UNITED STATES BUREAU OF MINES

UNITED STATES DEPARTMENT OF THE INTERIOR

RI 9576 REPORT OF INVESTIGATIONS/1995

Rock Mechanics Study of Shaft Stability

and Pillar Mining, Homestake Mine,

Lead, SD

(In Three Parts)

2. Mine Measurements and Confirmation

 of Premining Results
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administration.
Report of Investigations 9576

Rock Mechanics Study of Shaft Stability

and Pillar Mining, Homestake Mine,

Lead, SD

(In Three Parts)

2. Mine Measurements and Confirmation

 of Premining Results

By W. G. Pariseau, J. C. Johnson, M. M. McDonald, 

 and M. E. Poad 

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

Instruments ........................................................................................ 3

Numerical quality ................................................................................... 4

Model calibration ................................................................................... 6

Elastic properties scale factor ....................................................................... 6

Strength properties scale factor ...................................................................... 7

Shaft analysis results ................................................................................. 10

Shaft wall displacements ........................................................................... 10

Shaft wall yielding and safety factor .................................................................. 10

Summary and conclusions ............................................................................ 13

Acknowledgments ................................................................................... 13

References ......................................................................................... 13

ILLUSTRATIONS

1. Schematic of Homestake Mine development ......................................................... 2

2. Multipoint borehole extensometers on 3650 level ..................................................... 3

3. Finite-element mesh of a vertical section through Ross shaft pillar ........................................ 5

4. Refined insert mesh for two-pass calibration analyses .................................................. 7

5. Recorded stope displacements, extensometers E14, E15, and E16 ........................................ 8

6. Recorded stope displacements, extensometers E17, E18, and E19 ........................................ 8

7. Sloughing on stope side of hanging wall drift ......................................................... 9

8. Extent of yield zone as a function of strength scale factor ............................................... 9

9. Window of mesh showing extent of yielding after ore reserve in shaft pillar has been mined .................. 11

10. Distribution of principal stresses in window plot of mesh ............................................... 12

TABLES

1. Project chronology .............................................................................. 2

2. Finite-element runs and displacement estimates ....................................................... 4

3. Maximum shaft wall displacement ................................................................. 10
UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT

 Metric Units

cm centimeter mm millimeter

kg kilogram MPa megapascal

m meter pct percent

U.S. Customary Units

ft foot psi pound per square inch

in inch tr oz troy ounce
McKinnon Professor of Mining Engineering, University of Utah, Salt Lake City, UT. 1

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

Research civil engineer, Spokane Research Center (retired). 3

Supervisory mining engineer, Spokane Research Center. 4

Rock Mechanics Study of Shaft Stability and Pillar Mining, 

Homestake Mine, Lead, SD

(In Three Parts)

2. Mine Measurements and Confirmation of Premining Results

By W. G. Pariseau, J. C. Johnson, M. M. McDonald, and M. E. Poad 1 2 3 4

ABSTRACT

A U.S. Bureau of Mines case study of pillar recovery in high-grade ore near the Ross shaft at the Homestake

Mine, Lead, SD, has demonstrated the usefulness of the finite-element method for evaluating shaft pillar mining

plans and shaft stability. This report focuses on mine measurements and calibration of the two-dimensional

computer model and is the second in a series of three Reports of Investigations describing the Ross shaft study.

In this study, borehole extensometers and other instruments were installed to provide data for model

verification and to monitor the shaft. Results of the recalibrated two-dimensional model (UTAH2) confirmed

the premining stability evaluation. 

However, after mining began, concern was expressed because cracks and other signs of ground motion

appeared at considerable distances from the area of active pillar mining. In part 3 of the study, an intense threedimensional modeling effort using UTAH3 was initiated. The results again showed that the observed effects

were within expectations and that the shaft would remain safe. Three-dimensional analyses of alternative pillar

mining scenarios indicated that more of the shaft pillar ore reserve could be recovered than previously thought.
2

INTRODUCTION

Because of the importance of shaft pillar design to the experience in the early 1950's that led to definition of the

mining industry, researchers from the U.S. Bureau of Mines existing shaft pillar. Additional pillars within the shaft pillar

(USBM) initiated a study to investigate the extraction of were then defined in response to the perceived threat of

valuable reserves within the Ross shaft pillar at the Homestake renewed ground movement.

Mine, Lead, SD. The study was a cooperative effort and The first Report of Investigations (RI) of this series

involved the USBM, the Homestake Mining Co., and the (Premining Geomechanical Modeling Using UTAH2)

University of Utah, Salt Lake City, UT. Table 1 shows the described the general objectives of the study, site geology,

chronology of the main project phases. practical shaft stability criteria, and the approach taken to the

Table 1.—Project chronology

Phase Topic Beginning date

1 ............... Premining stability analysis. April 1987.

2 ............... Installation of instruments October 1987.

 and validation of two-

 dimensional model.

3 ............... Three-dimensional stability August 1990.

 analysis.

4 ............... Installation of additional in- June 1994.

 struments and update of

 three-dimensional model.

The Homestake Mine is located in the northern Black Hills

of South Dakota. Figure 1 shows the general layout of the

mine, which is the oldest and deepest in North America.

Development extends to the 8000 level (2,440 m or 8,000 ft

below surface), with the Yates and Ross shafts providing access.

About 8,400 kg (270,000 tr oz) of gold and 1,500 kg (50,000 tr

oz) of silver are recovered from 1.5 million metric tons (1.7

million short tons) of ore milled each year. Most of the ore

reserve in the Ross shaft pillar lies between the 3200 and 3800

levels on the west side of the shaft. Stoping methods are mainly

mechanized cut-and-fill and vertical crater retreat.

Pillar mining began below the 3650 level in late 1988.

Shortly afterward, movement was observed on the 3200 level,

where the shaft had been damaged in the early 1950's. In fact,

i t was th e

problem (Pariseau and others, 1995). Also described in detail

were two-dimensional, finite-element simulations of (1)

historical mining leading to the present shaft pillar and (2)

future mining of the ore reserve in the shaft pillar. The results

indicated that the Ross shaft remained in elastic ground and

that no large, catastrophic ground failures were likely. Hence,

the proposed pillar mining plan was safe.

In this second RI (part 2), instrument calibration and

updating of the original two-dimensional, finite-element model

are described. The premining analysis focused on a plan view

of the 3500 level that allowed for sequential excavation of old

stopes followed by mining in the shaft pillar. This RI focuses

on a vertical section that allows for sequential, lift-by-lift

simulation of cut-and-fill extraction of the ore reserves in the

shaft pillar and addresses several numerical modeling concerns

that arose during the premining study.

The basic input data were (1) stope geometry and

geological descriptions obtained from mine maps and sections,

(2) in situ stresses obtained using a number of measurement

techniques at various locations in the mine (Johnson and

others, 1993), (3) rock and fill properties obtained from

laboratory tests, and (4) the pillar mining sequence established

b y planning engineers .

Several types of instruments were installed at the study site.

Measurements taken from borehole extensometers positioned

near the plane of the section being analyzed were compared

with computer estimates to validate and calibrate the numerical
3

Figure 1

Schematic of Homestake Mine development.

model. The results justified the use of an anisotropic, elastic- The approach to the particular problem of model calibration

plastic material law in the model. Calibration provided the was (1) to install instruments prior to stoping for the purpose of

scale factors for adjusting elastic moduli and strengths to rock measuring rock mass response to the first lifts taken in the shaft

mass conditions at the study site. The initial scale factors for pillar and (2) to install instruments near the shaft to monitor

elastic and strength properties were 0.36 and 0.80, respectively, shaft stability. Stope instruments would provide initial data for

which were obtained from an earlier study of vertical crater mod-el validation, calibration, and updating. Shaft instruments

retreat mining (Pariseau, 1985). would provide objective measurements of ground movement

An important objective of the current analysis was to verify around the shaft in response to pillar mining and would also

the adequacy of the rock properties scale factors and thus to test warn of any potential threat to shaft stability, independently of

the reliability of the premining analysis very early in the shaft numerical model results. This work is in support of the USBM

pillar mining project. Once calibrated, the model could then be mission to improve the safety and productivity of mining.

used to analyze alternative mining sequences in the shaft pillar.

INSTRUMENTS

Two sets of instruments were installed, one in the stope and The MPBX's in the main stope were arrayed in twin fans of

one in the shaft. Stope instruments consisted entirely of multi- three holes each that extended from the hanging wall drift

point borehole extensometers (MPBX's). Shaft instruments toward the stopes on the north and south sides of the original

were primarily MPBX's, but also included several shaft set load shaft pillar. These sides are defined by the north and south

cells, borehole temperature sensors, strain potentiometers, and pillar walls, il-lustrated in figure 2. The hanging wall drift

rock bolt load cells. Figure 2 shows the MPBX's in bore-holes provided access to the motor barn and connected with ramps to

col-lared on the 3650 level. The remote MPBX's are directed the shaft pillar stopes.

away from the shaft into undisturbed ground.
4

Figure 2

Multipoint borehole extensometers on 3650 leve. Dotted lines indicate contacts between
5

NUMERICAL QUALITY

The issue of numerical quality was addressed in some detail Several kinds of numerical questions relating to both

before conclusions were drawn from a final series of two- categories of runs were addressed. These questions concerned

dimensional stope and shaft analyses using UTAH2 (Pariseau the effects of mesh size, the effects of including the hanging

and others, 1991), a computer program that handles cutting wall drift, the amount of computational effort required, and the 5

and filling of initially stressed anisotropic rock masses. A effects of the presence of an old stope near the shaft pillar.

general-ized Hooke's law was used to relate stresses and strains Results are summarized in table 2.

in the purely elastic domain. A nonlinear, anisotropic yield

condition appropriate for geologic media was employed to limit Mesh Size

the range of purely elastic deformation (Pariseau, 1972).

Associated flow rules were selected when yielding occurred More economical runs favor small meshes, while better

and deformation progressed beyond the elastic limit into the quality runs favor larger meshes with boundaries well away

elastic-plastic range. from the excavation. Comparing run 1 with run 2 showed the

Seventeen computer analyses were completed using an up- de-sirability of enlarging the mesh by adding a border (figure

dated version of the original vertical section through the shaft 3). The calculated displacement then increased by

pillar. The update was based on geologic and production plan- approximately 50 pct, indicating that the original mesh borders

ning information developed from drilling completed after the were close enough to the excavation to affect the results

 premining analysis. Figure 3 shows a portion of the mesh in significantly. This result was expected; indeed, the reason for

the vicinity of the D-limb stope and hanging wall drift. doing the comparison run was to verify this effect.

The 17 runs were divided into two categories. The first

category consisted of "one-shot mineouts" in which the entire Hanging Wall Drift

ore reserve was excavated in a single cut by the computer.

One-shot runs save computer time and operator effort and are A more subtle and difficult numerical question concerned

useful for laying out the problem. The second category modeling extensometer response. The difficulty arose when

consisted of sequential excavation analyses. Sequential attempting to represent the small hanging wall drift containing

excavation analyses follow the mining sequence and are needed the extensometer hole collars and the much larger stopes of the

to obtain estimates of instrument readings, which in turn are shaft pillar in the same mesh. Mesh refinement suitable for a

necessary for model calibration. drift-size excavation would lead to an enormous number of

See also Pariseau, W. G. Interpretation of Rock Mechanics Data

5

(Volume 2) (A Guide to Using UTAH2). Contract HO220077, Univ. UT.

USBM OFR 47(2)-80, 1978, 41 pp.

elements when extended over the entire mesh, while mesh

refinement suitable for the stopes would not allow accurate

Table 2.—Finite-element runs and displacement estimates

Run File name Description Displacement1

mm in 

ONE-SHOT

1 ................ Original Original report run, old mine geometry, no border. &4.0 &0.158

2 ................ Owbor Old mine geometry, with border (border effect). &5.9 &0.232

3 ................ Borone New mining geometry with border (stope geometry effect). 13.7 0.539

4 ................ Cutl 1st lift without hanging wall drift. &3.0 &0.117

5 ................ Hwcut 1st lift with hanging wall drift. 1.4 0.056

6 ................ Bcut 2 lifts, 1st and bottom lift, with hanging wall drift. 14.8 0.584

7 ................ Bcut>hafmat Same as run 6, but at 1/2 original strength. 15.9 0.624

8 ................ Sand0 Excavation of old sand-filled stope 9m (30 ft) south of shaft &4.1 &0.161

 center.

9 ................ Sand1 Sand stope plus 2 lifts without hanging wall drift. 12.1 0.475

10 ............... Sand2 Sand stope plus 2 lifts with hanging wall drift. 17.1 0.675

11 ............... Qsand1 Same as run 9, but with 2 times load steps and iterations 12.1 0.475

 (computational effort).

SEQUENTIAL

12 ............... Seq>bcut Sand stope, 2 lifts, without hanging wall drift (sand stope first, 16.1 0.632

 lifts next).

13 ............... Seq>cut12 Same as run 12, but at 1/2 strength. 17.7 0.698

14 ............... Seq>hwbcut Sand stope, 2 lifts, with hanging wall drift. 21.1 0.832

15 ............... Seq>hwcut12 Same as run 14 but at 1/2 strength. 22.8 0.898

16 ............... Seq>hlimb>bcut Same as run 14 without hanging wall drift. 16.0 0.628

17 ............... Seq>hlimb>qtrbcut Same as run 16 at 1/4 strength. 20.4 0.803
6

Figure 3

Finite-element mesh of a vertical section through Ross shaft pillar. A, Border mesh surrounding analyzed region; B,

mesh of analyzed region (Ross shaft centerline); C, detail of B showing insert mesh match

 Relative displacement between anchor point and collar parallel to an extensometer hole in the plane of the analysis. A positive displacement 1

implies elongation or stretching of the hole.
7

modeling of the much smaller hanging wall drift. A compro- Old Stope

mise was to model the hanging wall drift with elements

available in the stope-scale mesh.

Although the modeling was coarse, the usefulness of the

compromise was seen when run 4 was compared with run 5

(table 2). The sign of the displacement was reversed, and there

was a noticeable change in magnitude when the hanging wall

drift was modeled even crudely. Comparisons of run 9 and run

10 showed an increase of about 40 pct when excavation of the

hanging wall was included in the stope-scale mesh (figure 3).

Sequential runs 14 and 16 (table 2) showed the same effect—an

increase of more than 30 pct when excavation of the hanging

wall drift was modeled.

These results indicate that extensometer boreholes should be

collared in openings that can be represented in the nu-merical

model of choice. If the excavation containing the collar is not

represented in the model, even if only crudely, then

comparisons of model results with instrument readings will be

suspect. Mine instruments should be located with re-gard not

only to convenience of access, but also to model requirements

and constraints. Instrument planning and model-ing should be

done in concert, so that more comparisons can be made

between mine measurements and model calculations.

Computational Effort

Comparing run 11 with run 9 showed that the computational effort and convergence obtained weresatisfactory. No

change in calculated displacement occurred in the third significant digit when the computational effort was quadrupled

(double load steps and double iterations).

A limitation of two-dimensional analysis is that stopes

excavated along strike, and thus out of the plane of analysis

(perpendicular to strike), cannot be rigorously taken into

account. Although old stopes that were completed before

installation of extensometers cannot directly affect subsequent

readings, there is an indirect effect in that the rock mass

becomes more deformable and compliant. An example is

shown in figure 3, where a large, sand-filled stope near the

south wall of the shaft pillar was projected onto the analysis

plane. Comparing run 10 with run 6 (table 2) showed that this

indirect effect was noticeable and increased the calculated

displacement by approximately 16 pct.

Strength Reduction

The potential effect of a 50-pct reduction in strength on

calculated extensometer readings can be judged by comparing

run 14 with run 15, and run 12 with run 13. Extensometer

estimates were increased by 8 to 10 pct, depending on how the

hanging wall drift was modeled at the point where the actual

instrumentation holes were collared. Comparing run 16 with

run 17 shows that the effect of strength reduction was nonlinear. An additional 50-pct reduction (quarter strength)

resulted in a more than 27-pct increase in estimated readings

relative to the full-strength estimate. The nonlinearity was a

consequence of yielding in the stope hanging wall and in the

skin of the hanging wall drift.

MODEL CALIBRATION

A two-pass, insert mesh technique was used for model points in holes E14, E15, and E16 (figure 5) amounted to

calibration. This technique allowed mesh refinement in the

area of greatest interest, that is, in the region between the

stope hanging wall and the hanging wall drift. Figure 4

shows the refined insert mesh in relation to the updated and

enlarged parent mesh. Mesh refinement in the region

between the stope hanging wall and hanging wall drift was

particularly desirable for estimating the extent of yielding

around stope exten-someter collars and downhole anchor

points.

The most important results from the insert mesh were (1)

obtaining the estimated extensometer readings necessary to

determine the scale factor for elastic properties and

(2) determining the extent of yielding in the vicinity of the

stope extensometers, which was used to determine the scale

factor for the strength properties.

ELASTIC PROPERTIES SCALE FACTOR

The relative displacements between the anchor and collar

about 3.8 cm (1.5 in) at day 440, whereas in holes E17, E18,

and E19, relative displacement came to about 2.5 cm (1 in)

(figure 6). Figures 5 and 6 also show that the two anchor

points in each hole appeared to move about the same amount;

thus, relative displacements between these anchor points

were small. Approximately 16 weeks after completion of

instal-lation (November 1987) and approximately 10 weeks

after mining began, most of the extensometers showed

somewhat more than 2.5 cm of displacement. Some anchors

were lost. Small rock falls, blasting, and wire breakage were

possible causes. These actual displacements compared well

with the largest calculated displacement of 2.3 cm (0.9 in).

Extensometers E14, E15, E16, and E19 showed relative

displacements of about 0.064 cm (0.025 in) between

downhole anchor points 1 and 2. Finite-element results

indicated about 0.023 cm (0.009 in) of relative displacement.

E17 and E18 showed about 0.318 cm (0.125 in) of relative

displacement between anchor points 1 and 2, while the

corresponding result from the finite-element analysis was

about 0.706 cm (0.278 in). E12 and E20 showed similar
8

Figure 4

Refined insert mesh for two-pass calibration analyses.

behavior, that is, a large relative displacement between the

collar and the bottom anchor point, but a small relative

displacement between anchor points 1 and 2 in the hole.

The large displacements of anchor points down the hole

relative to the collar points and the small displacements 

between anchor points in the hole indicated an elastic response model until the extent of inelasticity or yielding in the model

downhole and an inelastic response near the hole collars. The matched the inelasticity observed. In fact, two series of finiteinference was that stress concentrations in the periphery of the element analyses were done, one with and one without the sand

hanging wall drift were sufficient to cause localized yielding stope. Both were done using the two-pass, insert mesh

and displacement in excess of that expected on the basis of a technique. The first run simulated an excavation step on a relpurely elastic response. Displacements relative to collar points atively coarse mesh; the second simulated the same excavation

could not, therefore, be used to determine the scale factor for step using the refined insert mesh. The excavation sequence

elastic moduli. However, relative displacements between itself represented the major stope cuts taken in the shaft pillar.

downhole anchor points can be used if they are within the Strength scale factors of 0.8, 0.6, 0.4, and 0.3 were used in both

elastic range. Since the results from the finite-element analysis series.

straddled the few applicable measured results, there was no Observations at the study site indicated that localized

indication that a change in the assumed scale factor (0.36) for yielding occurred in the hanging wall drift as a consequence of

the elastic moduli was necessary or justified. stoping in the shaft pillar. Figure 7 shows the physical

STRENGTH PROPERTIES SCALE FACTOR for a finite-element model is that no yielding occur with the

The scale factor for strength properties was determined by near the hanging wall drift should occur only with stope cuts

systematically reducing the strengths of the finite-element and should be localized. Some yielding in the stope model was

appearance of the hanging wall drift. A minimum requirement

development cut that excavates the hanging wall drift. Yielding
9

Figure 5

Recorded stope displacements, extensometers E14, E15, and E16.

Figure 6

justified because of several rock falls in the stopes and the loss

of several deep extensometer anchor points. In this regard, the

orientation of foliation had a noticeable effect on the yielding

pattern. A 60E dip was used in all analyses. This angle was

representative of the general orientation of the major

stratigraphic units at the study site (Poorman, Homestake, and

Ellison Formations), which are anisotropic (orthotropic).

There was no yielding in any of the finite-element analyses

as a result of excavating the development cut in the hanging

wall drift, nor did yielding occur near the hanging wall drift as

a result of excavating stope cuts on the H- and D-limbs at

strength scale factors of 0.8 and 0.6, respectively, in the series

without the old sand-filled stope. Some yielding occurred at

0.4; more extensive yielding occurred in the shaft pillar stope

hanging wall at a strength scale factor of 0.3.
10

Recorded stope displacements, extensometers E17, E18, and E19

The inclusion of the sand stope in the analyses resulted in

yielding in the stope hanging wall at all strength scale factors.

Figure 8 shows the extent of yielding between the hanging wall

drift and the shaft pillars stope cuts with the sand stope present.

For direct comparison, the calculated extent of yielding without

the sand stope is also shown in figure 8 using a strength

reduction factor of 0.6.

The justifiable amount of strength reduction depends on the

importance given to the influence of the sand stope. A

relatively small value of 0.3 might be justified if the sand stope

had no influence on present stoping. A large value would be

justified under the greater influence of the sand stope. Some

intuitive guidance in the matter can be found in considering the

strain-to-failure and the strain energy density of a uniaxially

loaded test specimen. Strain-to-failure is simply the ratio of

unconfine d

compressive strength to

Young's modulus. If the strain-to-failure as a dimensionless

quantity is considered to be independent of scale, then the

strength and modulus scale factors should be equal. This

suggests a strength scale factor of 0.36. However, if the strain

energy density at failure is considered scale invariant, then the

strength scale factor is equal to the square root of the modulus

scale factor. This suggests a strength scale factor of 0.6, since

the modulus scale factor is 0.36. These two criteria were in

close agreement with the range of strength scale factors

suggested by the finite-element results. Considering the large

size and nearness of the old sand-filled stope to the shaft pillar

stopes and the more appealing energy scaling rule, the strength

scale was reduced to 0.6 from the original value of 0.8 for

future analyses.
11

Figure 7

Sloughing on stope side of hanging wall drift. Shaft side remains intact. Note

pronounced foliation.

Figure 8
12

Extent of yield zone as a function of strength scale factor.
13

SHAFT ANALYSIS RESULTS

The important results from the shaft analysis were the accuracy. Runs 1, 2, and 3 involved excavation of the entire

displacement estimates and the finding that there was not a ore reserve.

potential for large-scale yielding and catastrophic rock mass Shaft wall displacement was thus an estimate of what the

motion near the Ross shaft. A quantitative index to evaluating total displacement would be several years in the future after the

safety and stability is the factor of safety, which is the ratio of shaft pillar had been mined. The updated analyses using the

strength to stress. Yielding is associated with a safety factor of new mining geometry indicated a maximum horizontal

1. Safety factors greater than 1 indicate elastic ground. displacement of about 3.9 cm (1.5 in) and a vertical

SHAFT WALL DISPLACEMENTS

The maximum horizontal and vertical displacements along

the Ross shaft are presented in table 3. The most important The extent of yielding after the entire ore reserve in the shaft

runs were the first three. Run 1 was from the original pillar had been mined is shown in figure 9. The pattern of

analysis, while run 2 was the same but used an enlarged mesh yield-ing was similar to that observed earlier. Yielding first

for greate r occurred on the footwall side of the stoped area in the upper left

Table 3.—Maximum shaft wall displacement

Run 

Vertical Horizontal 1 2

mm in mm in 

ONE-SHOT

1 ........ 10.7 0.42 &12.7 &0.50

2 ........ 6.9 0.27 &19.3 &0.76

3 ........ 16.8 0.66 &38.9 &1.53

4 ........ 0.5 0.02 &2.5 &0.1

5 ........ 0.8 0.03 &0.5 &0.02

6 ........ 0.5 0.02 &0.8 &0.03

7 ........ 1.3 0.05 &1.8 &0.07

8 ........ 4.6 0.18 &9.4 &0.37

9 ........ 6.1 0.24 &11.9 &0.47

10 ....... 6.4 0.25 &11.9 &0.47

11 ....... 6.4 0.25 &9.9 &0.39

SEQUENTIAL

12 ....... 2.0 0.08 &1.8 &0.07

13 ....... 2.01 0.08 &2.0 &0.08

14 ....... 2.0 0.08 &2.0 &0.08

15 ....... 2.3 0.09 &2.0 &0.08

16 ....... 2.0 0.08 &1.8 &0.07

17 ....... 2.3 0.09 &2.3 &0.09

Positive values indicate settling. 1

Negative values indicate movement toward stope. 2

displacement of 1.7 cm (0.7 in).

SHAFT WALL YIELDING AND SAFETY FACTOR

of the excavation and also in the hanging wall at the toe of the

stoped area, where another sharp corner was present in the

mesh. Yielding was confined to the stope walls and did not

extend to the shaft centerline.

Contours of the local factors of safety are also shown in

figure 9, rounded to the nearest whole integer. The safety

factor along the shaft centerline varied from 2 to 5. However,

because the shaft cannot be explicitly represented in the plane

of analysis, stress concentration effects at the shaft wall were

absent, meaning that the actual safety factors would be less.

Hence there was the possibility that small-scale yielding at the

shaft wall would not be revealed by the analysis. Small-scale

yielding in the skin of the shaft wall would be handled by

ordinary ground control measures and would not be expected

to pose a threat to shaft operations.

The distribution of principal stresses after the ore reserve

was mined is shown in a window of the mesh in figure 10. An

arrowhead indicates tension. Comparing data in figures 9 and

10 shows that the zones where the safety factor was relatively

low were associated with compressive stress states. High safety

factors were present in zones of induced tension.
14

Figure 9

Window of mesh showing extent of yielding after ore reserve in shaft pillar has been mined. Safety factor contours also

shown.
15

Figure 10

Distribution of principal stresses in window plot of mesh.
16

SUMMARY AND CONCLUSIONS

Advances in rock mechanics and mine design suggest that such as a new hanging wall drift, and mesh refinement were

it is possible to devise methods for recovering valuable ore left also examined in order to maintain numerical quality and

in shaft pillars in hard-rock mines. A case study involving a reliability of the analysis.

shaft pillar in high-grade ore near the Ross shaft at the Comparisons of extensometer readings taken during the

Homestake Mine demonstrated the usefulness of this new initial stages of mining with calculated readings using the

technology. A two-dimensional, premining stability evaluation updated mesh showed that some displacements were

(part 1 of this three-part study) indicated that the shaft remained overestimated while some were underestimated. Thus,

in elastic ground as the ore reserve was mined. Large-scale although the data were quite limited, there was no indication

ground motion and the potential for catastrophic failure were that the elastic moduli scale factor of 0.36 should be changed.

not indicated. Thus, the effects of pillar mining did not appear A systematic reduction of strength using scale factors

to pose a threat to shaft stability. ranging from the original value of 0.8 through 0.3 was used in

Subsequent definition drilling and detailed mine planning the updated model in conjunction with a two-pass

allowed more accurate models of geology and stope geometry computational technique to determine a scale factor for rock

in the shaft pillar to be constructed. Installation of borehole mass strength at the study site. The two-pass technique allows

extensometers in the hanging wall of the stope in advance of one to use a refined mesh in the vicinity of the first stopes in the

mining provided data for a check on elastic moduli and strength shaft pillar and to follow the progress of yielding in greater

scale factors assumed from a previous study at the mine. Scale detail. Comparisons of the extent of yielding in the finitefactors adjust values of rock properties obtained in a laboratory element model with that observed at the study site indicated that

to values obtained from a rock mass and are essential for a strength scale factor of 0.6 was appropriate.

calibrating models and for reliable design analysis. Subsequent updated and calibrated two-dimensional, finiteA number of concerns about modeling were successfully element models showed that the Ross shaft remained in elastic

addressed in a series of two-dimensional analyses of a vertical ground and substantiated the conclusion from the original

section through the center of the shaft pillar. Questions of premining study that shaft pillar mining did not pose a serious

mesh size, computational effort, and effects of out-of-plane threat to shaft safety. No large, catastrophic movement of

stopes were considered. Modeling of small development ground near the shaft was indicated.

openings ,

ACKNOWLEDGEMENTS

The Ross shaft pillar project involved the efforts of many of the project. A grant of computer time from the UTAH Suindividuals. Special thanks go to Allen Winters, general man- percomputing Institute, which is funded by the State of Utah

ager, and his excellent team at the Homestake Mine, for and IBM Corp., is also gratefully acknowledged.

providing access to the mine and assistance during all phases

REFERENCES

Johnson, J. C., W. G. Pariseau, D. F. Scott, and F. M. Jenkins. In Situ Pariseau, W. G., J. C. Johnson, M. M. McDonald, and M. E. Poad. Rock

Stress Measurements Near the Ross Shaft Pillar, Homestake Mine, South Mechanics Study of Shaft Stability and Pillar Mining, Homestake Mine, Lead,

Dakota.. USBM RI 9446, 1993, 17 pp. SD (In Three Parts): 1. Premining Geomechanical Modeling Using UTAH2.

Pariseau, W. G. Plasticity Theory for Anisotropic Rocks and Soils. Paper USBM RI 9531, 1995, 20 pp.

in Basic and Applied Rock Mechanics, 10th Symposium on Rock Mechanics Pariseau, W. G., M. M. McDnald, J. C. Johnson, and M. E. Poad. Personal

(Univ. TX at Austin, 1968). SME-AIME, 1972, pp. 267-295. Computer Finite-Element Modeling for Ground Control and Mine Design.

 . Pariseau, W. G. Research Study on Pillar Design for Vertical Crater Pres. at USBM Workshop on UTAH2 PC, Denver, CO, Mar. 1, 1991; 43 pp.;

Retreat (VCR) Mining contract JO215043, Univ. UT). USBM OFR 44-86, available from J. C. Johnson, Spokane Res. Cent., Spokane, WA

1985, 233 pp.; NTIS: PB 86-210960.