The pillar design guidelines developed through the
observational and numerical simulations discussed
above will require further field confirmation. This
information has been presented so that mine planners,
operators, and workers can recognize the potential
hazards that exist when designing stone pillars. This
approach can help to form a part of a comprehensive
pro-active mine safety ground control plan for
underground stone mines.

REFERENCES

Anon, “Highway-Building Surge”, Wall Street Journal,
June 2, 1998, PP, pA1(W}-pA1(E).

Anon, “FLAC: Fast Lagrangian Analysis of Continua
User's Guide", Itasca Consulting Group, Inc.,
Minneapolis, MN, 1998.

Barron, K., “An Analytical Approach to the Design of
Coal Pillars, CIM Bull., Vol. 77, No. 868, Aug. 1984, pp.
37-44,

Bieniawski, Z.T., it
Tunneling, Balkema, Rotterdam, 1984, pp. 193-209.

Brady, B.H.G. and E.T. Brown, “Rock Mechanics for
Underground Mining”, George Allen and Unwin, London,
1985, pp. 320-325,

Farmer, |.W., ineerin
Chapman and Hill, tondon, 1983, pp. 151-158.

Hardy, M.P. and J.F.T. Agapito, “Pillar Design in
Underground Oil Shale Mines”, In Design Methods in
Rock Mechanics, Proc. 16" Symp. on Rock Mechanics,
C Fairhurst and S.L. Crouch (ed), Minneapolis, MN,
1975, pp. 257-266.

Hedley, D.G.F. and F. Grant, “Stope-and-Pillar Design
for the Elliot Lake Uranium Mines”, CIM Transactions,
Vol. 75, 1972, pp. 121-128.

lannacchione, A.T., T. P. Mucho, and L. J. Prosser,
“Ground Control Problems in the Underground
Limestone Industry,” Proc. of the Environment, Safety,
and Health Forum (National Stone Assoc), Nashville,
TN, Oct. 22-24, 1995.

lannacchione, A. T. and L. J. Prosser, “Roof and Rib
Hazard Assessment for Underground Stone Mines,”
SME Preprint 97-113, SME Annual Meeting, Denver,
CO, Feb. 24-27, 1997, 5 pp.

Parker, J., “How to Design Better Mine Openings:
Practical Rock Mechanics for Miners,” Engineering and
Mining Journal, Part 5, December 1973, pp. 76-80.

Parker, J., “Everybody Goes Underground Eventually”,
Aggregate Manager, June 1996, pp. 30-35.

Salamon, M.D.G. and A.H. Munro, “A Study of the
Strength of Coal Pillars”, Journal of the South African
Institute of Mining and Metallurgy, Sept. 1967, pp. 55-67.

Salamon, M.D.G. and H. Wagner, “Practical Experience
in the Design of Coal Pillars”, Proc. of the 21 int. Conf.
of Safety in Mines Research Institutes, Sydney,
Australia, 1985, pp. 3-10.

Stacey, T.R. and C.H. Page, “Practical Handbook for
Underground Rock Mechanics”, Series on Rock and Soil
Mechanics, Vol. 12, Trans Tech Publications, 1986, pp.
53-63.


envelope, which is defined by the friction angle and the
material cohesion used in the model.

THE EFFECT OF DISCONTINUITIES ON STONE
PILLAR STABILITY

The stability of a stone pillar is highly influenced by
overburden stresses and the occurrence of geologic
discontinuities. Observations of pillar conditions have
shown that the presence of geologic discontinuities
represents a more likely potential safety concern for
mine workers than excessive stress levels. When a
room is heightened, the area of the rib increases, which
elevates the potential for exposure of geologic
discontinuities and mining induced damage intersecting
the rib. Characteristics of geologic discontinuities, such
as bedding planes, slips, faults, and joints, include
frequencies, persistence, straightness, strike, dip, and
material properties. Mining induced damage can result
from drilling, blasting, or scaling operations, and is an
extremely important factor in designing safe, stable
pillars, but is not considered in this report.

Bench Mining Case Studies

The best way to analyze the influence of geologic
discontinuities on pillar stability is to evaluate the pillar
performance in benching operations where pillar shapes
are generally slender. A comparison of pillar shape,
room width, and pillar height of 35 square bench pillar
designs is shown in Figure 8. There appears to be no
clear correlation between pillar height or room width and

Opening Width, ft
2 30 35 4S DSH DS,

*
af = .
oa, od »
° g
£ 2B
P| ° Be B
2°
:
Foy 8 a
a 20
: _
FB esigna) with tated piers) to
° °

Opening Width, m

Figure 8. - Comparison of pillar shape, opening width,
and pillar height of 35 square bench pillar designs.
Note that changes in square size are proportional to
changes in pillar sizes.

pillar failure. Indeed, three of the four designs with some
failed pillars had only moderate pillar widths and heights
(Figure 8, Points B, C, and D). These operations were
all mining in a formation which is known to have a higher
than normal occurrence of large, angular geologic
discontinuities. The fourth design with failed pillars
(Figure 8, Point A) was used in a formation not known to
have a high occurrence of geologic discontinuities. Here
pillar failure was probably associated with the
slendemess of the pillar (w/h=0.5).

There are several factors that make the character of
the geologic discontinuity significant:
Persistence - the length of the discontinuity must be
on the same scale as the pillar it is effecting if
strength is to be impacted,
Dip - the dip of the discontinuity can dramatically
affects pillar strength (Figure 9),
Frequency - the spacing between discontinuities is
very important in determining the potential for failure
in a large mining area,
Material Properties - the properties of the
discontinuity can be used to assess the magnitude of
strength reduction, and
Orientation - the orientation of the discontinuity is
important when the pillars are rectangular, in that,
strength will be most affected when the orientation of
the discontinuity is aligned with the long axis of the
pillar.

Figure 9 - The left pillar has a discontinuity dipping at
approximately 20° while the right pillar’s discontinuity
dips at approximately 60°.

Characteristics of Discontinuities

Several of these factors can be considered by
utilizing the analytical procedure discussed by Farmer
(1983):

go = —2Gat2o; tangy
' (1-cot Btang,)sin2p
where

©, = Vertical strength,

©, = Confinement,

C, = Cohesion along the discontinuity,

4 = Friction angle along the discontinuity, and

8 = Dip of discontinuity measured from the vertical

axis.




6000
g 3
$ 5000 &
g 4000 $
é a
3 b 3000 8
4 Width—to-Height Rotio = 0.8 5
3 2000 *
< 1000 *
°
00 ©0025 = 0.050.075 .01

Strain

Figure 12 - Stress versus strain for model pillars
(width-to-height ratio = 0.8) with discontinuity dips
ranging from 0 to 90°.

a discontinuity dips of 60°, the model pillar exhibited very
low strength. Finally, strain softening material behavior
occurred as discontinuity dips increased to 90°. The
conclusion of this effort is that both observation and
numerical data suggest that when discontinuities are
present at a particular angle and composition, they can
control the behavior and strength of pillars.

The impact of this analysis is detailed in Figure 13.
The strength of pillars with various shapes and different
discontinuity dips are very sensitive to changes in
extraction ratio and overburden. For example, a
discontinuity dipping at 60°, under approximately 50 m
(165 ft) of overburden, with a width-to-height ratio of 0.8,
and passing through the entire 15 m (50 ft) high pillar,
could fail if it's properties were equivalent to 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 (820 ft) of overburden is encountered.
Figure 13 is presented to illustrate the significant
impact that pillar shape, overburden, and discontinuities
can have on stone pillar strength and is not meant to be
a design guideline.

. 204 42000
g FLAC ubiquitous jpint model | 19999 a
$ 60 e000 £
a Overburden %
B | \os0 m g
= 40-4 (829 tt) 5009 3
5 - 2
’ 4000 5
E20 =
2000
50 m 4
2 eh
° oO

0.4 06 O8 1.0 1.2 4.4
Width—to-Height Ratio
Figure 13 - Relationship between pillar shape,
overburden, discontinuity dip and pillar strength.

SUMMARY AND CONCLUSIONS

The intent of this report is to create an awareness in
relation to mine worker safety of the potential for pillar
failure, particulary in operations that bench. As
underground stone mining expands and depth of
overburden increases, consideration of the appropriate
size and shape of pillars should be an integral part of the
overall mine design. Using data gathered from in mine
visits, mine maps, discussions with operators, and
numerical simulations, stone pillar design issues were
investigated and general guidelines were discussed.
The important pillar design issues and guidelines can be
summarized as follows:

+ Most stone pillar 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 shapes that are slender with
relatively large adjacent mine openings.

+ 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 (average overburden = 80 m (262
ft]). However, there are a few known cases where
pillars have failed due to excessive stress levels.
These cases were associated with local unintentional
pillar size reduction, overburdens greater than 200 m
(630 ft), width-to-height ratios less than 1.25, or
extraction ratios greater than 0.83. As depth of
mining increases, the potential for excessive stress
levels that adversely affect pillar stability will also
increase substantially.

+ The strength of slender pillars is best understood by
examining models which allow for shape variations
and progressive failure through elastic-plastic or
strain softening behavior. Models which met this
criteria were examined in the paper and
demonstrated that stone pillar strength should not
follow a linear relationship with pillar shape.
Empirical strength formulas for metal/nonmetal mines
produce power curves which 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).

+ Bench mining produces slender pillars. Where
geologic discontinuities are present, the potential for
pillar failures increases. The persistence, dip,
frequency, and material properties of these
discontinuities control pillar strength.

+ Astrong correlation was found between the material
properties and dip of discontinuity and the modeled
pillar strength. As discontinuity dips increased from
0 to 45+ 4/2, pillar strength gradually decreased.
When the dips were equal to 45 + 9,/2, pillars
exhibited a very unstable behavior, losing
considerable levels of their original strength. As
vertical orientations were approached, columns
defined by discontinuities can control pillar behavior.


g°
C
f°
ao ®
Plasticity Indicator by B
+ at yield in sheor &
© at yield in tension Ba
2 A
Fo
oT? ittan
root Foc Steps, x 1000
A B
pillor
floor moderate stress levels
c oD

near peak strength residual strength

Figure 6 - An elastic-plastic model, which produces
progressive failure patterns, can exhibit strain-
softening behavior within full scale pillars.

decrease in the rise in pillar strength. In fact, in practice
just the opposite appears to occur. Pillar stability is most
endangered at low width-to-height ratios. As typical
stone pillars reach a width-to-height ratio >1.5, they
begin to exhibit an almost indestructible character. The
Stacey and Page (1986) formula appears to
accommodate both the traditional strength flattening at
moderate width-to-height ratios (~4 to 5) as proposed by
Salamon and Munroe (1967) and the exponential 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 all
stone mines surveyed.

STONE PILLAR BEHAVIOR - Progressive Failure

The above techniques do not provide a totally
realistic picture of stone pillar behavior. Additionally, a
large database of pillar specific information of past
successes and failures hasn't been established to aid in
constructing a reliable pillar design technique for stone
mines. In the absence of this information, numerical
simulations can produce a potentially useful means to
test engineering methods. The simulation used for this
study was the 2 and 3-dimensional finite difference code
(ANON, 1998). The 2-dimensional calculations were
performed under plane-strain conditions, so the model
sample is equivalent to a long pillar. It is assumed that
individual elements in the model behave in an elastic-
perfectly plastic behavior, however, the overall pillar

behavior can include strain-softening and _ strain-
hardening. Model shapes mirrored those observed in
the field ranging from a very slender pillar with a width-
to-height ratio of 0.4 through intermediate pillars with a
width-to-height ratio of 1.4. With slender shapes, pillars
failed rapidly by yielding from the ribs inward to the pillar
core, indicating a relatively low strength structure. As
pillars become more squat, elevated horizontal
confinement dramatically increases pillar strength.
Model symmetry was constructed so as to simulate a
reoccurring pattern of rooms and pillars of equal
dimensions. The roof and floor material were modeled
to be elastic.

The model pillars had a moduli of 41.4 GPa
(6,000,000 psi), an angle of internal friction of 40°, and
a cohesion of 6.9 MPa (1,000 psi). 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 gradually
loading the pillars through several distinct strength
phases. During the early loading phase the modeled
pillar displays relatively elastic characteristics (Figure 6,
Points A to B), where the pillar deformation is
proportional to increases in average vertical stress levels
within the pillar.

During this phase dominated by elastic behavior,
minor yielding of the pillar edges begins to occur.
Continued progressive failure of the pillars outer
perimeter produces an hour-glass shaped elastic core.
It also has the effect of moving the peak vertical stress
away from the pillar edge and toward the pillar center
(Figure 6, Points B to C).

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

THE EFFECT OF EXCESSIVE STRESS ON STONE
PILLAR STABILITY

Pillar failure due to excessive stress levels was not
frequently observed during field visits to underground
stone mines. In fact, there were only seven
development pillars at four mines that 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 (30 to 20 ft) under less than 30 m (100
ft) of overburden. This pillar had an average vertical
stress of less than 7 MPa (1000 psi). Failure of the pillar
perimeter due to crushing left only a narrow core of




sized and currently stable. However, pillar design is
seldom explicitly addressed. Pillar stability should be
more closely examined under: 1) excessive stress levels,
2) adverse geologic conditions, and 3) increasing time.

Stress Levels

Generally, stone pillars are less stable if overburden
is substantial because of the higher stress. Pillars are
also less stable as the width-to-height ratio decreases
such as in benching operations. Stress levels within
pillars can be approximated by using the tributary area
theory (Brady and Brown, 1985):

r
3, =0, x! +w)x(r+l)
wx!

where: a,
%

verage post mining vertical stress
premining vertical stress

Pillar stress levels are affected by the overburden and
the relationship between the area supported by the pillar
and the area of the pillar. This relationship is illustrated
by comparing the post mining vertical stress levels as
the overburden and the extraction ratio increase. Figure
4 shows the relationship between average pillar stress,
overburden, and extraction ratio for a 13.7 m (45ft) wide
opening with square pillars. As overburden and
extraction ratios increase, the stress levels rise
exponentially. Incremental changes in overburden result
in a proportional change in the average pillar stress
levels at specific extraction ratios. Increasing extraction
ratios produce an exponential rise in the average pillar
stress levels at specific overburdens. At most
underground stone mines, overburden averages 80 m

8000
°
£50 4 =
ee | + 7000 3
é L ¢
$40 6000 g
a 4 + 5000 H
330 4 L 4000 2
e 4 a
2 i. 2
§ 20 “overbura 5000 5
B Wee Ny L L 2000 &
eee :
2 | + 1000 £
ea By
° : : ; 0

05 #06 07 O08 O09
Extroction Ratio
Figure 4 - Relationship between average pillar stress

levels, extraction ratio, and overburden for a 13.7 m
(45 ft) wide opening with square pillars.

(262 ft), thus excessive stress levels would not be
expected to result in pillar failure. The relatively shallow
depth of most underground stone mines is 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
determining pillar strength, defined as the ultimate load
per unit area of a pillar, use empirical derivations based
on survey data from actual mining conditions. The
power of the empirical method is that specific failure
mechanism need not be considered. The failings of the
method stems from an inability to extend these formulae
beyond the specific material properties, sizes, shapes,
and overburdens found in the survey data. Bieniawski
(1984) wrote that the strength of mine pillars is
dependent upon 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
formulas have largely been derived from some form of
the following power formula:

where Pillar strength (ultimate)

Material strength

pillar height

b = constants derived from laboratory or

id experiments:

9,
G,
h
a,
fi

This formulation considers both material strength and
pillar shape to calculate pillar strength.

Material Strength: In these equations, the material
strength (g,,) of a nominal size pillar is generally
approximated by reducing the uniaxial compressive
strength (0,) of the material from laboratory testing of
small cylindrical or cubed shaped specimens.
Laboratory test samples typically over-estimate rock
material strength values because larger flaws or
fractures are exhibited as specimen size increases. At
some point specimen size becomes large enough so
that further reductions in material strength become
insignificant. This is often referred to as rock mass
strength. Bieniawski (1984) suggested that cubic coal
specimens from 0.9 to 1.5 m (3 to 5 ft) are of a critical
size and are representative of rock mass characteristics.
Hedley and Grant (1972) used an equivalent material
strength value representative of a 0.3 m (1 ft) cube of
quartzite. Others have used reduction factors ranging
from 40 to 80 % to determine material strength from
uniaxial compressive strength values.






Pillar Design Issues for Underground Stone Mines

A. T. lannacchione, Deputy Director
National Institute for Occupational Safety and Health
Pittsburgh Research Laboratory
Pittsburgh, PA.

ABSTRACT

Underground stone mining represents an emerging
sector for the U.S. mining industry. As this expansion
takes mines under deeper cover and as more efficient
mining methods are utilized, adequate stone pillar
design methods will become more important. It is the
purpose of this paper to examine current design
practices arid to discuss issues for safe mine layouts so
that a rational first approach towards balancing the
demands for increased production can be weighed
against increased risk to worker safety from rib
instabilities and pillar failures. Seventy-two stone mine
pillar designs were examined. Pillars with width-to-
height ratios below 1.5 and subjected to excessive
stress levels appear more likely to fail. When width-to-
height ratios fall below 1.0, defects in the pillars, such as
through-going discontinuities, can have a significant
influence on stability. Discontinuity persistence, dip,
material properties, and orientation are important factors
controlling pillar strength. The influence of discontinuity
dip, a characteristic easily identified in the field, was
examined so that its presence could be accounted for in
developing generalized guidelines for pillar design.

INTRODUCTION

During the last three years the number of active
underground stone mines in the U.S. has ranged
between 90 and 100. This number is expected to
increase as the crushed stone industry responds to
growing demands for their products (Anon, 1998).
Additionally, production at underground stone mines is
expected to increase above its current level of
approximately 66 million metric tons (60 m.st) per year
as more of the industry moves towards the unique
advantages of underground mining. Parker (1996)
identified three advantages for underground operations:
1) -surface developments, zoning laws, and
environmental concerns are often less of an issue, 2)

stripping and restoration requirements are eliminated,
and 3) additional reserves are often available beneath
the quarry floor, under pit slopes, or under adjoining
property. There are also the added benefits of: 1)
working in a constant underground climate rather than
the variable surface climate, 2) minimizing community
concems by placing the crushing, sizing, and stowing
operations underground, and 3) reducing surface
vibration concems with smaller blast sizes. Drawbacks
of underground mining relate to the added health and
safety hazards for the stone miners associated with;
increased exposure to falls of ground, airborne
contaminants, and fog in large underground openings.
Also, injuries from falls of ground have occasionally
been above incident rates for other mineral resources
mined underground (lannacchione, et al., 1995).

It is clear that existing underground stone operations
mine more stone at a faster rate and with larger
equipment. Because of high demand there is increasing
pressure to yield more stone per production blast. A
large majority of the industry uses the V-cut blasting
pattern, that limits the magnitude of depth or pull for
each shot to about 4 m (13 ft). Therefore, to produce
more stone the miners must work more faces or existing
faces must be enlarged.

Enlarging underground openings poses problems for
maintaining strata stability. First, widths of the mine
entries partially contro! the amount of sag or deflection
any given roof beam can withstand before failure. This
deflection is, in general, very small and can take place
quickly after an opening is excavated or much later as
weathering processes aid in forming new, thinner
beams. Because increasing deflection increases the
potential for roof beam failure, there is some limit to
safely widening rooms and these limits depend on local
geologic and stress conditions.

Room width limitations have placed more attention
‘on expanding production through benching. Heights of


broken rock (photo on right, Figure 1). It was surmised
that additional stresses were applied to the pillar either
as a result of its unique position near the highwall or due
to some undetected geologic characteristic.

In Case 2, the initial mine development had occurred
with random room-and-pillar methods. One failed pillar
was observed that was narrower than the surrounding
pillars, This pillar had a width-to-height ratio of 1.25
while adjacent pillars were in excess of 2.0. Here again
it was difficult to determine what level of stresses caused
failure since the overburden was very low.

Table 2 - Characteristics of development pillars
that failed
case | ob | pitar | Pinar | wm | extrac. Remark.

served | width, | height, | ratio | tion ratio
failed | mit) | mf)

pitars
1 1 61 61 | 1.0 | 0.94 | Reduced pillar
(20)_| (oy size
2 1 61 49 | 1.25 | 0.92 | Smattest pitarin
oy | (16) ‘@ non-regular
mining area
3 4 55 | 61 | 09 | 0.86 | High overburden
(18) | (oy ‘stress and
reduced pillar
size
4 4 | 3061] 73 | 0.42 | 0.9t0 | High overburden
oto | (24) | to | 083 stress
20) 0.83

In Case 3, a pillar with a width-to-height ratio of 0.9
was inadvertently reduced from 9.1 to 6.1 m (30 to 20 ft)
under a high overburden condition of approximately 275
m (900 ft). Average vertical stresses on this pillar could
have exceeded 28 MPa (4000 psi). 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 (photo on left, Figure 1).

In Case 4, the overburden ranged from 230 to 260 m
(750 to 850 ft), producing an average vertical stress that
was generally less than 14 MPa (2000 psi) on pillars with
openings that ranged between 15 to 18 m (50 and 60 ft)
in width and width-to-height ratios that averaged 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 (5000 psi). 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.

As underground stone production expands, mining
depths (overburden) are expected to increase. Presently
six mines in the Valley and Ridge Province of
Pennsylvania, Virginia, and Tennessee and two mines in
Kentucky are mining at depths between 250 to 600 m
(800 to 2000 ft). Many more mines will soon be

encountering their first 100 to 150 m (330 to 500 ft)
overburdens. As depth of mining increases the potential
for excessive stress levels that adversely affect pillar
stability will also increase substantially.

20 17000
g “ z
= Pa 10000 &
8 60 g
& 8000 =
ca 5
3 3B
2 40 6000 2
Es =
7 4000 5
= 20 =
2000
z z
< 2
° °

04 06 O8 10 12 14
Width—to—Height Ratio

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

In the absence of specific design information for
underground stone mines, the following pillar design
guidelines related to excessive stress levels are
Proposed. These guidelines consider the previous
numerical simulations as a means of examining how
pillars of various shapes will be effected under different
overburdens. Figure 7 shows the changes in average
vertical stress conditions at different overburdens and
different width-to-height ratios using the tributary area
theory. The solid black line represents the strength of a
modeled pillar, free of discontinuities, as its shape
changes from a slender pillar (w/h=0.4) to an
intermediate pillar (w/h=1.4). This modeled pillar has a
stiffness of 41.4 GPa (6 million psi) and a failure
envelope defined by a friction angle () of 40° and a
cohesion of 6.9 MPa (1000 psi). These values represent
typical material strength characteristics of Loyalhanna
Limestone of Pennsylvania and West Virginia.

In this example, our model pillar with a width-to-
height ratio of 1.4 could potentially accommodate an
average vertical stress of approximately 80 MPa (12000
psi). Clearly a pillar of this strength, free of
discontinuities, could withstand all of the extraction ratio
and overburden conditions shown in Figure 4.
Conversely a slender pillar, with a width-to-height ratio of
0.6 and 250 m (820 ft) of overburden, might fail. Note
that the FLAC model strength curve has a shape very
different from those curves determined by the empirical
design techniques illustrated in Figure 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 increases considerably. At a width-to-height
ratio of greater than 1.5, pillars free of geologic
discontinuities are unlikely to fail. The shape of the pillar
strength curve shown in Figure 7 is defined by the
stiffness of the material and shape of the failure




Pillar Shape: Several pillar strength equations have
been expressed as a power function of the pillar's height
and width. Salamon and Munro (1967) derived the
following equation after analyzing 125 case studies from
South African coal mines:

0-46
op= 1320 * Trae (esi)

In this equation a material strength (c,,) equivalent to 9.1
Mpa (1320 psi) was used because coal has a relatively
low material strength compared to most industrial
minerals and metal mine rocks. Hedley and Grant
(1972) extended this power function to describe thé
strength of quartzite pillars in deep uranium mines near
Elliot Lake, Canada:

05
op = 26000 x p75-(psi

The equation is similar to Salamon and Monroe with the
exception of a higher material strength value for the stiff
uranium host rock, In this case the material strength of
uranium pillars is close to 20 times greater than for
South African coal. An alternative application of a pillar
strength formula was suggested by Hardy and Agapito
(1975). From a study of oil shale pillars in westem
Colorado, the appropriate pillar strength formula was
inferred to be of the form:

. ~O118 “> “, 0.833
op=o,x| i ea

8. p os

Where: 0, = Uniaxial compressive strength of
sample
v = Volume of pillar/sample

This method involves determining the uniaxial
compressive strength of a specimen where subscripts p
and s refer to pillar and specimen, respectively.

Power functions produce a very distinctive
relationship between strength and width-to-height ratio
(Figure 5). At low width-to-height ratios (< 1.0), pillar
strength rises rapidly. At higher width-to-height ratios
strength increases occur at diminishing rates. In other
words, at some point the pillar would begin to display
some plastic behavior. Barron referred to this as
pseudo-ductile behavior (Barron, 1984). The occurrence
of pseudo-ductility in coal pillars has been debated for
years. It seems unlikely that stiff, brittle materials like
stone or other hard rocks would display this same type
of plastic behavior. In fact, there has been a recognition
that at width-to-heigh ratios greater than 4 or 5, strain
hardening behavior can occur (Salamon and Wagner,
1985, Stacey and Page, 1986).

180
2 1604— stocey/Page
s —~— Hordy/Agapito
~ 140 ---= Hedley/Grant
<
= 120-4
5 1004
5 -
® so om
Bool onc
o aan
. 405 gr
P ol A
2 2
° T T T

°

2 4 6
Width—to—Height Ratio

Figure 5 - Comparison between pillar width-to-height
ratio and average pillar strength for several different
empirical equations based on a power function. Note:
material strength was normalized for each equation
for comparative purposes.

The approach suggested by Stacey and Page (1986)
takes this behavior into account by producing
exponential rises in pillar strength at higher width-to-

height ratios:
for wh < 4.5
w 05
Spe kx 7 (MPa)
no
for wih > 4.5
45
()
25 h
pak soar * 013 x] ]~E“| 1] +1 (MPa)
Where: k = 0, * DRMS (Design Rock Mass
Strength)
DRMS = 6, adjustment factor (Stacey and
Page, 1986)
Vewy xh
Wer = 4 xX AJR
A, = plan area of the pillar
R = perimeter

Here the pillar strength follows a power function for
relatively low width-to-height ratio (< 4.5) and then
begins to follow an exponential rise above width-to-
height ratio > 4.5 (Figure 5).

The application of these formula to underground
stone is problematic. It seems unlikely that increasing
the pillar width-to-height ratio would result in a gradual


square pillar designs and 9 rib pillar designs were
examined. Development pillar sizes averaged 12.2 m
(40 ft) wide by 7 m (23 ft) high (Table 1). Adjacent
rooms averaged 13.1 m (43 ft) in width.

If the stone deposit is thick enough, benching of the
floor often occurs. Bench faces are advanced by drilling
vertical floor holes from development entries and
blasting the rock back into the benched headings.
Bench depths average 7.6 m (25 ft). A few of the
deeper benches are mined in multiple lifts. Benching
does not alter either the widths of the entries or the
pillars. It does have an influence on the height of the
rooms and pillars, which directly impacts the pillar width-
to-height ratio (Table 1). Thirty-five mines bench with
the room-and-pillar method.

The distribution of width-to-height ratios for all of the
70 mines surveyed in this study is shown in Figure 2.
Two distinct distributions exist based upon the functional
characteristics of the pillar. The average pillar width-to-
height ratio for development pillars was 1.73 with a
standard deviation of 0.48, while the average width-to-
height ratio for benched pillars was 0.92 with a standard
deviation of 0.35. The distribution of the 72
development pillar designs is somewhat normal while
‘the distribution of the 35 benched pillars is somewhat
skewed to the left (Figure 2).

w/h < 1.0 w/h = 1.0 to 2.0 w/n > 2.0
senaer S.temecote {smut
15 1
[A develop—
yt
oT Ns
> SY
3 RRS
8 NS
2 ReES
go BS SS
g RR
“5 RESBS
NSS
RES
they]
f
SEA
H
BS PAY ix y
° MS :

0 1 2 3
Width-to-Height Ratio (w/h)

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

PILLAR PERFORMANCE ISSUES

The extraction ratio is another geometric
characteristic which analyzes 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
following relationship:

(w+r)x(l+r)-wxl
(w+r)x (+r)

where xtraction ratio
w= pillar width
1 = pillar length
T= opening width
1.09
n=63
0.9 | 8
°
2 ° oP
é 084 So
c Qo
§ O@EREEDO O_o
8 074 S. °
3
0.64
ea)
0.5 +.
0.0 10 #20 30 40

Width—to—Height Ratio

Figure 3 - Comparison between square pillar width-
to-height ratios and the extraction ratios for
development mining.

Figure 3 shows the relationship between the extraction
ratio for square development rooms-and-pillars and the
width-to-height ratios for these same pillars. In general,
the extraction ratio decreases as the width-to-height ratio
increases. This is expected because both ratios
consider the pillar width as a factor. The safety concern
is that as the extraction ratio increases the pillars receive
higher levels of stress, while these pillars in a sense are
becoming more slender. Obviously, slender pillars are
inherently less stable.

Depending on the years of mining, an underground
stone mine may have a few dozen to several thousand
pillars. The vast majority of these pillars are adequately








rooms partially contro! 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 extremely
strong, however, when the width-to-height ratio falls, the
potential for pillar rib instabilities and pillar failures
increases (Figure 1).

: 2 cre :
Figure 1 - Photographs of failing pillars. Photo on
left shows a crushed edge with a concaved shape
and photo on right shows a failed pillar in the
foreground [Note the crushed ribs and the slender
appearance, w/h < 1 while the pillar in the
background is stable with a w/h > 1].

In this environment the desire to utilize wider rooms,
higher benches, and multilevel mining may result in the
potential for more unstable ground conditions. While the
number of failed pillars is currently very low, the potential
for additional failures will grow if more slender pillars are
developed: 1) especially under deeper cover, 2) with
wider mining sections, and 3) in multilevel mining
scenarios. It should also be noted that time acts to
decrease the strength of many existing pillars. It is the
purpose of this paper to examine current design
practices and to discuss issues for safe mine layouts so
that a rational first approach towards balancing the
demands for increased production can be weighed
against increased risk to worker safety from rib
instabilities and pillar failures.

CURRENT STONE PILLAR DESIGN PRACTICES

The National Institute for Occupational Safety and
Health (NIOSH) surveyed 70 underground stone mines
to collect information on pillar design practices. Every
mine (with one exception) used the room-and-pillar
mining method; however, this method has many
variations in practice:

+ When used in relatively flat lying seams, the pillars
are often arranged in regular, reoccurring patterns.
Based on the 70 mines surveyed, 93% are regular.

* Occasionally random pattems have been used,
although this practice is decreasing in response to
improvements in surveying and mine planning.
Currently only two mines use the random method.

+ The majority of mines use square pillars where the

width of the pillars are equal to the length of the
pillars. Nine mines use rectangular pillars (herein
referred to as rib pillars) where the pillar length is
greater than the pillar width. This design technique
has been championed by two prominent consultants
in the field, Jim Scott (lannacchione, 1997) and Jack
Parker (1973).

+ The room-and-pillar method takes on some unique

characteristics when mining steeply dipping beds
with multitevels. Generally, one to three entries are
driven along the strike of the strata which may dip
from 45 to 70 degrees. Crosscuts are developed
horizontally, perpendicular to the entries. Raises or
windows between the outer, up-dip crosscuts and the
inner, down-dip crosscuts provide for ventilation
passages between mining levels. Only 2 mines used
this method.

* Finally, the stoping method which employs raises,
crown pillars, etc. is used by only one mine.

Because 93% of the mines surveyed uses the regular
room-and-pillar technique in a flat lying seam, this paper
will focus on analyzing this design method.

In the room-and-pillar mining method, entries and
crosscuts are generally driven perpendicular to each
other. When these headings are developed horizontally
into unmined strata they are called development entries
which outline development pillars. Faces are advanced
by drilling horizontal holes and blasting the rock back
into the development headings. Seventy-two.
development mining scenarios (two of the 70 mines
surveyed used multiple development designs) with 63

Table 1 - Mine layout characteristics for underground
U.S. stone mines.

‘Characteristic | Mean | Standard | Median | Minimum } Maximum
Geviation
Par 7 47 7 37 122
height, | 23) | (6.6) 23) (12) (40)
itt)
Opening | 13.1 26 128 61 183
width, | (43) | (66) | (42) (20) 60)
Pa
5
€| pier | 122 | 44 | 12.240) | 46 24
S| width,m | (40) | (13.3) (15) (90)
sie
8] exrac | 076 | oor | 075 | 056 | ost
tion ratio
Pitarwmh | 1.73 | 048 172 | 054 313
Overbur- | 80 98 46 7 610
den, mf | (262 | Gz | (50 | 23) | (2000)
Pilar | t46 | 38 146 87 244
eight, | (48) | (125) | (48) 2) (80)
anf)
Opening | 137 | 24 137 9A 183
| wan | as | ea | 48) G0) (60)
S| my
3 oar | oa | ae 137 61 24
width, | 43) | (133) | (45) 20) (0)
(tt)
Pitarwn | 092 | 0.35 | 090 04 1.92





Figure 10 shows how sample strength varies for different
discontinuity dip angles under a range of discontinuity
material properties. This analysis is instructive in
demonstrating the relative magnitude of strength
reduction based on discontinuity dip angle. It also shows
how friction angle and cohesion along the discontinuity
individually affect unit strength. However, this technique
can have limited value in analyzing stone pillar behavior
with discontinuities because it treats the material as one
uniform elastic mass.

100.
‘4000
%0
12000
i Froctue A, @ =20 *
~ Gonn53 we (500 ps) tocoo =
: :
g i
a é
3 ooo
§ sooo §
& &
i soo §
2000
0
° °

0 10 2 30 4 $0 60 7 80
Angle of Tarough-Going Froctures

Figure 10 - The affect of angular geologic
discontinuities on vertical strength using an analytical
technique.

An alternative approach is to introduce simulated
discontinuities 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 utilizing the ubiquitous joint model in the FLAC 3D
program. The ubiquitous-joint model is an anisotropic
plasticity model that includes weak planes of specific
orientation embedded in a Mohr-Coulomb solid. In this
model, yield may occur in either 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.

Parametric analysis of the effect of discontinuities on
pillar strength was conducted by varying the dip and
material properties within the ubiquitous joint model.
These simulations passed discontinuities through
modeled pillar shapes that ranged from width-to-height
ratios of 0.6 to 1.2. Three distinct pillar behaviors were
observed based on the dip of the discontinuities. Figure
11 shows the strength profiles for pillars with a stiffness
of 41.4 GPa (6 million psi) and a Mohr-Coulomb failure
envelope defined by a friction angle of 40° and a
discontinuity friction angle of 25°. The lowest pillar

strength occurred at a discontinuity dip angle of 57.5°
(Figure 11). It should be noted that the point of lowest
strength is defined in the ubiquitous joint model by the
following relationship:

= 45 aoa

6 2

min
where:
Brin = Angle of through-going discontinuity which
produces the lowest average vertical peak stress,
, = Internal angle of friction for the discontinuity.

How well this model characteristic fits field conditions
needs to evaluated further. The highest pillar strength
occurred with a discontinuity dip of 0° and gradually
decreased as discontinuity dip angle increased. As the
discontinuity dip angle increased above 57.5°, pillar
‘strength began to increase again; however, the original
strength for the intermediate to squat pillar shapes was.
not reestablished.

For all model shapes, and for a given set of material
properties, pillar strength associated with the
discontinuity dip of 90° was the same. In the case of the
example shown in Figure 11 that value was
approximately 29 MPa (4200 psi). It should be noted
that this characteristic may be model driven and not
representative of field conditions. The ubiquitous joint
model would attempt to forces discontinuities through
columns of equally sized grid elements. While this
behavior 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.

‘Sp_clong Discontinuities

Bucking of Cotumn(s)
10000

70
xf

° p12. ite [45 + 6/2 3
§ 00 ‘ a
: 000 =
g g
a) 000
é a
3” 4000 5
= 20 3
3 2
= y, +2000

ge | SE z

° °

0 1 2 30 40 $0 60 70 80 90
Angle of Through~Going Discontinuity

Figure 11 - Changes in average vertical peak stress.
as discontinuity dips are varied from 0 to 90° for four
different width-to-height ratio model pillars.

Stress versus strain plots for these numerical
simulations are shown in Figure 12. For discontinuity
dips between 0 and 45° the material displayed an
elastic-plastic behavior. When this models was run with