INITIAL STABILITY STUDY OF LARGE OPENINGS FOR THE

NATIONAL UNDERGROUND SCIENCE LABORATORY AT THE

HOMESTAKE MINE, LEAD, SD

Doug Tesarik, Jeff Johnson, and Karl Zipf, Jr.

Spokane Research Laboratory, National Institute for Occupational Safety and Health, Spokane, WA USA

Kenneth Lande

University of Pennsylvania, Philadelphia, PA USA

ABSTRACT: The study of neutrinos—particles infinitesimally smaller than atoms—would be significantly advanced if a deep

underground facility were available that would filter out unwanted cosmic radiation. Encouraging progress has been made in satisfying

the criteria for such a facility with the selection of the Homestake Mine in Lead, SD, by the National Underground Laboratory

Committee as the recommended site for a National Underground Science Laboratory (NUSL). The Homestake Mine is America’s

oldest and deepest underground mine, and its well-maintained infrastructure to depths of 2438 m below the surface makes the mine an

excellent site for such a laboratory. The investigation reported here is an initial study of the stability of the first of the proposed

chambers. A cylindrical room with a dome-shaped roof and floor was analyzed in three dimensions using the finite-difference program

FLAC3D. The results were compared to recommended support requirements based on Barton’s Tunneling Quality Index, Q. Based

on model results and observations from previous mining studies, large rooms with 50-m roof spans can be constructed and will remain

stable at 2141 m below the surface in the Poorman Formation when the rock is reinforced with cable bolts. Construction may be possible

at lower levels in the Yates Formation if more extensive laboratory strength tests confirm initial results. 

1. INTRODUCTION

Observation of solar neutrinos began in 1965, when

Raymond Davis installed a 600-ton detector at the

4850 level of the Homestake Mine in Lead, SD [1].

From that beginning, neutrino astrophysics has grown

into a worldwide research effort. There are large

underground laboratories at Gran Sasso in Italy, Baksan in Russia, Kamioka in Japan, and Sudbury in

Canada. Although there are U.S. participants in these

experiments, until now, U.S. scientists have not been

able to follow up on the original work by Davis at a

U.S.-based facility. The end of gold mining at the

Homestake Mine in December 2001 has provided a

unique opportunity for the creation of what would be

the deepest and largest underground laboratory in the

world. The great thickness of overburden would filter

unwanted cosmic radiation, allowing neutrinos to to

be “captured” for study. 

The primary reason for this growing interest in neutrinos is that understanding their properties is important to answering many cosmological and astrological

problems, such as why the neutrino flux emitted by 

the Sun as a result of nuclear fusion is less than expected, the processes involved during the collapse of

a massive star into a neutron star and associated

supernova emissions, proton decay, and dark matter.

Among the proposals for a National Underground

Science Laboratory (NUSL) is one for a one-millionton water Cerenkov detector that would be about 20

times the size of the largest present detector,

SuperKamiokande in Japan. The proposed Cerenkov

detector would consist of 10 cylindrical modules each

50 m in diameter and 50 m high located between the

6950 and 7100 levels of the Homestake Mine in the

Yates Formation. (Most mining has been in the Poorman and Homestake formations.) The investigation

reported here is an initial study of the stability of the

first of 10 proposed chambers and the first step in

ensuring the safety of miners during excavation. A

cylindrical room with a dome-shaped roof and floor

was analyzed in three dimensions using the finitedifference program FLAC3D [2]. The results were

compared to recommended support requirements

based on Barton’s Tunneling Quality Index, Q [3, 4].
Figure 1.—Finite-difference mesh with excavation in one-eighth symmetry.

2. COMPUTER MODEL AND PREDICTED

RESPONSE

The modeled room was a 50-m-high cylinder with 50-

m-diameter hemispheres representing the mine roof

and floor and a volume of 163,624 m3. One-eighth

symmetry was used to reduce the size of the finitedifference mesh, which consisted of 140,800 zones

shaped like extruded annulus sectors having a 2.3-m

radial thickness and an extruded length of 2.5 m (fig.

1). Sector dimensions were reduced to approximately

1.5 m for one computer run to confirm that the mesh

size was small enough to estimate the depth of failure

into the rock mass. The initial in situ state of stress

used in these analyses was based on stress measurements made in the 1970's through 1980's at the Homestake Mine. Measurements between 930 and 2256 m

in the mine resulted in a linear stress formula (Eq. 1)

dependent on depth below the mine surface [5]. The

initial stress state in the model was achieved by applying the three orthogonal stresses at the finite-difference mesh boundary seven radii from the rib of the

cylindrical room and iterating to equilibrium. 

Fv = 28.28 h,

Fh1 = 14,327.8 + 11.99 h,

and Fh2 = 834.3 + 12.44 h, (Eq. 1)

where h = depth in meters, 

Fv = vertical stress in kilopascals (kPa), 

and Fh1 and Fh2 = horizontal stresses in kPa.

The room was assumed to be excavated in a homogenous, isotropic rock mass constructed between

existing levels below 2118 m. The average depth between levels was used for parameter h (Eq. 1) to

calculate initial stresses. A Mohr-Coulomb failure

criterion defined by cohesion and angle of internal

friction was used to limit the elastic behavior of the

material or the strength of the rock mass. Because

there was a limited amount of material property information on the Yates Formation, three values for cohesion were used—12.2, 18.3, and 24.4 MPa. These

values represent 50%, 75%, and 100% of average

strengths calculated from unconfined compressive

strength test results conducted on specimens from the

Poorman Formation and a value of 30° for the angle

of internal friction. The field-scale unconfined compressive and tensile strengths in the Poorman Formation (42.3 and 6.58 MPa, respectively) were 50% of

the average laboratory values. They were obtained by

monitoring the loss of borehole extensometer anchors

during mining of large vertical crater retreat stopes

between 2118 and 2164 m at the Homestake Mine [6].

These extensometers were also used to calibrate a

three-dimensional, finite-element program, resulting

in a field-scale modulus of deformation equal to
Figure 2.—Failure zones in x-y plane through the origin.

23,615 MPa, or 25% of average laboratory values.

This value was used in the finite-difference analyses.

Two specimens were prepared for unconfined compression tests and five specimens were prepared for

Brazilian tensile tests from a grab sample of rock from

the Yates Formation measuring approximately 1 by

0.5 m. The average tensile strength of these specimens

was about the same as the average tensile strength of

rock from the Poorman Formation, but the unconfined

compressive strength was more than two times the

values for the Poorman Formation. This implies that

24.4 MPa is about half the cohesion value for the

Yates Formation and, based on these tests, is a reasonable estimate of the field, or rock mass, value of

cohesion. It is important to emphasize that these specimens may not represent the entire Yates Formation.

A thorough site investigation is essential to characterizing the rock more accurately. The high strength of

the laboratory specimens combined with their elasticbrittle behavior when loaded to failure indicate that

Yates rock may be prone to bursting. 

Results from the finite-difference model indicate that

the maximum depth of failure into the rock around the

cavity is 10 m and occurs in the lower roof (fig. 2S).

The maximum yield width in the room’s rib is 6.8 m.

Yield zones in the y-z plane through the origin are

similar in shape, but not as extensive as yield zones in

the x-y plane. If the centroid of the chamber is located

2141 m below the surface in rock equal in strength to

that of the Poorman Formation, the model calculates

yield zones in both the lower roof and ribs (fig. 2A).

Previous mining experience confirms that a stope 24

m wide, 30 m long, and 46 m high excavated with the

vertical crater retreat method at 2141 m suffered some

caving, but remained open when the roof was supported with cable bolts [6]. Conversations with mine

personnel indicated that large structures (45.7 m high,

wide, and long) have been excavated, but are unstable

at depths of 2416 m. These observations, combined

with the finite-difference results, imply that 2141 m

may be the deepest opening that can exist in the Poorman or Homestake formations without encountering

stability problems (figs. 2A, S). However, if the rock

strength of the Yates Formation is approximately

twice that of the Poorman Formation, as initial

laboratory tests indicate, then failure will be limited

around the room constructed in Yates rock even at

2416 m underground (fig. 2U). Results could differ if

the Yates rock has anisotropic material properties.
Failure zones were initiated where redistributed

stresses became concentrated near the lower roof of

the chamber and propagated into the ribs as mining

depth increased. The thickness of the failure zone

diminished to zero near the apex of the hemispherical

roof because the arched opening eliminated a wedge

of material of a type that often fails and requires

support.

3. ROCK MASS CLASSIFICATION

A comparative rock mass characterization using Q

(Eq. 2) was performed with data obtained from three

locations at the Homestake Mine to determine if the

support recommendations from this system could be

reasonably applied to the large chamber proposed in

the Yates Formation. Geomechanics data were

collected at three different sites.

Q = RQD/Jn x Jr

/Ja x Jw/SRF (Eq. 2)

where Q = tunneling quality index,

RQD = rock quality designation,

Jn = joint set number,

Jr

 = joint roughness number,

Ja = joint alteration number,

Jw = joint water reduction factor, 

and SRF = stress reduction factor.

Site 1 is located 2118 m underground in rock

primarily of the Homestake Formation, although a

small amount of Poorman rock is present. Some areas

are fractured, presumably from high stress caused by

nearby stoping. Steeply dipping bedding planes are

the major discontinuity at this site. The bedding

planes are tightly healed; however, in highly stressed

areas, the spacings between open bedding planes is 5

to 10 cm. These bedding planes are discontinuous,

and most of them can not be traced more than 1 m.

Occasionally, joints with random orientations were

observed. These joints are tight and smooth, contain

no filling material, and can be traced for 3 to 6 m. The

estimated number of bedding planes, joints, and

fractures per cubic meter was 16.

Site 2 is located 2141 m below the surface in the

Homestake and Poorman formations. The area is

heavily jointed. Steeply dipping bedding planes are

spaced 15 to 30 cm apart and, similar to rock at site 1,

stress redistributed from nearby stopes has opened up

discontinuities that were otherwise tightly healed. One

poorly developed joint set was observed that had a

spacing of about 30 cm and a continuity of 3 to 6 m.

These fractures are tight and rough, and contain a hard

filling. The estimated number of bedding planes,

joints, and fractures per cubic meter was 12.

Site 3 is 1508 m deep in the Yates Formation, the proposed host rock for the NUSL. Site 3 rock is massive

with no or few joints. The estimated number of

bedding planes, joints, and fractures per cubic meter

was less than 4.

The RQD of the rock at these sites was estimated

from the number of joints per cubic meter. All sites

were dry. Laboratory unconfined compressive

strengths of the intact rock used to calculate the stress

reduction factor were 84.6 MPa for sites 1 and 2, and

186 MPa for site 3. Vertical stress (Eq. 1) was used as

the major principal stress because three out of four in

situ stress measurements at the mine indicated that the

major principal stress direction aligned with the

vertical [5].

On the basis of empirical charts developed by Barton

et al. [3] (fig. 3) and Grimstad and Barton [4] (fig.4),

the recommended support for all three sites agreed

well with the support used at these sites (table 1),

indicating that it is reasonable to apply these charts to

the large chamber proposed at the Homestake Mine

(table 2).

The Grimstad and Barton chart recommends systematic bolting with 40 to 50 mm of unreinforced

shotcrete for 25- and 50-m spans. The Barton chart

recommends tensioned bolts with 2- to 3-m spacings

for these spans. There are no support recommendations for spans exceeding 70 m because the plotted

data exceed the range of the charts.
Figure 4.—Recommended support as a function of tunneling quality index and equivalent dimension (after

[4])

Figure 3.—Recommended support as a function of tunneling quality index and equivalent

dimension (after [3])
Table 1.—Support recommendations based on Q compared to actual support used at three sites at the Homestake Mine.

Parameter Site 1 Site 2 Site 3

Joints/m3

, Jv 16 (13 bedding planes + 3 joint

sets)

12 (7 bedding planes + 5 joint

sets)

<4

RQD = 115 - 3.3 Jv 60 75 85 (reduced from 100 for

unknown joints)

Joint set number, JN 3 (one joint set + random

joints)

4 (2 joint sets) 0.75 (massive, no or few

joints)

Joint roughness number, JR 1 (smooth, planar) 1 (smooth, planar) 4 (discontinuous joints)

Joint alteration number, JA 1 (unaltered joint walls) 1 (unaltered joint walls) 0.75 (tightly healed joints)

Joint water reduction number,

Jw

1 (dry) 1 (dry) 1 (dry)

Stress reduction factor, SRF 20 (Fc /F1

1

 = 0.7) 20 (Fc /F1 = 1.2) 10 (Fc /F1 = 4.4)

Tunneling quality index, Q 1.0 0.9 60

Excavation support ratio 1.6 (permanent mine opening) 1.6 (permanent mine opening) 1.6 (permanent mine opening)

Span, m 4 4 5

Equivalent span, m 2.5 2.5 3.1

Recommended support [4] Category 4

Rock bolts at 1.3-m spacing,

50-mm shotcrete

Category 4

Rock bolts at 1.3-m spacing,

50-mm shotcrete

No support required

Recommended support [3] Category 25

Untensioned bolts at 1-m

spacing, chain link mesh

Category 25

Untensioned bolts at 1-m

spacing, chain link mesh

No support required

Actual support used Friction bolts at 1-m spacing,

chain link mesh

Friction bolts at 1-m spacing,

chain link mesh

Spot bolting with mechanicalanchor bolts, friction bolts at

1.5-m spacing, chain link mesh

1

Fc = rock unconfined compressive strength. F1 = major principal stress.

Table 2.—Support recommendations for three roof spans where Q = 60.

Parameter Span = 25 m (82 ft) Span = 50 m (164 ft) Span = 100 m (328 ft)

Excavation support ratio,

ESR

1 (large civil cavern) 1 (large civil cavern) 1 (large civil cavern)

Equivalent span, m (ft) 25 (82) 25 (82) 100 m (328 ft)

Required support [4] Category 4

Systematic bolting

40-50-mm shotcrete

Category 4

Systematic bolting

40-50-mm shotcrete

No recommendations

Required support [3] Category 11

Tensioned bolts

2-3-m spacing

Category 12

Tensioned bolts

 2-3-m spacing

No recommendations

5. CONCLUSIONS

The stability of a mine opening spanning 50 m with a

volume of 163,624 m3

 was analyzed at depths from

2141 to 2416 m using the three-dimensional, finitedifference numerical model FLAC3D and empirical

rock characterization techniques. Material properties

and in situ stresses from a previously calibrated finiteelement model applied to vertical crater retreat stopes

in the Poorman and Homestake formations were used.

The model calculated zones of plasticity around the

mine opening at all mining depths below 2141 m. The

maximum extent of failure into the rock was 10 m and

would occur in the lower roof at all mining depths

modeled. However, the thickness of the failure zone

diminished to zero near the apex of the hemispherical

roof. The maximum yield width in the room’s rib was

6.8 m.

These results, combined with observations of

instability of rooms by mine personnel at 2438 m

underground, suggest that 2141 m may be the deepest

level that a room spanning 50 m can be mined and

maintained in rock with strengths equal to those of the

Poorman and Homestake formations. If the rock

strength obtained from the specimens of Yates Forma-
tion rock are representative of the entire formation,

then construction of large rooms may be possible at

levels below 2141 m in this host rock, but may raise

rock bursting concerns. A thorough site investigation

in the Yates Formation, including joint mapping and

directional drilling to obtain core for laboratory tests,

is essential for a more accurate stability assessment.

Rock support requirements were validated at three

existing sites using empirical design methods, indicating that it is reasonable to apply these methods to the

large chamber proposed at the Homestake Mine. The

recommended spacing between bolts for a 50-m span

constructed in rock believed to be characteristic of the

Yates Formation is 2 to 3 m. A 50-mm-layer of

shotcrete is also advised.

ACKNOWLEDGMENTS

The authors wish to express their appreciation to

Mark Laurenti, chief mine engineer; Mike Stahl, mine

production engineer; and Kathy Hart, chief geologist,

Homestake Mining Co., for providing access to

underground workings and providing historic stability

information on large excavations at the Homestake

Mine. Modeling suggestions made by John D. Osnes,

manager of Geomechanics, RESPEC, Rapid City, SD,

are also much appreciated.

REFERENCES

1. Davis, Rachel, ed. 2001. Underground lab to mine secrets of

the universe. Engineering Times, Aug./Sep.

2. Itasca Consulting Group, Minneapolis, MN. 1998. FLAC -

Fast Lagrangian analysis of continua, version 3.4. 1485 pp.

3. Barton, N.R., R. Lien, and J. Lunde. 1974. Engineering

classification of rock masses for the design of tunnel

support. Rock Mech. 6(4):189-239.

4. Grimstad, E., and N. Barton. 1993. Updating the Q-system

for NMT. In Proceedings of the International Symposium

on Sprayed Concrete: Modern Use of Wet Mix Sprayed

Concrete for Underground Support. Oslo: Norwegian

Concrete Assn.

5. Pariseau, William G. 1985. Research study on pillar design

for vertical crater retreat (VCR) mining. Bureau of Mines

Contract Report J0215043, Oct.

6. Pariseau, William, F. Duan, and C.S. Schmuck. 1987.

Stability analysis of the VCR stope at the Homestake Mine.

Gold Mining 87, pp. 199-213.