Vol.:(0123456789) 1 3

Rock Mechanics and Rock Engineering 

https://doi.org/10.1007/s00603-019-01959-6 

 

   

 

 

ORIGINAL PAPER 

A Case Study of the Collapse of Slender Pillars Afected 

by Through‐Going Discontinuities at a Limestone Mine in Pennsylvania 

Gabriel S. Esterhuizen1  · Paul L. Tyrna2 · Michael M. Murphy1 

Received: 1 November 2018 / Accepted: 23 August 2019 

© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2019 

Abstract 

The sudden collapse of approximately 3 Ha of room-and-pillar workings at a limestone mine in southwestern Pennsylvania 

in 2015 resulted in an air blast that injured three mine workers. Subsequent investigations showed that an area encompassing 35 pillars had collapsed. The pillars were 9–10 m wide and up to 18 m high. A notable geologic feature is the throughgoing joints that dip at 50–80° and can extend from the roof to the foor of the pillars. These structures are thought to have 

weakened the pillars well below the strength that is predicted by empirical equations for hard-rock pillar design. This paper 

presents the relevant geotechnical data related to the collapsed area and numerical model results that were used to estimate 

the pillar loading underneath the variable topography, and compares the pillar loads to some established hard-rock pillar 

strength equations. The outcome is also compared to a strength equation that was developed specifcally for limestone mines 

in which the negative impact of large angular discontinuities is explicitly accounted for. The results show that established 

hard-rock pillar strength equations do not adequately account for the impact of large through-going discontinuities on the 

strength of slender pillars. The equations would have signifcantly overestimated the strength of the pillars at the case study 

mine. The critical state of the workings would have been predicted correctly by the limestone pillar strength equation that 

accounts for the large discontinuities. 

Keywords Mining · Pillars · Pillar strength · Pillar collapse · Limestone · Discontinuities 

1 Introduction 

On April 29, 2015, three mine workers were waiting near 

the access portal of an underground limestone mine in 

southwestern Pennsylvania when they heard something that 

sounded like shots being fred in the mine. This was followed 

by a massive collapse of the room-and-pillar workings in 

the mine. The air blast from the collapse knocked the mine 

workers to the ground, causing serious injuries to each one. 

Subsequent investigations revealed that subsidence of the 

Disclaimer The fndings and conclusions in this paper are those

of the authors and do not necessarily represent the ofcial

position of the National Institute for Occupational Safety and

Health, Centers for Disease Control and Prevention. 

• Gabriel S. Esterhuizen 

eee5@cdc.gov 

mountainside overlying the mine workings had occurred. 

The subsidence area encompassed about 3 Ha. Underground 

inspections to delineate the collapsed area showed that about 

35 pillars had collapsed. A wide-angle, aerial camera view 

of the mine showing the access portal and the subsidence 

area is presented in Fig. 1. The mine owners have requested 

that the name of the mine operation remains anonymous in 

this publication and will be referred to as ‘the case study 

mine’. 

The objective of this paper is to describe the geotechnical and mining factors associated with the pillar failure 

and to demonstrate how large through-going discontinuities reduced the pillar strength well below the strength that 

would have been predicted by established hard-rock pillar 

strength equations. An equation that explicitly accounts for 

the impact of such large discontinuities is presented, and it 

is shown that this equation would have identifed the critical 

stability of the pillars at the case study mine. 

1 NIOSH Pittsburgh Mining Research Division, 626 Cochran’s

Mill Road, Pittsburgh, PA, USA 

2 MSHA Technical Support Group, Triadelphia, VW, USA 
G. S. Esterhuizen et al. 

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Fig. 1 Aerial view of the mine showing extent of surface subsidence 

associated with the collapse of the pillars 

2 Geotechnical Parameters 

2.1 Geologic Setting 

The case study mine is located within the Appalachian Plateau province and is situated 120 m beneath the crest of 

Chestnut Ridge in southwestern Pennsylvania, USA. The 

Appalachian plateau is the westernmost physiographic 

province of the Appalachian mountain belt (Fig. 2) and is 

characterized by broad folding with dips ranging from 20° 

to less than 5° and wavelengths ranging from 8 to 32 km. 

Structural relief ranges from less than 100 m to more than 

1000 m (Kerrigan 2016). 

The Appalachian Plateau is bounded on the east by the 

Allegheny structural front, which marks the transition into 

the more intense structural deformation in the Valley and 

Ridge province (Rodgers 1970; Sak et al. 2012; Trapp and 

Horn 1997). Chestnut Ridge is a northeast trending, roughly 

150 km long, doubly plunging anticline with a maximum 

topographical relief of 300 m in the vicinity of the mine. It 

is asymmetrical, with steeper dipping strata on the northwest 

side. 

Fig. 2 Mine location and physiographic provinces of the Appalachian Mountains 
A Case Study of the Collapse of Slender Pillars Afected by Through‐Going Discontinuities at...

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The Loyalhanna limestone extracted at the mine typically 

occurs at depth in the region, but is mined in numerous locations where folding has brought it nearer to the surface. The 

folding of the Loyalhanna limestone is gentle and is hardly 

noticeable at the scale of the collapsed mine workings. In 

southwestern Pennsylvania, the Loyalhanna is stratigraphically a lower member of the 1000- to 1500-m-thick, Mississippian-age Mauch Chunk Formation. The Loyalhanna 

limestone has a maximum thickness of 30 m, but is typically 20 m thick in the Chestnut Ridge mines. It is light to 

greenish gray and compositionally ranges from a calcareous 

sandstone to a sandy limestone (Edmunds et al. 1979). At the 

mine, the Loyalhanna limestone bed is overlain by distinctive reddish-brown mudstones, shales, and siltstones of the 

Mauch Chunk beds, as shown in Fig. 3. 

2.2 Geologic Structure 

Geologic structure typically associated with folding in the 

Appalachian plateau includes faults and joints. Transverse 

and longitudinal joints that strike perpendicular and parallel 

to fold axes, respectively, are typically dominant (Hatcher 

et al. 1989; Nickelsen and Hough 1967). In areas were salt 

deposits underlie deformed strata, shallow, low angle thrust 

faults, parallel to fold axes occur (Gillespie and Kampfer 

2017). These faults have been interpreted as late-stage 

breakthrough faults (Mount 2014). All three of these types 

of geologic structure were observed at the study mine and 

are consistent with other structural patterns described in previous studies (Iannacchione and Coyle 2002). 

A well-defned thrust fault was visible in the highwall 

immediately north of the Haulage (south) Portal. The 

N25°E striking fault was planar with approximately 1.5 m 

Fig. 3 Access portal entering the mine with Mauch Chunk beds 

exposed in the highwall 

of apparent ofset. Dip was calculated at 15° southeast. The 

fault intersected the top of the mining horizon near the south 

portal and intersected the surface along the southeast edge 

of the pillar collapse subsidence trough. Within the mining horizon, the fault was coincident with ground control 

mitigation features, including a steel canopy in the main 

roadway and larger, non-uniform pillars in older mine workings. Degraded ground conditions associated with the fault 

were more pronounced in the eastern portion of the mine. 

The strike of the fault was approximately parallel with the 

axis of the Chestnut Ridge anticline and other fault structures described in previous studies (Iannacchione and Coyle 

2002). 

Jointing observed underground showed multiple orientations, although most joints fell generally into a northwest 

and northeast set with dips ranging from vertical to less than 

30°. One particular set of joints stood out in terms of prominence, persistence, and uniformity. This set, with a strike of 

N60°W, occurred in a well-defned zone 150 m wide that 

intersected the main portal area and the eastern half of the 

pillar collapse zone. Joints in the zone were typically spaced 

3–5 m apart and dipped 60–80° to the southwest, as shown 

in Fig. 4. Some joints traces exposed by the within pillars 

were curvilinear with dips less than 60° in the lower portion 

of the pillar. Many of the joints near the collapsed area were 

dilated by groundwater dissolution and some showed apertures up to 15 cm. The joints, which were perpendicular to 

both the axis of the Chestnut Ridge anticline and the strike 

of the thrust fault are interpreted as transverse joints associated with anticline formation. 

Fig. 4 Prominent N60°W striking joint intersecting a pillar south of 

the collapsed area 
G. S. Esterhuizen et al. 

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2.3 Rock Strength and Rock Mass Classifcation 

Rock samples were collected from the operational area of the 

mine, and fve of these samples were tested by the National 

Institute for Occupational Safety and Health (NIOSH) in 

accordance with ASTM standard D2398-95 (2002) providing an average uniaxial compressive strength (UCS) of 

181.8 MPa, as shown in Table 1. The average UCS is somewhat lower than expected for the Loyalhanna limestone, 

which is usually in the range of 200–220 MPa (Esterhuizen 

et al. 2006). However, the lower rock strength is consistent with the rock strength testing results determined during 

the initial mining permit application to the Pennsylvania 

Department of Environmental Protection (Smith personal 

communication 2016). 

Rock mass classifcation of the Loyalhanna limestone at 

the case study mine was conducted by NIOSH (Esterhuizen 

et al. 2006) as part of a survey of pillar design practices in 

limestone mines. The rock mass was classifed at three locations using the Bieniawski (1989) rock mass rating (RMR). 

The unadjusted ratings were found to range from 69 to 76, 

as shown in Table 2, placing the rock mass slightly below 

the average RMR of 75 found in the NIOSH survey of US 

limestone mines (Esterhuizen et al. 2006). The rock mass 

classifcation outcome was not used in the assessment of the 

collapsed pillars, but is provided to allow comparison with 

other hard rock mines. 

2.4 State of Ground Stress 

Limestone mines operating within the Loyalhanna limestone can experience roof instability that is related to tectonic horizontal stress within the Mid-North American plate 

(Iannacchione et al. 2002; Zoback 1992). The limestone beds 

are much stifer than the surrounding strata and the pervasive 

tectonic loading produces greater stress within these stif 

beds (Mark and Gadde 2008; Dolinar 2003). At the case 

study mine, signs of horizontal stress-related roof damage 

were observed in deeper sections of the mine that are remote 

from the collapsed area. In the vicinity of the collapsed area, 

there were no signs of excessive horizontal stress in the 

roof of the workings. Signs of stress relaxation were rather 

observed, manifested by the presence of open joints in the 

roof and in some of the pillars. The absence of the typical 

high horizontal stress feld in this part of the mine is likely 

the result of the limestone outcropping on three sides around 

the area of collapsed workings, which provides relief from 

current day tectonic loading. Stress measurements were not 

conducted within the limestone beds at the mine. 

3 Mining Plan 

3.1 Mining Layout and Original Pillar Design 

The case study mine employed the room and pillar method 

which is well suited for extracting fat lying deposits. The 

method recovers the resource in open stopes or rooms, and 

pillars are left to support the overlying strata. The rooms 

and pillars are normally arranged in regular patterns and 

are equal in size. The aim is to leave the smallest possible 

pillars to maximize the extraction (Hamrin 2001). When the 

resource being mined has large vertical height, mining is 

conducted in horizontal lifts by extracting the foor between 

the pillars, known as bench mining (Esterhuizen et  al. 

2007). The room-and-pillar method has the advantage that a 

Table 1 Uniaxial compressive Sample no. UCS (MPa) Tangent elastic modulus at Poisson’s ratio at 50% Specifc gravity strength (UCS) testing results of 50% of peak strength (GPa) of peak strength core samples collected from the 

case study mine 1 173.6 

2 174.4 

3 182.5 

4 186.4 

5 192.1 

Average 181.8 

38.4 0.17 2.70 

46.1 0.17 2.75 

46.6 0.04 2.63 

47.2 0.20 2.66 

51.9 0.18 2.68 

46.1 0.20 2.70 

Table 2 Rock mass 

classifcation conducted at three 

sites in the case study mine 

using the Bieniawski (1989)

rock mass rating (RMR89) 

Site no. 

1 

2 

Rock strength 

rating 

12 

12 

RQD rating 

12 

12 

Joint Spacing

rating 

11 

10 

Joint condition 

rating 

24 

27 

Ground water 

rating 

15 

15 

RMR89 

74 

76 

3 12 8 8 26 15 69 

Average 12.0 10.7 9.7 25.7 15.0 73 
A Case Study of the Collapse of Slender Pillars Afected by Through‐Going Discontinuities at...

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minimum of development is needed to recover the resource. 

Environmental impacts are also minimized because surface 

subsidence and groundwater disturbances can be minimized 

in comparison to most other mining methods (Benardos 

et al. 2001). 

The initial mining plan described in the mining permit 

called for a room-and-pillar layout with 10.7-m × 10.7-m 

square pillars and rooms that are 13.7 m wide. The limestone 

bed at the case study mine is up to 20 m thick and therefore 

mining was planned to be conducted in two lifts, frst mining 

the upper 7.0 m and followed by bench mining between the 

pillars to increase the mining height to 16.1 m. The layout 

is thought to be largely driven by mining practices at other 

mines in the area. The designed pillars, therefore, would 

have width-to-height ratios of 0.66. The maximum depth of 

cover under the mountain that overlies the limestone body is 

120 m. In the collapse area, the depth of cover ranges from 

about 30–90 m. 

Figure 5 shows the mining layout and the outline of the 

area that collapsed. A relatively regular pillar layout was 

followed starting at the portals, but as the mine progressed, 

it appears that poor ground conditions were encountered 

near the low-angle fault exposed in the highwall and underground. As a result, large blocks of ground were left intact 

with the objective to resume mining beyond the poor ground. 

During this time, bench mining was conducted in the area 

near the portals. Bench mining more than doubled the height 

of the pillars, exposing continuous angular joints that caused 

sections of the intended pillars to fall away during the blast. 

Figure 6 shows such a pillar observed around the year 2001 

(Iannacchione personal communication 2016). 

In subsequent years, portions of the benched area were 

backflled with fne crusher waste that may have provided 

some confnement to the lower half of the pillars. The backflling did not extend above the mid-height of the benched 

pillars. The area that collapsed had not been actively mined 

for approximately 15 years when the collapse occurred. Over 

the lifetime of the mine, a secondary escapeway had at times 

passed through the event area. 

4 Observations Around the Perimeter 

of the Collapsed Area 

During the inspection mine visit, it was possible to enter 

the mine through the portal at the northern extent of the 

mine, right next to the collapsed area. The mine escapeway 

was open, and it was possible to travel along the northern 

n 

Access portal 

Highwall 

Highwall 

Ven
la
on 

portal 

Main portal 

Canopy 

0 120 m 

Outline of 

collapsed area 

Depth of cover 

Bench mining 

Fig. 5 Plan view of the mine workings showing the room-and-pillar layout, the outline of the collapsed area and depth of cover contours 
G. S. Esterhuizen et al. 

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Fig. 6 Pillar impacted by large angular joints along the edge of bench 

mining showing sections of the pillar that fell away during bench 

mining (photo by A. T. Iannacchione) 

limit of the collapse and around to the southern extent of 

the collapse. It appeared that the backflling material may 

have prevented some of the benched pillars adjacent to the 

collapsed area from failing. The exact extent of backflling 

was unknown. 

4.1 Measured Pillar Dimensions 

During an inspection of the collapsed area in August 2016, 

measurements were made of the actual pillar dimensions 

around the perimeter of the collapsed area. It was found that 

the average pillar width was 9.5 m with a standard deviation 

of 1.3 m. The average room width was 14.5 with a standard deviation of 0.6 m. It was not possible to measure the 

full height of the pillars within the collapsed area; however, 

in adjacent stable areas, measurements showed the mining 

height to be 17.7 m. The average width-to-height ratio is 

therefore 0.54 with 84% extraction ratio in the room-andpillar panels. 

Figure  7 shows a pillar along the escapeway, which 

demonstrated the type of roof-to-foor jointing observed in 

this part of the mine. Note that the walkway was not bench 

mined and was, therefore, about 10 m above the foor of the 

benched area. 

Fig. 7 Pillar afected by angular jointing adjacent to the collapsed 

area 

Figure 8 shows the roof rubble that fowed between the 

pillars during the collapse. None of the collapsed pillars 

were visible, owing to the volume of roof rubble that fowed 

into the mine voids. This raised the question of whether 

the event may have simply been a roof collapse. However, 

the signifcant depth of subsidence, without signs of pillar 

humps on the surface, and the abruptness of the collapse 

rules out that the pillars may still be standing in the collapsed area. A roof collapse would be expected to be more 

progressive, taking place over an extended period of time. 

Fig. 8 Rubble from the roof collapse and a stable pillar along the 

edge of the area that collapsed 
A Case Study of the Collapse of Slender Pillars Afected by Through‐Going Discontinuities at...

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5 Analysis of Pillar Loading 

Back analysis of the pillar strength in a fat-lying collapsed 

panel is usually based on the assumption that, at the time of 

collapse, the pillar strength was equal to the imposed overburden load. In this case, the overburden depth varies from 

about 30 to 90 m, which complicates the calculation of the 

overburden loading. Also, the overburden load will vary signifcantly based on the depth. Consequently, the FLAC3D 

fnite diference program (Itasca Consulting Group 2012) 

was used to create a model of the mountain and the mine 

workings within the mountain. The model calculated vertical 

stress within the pillars which was used as an estimate of the 

actual vertical loading of the pillars. 

5.1 Model Setup 

The model material was assumed to be elastic so that the 

pre-failure stress distribution within the collapsed pillars 

could be determined. The mined-out region was discretized 

with sufcient detail to simulate the pillars and benched 

areas. The element width for modeling the mined zone was 

selected as 2.0 m, allowing each pillar to be modelled with 

fve elements across its width. Pillars were modelled to be 

10.0 m wide, and the rooms were modelled to be 14.0 m 

wide. The overlying strata were modelled using 3-m wide 

elements. The immediate roof of the mined workings consisted of about 2 m of limestone left intact to prevent breakthrough to the weaker overlying Mauch Chunk strata. This 

stifer roof layer was included in the model. Figure 9 shows 

Fig. 9 Numerical model of the mine and overlying mountain shaded by the vertical stress magnitude. The collapsed area is outlined with dashed 

lines, and the cluster of pillars with the highest average vertical stress is outlined with a dotted line 
G. S. Esterhuizen et al. 

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a cutaway view of the model in which the pillars were horizontally sliced at mid-height and with the mountain shown 

as a transparent overlay. 

The boundary conditions along the sides of the model 

were set to restrict horizontal displacement only, while the 

bottom surface was fxed in the vertical direction. The model 

loading was purely by gravity with horizontal stress only 

being generated by the Poisson efect of the rock material. 

As discussed earlier, the presence of outcropping limestone 

on three sides of the collapsed workings provides relief from 

horizontal stress associated with current tectonic loading. 

The model included the “nose” of the mountain, the collapsed workings, and a portion of the mine beyond the 

collapsed area. The shading of the model shown in Fig. 9 

depicts the resulting vertical stress distribution in the pillars 

and surroundings. 

5.2 Pillar Loading Results 

The FLAC3D-calculated vertical stress at mid-height of the 

pillars was used to calculate the average vertical stress in 

each pillar. The average vertical stress of the individual pillars within the collapsed area varied from the maximum of 

11.7 MPa down to 5.3 MPa for the pillars under the shallowest cover. A simple tributary area pillar stress calculation, based on a depth of cover of 90 m and 84% extraction, 

results in an average predicted pillar stress of 13.3 MPa. This 

slightly higher stress is expected because it assumes a fat 

ground surface, while the FLAC3D model accurately models 

the efect of the sloping topography. 

The model stress results showed that there was a cluster 

of fve pillars near the edge of the collapsed area, under the 

ridge of the mountain that had the greatest vertical stress. 

The calculated average vertical stress in each of these pillars varied from 10.0 to 11.7 MPa, with an average value 

of 11.0 MPa for the fve pillars combined. It was assumed 

that the collapse initiated when one or more of these pillars 

failed. 

6 Analysis of Pillar Strength 

The strength of a pillar in mining applications is usually 

defned as the peak load bearing capacity of the pillars 

(Brady and Brown 2006). In the case study mine, the average vertical stress 11.0 MPa in the cluster of fve pillars represents the best estimate of the actual strength of the pillars. 

This pillar strength is only 6% of the intact rock strength as 

tested in the laboratory. Knowledge of the actual strength 

of the pillars provides an opportunity to determine whether 

some of the widely used empirical hard-rock pillar strength 

equations would have provided reasonable estimates of the 

pillar strength. 

6.1 Comparison of Actual Pillar Strength 

to Empirical Hard‐Rock Pillar Strength 

Equations 

Empirical pillar strength equations are developed from retrospective analysis of actual stable and failed pillar case histories are commonly used to design pillars in mines (Martin 

and Maybee 2000). Three of the more widely used empirical 

equations for hard rock mines were selected to calculate the 

strength of the collapsed pillars at the case study mine. The 

results were compared to the 11.0 MPa pillar strength determined above. The following three hard rock pillar strength 

equations were selected for the comparison.The Hedley and 

Grant (1972) equation: 

0.5 w S = k . (1) h0.75 

The Krauland and Soder (1987) equation for limestone 

pillars: 

 ̃  ̃ °° w S = k 0.778 + 0.222 . (2) h 

The Lunder and Pakalnis (1997) equation: 

S = 0.44 ̃ c (0.68 + 0.52°). (3)

In these equations, k is the large-scale rock strength, w 

is the pillar width, h is the pillar height, σc is the uniaxial 

compressive strength of the intact rock, and κ is a confnement parameter. The pillar strengths for 17.7-m-high pillars 

of various widths were calculated using each equation and 

are shown in Fig. 10. For the Hedley and Grant equation, 

the strength factor relating the large-scale rock strength to 

the laboratory-scale UCS is 0.58, and for the Krauland and 

Soder equation the strength factor is 0.354. The calculated 

11.0 MPa pillar strength from this case study is also shown 

in Fig. 10. It is clear that the empirically based strength 

equations would have grossly overestimated the actual pillar strength and would have predicted stable conditions at 

the mine. 

The reason for the discrepancy between the empirical 

equations and the actual pillar strength at the case study 

mine is ascribed to the presence of large angular discontinuities cutting through the slender pillars. It appears that 

the case studies that were used to develop the empirical 

equations did not include any cases of such slender pillars with large through-going discontinuities. The impact 

of large through-going discontinuities is also not explicitly 

included as an input parameter in the selected pillar strength 

equations. 
A Case Study of the Collapse of Slender Pillars Afected by Through‐Going Discontinuities at...

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Pillar strength (MPa) 120.0 

110.0 

100.0 

90.0 

80.0 

70.0 

60.0 

50.0 

40.0 

30.0 

20.0 

10.0 

0.0 

0.00 0.50 1.00 1.50 2.00 2.50 3.00 

Hedley & G 

Lunder & Pakalnis 

rant 

Krauland & Soder 

Calculated pillar stren 

d area 

gth 

in collapse 

Width to height ra ̃o 

Fig. 10 Calculated pillar strength in the collapsed area compared to 

predictions using established hard-rock pillar strength equations 

6.2 Accounting for Large Discontinuities 

The potential importance of large through-going discontinuities on the strength of slender pillars was recognized during previous NIOSH research into US limestone mine pillar 

strength (Esterhuizen et al. 2006; Esterhuizen et al. 2011). 

Large through-going discontinuities can be defned as planar 

or semi-planar structures with visible trace lengths greater 

than 50% of the pillar height. They are typically persistent 

joints that extend through the pillar or extend from the roof 

to the foor of a pillar. 

During this research, several single pillar failures associated with large through-going discontinuities were observed 

in otherwise stable workings, but no wide area collapses had 

occurred that would allow back analysis of average pillar 

loading and average pillar strength. Simple two-dimensional 

models of pillars were used, therefore, to investigate the 

potential impact of large through-going discontinuities on 

pillar strength. The UDEC (Itasca Consulting Group 2004) 

discrete element stress analysis software was used to simulate numerous pillar and discontinuity confgurations. The 

model input parameters were selected to correctly simulate 

the stability of actual pillars with large through-going discontinuities that had not failed. 

It was found that the impact of such large through-going 

discontinuities diminished as the pillar width-to-height ratio 

increased. Tall, slender pillars were shown to be signifcantly 

impacted, while wider pillars at width-to-height ratios 

exceeding 1.2 showed reduced impact. Discontinuity dips 

of around 60° were found to have the most signifcant impact 

on pillar strength. 

Since the established hard-rock pillar strength equations 

did not explicitly account for the presence of large angular discontinuities, a new design equation for US limestone 

mines was developed specifcally to address this need. The 

empirical basis for the limestone pillar strength equation 

was decades of observations of failed and stable pillars by 

Roberts et al. (2007) in the Missouri lead belt mines. The 

impact of large discontinuities was introduced as an explicit 

parameter that accounts for both the frequency and inclination of any large through-going discontinuities, based on 

the numerical modeling results and feld observations. The 

procedures followed in developing the limestone mine pillar strength equation, together with feld data and numerical 

model results are fully described in Esterhuizen et al. (2011). 

The equation takes the following form: 

0.30 w S = 0.65 × UCS × LDF × , (4) h0.59 

where UCS is the uniaxial compressive strength of the intact 

rock, LDF is a factor to account for the presence of large 

discontinuities, and w and h are the pillar width and height 

in meters. The large discontinuity factor accounts for the dip 

and frequency of the discontinuities as follows: 

LDF = 1 − DDF × FF, (5) 

where DDF is the discontinuity dip factor shown in Table 3 

and FF is the frequency factor related to the frequency of 

large discontinuities per pillar shown in Table 4. 

The DDF was developed from the results of numerical 

model analyses in which single discontinuities at variable 

dips were modeled in pillars with variable width-to-height 

ratios. The discontinuities were modeled with 30° friction 

angle and nominal cohesion of 100–300 kPa to account for 

joint surface roughness. 

The FF accounts for the number of discontinuities within 

the pillar, again based on numerical model results in which 

the number and location of discontinuities within pillars of 

diferent width-to-height ratios were evaluated. The impact 

of these discontinuities on the pillar strength was determined 

from the numerical model results to produce the FF values in 

Table 4, as described in Esterhuizen et al. (2011). 

To simplify the calculation of pillar loads, pillar strength, 

and the impact of large angular discontinuities, a small 

software package named S-Pillar (NIOSH 2018) has been 

developed. The S-Pillar software is now used as a basis 

for designing pillars in the United States limestone mining 

industry. 
G. S. Esterhuizen et al. 

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Table 3 The discontinuity dip

factor (DDF) representing the 

strength reduction caused by a 

single discontinuity intersecting 

a pillar at or near its center, 

used in Eq. (5) (Esterhuizen 

et al. 2011) 

Dip (°) 

30 

40 

50 

Pillar width-to-height ratio 

≤ 0.5 0.6 0.7 

0.15 0.15 0.15 

0.23 0.26 0.27 

0.61 0.65 0.61 

0.8 

0.15 

0.27 

0.53 

0.9 

0.16 

0.25 

0.44 

1.0 

0.16 

0.24 

0.37 

1.1 

0.16 

0.23 

0.33 

1.2 

0.16 

0.23 

0.30 

> 1.2 

0.16 

0.22 

0.28 

60 0.94 0.86 0.72 0.56 0.43 0.34 0.29 0.26 0.24 

70 0.83 0.68 0.52 0.39 0.30 0.24 0.21 0.20 0.18 

80 0.53 0.41 0.31 0.25 0.20 0.18 0.17 0.16 0.16 

90 0.31 0.25 0.21 0.18 0.17 0.16 0.16 0.15 0.15 

Table 4 The frequency factor (FF) used in Eq. (5) to account for the 120.0 

spacing of large discontinuities (Esterhuizen et al. 2011) 

110.0 

Average frequency of large discontinuities per pillar Frequency 

factor (FF) 100.0 

0.0 0.00 90.0 

0.1 0.10 

0.2 0.18 80.0 

0.3 0.26 

No large discon ̃nui ̃es 

Discon ̃nui ̃es at 5.0 m spacing and 80° dip 

Discon ̃nui ̃es at 4.0 m spacing and 70° dip 

Discon ̃nui ̃es at 2.0 m spacing and 60° dip 

Actual pillar strength 

collapsed area 

in 

0.5 0.39 

1.0 0.63 

2.0 0.86 

3.0 0.95 

Pillar strength (Mpa) 

70.0 

60.0 

50.0 

> 3.0 1.00 

40.0 

30.0 

6.3 Application of the Limestone Mine Pillar 

Strength Equation 20.0 

10.0 

The pillar strength equation for limestone mines (Eq. 4) 

was used to calculate the strength of the collapsed pillars 

at the case study mine and the results were compared to the 

11.0 MPa pillar strength determined above. Based on the 

available geotechnical data, the following input values and 

ranges of values were used in the calculation: 

UCS of intact rock = 182 MPa. 

Dip of large discontinuities = 50°–80°. 

Spacing of large discontinuities = 2–5 m. 

Pillar width = 9.5 m. 

Pillar height = 17.7 m. 

The range of pillar strengths predicted by the equation 

varied between a minimum of 3.9 MPa for the most unfavorable combination of parameters to 25.3 MPa for the 

most favorable combination. The range of results obtained 

is shown in Fig. 11. The indicated range of strengths was 

determined by varying only the large discontinuity spacing 

and dip. The equation predicts minimum strength when the 

discontinuity dip is 60°. The upper solid curve is obtained 

by selecting the maximum discontinuity spacing of 5.0 m 

0.0 

0.0 0.5 1.0 1.5 2.0 2.5 

Width to height ratio 

Fig. 11 Graph showing the likely range of pillar strengths for different width-to-height ratios at the case study mine calculated using 

Eq. (4). The range of likely pillar strengths is shaded and the actual 

strength of 11.0 MPa of the collapsed pillars is indicated on the graph 

and a dip of 80°. The fgure also shows the pillar strength 

curve predicted by Eq. (4) in the absence of any large 

discontinuities. 

The results show that Eq. (4) predicts a signifcant drop in 

pillar strength at the lower width-to-height ratios. Also, the 

range of likely strengths based on the variability of the large 

discontinuity geometry brackets the actual pillar strength of 

11.0 MPa. If the average dip and spacing of the most prominent joint set is used as input, at 70° and 4.0 m, respectively, 

the equation predicts a pillar strength of 12.9 MPa, clearly 

indicating the potentially critical loading condition of these 

pillars. By comparison, the Krauland and Soder (1987) pillar 

strength equation developed for limestone pillars predicts a 

3.0 
A Case Study of the Collapse of Slender Pillars Afected by Through‐Going Discontinuities at...

1 3

 

 

 

 

  

 

strength of 57.8 MPa for these pillars, while Eq. (4) predicts 

a strength of 42.8 MPa in the absence of any large throughgoing discontinuities. 

7 Discussion 

The unfortunate events at the case study mine have demonstrated the need to include additional geotechnical 

parameters in the pillar design equations that are used by 

the mining industry to design pillars for room and pillar 

mines. The established pillar strength equations essentially 

only consider the UCS of the rock and the shape of the pillars, while the discontinuity characteristics and other rock 

mass-related parameters are excluded. The results of this 

case study clearly demonstrate the need to explicitly account 

for the presence of large through-going discontinuities in the 

estimation of pillar strength. Ignoring these discontinuities 

using established pillar strength equations would grossly 

overestimate the pillar strength. 

The established empirical pillar strength equations that 

are widely used for pillar design in room-and-pillar mines do 

not appear to adequately account for the weakening efect of 

discontinuities on pillar strength when the width-to-height 

ratio falls below a value of 1.0. This may be accredited to the 

limited number of low width-to-height ratio cases included 

in the empirical databases used for developing the equations. 

This case study clearly demonstrates how, for example, the 

Krauland and Soder (1987) empirical pillar strength equation for limestone predicts a strength of 57.8 MPa for the 

pillars at the case study mine, while they collapsed at a load 

of only 11.0 MPa. 

During the NIOSH survey of limestone mine stability in 

the United States, numerous single failed pillars that contained through-going discontinuities were observed (Esterhuizen et al. 2006). Analysis of these pillars using established hard-rock pillar strength equations overestimated 

the strength of these pillars. This led to the realization that 

such through-going discontinuities needed to be explicitly 

accounted for in pillar design. The NIOSH-developed pillar 

strength equation (Eq. 4) made use of feld observations and 

numerical model analysis to develop a relatively simple pillar strength equation that explicitly accounts for the presence 

of large through-going discontinuities. The NIOSH-developed equation predicts the pillar strength in the collapsed 

area of the mine as 12.9 MPa when using the ‘average’ spacing and inclination of the through-going discontinuities, 

while the lower limit of the pillar strength is estimated as 

3.9 MPa. This result clearly indicates the critical condition 

of the pillars in question. 

The need to incorporate the rock mass strength rather 

than just the UCS of the rock in pillar design has been recognized by the rock engineering community. Hoek and Brown 

(1980) suggested combining numerical model analysis with 

rock mass strength parameters to estimate the strength of pillars. Martin and Maybee (2000) also made use of numerical 

models to investigate pillar strength in strong rock. More 

recently, the impact of discrete discontinuities on pillar 

strength has received increased attention. For example, Elmo 

and Stead (2010) have used discrete element models to investigate rock mass characteristics and discrete joints on pillar 

strength, while Oke and Esterhuizen (2017) used a more 

pragmatic approach to account for both rock mass strength 

and the impact of discontinuity dip. These approaches are 

likely to further contribute to improved estimates of pillar 

strength, especially in the low width-to-height ratio ranges 

encountered in shallow underground room-and-pillar mines. 

8 Conclusions 

A case study has been presented in which tall, slender pillars collapsed causing an air blast at a limestone mine in 

southwestern Pennsylvania. The pillars were about 17 m tall 

and 9.5 m wide. The collapsed pillars were evaluated using a 

three-dimensional numerical model to estimate the loading 

on the pillars. Using these results, it was demonstrated that 

widely used pillar strength equations for hard-rock mines 

would have signifcantly overestimated the strength of the 

collapsed pillars. It was concluded that large angular discontinuities within the pillars contributed to the collapse. 

The NIOSH-developed pillar strength equation (Esterhuizen 

et al. 2011) with an explicit parameter to account for the 

presence of such through-going discontinuities was shown 

to be able to satisfactorily capture the reduced strength of 

the pillars. Pillar design engineers need to be aware of the 

potential to overestimate the strength of slender pillars that 

are afected by large angular discontinuities. 

Acknowledgements The case study presented in this paper was conducted as part of the mission of NIOSH and MSHA to improve the

safety of mineworkers. The authors wish to acknowledge the cooperation of the mining company in providing safe access to the mine

after the collapse event and providing relevant geologic data and mine

maps for the analysis. The thoughtful suggestions and comments of the

reviewers, as well as their commitment to the rock engineering discipline, are acknowledged with thanks. This paper was published in an

abbreviated form in the proceedings of the 52nd US Rock Mechanics

Symposium, Seattle, Washington, USA, 17–20 June 2018, as paper

no. 18-363. 

Compliance with Ethical Standards 

Conflict of interest The authors declare that they have no confict of 

interest. 
G. S. Esterhuizen et al. 

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References 

ASTM D2938-95 (2002) Standard test method for unconfned compressive strength of intact rock core specimens. ASTM International,

West Conshohocken, CA, 1995 

Benardos AG, Kaliampakos DC, Prousiotis JG, Mavrikos AA,

Skoparantzos KA (2001) Underground aggregate mining in Athens: a promising investment plan. Tunn Undergr Space Technol

16(4):323–329

Bieniawski ZT (1989) Engineering rock mass classifcations. Wiley,

New York 

Brady BHG, Brown ET (2006) Rock mechanics for underground mining. Springer, Dordrecht

Dolinar D (2003) Variation of horizontal stresses and strains in mines

in bedded deposits in the eastern and midwestern United States.

In: Proceedings 22nd international conference on ground control

in mining, 6–7 August 2003, Morgantown, USA, pp 178–185

Edmunds WE, Berg TM, Sevon WD, Piotrowski RC, Heyman L, Rickard RV (1979) The Mississippian and Pennsylvanian (Carboniferous) systems in the United States. USGS professional paper 

1110-A-L 

Elmo D, Stead D (2010) An integrated numerical modelling discrete

fracture network approach applied to the characterization of rock

mass strength of naturally fractured pillars. Rock Mech Rock Eng

43:3–19 

Esterhuizen GS, Iannacchione AT, Ellenberger JL, Dolinar DR (2006)

Pillar stability issues based on a survey of pillar performance in

underground limestone mines. In: 25th international conference

on ground control in mining, Morgantown, WV, pp 354–361

Esterhuizen GS, Dolinar DR, Ellenberger JL (2007) Observations

and evaluation of foor benching efects on pillar stability in US

limestone mines. In: 1st Canada–US rock mechanics symposium,

American Rock Mechanics Association, Vancouver, BC, Canada, 

27–31 May

Esterhuizen GS, Dolinar DR, Ellenberger JL (2011) Pillar strength in

underground stone mines in the United States. Int J Rock Mech

Min Sci 48(1):42–50

Gillespie P, Kampfer G (2017) Mechanical constraints on kink band

and thrust development in the Appalachian plateau, USA, vol 458.

Geological Society, London, pp 245–256 (Special Publication) 

Hamrin H (2001) Underground mining methods and applications.

Underground mining methods: engineering fundamentals and

international case studies. In: Hustrulid WA, Bullock RL (eds)

Society for Mining, Metallurgy, and Exploration, Inc., Littleton,

Colorado, USA, pp 3–14

Hatcher RD, Thomas WA, Viele GW (eds) (1989) The AppalachianOuachita Orogen in the United States, vol F-2. Geological Society

of America, Boulder, Colorado, p 275

Hedley DGF, Grant F (1972) Stope-and-pillar design for the Elliot Lake

uranium mines. Bull Can Inst Min Metall 65:37–44 

Hoek E, Brown ET (1980) Underground excavations in rock. England, 

Institute of Mining and Metallurgy, London, p 200

Iannacchione AT, Coyle PR (2002) An examination of the Loyalhanna

limestone’s structural features and their impact on mining and

ground control practices. In: Peng SS, Mark C, Khair AW, Heasley

KA (eds) 21st international conference on ground control in mining, August 6–8, 2002, Morgantown, WV, pp 218–227

Iannacchione AT, Dolinar DR, Mucho TP (2002) High stress mining

under shallow overburden in underground U.S. stone mines. In: 

First international seminar on deep and high stress mining, section 32. Australian Center for Geomechanics, Nedlands, Australia, 

11 pp

Itasca Consulting Group (2004) Software: Universal distinct element

code (UDEC) version 4.0, Minneapolis, Minnesota

Itasca Consulting Group (2012) Software: Fast Lagrangian analysis of

continua in 3 dimensions (FLAC3D) Version 5.01, Minneapolis,

Minnesota 

Kerrigan R (2016) Structural geology of the southwestern section of

the Appalachian Plateau: energy and environments: geology in the

‘Nether World’ of Indiana County, Pennsylvania. In: Guidebook

for the 81st annual feld conference of Pennsylvania Geologists,

Indiana, Pennsylvania, Editors: Robin Anthony, pp 3–10

Krauland N, Soder PE (1987) Determining pillar strength from pillar

failure observations. Eng Min J 8:34–40

Lunder PJ, Pakalnis R (1997) Determination of the strength of hardrock mine pillars. Bull Can Inst Min Metall 90:51–55

Mark C, Gadde M (2008) Global trends in coal mine horizontal stress

measurements. In: Proceedings 27th international conference on

ground control in mining, WV University, Morgantown, USA,

pp 319–331

Martin CD, Maybee WG (2000) The strength of hard-rock pillars. Int

J Rock Mech Min Sci 37(8):1239–1246

Mount VS (2014) Structural style of the Appalachian Plateau fold belt, 

north-central Pennsylvania. J Struct Geol 69:284–303

Nickelsen RP, Hough VND (1967) Jointing in the Appalachian plateau

of Pennsylvania. Geol Soc Am Bull 78(5):609–630

NIOSH (2018) Mining product: S-pillar—software for stone mine pillar design. National Institute for Occupational Safety and Health.

https://www.cdc.gov/niosh/mining/works/coversheet1817.html. 

Accessed 16 Oct 2018 

Oke J, Esterhuizen GS (2017) Improving hard rock pillar design by

including rock mass classifcation and failure mechanisms. In:

51st US rock mechanics/geomechanics symposium, San Francisco, California, 25–28 June 

Roberts D, Tolfree D, McIntyre H (2007) Using confnement as a

means to estimate pillar strength in a room and pillar mine. In:

1st Canada–US rock mechanics symposium, American Rock

Mechanics Association, Vancouver, BC, Canada, 27–31 May, pp

1455–1461 

Rodgers J (1970) The tectonics of the Appalachians. Wiley, New York

Sak PB, McQuarrie N, Oliver BP, Lavdovsky N, Jackson MS (2012)

Unraveling the central Appalachian fold-thrust belt, Pennsylvania:

the power of sequentially restored balanced cross section for a 

blind fold–thrust belt. Geosphere 8(3):685–702

Trapp H Jr, Horn MA (1997) Ground water atlas of the United States—

delaware, Maryland, New Jersey, North Carolina, Pennsylvania,

Virginia, West Virginia. USGS Hydrologic Atlas 730-L

Zoback ML (1992) First- and second-order patterns of stress in 

the lithosphere: the world stress map project. J Geophys Res

97(11):703–711 

Publisher’s Note Springer Nature remains neutral with regard to 

jurisdictional claims in published maps and institutional afliations.