Absolute stress measurements at the rangely anticline, Northwestern Colorado

Int. J. Rock Mech. Min. Sci. Vol. 9, pp. 625-634. Pergamon Press 1972. Printed in Great Britain

ABSOLUTE

STRESS MEASUREMENTS

ANTICLINE,

NORTHWESTERN

AT THE

RANGELY

COLORADO

R. V. DE LA CRUZ and C. B. RALEIGH National Center for Earthquake Research, U.S. GeologicalSurvey, Menlo Park, California (Received 2 November 1971) Abstract--Five different methods of measuring absolute state of stress in rocks in s i t u were used at sites near Rangely, Colorado, and the results compared. For near-surface measurements, overcoring of the borehole-deformation gage is the most convenient and rapid means of obtaining reliable values for the magnitude and direction of the state of stress in rocks in situ. The magnitudes and directions of the principal stresses are compared to the geologic features of the different areas of measurement. The in situ stresses are consistent in orientation with the stress direction inferred from the earthquake focal-plane solutions and existing joint patterns but inconsistent with stress directions likely to have produced the Rangely anticline. INTRODUCTION

THE purposes of this project are three-fold: first, to assess the suitability of each technique in the determination ot the absolute state of stress in rocks in situ; second, to compare the results obtained by the different methods as they are applied under similar conditions in a given rock mass; and third, to correlate the surface stress distribution to the geologic features, such as location of measurement with respect to the anticline and existing jointing patterns. Numerous techniques have been developed for the determination of the state of stress in rocks in situ. Unfortunately, most of these methods are feasible only at relatively shallow depths, less than about 40 ft, and become economically and practically prohibitive at greater depths. These methods are all based on the principle of complete stress relief either by overcoring, in which a smaller instrumented pilot hole is overcored by a larger concentric hole, or by trepanning, in which slots are created by diamond saws or overlapping drill holes. Generally, each method has been designed, calibrated and tested independently of all other existing techniques. Some attempts at comparative evaluation of the more common stress-measuring techniques were carried out by a few investigators, such as BONNECHERRE[1] and VAN HEERDEN et al.[2]. Bonnecherre's findings showed very high scatter in spite of exceptional care in the testing program and concluded that the results from current techniques should not be relied upon within -4-20 or 30 ~ of the mean values. Van Heerden, on the other hand, comparing only two techniques, concluded that good agreement in both magnitude and direction of the principal stresses were obtainable. This contradictory conclusion and the desirability of determining which of the current stress-measuring methods is the most suitable initiates this study. Suitability of the technique is defined, for the purposes of this investigation as: ease of carrying out field tests; accuracy and reproducibility of results; and soundness of the theoretical background of the method. The absolute stress-measurement tests were carried out in exposures of Mesa Verde sandstone at three different sites on the Rangely anticline in northwestern Colorado. The 625

626

R.V. DE LA CRUZ AND C. B. RALEIGH

sites were specially chosen to provide some indication o f the stress distribution on the different parts of the anticline; e.g. nose o f the anticline, and the north and south flanks o f the anticline. The directions of principal stresses may also be c o m p a r e d with those derived from focal-plane solutions o f earthquakes at Rangely. The mechanical properties of the rock were obtained in the laboratory in the usual manner. The calculated Y o u n g ' s modulus and Poisson's ratio o f the Mesa Verde sandstone were 0.75 × l06 psi and 0.20, respectively. METHODS AND RESULTS OF MEASUREMENTS

USB M three-component borehole.deformation gage The borehole-deformation m e t h o d o f absolute stress measurement consists o f placing a transducer in a previously drilled pilot hole to detect the diametral deformation when a larger concentric hole is drilled, thereby relieving the stresses existing in the core prior to the overcoring operation. A detailed description o f the method and the theoretical relationships between the measured deformation and the initial state o f stress is covered in the literature and will not be repeated here [3]. This m e t h o d may be considered at the m o m e n t as the standard m e t h o d for measuring stresses in rock in situ. Its principal disadvantage relative to the other methods studied here lies in the purely mechanical coupling between the instrument and the borehole walls. A total o f 16 measurements at depths f r o m 2 to 6 ft were carried out with this technique, six each in sites 1 and 3 and only four in site 2 (Fig. 1). The calculated values for the principal stresses and their orientations are shown in Table I. In site n u m b e r 1, the nose o f the anticline, the major principal stresses vary f r o m a low o f 5 psi in tension to a high o f 153 psi in compression; while the minor principal stresses have a low o f 6 psi in tension and a high o f 112 psi in compression. These extreme values were recorded from two different sites (2 and TABLE 1. SUMMARY OF RESULTS--USBM THREE-COMPONENT BOREHOLE-DEFORMATION GAGE

Location Site 1, nose of anticline (6 measurements)

Average values Site 2, North flank of anticline (4 measurements)

Azimuth reckoned north (deg.)

Site 3, South flank of anticline (6 measurements)

Average values

7"max (psi)

48 67 50 6 128 77 63

81 5 70 67 103 153 78

22 --6 33 43 31 112 39

29 1 18 12 36 20 19

142 20

49 74

32 12

139 100

114 98 44 106 90

106 141 75 125 68 67 97

139 29 -- 15 136 72 162 87

100

Average values

( P - Q)/2 Principal stress (psi) P-Stress Q-Stress

N.B. Sign convention: positive is compression.

31

6

13 42

46 24

90 4 --22 123 59 120 62

24 12 3 6 7 21 12

ABSOLUTE STRESS MEASUREMENTS AT THE RANGELY ANTICLINE

627

6) and result in a fairly wide spread in the principal stress values. If these two measurements are discarded, the resulting stress values are quite consistent. The extreme azimuths of the principal stresses are 6-128 ° but the orientations of the other measurements are very close to each other. It is not uncommon to average several stress measurements to give a mean value representative of the site. When this is done, the average major and minor principal stresses are 78 and 39 psi, both in compression with an orientation of N63°E for the major principal stress. The maximum shear stresses, (P-Q)/2, also shown in the table indicate that when only the principal stress differences are considered, fairly consistent measurement values are obtainable. Essentially similar analysis and conclusions can be made with the readings carried out at the north and south flanks of the anticline. Direct strain-gage technique

The direct strain-gage technique of measuring the absolute state of stress in rocks in situ consists of bonding single-element or multiple-element electric resistance strain gages at a prepared surface of the rock and overcoring the gage locations [4]. The theoretical details are straightforward and the actual operation is simple but care must be exercised in completely waterproofing the gages and its lead wires in order to obtain representative values. Four measurements were carried out using this technique, all at site 1. A summary of the results are given in Table 2. The major principal stresses vary from a minimum of 103 psi and a maximum of 437 psi; while the minor principal stresses vary from 29 to 231 psi, all compressive. These large differences between measurements is not unexpected if we consider that electric resistance strain gages are extremely sensitive to the efficiency of bonding to the rock surface as well as to the condition of the prepared rock surface. The calculated orientations of the principal stresses were, however, very close to each other varying from N61 °E to N88°E. Also the shear stresses were fairly consistent from one measurement to the other except for measurement number 4. TABLE 2. SUMMARY OF RESULTS---DIRECT STRAIN-GAGE TECHNIQUE

Location Site 1, Nose of anticline (4 measurements) Average values

Azimuth reckoned north (deg.) 73 63 88 61 71

Principal stress (psi) P-Stress Q-Stress 388 186 437 103 278

231 48 268 29 144

( P - Q)/2 = rmax (psi)

78 69 85 37 67

' Doorstopper' technique

The 'doorstopper' method of measuring the absolute state of stress in rocks is similar to the direct strain-gage technique, the only distinction being that the strain gages are already initially potted to the base of a low-modulus cylindrical solid [5]. The doorstopper is glued to the prepared bottom face of a previously drilled hole and overcoring follows. There are some difficulties involved in the theoretical relationship between the stresses measured at the bottom of the hole to the field stresses. Obtaining a perfect bond between the rock surface and the strain-gage instrumented disc is fairly difficult in vertical holes drilled downward.

628

R.V. DE LA CRUZ AND C. B. RALEIGH

Four measurements were carried out at the three sites, two of them at the nose of the anticline (site 1). The calculated values are given in Table 3. The average stresses in site 1 showed a compressive major principal stress of 395 psi but the minor principal stress is tensile at 431 psi. These values for the tensile stresses seem high as the uniaxial tensile strength of the rock is unlikely to exceed a few hundred psi. The stress values at the other two sites were not any more reasonable and are extremely doubtful. The only fairly consistent results are the calculated orientations where only a difference of 7 ° was obtained in site 1. TABLE 3. SUMMARY OF RESULTS--'DoORSTOPPER' TECHNIQUE

Azimuth reckoned north (deg.)

Location

Principalstress (psi) P-Stress Q-Stress

( P - Q)/2 ~max (psi)

Site 1, nose of anticline (2 measurements) Average values

92 85 87

529 262 395

-530 -332 --431

530 297 413

Site 2, North flank of anticline (1 measurement)

93

14

--48

31

South flank of anticline (1 measurement)

89

400

116

258

Site 3,

--

USGS nine-component spherical gage The USGS nine-component spherical gage, developed in Denver by NICHOLS et al. [6] involves the cementing of an encapsulated sphere in a drill hole and then overcoring the entire device. Three strain-gage rosettes bonded orthogonally at the surface of the sphere detects any deformation in the relieving operation. This gage can theoretically determine the complete state of stress from a single installation. There are no major deficiencies inherent in the technique but in soft-rock types, the device may need some modification. Only one measurement was carried out using this method and the result is shown in Table 4. The principal stress values are very low so that the calculated orientations are doubtful. TABLE 4. SUMMARY OF R E S U L T s - - U S G S SPHERICAL GAGE

Location

Azimuth reckoned north (deg.)

Site 1, nose of anticline (1 measurement)

41

Principal stress (psi) P-Stress Q-Stress 25

11

( P - Q)/2 = Tmax (psi) 18

Photoelastic strain-gage technique The photoelastic strain-gage technique consists of bonding photoelastic rosettes on the prepared surface of the rock and overcoring the installation [7]. Readings were taken before and after overcoring and several more times afterwards until the rock-gage system had stabilized. This technique is fairly sensitive to atmospheric variations in temperature.

ABSOLUTE STRESS MEASUREMENTS AT THE RANGELY ANTICLINE

629

Nine measurements within a limited area of the nose of the anticline were carried out with this technique (Table 5). The values of the principal stresses alternated from compression to tension for both the major and minor components in the several measurements. Very high tensile stresses will also be noted for the minor principal stresses and it is very doubtful that the rock mass can withstand such tensile stresses without fracturing. The average of the nine measurements still shows the principal stresses to be very high and of opposite sign. The predicted stress directions, however, are very close to one another and here the value o f this technique may be realized.

TABLE 5. SUMMARY OF RESULTS--PHOTOELASTIC ROSETTES TECHNIQUE

Location

Azimuth reckoned north (deg.)

Site 1, nose of anticline (9measurements)

80 75 63 88 80 84 69 73 83 77

Average values

( P - Q)/2 Principal stress (psi) P-Stress Q-Stress 455 265 440 -120 -29 100 295 250 310 218

-515 29 310 -265 --280 --175 --29 --120 75 --108

zmax (psi) 485 118 65 73 125 138 162 185 118 163

COMPARISON OF THE DIFFERENT METHODS The comparison of the different stress-measuring techniques is made less meaningful by the different number of measurements carried out by each method especially when only one measurement is obtained by a method. With the USGS nine-component spherical gage, two tests were carried out but one installation was unsuccessful due to the inadequate cementation between the gage and the rock, and, therefore, only one set of data was considered acceptable. Nevertheless, it will be attempted here to compare the desirability of the different techniques based not only on the results of the field measurements but also on the practical difficulties and inaccuracies inherent in the technique and in the soundness of its theoretical basis.

Soundness of the theoretical basis Theoretically, of the five different techniques presented here, the 'doorstopper' technique has the weakest basis, mainly because the governing equations for the reduction of measured values into the field stresses were obtained empirically since the solution for the stress distribution at the b o t t o m face of a hole cannot be obtained analytically. This prompted the first author to determine a more accurate transformation formula by using approximate solution techniques using numerical procedures, specifically the finite-element method of stress analysis. The resulting equations which is considered more accurate than those previously applied are [8]:

630

R.V. DE LA CRUZ AND C. B. RALEIGH ~111 = 1.30 ~"11 + (0.085 + 0-15v--v 2) T'22 "~- (0"473 + 0"91 0 T'33 ~122 ~-- 1.30 r'22 + (0"085 + O'15v--v z) ~-*11 + (0-473 + 0.9Iv) 7*33 ~112 = (1"423 -- 0.027v) ~"12

where the axis of the hole is in the X3 direction, and: ~Ij = calculated stresses at the center of the bottom of the hole 7*ij = field stresses v

= Poisson's ratio of the rock.

The theoretical basis of the USGS spherical-gage technique is not in question per se but the assumptions in the theory are already quite different from the conditions in the actual field installation. Firstly, a solid cylinder was used for the elastic approximation of a spherical inclusion. Besides this approximation, the construction of the probe is such that the solid sphere is bounded by only one diameter of low-modulus material (epoxy host cylinder) in contrast to the required semi-infinite size of the host (2-3 times the diameter of the sphere is practically equivalent to an infinite medium according to St. Venant's principle). With these inaccuracies and the additional cementing agent still to be introduced into the hole, we have in actuality, the transmission of the external force fields through the cementing agent (the same epoxy material as the cylinder) to the cylindrical host and finally into the instrumented sphere. This complex boundary-value problem is admittedly theoretically intractable, at least to the authors, but the finite-element method of stress analysis in its present stage of development could handle this problem quite readily. The complete theoretical basis of the USGS spherical-gage technique as now presently constructed will be presented in a later paper. The theoretical basis of the other methods, borehole-deformation method, photoelastic strain-gage technique and the direct strain-gage technique, are certainly sound. However, there are practical difficulties involved as well as inaccuracies in all the methods. Practical difficulties and inaccuracies in the techniques The practical difficulties and inaccuracies in the direct strain-gage technique, the photoelastic strain-gage technique, and the 'doorstopper' technique are similar since, as we have mentioned earlier, they all involve strain gages bonded into the rock for measurement of surface strains. The major objection to making measurement of strain on the free surface is that, besides the surface being acted upon by high stress concentrations and resultant destressing by creep or plastic flow, the natural and induced fractures in the rock produces also a highly variable stress relaxation in the surface. These factors make it virtually impossible to interpret surface measurements with any degree of confidence. Further, the size of the strain gage used relative to the grain sizes of the rock are extremely significant since the strain readings are dependent on the number and type of minerals of the grains involved in the measurement. Also, small surface irregularities affect not only the bonding but also the strain readings obtainable. For the 'doorstopper' technique, the required flattening of the end face of the borehole before the installation of the gage, changes the location of measurement and thus would introduce error into the computation. It is also very likely that fracturing at the corners of flat-bottom holes could occur especially in regions of high stress fields making uncertain the applicability of the derived stress coefficients. This suggests consideration of hemispherically bottomed holes as used by HOSKINS[9].

ABSOLUTE STRESS MEASUREMENTS AT THE RANGELY ANTICLINE

631

The USGS solid-inclusion gage requires modification in its current design for it to be a more effective transducer. Firstly, adequate temperature compensation should be provided for each of the nine active gages instead of a single independent thermal gage. Secondly, the extremely high modulus of the sphere makes the present design unsuitable for very lowmodulus type rocks especially when the state of stresses being considered are very low. This means the use of relatively lower modulus for the inclusion. Finally, the use of much faster curing time for the cementing agent is suggested in order to obtain more measurements in a given time. The USBM borehole-deformation gage has the least practical problems, although they could be quite serious. Firstly, more adequate seals should be provided for the contact buttons to prevent water and dust from entering into the electric resistance strain-gage locations. Secondly, independent extend-retract mechanisms for the contact buttons would allow much easier installation and a more certain solid contact between rock and transducer. Finally, the support provided primarily by the contact buttons and secondarily by the steel springs are inadequate in holding the gage stationary during the overcoring operation. Any slight motion or displacement of the gage would invalidate any measurements.

Comparison offield measurements A summary of the results of absolute stress measurements by the five different techniques are presented in Table 6. Since all the methods were tested in only one site, the results in this site are the only ones that can be compared (Table 7). Techniques employing surface measurement of strain (direct strain gage, photoelastic strain gage, and 'doorstopper') give results that are much higher than those obtained by either the deformation gage or the solidinclusion gage. These quite persistent large discrepancies between the strain type and the deformation type of stress measurement may be inferred as due to the existence of large residual stresses in the rock mass where the strain gage, being directly bonded to the grains, can detect their relief during overcoring while the deformation gage could not. A detailed explanation of the basis of this inference may be obtained from DE LA CRUZ [10]. TABLE6.

SUMMARY OF RESULTS--ABSOLUTESTRESSMEASUREMENTS

Azimuth reckoned north Principal stress (psi) (deg.) P-Stress Q-Stress USBM three-component gage Site 1 63 Site 2 100 Site 3 97 Direct strain gage Site 1 71 'Doorstopper' technique Site 1 88 Site 2 93 Site 3 89 USGS spherical gage Site 1 41 Photoelastic rosettes technique Site 1 77

Tma~ (psi)

Number of measurements

78 90 87

39 42 62

19 24 12

6 4 6

278

144

67

4

322 13 313

--348 --38 --105

335 26 209

2 1 1

25

11

18

1

218

--108

163

9

N.B. Sign convention: positive is compression.

632

R.V.

DE LA CRUZ AND C. B. RALEIGH

TABLE 7. COMPARISON OF AVERAGE VALUES OBTAINED AT SITE 1 USING FIVE DIFFERENT METHODS

Azimuth reckoned north (deg.)

Method of measurement Borehole deformation method Direct strain-gage technique 'Doorstopper' technique Spherical-gage method Photoelastie strain-gage technique Average values

(P-- Q)/2 ~ ~

Principal stress (psi) P-Stress Q-Stress

63 71 88 41 77 68

78 278 322 25 218 184

39 144 -348 -ll -108 -52

*m.~x (psi) 19 67 335 18 163 120

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. The principal stress values obtained by the borehole-deformation gage appears most reasonable and in fact are more consistently reproducible within a very narrow range. The magnitudes of the principal stresses relative to the results of the other four techniques are somewhat intermediate between the very low values obtained by the USGS spherical gage and the very high values obtained by strain-type devices. Notwithstanding this wide scatter in the magnitudes of the principal stresses obtained by the different methods, it is encouraging to note that the calculated orientations of the principal stresses are very close to one another. This agreement is made more precise if we disregard the doubtful value obtained by the solid-inclusion gage (because of the very low stresses obtained by this method, the accuracy of the calculated orientation is also greatly affected). Finally, considering all the factors involved in the evaluation of the suitability of the techniques in measuring the absolute state of stress in rocks, unfortunately for near-surface measurements only, factors such as: (1) soundness of the theoretical background of the method (2) practical difficulties and inaccuracies in the technique (3) ease of field operation, and (4) accuracy and reproducibility of results it is concluded that, at least at the present state of development, the borehole-deformation type appears most suitable for measuring the absolute state of stress in rocks. DISCUSSION AND CONCLUSIONS R e l a t i o n o f surface stresses to geologic structures

The orientations of the principal horizontal stresses measured at the three sites are shown in Fig. 1. Except for site 1, alongside the plunging nose of the anticline, the maximum compressive stress is oriented parallel to the axis of the Rangely anticline. If the Rangely structure were formed by buckling in a horizontal compression, the maximum principal stress at the initiation of folding would be perpendicular to the fold axis. If, however, drapefolding over a buried fault took place, the maximum principal stress al, might be vertical and the larger of the horizontal principal stresses parallel to the fold axis. It seems equally plausible, however, that the stresses measured data from some time later than the folding.

ABSOLUTE STRESS MEASUREMENTS AT THE RANGELY ANTICLINE

633

Principal stresses at different points of anticline by the borehole deformation method and mean principal stress directions a t

--

--

--

\\

~N

°

1

~[

'Kilometers FIG. 1

The Rangely anticline was most probably developed during the Paleocene-Eocene orogenic episodes in which major structures of the Uinta Basin were formed. Other structures present in the area may be consistent with the measured stress directions. The relatively massive Mesa Verde sandstone in the N50°W plunging nose of the Rangely anticline, although not too highly fractured, contains joints spaced about 6 ft apart with less conspicuous joints at closer intervals. The joints which are ubiquitous may be classified into three joint sets as measured by BROWN [11]. They are essentially vertical and have average strikes of E-W, N26°W and N44°E. A plot showing the orientation of the three joint sets (conveniently drawn in a triangle) together with the principal stresses and an extension of the anticlinal axis is shown in Fig. 2. The maximum horizontal stress bisects the joint sets 1 and 3 (J1 and Ja) which suggests that these joints are shear fractures lying at an angle of about 25 ° to ,/i. \

\ \

-..,/\/ J3

Jz

\

PIG. 2 ROCK

9/5--E

\

\

634

R. V. DE LA CRUZ AND C. B. RALEIGH

P r e l i m i n a r y evidence f r o m f o c a l - p l a n e solutions for the R a n g e l y e a r t h q u a k e s a p p e a r s to agree with the directions o f the surface stresses (Fig, 1). In the s o u t h e r n m a r g i n o f the field, f r o m these solutions c o m p r e s s i o n (J1) axes, lie W N W , with tension (J3) being h o r i z o n tal a n d N N E . These results are consistent with surface m e a s u r e m e n t s a l o n g the flanks o f the R a n g e l y structure. M e a s u r e m e n t s o f residual stresses in core, p e t r o f a b r i c m e a s u r e m e n t s o f d e f o r m a t i o n lamellae in q u a r t z a n d c o m p i l a t i o n o f larger n u m b e r s o f e a r t h q u a k e d a t a are being p r e s e n t l y c o n d u c t e d a n d c o m p a r i s o n o f these results will f o r m the basis for a m o r e c o m p r e h e n s i v e study. In conclusion, m e a s u r e m e n t o f in s i t u stress in shallow b o r e h o l e s a p p a r e n t l y can p r o v i d e valuable d a t a on the o r i e n t a t i o n , a n d a p p r o x i m a t e l y the m a g n i t u d e , o f the p r e s e n t state o f stress in rocks. The m e t h o d f o u n d to be m o s t convenient in p r a c t i c e is overcoring using the b o r e h o l e - d e f o r m a t i o n gage o f the U.S. Bureau o f Mines. Large n u m b e r s o f m e a s u r e m e n t s are an i m p o r t a n t r e q u i r e m e n t in the d e t e r m i n a t i o n o f the stress field in o u t c r o p s where n a t u r a l fractures give rise to significant i n h o m o g e n e i t y . Acknowledgments--The authors gratefully acknowledge the following investigators for permission to use the results of their in situ state-of-stress measurements at outcrops of the Mesa Verde sandstone of the Rangely anticline, northwestern Colorado. Drs J. HANI)INand D. W. SXEARNSof the Center for Tectonophysics, Texas A & M University, used foilresistance gages and A. BROWN used photoelastic gages. Mr R. A. FARROWand associates of the U.S. Geological Survey, Denver, Colorado, used the three-dimensional solid inclusion borehole probe developed by T. C. NICHOLSet al. The assistance of D. ANDERSON,U.S. Geological Survey, Menlo Park, California, in the testing by the authors of the 'doorstopper' technique and the three-component borehole-deformation method is also acknowledged.

REFERENCES 1. BONNECHERREF. A Comparative Field Study of R o c k Stress Determination Techniques, Technical Report No. 1-69, Missouri River Division, Corps of Engineers, Omaha, Nebraska (1969). 2. HEERDENW. L. VAN and GRANT F. A comparison of two methods of measuring stress in rock. Int. J. Rock Mech. Min. Sci. 4, 367-382 (1967). 3. OLSEN O. J. Measurement of residual stresses by the strain relief method. Colo. Sch. Mines Q. 52, 185-204 (1957). 4. HANDIN J. Studies in Rock Fracture, Twelfth Quarterly Technical Report, Texas A & M Research Foundation, Texas (1971). 5. LEEMANE. R. A Trepanning Stress Relieving Technique for Rock Stress Measurements, Proceedings o f the Sixth Symposium on Rock Mechanics (E. M. Spokes, Ed.) Rolla, Missouri, pp. 407-426 (1964). 6. NICHOLST. C., ABELJ. F. and L~E 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, C1-C28 (1968). 7. EMERY C. L. In situ Measurements applied to Mine Design, Proceedings o f the Sixth Symposium on Rock Mechanics (E. M. Spokes, Ed.) Rolla, Missouri, pp. 218-230 (1964). 8. CRuz R. V. DE LA The Borehole Deepening Method o f Absolute Stress Measurement, Ph.D. Dissertation, University of California, Berkeley (1969). Unpublished. 9. HOSKINS E. R. Strain rosette relief measurements in hemispherically ended boreholes. Int. J. Rock Mech. Min. Sci. 5, 551-559 (1968). 10. CRUZ R. V. DE LA Mechanism of existence and release of residual stresses in rocks. To be published. 11. BROWNA. Private communication (1970).