Int. 1. Rock Mech. Min. Set. Vol. 9, pp. 625-634. Pergamon Press 1972. Printed in Great Britain
ABSOLUTE STRESS MEASUREMENTS AT THE RANGELY
ANTICLINE, NORTHWESTERN COLORADO
R. V. DE LA CRUZ and C. B. RALEIGH
National Center for Earthquake Research,
U.S. Geological Survey, Menlo Park, California
(Received! November 1971)
Abstract—Five different methods of measuring absolute state of stress in rocks in situ 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
5)
THE purposes of this project are three-fold: first, to assess the suitability of each technique
in the determination of 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[! ]
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 ±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
R. V. DE LA CRUZ AND C. B. RALEIGH
ABSOLUTE STRESS MEASUREMENTS AT THE RANGELY ANTICLINE
sites were specially chosen to provide some indication of the stress distribution on the
different parts of the anticline; e.g. nose of the anticline, and the north and south flanks of
the anticline. The directions of principal stresses may also be compared with those derived
from focal-plane solutions of earthquakes at Rangely. The mechanical properties of the
rock were obtained in the laboratory in the usual manner. The calculated Young's modulus
and Poisson's ratio of the Mesa Verde sandstone were 0-75 x 106 psi and 0-20, respectively.
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.
626
METHODS AND RliSULTS OK MEASUREMENTS
USBM three-component borehole-deformation gage
The borehole-deformation method of absolute stress measurement consists of 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 ovcrcoring operation. A detailed description of the method and the theoretical relationships between the measured deformation and the initial state of stress is covered in the
literature and will not be repeated here [3]. This method may be considered at the moment
as the standard method 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 of 16 measurements at depths from 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 1. In site number 1, the nose of the anticline, the major principal stresses vary from a low of 5 psi in tension to a high of 153 psi in
compression; while the minor principal stresses have a low of 6 psi in tension and a high of
I 12 psi in compression. These extreme values were recorded from two different sites (2 and
TABLE 1. SUMMARY OK RESULTS—USHM iHRi.i:-coMi*ONLNr uoRtuoi.E-nbKJRMAiioN I;A(;C
Location
Site 1, nose of anticline
(6 measurements)
A/iimith
reckoned north
(deg.)
128
77
63
81
-5
70
67
103
153
78
29
1
18
12
36
20
19
142
20
I(X)
139
I(K)
114
98
44
106
90
49
74
31
13
42
32
12
6
4(>
24
106
141
75
125
68
67
97
139
29
-15
136
72
162
87
90
4
24
12
3
6
7
21
12
48
67
50
Average values
Average values
Site 3, South Hank of anticline
(6 measurements)
Average values
N.B. Sign convention: positive is compression.
•>•>
123
59
120
62
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.
(/" - C')/2
T,,,,,
(psi)
22
-6
33
43
31
112
39
6
Site 2, North Hank of anticline
(4 measurements)
Principal stress (psi)
0-Stress
/'-Stress
627
TABLE 2. SUMMARY OK RLSULTS—DIRECT STRAIN-GAUE TEC .•UNIQUE
Locution
Site 1, Nose of anticline
(4 measurements)
Average values
Azimuth
reckoned north
(deg.)
73
63
88
61
71
Principal stress (psi)
/"-Stress
C-Stress
388
186
437
103
278
231
48
268
29
144
(f - - 0)/2
(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.
R. V. DE LA CRUZ AND C. 13. RALEIGH
ABSOLUTE STRESS MEASUREMENTS AT THE RANGELY ANTICLINE
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.
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
of this technique may be realized.
628
629
TABLE 3. SUMMARY OK RESULTS— 'DOORSTOPPER' TECHNIQUE
Azimuth
(deg.)
Location
42
85
87
529
262
395
Site 2, North flank of anticline
(1 measurement)
93
14
Site 3, South flank of anticline
(1 measurement)
89
400
Site 1, nose of anticline
(2 measurements)
Average values
-530
-332
-431
-48
-116
?n»I
(psi)
530
297
413
31
TABLE 4. SUMMARY OK RLSULIS—USGS SPHERICAL GACJK.
Location
Site I, nose of anticline
(1 measurement)
41
• - C»/2
Principal stress (psi)
/'-Stress
C-Stress
25
Location
Azimuth
reckoned north
(deg.)
Situ 1, nose of anticline
(9 measurements)
80
75
63
88
80
84
69
73
83
77
258
USGS nine-component spherical guge
The USGS nine-component spherical gage, developed in Denver by NICHOLS et at. [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.
Azimuth
reckoned north
(deg.)
TABLE 5. SUMMARY OK RESULTS—PIIOTOELASTIC ROSETTES TECHNIQUE
<P-G>/2 Principal stress (psi)
Q-Stress
P-Stress
(psi)
18
Pholoelastic 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.
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
(PS'')
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 ol 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 tlie 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 bottom 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]:
ABSOLUTE STRESS MEASUREMENTS AT THE R A N G E L Y ANTICLINE
631
R. V. DE LA C R U Z AND C. B. RALEIGH
T ' M = 1-30 T* U -h (0-085 - | - O - I S i — x 2 ) T * 2 2 + (0-473 + 0-91*) T* 33
r' 2 2 = 1-30 r* 22 + (0-085 -|- (MSi—K^T*,, + (0-473 -I 0-9lv) T* 33
T ' I 2 - (1-423 - 0-027^) r*, 2
;re the axis of the hole is in the A'3 direction, and:
T' U = calculated stresses at the center of the bottom of the hole
T*,J = field stresses
v
— Poisson's ratio of the rock.
The theoretical basis of the USGS spherical-gage technique is not in question per sc but
: assumptions in the theory are already quite different from the conditions in the actual
Id installation. Firstly, a solid cylinder was used for the elastic approximation of a
herical inclusion. Besides this approximation, the construction of the probe is such that
e solid sphere is bounded by only one diameter of low-modulus material (epoxy host
Under) in contrast to the required semi-infinite size of the host (2-3 times the diameter of
e sphere is practically equivalent to an infinite medium according to St. Venant's principle),
'ith these inaccuracies and the additional cementing agent still to be introduced into the
.)le, we have in actuality, the transmission of the external force fields through the cementing
ietH (the same epoxy material as the cylinder) to the cylindrical host and finally into the
istrumented sphere. This complex boundary-value problem is admittedly theoretically
itractable, at least to the authors, but the finite-element method of stress analysis in its
'resent stage of development could handle this problem quite readily. The complete
heoretical basis of the USGS spherical-gage technique as now presently constructed will be
>resented
in a laterbasis
paper.
The theoretical
of the other methods, borehole-deformation method, photoelastic
.train-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.
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 he 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 of field 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 DC LA CRUZ [10].
TABLE 6. SUMMARY OF RESULTS—ABSOLUTE STRESS MLASUREMENTS
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].
Azimuth reckoned north
Principal stress (psi)
(deg.)
/"-Stress
(?-Slress
USBM three-component gage
Site I
63
Site 2
100
Site 3
97
Direct strain gage
Site I
71
'Doorstopper' technique
Site 1
88
Site 2
93
Site 3
89
USGS spherical gage
Site I
41
Photoelastic rosettes technique
Site 1
77
78
90
87
(psi)
39
42
62
19
24
12
278
144
67
322
13
313
-348
-38
- 105
335
26
209
25
It
18
218
-108
163
N.B. Sign convention: positive is compression.
Number of
measurements
632
••LORADO SCHOOL OK M1NQ
fiOLDEN. COLORADO
R. V. DE LA CRUZ AND C. B. RALEIGH
ABSOLUTE STRESS MEASUREMENTS AT THE RANGELY ANTICLINE
TABLI; 7. COMPARISON OF AvtKAct V A I H I S OHTAIM i> AT SITE 1 USINU nvi; DIFFERENT METHODS
Method of measurement
Borehole deformation method
Direct strain-gage technique
'Doorstopper' technique
Spherical-gage method
Pholoelastic strain-gage technique
Average values
Azimuth
reckoned north
(deg.)
63
71
88
41
77
™
Principal stress (psi)
Q-Stress
/>-Stress
78
278
322
25
218
184
39
144
-348
-11
-108
-52
(/*— (?)/2 rm,t
(psi)
633
Principal stresses at different points of anticline by the borehole
deformation method and mean principal stress directions at
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.
Fici. I
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 [ I I ] . 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 (/, and /3) which suggests that these joints are shear fractures lying at an angle of
about 25° to/,.
DISCUSSION AN1> CONCLUSIONS
Relation of 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 a,, 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.
FIG. 2
634
R. V. DE LA CRUZ AND C. B. RALEIGH
Preliminary evidence from focal-plane solutions for the Rangely earthquakes appears to
agree with the directions of the surface stresses (Fig. 1). In the southern margin of the
field, from these solutions compression (J:) axes, lie WNW, with tension (J}) being horizontal and NNE. These results are consistent with surface measurements along the flanks of the
Rangely structure.
Measurements of residual stresses in core, petrofabric measurements of deformation
lamellae in quartz and compilation of larger numbers of earthquake data are being presently
conducted and comparison of these results will form the basis for a more comprehensive
study.
In conclusion, measurement of in situ stress in shallow boreholes apparently can provide
valuable data on the orientation, and approximately the magnitude, of the present state of
stress in rocks. The method found to be most convenient in practice is overcoring using the
borehole-deformation gage of the U.S. Bureau of Mines. Large numbers of measurements
are an important requirement in the determination of the stress field in outcrops where
natural fractures give rise to significant inhomogeneity.
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. HANDIN and D. W. STEARNS of the Center for Tectonophysics, Texas A & M University, used foilresistance gages and A. BROWN used photoelastic gages. Mr R. A. FARROW and associates of the U.S.
Geological Survey, Denver, Colorado, used the three-dimensional solid inclusion borehole probe developed
by T. C. NICHOLS et 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. BONNECHERRE F. A Comparative Field Study of Rock Stress Determination Techniques, Technical Report
No. 1-69, Missouri River Division, Corps of Engineers, Omaha, Nebraska (1969).
2. HEERDEN W. 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,
1855-204(1957).
4. HANDIN J. Studies in Rock Fracture, Twelfth Quarterly Technical Report, Texas A & M Research
Foundation, Texas (1971).
5. LEEMAN E. R. A Trepanning Stress Relieving Technique for Rock Stress Measurements, Proceedings of
the Sixth Symposium on Rock Mechanics (E. M. Spokes, Ed.) Rolla, Missouri, pp. 407^126 (1964).
6. NICHOLS T. C., ABEL 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, C1-C28 (1968).
7. EMERY C. L. In situ Measurements applied to Mine Design, Proceedings of 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 of 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. BROWN A. Private communication (1970).