UNITED STATES BUREAU OF MINES

UNITED STATES DEPARTMENT OF THE INTERIOR

RI 9567 REPORT OF INVESTIGATIONS/1995

In Situ Stress at the Lucky Friday Mine

(In Four Parts):

3. Reanalysis of Overcore Measurements

From the Star Mine
U.S. Department of the Interior

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administration.
Report of Investigations 9567

In Situ Stress at the Lucky Friday Mine

(In Four Parts):

 3. Reanalysis of Overcore Measurements

From the Star Mine

By J. K. Whyatt, M. J. Beus, and M. K. Larson

UNITED STATES DEPARTMENT OF THE INTERIOR

Bruce Babbitt, Secretary

BUREAU OF MINES

Rhea Lydia Graham, Director
International Standard Serial Number

ISSN 1066-5552
CONTENTS

Page

Abstract ...................................................................................... 1

Introduction .................................................................................... 2

Review of available information ...................................................................... 2

Exploratory boreholes and physical property tests ....................................................... 2

Overcore procedure ............................................................................ 6

Data-reduction procedure ........................................................................ 6

Stress field estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Evaluation of strain data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

7300-level stress field estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Stress field characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Doorstopper-scale assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Site-scale assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Local stress variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Appendix A.—Sensitivity of stress field estimate to choice of stress concentration factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Appendix B.—Doorstopper cell local solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Appendix C.—Ranking criteria for quality designation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

ILLUSTRATIONS

1. Location of Star and Lucky Friday Mines in Coeur d'Alene Mining District of northern Idaho ...................... 3

2. Location of 7300- and 7500-level test sites with detail of 7300-level site ..................................... 4

3. Borescope maps ............................................................................. 5

4. Schematic of CSIR doorstopper cell in borehole ...................................................... 7

5. Normal strain orientations used in equation 1 ........................................................ 9

6. Range of stress fields measured on end of borehole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

7. Range of principal stress orientations and magnitudes plotted by relative position in each borehole . . . . . . . . . . . . . . . . . . 20

8. Location of doorstopper cells and orientation of bedding for each overcore measurement borehole . . . . . . . . . . . . . . . . . . 22

TABLES

1. In situ modulus as measured by CSM dilatometer ..................................................... 3

2. Summary of strain data from doorstopper cell overcoring at Star Mine ...................................... 8

3. Average strain readings ........................................................................ 9

4. Selection and interpretation of strain measurements .................................................... 9

5. In situ stress field at 7300-level site as calculated using principal stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

6. Range-screen classification by spread of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

7. Strain screen of data from doorstopper cell overcoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

8. Comparison of screen results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

9. In situ stress estimates from 7300-level data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

10. Best estimate of stress field in map coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

11. In situ stress estimates from 7300- and 7500-level data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

12. Best estimate of average stress state at 7300-level measurement site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

A-1. Stress solutions based on original six composite strain measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

B-1. Stress solutions for end of borehole using various combinations of three strain gauges at each doorstopper cell location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

B-2. Range of individual doorstopper cell solutions for stress on end of borehole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT

Metric Units

cm centimeter m meter

deg degree MPa megapascal

GPa gigapascal pct percent

kg/m kilogram per cubic meter μ, microstrain 3

km kilometer

U.S. Customary Units

ft foot lb/ft pound per cubic foot 3

in inch psi pound per square inch

Reference to specific products does not imply endorsements by the U.S. Bureau of Mines
In Situ Stress at the Lucky Friday Mine

(In Four Parts):

3. Reanalysis of Overcore Measurements From the Star Mine

By J. K. Whyatt, M. J. Beus, and M, K. Larson 

ABSTRACT

U.S. Bureau of Mines researchers reviewed an in situ stress estimate developed from measurements of overcore

strain taken at test sites on the 7300 and 7500 levels of the Star Mine near Mullan, ID. Although the field

measurements of overcoring strain were found to be useful, significant deficiencies were found in the stress

estimation procedure. A new stress estimate was developed incorporating statistical methods and an improved

understanding of stress concentration factors for interpreting overcore strains recorded by doorstopper cells. Spatial

variability of overcore strains and the implications for stress field variability were explored.

Mining engineer, Spokane Research Center, U.S. Bureau of Mines, Spokane, WA. 1
2

INTRODUCTION

Researchers from the U.S. Bureau of Mines (USBM) the accuracy of the analysis by applying a least squares procedure

undertook the investigation described in this Report of and improved doorstopper cell stress concentration factors.

Investigations (RI) to increase basic knowledge of the in situ Reanalysis of this stress estimate 15 years after the overcore

stress field in the vicinity of the Lucky Friday Mine of the Coeur measurements were taken and over 10 years after publication of

d'Alene Mining District of northern Idaho. The study is based on a USBM RI describing the work (Beus and Chan, 1980) was

an overcore stress measurement reported by Beus and Chan made possible by the existence of good, detailed records

(1980) as part of a USBM investigation into shaft design criteria maintained in USBM research files.

for the Coeur d'Alene district. This stress measurement was Previous reports in this series [Whyatt and Beus, 1995 (part

chosen for reconsideration because the measurement site is 1); Whyatt and others, 1995a (part 2)] analyzed overcore stress

conveniently located with respect to active USBM research measurements conducted on the 4250 and 5300 levels of the

projects at the Lucky Friday Mine (figure 1). Knowledge of the Lucky Friday Mine. A fourth and final report presents

in situ stress field will provide important information for ongoing observational evidence of stress field orientation (Whyatt and

projects aimed at developing improved mining methods and others, 1995b). The final report also characterizes the stress field

mitigating rock-burst hazards at this mine. There was in the vicinity of the Lucky Friday Mine.

considerable potential for increasing

REVIEW OF AVAILABLE INFORMATION

The Star Mine stress measurement was originally pursued Bedding at the 7300-level site is nearly vertical, and some

to develop an estimate of the natural in situ stress field in the beds are overturned. Strike of the beds varies across the Morning

vicinity of the mine. A good estimate of the natural stress East vein. There is a significant change in lithology as well.

condition required that the overcore measurement site be located Rock south of the Morning East vein is a relatively stiff quartzite,

far enough from mining to avoid mining-induced stress. On the while rock to the northeast of the vein is a relatively soft sericitic

other hand, cost considerations required that the site lie within quartzite.

mine development openings. Furthermore, a site with competent The 7500-level site lies on the north side of the Morning East

rock was sought to ensure that sufficient core recovery could be vein but south of the Main vein and toward the middle of the

obtained for a successful measurement. mine. It also lies in the Revett Formation. Bedding dips steeply

The stress field reported by Beus and Chan (1980) was based and strikes to the north and slightly west.

on 30 doorstopper cell overcore measurements in 3 boreholes at

a site located on the east end of the 7300 level (figure 2). These EXPLORATORY BOREHOLES AND PHYSICAL

measurements were taken between July and October 1975. In PROPERTY TESTS

April and May 1975, six doorstopper cell overcore measurements

were taken in a single borehole on the 7500 level 350 m (1,150 The important role of geology at the site was recognized at the

ft) to the west of the 7300-level site. The 7500-level outset by the investigators. EX-size boreholes were drilled

measurements were not included in the original analysis. parallel, perpendicular, and diagonal to bedding about 30 cm (12

The 7300-level site lies in rocks of the Revett Formation near in) below the planned BX-size overcore boreholes. A borescope

the intersection of the Morning East and Grouse veins. The survey of the EX boreholes was used to map fractures and

Revett Formation is part of the Belt Supergroup and consists of identify depths at which in situ modulus measurements would

(1) sericitic quartzite beds that range in thickness from 15 to 61 have the best chance of success (figure 3).

cm (6 in to 2 ft) and (2) thin interbeds of argillite generally less The in situ modulus tests (table 1) were conducted with a

than 2.5 cm (1 in) thick. Variations in sericite produce rocks with Colorado School of Mines (CSM) dilatometer (Hustrulid, 1971)

a considerable range of stiffness, strength, and brittleness. The in November 1975. The four basic components of this device are

quartzite beds also contain a small-scale depositional fabric, which a polymeric cell (packer) that fits an EX borehole, a water-based

has been shown to be associated with strength and deformational fluid, a hydraulic pump, and a pressure gauge. The packer is

anisotropy at some locations within the district (Whyatt, 1986). inflated inside the borehole by hand cranking a screw-type pump

that displaces a measured amount of fluid with each crank.

Deformation of the borehole is reflected by
3

Table 1.—In situ modulus as measured by CSM dilatometer

Borehole

Borehole

angle to

bedding

Number

of test

locations

Mean modulus

of deformation

Standard

deviation

GPa i 10 ps 6 GPa si 10 p6

E1 . . . . 0E 3 48 7.0 19 2.7

E2 . . . . 90E 3 77 11.1 19 2.7

E3 . . . . 45E 12 68 9.8 25 3.6

the amount of fluid pumped into the packer. The modulus of drilling. The source of this discrepancy is not evident but may

deformation is obtained by comparing pressure and volume field arise from differences in the rocks tested. Cores from borehole

records with records from laboratory tests on known materials. E1 sampled a very limited thickness of strata that lay on top of

The dilatometer tests found marked anisotropy of in situ the strata drilled in borehole E2. Unfortunately, further

modulus with bedding (Patricio and Beus, 1976), with results information on the type of rock involved in these tests was not

reproducible to within ±2 pct. However, the dilatometer is available.

calibrated to estimate the elastic modulus of an isotropic material.

That is, the inflation of the packer is assumed to proceed

uniformly around the circumference of the borehole. If rock

stiffness is anisotropic, expansion of the borehole will be greater

in some directions than in others.

Amadei and Savage (1991) provide the anisotropic solution

for the dilatometer, but require measuring diameter deformation

in a number of directions as provided by modern versions of the

dilatometer. Thus, their solution cannot be applied to estimating

orthotropic properties from available CSM dilatometer

information. Volume change will approximately reflect the

average change in borehole radius. This is not a problem where

a borehole is perpendicular to bedding because of the symmetry

perpendicular to the borehole. At other orientations, however,

resistance to change of radius in the stiff direction dilutes the

impact of the soft direction, producing an intermediate estimate

of elastic modulus. Thus, the in situ modulus measurements

shown in table 1 likely understate the degree of anisotropy. Beus

and Chan (1980) acknowledged this apparent anisotropy but did

not pursue it further in laboratory testing or integrate it into their

in situ stress estimates. The large standard deviations for the in

situ measurements considerably exceeded the expected ±2 pct

variation. The extra variability reflected changing rock properties

with position in the borehole.

Laboratory tests on the EX core samples from borehole 1 only

were used to determine the average elastic modulus of 63.8 GPa

(9.26 million psi) reported for the site by Beus and Chan (1980).

The orientation of bedding or structure in these samples was not

recorded, but at the collar, bedding paralleled the borehole. The

in situ modulus measured in borehole E2, which loaded the rock

approximately parallel to bedding, exceeded the laboratory value

for cores from borehole E1, which were also loaded parallel to

bedding. In situ values of modulus were generally lower than

laboratory values because of the larger volume of rock tested and

because flaws were included that broke core samples during
4
5
6

OVERCORE PROCEDURE early Coeur d'Alene district investigations that have been found

The Council for Scientific and Industrial Research (CSIR)

biaxial strain cell, commonly known as a doorstopper, was

selected for the overcore strain measurements. The doorstopper

cell uses a four-element strain gauge rosette (figure 4) to measure

strain release as a diamond drill passes (overcores) the cell. The

difficulty of obtaining good core recovery at the site made the

doorstopper cell a particularly good choice. The doorstopper cell

requires only about 8 cm (3 in) of 6-cm (2.375-in) diam core for

a successful measurement (Jenkins and McKibbin, 1986), while

alternative types of cells require longer and larger diameter cores.

Although the doorstopper cell was not included in

International Society for Rock Mechanics (ISRM) standard test

procedures for overcore stress measurements (ISRM, 1987), the

procedure described was generally consistent with guidelines for

overcoring similar instruments and the manufacturer's

recommended procedure. An installation tool helps with the task

of centering and orienting the doorstopper cell, which is glued to

the polished end of the borehole to measure distortion as the

borehole is drilled. Load on the end of the rock core is relieved

where the cell is glued. The installation tool houses a second

doorstopper cell glued to a similar piece of core to compensate for

changes in temperature.

The doorstopper cell glue is allowed to set up overnight, after

which a series of readings is taken to establish baseline strain.

The installation tool and wiring are then removed for overcoring.

The doorstopper cell is small enough that properly centered cells

are not affected by extending the diamond-drilled borehole

(overcoring) to release stress on the face of the core. After

overcoring, the installation tool is reattached to the doorstopper

cell and a number of final readings are taken.

Determination of a full three-dimensional in situ stress state

requires data from doorstopper cells in three boreholes. However,

the gauges are fairly inexpensive, so installing several cells in

each borehole is economically feasible.

Overcoring procedures have changed somewhat since this

measurement was completed. The changes have improved the

likelihood that a doorstopper cell installation will be successful,

but have not changed the accuracy or validity of a successful

overcore. This review of overcoring procedure and field notes

encouraged confidence in the quality of the field measurements.

DATA-REDUCTION PROCEDURE

The procedure used by Beus and Chan (1980) to develop the

reported Star Mine stress field estimate was typical of

to suffer from a number of shortcomings (Whyatt and Beus,

1995). The application of this procedure to the Star Mine

overcore measurements is traced through the remainder of this

section.

Evaluate measurement quality.

The first step in the original procedure was to filter unreliable

measurements. About half of the strain readings survived this

step. Notes for discarded measurements attributed failure to a

number of problems, including difficulties with gluing the gauges

to the end of the borehole, water fouling the gauges, and lapses

in overcoring procedure. Although data were collected for one

borehole at the 7500-level site and three boreholes at the 7300-

level site, only the 7300-level site was fully analyzed and reported

by Beus and Chan (1980).

The measurements deemed to be reliable are underlined in

table 2, which includes some notes about the specific difficulties

encountered during overcoring.

Develop strain estimates for each gauge orientation.

The best overcore strains (underlining in table 2) were

averaged to obtain the set of 12 composite overcore strains shown

in table 3 (one for each gauge orientation in each borehole).

Collect strain components in a convenient coordinate system.

Eight of the composite overcore strains that happened to lie in

a convenient coordinate system were selected and the rest were

dismissed. That is, data selected in the previous step from !45E

gauges in all boreholes and from +45E gauges in one borehole

were excluded from the stress solution. The vertical overcore

strains from each borehole were combined into a single average

vertical overcoring strain measurement to reduce the set further,

resulting in the six overcore strain measurements presented in

table 4. This rather arbitrary elimination of data appeared to be

mandated by a stress solution program requirement that strain

components must lie conveniently in a local Cartesian coordinate

system and that the solution be exactly determined. The

coordinate system was defined by the two outer and roughly

horizontal boreholes, which represented the x and y axes, and an

upward z axis.
7
8

Table 2.—Summary of strain data from doorstopper cell overcoring at Star Mine

Doorstopper

cell depth, m

Strain by gauge orientation, μ, Borehole Notes

+45E !45E Vertical Horizontal

7300-LEVEL SITE

Borehole S1,

 oriented

 S 35E W, 5.5E:

 1 . . . . . . . . . . 577 !28 619 !59 1.2 Induced stress zone.

 2 . . . . . . . . . . 363 133 521 !42 1.3 Bad glue joint.

 3 . . . . . . . . . . 39 !230 !27 !100 1.7 Induced stress zone, bad glue joint, bad surface preparation.

 4 . . . . . . . . . . 24 267 492 !212 7.2 

 5 . . . . . . . . . . 275 704 629 205 7.4 Conglomerate marker bed.

 6 . . . . . . . . . . 46 !78 !7 !55 7.7 Problem with reading gauges.

 7 . . . . . . . . . . 320 283 210 355 7.9 Crack at center of face.

 8 . . . . . . . . . . 471 29 312 135 8.4 

 9 .......... !69 !113 !251 26 11.5 Bad glue joint.

 10 . . . . . . . . . 525 455 257 515 11.8 Poor bond, fracture along core.

Borehole S2,

 oriented

 S 55E W, 3.5E:

 1 . . . . . . . . . . 456 869 325 890 4.0

 2 . . . . . . . . . . 665 530 498 645 5.4

 3 . . . . . . . . . . 741 338 43 962 6.0

 4 . . . . . . . . . . 138 37 !132 282 9.1

 5 .......... !15 379 112 256 9.4

 6 . . . . . . . . . . 120 284 118 390 9.7

 7 . . . . . . . . . . 114 1,153 207 968 10.2

 9 . . . . . . . . . . 72 315 !105 452 11.0

 11 . . . . . . . . . 40 131 !91 392 11.8 Poor bond.

 12 . . . . . . . . . 57 527 66 459 11.9

 13 . . . . . . . . . !11 !40 !24 !15 12.2 Poor bond.

 14 . . . . . . . . . 68 !36 !125 228 12.6

Borehole S3,

 oriented

 S 10E W, 5.5E:

 1 . . . . . . . . . . 206 19 96 221 3.4

 2 . . . . . . . . . . 567 185 204 530 3.7

 3 . . . . . . . . . . 573 180 224 476 4.0

 4 . . . . . . . . . . 500 141 395 202 4.3

 5 . . . . . . . . . . 209 27 147 83 4.7

 6 . . . . . . . . . . 195 147 !36 390 5.0 Microfractured core face.

 7 . . . . . . . . . . 382 318 336 322 5.3

 9 . . . . . . . . . . 472 534 533 409 11.8

7500-LEVEL SITE

Borehole 1,

 oriented

 S 40E E, 8E:

 1 . . . . . . . . . . 432 1,890 639 !161 2.9

 2 . . . . . . . . . . 442 116 371 159 3.1

 3 . . . . . . . . . . 687 408 500 467 5.9

 4 . . . . . . . . . . 217 !328 178 !46 6.1 Poor bond, fracture along core.

 5 . . . . . . . . . . 56 !28 123 !105 8.2 Poor bond, water on surface.

 7 . . . . . . . . . . 352 44 301 46 8.7 Core broke up.

NOTE.—Underlining indicates that these strain readings were used in calculating mean strains shown in table 3.
9

Table 3.—Average strain readings

Number of samples Strain gauge

orientation

Mean,

 μ,

Standard

deviation

Borehole S1; doorstopper

 cells 5, 7, 8, 10:

 4 ............... Horizontal 303 169

 4 . . . . . . . . . . . . . . . +45E 398 119

 4 ............... Vertical 352 189

 4 ............... !45E 368 284

Borehole S2; doorstopper

 cells 1, 2, 3, 7, 12:

 5 ............... Horizontal 785 225

 5 . . . . . . . . . . . . . . . +45E 407 312

 5 ............... Vertical 228 189

 5 ............... !45E 683 325

Borehole S3; doorstopper

 cells 2, 3, 4, 7, 9:

 5 ............... Horizontal 388 130

 5 . . . . . . . . . . . . . . . +45E 499 78

 5 ............... Vertical 338 134

 5 ............... !45E 272 161

Table 4.—Selection and interpretation of strain measurements

Borehole Strain gauge Average, Assumed strain

orientation μ, component 

S1 . . . . . . . . . Horizontal 303 , x

S2 . . . . . . . . . Horizontal 785 , y

S1, S2, S3 . . Vertical 306 , z

S3 . . . . . . . . . Horizontal 388 ( 1

xy

S2 . . . . . . . . . +45E 407 ( 1

yz

S1 . . . . . . . . . +45E 398 ( 1

xz

inition of shear strain. This is an incorrect def 1

Unfortunately, the last three composite strains in table 4

were interpreted as shear strains instead of normal strains in a

direction diagonal to the coordinate axes. In other words, the

+45E strain gauge data from the doorstopper cell were taken as

shear strain on the face of the borehole. In fact, the shear strain

arises from normal strains according to the relationship

( = 2, ! , ! , , (1) PR Q P R

where ( = shear strain on borehole face, PR

and , = normal strain measured by strain gauges in

various orientations (shown in figure 5).

A complete development of strain components from a 45Estrain gauge rosette like that used by a doorstopper cell can be

found in most texts on experimental stress analysis 

(e.g., Dalley and Riley, 1978). This error was sufficient to

invalidate the reported strain field, and, as carried through the

next two steps, to invalidate the stress field estimate.

Calculate three-dimensional strain tensor.

The strain tensor follows exactly from a set of six independent strain components. These results were invalidated by

the incorrect definition of shear strain, as noted in the previous

step.

Calculate three-dimensional stress tensor.

The strain tensor (table 4) was converted to the stress tensor

using Hooke's law and adjusted for the stress concentration

effect at the end of the borehole. Elastic properties for the

stress estimate were determined by laboratory tests on core

samples. Beus and Chan (1980) report material properties of

Young's modulus = 63.8 GPa (9.26 million psi) and Poisson's

ratio = 0.29.

The modern description of the relationship between in situ

stress and concentrated stress at the end of a borehole is given

by equations 2 through 4 (Rahn, 1984).

s = aF + bF + cF , (2) xx xx yy zz

s = bF + aF + cF , (3) yy xx yy zz

and s = (a - b)F = dF , (4) xy xy xy

where s = stress on end of borehole,

a, b, c, and d = constants,

F = in situ stress field components,

and x, y, and z = coordinate axes.

The constants a, b, c, and d link the in situ stress field borehole(s). The solution procedure originally followed used

components (F) with the stress components on the end of the borehole stress concentration factors of a = d = 1.25 and b = c =
10

Table 5.—In situ stress field at 7300-level site

as calculated using principal stress

Stress component Magnitude Bearing Plunge GPa psi 

F .............. 1 76 11,000 S 12E E 28E 

F .............. 2 51 7,400 N 84E W 33E 

F .............. 3 42 6,100 N 54E E 45E 

F .............. h1 67 9,700 N 21E W 

F .............. h2 50 7,200 S 69E W 

F .............. v 53 7,700

 NOTE.—Empty cells in columns intentionally left blank.

 NOTE.—Principal stresses are presented as reported by Beus and

Chan (1980), except for secondary horizontal (F , F ) and vertical (F ) h1 h2 v

principal stress components, which are corrected values reported by

Whyatt (1986).

0, attributed to an unpublished finite-element analysis by Chan the estimated overburden stress of 60 MPa (8,670 psi) for the site

and Beus. estimated by Beus and Chan (1980). 2

The theoretical basis for estimating the in situ stress field from

doorstopper cell strain measurements has evolved considerably

since introduction of the cell, and a number of sets of constants

have been proposed since Beus and Chan (1980) reported this

measurement. The variations in stress field estimates that result

from the various sets of constants are examined in appendix A.

The resulting stress field estimate is presented in table 5. Although the estimate suffers from misdefinition of shear

strain, it still provides a reasonable direction for the maximum

principal stress and is reasonably close to 

STRESS FIELD ESTIMATE

An accurate estimate of the in situ stress field relies on EVALUATION OF STRAIN DATA

determining which of the many overcore strain measurements

were reliable and then applying statistical procedures and accurate The evaluation of strain data, especially the identification of

stress concentration factors to minimize estimate error. Ideally, invalid measurements, is a critical step in estimating the in situ

the mine rock mass would be homogeneous and isotropic and stress field. Field notes describing difficulties with the

would not be influenced by mining. In this case, the estimate instruments, bad glue joints, or rock defects are the most

would accurately represent the natural stress field that is loading important source of information (table 2). Further insight can be

mine openings. gained by applying a number of screens that numerically test the

Stress estimates were calculated from strain data using the overcore strains against various criteria.

computer program STRESsOUT (Larson, 1992). STRESsOUT A simple screen consists of solving for the stress field (S and

uses a standard set of assumptions to develop estimates of in situ S ) measured by each of the various sets of three strain gauges at

stress from overcore strain measurements by minimizing the each doorstopper cell and comparing the results. A sound

squared error for each strain measurement. By treating all doorstopper cell overcore measurement should produce

measurements throughout the test site equally, it is assumed that substantially the same stress field regardless of which gauges are

(1) stress and material properties at a site are homogeneous and chosen. Local solutions for the overcore strains in table 2 are

(2) the rock mass is linearly elastic and has no discontinuities. developed in appendix B and illustrated in figure 6. The relative

The program is capable of providing statistical treatment of the quality of each solution is ranked by assigning it to one of five

data and improved adjustments for the induced stress field on the arbitrarily defined groups (table 6). Definition of these groups 3

borehole. followed criteria that proved to be useful in analyzing overcore 4

Chan, S. S. M., and M. J. Beus. Determination of Three-Dimensional 2

Stress in Brittle Rocks of Deep Mines With Biaxial-Strain Cells. Paper 2666

presented at Spring Meeting of the Society for Experimental Stress Analysis,

Dallas, TX, May 15-20, 1977, 17 pp.

A least squares routine ensures equal (or specified) weighting of all data 3

points. This program runs on 8088 or better DOS-based personal computers in

a matter of minutes, providing the capability to conduct parametric studies if

needed.

Advanced modeling techniques have led to development of more exact 4

stress concentration factors that include the effect of Poisson's ratio. The

program uses stress concentration factors specified by the user.

1

2

5

measurements from the 5300 level of the Lucky Friday Mine in

part 2 (Whyatt and others, 1995a) of this series of reports.

A related screen checks the self-consistency of a doorstopper

cell by determining whether all four gauges of a

cell are measuring the same strain field. This "strain

S and S are nonstandard notations for the principal stress components on 5

1 2

the end of a borehole (standard notations are F1  and F2). These nonstandard

notations are needed to emphasize that they are not far-field in situ stress

components.
11
12
13
14
15

Table 6.—Range-screen classification by spread of solutions1

Doorstopper

cell

Percent of variation

Quality 2

Orientation S1 S2

Borehole S1:

 1 .............. 0 2 2 Excellent.

 2 .............. 1 3 3 Excellent.

 3 . . . . . . . . . . . . . . 7 29 31 Bad.

 4 .............. 0 3 3 Excellent.

 5 . . . . . . . . . . . . . . 6 19 19 Poor.

 6 . . . . . . . . . . . . . . 7 35 33 Bad.

 7 .............. 8 8 9 Poor.

 8 . . . . . . . . . . . . . . 3 12 12 Poor.

 9 . . . . . . . . . . . . . . 5 20 10 Bad.

 10 . . . . . . . . . . . . . 23 25 30 Bad.

Borehole S2:

 1 . . . . . . . . . . . . . . 4 11 11 OK.

 2 .............. 7 7 7 Good.

 3 .............. 2 8 8 Good.

 4 . . . . . . . . . . . . . . 2 10 10 Good.

 5 .............. 0 1 1 Excellent.

 6 . . . . . . . . . . . . . . 9 26 25 Bad.

 7 .............. 2 8 8 Good.

 9 .............. 2 9 9 Good.

 11 . . . . . . . . . . . . . 8 37 34 Bad.

 12 . . . . . . . . . . . . . 2 11 11 OK.

 13 . . . . . . . . . . . . . 12 27 30 Bad.

 14 . . . . . . . . . . . . . 6 38 36 Bad.

Borehole S3:

 1 . . . . . . . . . . . . . . 12 32 34 Bad.

 2 .............. 1 3 3 Excellent.

 3 .............. 3 9 9 Good.

 4 .............. 3 9 9 Good.

 5 .............. 1 3 3 Excellent.

 6 .............. 1 3 3 Excellent.

 7 . . . . . . . . . . . . . . 18 10 8 Good.

 9 . . . . . . . . . . . . . . 13 9 10 Good.

Borehole 1-7500:

 1 . . . . . . . . . . . . . . 700 76 68 Bad.

 2 .............. 2 6 6 Good.

 3 . . . . . . . . . . . . . . 14 17 15 Poor.

 4 . . . . . . . . . . . . . . 12 68 74 Bad.

 5 . . . . . . . . . . . . . . 1 10 10 Good.

 7 . . . . . . . . . . . . . . 3 14 14 Poor.

 explanation of S d S See footnote 5 for 1

1 2 an .

See appendix C for definition. 2

Table 7.—Strain screen of data

from doorstopper cell overcoring

Doorstopper

cell

Summation, μ, Difference Depth,

m ±45E Horizontal +

vertical 

F, pct

7300-LEVEL SITE

Borehole S1:

 1 . . . . . . . . . 549 560 11 2 1.2

 2 . . . . . . . . . 496 479 42 8 1.3

 3 ......... !191 !127 64 34 1.7

 4 ........ 1 291 280 11 4 7.2

 5 ........ 1 979 834 145 15 7.4

 6 ......... !32 !62 30 50 7.7

 7 ........ 1 603 565 38 6 7.9

 8 ........ 1 500 447 53 12 8.4

 9 ......... !182 !225 43 17 11.5

 10 . . . . . . . . 980 772 208 21 11.8

Borehole S2:

 1 ........ 1 1,325 1,215 110 8 4.0

 2 ........ 1 1,195 1,143 52 4 5.4

 3 ........ 1 1,079 1,005 74 7 6.0

 4 ........ 1 175 150 25 14 9.1

 5 ........ 1 364 368 4 1 9.4

 6 ........ 1 404 508 104 20 9.7

 7 ........ 1 1,267 1,175 92 7 10.2

 9 ........ 1 387 347 40 10 11.0

 11 . . . . . . . . 171 301 130 43 11.8

 12 . . . . . . . 1 584 525 59 10 11.9

 13 . . . . . . . . !51 !39 12 24 12.2

 14 . . . . . . . . 32 103 71 69 12.6

Borehole S3:

 1 . . . . . . . . . 225 317 92 29 3.4

 2 ........ 1 752 734 18 2 3.7

 3 ........ 1 753 700 53 7 4.0

 4 ........ 1 641 597 44 7 4.3

 5 ........ 1 236 230 6 3 4.7

 6 ........ 1 342 354 12 3 5.0

 7 . . . . . . . . . 700 658 42 6 5.3

 9 . . . . . . . . . 1,006 942 64 6 11.8

7500-LEVEL SITE

Borehole 1:

 1 ........ 1 2,322 478 1,844 79 2.9

 2 ........ 1 558 530 28 5 3.1

 3 . . . . . . . . . 1,095 967 128 12 5.9

 4 ......... !111 132 243 185 6.1

 5 . . . . . . . . . 28 18 10 36 8.2

 7 ........ 1 396 347 49 12 8.7

ed screen test. Doorstopper pass 1

arbitrarily as being a difference greater than either 300 F, or

test" takes advantage of the fact that any two perpendicular measurements of normal strain define the center of Mohr's

circle in strain. Thus, each of two pairs of perpendicular gauges

in a doorstopper cell should sum to the same total strain. If the

sums are drastically different, the doorstopper cell is failing to

measure a single strain field at the end of the borehole. This

failure may be attributable to a number of factors, including an

electrical fault, the presence of a fracture on or near the face, a

poor or nonuniform glue joint, or improper centering of the cell.

However, this method will not

indicate the source of the strain state, including whether or not

isotropic elastic rock is present.

A large difference between the sums for a single cell suggests

that the cell should be considered suspect in 

estimating the in situ stress field. However, defining "large"

proved to be problematic. The definition of "large" was chosen

about 20 pct of the largest sum. This definition was taken from

reanalysis of the 4250-level measurement in the first RI (Whyatt

and Beus, 1995) of this series, where it proved to be convenient.

The strain-screening process and resulting strain-screened data set

are summarized in table 7. In this case, all of the cells that failed

did so in percentage terms, and a threshold as low as 200 F,

would not have changed the result.
16

The range and strain screens provide generally consistent the range and strain screens. This combination of screens

results (table 8). The exceptions, like doorstopper cells 3 and 9 disqualified four doorstopper cells that appeared to be successful

in borehole S1, are associated with observations that cast doubt on the basis of field observations. The doorstopper cells that

on the measurement. A rational screening process could start passed the combination of screens are noted in bold italics in table

with elimination of cells where field observations suggested 8.

problems, then determination of agreement among

Table 8.—Comparison of screen results

Doorstopper Range Strain

cell screen screen

Strain by gauge orientation, μ, Notes

+45E !45E Horizontal Vertical

7300-LEVEL SITE

Borehole S1:

 1 . . . . . . . . 577 !28 619 !59 Excellent ....... Good ........ Induced stress zone.

 2 . . . . . . . . 363 133 521 !42 Excellent ....... Good ........ Induced stress zone.

 3 . . . . . . . . 39 !230 !27 !100 Bad . . . . . . . . . . . Good ........ Induced stress zone, bad glue joint,

 bad surface preparation.

 4 ....... 1 24 267 492 !212 Excellent ....... Good ........

 5 ....... 1 275 704 629 205 Poor ........... Good ........ Conglomerate marker bed.

 6 . . . . . . . . 46 !78 !7 !55 Bad . . . . . . . . . . . Bad . . . . . . . . . Problem with reading gauges.

 7 . . . . . . . . 320 283 210 355 Poor ........... Good ........ Crack at center of face.

 8 ....... 1 471 29 312 135 Poor ........... Good ........

 9 ........ !69 !113 !251 26 Bad . . . . . . . . . . . Good ........ Bad glue joint.

 10 . . . . . . . 525 455 257 515 Bad . . . . . . . . . . . Bad . . . . . . . . . Poor bond, fracture along core.

Borehole S2:

 1 ....... 1 456 869 325 890 OK . . . . . . . . . . . . Good ........

 2 ....... 1 665 530 498 645 Good .......... Good ........

 3 ....... 1 741 338 43 962 Good .......... Good ........

 4 ....... 1 138 37 !132 282 Good .......... Good ........

 5 ....... 1 !15 379 112 256 Excellent ....... Good ........

 6 ....... 1 120 284 118 390 Bad . . . . . . . . . . . Bad . . . . . . . . .

 7 ....... 1 114 1,153 207 968 Good .......... Good ........

 9 ....... 1 72 315 !105 452 Good .......... Good ........

 11 . . . . . . . 40 131 !91 392 Bad . . . . . . . . . . . Bad . . . . . . . . . Poor bond.

 12 . . . . . . 1 57 527 66 459 OK . . . . . . . . . . . . Good ........

 13 . . . . . . . !11 !40 !24 !15 Bad . . . . . . . . . . . Bad . . . . . . . . . Poor bond.

 14 . . . . . . . 68 !36 !125 228 Bad . . . . . . . . . . . Bad . . . . . . . . .

Borehole S3:

 1 . . . . . . . . 206 19 96 221 Bad . . . . . . . . . . . Bad . . . . . . . . .

 2 ....... 1 567 185 204 530 Excellent ....... Good ........

 3 ....... 1 573 180 224 476 Good .......... Good ........

 4 ....... 1 500 141 395 202 Good .......... Good ........

 5 ....... 1 209 27 147 83 Excellent ....... Good ........

 6 . . . . . . . . 195 147 !36 390 Excellent ....... Good ........ Microfractured core face.

 7 ....... 1 382 318 336 322 Good .......... Good ........

 9 ....... 1 472 534 533 409 Good .......... Good ........

7500-LEVEL SITE

Borehole 1:

 1 . . . . . . . . 432 1,890 639 !161 Bad . . . . . . . . . . . Bad . . . . . . . . .

 2 ....... 1 442 116 371 159 Good .......... Good ........

 3 ....... 1 687 408 500 467 Poor ........... Good ........

 4 . . . . . . . . 217 !328 178 !46 Bad . . . . . . . . . . . Bad . . . . . . . . . Poor bond, fracture along core.

 5 . . . . . . . . 56 !28 123 !105 Good . . . . . . . . . . Bad . . . . . . . . . Poor bond, water on surface.

 7 . . . . . . . . 352 44 301 46 Poor ........... Good ........ Core broke up.

nge, and strain screens. Passed observational, ra 1

NOTE.—Numbers in bold italics indicate a STRESsOUT-screened strain reading. 
17

Table 9.—In situ stress estimates from 7300-level data

 sets passing various screens and reported in situ

stress estimate from Beus and Chan (1980)

 Stress component Magnitude Bearing Plunge GPa psi 

A. Originally reported

 stress field estimate:

 F .................... 1 76 11,000 N 12E W !28E

 F .................... 2 51 7,400 N 84E W 33E

 F .................... 3 42 6,100 N 54E E 45E

 F .................... v 50 7,700 

B. Originally selected

 strains:

 F .................... 1 81 11,800 N 15E W 13E

 F .................... 2 65 9,400 N 88E E 45E

 F .................... 3 59 8,600 S 63E E 43E

 F .................... v 63 9,200 

C. All measurements

 (7300-level site):

 F .................... 1 44 6,300 N 43E W6E

 F .................... 2 36 5,300 N 56E E 56E

 F .................... 3 29 4,200 S 42E W 33E

 F .................... v 34 5,000 

D. Screened for field ob-

 servations of prob-

 lems:

 F .................... 1 50 7,300 N 33E W 11E

 F .................... 2 42 6,000 N 71E E 52E

 F .................... 3 35 5,000 S 49E W 36E

 F .................... v 40 5,700 

E. Range screen (bad

 measurements re-

 moved):

 F .................... 1 57 8,200 N 29E W 15E

 F .................... 2 47 6,900 N 84E E 56E

 F .................... 3 38 5,600 S 52E W 30E

 F .................... v 46 6,600 

F. Range screen (bad and

 poor measurements

 removed):

 F .................... 1 51 7,500 N 14E W 14E

 F .................... 2 42 6,100 N 78E E 61E

 F .................... 3 27 3,900 S 46E W 26E

 F .................... v 40 5,800 

G. Strain-screened data

 set:

 F .................... 1 54 7,800 N 36E W 11E

 F .................... 2 43 6,200 N 76E E 62E

 F .................... 3 33 4,800 S 49E W 25E

 F .................... v 41 6,000 

H. Measurements included

 in data sets D, E, and

 G (best estimate):

 F .................... 1 54 7,800 N 38E W 10E

 F .................... 2 42 6,000 N 74E E 66E

 F .................... 3 34 4,900 S 48E W 22E

 F .................... v 41 5,900 

I. Data set D with 16 out-

 lying strains removed:

 F .................... 1 36 5,200 N 56E W8E

 F .................... 2 32 4,600 N 47E E 56E

 F .................... 3 14 2,100 S 29E W 33E

 F .................... v 26 3,800 

NOTE.—Empty cells in columns intentionally left blank.

A widely used screen that is included in the STRESsOUT

data-reduction program identifies outlying strains. These are

strains that deviate substantially from the average and greatly

increase the squared error of the least squares fit estimate of the

stress field. The governing assumption in this approach is that

outlying data points are attributable to error and not to real

conditions. Outlier data can be examined by comparing the

results of the range- and strain-screening procedures with the

outlier elimination routine in STRESsOUT. In both cases, the

field observation screen is applied first. Since the range and strain

screens eliminated an additional 4 doorstopper cells with 16 strain

readings (about 19 pct of the total remaining 7300-level overcore

strains), STRESsOUT was asked to eliminate an equal number of

outlying strains, which are identified in table 8. Only one of

these, from the !45E gauge of doorstopper 14 in borehole S2,

failed to pass the range and strain screens. The lack of overlap

between strains eliminated by these two methods suggests that the

outlying strains were valid measurements.

7300-LEVEL STRESS FIELD ESTIMATE

Stress estimates were developed with stress concentration

factors reported by Rahn (1984) and physical properties reported

by Beus and Chan (1980) [i.e., an elastic modulus of 63.8 GPa

(9.26 million psi) and a Poisson's ratio of 0.29]. Stress estimates

for the full and variously screened data sets gathered at the 7300-

level site are presented in table 9.

The original data set produced estimates A and B using the

original and current data-reduction procedures, respectively. The

difference between these estimates arises from refinements in

stress concentration factors, application of a least squares

procedure, and recalculation of shear strains. These changes

primarily affected the plunge of F1 and the magnitudes of the

lesser principal stresses.

All of the 7300-level strain measurements were used for

developing stress estimate C, a relatively hydrostatic result.

Although this unscreened data set contains doorstopper cell

measurements corrupted by a wide range of problems, some valid

information was probably thrown out in forming the various data

sets. For example, the current screen checks to see if all four

strain gauges are measuring the same strain field. If only one of

the four strain gauges is corrupt, the entire cell, possibly including

valid strain information from the other three gauges, is thrown

out. These remaining strains might have contributed accurate and

vital information that would be lost by screening.
18

Table 10.—Best estimate of stress field in map coordinates

Stress component Magnitude

MPa psi 

F .......................... ns 46 6,700

F .......................... ew 42 6,100

F .......................... v 41 5,900

J ........................ ew/ns !9 !1,300

J ......................... ew/v 1 100

J ......................... ns/v 3 500

Field notes on installation problems and other adverse a depth of 2,240 m (7,340 ft) and a rock density of 2,730 kg/m

conditions listed in table 8 were used to screen the data set for (170 lb/ft ). This estimate is very close to estimates produced

stress estimate D. The field notes provided the best rational basis with the original data set, especially after applying the updated

for removing overcore strain data, especially in instances where analysis process (estimate B in table 9). However, the overburden

overcore and glue defects were noted. The range and strain estimate is probably high as the mine lies under a 460-m (1,500-

screens were used to develop estimates E through G. They ft) high hill that is included in the overburden height. A reduced

resulted in still higher magnitudes and also rotated F1 back toward estimate of vertical stress would be more in line with the screened

north-northwest. The most thoroughly screened data set, used in data estimates, but calculation of the topographic influence on

estimate K, was formed from strains that survived a combination overburden stress is deferred to part 4 (Whyatt and others, 1995b)

of field observation, range, and strain screens. This set, of this series. Most of the stress estimates provide a generally

containing the common elements of the data sets used to develop northwest-trending tectonic stress field. This direction agrees

estimates D, E, and G, provided a solution that roughly averaged with recent movement on the Osburn Fault (Hobbs and others,

the solution from these latter data sets. 1965), which indicates that the maximum stress is horizontal and

The effect of the screening process as applied both in the in the northwest quadrant.

original and current analyses was to produce in situ stress field The best stress estimate for the 7300-level site is estimate H in

estimates with higher magnitudes of stress, a greater contrast table 9, which follows from the most screened data. This estimate

between maximum and minimum stresses, and a rotation of the is shown in map coordinates in table 10. The insensitivity of the

maximum principal stress direction toward the north. The stress estimates to changes in the screening procedure (except for

increased magnitude likely arose from discarding measurements screening of outlying strains) suggests that the estimate of major

in those instances where the doorstopper gauges did not firmly stress field characteristics, like orientation of the maximum

adhere to the rock. principal stress, is fairly robust.

The final data set (I) was developed from data set D with the

outlying 16 strains removed. The independence of the 16

outlying strains from those 16 strains removed by range and

strain screening of data set D, noted earlier, resulted in

significantly different stress estimates. Removal of good outlying

measurements and inclusion of questionable data (by strain- and

range-screen standards) cast doubt on this estimate.

These stress estimates can be compared to estimates of

gravitational stress and geologic indications of the orientation of

tectonic forces. Beus and Chan (1980) estimated overburden

stress at 60 MPa (8,670 psi) based on ••••••••••

3

3

STRESS FIELD CHARACTERIZATION

The stress field at the measurement site and throughout the DOORSTOPPER-SCALE ASSUMPTIONS

mine is fully described by the in situ stress estimate in only the

most ideal of cases. That is, the rock mass and stress field are The rock immediately surrounding the doorstopper cells

often considerably more complex than the assumptions implicit was assumed to be homogeneous, continuous, isotropic, and

in the STRESsOUT program's calculations. These linearly elastic. Uniaxial compression tests showed the rock to

assumptions require ideal elastic, homogeneous conditions at be linearly elastic, although some hysterisis at low loads was

each doorstopper cell and across the site as a whole. Often, noted. The available information suggests elastic anisotropy

these conditions are also assumed between sites and throughout may be a significant factor. However, the scale of the in situ

the mine. This section attempts to go beyond these modulus measurements is larger than the scale of the

assumptions in order to better characterize the stress field. doorstopper cell measurements. The presence of beds of

various stiffnesses undoubtedly generates
19

Table 11.—In situ stress estimates from 7300- and 7500-level

data sets

Stress component Magnitude Bearing Plunge

GPa psi 

A. All measurements, 7300-

 and 7500-level sites:

 F ....................... 1 44 6,400 N 41E W 7E

 F ....................... 2 38 5,500 N 60E E 58E

 F ....................... 3 32 4,600 S 45E W 31E

 F ....................... v 36 5,300

B. All measurements, bore-

 hole S1 omitted:

 F ....................... 1 46 6,600 N 36E W 9E

 F ....................... 2 41 5,900 N 62E E 41E

 F ....................... 3 34 5,000 S 44E W 47E

 F ....................... v 37 5,400 

C. Screened for field observa-

 tions of problems:

 F ....................... 1 55 8,000 N 14E W 10E

 F ....................... 2 47 6,800 N 82E E 31E

 F ....................... 3 45 6,600 S 61E W 57E

 F ....................... v 46 6,700 

D. Screened for field observa-

 tions of problems, bore-

 hole S1 omitted:

 F ....................... 1 63 9,200 N 6E E 12E

 F ....................... 2 53 7,700 S 82E E 10E

 F ....................... 3 49 7,100 S 48E W 74E

 F ....................... v 49 7,200 

E. Screened measurements

 (data set B after range

 and strain screens):

 F ....................... 1 58 8,500 N 21E W 20E

 F ....................... 2 50 7,300 N 88E E 42E

 F ....................... 3 42 6,200 S 50E W 42E

 F ....................... v 48 6,900 

NOTE.—Empty cells in columns intentionally left blank..

large-scale orthotropic anisotropy, but it is not clear if there is

anisotropy within these beds at the scale of a doorstopper cell magnitude are evident, even among the best measurements.

overcore as well. Unfortunately, there was insufficient These local variations overshadow any systematic variation that

information to determine the thickness of the beds, the proximity might exist between boreholes 1 and S1. These local variations

of the cells to bed boundaries, or a useful estimate of the degree may be changes in stress. Alternatively, they may reflect a

of anisotropy. homogeneous stress field with variations in elastic properties

SITE-SCALE ASSUMPTIONS uniform loading is violated.

Assumptions on the scale of a measurement site or sites are evident in stress estimates that use borehole 1 (7500- level site)

particularly important when using two-dimensional cells. These strains to augment or replace borehole S1 (7300-level site) strains

cells are capable only of measuring stress on the face at the end of used in developing the estimates given in table 9. These estimates

the borehole. This local stress field has three components, but is are developed in table 11. No adjustments were made to account

determined by four components of the in situ stress field. Thus, for the presence of softer argillaceous quartzite observed at the

the in situ components are underdetermined, and additional 7500-level site. However, placement of doorstopper cells in

information from boreholes in other directions is needed before zones of good core recovery probably meant that strong, stiff

in situ conditions can be estimated. Data from doorstopper cells rock was selected at both sites. Unfortunately, more- specific

in three nonparallel boreholes are needed to estimate the three- information was not available.

dimensional stress state.

The least squares procedure described in the previous section

assumes that all doorstopper cells were installed in a

homogeneous material experiencing uniform loading. Any

deviations from the average of measured material properties or the

stress field estimate are considered random errors. The potential

for real variability in stress field and/or rock mass properties

throughout the measurement site or sites raises two important

issues: assessment of stress field variability and the potential for

sampling bias. Assessment of stress variability is needed to

determine if deviations from ideal conditions are of significant

magnitude to influence engineering design, i.e., whether the

pattern and/or degree of stress variability can create ground

control problems, including rock bursting, if not dealt with

explicitly. Furthermore, sampling procedures need to be

evaluated in light of any stress field and/or rock property

variations to reveal any bias that may exist in estimating average

stress conditions.

Local Stress Variability

The degree of local stress variability can be investigated by

examining the consistency of similarly oriented overcore

measurements. Under ideal conditions, there should be little

variability among doorstopper cells installed in a single borehole

far from the influence of mine openings. This is rarely the case.

Thus, the evaluation process boils down to an investigation of the

validity of, and reason for, outlying strain measurements.

Spatial variations in stress can be examined within a borehole,

and in the case of parallel boreholes S1 and 1, between boreholes,

through the estimates of stress at each doorstopper cell location

(figure 6). These solutions, developed for the screening process,

are plotted by location in

 summary plots (figure 7). Large local variations in stress

along the boreholes, or some combination of these alternatives.

In any case, the assumption of a uniform rock mass under

The degree of variation in stress among the sites might be
20
21
22

Combining site stress field estimates A, C, and E (table 11), overcore strains arising from changes in rock properties and variaincluding data from the 7500-level site, causes stress magnitudes tions reflecting a true change in stress regime.

to increase and maximum principal stresses to be rotated

northward. Omitting borehole S1 strains (estimates B and D) Sampling

accentuates this trend. The relatively small number of 7500-level

measurements that generate this shift (e.g., 6 out of 36 Estimation of a true average stress field for this site is seriously

doorstopper cells for the unscreened estimate) suggests that there complicated by the presence of real variations in stress and/or

is a larger difference among sets of overcore strains than was rock properties. The spatial distribution of measurements was not

evident from the local stress plots. Moreover, changes in a great concern so long as each measurement could be considered

direction and magnitude cannot be explained by changes in depth an independent, randomly selected data point. But now that

alone. Because the 7500-level site is north of the Morning East spatial dependence of stress and/or material properties has been

vein in a distinct geologic structure with softer rock and bedding established, increased attention must be paid to the actual position

rotated to the north, it would not be surprising to find of the measurement site.

significantly different overcore strains. The relative influence of The measurable and unmeasurable sections in each borehole

changes of rock properties, rotation of orthotropic anisotropy are shown in figure 8. Doorstopper cell core recovery reassociated with bedding, and/or changes in stress field quirements disqualified a large portion of each borehole. For

characteristics cannot be determined from the available data. example, 10 measurements in borehole 1 were concentrated in 3

Thus, this estimate may not describe conditions sampled at the sections composing only 3 m (6 ft) of the available 12 m

7500-level site. (36 ft). Whether poor core recovery was a result of preexisting

It is clear that significant local variations in overcore strains fractures, core discing, or drilling is unclear. The unmeasured

were measured. Moreover, these strains had a significant impact sections probably represent zones of relatively weak, soft rock

on the stress field estimate. The next logical step in this analysis with relatively lower levels of stress, while the measured portions

might be to develop a test site or mine model, as was attempted were probably selectively positioned inside thicker beds. Thus,

in part 1 (Whyatt and Beus, 1995) of this series for the 4250-level this measurement was likely biased by concentrated sampling.

measurement site. However, there is not enough physical Unfortunately, there is insufficient information available to

property information to differentiate between variations in evaluate the degree of bias.
23

Table 12.—Best estimate of average stress state at 7300-level

measurement site 

Stress component Magnitude Bearing Plunge GPa psi 

F ................ 1 54 7,800 N 38E W 10E 

F ................ 2 42 6,000 N 74E E 66E 

F ................ 3 34 4,900 S 48E W 22E 

F ................ v 41 5,900 

NOTE.—Empty cells in columns intentionally left blank.

DISCUSSION AND CONCLUSIONS

The estimated in situ stress field deep in the Star Mine was geologic structure and stress patterns at a site. If an estimate of

updated by applying contemporary data-reduction procedures and average far-field stresses is sought, a priori investigation of

systematic data-screening methods to overcore stress possible stress contorting geologic structures is appropriate. The

measurements reported by Beus and Chan (1980). The estimated change in rock type across the Morning East vein and the interstress was reduced in magnitude and rotated toward the northwest section of veins near the 7300- and 7500-level sites are probably

by the new procedure, which resulted in the estimates shown in representative of stress-contorting structures. Site investigations

table 12. and stress measurement studies need to include comprehensive

e in line with tectonic Friday Mine and attempts to discover how the in situ stress field

The direction of F in this estimate is mor 1

evidence of a northwest stress field than the direction indicated in

the original analysis by Beus and Chan (1980). The vertical

stress estimate is lower than the previous estimate and lower than

simple overburden calculations would suggest, but the

measurement site is located under a hill, and as the 5300-level

measurement investigated in part 2 (Whyatt and others, 1995a)

demonstrated, equilibrium can only be used to estimate average

overburden stress. In situ tests conducted at the site suggested

significant anisotropy at comparatively large scales (a meter or

two). There was no indication of the degree of doorstopper-scale

anisotropy, and this factor was not considered in either the

estimate of Beus and Chan or the current estimate.

Inspection and screening of individual doorstopper cell

measurements revealed that there was considerable variability

among cells, even cells mounted within a fraction of a meter of

each other in the same borehole. Furthermore, sets of outlier

strains were almost completely independent of one another, and

these contributed most significantly to the measurements of

squared error and sets of questionable strains identified by other

means. This independence demonstrates that the variability was

real and could not be attributed to measurement error. The

admission that local overcore strain variability exists violates

many of the assumptions underlying contemporary stress

estimation procedures and introduces the question of sampling

bias. Unfortunately, there is insufficient geologic and rock

property information to address these issues. If more information

were available, alternative models of stress site conditions could

be proposed, as was done for the Lucky Friday 4250-level

analysis described in part 1 (Whyatt and Beus, 1995) of this

series.

While this analysis improved the stress field estimate, it also

highlighted the sources of uncertainty that plague overcore

measurements in complex geologic settings. Moreover, it served

to underscore the importance of treating an overcore stress

measurement as a geomechanical experiment investigating the

rock testing programs that evaluate stress estimation assumptions

as well as supply the required elastic properties.

Finally, mines containing complex geologic structures cannot

be considered to lie in homogeneous stress fields. Rock-burst

experience at the 5300-level site discussed in part 2 (Whyatt and

others, 1995a) demonstrates that variations in the stress field may

have significant ground control implications. Obviously, minescale stress variations cannot be measured by overcore methods

alone. However, stress characteristics are often revealed in the

course of normal mine exploration drilling and the excavation of

normal mine openings. The final report of this series examines

nonovercore evidence of stress field characteristics at the Lucky

varies throughout the host geologic structure.

A favored or "best guess" estimate of the stress field at the Star

Mine can be derived in two different ways. The first, used in the

original analysis of these data, considers other evidence of stress

field characteristics and looks for consistency as an indicator of

measurement quality. The second, applied in the screening

process presented here, includes a test to eliminate prejudgment

of results in favor of decisions based on self-consistency of

instrument readings. Both approaches incorporate field

observations of instrument operation.

The choice depends primarily on understanding the possible

stress field characteristics at a measurement site. With the

tremendous increase in the number of in situ stress studies that

have become available in the 15 years since this measurement was

made, it has become increasingly clear that local deviations in the

stress field are common and may include substantial residual and

structural stresses. Thus, confidence in estimates of what a stress

field "ought to be" has been significantly eroded, and the best

policy is to avoid biasing the result with expectations. 

The screened data set with the 7500-level site data removed

was judged to provide the best estimate of the in situ stress field

(estimate F in table 9). The reasons for this judgment include the

rational and consistent screening of data and the elimination of

measurements from a potentially different stress field at the 7500-

level site.
24

REFERENCES

Amadei, B., and W. Z. Savage. Determination of the Elastic Properties of Jenkins, M., and R. McKibbin. Practical Considerations of In Situ Stress

Anisotropic Rock Masses From In-Situ Expansion Tests. Paper in Rock Determination. Ch. in Proceedings, International Symposium on Application

Mechanics as a Multidisciplinary Science: Proceedings of the 32nd U.S. of Rock Characterization Techniques in Mine Design, ed. by M. Karmis. Soc.

Symposium, ed. by J.-C. Roegiers (Univ. OK, Norman, OK, July 10-12, Min. Eng., 1986, pp. 33-39.

1991). Balkema, 1991, pp. 303-312. Larson, M. K. STRESsOUT—A Data Reduction Program for Inferring

Beus, M. J., and S. S. M. Chan. Shaft Design in the Coeur d'Alene Mining Stress State of Rock Having Isotropic Material Properties: A User's Manual.

District—Results of In Situ Stress and Physical Property Measurements. USBM IC 9302, 1992, 163 pp.

USBM RI 8435, 1980, 39 pp. Patricio, J. G., and M. J. Beus. Determination of the In Situ Modulus of

Bonnechere, F. A., and C. Fairhurst. Determination of Regional Stress Deformation in Hard Rock Mines of the Coeur d'Alene District, Idaho. Paper

Field From "Doorstopper" Measurements. Paper in International Symposium in Site Characterization, 17th Symposium on Rock Mechanics (Salt Lake City,

on the Determination of Stresses in Rock Masses (Proc., Lisbon, Portugal, UT). UT Eng. Exper. Stat., Univ. UT, Salt Lake City, UT, 1976, pp. 4B9-1

1969). Natl. Lab. Civil Eng., Lisbon, Portugal, 1971, pp. 307-333. to 4B9-7.

Dalley, J. W., and W. F. Riley. Experimental Stress Analysis. McGraw- Rahn, W. Stress Concentration Factor for the Interpolation of

Hill, 2nd ed., 1978, pp. 318-333. "Doorstopper" Stress Measurements in Anisotropic Rocks. Int. J. Rock Mech.

Goodman, R. E. Introduction to Rock Mechanics. John Wiley, 1980, Min. Sci. Geomech. Abstr., v. 21, No. 6, 1984, pp. 313-326.

pp. 121-123. Van Heerden, E. W. Stress Concentration Factors for the Flat Borehole

Hobbs, S. W., A. B. Griggs, R. E. Wallace, and A. B. Campbell. Geology End for Use in Rock Stress Measurements. Eng. Geol., v. 3, 1969, pp. 307-

of the Coeur d'Alene District, Shoshone County, Idaho. U.S. Geol. Surv. Prof. 323.

Pap. 478, 1965, 139 pp. Whyatt, J. K. Geomechanics of the Caladay Shaft. M.S. Thesis, Univ. ID,

Hocking, G. Three-Dimensional Elastic Stress Distribution Around the Flat Moscow, ID, 1986, 195 pp.

End of a Cylindrical Cavity. Int. J. Rock Mech. Min. Sci. Geomech. Abstr., v. Whyatt, J. K., and M. J. Beus. In Situ Stress at the Lucky Friday Mine (In

13, No. 12, 1976, pp. 331-337. Four Parts): 1. Reanalysis of Overcore Measurements From 4250 Level.

Hustrulid, W. Development of a Borehole Device To Determine the USBM RI 9532, 1995, 26 pp.

Modulus of Rigidity of Coal Measure Rocks. USBM OFR 12-72, 1971, 119 Whyatt, J. K., F. M. Jenkins, and M. K. Larson. In Situ Stress at the Lucky

pp.; NTIS PB 209 548/AS. Friday Mine (In Four Parts): 2. Analysis of Overcore Measurement From 5300

International Society for Rock Mechanics. Suggested Methods for Rock Level. USBM RI 9560, 1995a.

Stress Determination. Int. J. Rock Mech. Min. Sci. Geomech. Abstr., v. 24, Whyatt, J. K., T. J. Williams, and W. Blake. In Situ Stress at the Lucky

No. 1, 1987, pp. 53-74. Friday Mine (In Four Parts): 4. Characterization of Mine In Situ Stress Field.

USBM RI, 1995b, in press.
25

APPENDIX A.—SENSITIVITY OF STRESS FIELD ESTIMATE

TO CHOICE OF STRESS CONCENTRATION FACTOR

The influence of the updated data-reduction process in estimate and an estimate derived using the original stress

STRESsOUT and application of better concentration factors concentration factors and the STRESsOUT program. A similar

proposed by a number of researchers (Bonnechere and Fairhurst, but opposite shift is evident as updated stress concentration

1971; Hocking, 1976; Rahn, 1984; Van Heerden, 1969) are factors are applied. Thus, it appears that the problems with strain

explored in table A-1. All of these calculations proceed from the misdefinition and poor stress concentration factors were compenoriginal six strain measurements, correctly interpreted, that were sating conditions, resulting in a surprisingly good estimate of in

used in the original solution. A very large contrast is evident situ stress.

between the originally reported stress

Table A-1.—Stress solutions based on original six composite strain measurements

Stress component Bearing Plunge Magnitude

GPa psi 

A. Originally reported stress field:

 F ................................................................................. 1 76 11,000 N 12E W !28E

 F ................................................................................. 2 51 7,400 N 84E W 33E

 F ................................................................................. 3 42 6,100 N 54E E 45E

 F ................................................................................. v 50 7,300

B. Original stress concentration factors, where a = 1.25, b = 0, c = 0, and d = 1.25 (Chan and

 Beus, see footnote 2 in main text):1

 F ................................................................................. 1 51 7,300 N 18E W 12E

 F ................................................................................. 2 25 3,700 S 79E E 66E

 F ................................................................................. 3 20 2,900 S 68E W 21E

 F ................................................................................. v 26 3,800

C. Factors reported by Bonnechere and Fairhurst (1971), where a = 1.25, b = 0, c = !0.51,

 and d = 1.25:1

 F ................................................................................. 1 74 10,700 N 17E W 18E

 F ................................................................................. 2 52 7,500 S 88E E 45E

 F ................................................................................. 3 47 6,800 S 58E W 39E

 F ................................................................................. v 52 7,500

D. Factors developed for Poisson's ratio = 0.18 (after Van Heerden, 1969), where a = 1.36,

 b = !0.03, c = !0.69, and d = 1.39:1

 F ................................................................................. 1 81 11,700 N 16E W 19E

 F ................................................................................. 2 61 8,900 S 89E E 43E

 F ................................................................................. 3 57 8,300 S 56E W 42E

 F ................................................................................. v 61 8,900

E. Factors developed according to equations reported by Rahn (1984), where a = 1.34,

 b = !0.03, c = !0.68, and d = 1.38:1

 F ................................................................................. 1 81 11,800 N 16E W 19E

 F ................................................................................. 2 61 8,900 S 88E E 43E

 F ................................................................................. 3 57 8,200 S 56E W 42E

 F ................................................................................. v 61 8,900

Stress concentration factors are used in equations 2, 3, and 4 in the main text. 1

NOTE,—Empty cells in columns intentionally left blank.
26

APPENDIX B.—DOORSTOPPER CELL LOCAL SOLUTIONS

The strain field at the end of a borehole can be estimated from These solutions are illustrated in figure 6 and summarized in

doorstopper cell strain readings (e.g., equation 1). By using figure 7. These figures show the range of stress solutions that

Hooke's law, the stress on the end of the borehole can be follow from solutions using various combinations of three of the

determined easily [see Goodman (1980) for a more complete four doorstopper cell strain gauges. These estimates were detreatment]. The solutions for each doorstopper are presented in veloped for a rock modulus of 63.8 GPa (9.26 million psi) and

table B-1, and the ranges are summarized in table B-2. a Poisson's ratio of 0.29.

Table B-1.—Stress solutions for end of borehole using various combinations of three strain

gauges at each doorstopper cell location1

Stress attributes Solution 1 Solution 2 Solution 3 Solution 4

BOREHOLE S1

Doorstopper 1:

1, deg . . . . . . . . 69 69 69 69

S , MPa . . . . . . 1 5.13 5.12 5.17 5.07

S , MPa . . . . . . 2 0.31 0.22 0.27 0.26

Doorstopper 2:

1, deg . . . . . . . . 78 79 80 79

S , MPa . . . . . . 1 3.97 3.99 3.94 4.08

S , MPa . . . . . . 2 0.68 0.83 0.72 0.74

Doorstopper 3:

1, deg . . . . . . . . 55 58 51 46

S , MPa . . . . . . 1 !0.04 !0.12 0.29 !0.21

S , MPa . . . . . . 2 !1.20 !1.73 !1.53 !1.65

Doorstopper 4:

1, deg . . . . . . . . 99 100 100 99

S , MPa . . . . . . 1 3.34 3.38 3.36 3.43

S , MPa . . . . . . 2 !0.62 !0.55 !0.64 !0.61

Doorstopper 5:

1, deg . . . . . . . . 107 118 117 109

S , MPa . . . . . . 1 5.41 6.12 5.96 6.66

S , MPa . . . . . . 2 2.69 3.39 2.14 2.85

Doorstopper 6:

1, deg . . . . . . . . 54 49 59 61

S , MPa . . . . . . 1 0.13 0.18 !0.02 0.24

S , MPa . . . . . . 2 !0.73 !0.49 !0.58 !0.55

Doorstopper 7:

1, deg . . . . . . . . 14 6 0 10

S , MPa . . . . . . 1 3.18 3.43 3.13 3.23

S , MPa . . . . . . 2 2.31 2.43 2.36 2.63

Doorstopper 8:

1, deg . . . . . . . . 55 53 57 59

S , MPa . . . . . . 1 3.58 3.66 3.31 3.76

S , MPa . . . . . . 2 0.77 1.20 1.03 1.10

Doorstopper 9:

1, deg . . . . . . . . 9 4 0 5

S , MPa . . . . . . 1 !0.32 !0.02 !0.35 !0.25

S , MPa . . . . . . 2 !1.87 !1.75 !1.83 !1.52

Doorstopper 10:

1, deg . . . . . . . . 24 4 !14 27

S , MPa . . . . . . 1 4.76 6.02 4.53 4.99

S , MPa . . . . . . 2 2.74 3.50 2.97 4.5

BOREHOLE S2

Doorstopper 1:

1, deg . . . . . . . . !14 !16 !21 !21

S , MPa . . . . . . 1 7.61 8.55 7.96 8.08

S , MPa . . . . . . 2 4.19 4.32 3.84 4.79 

See footnote at end of table. Table B-1.—Stress solutions for end of borehole using various combinations of three strain

gauges at each doorstopper cell location —Continued 1

Stress attributes Solution 1 Solution 2 Solution 3 Solution 4

BOREHOLE S2—Continued
27

Doorstopper 2:

1, deg . . . . . . . . 26 17 15 27

S , MPa . . . . . . 1 6.19 6.45 6.00 6.25

S , MPa . . . . . . 2 4.92 5.16 5.10 5.36

Doorstopper 3:

1, deg . . . . . . . . 14 11 10 13

S , MPa . . . . . . 1 7.65 8.11 7.49 7.74

S , MPa . . . . . . 2 2.11 2.30 2.27 2.74

Doorstopper 4:

1, deg . . . . . . . . 8 6 5 7

S , MPa . . . . . . 1 1.89 2.05 1.85 1.92

S , MPa . . . . . . 2 !0.43 !0.35 !0.40 !0.22

Doorstopper 5:

1, deg . . . . . . . . !35 !35 !35 !35

S , MPa . . . . . . 1 2.92 2.89 2.90 2.89

S , MPa . . . . . . 2 0.66 0.65 0.68 0.64

Doorstopper 6:

1, deg . . . . . . . . !22 !22 !6 !12

S , MPa . . . . . . 1 3.49 2.59 3.21 3.06

S , MPa . . . . . . 2 1.45 1.33 1.72 0.87

Doorstopper 7:

1, deg . . . . . . . . !26 !25 !28 !29

S , MPa . . . . . . 1 8.95 9.75 9.35 9.46

S , MPa . . . . . . 2 2.46 2.56 2.06 2.85

Doorstopper 9:

1, deg . . . . . . . . !10 !11 !13 !13

S , MPa . . . . . . 1 3.27 3.60 3.36 3.41

S , MPa . . . . . . 2 0.10 0.16 0.02 0.35

Doorstopper 11:

1, deg . . . . . . . . !12 !7 2 !4

S , MPa . . . . . . 1 2.88 1.80 2.76 2.49

S , MPa . . . . . . 2 0.04 !0.14 0.17 !0.83

Doorstopper 12:

1, deg . . . . . . . . !23 !23 !27 !27

S , MPa . . . . . . 1 4.07 4.58 4.31 4.38

S , MPa . . . . . . 2 1.03 1.09 0.79 1.30

Doorstopper 13:

1, deg . . . . . . . . 31 48 39 27

S , MPa . . . . . . 1 !0.14 !0.17 !0.08 !0.15

S , MPa . . . . . . 2 !0.24 !0.33 !0.30 !0.34

Doorstopper 14:

1, deg . . . . . . . . 3 10 13 7

S , MPa . . . . . . 1 1.45 0.96 1.55 1.32

S , MPa . . . . . . 2 !0.45 !0.65 !0.55 !1.01

BOREHOLE S3

Doorstopper 1:

1, deg . . . . . . . . 19 40 33 20

S , MPa . . . . . . 1 1.96 1.60 2.36 1.86

S , MPa . . . . . . 2 1.12 0.59 0.72 0.33

Doorstopper 2:

1, deg . . . . . . . . 25 24 24 26

S , MPa . . . . . . 1 4.94 5.03 4.87 4.96

S , MPa . . . . . . 2 2.19 2.28 2.26 2.34

Doorstopper 3:

1, deg . . . . . . . . 30 26 27 32

S , MPa . . . . . . 1 4.77 4.99 4.53 4.83

S , MPa . . . . . . 2 2.03 2.33 2.27 2.48 

See footnote at end of table.
28

Table B-1.—Stress solutions for end of borehole using various combinations of three strain

gauges at each doorstopper cell location —Continued 1

Stress attributes Solution 1 Solution 2 Solution 3 Solution 4

BOREHOLE S3—Continued

Doorstopper 4:

1, deg . . . . . . . . 58 56 61 62

S , MPa . . . . . . 1 4.09 4.15 3.89 4.26

S , MPa . . . . . . 2 1.71 2.07 1.91 1.96

Doorstopper 5:

1, deg . . . . . . . . 54 54 55 56

S , MPa . . . . . . 1 1.65 1.66 1.62 1.67

S , MPa . . . . . . 2 0.59 0.64 0.62 0.62

Doorstopper 6:

1, deg . . . . . . . . 2 3 4 3

S , MPa . . . . . . 1 2.86 2.78 2.87 2.84

S , MPa . . . . . . 2 0.58 0.55 0.57 0.48

Doorstopper 7:

1, deg . . . . . . . . 49 33 61 66

S , MPa . . . . . . 1 3.48 3.59 3.27 3.63

S , MPa . . . . . . 2 2.91 3.21 3.13 3.17

Doorstopper 9:

1, deg . . . . . . . . 90 113 113 99

S , MPa . . . . . . 1 4.91 5.12 5.05 5.42

S , MPa . . . . . . 2 4.24 4.66 4.10 4.36

BOREHOLE 1-7500

Doorstopper 1:

1, deg . . . . . . . . 77 153 128 104

S , MPa . . . . . . 1 4.70 16.07 11.40 19.35

S , MPa . . . . . . 2 !0.05 6.48 !6.76 3.21

Doorstopper 2:

1, deg . . . . . . . . 60 60 63 63

S , MPa . . . . . . 1 3.68 3.71 3.55 3.79

S , MPa . . . . . . 2 1.47 1.71 1.60 1.63

Doorstopper 3:

1, deg . . . . . . . . 47 36 51 60

S , MPa . . . . . . 1 5.79 6.11 5.11 6.18

S , MPa . . . . . . 2 3.60 4.53 4.28 4.46

Doorstopper 4:

1, deg . . . . . . . . 63 65 53 44

S , MPa . . . . . . 1 1.65 1.38 2.83 0.92

S , MPa . . . . . . 2 !0.36 !2.46 !1.55 !2.00

Doorstopper 5:

1, deg . . . . . . . . 79 79 81 80

S , MPa . . . . . . 1 0.75 0.76 0.73 0.81

S , MPa . . . . . . 2 !0.57 !0.49 !0.55 !0.54

Doorstopper 7:

1, deg . . . . . . . . 63 62 67 67

S , MPa . . . . . . 1 2.86 2.91 2.66 3.08

S , MPa . . . . . . 2 0.51 0.93 0.71 0.77

d S See footnote 5 in main text for explanation of S an . 1 2
29

Table B-2.—Range of individual doorstopper cell solutions for stress on end of borehole1

Doorstopper cell Orientation of S , deg Pa Pa 1 S , M1 S , M2

Minimum Maximum Minimum Maximum Minimum Maximum

Borehole S1:

 1 . . . . . . . . . . . . . . . 69 69 5.07 5.17 0.22 0.31

 2 . . . . . . . . . . . . . . . 78 80 3.94 4.08 0.68 0.83

 3 . . . . . . . . . . . . . . . 46 48 !0.21 0.29 !1.73 !1.20

 4 . . . . . . . . . . . . . . . 99 100 3.34 3.43 !0.64 !0.55

 5 . . . . . . . . . . . . . . . 107 118 5.41 6.66 2.14 3.39

 6 . . . . . . . . . . . . . . . 49 61 !0.02 0.24 !0.73 !0.49

 7 . . . . . . . . . . . . . . . 0 14 3.13 3.43 2.31 2.63

 8 . . . . . . . . . . . . . . . 53 59 3.31 3.76 0.77 1.20

 9 ............... 0 9 !0.35 !0.02 !1.87 !1.52

 10 . . . . . . . . . . . . . . !14 27 4.53 6.02 2.74 4.50

Borehole S2:

 1 ............... !21 !14 7.61 8.55 3.84 4.79

 2 . . . . . . . . . . . . . . . 15 27 6.00 6.45 4.92 5.36

 3 . . . . . . . . . . . . . . . 10 14 7.49 8.11 2.11 2.74

 4 ............... 5 8 1.85 2.05 !0.43 !0.22

 5 ............... !35 !35 2.89 2.92 0.64 0.68

 6 ............... !22 !6 2.59 3.49 0.87 1.72

 7 ............... !29 !25 8.95 9.75 2.06 2.85

 9 ............... !13 !10 3.27 3.60 0.02 0.35

 11 . . . . . . . . . . . . . . !12 2 1.80 2.88 !0.83 0.17

 12 . . . . . . . . . . . . . . !27 !23 4.07 4.58 0.79 1.30

 13 . . . . . . . . . . . . . . 27 48 !0.17 !0.08 !0.34 !0.24

 14 . . . . . . . . . . . . . . 3 13 0.96 1.55 !1.01 !0.45

Borehole S3:

 1 . . . . . . . . . . . . . . . 19 40 1.60 2.36 0.33 1.12

 2 . . . . . . . . . . . . . . . 24 26 4.87 5.03 2.19 2.34

 3 . . . . . . . . . . . . . . . 26 32 4.53 4.99 2.03 2.48

 4 . . . . . . . . . . . . . . . 56 62 3.89 4.26 1.71 2.07

 5 . . . . . . . . . . . . . . . 54 56 1.62 1.67 0.59 0.64

 6 ............... 2 4 2.78 2.87 0.48 0.58

 7 . . . . . . . . . . . . . . . 33 66 3.27 3.63 2.91 3.21

 9 . . . . . . . . . . . . . . . 90 113 4.91 5.42 4.10 4.66

Borehole 1-7500:

 1 . . . . . . . . . . . . . . . 77 153 4.70 19.35 !6.76 6.48

 2 . . . . . . . . . . . . . . . 60 63 3.55 3.79 1.47 1.71

 3 . . . . . . . . . . . . . . . 36 60 5.11 6.18 3.60 4.53

 4 . . . . . . . . . . . . . . . 44 65 0.92 2.83 !2.46 !0.36

 5 . . . . . . . . . . . . . . . 79 81 0.73 0.81 !0.57 !0.49

 7 . . . . . . . . . . . . . . . 62 67 2.66 3.08 0.51 0.93

ext for explanation of S d S See footnote 5 in main t an . 1

1 2
1 & 1

E

& & &

&

& & &

&

30

Quality Maximum percent of variation

Orientation2 S

3

1 S

4

2

Excellent ......... 1 5 5

Good . . . . . . . . . . . . 3 10 10

Acceptable . . . . . . . . . 5 15 15

Poor . . . . . . . . . . . . . . 10 20 20

Bad . . . . . . . . . . . . . . . >30 >20 >20

 text for explanation of S d S See text footnote 5 in main 1

1 2 an .

APPENDIX C.—RANKING CRITERIA FOR QUALITY DESIGNATION1

 

2

180 × 100.

 3

 

 × 100.

 

4

 

 × 100.