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Fig. 5 Prevention approgch: (a) unstable pillar failure is impossible because of either adequate stabil-
ity factors (greater than 2) or high W/H ratios of pane! pillars; (6) stability condition is such that high
W/H-ratio panel pillars satisfy local mine stiffness stability criterion and CPF is physically impossible.

Extraction for layout shown is 63%

the operator wants to ensure that CPF will not occur. There
are two separate but related ways to prevent CPF. The first is
to design pillars with an adequate stability factor (greater than
2) so that the risk of pillar failure is very small. The second is
to design panel pillars that satisfy the local mine stiffness sta-
bility criterion, as shown in Fig. 5(8). Therefore, they cannot
fail violently and CPF becomes a physical impossibility. The
panel pillars will usually have high W/H ratios (greater than 4
for coal) and may have high stability factors as well (greater

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than 2). Strictly speaking, this approach does not need barrier
pillars to ensure overall mine stability; however, their use is
still advisable. Barrier pillars will always provide an additional
margin of structural safety and may serve other purposes,
such as ventilation control.

In the mine layout shown in Fig. 5(a) 12-m square pillars
are developed on the advance with 6 m wide rooms. Instead
of splitting the development pillar into two 3 m wide fenders
with a WH ratio of 1, two sides of that pillar are mined on

PANEL PILLAR REMNANTS

BARAER PLLAR | [7] | BARRIER PRLAR FAIL IMMEDIATELY AFTER
OOMOO000O( 1 FULL EXTRACTION MINING
oe Os; 2

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Fig. 6 Full extraction approach: (a) failure of pillar remnants along with overburden occurs immedi-
ately after pillar extraction; (6) retreat mining must ensure development of sufficiently weak remnant

pillars. Extraction for layout shown is 67%


° 2 Pa © ey 100
DEPTH OF COVER (METRES)

Fig. 10 Suggested minimum square pillar size for 5.5-m and 6-m entries

Discussion and conclusions

CPF is a potential problem faced at all room-and-pillar
mines. It occurs when one pillar fails suddenly and thereby
overstresses the neighbouring pillars causing them to fail, and
so forth in very rapid succession. Very large mining areas can
collapse via this mechanism within seconds and with little or
no warning. The collapse itself can pose grave danger to
nearby mining personnel. In addition, the collapse can induce
a violent air blast that disrupts or destroys the ventilation
system. Further grave danger to miners exists if the mine
atmosphere becomes explosive or contaminated as a result of
the CPF.

The study presented here has documented collapses in
coal, metal and non-metal mines that have occurred within
the past twenty years in the U.S.A. CPF, also known as
‘massive pillar collapse’, ‘domino-type failure’ or ‘rapid pro-
gressive pillar collapse’, is the likely mechanism behind these
major mine failures. The mechanics of CPF are well under-
stood. Strain-softening behaviour is the essential mechanical
characteristic of pillars that fail rapidly via this mechanism.
Pillars that exhibit strain-softening behaviour undergo a rapid
decrease in load-bearing capacity on reaching their ultimate
strength. The strain-softening behaviour of pillars is in part
material-dependent; however, it also depends on pillar geom-
etry. Pillars with a low W/H ratio tend to exhibit a greater
degree of strain-softening behaviour than those with a higher
WIH ratio, which typically show elastic-plastic or strain-hard-
ening material behaviour.

The mechanics of a CPF differ significantly from those of
coal-mine bumps and rockbursts. In a CPF pillars fail vio-
lently owing to the applied vertical load and the post-failure
behaviour of the pillars. Research shows that coal-mine
bumps and rockbursts result from nearby mining-induced
seismic events that damage susceptible mine workings and
structures, The mechanics of how a mining-induced seismic
event damages a mine remains an important research topic.
“Thus, the design recommendations developed herein to con-
trol CPF do not apply to coal-mine bumps and rockbursts.

For coal-mine bump control pillars less than about 10 m
wide, ive. yield pillars with W/H ratios less than about 3-4,
generally do not fail explosively in a mining-induced seismic
event. Pillars that are 15-25 m wide, ie. abutment pillars
with a W/H ratio ranging from 5 to 8, are most susceptible to
explosive failure. Pillars greater than 30 m wide with a WiH
ratio greater than 15 generally do not fail explosively.232425

The local mine stiffness stability criterion developed by
Salamon! provides a means to distinguish between mine lay-
outs that fail in a stable, non-violent manner and those which
fail in an unstable, violent manner via CPF. This stability cri-
terion suggests three design approaches to minimize the risk
of CPF—containment, prevention and full extraction. In an
array of pillars that violate the stability criterion the contain-
ment approach applies. In this approach low W/H-ratio panel
pillars that violate the stability criterion are surrounded by
high-W/H barrier pillars that can shield the panel pillars from
full tributary area stresses and ‘contain’ panel pillar failure
should it initiate. However, if all panel pillars in an array
satisfy the stability criterion or if their stability factor is very
high (>2), the prevention approach applies. The panel pillars
do not exhibit much strain-softening behaviour because their
W/H ratio is sufficiently high (probably greater than 4). In the
full extraction approach the stability issue becomes a moot
point, because complete closure of the openings is assured
soon after retreat mining is completed.

References

1, Salamon M. D. G. Some applications of geomechanical model-
Jing in rockburst and related research. Keynote address in Rockbursts
and seismicity in mines Young R. P. ed. (Rotterdam: Balkema, 1993),
297-309.

2. Boler F, M., Billington S. and Zipf R. K. Seismological and
energy balance constraints on the mechanism of a catastrophic bump
in the Book Cliffs Coal Mining District, Utah, U.S.A. Int. J. Rock
‘Mech. Min, Sci., 34, 1997, 27-43.

3. Bryan A., Bryan J. G. and Fouche J. Some problems of strata
control and support in pillar workings. The Mining Engineer, 123,
1966, 238-54

4. Touseull J. and Rich C. Documentation and analysis of a mas-
sive rock failure at the Bautsch mine, Galena, Ill. Rep. Invest. U.S.


PEAK STRENGTH

LOAD

CONVERGENCE

Fig. 3 Complete load-deformation curve for pillar. Peak strength
at A. Left of A is pre-failure, right of A is post-failure

design are proposed to control CPF—-containment of failure,
prevention of failure and full-extraction mining.

Containment approach
The containment approach, shown in Fig. 4(a), limits the
spread of a potential CPF with barrier pillars. It is used dur-
ing retreat mining when the operator wants to reduce the
likelihood and potential impact of a CPF. It is a non-caving
room-and-pillar method in which low W/H-ratio panel pillars
are surrounded by high W/H-ratio barrier pillars. The panel
pillars violate the local mine stiffness stability criterion, as
shown in Fig. 4(6), and can, therefore, fail violently.
However, two factors will decrease the risk of a catastrophic
CPF. First, the barrier pillars will tend to shield the panel pil-
Jars from full overburden stresses and thereby increase their
safety factor and decrease their probability of failure. Second,

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if the panel pillars do begin to fail, the failure will not propa-
gate beyond the barrier pillars. A conservative approach is to
size the barrier pillars on the assumption that all the panel pil-
lars within have failed. These barrier pillars must also have a
large W/H ratio to eliminate any strain-softening behaviour.

If an engineer chooses to use panel pillars with a low W/H
ratio that exhibit strain-softening behaviour and can violate
the local mine stiffness stability criterion, it is imperative to
limit the panel sizes and surround all panels with adequate
barrier pillars. The load-transfer distance method presented
by Abel? provides an approach for estimating the maximum
panel width. Use of this method will help to ensure that panel
pillars never experience the full tributary area stress. Even
though the barrier pillars shield the panel pillars from the full
tributary area stress, the small pillars should have the ability
to withstand the full tributary area stress if possible.

To summarize, the main design characteristics of the con-
tainment approach are:
(1) Panel pillars have low W/H ratios (less than 4) and violate
the local mine stiffness stability criterion. Their stability fac-
tor is at least 2 on advance and may be less than 1 on retreat.
(2) Barrier pillars have high strength and high W/H ratios
(usually greater than 10). They must remain stable even if all
panel pillars should fail.
(3) Panel sizes are limited by the minimum load-transfer dis-
tance to ensure that panel pillar stresses are less than full
tributary area stresses,
(4) Panel sizes are also limited by the degree of damage due
to an air blast that the mine layout can withstand should a
CPF occur within the panel.

Prevention approach
‘The prevention approach, shown in Fig. 5(a), ‘prevents’ CPF
from ever occurring by the use of panel pillars with proper
mechanical characteristics. This approach is another non-
caving room-and-pillar system, in which, however, high
W/H-ratio panel pillars and optional barrier pillars are left.
The approach should be used during advance mining when

PANEL PILLARS VIOLATE
LOCAL MINE STIFFNESS
STABILITY CRITERION.
BARRIER PILLARS CONTAIN
POSSIBLE FAILURE.

CONVERGENCE

Fig. 4 Containment approach to room-and-pillar mine layout: (a) pillar failure is ‘compartmental-
ized’; (b) stability condition is such that panel pillars with low W/H ratio violate local mine stiffness
stability criterion; panel pillars can, therefore, fail violently, but adequate barrier pillars that restrict
spread of unstable failure surround them. Extraction for layout as shown is 59%


the retreat, leaving a 9-m square remnant with a W/H ratio of
3. With this approach the remnant pillars with a W/H ratio of
3 satisfy the local mine stiffness criterion and a violent failure
(CPF) is a physical impossibility. Otherwise, the remnant
pillars with a W/H ratio of 1 would violate the local mine stiff-
ness stability criterion and a CPF and damaging air blast
could result.

Extraction is about the same whether the development pil-
lar is split into potentially unstable remnants or whether the
prevention approach is applied and the pillar is shaved into an
inherently stable remnant. The only potential drawback in
this system from a ground-control perspective is room width.
‘Mine layouts that use the prevention approach must usually
have wider room spans during retreat mining. In this case
the room width increases from 6 to 9 m during retreat.
Therefore, this retreat-mining scheme is applicable only
under a relatively competent roof and supplemental support,
such as timber or mobile roof supports, may be required.

Full extraction approach

The full extraction approach, shown in Fig. 6(a), avoids the
possibility of CPF altogether by ensuring total closure of the
opening (and surface subsidence) on completion of retreat
mining. This approach does not require barrier pillars for
overall panel stability; they are, however, needed to isolate
extraction areas and protect mains and bleeders. The main
design characteristics of a full extraction approach are:

(1) Panel pillars on the advance must have adequate safety
factors (greater than 2) and high W/H ratios (greater than 4).
They should satisfy the local mine stiffness stability criterion.

(2) Panel pillars on the retreat must have safety factors much
less than 1 to ensure their complete, controlled collapse soon
after the retreat-mining phase, as indicated in Fig. 6(6).

Practical design examples for coal mining at
shallow depth

The three design approaches outlined above lead to three
practical options for maximizing extraction in coal-mine
panels: partial pillar recovery on the retreat (a containment
approach); small-centre mining on the advance (a prevention
approach); and full pillar extraction on the retreat.

Full pillar extraction is relatively complex and has histori-
cally required special expertise to succeed. The development
of remote-control continuous miners and mobile roof sup-
ports has made it economic for some mines to adopt this
method.?! Small-centre mining and pillar splitting, however,
have important advantages of simplicity and predictability.
A recent survey found that of 239 room-and-pillar mines with
active gob areas, nearly half were practising partial recovery
only.22 Evidently, most employ small-centre mining
exclusively.

Small-centre mining and pillar splitting both leave signifi-
cant remnant pillars in the worked-out gob areas. For
example, mining on 15-m centres with 6-m entries leaves
about 35% of the coal in 9 m x 9 m pillars. Splitting pillars
developed on 18 m x 18 m centres leaves about 22% of the
coal. The remnant pillars can help support the roof over very
large areas, and caving may not occur for some time.

The analyses presented here use the computer program
ARMPS developed by the U.S. Bureau of Mines.!! ARMPS
calculates the stability factor based on estimates of the loads
applied to, and the load-bearing capacities of, pillars during
retreat-mining operations. Loads considered include develop-
ment loads from the tributary area formula and abutment
loads from gob areas in front and to the sides of the active
mining zone. The strength of a pillar is determined with the
Mark-Bieniawski formula for rectangular pillars given by

2
Sp = 5 0.64+0.54%.-0 ra @)

where S, is in-situ coal strength of 6.2 MPa, Wis pillar width,
His pillar height and L is pillar length. A database of 130 case
histories has been collected from room-and-pillar mines
throughout the U.S.A. to verify ARMPS. With a stability fac-
tor of 1.5 only two of the 130 case histories experienced pillar
failure. For a stability factor greater than 2.0 none of the cases
showed failure.

Pillar splitting—a containment approach

Fenders left from pillar-splitting operations appear to be
potential candidates for failure even at shallow depths. For
example, 3 m x 12 m fenders in a 3-m seam have a stability
factor of 2.0 at only 36 m of cover. If air blasts and massive
collapses are not to result from partial pillaring, the size of the
gob areas must be minimized. To separate the gob areas,
rows of unsplit development pillars can be left as a barrier.
‘This strategy is analogous to the way submarines are ‘com-
partmentalized.’ It is based on two assumptions: limiting the
span above the mined-out area renders a bridging failure of
the strong overburden less likely; and minimizing the size of
the gob area would reduce the power of an air blast resulting
from a collapse that did occur.

‘Table 1 shows that no major collapses have been docu-
mented where the gob area was smaller than 15 000 m?. In
the five cases where the gob area was between 15 000 and
19 000 m? about 60% of the incidents resulted in major dam-
age. Also, none of the damaging incidents has occurred where
the minimum dimension of the mined-out area was less than
100 m. On the basis of these data acceptable dimensions for a
pillar-splitting operation might be a maximum area of
12.000 m? and a maximum width less than 90 m. For exam-
ple: on the assumption of 18 m x 18 m centres and a
nine-entry system, with four rows split, the mined-out area

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Fig. 7 Possible pillar-splitting plans for air-blast control using 6 m
wide entries and 12 m wide pillars: (a) nine-entry system, two rows
of unsplit pillars for barrier; (6) nine-entry system, three rows of
unsplit pillars for barrier; (c) six-entry system, two rows of unsplit pil-
Jars for barrier; (d) six-entry system, three rows of unsplit pillars for
barrier


Bur. Mines RI 8453, 1980, 49 p.

5. Straskraba V. and. Abel J. F. The differences in underground
mines dewatering with the application of caving or backfilling mining
methods. Mine Waver and the Environment, 13, no. 2, 1994, 1-20.

6. Davidson, J. Ground stability evaluation—Troy mine—ID No.
24-01467. (Denver, CO: Mine Safety and Health Administration,
1987), 15 p.

7. Swanson P. L. and Boler F, The magnitude 5.3 seismic event
and collapse of the Solvay trona mine: analysis of pillar'floor failure
stability. U.S. Bureau of Mines OFR 86-95, 1995, 82 p.

8. Mine Safety and Health Administration. Report of technical
investigation, underground non-metal mine, mine Collapse accident,
Solvay mine, Solvay Minerals Inc., Green River, Sweetwater County,
‘Wyoming, February 3, 1995, 1996,

9. Spruell J. L. Accident investigation report—Unimin Specialty
Minerals, Inc. Birk 2A—ID No. 11-02598. (Duluth, MN: Mine
Safety and Health Administration, 1992), 12 p.

10, Denk J. M. et al. Accident investigation report—Akzo Nobel
Salt, Inc. ID. No. 30-00662 (Pittsburgh, PA: Mine Safety and
Health Administration, 1994), 141 p.

11, Mark C., Chase F. E. and Campoli A. A. Analysis of retreat
mining pillar stability. In Proc. 14th Conf. Ground control in mining,
West Virginia University, 1995, 63-71.

12, Das M.N. Influence of width/height ratio on postfailure behav-
iour of coal. Int. J. Min. geol. En, 4, 1986. 79-87.

13, Chase F. E., Zipf R. K. and Mark C. The massive collapse of
coal pillars—case histories from the United States. In Proc. 13th Conf.
‘on Ground control in mining, West Virginia University, 1994, 69-80.

14, Bieniawski Z. T, Zn situ strength and deformation characteris-
tics of coal. Engng Geol., 2, 1968, 325-40.

15, Wagner H. Determination of the complete load-deformation
characteristics of coal pillars. In Proc. 3rd. Int. Congress on Rock
Mechanics National Academy of Sciences, vol. 2B, 1974, 1076-81.
16. Van Heerden W. L. In situ determination of complete
stress-strain characteristics of large coal specimens. J. S. Afr. Inst.
Min. Metall., 75, 1975, 207-17.

17, Skelly W. A., Woigamott J. and Wang F. D. Coal pillar
strength and deformation prediction through laboratory sample test-
ing, In Proc. 18h U.S. Rock mechanics symposium, Colorado School of
Mines, Golden, CO, 1977, 2B5-1 to 2B5-5.

18, Salamon M. D. G, Stability, instability and design of pillar
workings. Int. J. Rock Mech. Min. Sci., 7, 1970, 613-31

19. Zipf R. K. Analysis and design methods to control cascading
pillar failure in room-and-pillar mines. In Milestones in rock engineer
ing Bieniawski Z. T. ed. (Rotterdam: Balkema, 1996), 225-64

20. Abel J. F. Soft rock pillars. Int. J. Min. geol. Engng, 6, 1988,
215-48.

21. Chase F. E. et al. Practical aspects of mobile roof support
usage. In Proc. 15th Int. Conf. Ground control in mining (Golden, CO:
Colorado School of Mines, 1996)

22. Urosek J. E., Zuchelli D. R. and Beiter D. A. Gob ventilation
bleeder systems in U.S. coal mines. SME Preprint 95-78, 1995, 5 p.
23. Tannacchione A. T. and Zelanko J. C. Occurrence and remedi-
ation of coal mine bumps: a historical review. In Proc. Mechanics and
‘mitigation of violent failure in coal and hard-rock mines Maleki H. et al.
eds. Spec. Pub. U.S, Bureau of Mines 01-95, 1995, 27-68.

24. Guana M. Coal pillar design for deep conditions: an opera-
tional approach. In Proc. Workshop on Coal pillar mechanics and design
Tannacchione A.T. et al. eds. Inf. Circ. U.S. Bur. Mines IC 9315,
1992, 214-24.

25. Koehler J. R. Longwall gateroad evolution and performance at
the Sunnyside Coal Mines. SME Preprint 94-179, 1994, 11 p.

Authors

R. Kar! Zipf Jr received a Ph.D. in mining engineering in 1988 from
Pennsylvania State University, U.S.A. He worked for the former U.S.
Bureau of Mines from 1988 until 1995 before assuming his current
position as senior lecturer in mining engineering at the University of
Queensland.

Address: Department of Mining, Minerals and Materials Engineering,
University of Queensland, Brisbane, Queensland 4072, Australia,

Christopher Mark received a Ph.D. in mining engineering in 1987
from Pennsylvania State University, U.S.A. He has worked for the
former U.S. Bureau of Mines, now the Mining Research Division of
the National Institute for Occupational Safety and Health, since 1987
and is chief of the Fires, Explosions and Ground Failure Prevention
Branch, based at NIOSH’s Pittsburgh Research Laboratory.


Design methods to control violent pillar failures in room-and-

pillar mines

R. Karl Zipf Jr. and C. Mark

Synopsis
The sudden, violent collapse of large areas of room-
and-pillar mines poses a special hazard for miners and
mine operators. This type of failure, termed a ‘cascad-
ing pillar failure’ (CPF), occurs when one pillar in a
mine layout fails, transferring its load to neighbouring
pillars, which causes them to fail, and so forth. Recent
examples of this kind of failure in coal, metal and non-
metal mines in the U.S.A. are documented. Mining
engineers can limit the danger presented by these fail-
ures through improved mine design practices.

Whether failure occurs in a slow, non-violent manner
or in a rapid, violent manner is governed by the local
mine stiffness stability criterion. This stability criterion
is used as the basis for three design approaches to con-
trol cascading pillar failure in room-and-pillar
mines—the containment approach, the prevention
approach and the full extraction mining approach.
These design approaches are illustrated with practical
examples for coal mining at shallow depth.

Cascading pillar failure (CPF) in room-and-pillar mines can
go by many other names, such as ‘progressive pillar failure’,
‘massive pillar collapse’, ‘domino-type failure’ or ‘pillar run’.
In this kind of failure when one pillar collapses the load that it
carried transfers rapidly to its neighbours, causing them to
fail, and so forth. This failure mechanism can lead to the
rapid collapse of very large mine areas. In mild cases only a
few tens of pillars might fail; in extreme cases, however, hun-
dreds, even thousands, of pillars can fail.

CPF can have catastrophic effects on a mine, and some-
times these effects pose a greater risk to health and safety than
the underlying ground-control problem. Usually, the CPF
induces a devastating air blast as a consequence of the dis-
placement of air from the collapse area. An air blast can
disrupt the ventilation system totally by destroying ventilation
stoppings, seals and fan housings. Flying debris can seriously
injure or kill mining personnel. The CPF might also fracture
a large volume of rock in the pillars and immediate roof and
floor. In coal mines and certain other mines this can lead to
the sudden release of large quantities of methane gas into the
mine atmosphere; a methane explosion might result from the
CPF.

CPF is at the far end of the spectrum of unstable pillar
failure. At the other end are slow ‘squeezes’ that develop over
days to weeks and, because of their slow progress, do not
pose an immediate danger to mining personnel. There is
ample warning time for men and machinery to get out of the
way of the failure. In a CPF, however, the failure progresses
so rapidly that men and equipment cannot be evacuated in
time. Significant seismic energy is released as a consequence

of the rapid failure and collapse.

CPF should not be confused, however, with coal-mine
bumps and rockbursts. In some cases the damage can appear
similar, but the underlying mechanics are completely differ-
ent. As will be shown later, the mechanics of CPF depend on
the applied vertical stress and the post-failure, i.e. strain-soft-
ening, behaviour of the pillars. In a CPF pillars shed their
applied load rapidly and have very little residual strength after
failure. The collapse itself may release significant seismic
energy, but otherwise the mine is seismically quiet. After a
CPF the openings in the affected mine workings have usually
closed completely.

In contrast, coal-mine bumps and rockbursts occur in seis
mically active mines. Research has shown that coal-mine
bumps and rockbursts are seismic events induced by mining
that damage underground mine workings. Bumps and bursts
are thus a subset of a much larger set of mining-induced seis-
mic events.! Only some of these seismic events damage mine
workings; fortunately, most do not. The mechanisms by
which a mining-induced seismic event can lead to a damaging
coal-mine bump or rockburst is still a significant research
area? After a bump or rockburst the affected mine workings
may or may not be completely closed. For example, in the
coal-mine bump described by Boler and co-workers? the
mine workings remained open even though the pillars were
destroyed during the bump event.

Because CPF differs from a coal-mine bump or rockburst,
the design approaches to control their occurrence also differ.
The design recommendations developed here apply to CPF
and not to bump- or burst-prone mines.

Cascading pillar failure examples
Unfortunately, CPF has occurred in room-and-pillar coal,

metal and non-metal mines. The most infamous example is
the Coalbrooke colliery in South Africa, where 437 miners

perished wheru@wamaucfuthruspicarociapenwnrichshonanicrernccixsanmman

utes on 21 January, 1960.3 Table 1 summarizes the mining
dimensions of 13 examples of rapid pillar collapse in U.S.
coal mines. All occurred during the 1980s and 1990s, and all
happened suddenly or without significant warning. Most
resulted in air blasts and damage to the ventilation system.

Table 2 gives the mining dimensions of six room-and-pillar
metal and non-metal mines in the U.S.A. where failure
occurred in all probability by the CPF mechanism. The col-
lapse areas can be huge. Fortunately, some of these failures
gave advance warning. At the lead-zinc mine slabbing from
pillars and roof falls began four weeks prior to the main col-
lapse.3 At the copper mine considerable rock noise and
‘smaller failures preceded the main collapse by five days.> At
the copper-silver mine it is not known if nature provided a
warning.¢ Evidently, the trona mine collapsed without warn-
ing.7® Rock noise and other failure warnings preceded the
silica mine collapse by three weeks.? The presence or absence
‘of warnings at the salt mine is not known.!° Most of these
collapses induced a substantial air blast; damage to the venti-
lation systems was limited, however, to bent airdoors and a
few downed stoppings, except at the trona mine, where
extensive damage to the ventilation system resulted.


would have a minimum dimensicn of 72 m and an area of
about 11 000 m? (Fig. 7(a) and (})). For the same pillar size
in a six-entry system, with five rows split, the minimum
dimension would be 90 m and the area would be about
10 000 m? (Fig. 7(c) and (d)).

‘The next question is how many unsplit rows should be left
between these mined-out areas. The goal is to leave enough
ofa ‘barrier’ that the failure of one gob area does not spread
to adjacent areas. ARMPS was used to evaluate the loading
on unsplit pillars between two mined-out areas. The program
was modified so that two ‘front’ gobs could be applied to the
unsplit pillars. The analyses were run with abutment angles of
90°, which assumes that none of the load is carried by the
gob, but is transferred instead to the barrier.

In the first set of analyses two rows of full-size pillars were
used as the barrier. An ARMPS stability factor of 1.5 was

rows that were split (three, four and five), the entry width
(5.5 and 6 m), the seam height (2, 2.5 and 3 m), and the
number of entries in the section (five, seven and nine). The
results are presented in the form of graphs (e.g. Fig. 8),
showing the suggested maximum depth of cover for each
combination of parameters. In general, for 5.5-m entries in a
2.5m seam, it appears that two rows of unsplit pillars might
be an adequate barrier at depths less than about 90 m, and
three rows might be acceptable to about 170 m of cover.

Barriers must also be left between extracted panels. These
can be unsplit development pillars or solid coal. If unsplit
development pillars are used, the analysis in Fig. 8 should
apply. For solid coal barriers Fig. 9 shows the suggested
widths, under the same loading assumptions as before. For a
2.5-m seam a 17 m solid barrier seems appropriate at 75 m of
cover, and 23 m might be needed at 120 m.

8

[MAXIMUM ALLOWABLE DEPTH OF COVER (METRES)

[== tar «roe ait]
ows urepit
Jets = 24:3 rows st
2 rows unspit
Je 24m: 4 rows at)
rows unset
|-- 14 24m: 5 cows sot
‘rows epi

|e H = 20m 4 rows at
rows unplt|

|e = 1.0m: 4 rows spt
Sows urspit,

JH = 24m: 3 rows spt}
Sows unspl

0.
°
5 7
NUMBER OF ENTRIES
Fig. 8 Suggested maximum depth for two and three rows of unsplit pillars as barrier between gob

areas with 5.5-m entries and 12.5 m x 12.5 m pillars

errWoF coven ETRE)

Fig. 9 Suggested solid coal barrier width between two areas where
pillars have been split

assumed to prevent the collapse of one gob area from trigger-
ing the collapse of an adjacent area. With a stability factor of
1.5 only two of the 130 case histories with ARMPS showed
pillar failure. Three rows of pillars were used in the second set
of analyses, and the required stability factor was reduced to
1.0 because of the greater stiffness of the barrier. Pillars on
18 m x 18 m centres were used in all cases.

Other parameters that were varied included the number of

Small-centre mining—a prevention approach

Square pillars are generally used in small-centre mining.
Table 1 indicates that three collapses have involved 9-m
square pillars and one involved 12-m square pillars. Square
pillars can be designed to be collapse-resistant in two ways.
‘The first is to increase their W/H ratio. Since no collapses
have been documented where the W/H ratio was greater than
3.0, a design W/H ratio of 4.0 is recommended to provide an
adequate margin of safety.

Pillar collapses may also be avoided by maintaining a suffi-
ciently large stability factor. A design ARMPS stability factor
of 2.0 is suggested for long-term stability. For a stability
factor greater than 2.0 none of the ARMPS case histories
showed failure. A greater pillar stability factor can be
achieved by increasing the pillar width, decreasing the extrac-
tion ratio, or both.

These two design criteria have been combined to develop
guidelines for small-centre mining. Fig. 10 was developed on
the assumption of square pillars with a stability factor of 2.0
or a WIH ratio of 4.0. When 6 m wide entries are used the
minimum suggested pillar sizes are increased by about 6%. It
should be noted that these design criteria are only for control-
ling massive pillar collapses. At greater depths pillar sizes may
have to be increased beyond W/H = 4 to maintain an
adequate stability factor. Should pillars of W/H = 4 become
overloaded, however, a squeeze would be expected rather
than a sudden collapse.



Table 1 CPF examples in U.S. coal mines

Case State Depth, Pillarsize, ARMPS | WiHratio Collapse area, Collapse size, Damage from air blast
m m safety factor m? m

A wy 84 3x12 0.75 1.05 22.500 150 x 150 26 Stoppings, | injury
BL wy 3 3x12 0.84 1.00 - - 32 Stoppings, fan wall out

3x18 0.96 1.00
B2 wy 5 3x12 0.82 1,00 15.000 100 x 150 40 Stoppings
BS wv 85 9x9 1.46 3.00 32.400 180 x 180 70 Stoppings

6x12 1.30 2.00
c wy 60 3x12 1.05 1.00 21.000 140 x 150 103 Stoppings
cz wv 99 9x9 115 3.00 18 000 100 x 180 Minimal
D wy 69 6x6 115 1.82 16 000 100 x 160 37 Stoppings

9x9 1.42 2.73
NL) wv - - 1.03 25 18.000 120 x 150 -
R co 120 4x24 0.57 LT 27.000 180 x 150 Minor
EI wv 1 3x12 0.79 1.42 69 600 240 x 290 Major
B2 wy 1 3x12 071 La 60 500 220 x 275 Major
F OH 16 2x12 0.66 2.12 19 500 90 x 215 Minimal
G UT 168 12x12 0.95 2.29 72.000 150 x 490 Major, 1 injury
Table 2 CPF examples in U.S. metal and non-metal mines

State Depth, Pillar size, WH ratio Extraction, Collapse area, Collapse size, Damage from air blast
m m % m m
Pb-Zn mine IL 75 1ixll 04 90 32.000 90 x 360 Minimal
Cu-Agmine MT 300 9x90 05 60- 11000 90 x 120 -
65
Cu mine MI 600 TXT 20-09 68 540.000 600x900 Minor
Tronamine WY 490 4x29 14 60- 1600 000 760x2100 Major
70

Silica mine IL 18 9015 10 56 6 800 75x90 -
Salt mine NY 330 55x55 15 92 40 000 200x200 ~

The mine dimensions summarized in Tables 1 and 2 can
cover a wide range of mining practice. However, mines that
have had a CPF have several important commonalties. In
general, the pillars themselves must be the weak link in the
roof-pillar-floor system. Extraction ratios are usually more than
60%. Where the safety factor of pillars involved in a failure
can be estimated it has usually been close to 1. The width-to-
height (W/H) ratio of panel pillars is always less than 3 for
coal-mine failures, usually much less than 1 in the metal
mines and may be less than 2 in the non-metal mine failures.
Substantial barrier pillars with W/H ratios of more than 10
are usually absent from the part of the mine where the CPF
occurs. For coal-mine failures the stability factor for the
pillars is less than 1.5 according to the Mark-Bieniawski pillar
strength formula in the Analysis of Retreat Mining Pillar
Stability (ARMPS) method.!! Further descriptions of the
ARMPS method appear here under ‘Practical design
examples’. Typically, the roof rock is stiff and massive and
can bridge wide spans without caving. Most importantly,
though, for collapse events that caused significant damage the
collapse area is at least 15 000 m?, with a minimum dimen-
sion of at least 100 m.

Mechanics of cascading pillar failure

The simple explanation of CPF given above indicates that
rapid load transfer away from failing pillars is an important
part of the failure mechanism, The underlying mechanics of
CPF are, however, more complex. The nature of the pillar
failure process depends on the relative mechanical properties
of the rock mass and the pillar. The most important struc-
tural characteristic is the post-failure stiffness and strength of

the remnant pillars. Slender pillars with a low W/H ratio shed
load rapidly when they fail. The transferred weight can over-
load adjacent pillars, and a rapid ‘domino’ failure of adjacent
pillars can ensue. Pillars that are squatter, with a large WH
ratio, retain most of their load even after failure, Such pillars
will squeeze slowly, rather than collapsing.

Laboratory data from the work of Das!? illustrate this
behaviour. As shown in Fig. 1, beyond a W/H ratio of about 8
the behaviour of the laboratory-scale specimens is nearly elas-
tic-plastic, meaning that they shed little load after failure.
Some data on the post-failure behaviour of full-scale coal pil-
lars are also available. As shown in Fig. 1(6), beyond a WIHT
ratio of about 4 the post-failure modulus of full-scale coal pil-
lars becomes positive and their behaviour is elastic-plastic.
Again, such coal pillars do not shed their load rapidly when
they fail.

On the basis of an analogy between a laboratory test speci-
men and a mine pillar Salamon!® developed a criterion to
predict whether the failure process occurs in a stable, non-
violent manner or in an unstable, violent manner; Fig. 2
illustrates this well-known criterion.

Stable, non-violent pillar failure occurs when

IKims! > 1Kpl qa
and unstable, violent pillar failure occurs when
IKims! < |pi @)

where Ky ws is local mine stiffness and Kp is post-failure stiff-
ness at any point along the load-convergence curve for the
pillar. As long as equation 1 is satisfied, CPF is unlikely to


Ww/h=13.5

120

w/h=10

STRESS, MPa
8

fs)

mt n L

100 150_200 250
STRAIN, 107°

@
90
ao
1
‘peer
3 oe,
9
= .
id
FI
a
5
2
° te
pei} | po yoy toy it jy

23 ¢ 5 6 7 8 8 0 1 2 99 44
WIDTH / HEIGHT RATIO
©

Fig. | (a) Complete stress-strain curves for Indian coal specimens,
showing increasing residual strength and post-failure modulus with
increasing WH ratio;}2 (4) post-failure modulus of coal pillars, in-
situ coal specimens and laboratory samples!%17 (filled circles, Das3!?
squares, Bieniawski;!4 blank circles, Wagner;!° inverted triangles, van
Heerden;! mriangles, Skelly and co-workers!7)

occur; however, if equation 2 is satisfied, CPF is possible.

Kzms depends on the modulus of the immediate roof,
floor and pillar materials and the layout of pillars, mine open-
ings and barrier pillars. Numerical methods, such as the
boundary-element method,!® can be applied to calculate
Kms. The post-failure stiffness, Kp, depends on the size and
WIH ratio of the pillar. Some field measurements of the post-

LOAD
LOAD

CONVERGENCE CONVERGENCE

Fig. 2. Unstable, violent failure versus stable, non-violent failure:
(@) local mine stiffness less than post-failure stiffness in ‘soft loading
system; (8) local mine stiffness greater than post-failure stiffness in
stiff loading system

failure stiffness, Kp, exist for full-scale coal pillars, as shown
in Fig. 1(6). Unfortunately, there is a paucity of similar data
for full-scale pillars in room-and-pillar metal and non-metal
mines.

‘As shown in Table 1, CPF in room-and-pillar coal mines
occurs only when the W/H ratio of the affected pillars is less
than about 3 or 4. Fig. 1 explains this observation. Kp
becomes positive, i.e. the post-failure behaviour changes from
strain-softening to elastic-plastic, at a W/H ratio of about 3
or 4. At that point CPF becomes a physical impossibility
because the local mine stiffness stability criterion is necessar-
ily always satisfied.

Similarly, for metal and non-metal mines Table 2 shows
that CPF only occurs in room-and-pillar mines that have
pillars of low W/H ratio (less than about 1 or 2). Kp must
become positive beyond some critical W/H ratio. On the basis,
of the coal observations that transition may also occur at the
WIH ratio range of 3-4.

Back-analysis or numerical simulations may provide the
only route to estimate Kp for certain kinds of full-scale pillars.
Zipf!? followed this approach to calculate Kp and Ky ys and
then evaluate the local mine stiffness stability criterion. The
behaviour of the computer simulations changes depending on
whether the model satisfies or violates this stability criterion.
From a health and safety standpoint it is fortunate, however,
that rock mechanics engineers have few examples of CPF
from which to conduct back-analyses of the post-failure
behaviour of full-scale mine pillars.

Design principles for control of cascading
pillar failure

Most pillar design procedures merely consider the peak
strength of the pillar, shown as 4 in Fig. 3. If the applied
stress on the pillar reaches this level, its stability factor is 1
Similarly, if the applied stress on the pillar is half the peak
strength, shown as B in Fig, 3, its stability factor is 2. There is
a great economic incentive to design pillars with a low stabil-
ity factor in that as the stability factor decreases the extraction
ratio increases. Therefore, the most economic pillar designs
in terms of resource recovery are necessarily very close to A,
but still on the pre-failure side of the complete load-conver-
gence curve for the pillar. Because of the inherent variability
in pillar strength, however, it is important to consider what
happens to a particular room-and-pillar mine plan if some of
the pillars should exceed the peak strength at A and proceed
into the post-failure side at C.

Engineers have known for some time about the post-failure
behaviour of rocks and the implications of this behaviour for
mine safety. However, it is another matter to translate that
knowledge into efficient and economic mine designs for the
extraction of bedded deposits by room-and-pillar or other
mining techniques. Three different approaches to mine