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Absolute stress measurements at the rangely anticline, Northwestern Colorado
Int. d. Rock lffeett. Min. $ci. & Geomech. Abstr. Vol. 10. PP- ?$1-755. Perlamon Pt'tm 1973. lh'inttsl in Grtmt Britain
DISCUSSION Discussion of R. V. DE LA CRUZ and C. B. RALEIGH'S* paper A b s o l u t e Stress M e a s u r e m e n t s at the Rangel)" Anticline, Northwestern Colorado by T. C. NICHOLS, JR.,t and R. A. FARROW+ THISdiscussion is primarily directed to (1) errors in presentation o f d a t a and in assumptions made by the authors of Ref. [I] with regard to the U.S. Geological Survey 3-dimensional borehole probe, its construction, and theoretical basis for field application; (2) the implied assumption that the stress field was uniform at each test region in which the various stressmeasuring devices were deployed, and the consequent fallacy that discrepancies in the stress measurements from the various devices reflect mechanical and theoretical differences in techniques rather than variations in the in situ stress field; and (3) the probable(?) existence of residual stress as a contributing factor to the present-day stress field. The authors [I ], in presenting data from the USGS 3-D borehole probe, have shown only two of the three determined principal stresses (determined as ~t and ~,., but reported in [I] as P and Q), and apparently inferred these to be in the horizontal plane. Table I gives the TABLE I. QUOTED DATA AND 3-DIMENSIONAL DATA AS DETERMINED
Quoted data:
Location
Principal stress (psi)
Azimuth reckoned from north (degrees)
P stress
Q stress
41
25
I I* -lit
Site I
( P - Q ) / 2 ~ r max. psi
18 18
3-dimensional data as determined: Directions of principal stresses (plunge and bearing} 01
3" N. 41" E.
0' 2
24° N. 51'W.
Magnitudes of principal stresses (psi)
Magnitude of (at--aj)/2
(psi)
aj
01
~/1
O'j
"rmmI
66° S. 41° E.
25
il
--122
73
* Ret'. [I], Tables 4 and 6. t gcf. [11, Table 7. data both as quoted and as actually determined from the measurements. Figure 1 is a lowerhemisphere equal-area projection, showing the principal stress directions and the plane containing ~,, and
t U.S. Geological Survey; Denver Federal Center, Denver, Colorado 80225, U.S.A. 751
752
DISCUSSION
S
FIci. I. Lower-hemisphere equal-area projection showing the principal stress directions (at, ~,,. ,'.0 and the plane containing ~'t and ¢2.
plane, the secondary principal stress P is approximately equal to ~,, having the same azimtlth of 41 ° reckoned from north, but the secondary principal stress Q . . . . . I I psi is not approximately equal to ~,,. As for the stress determinations from the USGS 3-D borehole probe, t~t: LA CRUZ and RALI~IGIi [I] (p. 628) state: 'The principal stress values are very low, so that the calculated orientations are doubtful', and Ill (p. 632) "The USGS solid inclusion gage, in contrast to the strain type devices, gave stress values that are very low. The cause of this discrepancy is the insensitivity of the technique for measuring low stress levels.' floweret, the principal stress difference (,r t -- cr~ : 147 psi) is sufficiently large to indicate an accurate and reproducible reading. The instrument used was routinely calibrated prior to field installation and checked after recovery by subjecting the overcored annulus containing the borehole probe to an exterior hydraulic load. In both cases, principal stress differences o f 150 psi and larger were easily discernible and reproducible to within =t=10 per cent under replicate conditions. Plunge and bearing directions were repeatable within + 8 °. These values approach the lower limits of resolution, but we believe they are valid. At Rangely the range of 17 :,~ 10-6 strain, monitored on the probe's spherical brass sensor with a modulus of i × 10~' bars, and the corresponding calculated principal stress difference from 25 to --122 psi (147 psi), are in our experience repeatable within 20 per cent. The principal stress directions are repeatable within 16'. The theoretical basis of the USGS 3-D borehole probe has not been criticized by t)~ t.A CRUZ and RAt.J:tOH, but, rather, they question the theory as applied to the tield installation: first, that a solid cylinder was used for the elastic approximation o f a spherical inclusion, and second, that a finite low-modulus material contains the sphere in contrast to the required semi-infinite size of the host [I] (p. 630). The probe behaviour computed for the Rangley anticline and reported herein is based on the approximate elastic solution of a spherical inclusion surrounded by a finite solid cylinder contained within a semi-infinite
DISCUSSION
753
mass of rock. This solution has been approximated by two techniques, as suggested in the original work by NECHOLSet aL [2]. One technique combined the results of two plane strain analyses and the other uses the finite element method applied to an axisymmetric model. The agreement of these two solutions is excellent, and will be described in a forthcoming report. Furthermore, we are using a true 3-dimensional finite element solution for additional verification of behavior. Even the 3-dimensional finite element solution, however, is approximate rather than exact--no matter how well chosen the elements. For a more effective transducer, DE LA CRUZ and RALE,GHsuggested three modifications for the USGS 3-D borehole probe. First, they suggest that temperature compensation be provided for each of the nine active gages in place of a single independent thermal gage. In fact, compensation for thermally induced strains at all nine active gages in the probe is adequate, and conforms to generally accepted procedures. The strain gages used in the probe are so manufactured that thermally induced strains in the sphere are exactly cancelled by an opposite change of resistance of the gages. In addition to this self-compensation, there is an identical gage, bonded to another sphere, encapsulated in the same epoxy but separated from the external force field within an isolated rigid cup at the base of the probe. This gage is used as one compensating arm of a Wheatstone bridge for all of the active gages. Self-heating, at the power levels used, is negligible in both active and compensating gages. The high thermal conductivity of the brass spheres dissipates any local warm spots. The proximity of the active and compensating spheres (less than 7 in.) probably insures that the temperature gradient of the rock mass will not be large enough to cause spurious signals. The only temperature gradient that can affect the readings is caused by the drilling process during overcoring. This gradient is easily prevented either by keeping the drilling fluid temperature constant or by simply halting the drilling and allowing the cored annulus to return to rock temperature. Second, DE LA CRUZ and RALEIGHsuggest a lower modulus sphere for greater sensitivity in lower modulus rock. This is an excellent suggestion, and one on which we have done consider:lble work. We are now routinely using aluminum spheres (E = 0.75 × 106 bars) in field instruments. An experimental instrument, with a polycarbonate sphere (E = 0-30 × l0 s bars), has been constructed and is being tested in the laboratory. Third, they suggested that a more rapidly curing grout would allow time for more readings. Certainly a rapidly curing grout would be ideal, but there are other important considerations for grout properties and a good grouting technique. Determination of the optimum grout for the USGS borehole probe involved a careful laboratory analysis of both desirable and undesirable grout properties [2] (p. 9). Although the field curing time for our selected grout was 48 hr, we believed that the other desirable qualities far outweighed the slow curing time. Thus, we believe that the effectiveness of the transducer should be evaluated in terms of the overall desired grout quality rather than just the time of setting. DE LA CRUZ and RALEIGHhave stated, at various locations in their text, three reasons for not relying on stresses determined at the surface by direct strain measurements: I, [I] (p. 631), the existence of large residual stresses in the rock mass where the strain gages, directly bonded to the rock grains, can detect their relief; 2, [l] (p. 630), the existence of high stress concentrations with resultant destressing by creep or plastic flow and fractures that produce a highly variable stress relaxation; and 3, [I] (p. 627), the efficiency of strain-gage bonding and the condition of the prepared rock surface. Without any supporting quantitative data or discussion, these statements are, in our opinion, inconclusive and misleading. For instance, (l) what evidence is there that residual stress affects only the surface gages; (2) what are the
754
DISCUSSION
reasons for high stress concentrations and plastic flow; and (3) what evidence is there to indicate the degree o f efficiency o f strain-gage bonding or the condition of the prepared rock surface. These factors must be stated specifically before aspersions are cast on the strain-gage data. DE ~ CRUZ and RALEIGHhave briefly mentioned residual and other stress effects on the individual techniques applied. Yet they have not discussed the nature o f residual stress or its effect on the measuring techniques. For instance, they state that the reason for large discrepancies between the strain type and deformation type of stress measurements is [i] (p. 631 ) the existence of large residual stresses in the rock mass where the strain gages, directly bonded to the rock grains, can detect their relief. In contrast, DE t.A CRUZ and RALEIGHstate that the U.S. Bureau o f Mines 3-component borehole deformation gage readings, made at depths o f 61 to 183 cm, cannot detect the residual stresses detected by directly applied surface gages, because the instrument is not bonded to the grains. On the other hand, the USGS 3-dimensional borehole probe, positioned at a depth of 340 cm, was bonded to the grains and thus should have detected any residual stress concentrations. But according to DE tA CRUZ and RAtEmH [i] (p. 632), the instrument was too insensitive to measure the existing stress levels detected by the surface gages. Yet, as previously mentioned, we found in the laboratory that the instrument used for this field investigation was sufficiently sensitive to measure the range o f stresses determined at the surface and should have correctly monitored any higher stress levels if they were existent at 340 cm. Thus there is a suggestion in their article that the residual stresses at the surface are for some reason larger and more variable than at a depth of 340 cm. The statistical methods used by DE tA CRUZ and R^LEIGU are not clear. In their Table 7 [I] (p. 632) the values o f each o f the five methods cannot be validly compared without considering the number of individual observations made and the overall scatter. For instance, more observations at the depths investigated by the USBM and USGS instruments alight reveal that the scatter o f data may indeed be real, and that the stress field is not uniform, as apparently is assumed at each test location. Instead o f concluding that the variation o f stress magnitudes is caused by differences in individual techniques, which has not been conclusively proved, perhaps DE t.A CRUZ and R^LEmH should investigate further the variation of stress magnitudes with depth suggested by the data. For instance, the measurements made on the surface had the largest magnitudes and the greatest range o f variability. The stress data determined from the USBM deformation meter at depths of 61 to 183 cm were of lesser magnitudes than similar data determined at the surface, and P had a more northerly direction. The calculated stress data from the USGS horehole probe at 340 cm had the smallest magnitudes, and P had the most northerly direction. The depths at which the 'doorstopper' gage data were obtained are not indicated, and thus these data are not included in this argument, It can be seen that there is a definite trend for the in situ stress magnitude to decrease and the direction of P to migrate northward with depth. Further measurements should either confirm or negate this trend. DE u CRUZ and R^LEmU conclude that the present stress field dates from either (i) a stress field locally induced by drape folding during the Paleocene-Eocene orogenic episode, or (2) a stress field later than the folding event. It is unclear from this conclusion what the authors [i] interpret the present-day stress field to be; that is, (I) it consists of tectonic forces (i.e. a diminished portion of the fold-producing forces) acting at some distance, (2) it consists o f forces generated locally by mobilized residual stress (we use residual stress as defined by McCUNTOCK and ARGON [3] (p. 420), 'a stress system satisfying internal equili-
DISCUSSION
755
brium, with no external loads or temperature gradients'), or (3) it is some combination of both tectonic and mobilized residual forces. However, it is possible that if residual stresses are present they may be a significant contributing factor to the present-day stress field. The creation of new surfaces by overcoring may have mobilized residual strain energy [4] in such a manner as to mimic a diminished version of a previous stress field. If residual stress is a factor, then how much of a factor is it in the determination of the in situ stresses .9 Fg[EDMAN[5] contends that the in situ state of elastic stress at Site No. I, Rangely, consists in the main of residual stresses stored during the folding event. He based this conclusion on the nature of the outcrop having no present-day applied loads, the orientation of the greatest principal compressive strain (stress) determined from strain-relief work, and the fact that exactly the same orientation for the greatest compressive residual strain was measured on unloaded chips by X-ray diffractometry. Also, the question arises: can enough residual strain energy be mobilized to significantly contribute to the generation of earthquakes at Rangely.9 REFERENCES I. CRUZ R. V. OE LA and RALEIGHC. G. Absolute stress measurements at the Rangely Anticline, Northwestern Colorado. Int. I. Rock Mech. Min. Sci. 9, 625-634 (1972). 2. NICHOt~ T. C., AnEC J. F. and LEE F . T . A solid-inclusion borehole probe to determine three-dimensional stress changes at a point in a rock mass. Bull U.S. Geol. Surv. 1258-C, CI-C28 (1968). 3. McCu~crocK F. A. and ARGONA. S., Eds. Mechum'cal&'havior ofmaterial~, Addison-Wesley, Reading, Massachu~tts (1966). 4. VARNaS D. J. and L ~ F. T. Hypothesis of mobilization of residual stress in rock. Geol. Soc. Am. Bull. 83, 2863-2865 (1972). 5. FRIEO~SAN,M. Residual elastic strains in rock. Tcctonophysics 15, 297-330 (1972).
DISCUSSION Discussion of R. V. DE LA CRUZ and C. B. RALEIGH'S* paper A b s o l u t e Stress M e a s u r e m e n t s at the Rangel)" Anticline, Northwestern Colorado by T. C. NICHOLS, JR.,t and R. A. FARROW+ THISdiscussion is primarily directed to (1) errors in presentation o f d a t a and in assumptions made by the authors of Ref. [I] with regard to the U.S. Geological Survey 3-dimensional borehole probe, its construction, and theoretical basis for field application; (2) the implied assumption that the stress field was uniform at each test region in which the various stressmeasuring devices were deployed, and the consequent fallacy that discrepancies in the stress measurements from the various devices reflect mechanical and theoretical differences in techniques rather than variations in the in situ stress field; and (3) the probable(?) existence of residual stress as a contributing factor to the present-day stress field. The authors [I ], in presenting data from the USGS 3-D borehole probe, have shown only two of the three determined principal stresses (determined as ~t and ~,., but reported in [I] as P and Q), and apparently inferred these to be in the horizontal plane. Table I gives the TABLE I. QUOTED DATA AND 3-DIMENSIONAL DATA AS DETERMINED
Quoted data:
Location
Principal stress (psi)
Azimuth reckoned from north (degrees)
P stress
Q stress
41
25
I I* -lit
Site I
( P - Q ) / 2 ~ r max. psi
18 18
3-dimensional data as determined: Directions of principal stresses (plunge and bearing} 01
3" N. 41" E.
0' 2
24° N. 51'W.
Magnitudes of principal stresses (psi)
Magnitude of (at--aj)/2
(psi)
aj
01
~/1
O'j
"rmmI
66° S. 41° E.
25
il
--122
73
* Ret'. [I], Tables 4 and 6. t gcf. [11, Table 7. data both as quoted and as actually determined from the measurements. Figure 1 is a lowerhemisphere equal-area projection, showing the principal stress directions and the plane containing ~,, and
t U.S. Geological Survey; Denver Federal Center, Denver, Colorado 80225, U.S.A. 751
752
DISCUSSION
S
FIci. I. Lower-hemisphere equal-area projection showing the principal stress directions (at, ~,,. ,'.0 and the plane containing ~'t and ¢2.
plane, the secondary principal stress P is approximately equal to ~,, having the same azimtlth of 41 ° reckoned from north, but the secondary principal stress Q . . . . . I I psi is not approximately equal to ~,,. As for the stress determinations from the USGS 3-D borehole probe, t~t: LA CRUZ and RALI~IGIi [I] (p. 628) state: 'The principal stress values are very low, so that the calculated orientations are doubtful', and Ill (p. 632) "The USGS solid inclusion gage, in contrast to the strain type devices, gave stress values that are very low. The cause of this discrepancy is the insensitivity of the technique for measuring low stress levels.' floweret, the principal stress difference (,r t -- cr~ : 147 psi) is sufficiently large to indicate an accurate and reproducible reading. The instrument used was routinely calibrated prior to field installation and checked after recovery by subjecting the overcored annulus containing the borehole probe to an exterior hydraulic load. In both cases, principal stress differences o f 150 psi and larger were easily discernible and reproducible to within =t=10 per cent under replicate conditions. Plunge and bearing directions were repeatable within + 8 °. These values approach the lower limits of resolution, but we believe they are valid. At Rangely the range of 17 :,~ 10-6 strain, monitored on the probe's spherical brass sensor with a modulus of i × 10~' bars, and the corresponding calculated principal stress difference from 25 to --122 psi (147 psi), are in our experience repeatable within 20 per cent. The principal stress directions are repeatable within 16'. The theoretical basis of the USGS 3-D borehole probe has not been criticized by t)~ t.A CRUZ and RAt.J:tOH, but, rather, they question the theory as applied to the tield installation: first, that a solid cylinder was used for the elastic approximation o f a spherical inclusion, and second, that a finite low-modulus material contains the sphere in contrast to the required semi-infinite size of the host [I] (p. 630). The probe behaviour computed for the Rangley anticline and reported herein is based on the approximate elastic solution of a spherical inclusion surrounded by a finite solid cylinder contained within a semi-infinite
DISCUSSION
753
mass of rock. This solution has been approximated by two techniques, as suggested in the original work by NECHOLSet aL [2]. One technique combined the results of two plane strain analyses and the other uses the finite element method applied to an axisymmetric model. The agreement of these two solutions is excellent, and will be described in a forthcoming report. Furthermore, we are using a true 3-dimensional finite element solution for additional verification of behavior. Even the 3-dimensional finite element solution, however, is approximate rather than exact--no matter how well chosen the elements. For a more effective transducer, DE LA CRUZ and RALE,GHsuggested three modifications for the USGS 3-D borehole probe. First, they suggest that temperature compensation be provided for each of the nine active gages in place of a single independent thermal gage. In fact, compensation for thermally induced strains at all nine active gages in the probe is adequate, and conforms to generally accepted procedures. The strain gages used in the probe are so manufactured that thermally induced strains in the sphere are exactly cancelled by an opposite change of resistance of the gages. In addition to this self-compensation, there is an identical gage, bonded to another sphere, encapsulated in the same epoxy but separated from the external force field within an isolated rigid cup at the base of the probe. This gage is used as one compensating arm of a Wheatstone bridge for all of the active gages. Self-heating, at the power levels used, is negligible in both active and compensating gages. The high thermal conductivity of the brass spheres dissipates any local warm spots. The proximity of the active and compensating spheres (less than 7 in.) probably insures that the temperature gradient of the rock mass will not be large enough to cause spurious signals. The only temperature gradient that can affect the readings is caused by the drilling process during overcoring. This gradient is easily prevented either by keeping the drilling fluid temperature constant or by simply halting the drilling and allowing the cored annulus to return to rock temperature. Second, DE LA CRUZ and RALEIGHsuggest a lower modulus sphere for greater sensitivity in lower modulus rock. This is an excellent suggestion, and one on which we have done consider:lble work. We are now routinely using aluminum spheres (E = 0.75 × 106 bars) in field instruments. An experimental instrument, with a polycarbonate sphere (E = 0-30 × l0 s bars), has been constructed and is being tested in the laboratory. Third, they suggested that a more rapidly curing grout would allow time for more readings. Certainly a rapidly curing grout would be ideal, but there are other important considerations for grout properties and a good grouting technique. Determination of the optimum grout for the USGS borehole probe involved a careful laboratory analysis of both desirable and undesirable grout properties [2] (p. 9). Although the field curing time for our selected grout was 48 hr, we believed that the other desirable qualities far outweighed the slow curing time. Thus, we believe that the effectiveness of the transducer should be evaluated in terms of the overall desired grout quality rather than just the time of setting. DE LA CRUZ and RALEIGHhave stated, at various locations in their text, three reasons for not relying on stresses determined at the surface by direct strain measurements: I, [I] (p. 631), the existence of large residual stresses in the rock mass where the strain gages, directly bonded to the rock grains, can detect their relief; 2, [l] (p. 630), the existence of high stress concentrations with resultant destressing by creep or plastic flow and fractures that produce a highly variable stress relaxation; and 3, [I] (p. 627), the efficiency of strain-gage bonding and the condition of the prepared rock surface. Without any supporting quantitative data or discussion, these statements are, in our opinion, inconclusive and misleading. For instance, (l) what evidence is there that residual stress affects only the surface gages; (2) what are the
754
DISCUSSION
reasons for high stress concentrations and plastic flow; and (3) what evidence is there to indicate the degree o f efficiency o f strain-gage bonding or the condition of the prepared rock surface. These factors must be stated specifically before aspersions are cast on the strain-gage data. DE ~ CRUZ and RALEIGHhave briefly mentioned residual and other stress effects on the individual techniques applied. Yet they have not discussed the nature o f residual stress or its effect on the measuring techniques. For instance, they state that the reason for large discrepancies between the strain type and deformation type of stress measurements is [i] (p. 631 ) the existence of large residual stresses in the rock mass where the strain gages, directly bonded to the rock grains, can detect their relief. In contrast, DE t.A CRUZ and RALEIGHstate that the U.S. Bureau o f Mines 3-component borehole deformation gage readings, made at depths o f 61 to 183 cm, cannot detect the residual stresses detected by directly applied surface gages, because the instrument is not bonded to the grains. On the other hand, the USGS 3-dimensional borehole probe, positioned at a depth of 340 cm, was bonded to the grains and thus should have detected any residual stress concentrations. But according to DE tA CRUZ and RAtEmH [i] (p. 632), the instrument was too insensitive to measure the existing stress levels detected by the surface gages. Yet, as previously mentioned, we found in the laboratory that the instrument used for this field investigation was sufficiently sensitive to measure the range o f stresses determined at the surface and should have correctly monitored any higher stress levels if they were existent at 340 cm. Thus there is a suggestion in their article that the residual stresses at the surface are for some reason larger and more variable than at a depth of 340 cm. The statistical methods used by DE tA CRUZ and R^LEIGU are not clear. In their Table 7 [I] (p. 632) the values o f each o f the five methods cannot be validly compared without considering the number of individual observations made and the overall scatter. For instance, more observations at the depths investigated by the USBM and USGS instruments alight reveal that the scatter o f data may indeed be real, and that the stress field is not uniform, as apparently is assumed at each test location. Instead o f concluding that the variation o f stress magnitudes is caused by differences in individual techniques, which has not been conclusively proved, perhaps DE t.A CRUZ and R^LEmH should investigate further the variation of stress magnitudes with depth suggested by the data. For instance, the measurements made on the surface had the largest magnitudes and the greatest range o f variability. The stress data determined from the USBM deformation meter at depths of 61 to 183 cm were of lesser magnitudes than similar data determined at the surface, and P had a more northerly direction. The calculated stress data from the USGS horehole probe at 340 cm had the smallest magnitudes, and P had the most northerly direction. The depths at which the 'doorstopper' gage data were obtained are not indicated, and thus these data are not included in this argument, It can be seen that there is a definite trend for the in situ stress magnitude to decrease and the direction of P to migrate northward with depth. Further measurements should either confirm or negate this trend. DE u CRUZ and R^LEmU conclude that the present stress field dates from either (i) a stress field locally induced by drape folding during the Paleocene-Eocene orogenic episode, or (2) a stress field later than the folding event. It is unclear from this conclusion what the authors [i] interpret the present-day stress field to be; that is, (I) it consists of tectonic forces (i.e. a diminished portion of the fold-producing forces) acting at some distance, (2) it consists o f forces generated locally by mobilized residual stress (we use residual stress as defined by McCUNTOCK and ARGON [3] (p. 420), 'a stress system satisfying internal equili-
DISCUSSION
755
brium, with no external loads or temperature gradients'), or (3) it is some combination of both tectonic and mobilized residual forces. However, it is possible that if residual stresses are present they may be a significant contributing factor to the present-day stress field. The creation of new surfaces by overcoring may have mobilized residual strain energy [4] in such a manner as to mimic a diminished version of a previous stress field. If residual stress is a factor, then how much of a factor is it in the determination of the in situ stresses .9 Fg[EDMAN[5] contends that the in situ state of elastic stress at Site No. I, Rangely, consists in the main of residual stresses stored during the folding event. He based this conclusion on the nature of the outcrop having no present-day applied loads, the orientation of the greatest principal compressive strain (stress) determined from strain-relief work, and the fact that exactly the same orientation for the greatest compressive residual strain was measured on unloaded chips by X-ray diffractometry. Also, the question arises: can enough residual strain energy be mobilized to significantly contribute to the generation of earthquakes at Rangely.9 REFERENCES I. CRUZ R. V. OE LA and RALEIGHC. G. Absolute stress measurements at the Rangely Anticline, Northwestern Colorado. Int. I. Rock Mech. Min. Sci. 9, 625-634 (1972). 2. NICHOt~ T. C., AnEC J. F. and LEE F . T . A solid-inclusion borehole probe to determine three-dimensional stress changes at a point in a rock mass. Bull U.S. Geol. Surv. 1258-C, CI-C28 (1968). 3. McCu~crocK F. A. and ARGONA. S., Eds. Mechum'cal&'havior ofmaterial~, Addison-Wesley, Reading, Massachu~tts (1966). 4. VARNaS D. J. and L ~ F. T. Hypothesis of mobilization of residual stress in rock. Geol. Soc. Am. Bull. 83, 2863-2865 (1972). 5. FRIEO~SAN,M. Residual elastic strains in rock. Tcctonophysics 15, 297-330 (1972).