION In the general case in which there is a distinct intermediate principal stress our results show that crack damage caused by stressing of rocks is marked by the development of planar transverse isotropy determined by the major and minor principal stresses. This suggests a possible strategy for investigating crustal stresses by measurements on borehole rock cores, in which information about stress directions might be obtained from measurements of acoustic wave velocity as a function of orientation, and information about stress magnitudes might be obtained from measurements of AE as a function of the orientation of re-stressing directions. Such an experiment might be calibrated by independently determining principal stress directions using borehole breakout data, and principal stress magnitudes using hydrofracturing data. CONCLUSIONS Our experiments on a sandstone have confirmed that AE is primarily due to the growth of new dilatant cracks at deviatoric stresses above a threshold value, and that this
ROCK MECHANICS IN THE 1990s correlates with a reduction in acoustic wave velocity which is particularly apparent in directions normal to the planes o f the dilatant cracks.
This process is superimposed on a
separate process o f closure of pre-existing cracks by compressive stresses
normal
to their planes.
An
elementary model has been produced which gives an estimate of the increase or decrease of crack density as cracks open or close based on the acoustic wave velocity measurements.
The observed cumulative AE is shown to
correlate with the increase in crack density due to the growth o f new dilatant cracks at deviatoric stresses above some threshold value.
The experiments have confirmed
the existence of the Kaiser stress-memory effect in AE, where the AE depends on the difference between the major and minor principal stress.
If the principal stress
directions remain fixed then a reduction in the stress difference causes the AE to cease, and renewed AE only occurs when the stress difference exceeds the previous maximum value for fixed values of the minor and intermediate principal stresses.
However, because the
dilatant crack damage is highly anisotropic (in general producing planar transverse isotropy parallel to the plane containing the major and intermediate principal stresses), if the orientation o f the principal stresses is changed then AE will be observed at a different stress difference (this will be fully addressed in another paper).
These results
suggest a strategy for measuring crustal stresses based on borehole and borehole core measurements. REFERENCES 1. Paterson M.S. Experimental Rock Deformation-The Brittle Field. Ch.7,p. 112. Springer-Verlag,Berlin (1978). 2. O'Connell R. and Budiansky B. Seismic velocities in dry and saturated craeked solids.J. Geophys.Res.79, 5412-5426 (1974). 3. Hadley K. Comparison of calculated and observed crack densities and seismic velocities in Westerly granite. J. Geophys.Res.81, 3484-3494 (1976). 4. Soga N., Mizutani H., Spetzler H. and Martin R.J. The effect of dilatancy on velocity anisotropy in Westerly granite. J. Geophys.Res. 83,4451-4456 (1978). 5. Sayers C.M. Stress-induced ultrasonic wave velocity anisotropy in fractured rock. Ultrasonics.26, 311-317 (1988). 6. Sayers C.M., Munster J.G. and King M.S. Stress induced ultrasonic anisotropy in Berea sandstone, lnt.J.Rock Mech. Min.Sci. & Geomech. Abstr.27, 429-436 (1990). 7. Sayers C.M. and Munster J.G. Micro-crack induced seismic anisotropy of sedimentary rocks. J.Geophys.Res.96, 1652916533 (1991). 8. Jones C. and Murrell S.A.F. Acoustic compressional wave veloeity and dilatancy in triaxially stressed rock. In Rock At Great Depth, Proc. 1SRM/SPE International Symp. Pau, 1989. Eds. V.Maury & D.Fourrnaintraux.1,241-248. A.A.Balkema, Rotterdam (1989). 9. Stuart C.E. Evolution Of Anisotropic Microcrack Damage in
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Cyclically Stressed Rock, Characterized By Contemporaneous Acoustic Emission and Elastic Wave Velocity Measurements. Ph.D. Thesis, University of London (1992). 10.Fonseka G.M., Murrell S.A.F. and Barnes P. Scanning electron microscope and acoustic emission studies of crack development in rocks. Int.J. Rock Mech. Min. Sci. & Geomech. Abstr.22, 273-289 (1985). 11.Holeomb D.J. Memory, relaxation and mierofraeturing in dilatant rock. J. Geophys.Res. 86, 6235-6248 (1981). 12.Holcomb D.J. Using acoustic emissions to determine in-situ stress: problems and promise. Proc. ASME Symp. Mech. Rocks, Soils And Ice, Houston TX. 11-21. ASME, New York (1983). 13.Holeomb D.J. and Martin R.J. Determining peak stress history using acoustic emissions. Proc. 26th US Syrup. on Rock Mech., Rapid City, Nevada. 715-722. A.A.Balkema, Boston (1985). 14.Holcomb D.J. and Costin L.S. Detecting damage surfaces in brittle materials using acoustic emissions. J.AppLMech.108, (1986). 15.Costin L.S. Time-dependent deformation and failure. In Fracture Mechanics Of Rock, Ed. B.K.Atkinson, 167-215. Academic Press, London (1987). 16. ASTM. Standard method for laboratory determination o f pulse velocities and ultrasonic elastic constants of rock. In Vol. 04.08 Std.D, 2845-2883 (1988). 17.Murrell S.A.F. The effect of triaxial stress systems on the strength of rocks at atmospheric temperatures. Geophys.J.R.Astr.Soc.lO, 231-281 (1965). 18.Hoenig A. Elastic moduli of a non-randomly cracked body. lnt.J. Solids Structures. 15, 137-154 (1979). 19.Murrell S.A.F. and Digby P.J. The theory of brittle fracturer initation under triaxial stress conditions. Geophys.J.R.Astron.Soc.19. 1. 309-334. II. 499-512 (1970). 20.Hudson J.A. Wave speeds and attenuation of elastic waves in a material containing cracks. Geophys.J. R.Astron. Soc. 64, 133150 (1981).