The hydrofracturing stress measuring method and recent field results

Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. 15, pp. 167-178. © Pergamon Press Ltd 1978. Printed in Great Britain

0020-7624/78/0801-0167502.00/0

The Hydrofracturing Stress Measuring Method and Recent Field Results B. C. HAIMSON* The hydrofracturing technique is a recent development in the area of stress measurements in rock. Unlike most other methods, it does not measure strain at a point through the use of delicate instrumentation in the test-hole. Rather, it directly determines average stresses over large areas by recording two hydraulic pressures, one necessary to crack open a segment of the test-hole and the other required to keep the fracture open. To do so, it uses simple down-hole mechanical tools so that the method can be employed at any depth from the surface. Elementary elastic relationships exist between recorded pressures and in-situ stresses, and between fracture direction and stress orientation. Our laboratory experiments have confirmed these relationships, and in the last five years we have conducted a number of successful field measurements throughout the United States and elsewhere, at depths between very near the surface and 5000 m. The results of these measurements, details of which are given in the paper, have been used in studying earthquake control problems (Rangely, Colorado), underground power station design (California, South Carolina), hard rock tunnel design (Wisconsin), and geology and plate tectonics (all the measurements and particularly those in Michigan and Iceland). A general uniformity of maximum principal stress direction throughout the continental United States has been established. Stress magnitudes are affected by regional geologic conditions but generally show linear increases with depth. rock elastic parameters in order to convert measured strain to stress; (2) the very small areas at which The magnitude and direction of rock stresses are stresses are actually determined; and (3) the ineffectiveamong the most important factors affecting the stability ness in zones of highly differential stresses where overof surface and underground structures, the driving coring could produce discing. mechanisms of plate tectonics, the prediction and conThe only thing that hydrofracturing (or hydraulic trol of earthquakes, and the in-situ extraction of coal fracturing) has in common with the other methods is gas, leached copper, oil shale, and dry hot-rock geo- that it is conducted in boreholes. However, it does not thermal energy. The challenge of reliably measuring require overcoring and is not limited in depth except rock stresses has fascinated many rock mechanics by the length of the drilled borehole (stresses in a 5-km scientists and field experimentalists. However, the per- well were recently measured, as described elsewhere in fect method of determining in-situ stresses has thus far this paper). It determines stresses directly and is not eluded their ingenuity. dependent on knowledge of precise values of the elastic Most of the methods developed to date require a rock parameters. It estimates stresses over large areas borehole drilled from the point of access to the depth providing a better average than point measurements. where stresses are to be determined. With the exception It is not affected by highly differential stresses. Last, of hydrofracturing, all these methods use strain or but not least, it does not employ sophisticated downdeformation gages capable of sensing changes in diame- hole instrumentation, but rather rugged equipment, tral, circumferential or bottom-hole dimensions when which is in part commercially available and ready to existing stresses are relieved. Stress relief requires 'over- be rented or purchased. coring', and it is this operation that is primarily responThe hydrofracturing stress measuring technique consible for the limit on the effective length of test-holes sists of sealing-off a section of a borehole at the (50m or less). Other distinct disadvantages of these required depth by means of two inflatable rubber methods are: (1) the requirement to precisely determine packers, and pressurizing the isolated segment using a hydraulic fluid such as water. At some critical (also * Professor of Rock Mechanics, Department of Metallurgical and called breakdown) pressure, the rock at the borehole Mineral Engineering, University of Wisconsin. Madison. WI 53706, bursts and develops a tensile fracture. This fracture can U.S.A. INTRODUCTION

167

168

B . C . Haimson

be extended away from the hole by continuing the pumping. When the pump is shut off with the hydraulic circuit kept closed, a 'shut-in' pressure is recorded. This is the pressure necessary to keep the fracture open. The breakdown and shut-in pressures, which are carefully monitored during the test, can be related to the prevailing in-situ stresses. An impression packer or other borehole and surface geophysical devices can be used to determine the orientation and inclination of the hydrofracture which develops along a plane perpendicular to the direction of the least principal stress. In this manner, both the magnitudes and the directions of the principal stresses can be evaluated. The hydrofracturing theory, its limitations, laboratory results and selected field experience to date are detailed in the following sections. f

C A L C U L A T I O N O F STRESSES Theoretical expressions relating hydrofracturing pressures to in-situ stresses have so far been developed only for linear elastic and isotropic rocks in which one of the principal stresses acts in a direction parallel to the axis of the test-hole. The parallelism prerequisite between hole axis and a principal stress direction is usually achieved by drilling vertical test-holes, since the overwhelming field evidence is that one of the principal stresses is nearly vertical in most locations. Two distinct situations exist. In one, the vertical stress (av) is the least principal compressive stress, and in the other the vertical stress is either the intermediate or the largest principal stress. The hydraulic fracture will follow the path of least resistance, i.e. a direction perpendicular to that of the least-principal stress. Theoretical calculations [-1], as well as abundant laboratory [2] and field results (this paper) show that when rubber packers are used to seal off an unprefractured interval, the initial hydrofracture is always vertical and perpendicular to the least horizontal principal stress (am, i.), regardless of the magnitude of av. If av is the least principal stress, the hydrofracture will turn around as it travels away from the stress field imposed by the pressurized test-hole, and will become horizontal. Alternatively, existing sub-horizontal weakness planes may open up, thus diluting the pressure in the hydrofracture and stopping its advance. If av is not the least principal stress, the induced vertical hydrofracture will extend along its initial direction. The shut-in pressure (Ps) needed to keep the hydrofracture open when pumping is stopped is equal to the in-situ compressive stress perpendicular to the fracture plane. If Crv is not the least principal compressive stress, P~ will stay constant provided there are no leakages through the pipe, past the packers, or into rock pores and joints, and the relationship P~ = crH~i. (1) will determine the least horizontal principal stress (am, i,). The vertical principal stress (av) will then be calculated from the weight of the overlying rock: ~,d = av

(2)

where ~ is the rock weight gradient, and d is the depth. If av is the least principal compressive stress, a vertical fracture will nonetheless initiate at the borehole wail, yielding the first shut-in pressure (P~I). Often the fracture will run into a nearly horizontal weakness plane and open it up. If this plane crosses the pressurized interval a second shut-in pressure (P.,2) will be recorded. Clearly Ps~ > Ps2 and (3)

P s i = O'Hmin Ps2

=

(4)

fly"

In this situation, both the least horizontal principal stress and the vertical stress will be directly determined by hydrofracturing pressures. Often the shut-in pressure will not stay constant as explained above. It is then advisable to obtain several pressure plateaus for various flow-rates of fluid pumped into the fracture. If pumping is very slow (say, in the range of a few l/min) and if simultaneous time-base recording of both pressure and flow-rate (Q) is conducted, a simple relationship resulting from equations formulated by Perkins and Kern [3] and suggested by Aamodt (R. L. Aamodt, personal written communication, 1975), can be used to obtain shut-in pressure (P~) values : (P1 - P s ) / ( P 2 - Ps) = ( Q I / Q 2 ) 1/2 (5) where P1 and P2 a r e two pressure levels corresponding, respectively, to the two flow-rates, Q1 and Q2. In order to estimate the value of the major horizontal principal stress (am.,x) the poro-elastic relationship between the critical (breakdown) pressure (P,) necessary to induce a vertical hydrofracture and the two horizontal principal stresses is used [-2,4,5]: Pc - P0

T + =

3trUmin -- O'Umax --

K

2Po

(6)

where compressive stresses are taken as positive and: P0 is the pore pressure in the rock at the tested depth; T is the hydrofracturing tensile strength and is equal to Pc when cru,,i,, = ou ..... = Po = 0 and K = 1; K is a poro-elastic parameter which can be indcpendently determined in the laboratory. The range of K is 1 < K < 2. K = 1 when the formation is impermeable to the fracturing fluid. K = 2 when the rock matrix compressibility and the rock bulk compressibility are equal, or when the Poisson's ratio equals 0.5 [2,5]. In practice, the values of T and K can be derived from a plot of ( P c - Po) vs (3anmi,- 6u,nax- 2Pot. based on laboratory-simulated hydrofracturing tests in which the principal stresses are known since they are the applied loads. The trend emerging from such series of tests in 5 rock types [6] is presented in Fig. 1. Note that in these tests P0 was kept at zero. As expected, K is not constant as it varies with the amount of pressure applied to the rock, and therefore the observed relationship between (Pc - P~) and (3am,,, , crn .......

The Hydrofracturing Stress Measuring Method 1

1.0 $

fl

i

K"l'-~J

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169

the vicinity of the test-hole is determined from the results of two operations: pressurization and impression.

/

0.5

LABORATORY AND PRELIMINARY FIELD RESULTS

Od~ ~ 1 0.5~''

I

1.0

3~rHmin--

I

1.5

I 2.0

2.5

O'Hr.a x (kb)

Fig. 1. Relationship between b r e a k d o w n pressure and horizontal insitu stresses as obtained by averaging results in five hard rock types and normalizing them for T = 0. In these tests, P0 was held at zero. The rocks tested were: Tennessee sandstone, Tennessee marble,

Weber sandstone, Dresser basalt and Valders limestone[6]. 2P0) is not linear. However, in the approximate range of 0 < Pc - Po - T / K < 250 bars, K is approximately 1.0. Beyond 250 bars. the value of K increases at various rates and approaches asymptotically the value of 2.0. Roughly, between 250-500 bars K can be approximated at 1.5 and beyond that at 2.0. In all the field tests undertaken by us to date, the hydrofracturing pressures were such that K = 1.0 was always the best approximation of the poro-elastic parameter. Depending on the relative magnitude of av, equations 1, 2 and 6 or 3, 4 and 6 determine the values of all three principal stresses. Based on the sound theoretical relationship, on the consistency of results when several hydrofracturing tests are run at the same location or in the immediate meighborhood, and on the close correlation between the Ps value obtained by using equations (1), (3) or (4) and that obtained from equation (5), it can be firmly stated that the smallest principal compressive stress is accurately determined by the hydrofracturing method. The value of am, ax which is obtained by using equation (6) is necessarily only an estimate because of the approximated value of K and the assumption of linear elasticity. The value of gv as determined by hydrofracturing is always found to be closely approximated by the weight of the overlying rock (see field results, this paper). As stated above, the direction of hydrofracturing can be determined by a number of methods. The most common and reliable way is to use an impression packer, an inflatable sleeve covered with a sheet of very soft rubber. When forced against the wall of the borehole the soft rubber takes an imprint of the rock face condition and maintains a clear picture of it, long after the packer has been deflated and raised to the surface. Packer impressions are oriented by employing a borehole magnetic surveying tool or other techniques. Impressions of successful hydrofractures in unprefractured rock invariably yield vertical fractures, the directions of which are consistent within the same area, and which determine the directions of a m , i, and aHmax. When a v is the smallest compressive stress both a vertical and a horizontal hydrofracture are often traced by the impression packer. Thus. the complete state of stress in

Extensive laboratory-scale experiments have been conducted to verify the relationships between hydrofracturing pressures and in-situ stresses and between fracture orientation and stress direction [2,6-10]. The highlights of the experimental results are: 1. All the induced hydrofractures are tensile ruptures and no shear fractures are observed. 2. When rubber packers are used, all hydrofractures were vertical and perpendicular to a m , i,. 3. The critical pressures for vertical fracture initiation is related to the horizontal principal stresses as shown in Fig. 1. 4. Studies in foliated slate and pre-cracked quartzite show that provided sufficient laboratory testing is conducted, such rocks are amenable to hydrofracturing stress measurements within limit. In some cases, lining of the test-hole may be required to ensure pressurization and vertical fracture initiation. The first indications of the potential of hydraulic fracturing as a stress measuring technique came from calculations reported by Scheidegger [11] and Kehle [12] based on routine oil-well hydraulic fracturing jobs run for production stimulation purposes. Haimson and Stahl [13] reported on three series of oil field hydrofracturing jobs (in the states of New York, Illinois and Ohio) in open holes, where impression packers and bottom-hole pressure transducers were used to determine crack orientation and fracturing pressures, respectively. The results within each group of tests were very consistent with respect to critical and shut-in pressures, and fracture directions. The significance of the consistency of results was the strong indication that they were closely related to local in-situ stresses. Stress calculations based on these hydrofracturing jobs were subsequently published by Haimson [8].

MEASUREMENTS T H R O U G H O U T THE UNITED STATES Following the laboratory study and the initial field results, all indications were that hydrofracturing had a great potential as a deep-hole stress measuring technique. Our opportunity to test the method came in 1971 at Rangely, Colorado. The success of the Rangely experiment led to more measurements sponsored either by government agencies or private industry. We have been involved in a number of significant hydrofracturing stress measurements throughout the United States and Iceland in relation to a variety of mining, civil engineering, geological and geophysical projects. The more important of these measurements are described in the following sections.

170

B . C . Haimson

boundary of the oil field, near the earthquake-prone region (Fig. 2). The results obtained at the bottom of I ,,""--~~"><" co~rrou~ the well (1900m below the surface), were: av = 435 I/. _ _ . . . _ bars (vertical), an,,~. = 315 bars (horizontal at N 20°W), V i/ /i_ - - \ - - ' . , =~-'BDRY OF aH,,ax = 590 bars (horizontal at N 70°E). "\ k \ (.~ ,'.-.~ k " , , ~NC-B_Y ...... ( 41 "Z The hydrofracturing test showed that the vertical principal stress was intermediate in magnitude, strongly indicating strike-slip faulting. The horizontal principal EARTHQUAKE'%. ~ 7/7/ yb / \ stress directions were in accord with both the N 50~E strike of the fault and its right lateral slip direction. • I-NOR. FRAC. WF-.LL ... . . . . . . ....s The magnitudes of the measured principal stresses were o EXPERIMENTAL WELL used to predict a critical pore pressure of 240 bars for e • | i i 0 4 km fault slip to occur (Fig. 3). This value was within 10','~ of the earthquake related threshold pressure monitored Fig. 2. The Rangely Oil Field and the area where most earthquake epicenters concentrated. Shown also are the pressure contours (in at the site (Fig. 4). The Rangely stress measurement bars) in the oil-bearing Weber sandstone formation, the major fault, was considered very successful because of the close corthe 4 experimental wells through which reservoir pressure in the relation between the determined stresses and other field earthquake zone was controlled and monitored, and the hydrofracturing well.The short line crossing the latter is in the direction of observations. the largest horizontal compressive stress. ~b) Ground stability under nuclear detonation-- Nevada Test Site (a) Earthquake research--the Rangely Experiment Knowledge of the existing in-situ stress magnitudes The first major utilization of hydrofracturing as a and directions were required at the Nevada Test Site deep-borehole stress measuring technique was in confor stability evaluation of tunnel complex U12n during nection with the earthquake control research at underground nuclear tests. Previous measurements Rangely, Colorado [14-16]. Intense seismic activity using an overcoring method were conducted within centered in and around the Rangely Oil Field in the only 5 m from the tunnel wall [18]. We performed vicinity of a strike-slip fault had been recorded in the hydrofracturing measurements both in a 250-m hole, area for over a decade (Fig. 2). A primary objective drilled from the slope of the mesa to the level of the of the research program was to determine whether a tunnel, and in vertical and horizontal 25-m holes drilled correlation existed between earthquake triggering and from the tunnel wall (Fig. 5). The horizontal holes were formation pore pressure. The latter had been artificially drilled in the general direction of the expected miniraised through water flooding of the field. A quantitamum stress and only shut-in pressures were obtained tive solution relating pore pressure to slip initiation because instead of fracturing, existing discontinuities along the fault, which in turn could have triggered the perpendicular to the hole axis were opened up. Were earthquakes, required knowledge of the in-situ stress the horizontal holes drilled in the direction of the larger condition in or below the oil-bearing strata. Hydrofracprincipal stress, more information might have been turing was selected as the stress measurement method. gained. All the other tests, both in the tunnel wall and The borehole used was a newly drilled oil-well located in the deep borehole, enabled a full evaluation of the approximately l km west of the fault by the southern stresses [19]. A linear stress-elevation relationship was established for all principal stresses (Fig. 6). The in-situ stresses around the tunnel at 380 m below the surface I I were determined at av = 70 bars (vertical), a,,,,~, - 35 bars (horizontal at N 55'W), a,,,,x = 90 bars (horizonRANGELY v tal at N 35°E). Both the magnitudes and the directions to of the principal stresses are in agreement with the boreto laJ ~ , ~ MEASURED hole deformation measurements [18], and seismic inn," vestigation results [20], indicating again the reliability I--" to f-CRmC.,. / I of the method. ~N

/'*'~ ~--

~ " " " " . -.,.,,,~

RESERVOIRPRESSURE

/

1

(c) Pre-excavation design of underground powerhouses Helms and Bad Creek projects

lad "1" tO 0

0

.2

NORMAL

~Hmin

STRESS

~

~Hmox ~

6

(kb)

Fig. 3. Mohr diagram showing the measured stress regime (right circle) at Rangely, the critical effective stress conditions (left circle) that could induce slip along the existing fault (whose normal is at 70' to the direction of a.m..0, and the amount of pore pressure rcqnired to produce the critical effective stresses (240 barsj.

The determination of the in-situ principal stress magnitudes and directions is of crucial importance in the design of large permanent openings such as powerhouses which possess one very long axis reaching sometimes 150 m, and two considerably smaller dimensions (within 50 m). The orientation of the chamber and the layout of the penstock and tunnels leading to and from it depend on the stress distribution.

The Hydrofracturing Stress Measuring Method

200

171

EARTHQUAKE FREQUENCY AT RANGELY OIL FIELD, COLORADO Ikes

,in I kilometer of bottom total wells

.3

150

i¢1

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~

E

D

E

D TO INITIATE EARTHQUAKES

mc

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ua at -r

7, O

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~,-- FI.UIDINJECTION

-!-

, o,o

WITHDRAWAL

.I

U,O,NJECTION

J

1

Fig. 4. Relationship between earthquake frequency and reservoir pore pressure at Rangely. The threshold pressure was closely predicted by hydrofracturing stress determination, as shown in Fig. 3 (after reference [17]). Stress measurements in the vicinity of future powerhouses have been almost routinely conducted using overcoring methods. Because of the distance limitations of these methods, exploratory holes could not be used and expensive pilot tunnels had to be driven into the planned excavation area. In some cases, pilot tunneling was not feasible and stress measurements were only conducted during the actual excavation, rendering any change in shape or orientation of the original design extremely expensive. The use of hydrofracturing in deep exploratory holes provides the needed information well ahead of the final design stage and without necessitating additional drilling and tunneling expenses.

The Helms Pumped Storage Project will be located about 100 km east of Fresno, California in the Sierra Nevada Mountains. Analyses of the local conditions led to a design calling for a 98 m long, 25 m wide and 36 m high powerhouse to be constructed some 300 m deep in a granitic rock. Topographic difficulties and lack of excavation permit precluded the driving of a pilot tunnel. The only logical decision was to use hydrofracturing for stress measurements in the existing deep exploratory holes. Nine successful hydrofracturing stress measurements were conducted in two of the existing coreholes, seven in a vertical hole between the depths of 119 and 326 m, and two in an inclined hole at depths of 239 and 271 m [21]. All except for the shallowest test yielded nearly vertical fractures oriented between N 8~'E and N 55"~E and averaging N 25°E. This result indicated that the 2000

2:50 E

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\l.

ml

E

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. ,,2o \ o

o

max --

LLI

\

Z --

0

oo

,Tso,

0

,

\

, \ 40

i

i\ 80

~,

470

120

STRESS, bars

Fig. 5. Tunnel complex U12n, Nevada Test Site, and location of surface test-hole (UE7) and underground test-holes (in drifts 01 and 06).

Fig. 6. V a r i a t i o n of m e a s u r e d stresses with e l e v a t i o n o r w i t h d e p t h f r o m t h e t o p of the m e s a at t h e N e v a d a Test Site t u n n e l c o m p l e x U 1 2 n . T h e v e r t i c a l stress s h o w n is for the p a r t o f the t u n n e l u n d e r the mesa.

172

B.C. Haimson STRESS (bors) 50

150

|oo l

I

•

•

O" , |

E

¢t

2200

HELMS

E

"~

z O I-.-

22~

p-

X-O'Hmo X

bJ

~-O'.min

lad ..I

/°

300

\ ",,

2100 -

Fig. 7. Variation of measured stresses with depth at the site of the Helms Pumped Storage underground powerhouse.

principal stresses acted approximately in the vertical direction and the horizontal plane with the direction of the maximum horizontal stress (an.,ox) at N25°E. The magnitudes of an,.~x ranged from 54 to 100 bars, displaying a linear rate of increase with depth, almost identical to that of the vertical principal stress (Ov) (Fig. 7). The latter was calculated from the weight of the overlying rock. The least principal stress (art,.i.) ranged between 45 and 55 bars in the direction N 65°W. The uniqueness of these measurements was that for the first time an inclined hole was used for hydrofracturing tests in order to verify the orientation of the principal stresses. At the approximate depth of the future powerhouse (300m), the stresses as derived from Fig. 7 were ~rv = 82 bars, an,,,i, = 54 bars at N 65°W and aH,,.~ = 95 bars at N 25°E. Some important changes in the original layout were made as a direct result of the pre-excavation hydrofracturing measurements (Fig. 8). It was discovered that the minimum principal stress was apparently lower than the static pressure expected in the penstock area

~

(53 58 bars). This internal pressure would not be sufficient to fracture the wall of the penstock, but was high enough to open up existing joints or other discontinuities which were oriented perpendicular to the direction of am, i,. To prevent any communication to the powerhouse, the length of steel lining in the penstock would have to be sufficiently long to prevent joints intersecting any of the penstock branches at the end of the lining from reaching the powerhouse cavern. The original layout called for the bifurcation branch to be oriented at N 30°E, which subparallels the direction of obtained hydrofractures. To avoid opening up existing discontinuities in an axial direction, the decision was made to rotate the bifurcation branch about 90 ° so that the minimum principal stress acted parallel to its length. These and other changes in the original layout were easy to make in the early stage of the design. Were the stresses not determined in the pre-excavation stage, considerable expense and time delays would have been encountered in making any of the above corrections. No layout changes have yet been made in the powerhouse chamber itself but the stress measurement results, together with other rock properties determined, are being incorporated in a finite-element analysis designed to determine stresses and displacements in the crown and wall of the chamber and establish the stability of the cavity, its most suitable orientation and the amount of required reinforcement and support. The Bad Creek Pumped Storage Project will be located along the southeastern edge of the Blue Ridge Escarpment, in the upper part of Oconee County, South Carolina. The powerhouse chamber will contain four 250 MW generating/pumping units and its tentatively planned size is 27 m by 137 m and 40m high. As preliminary layout and design work progressed, it was realized that additional information would be required for the location, orientation and design of the underground facilities. In order to obtain the needed

Iollo ( I I -\

DRAJINAGE GALLERY

~i~ I~..~ RA NGE OF L 150m ~/'HYDRO FRACTURESI~t~C~[

ELEVATO4~ SH/kCT

,;;: /:;'" if-" .

EXCAVATION POWERHOUSE COMPLEX Fig. 8. Original and modified layout of the underground powerhouse complex

Helms Pumped Storage Project.

The Hydrofracturing Stress Measuring Method STRESS ( K b I O.I I

0.1

t

%, x,, E

•

\ "I" I-0. bJ

0.2

BAD (~REEK

/,,,o

\°

A

%%

O"Hmi n ~o

\

x • •

-

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O - O-H m i r a

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\, \O'v(O,,e~u,~)~

i

o

..,,.

"'.. \o

0.3

0.3

0.2

x "-

i

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Fig. 9. Variation of measured stresses with depth at the site of the Bad Creek Pumped Storage underground powerhouse.

data, a preliminary location for the powerhouse was established in the Toxaway gneiss and one NX size hole was drilled vertically, approximately 275 m deep into the zone of the future excavation. Seven successful hydrofracturing stress measurements were conducted at different depths in the hole between 120 and 2 7 0 m [21]. Two levels of shut-in pressures were recorded in most of the tests, the lower one always close to the calculated vertical stress based on the weight of the overburden. The impression packers showed clear traces of both vertical and horizontal fractures. The average orientation of the vertical fractures in the powerhouse zone was N 60°E. The breakdown pressure and the first value of the shut-in pressure were used to estimate the magnitudes of the horizontal principal stresses. The results shown in Fig. 9 indicate a linear increase in stress with depth; a remarkable coincidence in values of calculated and hydrofracturing determined vertical stresses; consistent least horizontal principal stresses; and a rather wide scatter in the magnitudes of the maximum principal stress. Based on Fig. 9, at the depth of 230 m which is about the center of the planned powerhouse, the following in-situ stresses are expected: ~rv = 62 bars, am, i. = 159 bars at N 3ff~W, an,,,~ = 228 bars at N 60°E. The stress results will be the basis for laying out a pilot tunnel into the powerhouse area. The pilot tunnel will provide further geological and mechanical details for the final design of the powerhouse, and in particular, its orientation. Analysis of the underground powerhouse by the finite-element method will be conducted prior to the completion of the pilot tunnel using the information obtained from the hydrofracturing tests as a guide in selecting the appropriate ranges of stresses. After the pilot tunnel is completed, the in-situ stresses will be determined again using several methods and the results will be compared to the values used in the present analysis.

underground annular tunnels. The tunnels will be subjected to high mechanical pressures and are to be built in rock of unquestioned quality, strength and stiffness, subjected to favorable in-situ stress conditions [22,23]. To test the applicability of a Pre-Cambrian granite site at Montello, Wisconsin, a vertical corehole, 7.5 cm in diameter was drilled and 7 hydrofracturating stress measurements were conducted between the depths of 75 and 188 m. Five of the borehole impressions after hydrofracturing yielded both vertical and horizontal (or inclined along the planes of previously closed joints) fracture traces, indicating that the least principal stress acts in the vertical direction (av). All five vertical fractures were within -t-20 ° from the mean direction of N 63°E. In these five tests, as in the Bad Creek Pumped Storage case, two shut-in pressures were identified, the first corresponding to the vertical fracture and, hence, yielding the least horizontal principal stress (am, i.), and the second approximately equal to the overburden weight (av). The latter was determined in the laboratory as 0.25 bars/m × depth (m). The least horizontal stress appeared insensitive to the minor depth variations of these tests and was limited between 62-82 bars. The maximum horizontal stress (an,.,~) calculated from the recorded breakdown pressure, the first shut-in pressure and the laboratory determined hydrofracturing tensile strength ( = 172 bars), varied between 140-200 bars (Fig. 10). For example, at 136 m depth the principal stresses were: or,, = 35 bars, an,.i. = 70 bars at N27°W, trn,,, ~ = 160 bars at N 63°E. These results have been incorporated in a finite-element program in order to determine the effect of the stress distribution on the magnet-tunnel stability. (e) Crustal stress Basin

an ultra deep well in the Michigan

Cratonic basins, because of their subsidising tendencies, preserve the most complete geologic record of continental interior histories. They are also the sites of large fossil fuel, salt, potash and oil shale deposits. Despite the importance of these basins, little is understood about the mechanics of their subsidence, and, hence, no adequate models exist relating cratonic STRESS

(bars)

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1

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= t

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(d) Underground storage caverns--Montello, Wisconsin

I

I

r

The University of Wisconsin--Madison is currently studying the feasibility of constructing superconductive magnets for electric energy storage in Wisconsin. The doughnut-shaped magnets, 50-100min in radius and about 5 × 10m in cross-section, will be mounted in

173

x

I

I

= i

Fig. 10. Variation of measured stresses with depth in Montello, Wisconsin.

174

B.C. Haimson STRESS (kb) I0

DEVONIA~,,O Z -SILURIAN . . . . . I I1 OI,I r~

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OF TRENTON LIMESTONE

(ORD~N)

Fig. 11. Map of the Michigan Basin showing the contours on top of the Trenton limestone and the location of the deep well where hydrofracturing was carried out.

events to global tectonic theory. A recently drilled, ultra deep oil well provided an excellent opportunity to conduct basic geophysical tests in the Michigan Basin in an effort to find answers to some of the major puzzles related to continental interiors. One of the important tests undertaken was the evaluation of the stress regime in the basin. A series of five hydrofracturing tests were conducted in the 5325-m deep well in Gratiot County, near the axis of the Michigan Basin (Fig. 11). These were probably the deepest stress measurements ever undertaken [24]. The top three tests were run through perforations in the casing and were limited by the availability of well-cemented cased zones. The controlled manner of hydrofracturing and the repeatability of results during repressurizations suggest that the perforation tests were probably as reliable as open-hole ones, at least with respect to the smallest horizontal principal stress (~r,,,,i,,). In calculating an ..... an arbitrary tensile strength of 100 bars was used since no core samples were available for testing. The vertical stress (O-v) was estimated at 0.250 bars/m x depth (m). The two deepest tests were run in open-hole. At 5320 m, the m a x i m u m allowable pressure (limited by pipe strength) of 1 kbar was not sufficient to hydrofracturc the gabbro zone. At 5110 m, a late P r e - C a m b r i a n red silty shale was hydrofractured yielding an,,i,, :

bars. The Mount

Simon

"~...

O'Hmift

N"~°'v

-:.-\.

.'AM..tA.

",~,

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

.5-LATE

PRECAMBRIAN

\ ~-

-

~-

b.

\, Ix

.

DE'I'~OIT

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Fig. 12. Variation of measured an,,~, and of av with depth near the center of the Michigan Basin.

,-I

.

MICHIGAN

~

I

(bo~)

1.0

~

~-~x-- -- --~ -

ORDOVICIAN

/

•

0.5

960 b a r s , a n d a n , , ~ x ± 1470

sandstone

was

tested

at

3660m: c~n,,i,=645 bars, a H , , a ~ 2 8 8 5 bars. The Prairie du Chien dolomite was tested at 2806m: am.i. = 400 bars, a n , , . ~ ~- 560 bars. The shallowest test, run at 1230 m in the Devonian Amhertsburg formation, gave a m , i, = 295 bars and anm,x - 505 bars. This a m . i , is considerably higher than expected from extending the linear curve fitting the three deeper values, and is very close to av (Fig. 12). This discrepancy could partially be due to the discontinuity between the Devonian and the Silurian (5--10 x 10 ~' years) and/or a result of stress relaxation in and above the Salina salt layers. A more detailed interpretation of the stress results can be found in Haimson, 1978 [24]. Directions of the principal stresses were not determined in these tests. However, by interpolating k n o w n results in the Midwest and Southern Ontario, we speculate that o-n,.~ is oriented at about N 6 0 ° E (Fig. 13).

MEASUREMENTS IN ICELAND Iceland occupies a unique position in plate tectonics theory because of its location at the boundary of the N o r t h American Plate, on the axis of a mid-ocean ridge underlain by shallow asthenosphere. The rift structure in Iceland and earthquake focal mechanism solutions along the mid-Atlantic Ridge support a crustal exten-

Fig. 13. Maximum horizontal stress directions in the Midwest and Ontario based on hydrofracturing (blocked squares) and strain relief (open circles} measurements [24].

The Hydrofracturing Stress Measuring Method

175

-~.j ,2 J J

IF ;R

Fig. 14. Map of Iceland showing the location of the mid-Atlantic Ridge boundaries (shaded area). Also shown are the more reliable of Hast's overcoring locations (B), and the hydrofracturing sites (A). Straight lines at A and B indicate direction of an,,,,~,. Representative focal mechanism solutions are shown by circles. Dark quadrants indicate direction of (~Hrain.

sion condition perpendicular to the ridge [25]. However, in-situ overcoring stress measurements by Hast [26] conducted in shallow boreholes around Iceland indicate relatively high horizontal compressive stresses. These results do not appear compatible with ocean floor spreading processes, nor are they in accord with focal mechanism solutions for Icelandic earthquakes (Fig. 14). Since Hast's data were probably affected to some extent by near surface topographic and thermal perturbations rather than by deep-seated tectonic forces it was considered essential that a set of deep measurements by a different technique be undertaken. During the summer of 1976 we conducted seven successful hydrofracturing experiments in two boreholes (H18 and H32) in Quaternary igneous rocks in Reykjavik, Iceland, on the flank of the Reykjanes Peninsula continuation of the mid-Atlantic Ridge. The holes are located about 20-25 km northwest of the axis of the active zone of rifting and volcanism (Fig. 14). These holes are relatively small diameter observation wells drilled 15-20 years ago near the periphery of the Laugarnes hydrothermal system. The major problem with the hydrofracturing tests was the pre-existing joints in the test-holes. In successful tests these joints appeared to be sufficiently tight or healed so as not to interfere with pressurization. In such cases a vertical hydrofracture was induced. To verify that hydrofractures were actually obtained, two packer impressions were taken in some tests, one before and one after pressurization. In each test both impressions showed pre-existing inclined cracks in the rock but only the impressions taken after hydrofracturing showed also the existence of a vertical fracture traversing the length of the interval. More details on test pro-

cedures and calculations are given by Haimson and Voight [27]. The calculated stresses are plotted with respect to depth in Fig. 15. The data suggest that each borehole site represents a distinct stress population. The quality of fit achieved by linear regressions is excellent for ~rn,,i, in both instances; the fit is good with respect to a n , . , x. The results for H32 are very consistent. Both an,.i, and an,..x increase steadily with depth at about the same rates, which are substantially lower than the rate of increase of overburden pressure. The relative orientation of crn,.,x remains virtually constant with depth at N 23°W 4- 3 °. The results of H18 are also relatively consistent: an,.~, and a v seem to increase steadily with depth at about the same rate; an,.ox also increases with depth, but perhaps at a higher rate. Throughout the depth range tested the vertical stress is the intermediate principal stress. The data from each series of tests displays internal consistency, although different states of stress are suggestive for boreholes H32 and H18 which are only 2 km apart. On the whole, the data indicate a dominant N N W to NW orientation for anm,x; at H18 the stress state favors strike-slip faulting (for d > 150 m), whereas this regime seems restricted (say 100m < d < 250m) at H32. A normal fault regime seems dominant at H32 (for d > 250 m). The hydrofracturing stress measurements at Reykjavik suggest a dominant regional orientation of am.ax approximately perpendicular to the axial rift zone (Fig. 14). This orientation is furthermore supported by Hast's shallow overcoring measurements in southeast Iceland. This state of stress is fundamentally different from that in the axial rift zones themselves (see focal mechanism solutions. Fig. 14). In the rift zones, an,,,~,, is consistently

176

B.C. Haimson

STRESS (bors) 4O

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w

!

120

i

40

80

120

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ix

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\ \" N "",.-,~ I~Hmax \ \ "-.,

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\

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\

0.4 i

_

L

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i

L

i

Fig. 15. Variation of measured stresses with depth in two boreholes in Reykjavik, Iceland.

aligned perpendicular to individual rift zone fissures and faults. For detailed interpretation of these results, see Haimson and Voight [27].

CRUSTAL STRESS IN THE UNITED STATES The accumulating data on crustal stresses in the United States, based on recent hydrofracturing measurements, and corroborated by other stress determinations and geological evidence have a common denominator in the direction of the major horizontal principal stress, which is consistently found to be approximately northeast (Fig. 16). Sbar and Sykes [28] have related this phenomenon to plate tectonics and

- ' - " o'Hrnox

seismicity in America. Although northeast is the major direction trend, local deviations up to +45 ° do exist which necessitate measurements where more precise stress orientation is required. The ability to use hydrofracturing for stress determination at depths never attempted before is beginning to provide us with a more complete picture of the stress profile. Figure 17 shows the variation of horizontal and vertical stresses with depth in the United States down to 5 km, and is based only on hydrofracturing measurements. Similar profiles have been obtained before, based on other stress determination methods [26,29-31], but they were the result of measurements conducted from underground openings and were limited in the overall depth.

DIRECTION

Fig. 16, M a x i m u m horizontal principal stress directions in the continental United States based on the orientation of vertical hydrofractures. Data obtained from measurements described in this paper and in references [l,8, 33-43] and s u m m a r ized by H a i m s o n [32].

T h e H y d r o f r a c t u r i n g Stress M e a s u r i n g M e t h o d s~ess 5

~

(XK)Zbo.)

in anm,x m a g n i t u d e s , w h i c h are also m o r e widely scatt e r e d with r e s p e c t to the a v e r a g i n g curve. M o r e o v e r , Fig. 17 is n o t i n t e n d e d for use in lieu of m e a s u r e m e n t s . L o c a l stresses c o u l d significantly vary from the p l o t t e d a v e r a g e as c a n be verified f r o m the results of the m e a s u r e m e n t s d e s c r i b e d in d e t a i l in this p a p e r .

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Acknowledgements--This contribution is based in part on a paper

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CONCLUSIONS H y d r o f r a c t u r i n g is the o n l y a v a i l a b l e m e t h o d of stress d e t e r m i n a t i o n in d e e p holes. In the last decade, it has seen ever i n c r e a s i n g use in the U n i t e d States a n d elsewhere. W e h a v e e m p l o y e d it in r e l a t i o n to e a r t h q u a k e c o n t r o l research, p r e - e x c a v a t i o n u n d e r g r o u n d o p e n i n g design, g r o u n d stability u n d e r n u c l e a r d e t o n a t i o n , a n d s t u d y of t h e l i t h o s p h e r e in M i c h i g a n and Iceland. H y d r o f r a c t u r i n g results to d a t e i n d i c a t e t h a t s t r e s s d i r e c t i o n s in the c o n t i n e n t a l U n i t e d States are r a t h e r uniform, while the increase of stress with d e p t h a p p e a r s to b e l i n e a r for the r a n g e of d e p t h s tested.

t::

ltfL

177

\

Fig. 17. Variation of principal stresses with depth in the continental United States based on hydrofraeturing results. Data obtained from measurements described in this paper and in references [1,8,33~,3] and summarized by Haimson [32].

T h e h y d r o f r a c t u r i n g r e s u l t s have been fitted with linear curves given by the f o l l o w i n g r e l a t i o n s h i p s : anmi, = 20 + 0.16 d

an,,,x = 75 + 0.24 d a v = 0.25 d where stresses a r e in b a r s a n d d e p t h s (d) in m e t e r s (limited to 0 - 5 0 0 0 m). T h e v e r t i c a l stress is the result of b o t h o v e r b u r d e n weight a n d h y d r o f r a c t u r i n g m e a s u r e m e n t s . T h e r e l a t i o n s h i p s s h o w t h a t at s h a l l o w depths the mean horizontal stress given by aHavo -= 50 -t- 0.20 d tends to b e higher t h a n the vertical stress, as p r e v i o u s l y n o t e d b y H a s t [26] a n d others. B e n e a t h 1 k m t h e m e a n h o r i z o n t a l stress is l o w e r t h a n the vertical stress and b e c o m e s 0.8 av at 5 k m . T h e t r e n d is s i m i l a r to that o b s e r v e d by G a y [30] in S o u t h ern Africa. It is to be r e m e m b e r e d t h a t m o s t of the h y d r o f r a c t u r i n g m e a s u r e m e n t s b e n e a t h 0 . 5 k m were t a k e n in s e d i m e n t a r y r o c k f o r m a t i o n s , a s s o c i a t e d with g e o l o g i c a l l y s t a b l e areas o f little seismic activity. F u r t h e r d e t a i l s on crustal stresses in the c o n t i n e n t a l U n i t e d States h a v e been p u b l i s h e d by H a i m s o n 1-32]. W e e m p h a s i z e here t h a t Fig. 17 is p r e l i m i n a r y in n a t u r e a n d m a n y m o r e m e a s u r e m e n t s are n e e d e d before the s t r e s s - d e p t h r e l a t i o n s h i p s can be u n e q u i v o cally e s t a b l i s h e d . W e also stress t h a t o u r c o n f i d e n c e in the a c c u r a c y of anmi~ values is s o m e w h a t h i g h e r t h a n

delivered at the ISRM Symposium on Investigation of Stress in Rock, held in Sydney, Australia in August 1976. The work reported was supported in part by the United States Geological Survey (grants 14-18-0001-12281 and 14-08-0001-6118), United States Bureau of Mines (contract HO220080), National Science Foundation (grants EAR 76-02952, EAR 76-03821, EAR 72-03564), Defense Nuclear Agency (contract DNA 001-73-CO212), American Petroleum Institute, Wisconsin Electric Utilities Research Foundation, Pacific Gas and Electric Co., Duke Power Co., and the Wisconsin Alumni Research Foundation. Among the graduate students contributing to the success of our measurements special thanks are due to J. Avasthi, L. Cheung, T. Doe, J. Edl, S. Erbstoesser and K. Kim. Receiced 19 Auoust 1977.

REFERENCES

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178

B.C. Haimson

12. Kehle R. O. Determination of tectonic stresses through analysis of hydraulic well fracturing. J. geophys. Res. 69, 259-266 (1964). 13. Haimson B, and Stahl E. Hydraulic fracturing and the extraction of minerals through wells. In Proc. 3rd Symp. on Salt, pp. 421~,32. Northern Ohio Geological Society, Cleveland, Ohio (1970). 14. Haimson B. C. Stress measurements in the Weber Sandstone at Rangely, Colorado. EOS Trans. Am. Geophys. U. 53, 524 (1972). 15, Haimson B. C. Earthquake related stresses at Rangely, Colorado. In New Horizons in Rock Mechanics; Proc. 14th Syrup. Rock Mech. (Edited by Hardy H. & Stefanko R.), pp. 689- 708. ASCE, New York (1973). 16. Raleigh C. B., Healy J. H. & Bredehoeft ,I. D. Faulting and crustal stress at Rangely, Colorado. In Flow and Fracture of Rocks, pp. 275-284. Geophysical Monograph 16, Am. Geophys. U. (1972). 17. Wallace R. E. Goals, Strategy and Tasks of the Earthquake Hazard Reduction Program. Geological Survey Circular 701 (1974). 18. Hooker V. E., Aggson T. R. & Bickel D. C. ln-situ Determination of Stresses in Rainier Mesa, Nevada Test Site. U.S. Bureau of Mines report (1971). 19. Haimon B. C., Lacomb J., Jones A. H. & Green S. J. Deep stress measurements in tuff at the Nevada Test Site. In Advances in Rock Mechanics, pp. 557-561. National Academy of Science, Washington, D.C. (1974). 20. Hamilton R. M. & Healy J. H. Aftershocks of the Benham nuclear explosion, Bull. seism. Soc. Am. 59, 2271-2281 (1969). 21. Haimson B. C. Design of underground powerhouses and the importance of pre-excavation stress measurements. In Design Methods in Rock Mechanics; Proc. 16th Syrup. Rock Mech. (Edited by Fairhurst C. & Crouch S. L.), pp. 197-204. ASCE, New York (1977). 22. Haimson B. C., Doe T. W., Erbstoesser S. R. & Fuh G. F. Site characterization for tunnels housing energy storage magnets. In Site characterization; Proc. 17th U.S. Syrup. Rock Mech., pp. 4B41-4B49. Utah Engrg Exper. Station, Salt Lake City, Utah (1976). 23. Haimson B. C., Doe T. & Fuh G. F. Geotechnical investigation and design of annular tunnels for energy storage. In Preprint Proc. of First Ira. Syrup. on Storage in Excavated Rock Caverns, Stockholm. 2, 59-66 (1977). 24. Haimson B. C. Crustal stress in the Michigan Basin. J. geophys, Res. (1978) In press. 25. Klein F. W., Einarsson P. & Wyss M. Microearthquakes on the mid-Atlantic plate botmdary on the Reykjanes Peninsula in Iceland. J. geophys. Res. 78, 5084-5099 (1973). 26. Hast N. Global measurements of absoh, te stress. Phil. Trans. R. Soc. 274, 409-419 {1973).

27. Haimson B. C. & Voight B. Crustal stress in Iceland. Pure appl. Geophys. 115, 1-38 (1977). 28. Sbar M. L. & Sykes L. R. Contemporary compressive stress and seismicity in Eastern North America: an example of intra-platc tectonics. Geol. Soc. Am. Bull. 84, 1861-1882 (1973). 29. Herget G. Ground stress determination in Canada. Rock Mech. 6, 53 64 (1974). 30. Gay N. C. In-situ stress measurements in Southern Africa. Tectonophys. 29, 447-459 (1975). 31. Ranalli G. & Chandler T. E. The stress field in the upper crust as determined from in-situ measurements. Geol. Rdsch. 64, 653-674 (1975). 32. Haimson B. C. Crustal stress in the continental United States as derived from hydrofracturing tests. In The Earth's Crust, pp. 576 592. Geophysical Monograph 20. Am. Geophys. U. (1977). 33, vc;n Schonfeldt H. A.. Kehle R. O. & Gray K. E. Mapping of stress field in the upper earth's crust of the U.S. Final Technical Report to U.S.G.S. (14-08-0001-122278) (1973). 34. Zoback M. D., Healy J. H. & Roller J. C. Preliminary stress measurements in Central California using the hydrofrac technique. Pure appl. Geophys. 115 (1977). 35. Bredehoeft J. D., Wolff R. G., Keys W. S. & Shutter E. Hydraulic fracturing to determine the regional in-situ stress field, Piceance Basin, Colorado. Geol. Soc. Am. Bull. 87, 250-258 (1976). 36, Haimson B. C. Stress measurements in faults and their vicinities. Final Report to U.S.G.S. (grant 14-08-0001-G118) (19771. 37. Power D. V., Schuster C. L., Hay R. & Twombly J. Detection of hydraulic fracture orientation and dimensions in cased wells. J. Petrol. Technol. 28, 1116-1124 (1976). 38. Strubher M. K., Fitch J. L. & Glenn E. E., Jr. Multiple vertical fractures from an inclined wellbore--a field experiment. J. Petrol. Technol. 27, 641 -647 (1975). 39. Tyler L. D. & Vollendorf W. C. Physical observations and mapping of cracks resulting from hydraulic fracturing in-situ stress measurements. Paper No. SPE 5542 presented at Soc. of Petrol. Engrg. of A1ME, Fall Mtg (1975). 40. Haimson B. C. A stress measurement in West Virginia and the state of stress in the Southern Appalachians. EOS Trans. Am. Geophys. U. 58, 493 (1977). 4l. von Schonfeldt H. A. An experimental study of open-hole hydraulic fracturing as a stress measurement method with particular emphasis on field tests. Ph.D. thesis. University of Minnesota (t970). 42. Parsons R. C. & Dahl H. D. A study of thc cause of roof it~stabilit 3' in the Pittsburgh coal seam. In Proc. 7th ('amsdia~7 R~'t, Mechanics Syrup., Mines Branch Dept. of Energy, Mines and Resources, pp. 79- 87 (1972). 43. Zoback M. D. and Healy J. H. In-situ stress measurcments ncar Charleston, South Carolina. EOS Trans. Am. Geophy. U. 58, 493 11977).