Estimating the state of stress from subhorizontal hydraulic fractures at the underground research laboratory, Manitoba

Int, ,I. Rock Mech. Min. Sci. & Geomech. Abstr. Vol.30, No,7, pp. 959-964, 1993

i/148-0(162/93 $6.00 + 0.00 Pergamon Press Ltd

Printed in Great Britain

Estimating the State of Stress from Subhorizontal Hydraulic Fractures at the Underground Research Laboratory, Manitoba B. H A I M S O N t M. LEE-~ N. C H A N D L E R S D. MARTIN:[:

We conducted 9 complete hydraulic fracturing in situ stress measurements in vertical borehole HF1 at the 420 Level of AECL's Underground Research Laboratory (URL), near Pinawa, Manitoba. The tests did not result in vertical fractures. Thus, a generalized least-squares criterion was employed to compute the estimated principal horizontal in situ stresses. The large number of redundant test results enabled us to estimate the stress condition with confidence, even though the hydraulic fractures were only gently inclined The estimated in situ stress regime within the range between 25 and 95 m below the 420 Level (445-515 m below the surface) is S~, = 12-14 MPa; S h = 36(±16) MPa; S H = 54(±13) MPa at 120°(:t:32°). The results are consistent with other independently conducted measurements at the URL.

INTRODUCTION The following information is taken from Martin [1]. The Underground Research Laboratory (URL), near Pinawa, Manitoba is an Atomic Energy of Canada Limited (AECL) facility that has been excavated in granitic rock of the Lac du Bonnet batholith, one of many igneous intrusions of the Canadian Shield. The batholith is about 75 x 25 km in surface area and extends downward about 10 km. Its age has been estimated at 2680 Ma. Two major thrust faults dipping 25-30 ° to southeast have been encountered at the URL, Fracture Zone 3 at about 100-m depth, and Fracture Zone 2 at about 280 m (Fig. 1). Fracture Zone 2 in particular appears to be the boundary between two separate stress domains. Previous stress measurements using a variety of techniques, such as biaxial and triaxial overcoring, microseismic monitoring, convergence measurements during shaft sinking, and hydraulic fracturing, indicate that the principal horizontal stress magnitudes increase considerably below Fracture Zone 2, and their directions rotate with respect to those established at the higher elevations (Fig. 1) [1]. However, there had been just one measurement below the 420 Level carried out prior to the excavation of the Underground Research Laboratory. That was an inconclusive hydraulic fracturing test, conducted at a depth of 540 m in the exploratory inclined hole URLI, which resulted in a gently inclined fracture (dip 25 ° to the SE, and striking at N69°E) [2]. We carried out a total of 14 hydraulic fracturing tests and 9 oriented-packer impressions in borehole HF 1, a 100m deep vertical N-size (76-mm dia.) hole drilled downward from the floor of the 420 Level. Details of the

Level SH Lac du Bonnet granite

420 Level NW SE Fig. 1. Three-dimensional profile of the URL, showing the two main fracture zones (identified as thrust faults) and the rotation in maximum horizontal stress (SH) direction. Also shown is the main shaft and the 420 Level, from which the tests were conducted (after Martin [1]).

? - University of Wisconsin, Madison, Wisconsin 53706 ++- AECL Research, Pinawa, Manitoba, Canada ROE 1L0 959

test procedures, results, interpretations, and stress calculations are presented in the following chapters.

TESTING EQUIPMENT

AND PROCEDURE

Hydraulic fracturing

The equipment used in these hydraulic fracturing measurements was specially prepared for the very high breakdown pressures anticipated. Previous tests were on occasion unsuccessful in fracturing the rock below Fracture Zone 2 because of equipment pressure limitations (typically _< 60 MPa). The hydraulic system used in the present tests was upgraded so that it could be operated safely at pressures reaching 100 MPa. The hydraulic fracturing straddle-packer consisted of two 75-cm-long inflatable rubber packer elements (rated for operation at a minimum of 80 MPa) rigidly connected

960

ROCK MECHANICS IN THE 1990s

so as to straddle a 70-cm interval. An internal hollow steel shaft separated two hydraulic lines, one for the inflation of the packers and the other for the pressurization of the interval. The straddle-packer was lowered into the test hole using a 5-ram-diameter wireline controlled by a compressed-air winch. Two lines of high-pressure stainless steel tubing (burst pressure rating of 150 MPa) were connected hydraulically to the top of the straddle packer and were lowered simultaneously by strapping them to the wireline. One of the two tubings was used for the pressurization of the test zone, and the other for the inflation of the packers. Downhole pressure transmitters were placed in a sealed housing on top of the straddlepacker for downhole monitoring of test-interval and packer pressures. The transmitters were connected to the surface power supply and recorders through a 4-conductor oceanographic cable. The surface equipment consisted of two air-activated hydraulic pumps (capacity 100 MPa), one for each hydraulic line, two pressure gages and two pressure transducers (140 MPa), and a precision flowmeter which could monitor both the forward flow into the test interval as well as the back flow upon depressurization. Testing procedures were similar to those described in an earlier publication [3]. During testing, the downhole packer and test-interval pressures and the flow rate were continuously monitored and recorded simultaneously on a 3-channel strip chart analog recorder, a data tape recorder, and a microprocessor (PC) via an analog-to-digital converter. The strip chart recording was for real-time monitoring of the test variables, the taped data served as a backup, and the digital recording was for later data reduction and analysis.

Hydraulic fracture delineation Knowledge of the hydraulic fracture orientation is crucial to determining the in situ stress tensor. We used an impression packer - orienting tool to obtain an oriented trace of the induced hydraulic fracture on the test-hole wall. The impression packer consisted of a 90-era-long inflatable packer element covered by an impression sleeve, a thin layer of semicured rubber that can be deformed permanently by a sharp protrusion or gap in the hole wall. The impression packer was lowered into the test hole, using the wireline, to the precise depth of a previously hydraulic-fractured interval. A magnetic orienting tool, consisting of a camera, angle unit, and magnetic compass, was rigidly attached to the top of the impression packer. The packer was pressurized to a level slightly higher than the estimated shut-in pressure recorded earlier in the interval. The packer pressure was maintained for about 30-45 minutes to allow the camera to photograph the compass face and the impression wrapping to take a permanent imprint of the fracture. At the completion of the test the impression packer was deflated and retrieved together with the orienting tool. The camera was removed and the photograph was developed. Fracture traces on the impression packer were marked with respect to a scribe line on a transparent sheet for later detailed analysis.

60

,

~

.

~

,

~

.

.'

~

, '" ]

,

~

,

URL. Hole HFI 504.$ m

Test no.S. c

40

. . . . . . . . ~. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~. . . . . . . . . . . . . . . . . . . . . . .

0 2

4

8

6

10

; 14

12

16

Time (min)

Fig. 2. Typical pressure-time flow rate-time test record (first three cycles), in which the shut-in pressure is clearly the inflection point duringthe pressuredecayafterpumpshutoff. 60

•

'~ .

.

.

.

=

=

r

~

~

]

=

[

=

--

[

"

U R L , H o l e HF1 Test no.6, 456.3 m

,o

i

.....

~---:

..................................................

i ......................

3o! .............................

, ...................

i ......................

~o ................

; ......................

i.~

10

i .......... i ........

[

1

-~

F).i ..........

. . . . . . . . . . . . . . . . . . . . . . . .

0 4

6

8

10

12

14

16

T i m e (rain)

Fig, 3. Pressure-time,flowrate-timetest record(firstthree cycles),in which the shut-in pressure is not as precisely identified by visual inspection

TESTDATAANALYS~

Hydraulicfracturing pressures Typical pressure-time plots obtained in our tests are shown in Fig.s 2 and 3. For vertically induced fractures the breakdown pressure Pc, the fracture reopening pressure Pr and the shut-in pressure Ps would all be used in the stress calculation process; however, since all the induced hydraulic fractures in the URL tests were gently sloping, only of the shut-in pressure values were used. The shut-in pressure Ps is the pressure reached, after the pump is shut off following breakdown or fracture reopening, when the induced hydraulic fracture has closed back. This pressure is approximately equal to the stress acting normal to the fracture plane. Theoretically, the testinterval pressure decrease following pump shutoff should show a sharp inflection point, signifying the closure of the fracture. In the reported tests the inflection point was often very clear (Fig. 2), but occasionally it was difficult to identify directly from the pressure-time record (Fig. 3). We determined the shut-in pressure in the third pressurization cycle (the commonly used cycle for estimating Ps). The technique used to locate this pressure on the decaying segment of the pressure-time curve involved the replotting of the digital pressure-time data in

ROCK MECHANICS IN THE 1990s cycle 3 in the form of the rate of pressure decay (dP/dt, where P is pressure and t is time) as a function of pressure (P). We then used a statistical nonlinear regression package to determine the best bilinear fit of the dP/dt versus P data (typical plot shown in Fig. 4). The steeper slope represents the rapid pressure decay after pump shutoff, when the fracture is still open; the gentler slope represents the much slower pressure decay after the fracture closes [3]. Thus, the intersection of the two straight lines (determined by regression analysis) is taken as an estimate of the shut-in pressure. The shut-in pressures obtained in the reported tests are listed in Table 1. 1.0--

'

!

!

fitting to the digitized inclined-fracture traces, and estimated their dip and strike with very low uncertainty. Fig. 5 shows a typical digitized fracture trace and the bestfitting fracture plane attitude). The expected error of measurement and statistical analysis of fracture orientation in the reported tests is estimated to be no more than +5 ° . The resulting dip and dip direction of the induced hydraulic fractures are listed in Table 1. We note a striking similarity between these test results and that obtained in an earlier test conducted at the 540-m depth with respect to both dip and dip-direction of most fractures [2].

--

U R L , Hole HF1 Test no.6, cycle 3 456.3 m

STRESS

0.6

~

0.4

CALCULATIONS

In tests resulting in inclined hydraulic fractures, the shut-in pressures recorded do not constitute an approximation of the least horizontal stress but merely o f the normal stress perpendicular to the fracture plane (also called fracture-normal stress S,, where n is the direction of the normal to the fracture plane):

0 iii

~

961

0.2

s. =P, O,C

~mUlq~w~r

15

~

I~

16

,

17

, 18

19

20

Pressure (MPa)

Fig. 4. Typical dP/dt vs. P plot (where P is downhole pressure and t is time) based on digital recording of the decaying portion of pressure with time in the third cycle. The discrete points show individual digitallyrecorded data. The intersection of the two straight lines obtained from bilinear regression is the best-fit estimate of the shut-in pressure. Azimuth (o) 360

270

.

.

.

180

.

90

oZ.oe.F1

i

Test no. 3, 510,g m ..........................................

E o

--L~

!...................................................

'%,

i

............. impression packer ~

........ ~

fracture trace i

i

J

i

i

i

i

Thus a test record consisting of the shut-in pressure and the fracture dip and dip direction yields an estimate of the magnitude and direction of a normal stress in the rock in a direction perpendicular to the pressurized fracture. Theoretically, knowledge of six normal stress magnitude s and directions at a point can uniquely define the complete in situ stress tensor there, since this information provides the six equations necessary to solve for the six unknown stress components of the tensor [5]:

Sni = ll2 Sxx + m2" yy +n2St zz + 2miniSy, + 2niliSzx + 21imi%

(2)

fitted fracture plane " " ~.-i(dip 29°; dip-dir 76 °)

~. . . .

(1)

,

i

i

Fig. 5. Typical analysis of hydraulic fracture trace. The digitized data are fed into a statistical program that determines the best-fitting plane (sinusoid in case of inclined fractures) represented by the packer impression. The program also calculates the dip and dip direction of the estimated fracture plane.

Hydraulic fracture orientation We digitized the hydraulic fracture traces from each test interval and employed statistical methods in order to improve the accuracy and objectivity of estimating the strike and dip of the induced fractures [4]. No axial fractures were detected in these tests; all the hydraulic fractures were inclined. We applied sinusoidal curve

where the subscript i stands for the ith test or equation (i = 1, 2, 3,...); x, y, z are a set of Cartesian coordinates; Sjk (j, k = x, y, z) are the six unknown stress components necessary to uniquely define the stress tensor; and l,, %, n i are the direction cosines of Sni with respect to x, y, z respectively. In practice in situ tests are not precise, and an adequate number of redundant measurements are needed to yield reliable stress results using an appropriate statistical evaluation. In order to use an analysis such as that in equation (2) for our tests, we made the following two assumptions: (1) within the narrow test depth range in hole HFI (445-512 m) the variation of the horizontal stresses with depth is insignificant, and (2) one of the three in situ principal stresses is vertical and approximately equal to the weight of the overburden: Sv = ~,D = 0.0265 ( M P a / m ) x D (m)

(3)

where S,, is the vertical stress, D is depth from the surface, and y is the average weight density of the URL granite.

962

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

Table 1. Hydraulic fracturing test data, computed principal in situ stresses, and back-calculated input values: Test

Depth

Depth backtalc.

Ps

P back ~talc.

No.

(m)

(m)

(MPa)

(MPa)

(°)

19.2 17.1 19.0 21.5

18 20 32 28 22 39 25 15 29

13 450.7 450.7 19.8 6 4 5 6 . 3 456.3 17.1 1 461.8 461.8 18.4 7 472.5 472.5 22.0 2* 483.9 483.9 13.0 4 496.8 496.8 21.7 5 5 0 4 . 8 504.8 20.7 11 5 0 5 . 7 505.7 18.2 3 5 1 0 . 8 510.8 18.8 UnceRmnties: ±0.25 2 * - Test results not used in the least-squares

22.1 20.6 17.8 19.2

Frac Frac dip dip (d) back-calf

Frat dip-dir (b)

Frac dip-dir back-fair

(°)

(°)

(°)

25 20 25 33

98 123 148 245 127 68 140 107 76

99 123 149 246

34 26 20 25

±10 procedure for estimating the stresses.

The measurements were conducted at depths between 26 and 95 m beneath the 420 Level, sufficiently far from the 3 m high by 19 m wide cavern at that Level to be practically unaffected by its presence. The assumption that the vertical component is a principal stress facilitates an important simplification of equation (2). If the Cartesian coordinates are taken so that z is in the downward vertical direction, it follows that x and y are in the horizontal plane. With the vertical direction (V) facing downward, we can select x as directed toward north (N), resulting in y heading to the east (E). Equation (2) now becomes Sni = 1.2,S N + m2i S E + n2i "yDi + 2limiSNL-

(4)

where the shear stresses SvN and SEz are zero since V is a principal direction. In terms of the new set of coordinates, the cosine angles can be def'med more specifically. Since Snj is the fracture-normal stress, its bearing is the same as the fracture-dip direction measured clockwise from north (fl), and its plunge is (90 ° - 8) where 8 is the hydraulic fracture dip. Thus

±10

67 140 107 76

S

Sh

SH

SH,dir

(MPa)

(MPa)

(°)

11.9 36.0 12.1 36.0 12.2 36.0 12.5 36.0 12.8 36.0 13.2 36.0 13.4 36,0 13.4 36.0 13.5 360 Standard deviations: 0 £17

54.0 54.0 54.0 54.0 54.0 54.0 54.0 54.0 54.0

120 120 120 120 120 120 120 120 120

±12

±27

(MPa)

statistical approach allows the assignment of measurement error to all the measured variables. It assumes that each measured variable follows a Gaussian distribution defined by the measured value and a standard deviation. The generalized procedure also requires an a priori rough estimate of the Gaussian distribution (reasonable mean and reasonable standard deviation) of the unknowns (the horizontal principal stress magnitudes and directions). Previous measurements and other stress indicators below Fracture Zone 2 [1] were used to supply these a priori values. The method dermes for each test (i) a vector ~i whose components are the measured data and a priori values for the unknown quantities. In our case ~r = ~i (Di, 8i, fli, Psi, Sh, Sn, 0). The objective of the generalized procedure is to search for vectors ~i (whose components are the back-calculated measured data and the best-fitting stress quantities resulting from the least-squares procedure) that satisfy the following equations:

(¢) = o

(7)

S ( ~ ) : ~., (~i - ~i ) 2 / S D i 2 reaches a minimum value(S) i=1

l i = sin8 i cosl3) m i = sinSi sinl3i n i = cos~5i

(5)

In the set of equations (4) there are only three unknowns (S N, S D a n d Sire.). In terms of the largest and smallest horizontal stresses, S n and St,, and S n direction (0 ), and substituting relationships (5) for I i, m i, and hi, equation (4) takes the form S,,i = "YDi cos2 8i + ½ sin 2 8j [SH + (SH - Sh) cos2(15i - 0)]

(6) where 8 i and fli are the dip and dip-direction of the ith fracture plane, respectively, and 0 is the direction of St-i clockwise from north. We employed the generalized least-squares procedure for nonlinear problems (also called total inversion method) [6, 7] to solve the set of equations (6) and obtain estimates of the three unknowns S h, S n, and SH direction. This

where (;) = Psi - 7Di cos2 8i + ½sinz 8i [SH + Sh + (SH - Sh) cos2(13, - 0)] and S D i is the ith vector of standard deviations assigned to each component of ~i. We solved equations (7 and 8) for the set of measurements at the URL using a Gauss-Newton iteration method [6].. The test results used in this procedure are listed in Table 1. The shut-in pressure in test no. 2 (13 MPa) yielded a considerably lower magnitude than in all the other tests (which ranged between 17.1 and 22 MPa). After a first iteration in which the results of all the tests listed in Table 1 were used, the data obtained in test no. 2 were excluded, resulting in considerable improvement in the uncertainties of the calculated principal stresses. In using the generalized least squares procedure we assigned the following standard deviations: S D ( P p = +2 MPa; SD('6) = +10°; SD(fl) = a:10 °. The initial (a priori) guesses for the unknowns, as the starting values for the iteration process, can be any reasonable estimates. We

ROCK MECHANICS IN THE 1990s made several runs with different a priori values resulting in very similar results. Specifically, the results reported here are based on the following a priori values: Sh = 40 (+20) MPa; S n = 50 (+20) MPa; S H dir = 135 ° (+45°). The resulting horizontal principal stresses from this computation were: S h = 36 (+16) MPa," S ~ = 54 (:~13) Mea; SHdir = 120 ° (±32 °)

(between 40 and 60 MPa) but found little change in S~, (mostly between 50 and 56 MPa), and always well within the calculated uncertainty of +13 MPa. This uncertainty of under 25% of the magnitude of Sn is quite common in classical hydraulic fracturing analysis of vertical fractures. Comparison with results of previous tests below Fracture Zone 2, shows that the average Sic magnitude falls between the values obtained from the conversion back-calculations and the other testing methods (Fig. 6).

(9)

where stress magnitudes have been rounded off to the nearest MPa. Table 1 gives a complete listing of the calculated vertical stresses, the statistically computed principal horizontal stresses, and the respective uncertainties.

963

S H direction 0°

45 °

90 °

S H magnitude (MPa)

135 °

q~

oooo

o

O**x,,°

00dFXlb

DISCUSSION OF RESULTS

~end

0

20

40

60

80 100 120

•

•

.Io

•

- - - 7 x xo

O USBM overcor:rcor~ xX..e •

The question most asked about the past and present hydraulic fracturing results below f r a c t u r e zone 2 at the URL is 'Why are the initiated fractures so consistently subhorizontal when in most other tests around the world subvertical fractures are created?' The answer has to do with the great difference in magnitude between the vertical and the two principal in situ horizontal stresses. As shown in equations (3) and (9), the ratios S h / S v and S n / S v are approximately 3/1 and 4.5/1 respectively! The result of this high stress differential has been stress-induced subhorizontal microcracks commonly observed in extracted borehole core. Such in situ stress conditions are believed to similarly influence the formation and attitude of the induced hydraulic fractures at the 420 Level. The relative randomness of the subhorizontal-hydraulicfracture dip directions has been beneficial to our tests in that all eight results used yielded eight independent equations (6). The principal horizontal stresses obtained from our analysis and reported in equations (9) meet a number of conditions and expectations that enhance their credibility: a. The direction of the maximum horizontal stress at 120 ° is very stable in the iteration procedure. We tried several other a priori values for Sn direction, including 90 ° (+90 °) and 45 ° (:~90°), and consistently the computed value was between 110° and 125 ° (i.e. very little affected by the initial guess), well within the uncertainty of +32 ° . The southeast trend of the maximum horizontal stress has been suggested by previous stress direction evidence from overcoring, convergence and microseismic methods, as well as by stress indicators such as breakouts in some drifts at the 420 level [1]. The results confirm that the S~ direction below the 420 Level is southeasterly. This supports the evidence presented by Martin [ 1] of a rotation o f S H from a northeastern trend above Fracture Zone 2 to a southeastern one below it (Fig. 6). b. The largest horizontal stress magnitude computed from the total inversion method (54 MPa) is also very stable. We attempted many reasonable a priori values

180 °

Convergence Ix

x Microseismie I I Hydraulic I

x

•

I fracturing ]

(a)

•

Sv

(b)

Fig. 6. Resultsof previousstress measurementsand calculationsbelow Fracture Zone 2 at the URL (after Martin [1]) juxtaposed against the present hydraulicfracturingtest results. In (b) we also plotted S v and hydraulicfracturingS h magnitudesfor comparison. c. The smallest horizontal stress magnitude emerging from the iteration procedure (36 MPa) is the least stable of the computed values. It has a higher than usual uncertainty of + 16 MPa (+44%), but when calculated under other reasonable conditions of a priori values (between 30 and 50 MPa) it fluctuates mainly between 30 and 40 MPa, considerably less than its standard deviation. It should also be realized that there are other constraints on the admissible magnitudes of Sh. This is because of the recorded breakdown pressures and fracture inclinations. The breakdown pressures in the 14 tests averaged 44 MPa, with the highest Pc at 55 MPa achieved in Test 9. Yet, we never fractured the rock vertically, which implies that the conventional criterion of hydraulic fracturing resulting in vertical fractures was never met, i.e., the recorded breakdown pressures Pc were always lower than the critical Pc c" magnitude required by the well-known relationship [3]: p~" = Tv + 3 s . - s h

(lO)

964

ROCK MECHANICS IN THE 1990s

where Thf is the hydraulic fracturing tensile strength, which for this granite is approximately equal to 10 MPa [1]. Since the largest Pc experienced in 14 tests was 55 MPa, the following relationship between the two horizontal principal stresses emerges: (11)

SH> Sh > S~/3 + I5

where 15 (MPa) = (55 MPa - 10 MPa)/3. In the present set of tests, therefore, S~ is constrained between 33 and 54 MPa. Thus, by default the uncertainty in Sh on the low side is only -3 MPa. It is interesting to note that inequalities (11) also set an absolute lower bound on Sh,which occurs when Sh satisfies the equations S H = S h = S J 3 + 15 (which is a special case of relationships (11)). This condition is met when Sh attains its absolute minimum allowable value, i.e., Sh = 22.5 MPa. d. Herget [8] summarized the experience of stress measurements in the Canadian Shield and derived average and extreme stress-depth relationships. Notable among these is the linear correlation between the mean horizontal stress (S H + Sh)/2 and depth. For extremely high stresses the mean stress is given by 12.4 (MPa) + 0.0586 (MPa/m) x D (m), which at the 500-m depth equals 41.5 MPa. The mean horizontal stress in our tests is 45 MPa, which compares well with the predicted value.

horizontal stresses do not vary appreciably with depth within the 70-m range tested by us. W e employed a generalized nonlinear procedure that allows for uncertainties in each variable to be taken into account. The computed stress regime is compatible with previous indications regarding both stress magnitudes and the general direction of the maximum horizontal stress S n. The resulting mean horizontal stress (S n + Sh)/2 of 45 MPa matches well the 41.5 MPa predicted by Herget [8] as the upper limit at the 500 m depth in the Canadian Shield. The major conclusion is that with sufficient carefullyconducted hydraulic fracturing tests in vertical boreholes, the in situ stresses can be computed with reasonable confidence even when the resulting fractures are only gently inclined. ACKNOWLEDGMENT-This work was funded by AECL Research. REFERENCES

1.

2.

3. CONCLUSIONS We carried out an extensive series of hydraulic fracturing stress measurements in hole HF1, a 100-m deep vertical borehole drilled downward from the floor of the 420 Level of the URL. All of our 14 hydraulic fracturing tests were successful in that they resulted in breakdown and the creation of fractures. However, the induced fractures in the nine tests for which packer impressions were taken were not vertical as is usually the case, but were gently dipping between 15° and 39 ° from the horizontal. For such fracture geometry the conventional hydraulic fracturing elastic criterion is not applicable. Therefore, we performed an analysis which is based solely on the theory of stress and makes no assumptions on the material behavior. The only assumptions made were that the vertical stress is a principal stress component equal to the rock density multiplied by depth, and that the principal

4.

5. 6.

7.

8.

Martin, C.D., Characterizing in situ stress domains at the AECL Underground Research Laboratory, Can. Geotech. J., 27, 631-646 (1990). Haimson, B.C., Hydrofracturing in situ stress measurements in the Lac du Bonnet Batbolith drillholes URL, I and WN-4, Report to AECL 106 p. (1982). Haimson, B.C., The hydrofracturing stress measuring method and recent field results, Int. J. Rock, Mech. Min. Sci. & Geomech. Abstr., 15, 167-178 (1978). Lee, M.Y. and B.C. Haimson, Statistical evaluation of hydraulic fracturing stress measurement paramoters, Int. d. Rock. Mech. Min. Sci. & Geomech. Abstr., 26, 447-456 (1989). Jaeger, J.C. and N.G.W. Cook, Fundamentals of Rock Mechanics, Second Ed., Chapman and Hall, 593 p. (1979). Tarantola, A and B. Valctte, Generalized nonlinear inverse problem solved using the least squares criterion, Rev. Geophys. Space Phys., 20, 219-232 (1982). Comet, F. H. and B. Valette, In situ stress determination from hydraulic injection test data, J, Geophys. Res., 89, 11527-11537 (1984). Herget, G., Regional stresses in the Canadian Shield, in Canadian Institute of Mining and Metallurgy, Special Volume 22, 9-16 (1980).