180

o 160 7—— Stacey/Page
S --- Hardy/Agapito

_ 140 -}- -.- Hedley/Grant
£
G 12074

© 100+
a] Le
n ao
5 weer
=

a

>
<x

1°) T T T
fe) 2 4 6 8

Width—to—Height Ratio

Fig. 5 Comparison between pillar width-to-height ratio and aver-
age pillar strength for different empirical equations based on power
function.%.!1,14 Material strength was normalized for each equation
for comparative purposes

Progressive failure in stone pillars

Owing to the limitations of survey data, the above empirical
methods do not provide a totally realistic picture of stone pil-
lar behaviour. Additionally, a large database of pillar-specific
information ‘that represents past successes and failures has
not been established to aid in construction of a reliable pillar
design technique for stone mines. In the absence of this infor-
mation numerical simulations can provide a potentially useful
means of testing engineering methods.

‘The simulation used for this study was the two- and three-
dimensional finite-difference code.!5 The two-dimensional
calculations were performed under plane-strain conditions,
so the model sample is equivalent to a long pillar. It was
assumed that individual elements in the model behaved in an
elastic-perfectly plastic manner; the overall pillar behaviour
could, however, include strain softening and strain harden-
ing. Model shapes mirrored those observed in the field and
ranged from a very slender pillar with a width-to-height ratio
of 0.4 to intermediate pillars with a width-to-height ratio of
1.4. Model symmetry was constructed to simulate a recurring
pattern of rooms and pillars of equal dimensions. ‘The roof
and floor materials were modelled to be elastic.

Slender-shaped pillars failed rapidly by yielding from the
ribs inwards to the pillar core, which indicated a relatively
low-strength structure. As the pillars became more squat, ele-
vated horizontal confinement increased their strength greatly.

The model pillars had a modulus of 41.4 GPa, an angle of
internal friction of 40° and a cohesion of 6.9 MPa. These
data were derived from laboratory tests of the Layolhanna
Limestone in Pennsylvania. The model pillars were subjected
to simulated loading conditions by moving distant boundaries
in the roof and floor together at very slow rates. This had the
effect of a gradual loading of the pillars through several dis-
tinct strength phases. During the early loading phase the
modelled pillar displayed relatively elastic characteristics (Fig.
6, points A-B), the deformation of the pillar being propor-
tional to increases in average vertical stress levels within it.

ge 60
s c
4 50
g D
a0
Plasticity Indicator & B
* at yield in shear ba ~
© at yield in tension g
30
: A
<0
O02 4 6 8 1012 4
roof Flac Steps, x 1000
A 8
pillar
floor moderate stress levels
Cc ip

near peak strength residual strength
Fig. 6 Elastic-plastic model, which produces progessive failure
patterns, can demonstrate strain-softening behaviour within full-
scale pillars

During this phase dominated by elastic behaviour minor
yielding of the pillar edges began to occur. Continued pro-
gressive failure of the pillar’s outer perimeter produced an
hourglass-shaped elastic core. It also had the effect of moving
the peak vertical stress away from the pillar edge towards the
pillar centre (Fig. 6, points B-C).

‘The maximum pillar strength was achieved when the high-
est vertical stress levels in the elastic core were supported by
the maximum horizontal confinement available to the pillar
Fig. 6, point C). Beyond this point any additional load to the
pillar resulted in rapid loss of strength. The zone of plastic
yield extended throughout the pillar, producing a residual pil-
lar strength (Fig. 6, point D) that was considerably less than
the maximum pillar strength.

Effect of excessive stress on stone pillar
stability

Pillar failure due to excessive stress levels was not frequently
observed during field visits to these mines. In fact, only seven
development pillars at four mines were observed to have
undergone progressive failure due to excessive loading (Table
2). In case 1 (Table 2), a pillar with a width-to-height ratio of
1.0 was inadvertently reduced from 9.1 to 6.1 m under less
than 30 m of overburden. The calculated average vertical
stress for this pillar was less than 7 MPa: in reality, the stress
levels may have been much higher. Failure of the pillar
perimeter due to crushing left only a narrow core of broken
rock (Fig. 1). It was surmised that additional stresses were
applied to the pillar either as a consequence of its unique
position near the highwall and the effect of some undetected
geological characteristic or by deflection of the roof in over-
wide openings.

In case 2 the initial mine development had taken place
by random room-and-pillar methods. One failed pillar was
observed to be narrower than the surrounding pillars. This


Parametric analysis of the effect of discontinuities on pillar
strength was conducted by varying the dip and material prop-
erties within the ubiquitous-joint model. In these simulations
discontinuities were passed through modelled pillar shapes
whose width-to-height ratios ranged from 0.6 to 1.2. Three
distinct pillar behaviours were observed in relation to the dip
of the discontinuities, Fig. 11 shows the strength profiles for

45

40
35
30
25

30°

45°
Width—to~Height Ratio = 0.8

Avg. Vertical Stress, MPa
x
cs)

15
10
5
O-+ T T T
0.0 0.025 0.05 0.075 0.01
Strain
Fig. 11 _ Stress versus strain for model pillars (width-to-height ratio

= 0.8) with discontinuity dips ranging from 0 to 90°

pillars with a stiffness of 41.4 GPa and a Mohr-Coulomb
failure envelope defined by a friction angle of 40° and a dis-
continuity friction angle of 25°. The lowest pillar strength
occurred at a discontinuity dip angle of 57.5° (Fig. 11). It
should be noted that the point of lowest strength is defined in
the ubiquitous-joint model by the relationship

Brain = 45488 (10)

where Brin is the angle of a through-running discontinuity
that produces the lowest average vertical peak stress and $4 is
the internal angle of friction of the discontinuity.

How well this model characteristic fits field conditions
needs further evaluation. The highest pillar strength occurred
with a discontinuity dip of 0° and gradually decreased as the
dip angle increased. As the discontinuity dip angle increased
above 57.5°, however, the pillar strength began to increase
again, but the original strength for the intermediate to squat
pillar shapes was not re-established as failure shifts to a differ-
ent mode.

For all model shapes and for a given set of material proper-
ties the pillar strength associated with a discontinuity dip of
90° was the same. In the case shown in Fig. 11 that value was
approximately 29 MPa. This characteristic may, however, be
model-driven and not representative of field conditions. The
ubiquitous-joint_model attempts to force discontinuities
through columns of grid elements of equal size. Although this
behaviour may be indicative of successive column failure
through a pillar with numerous, equally spaced vertical joints,
it may not be indicative of pillars affected by variably spaced
joints.

Stress versus strain plots for these numerical simulations
are shown in Fig. 11. For discontinuity dips between 0 and
45° the material displayed elastic-plastic behaviour. When
the model was run with a discontinuity dip of 60° the model

pillar exhibited very low strength. Finally, strain-softening
material behaviour occurred as the discontinuity dips
increased to 90°. Thus, both observation and numerical data
suggest that when discontinuities are present at a particular
angle and composition they can control the behaviour and
strength of pillars.

‘Slip along Discontir

1 Buckling of Column(s)

45 + 4/2

60

Avg. Vertical Peak Stress, MPa

0 10 20 30 40 50 60 70 80 90
Angle of Through—Going Discontinuity

Fig. 12 Changes in vertical peak stress as discontinuity dips are
varied from 0 to 90° for four different width-to-height ratio model
pillars

‘The implications of this analysis are revealed in Fig. 12. As
demonstrated, the strength of pillars of various shapes and
with different discontinuity dips is very sensitive to changes in
extraction ratio and overburden. For example, a discontinuity
dipping at 60°, under approximately 50 m of overburden,
with a width-to-height ratio of 0.8 and passing through the
entire 15 m high pillar, could cause failure if its properties
were equivalent those of material with a friction angle of 25°
and a cohesion of zero. If this same discontinuity dips at 45°,
the pillar might not fail until almost 250 m of overburden is
encountered. Fig. 13 is presented to illustrate the significant

80+
FLAC ubiquitous joint model
604 - ow
Overburden
‘250 m
40

Avg. Pillar Vertical Stress, MPa
N
3
‘

0.4 0.6 0.8 1.0 1.2 1.4
Width—to—Height Ratio

Fig. 13 Relationship between pillar shape, overburden, discontinu-
ity dip and pillar stress

impact that pillar shape, overburden and discontinuities can
have on stone pillar strength, but it is not meant to be a
design guideline.


mining conditions. The strength of the empirical method is
that specific failure mechanisms need not be considered. The
limitations of the empirical method stem from the inability to
extend the formulae beyond the specific material properties,
sizes, shapes and overburdens found in the survey data.
Bieniawski? wrote that the strength of mine pillars is depen-
dent on three elements: (1) the size or volume effect (strength
reduction from a small laboratory specimen of rock to full-
size mine pillars); (2) the effect of pillar geometry (shape
effect); and (3) the properties of the pillar material. For non-
coal pillars empirical formulae have largely been derived from
some form of the following power formula:8

w

Sp = om XE 8)
where 6, is pillar strength (ultimate), 6, is material strength,
his pillar height and a and 6 are constants derived from labo-
ratory or field experiments. This formula takes account of
both material strength and pillar shape to calculate pillar
strength.

Material strength

In these equations the material strength, 6,,, of a nominal size
of pillar is generally approximated by reducing the uniaxial
compressive strength, 6, of the material from laboratory test-
ing of small cylindrical or cubic specimens. Laboratory test
samples typically overestimate rock material strength values
because larger flaws or fractures are exhibited as the specimen
size increases. At some point the specimen size becomes suffi-
ciently large that further reductions in material strength are
insignificant. The point at which this occurs is often referred
to as ‘rock mass strength’. Bieniawski? suggested that cubic
coal specimens of side 0.9-1.5 m are of a critical size and are
representative of rock mass characteristics. Hedley and
Grant? used an equivalent material strength value representa-
tive of a 0.3-m cube of quartzite. Others have used reduction
factors that range from 40 to 80% to determine material
strength from uniaxial compressive strength values.

Pillar shape
Several pillar strength equations have been expressed as a
power function of the pillar’s height and width. Equation 4
was derived by Salamon and Munro!® after analysis of 125
case studies from South African coal mines:

=1320x

ots >
pees (b/in”) o)
In this equation a material strength, Om, equivalent to
7.2 MPa, was used because coal has a low materia! strength
by comparison with most industrial minerals and metal-mine
rocks. Hedley and Grant? extended this power function to
describe the strength of quartzite pillars in deep uranium

mines near Elliot Lake, Canada:
wo nn?
Op = 26000 ors (b/in?) (6)

‘This equation is similar to Salamon and Munro’s apart from
the much higher material strength value for the stiff uranium
host rock. In this case the material strength of the uranium
pillars is close to 20 times greater than that of South African
coal.

An alternative application of a pillar strength formula was
suggested by Hardy and Agapito.!! From a study of western
Colorado oil-shale pillars in which discontinuities are closely
spaced the appropriate pillar strength formula was inferred to

be of the form

0, 0.118
ox(2) x
Us

where 6, is uniaxial compressive strength of a sample and v is
volume of the pillar/sample. This method involves deter-
mination of the uniaxial compressive strength of a specimen
and the subscripts p and s refer to the pillar and specimen,
respectively.

Power functions produce a very distinctive relationship
between strength and the width-to-height ratio (see Fig. 5).
At low width-to-height ratios (<1.0) pillar strength rises
rapidly. At higher width-to-height ratios increases in strength
occur at diminishing rates. In other words, at some point the
pillar is believed to display some plastic behaviour. Barron
referred to this as pseudo-ductile behaviour.!2 The occur-
rence of pseudo-ductility in coal pillars has been debated for
years. It seems unlikely that stiff, brittle materials, such as
stone or other hard rocks, would display the same type of
plastic behaviour. In fact, some authors have argued that at
width-to-height ratios greater than 4 or 5 strain-hardening
behaviour can occur!3!4 because stress distributions and
confinement conditions change.

Stacey and Page! took this behaviour into account by
generating exponential rises in pillar strength at higher width-
to-height ratios:

0.833,

©

reir

wae ow,
ohxo oy (MPa) oO)

for wh <4.5 and

( yr

Wen

o> ah x aa * 0.13x|[S* 2) —1} 4a} (MPa)
®

for w/h >4.5

where k = Gm x DRMS, Design Rock Mass Strength!4
(DRMS) being the ¢, adjustment factor; and V = weg x hy
t0egq being equal to 4 x.4,/R where Ay is plan area of the pillar
and R is its perimeter. Here the pillar strength follows a
power function for a relatively low width-to-height ratio
(<4.5) and thereafter begins an exponential rise (see Fig. 5).
‘The pillar strength formula for wh >4.5 was taken almost
directly from the Salamon-Wagner squat pillar strength for-
mula published a year earlier. Stacey and Page’s formula is
used from here on because it was developed for hard rocks.

‘The application of these formulae to underground stone
is problematic. It seems unlikely that increasing the pillar
width-to-height ratio would result in a gradual decrease in the
rise in pillar strength. In fact, in practice just the opposite
appears to occur. Pillar stability is jeopardized most at low
width-to-height ratios. As typical stone pillars reach a width-
to-height ratio >1.5 they begin to exhibit an almost indes-
tructible character in shallow mines. Nevertheless, the Stacey
and Page! formula appears to accommodate both the tradi-
tional strength flattening at moderate width-to-height ratios
(ca 4-5) proposed by Salamon and Munro!3 and the expo-
nential rise in pillar strength at high width-to-height ratios.
Unfortunately, this strength adjustment occurs at width-to-
height ratios that are well outside the ranges of the stone
mines surveyed.


Table 2 Characteristics of development pillars that failed

Case Observed Pillar _—Pillar = Ratiow/h Extraction Reason for failure
failed pillars width,m height, m ratio

1 1 6.1 61 1.0 0.94 Reduced pillar size

2 1 6.1 49 1.25 0.92 ‘Smallest pillar in
non-regular mining area

3 1 5.5 6.1 0.9 0.86 High overburden stress
and reduced pillar size

4 4 36.1 73 0.42-0.83 0.9-0.83 High overburden stress

pillar had a width-to-height ratio of 1.25, whereas adjacent
pillars were in excess of 2.0. Here again it was difficult to
determine what level of stresses had caused failure because
the overburden was very low.

In case 3 a pillar with a width-to-height ratio of 0.9 was
inadvertently reduced from 9.1 to 5.5 m under a high over-
burden condition of approximately 275 m. Average vertical
stresses on this pillar could have exceeded 28 MPa. The
failed pillars had shear surfaces that began and terminated at
the pillar-roof and pillar-floor intersections and propagated
inward in a convex shape (Fig. 1).

In case 4 the overburden ranged from 230 to 260 m and
produced an average vertical stress that was generally less
than 14 MPa on pillars with openings that ranged between 15
and 18 m in width and with width-to-height ratios that aver-
aged 2.1. In several areas within this large mine pillars of
reduced width with width-to-height ratios ranging from 0.83
to 0.42 were subjected to average vertical stresses that could
have reached 35 MPa. At least four of these pillars exhibited a
very distinctive concave failure surface that resembled an
onion skin. As the failure process continued the pillar size was
reduced, thereby increasing the extraction ratio and resulting
in higher stress and more pillar deterioration.

Pillar design guidelines

As underground stone production expands mining depths
(overburden) are expected to increase. At present, six mines
in the Valley and Ridge Province of Pennsylvania, Virginia
and Tennessee and two mines in Kentucky are worked at
depths between 250 and 600 m. Many more mines will soon
encounter their first 100-150 m overburdens. As the depth of
mining is increased the potential for excessive stress levels
that affect pillar stability adversely will also increase.

In the absence of well-established design information for
underground stone mines pillar design guidelines related to
excessive stress levels are proposed. These guidelines make
use of the previous numerical simulations as a means of
examining how pillars of various shapes will be affected under
different overburdens. Fig. 7 shows changes in average verti-
cal stress conditions at different overburdens and different
width-to-height ratios based on the tributary area theory. The
solid black lines represent the strength of a modelled pillar,
free of discontinuities, as its shape is changed from a slender
pillar (w/h = 0.4) to an intermediate pillar (w/h = 1.4). This
modelled pillar has a stiffness of 41.4 GPa and a failure enve-
lope defined by a friction angle, $, of 40° and a cohesion of
6.9 MPa. These values represent typical material strength
characteristics of the Loyalhanna Limestone of Pennsylvania
and West Virginia, which is a relatively high-silica limestone
(10-40%) with extensive cross-bed structures.

In this example the modelled pillar with a width-to-height
ratio of 1.4 could accommodate an average vertical stress of
approximately 80 MPa. Clearly, a pillar of this strength, free
of discontinuities, could withstand all of the extraction ratio
and overburden conditions set forth in Fig. 4. Conversely, a

slender pillar, with a width-to-height ratio of 0.6 and 250 m
of overburden, might fail.

‘The FLAC model strength curve (Fig. 7) has a shape very
different from that of curves determined by the empirical
design techniques illustrated in Fig. 5. At low width-to-height
ratios pillars are low in strength. As width-to-height ratios
increase to 1.0 and beyond the pillar strength is increased
considerably. At a width-to-height ratio of greater than 1.5

80-4

60-4

Overburden

Avg. Pillar Vertical Stress, MPa

T T
0.6 0.8 1.0
Width—to—Height Ratio

Fig. 7 Changes in stone pillar strength at width-to-height ratios
ranging from 0.4 to 1.4

pillars that are free of geological discontinuities are unlikely to
fail. The shape of the pillar strength curve shown in Fig. 7 is
defined by the stiffness of the material and shape of the failure
envelope, which is defined by the friction angle and the mate-
rial cohesion used in the model.

Effect of discontinuities on stone pillar
stability

‘The stability of a stone pillar can be influenced greatly by
overburden stresses and the occurrence of geological discon
tinuities. Observations of pillar conditions have shown that
the presence of geological discontinuities is more likely to
represent a threat to workers’ safety than excessive stress
levels. When the height of a room is increased the area of the
rib is increased, which exposes more geological discontinu-
ities and creates more potential for mining-induced damage
to intersect the rib. Mining-induced damage can result from
drilling, blasting or scaling operations and is an extremely
important factor for the design of safe, stable pillars, although
it is not considered in detail here. Blast damage, for example,
can extend as much as 30 diameters from ANFO-filled blast-
holes (i.e. 1-2 m into the pillar), thus taking 2-4 m off the
dimensions of a square pillar.


Summary and conclusions

‘The aim of the present report is to enhance mine-worker
safety by increasing awareness of the potential for pillar fail-
ure—in particular, in operations that bench. As underground
stone mining expands and the depth of overburden is
increased consideration of the appropriate size and shape of
pillars should be an integral part of overall mine design. Data
gathered from mine visits, mine maps, discussions with oper-
ators and numerical simulations have been applied in an
investigation of stone pillar design issues and general guide-
lines have been discussed.

‘The important pillar design issues and guidelines can be
summarized as follows.

(1) Most stone pillars have relatively low width-to-height
ratios, ranging from 0.54 to 3.13, and high extraction ratios,
ranging from 0.56 to 0.91. This results in many pillars having
slender shapes with relatively large adjacent mine openings.
(2) Excessive vertical stress levels are generally not a serious
problem in stone mines because the pillar material is often
very strong and the overburdens are typically very low (the
average overburden is 80 m). A few cases are known, how-
ever, in which pillars have failed due to excessive local stress
levels. These failures were associated with local, uninten-
tional pillar size reduction, overburdens greater than 200 m,
width-to-height ratios less than 1.25 or extraction ratios
greater than 0.83. As the depth of mining increases the poten-
tial for excessive stress levels that affect pillar stability
adversely will also increase substantially.

(3) The strength of slender pillars is best understood by
examining models that allow for shape variations and pro-
gressive failure through elastic-plastic or strain-softening
behaviour. Models that meet these criteria have demon-
strated that stone pillar strength should not follow a straight
linear relationship with pillar shape. Empirical strength for-
mulae for metal and non-metal mines yield power curves that
produce higher pillar strengths at low width-to-height ratios
(<1.0) and lower pillar strengths at moderate to high width-
to-height ratios (>1.5).

(4) Bench mining produces slender pillars. Where geological
discontinuities are present the potential for pillar failures
increases. The persistence, dip, frequency and material pro-
perties of these discontinuities control pillar strength.

(5) A strong correlation was found between the material
properties and dip of discontinuities and the modelled pillar
strength. As discontinuity dips increased from 0 to 45° + 4/2
pillar strength gradually decreased. When the dips were equal
to 45° + 4/2 pillars exhibited a very unstable behaviour with
the loss of considerable amounts of their original strength. As
vertical orientations were approached columns defined by
discontinuities could have controlled pillar behaviour.

The pillar design guidelines developed through the obser-
vational and numerical simulations discussed above require
further field confirmation. The information has been pre-
sented so that mine planners, operators and workers can
recognize the potential hazards that exist when designing
stone pillars. This approach can help to form part of a com-
prehensive, proactive, ground-control plan to improve safety
in underground stone mines.

References

1. Anon. Highway-building surge. Wall Street J., June 2, 1998,
A1(W)-Al1).

2. Parker J. Everybody goes underground eventually. Aggregate
Manager, June 1996, 30-5.

3. Tannacchione A. T., Mucho T. P. and Prosser L. J. Ground con-
trol problems in the underground limestone industry. In Proc.
Environment, safety and health forum (National Stone Assoc.),
Nashville, TN, Oct. 22-24, 1995.

4. Tannacchione A. T. and Prosser L. J. Roof and rib hazard assess- ©
ment for underground stone mines. Presented at SME Annual
meeting, Denver, CO, Feb. 24-27, 1997. SME Preprint 97-113, 5 p.
5. Parker J. How to design better mine openings: practical rock
mechanics for miners. Engng Min. J., 174, December 1973, 76-80.

6. Brady B. H. G. and Brown E. T. Rock mechanics for underground
mining (London: George Allen and Unwin, 1985), 320-5.

7. Bieniawski Z. T. Rock mechanics design in mining and tunneling
(Rotterdam: Balkema, 1984), 193~<
8. Agapito J. F. T. Pillar stability in large underground openings:
applications from a case study in competent, jointed rock. Colorado
School of Mines Q., 8, no. 3, 1986, 52 p.

9. Hedley D. G. F. and Grant F. Stope-and-pillar design for the
Elliot Lake uranium mines. CIM Trans., 75, 1972, 121-8.

10, Salamon M. D. G. and Munro A. H. A study of the strength of
coal pillars. ¥. S. Afr. Inst. Min. Metall., 68, 1967, 55-67.

11. Hardy M. P. and Agapito J. F. T. Pillar design in underground
oil shale mines. In Fairhurst C. and Crouch S. L. eds Design methods
in rock mechanics, Proc. 16th Symposium on rock mechanics Minneapolis,
MN, 1975, 257-66.

12," Barron K. An analytical approach to the design of coal pillars.
CIM Bull., 77, no. 868, 1984, 37-44.

13. Salamon M. D. G. and Wagner H. Practical experience in the
design of coal pillars. In Proc. 21st Int. conf. of safety in mines research
institutes, Sydney, Australia, 1985, 3-10.

14, Stacey T. R. and Page C. H. Practical handbook for underground
rock mechanics (Trans Tech Publications, 1986), 53-63. Series on rock
and soil mechanics 12

15, Itasca. FLAC: Fast Lagrangian Analysis of Continua user’s guide
(Minneapolis: Itasca Consulting Group, Inc., 1998).

16. Farmer I. W. Engineering behaviour of rocks (London: Chapman
and Hall, 1983), 151-8.

Author

Anthony T. Iannacchione, who holds a Ph.D. in civil engineering
from the University of Pittsburgh and is registered as a professional
engineer and geologist in Pennsylvania, U.S.A., is Deputy Director of
the Pittsburgh Research Laboratory of the National Institute for
Occupational Safety and Health (NIOSH).

Address: National Institute for Occupational Safety and Health,
Pittsburgh Research Laboratory, P.O. Box 18070, Pittsburgh, PA
15236-0070, U.S.A.


Analysis of pillar design practices and techniques for U.S.

limestone mines

A.T. lannacchione

Synopsis

‘Underground stone mining is an emerging sector of the
U.S. mining industry. As this expansion takes mines
under deeper cover, and as more efficient mining
methods are utilized, effective stone pillar design
methods will become even more important. Current
design practices are examined and a discussion of safe
mine layouts is presented as a first approach towards
weighing the demands for increased production against
increased risk. Risks to underground stone-mine
workers include rib instabilities, pillar failures and roof
falls.

Seventy-two stone-mine pillar designs were exam-
ined. Pillars with width to height ratios of less than 1.5
appear more likely to fail when subjected to excessive
stress levels. When width to height ratios fall below 1.0
defects in the pillars, such as through-running discon-
tinuities, can have a significant influence on stability.
Discontinuity persistence, dip, material properties and
orientation are also important determining factors in
pillar strength.

During the past three years the number of active under-
ground stone mines in the U.S.A. has ranged between 90 and
100, This number is expected to increase as the crushed
stone industry responds to growing demands for its pro-
ducts.! As more of the industry moves to benefit from the
advantages of underground mining production from under-
ground stone mines is expected to increase above its current
level of approximately 66 000 000 vyear. Parker? identified
four advantages of underground mining operations: (1) sur-
face developments, zoning laws and environmental concerns
are often less of an issue; (2) stripping and restoration
requirements are eliminated; (3) additional reserves are often
available beneath the quarry floor, under pit slopes or under
an adjoining property; and (4) space is created for secondary
use. Underground mines enjoy the added benefits of work in
a constant underground climate, rather than in the variable
surface climate, minimization of community concerns by
placement of the crushing, sizing and stowing operations
underground and reduction of surface vibration concerns
through smaller blasts. The drawbacks of underground min-
ing include added health and safety hazards for the stone
miners, whose health can suffer from increased exposure to
falls of ground, airborne contaminants and fog in large under-
ground openings. Injuries from falls of ground in stone mines
have occasionally exceeded the incidence rates for other min-
eral resources mined underground.

Existing underground stone operations, by comparison

Manuscript first received by the Institution of Mining and
Metallurgy on 12 June, 1999; revised manuscript received on 3
November, 1999. Paper published in Trans. Insm Min, Merall,
(Sect, A: Min. industry), 108, September-December 1999, © The
Institution of Mining and Metallurgy 1999.

with stone operations a decade ago, mine more stone at a
faster rate and with larger equipment. Because of high
demand mines face increased pressure to yield more stone
per production blast. A majority of the miners use the V-cut
blasting pattern, which limits the depth or pull for each shot
to about 4 m. Therefore, to produce more stone, either the
mines must work more faces or existing faces must be
enlarged.

‘The enlargement of underground openings poses problems
in the maintenance of strata stability. First, the widths of the
mine entries partially control the amount of sag or deflection
that any given roof beam can withstand before failure. This
deflection can take place quickly after an opening is excavated
or much later as weathering processes form additional,
thinner beams. Because increased deflection increases the
potential for roof beam failure, there is a limit to how wide a
room can safely be made. These limits depend on local geo-
logical and stress conditions and, to some extent, the
cost-effectiveness of roof-bolting.

Given these room width limitations, underground stone
mines have placed more attention on expansion of produc-
tion through benching where mining thicknesses permit. The
heights of rooms partially control the strength characteristics
of adjacent pillars: as the room height increases for a given
pillar width the pillar width-to-height ratio (w/h) decreases. In
general, stone pillars are very strong, but when the width-to-
height ratio diminishes the potential for pillar rib instabilities
and pillar failures increases (see Fig. 1).

Fig. 1 Concave-shaped failing pillar. Note crushed ribs and slender
appearance (wl <1) of pillar compared with background stable pil-
far (caf >1)

In the underground environment the desire to utilize wider
rooms, higher benches and multi-level mining results in the
potential for unstable ground conditions. Although the
number of failed pillars is currently very low, the potential
for additional failures will grow if more slender pillars are
developed, especially under deeper cover, with wider mining
sections and in multi-level operations. It should also be noted
that the passage of time acts to decrease the strength of many
existing pillars. An examination of current design practices


Bench mining case studies
The best way to analyse the influence of geological disconti-
nuities on pillar stability is to evaluate pillar performance in
benching operations, where pillar shapes are generally slen-
der. A comparison of pillar shape, room width and pillar
height of 35 square bench pillar designs is shown in Fig. 8.

25 eos m a
&

i

20 8
€ & bed
Bas
z
3
sey 8 rss

8 x
5 Legens
EB vesign(s) with toiled pilor(s)

75 10 12.5 1s 175 20
Opening Width, m

Fig. 8 Comparison of pillar shape, opening width and pillar height
of 35 square bench pillar designs. Changes in square size are propor-
tional to changes in pillar sizes

‘There appears to be no clear correlation between pillar height
or room. width and pillar failure. Indeed, three of the four
designs with some failed pillars had only moderate pillar
widths and heights (Fig. 8, points B, C and D). These opera-
tions were all mining in a formation that is known to have a
higher than normal occurrence of large, high-angle geological
discontinuities. The fourth design with failed pillars (Fig. 8,
point A) was used in a formation that is not known to have
a high occurrence of geological discontinuities; failure here
was probably associated with the slenderness of the pillar
(wih = 0.5).

Several characteristics determine the significance of a
geological discontinuity: (1) persistence—the length of a dis-
continuity must be on the same scale as the pillar itself if its
strength is to be seriously impaired; (2) dip—the dip of a
discontinuity can affect pillar strength dramatically (Fig. 9);
(3) frequency—the spacing between discontinuities is very

Fig. 9 Left pillar has multiple sets of discontinuities that dip at
50-70%; right pillar has two prominent discontinuities that dip at
approximately 60°

important in determination of the potential for failure in a
large mining area; (4) material properties—the properties of a
discontinuity can be used to assess the magnitude of strength
reduction; and (5) orientation—the orientation of a disconti-
nuity is important when the pillars are rectangular in that
strength will be affected most if the discontinuity is aligned
with the long axis of the pillar.

Characteristics of discontinuities
Several of the factors outlined above can be considered by use
of the analytical procedure discussed by Farmer:!6

oy = 204203 tardy 6)
1° (= cot Pitan 6)sin 28
where Gj is vertical strength, 63 is confinement, C4 is cohe-
sion along the discontinuity, 94 is friction angle along the
discontinuity and B is dip of the discontinuity measured from
the vertical axis.

100

afnma

Frocture A, @ =20
Coh.a3.5 MPo

70

60

50

40

Avg, Squere Pillar Stress, MPo

3o 49 680 60 70 «890
Angle of Through=Going Fractures

Fig. 10 Effect of angular geological discontinuities on vertical
strength by use of analytical technique

Fig. 10 shows how sample strength varies with discontinu-
ity dip angles for different discontinuity material properties.
‘This analysis not only demonstrates the relative magnitude of
strength reduction based on discontinuity dip angle but it
also shows how friction angle and cohesion along the discon-
tinuity individually affect unit strength. However, the value of
this technique in the analysis of stone pillar behaviour with
discontinuities is limited because it treats the material as one
uniform elastic mass.

An alternative approach is to introduce simulated discon-
tinuities into the previously discussed finite-difference
elastic-plastic pillar model and rotate the interface through a
series of angles, In this way variations in material properties,
discontinuity dips and pillar shapes can be evaluated. This
was accomplished by use of the ubiquitous-joint model in the
FLAC 3D program. The ubiquitous-joint_ model is an
anisotropic plasticity model that includes weak planes of spe-
cific orientation embedded in a Mohr-Coulomb solid. In this
model yielding may occur either in the intact rock or along a
joint (discontinuity) or both, depending on the stress state,
the orientation of the joint plane and the material properties
of the intact rock and joint plane.


was undertaken with these trends in mind and the findings
are presented here together with a discussion of the principles
for safe mine layouts.

Current stone pillar design practices

The National Institute for Occupational Safety and Health
(NIOSH) of the U.S.A. surveyed 70 underground stone
mines between 1996 and 1998 to collect information on pillar
design practices. With one exception every mine used the
room-and-pillar mining method. There were, however, some
variations in the room-and-pillar method between the mines.

In relatively flat-lying beds the pillars are usually arranged
in regular, recurring patterns. Of the 70 mines surveyed, 93%
employed regular pillar patterns. Occasionally, random pillar
patterns have been used, but this practice has decreased in
response to improvements in surveying and mine planning.
Currently, only two of the surveyed mines retain the random
method.

‘The majority of mines use square pillars, i.e. whose width
is equal to the length. Nine mines use rectangular pillars

It should be noted that the application of averages from a
data-set such as this can produce unsatisfactory results on
account of variations in rock mass conditions. For example, a
wide range of discontinuity spacing orientation and persis-
tence was observed between field sites; in practice, very small
pillars can be stable when discontinuity occurrence is low.
Unfortunately, detailed information on the rock mass charac-
teristics was not collected in the present study.

If the stone deposit is thick enough, benching of the floor
can occur. Benching can alter slightly the widths of the
entries or the pillars. Bench faces are advanced by the drilling
of vertical floor holes from development entries and blasting
the rock back into the benched headings. Bench heights aver-
age 7.6 m. A few of the deeper benches are mined in multiple
lifts. More importantly, benching influences the height of the
rooms and pillars, which has a direct effect on the pillar
width-to-height ratio (see Table 1). Thirty-five of the mines
surveyed bench with the room-and-pillar méthod.

‘The distribution of width-to-height ratios for all 70 mines
surveyed in this study is shown in Fig. 2. Two distinct distri-
butions are observed, reflecting the functional characteristics

Table 1 Mine layout characteristics for underground U.S. stone mines
Characteristic Mean Standard Median Minimum Maximum
deviation
Development Pillar height, m 7 17 7 3.7 12.2
Opening width, m 13.1 2.6 12.8 61 18.3
Pillar width, m 12.2 41 12.2 4.6 27.4
‘Extraction ratio 0.76 0.07 0.75, 0.56 0.91
Pillar w/h 1.73 0.48 1.72 0.54 3.13
Overburden, m 80 98 46 7 610
Bench Pillar height, m_ 14.6 3.8 14.6 6.7 24.4
Opening width, m 13.7 21 13.7 o1 18.3
Pillar width, m 13.1 4. 13.7 6.1 27.4
Pillar wh 0.92 0.35 0.90 0.4 1.92
(hereafter referred to as rib pillars) whose length is greater wh <1.0 wih = 1.0 to 2.0 w/n > 2.0
than their width. Rib pillars have been employed by two
prominent consultants in the field, Jim Scott and Jack
Parker,> for special situations.

‘The room-and-pillar method takes on some unique char- . ' >
acteristics when used in mines with steeply dipping beds with slender “s___intermediote. | “Squat
multi-levels. Generally, one to three entries are driven along y {
the strike of the strata, which may dip from 45° to 70°. 15
Crosscuts are developed horizontally, perpendicular to the (A develop—
entries, Raises or windows between the outer, updip cross- (4 ment
cuts and the inner, downdip crosscuts provide for ventilation Ls
passages between mining levels. Only two of the surveyed a iN
mines use this method. 10 RY 18S Benched

The stoping method, which employs raises, crown pillars, REST yess
etc., is used by only one mine with steeply dipping beds. @ REY

Because 93% of the mines surveyed use the regular room-  § RSESY
and-pillar technique in a flat-lying seam, the present study = J RSES
focuses on the analysis of this design method. e RBS TSS

In the room-and-pillar method entries and crosscuts are 5 RIES ra
generally driven perpendicular to each other. When these SES
headings are developed horizontally into unmined strata they rei hs. Sg
are called room entries. These rooms outline development SN > $s Lc
pillars. Faces are advanced by the drilling of horizontal holes SNS SO yy
and blasting of the rock back into the development headings. ° bak xg

Seventy-two development mining scenarios (two of the 70
mines surveyed used multiple development designs) with 63
square pillar designs and nine rib pillar designs were exam-
ined. The average size of the development pillars was 12.2 m
wide x 7 m high (see Table 1). The width of adjacent rooms
averaged 13.1 m.

2
Width—to—Height Ratio (w/h)

Fig. 2. Width-to-height ratios of pillars used in development and
benching sections


ment pillars was 1.73 with a standard deviation of 0.48,
whereas the average ratio for benched pillars was 0.92 with a
standard deviation of 0.35. As shown in Fig. 2, the distribu-

tion of the 72 development pillar designs is relatively normal,
whereas that of the 35 benched pillars is slightly skewed to
the left.

Pillar performance issues

The extraction ratio is another geometric and economic fac-
tor that affects the relationship between the area of a pillar
and the area of the adjacent opening along the horizontal
plane. The extraction ratio for perpendicular intersections is
determined by the equation:

pe lotex(ter-axt

(o+r)x(t¥) °

where ¢ is extraction ratio, w is pillar width, / is pillar length
and ris room width.

1.05
n=63
0.9 4 8
°o 8.

2 o@®
@ 084 og
c Qo
§ O@GHEMDO OO
8 a7, Bo
x
uJ

0.6 4

0 O
0.5 1

T T T
0.0 1.0 2.0 3.0° 4.0
Width—to—Height Ratio

Fig. 3. Comparison between square pillar width-to-height ratios
and extraction ratios of development mining

Fig. 3 demonstrates the relationship between the extrac-
tion ratio for square development rooms and pillars and the
width-to-height ratios for the same pillars. In general, the
extraction ratio is decreased as the width-to-height ratio is
increased. This is expected because pillar width is a factor
considered in both ratios. The safety concern is that as the
extraction ratio is increased the pillars become more slender
and must support higher levels of stress.

Depending on the number of years over which it has been
mined, an underground stone mine may have a few dozen to
several thousand pillars. The vast majority of these pillars are
adequately sized and currently stable. Pillar design is, how-
ever, seldom addressed explicitly in planning. Pillar stability
should be more closely examined under (1) excessive stress
levels, (2) adverse geological conditions and (3) increasing
time.

‘Stress levels

Generally, stone pillars are expected to be less stable if the
overburden is substantial because of the higher stress. Pillars
might also be less stable as the width-to-height ratio is
decreased, as in benching operations. Stress levels in pillars
can be approximated by use of the tributary area theory:®

(r+w)x(r+J) (2)

wxl

where G, is average post-mining vertical stress and 6, is pre-
mining vertical stress.

¢ 50 4 /
g | /
o 40 4
ee /
30 4 / J
a 4 4 ,
2 af
s 20 “JOverburden.-~ LZ
oO = 250 me L2 7
gs 10 7150 a
< 4
50 m
0 T T T
0.5 06 #O7 O8 09

Extraction Ratio

Fig. 4 Relationship between average pillar stress levels, extraction
ratios and overburden for 13.7 m wide opening with square pillars

Pillar stress levels are affected, in part, by the overburden
and the relationship between the area supported by the pillar
and the area of the pillar. This relationship can be illustrated
by comparing the post-mining vertical stress levels as the
overburden and the extraction ratio increase. Fig. 4 shows the
relationship between average pillar stress, overburden and
extraction ratio for a 13.7 m wide opening with square pillars.
As the overburden and extraction ratios increase the stress
levels rise exponentially. Incremental changes in overburden
result in a parallel change in the average pillar stress levels at
specific extraction ratios. Likewise, increased extraction ratios
produce an exponential rise in the average pillar stress levels
at specific overburdens. The average overburden for most
underground stone mines is 80 m, so excessive stress levels
would not be expected to be the cause of pillar failure. The
relatively shallow depth of most underground stone mines has
historically been the reason why pillar shape and size are
often overlooked as a safety issue during mine design and
development.

Pillar strength
‘The most generally accepted techniques for estimating pillar
strength, defined as the ultimate load per unit area of a pillar,
use empirical derivations based on survey data from actual