Pillar and roof Span Design in Stone Mines

Gabriel S. Esterhuizen

NIOSH, Pittsburgh, Pennsylvania, United States

Dennis r. Dolinar

NIOSH, Pittsburgh, Pennsylvania, United States

John L. Ellenberger

NIOSH, Pittsburgh, Pennsylvania, United States

Underground limestone mines in the United States 

use the room-and-pillar method to extract limestone 

formations that are generally flat lying. Pillar stability is one of the prerequisites for safe working conditions in a room-and-pillar mine. Unstable pillars can 

result in rock sloughing from the pillar ribs and can 

lead to the collapse of the roof if one or more pillars should fail. In addition, the roof span between 

pillars should be stable to provide safe access to the 

working face. Falls of ground from unstable roof and 

pillar ribs account for about 15% of all lost working 

days in underground limestone mines (Mine Safety 

and Health Administration 2009). In the past, pillar and roof span dimensions were largely based on 

experience at nearby mines, developed through trial 

and error or designed by rock engineering specialists. 

This paper presents the results of research carried 

out by the National Institute for Occupational Safety 

and Health (NIOSH) in cooperation with participating underground stone mines to develop guidelines 

for designing stable pillars and roof spans in stone 

mines. The research is based on the observation of 

failed and stable pillars and roof spans at 34 operating stone mines supplemented by laboratory testing 

and monitoring of rock mass response.

StonE PiLLar DESiGn

In a room-and-pillar mine, the pillars are required 

to provide global stability which can be defined as 

providing support to the overlying strata up to the 

ground surface. In addition, local stability, which is 

defined as stable ribs and roof spans between the pillars, is required to provide safe working conditions. 

Pillar design typically estimates the pillar strength 

and the pillar stress, and then sizes the pillars so that 

an adequate margin exists between the expected pillar strength and stress. The factor of safety (FOS) 

relates the average pillar strength (S) to the average 

pillar stress (σp), as follows:

FOS = S

σ p

(1)

When designing a system of pillars, the FOS is critical to stability, because it must compensate for the 

variability and uncertainty related to pillar strength 

and stress and varying dimensions of rooms and pillars. The selection of an appropriate safety factor can 

be based on a subjective assessment of pillar performance or statistical analysis of failed and stable cases 

(Salamon and Munro, 1967; Mark, 1999; Salamon et 

al., 2006). As the FOS decreases, the probability of 

failure of the pillars can be expected to increase. In 

practical terms, if one or more pillars are observed to 

be failed in a layout, it is an indication that the pillar 

stress is approaching the average pillar strength. The 

relationship between FOS and failure probability, 

however, depends on the uncertainty and variability 

of the system under consideration (Harr, 1987).
PiLLar StaBiLity iSSuES in StonE MinES

A survey of stable and unstable pillars in underground stone mines within the Eastern and 

Midwestern United States identified the causes of 

pillar instability to provide data for estimating pillar 

strength (Esterhuizen et al., 2006). Mines that were 

likely to have unstable pillars owing to their depth of 

working or size of pillars were identified as targets 

for the survey. Data were collected that included both 

the intended design dimensions and the actual pillar 

and room dimensions in the underground workings. 

In older areas of mines, where the original design 

dimensions were unknown, the measured dimensions were assumed to adequately represent the 

design. The approximate number of pillars in each 

layout was recorded to the nearest order of magnitude and the depth of cover determined from surface 

topography and mine maps. The Lamodel software 

package (Heasley and Agioutantis, 2001) was used 

to estimate of the average pillar stress in cases where 

the tributary area method was considered inappropriate. Data from one abandoned limestone mine, which 

was not observed as part of this study, was added 

to the records owing to its great depth and reported 

stable conditions (Bauer and Lee, 2004).

At each mine rock samples were collected to 

determine the uniaxial compressive strength (UCS) 

and the rock mass was classified using the Rock Mass 

Rating (RMR) system (Bieniawski, 1989; Hoek et 

al., 1995). The UCS results were grouped into three 

categories based on the average strength obtained at 

the individual mine sites and are shown in Table 1. 

Average Range Samples 

Group MPa (psi) MPa (psi) tested Representative limestone formations

Lower Strength 88 44–144 50 Burlington, Salem, Galena-Plattesville

(12,800) (6,400–20,800)

Medium Strength 135 82–207 100 Camp Nelson, Monteagle, Plattin, Vanport, Upper 

(19,600) (11,900–30,000) Newman, Chickamauga

High Strength 220 152–301 32 Loyalhanna, Tyrone

(31,800) (22,000–43,700)

Dimension Average Minimum Maximum

Pillar width, m (ft) 13.1 (43.0) 4.6 (15.0) 21.5 (70.5)

Pillar height, m (ft) 11.1 (36.5) 4.8 (15.8) 40.0 (124.6)

Width-to-height ratio 1.41 0.29 3.52

Cover depth, m (ft) 117 (385) 22.9 (75) 670 (2,200)

The survey further showed that the following 

factors can contribute to pillar failure or instability:

• Large angular discontinuities that typically 

extend from roof-to-floor in a pillar. Sliding 

can occur along these discontinuities which 

can significantly weaken these slender pillars 

(Esterhuizen, 2006). Of the 18 unstable pillars 

observed, seven were affected by these large 

angular discontinuities. Figure 1 shows a pillar 

that is weakened by two angular discontinuities 

that contributed to failure of the pillar at a relatively low pillar stress.

• Weak bands within pillars that can extrude 

resulting in progressive spalling of the pillar ribs (Esterhuizen and Ellenberger, 2007). 

Figure 2 shows a pillar that has been severely 

compromised by this mechanism of failure. It 
appears that moisture on the weak beds was a 

contributing factor in this failure. Other pillars 

in the immediate surrounding area were unaffected, while a number of other pillars at this 

mine appeared to have been affected in the 

same manner.

figure 1. Partially benched pillar that failed 

along two angular discontinuities. Width-toheight ratio is 0.58 based on full benching height 

and average pillar stress is about 4% of the uCS.

figure 2. Pillar that had an original width to 

height ratio of 1.7 failed by progressive spalling. 

thin weak beds are thought to have contributed 

to the failure. average pillar stress is about 11% 

of the uCS.

High pillar stress caused by deep cover or high 

extraction ratios can cause spalling of the pillar 

ribs (Lane et al., 1999; Krauland and Soder, 1987; 

Lunder, 1994; Pritchard and Hedley, 1993). It was 

found that spalling can initiate when the average pillar stress exceeds about 10% of the uniaxial compressive strength of the pillar material. Pillars tend 

to take on an hourglass shape when spalling initiates. Figure 3 shows a pillar that has failed and taken 

an hourglass shape due to rib spalling. Figure 4 is 

a series of pillars at one of the deeper stone mines 

showing the effects of minor rib spalling. 

The observed unstable pillars were typically 

surrounded by pillars that appeared to be stable, 

showing minimal signs of disturbance. Therefore, 

the failed pillars represented a very small percentage 

(typically less than 1%) of the total number of pillars 

at any particular mine. The observations lead to the 

conclusion that the failed pillars represent the low 

end of the distribution of possible pillar strengths, 

and not the average pillar strength. As a result, the 

average safety factor of the layouts containing the 

failed pillars can be expected to be substantially 

higher than that of the failed pillars.

PiLLar StrESS anD StrEnGtH 

EStiMation

The stability of a pillar can be evaluated by comparing the average stress in the pillar to its strength. The 

average stress in pillars that are of similar size and 

are located in a regular pattern can be estimated with 

relative ease using the tributary area method. The 

overburden weight is simply assumed to be evenly 

distributed among all the pillars. The average pillar 

stress (σp) is calculated as follows:

σ p = γ × h × (C1 × C2 )

(w× l) (2)

Where γ is the specific weight of the overlying rocks, 

h is the depth of cover, w is the pillar width, l is the 

pillar length and C1 and C2 are the heading and crosscut center distances respectively. This provides an 

upper limit of the pillar stress and does not consider 

the presence of barrier pillars or solid abutments that 

can reduce the average pillar stress. In conditions 

where the tributary area method is not valid such as 

irregular pillars, limited extent of mining or variable 

depth of cover, numerical models such as Lamodel 

(Heasley and Agioutantis 2001) can be used to estimate the average pillar stress.
figure 3. Partially benched pillar failing under 

elevated stresses at the edge of bench mining. 

typical hourglass formation indicating overloaded pillar. 

figure 4. Stable pillars in a limestone mine at a 

depth of cover of 275m (900 ft). Slightly concave 

pillar ribs formed as a result of minor spalling of 

the hard, brittle rock.

Estimating pillar strength is more difficult and 

has been the subject of much research in the mining industry (Hustrulid, 1976). Owing to the complexity of pillar mechanics, empirically based pillar 

strength equations, that are based on the observation of failed and stable pillar systems, have found 

wide acceptance (Mark, 1999). A similar approach 

was followed to develop a pillar strength equation 

for underground stone mines. Very few pillar failures 

have occurred in stone mines, therefore the observations alone were inadequate to develop a stone 

pillar strength equation from the field data. A pillar 

strength relationship that was originally developed 

by Roberts et al. (2007) was used as a starting point. 

Their pillar strength relationship was based on the 

observation of a large number of collapsed and stable 

pillars in Missouri Lead Belt mines where the lead 

mineralization is hosted in dolomitic limestone rocks 

(Lane et al., 1999). The rock conditions and mining 

dimensions are similar to those found in stone mines. 

This relationship was expressed as a power equation 

incorporating the UCS of the rock, the pillar width 

and pillar height and was modified to account for 

the potential impact of large angular discontinuities (Esterhuizen et al., 2008). The final equation is 

expressed in the following form:

S = 0.92 ×UCS × LDF × w0.30

h0.59 (3)

where UCS is the uniaxial compressive strength of 

the intact rock, LDF is a factor to account for large 

angular discontinuities and w and h are the pillar 

width and height in feet (when using dimensions 

in meters the 0.92 factor becomes 0.65). If no large 

discontinuities are present the LDF will equal 1.0, in 

other cases, the value of the LDF can be calculated 

using the following equation:

LDF = 1− DDF × FF (4)

where DDF is the discontinuity dip factor shown in 

Table 3, and FF is a frequency factor related to the 

frequency of large discontinuities per pillar as shown 

in Table 4. 

rECtanGuLar PiLLarS

Rectangular pillars are used in stone mines to provide ventilation control and to assist with roof 

control. Rectangular pillars can be expected to 

be stronger than square pillars of the same width. 

Strength adjustments to account for the increased 

strength of rectangular pillars have been suggested 

by several researchers (Galvin et al., 1999; Wagner, 

1992; Mark and Chase, 1997). A numerical model 

study that simulated brittle rock failure in limestone 

pillars (Dolinar and Esterhuizen 2007), indicated that 

slender pillars are not expected to benefit as much 

from a length increase as wider pillars because of a 

lack of confinement. The numerical model results 
indicate that the benefit of an increased length is 

likely to be zero when a pillar has a width-to-height 

ratio of 0.5 and it gradually increases to a maximum 

as the width-to-height ratio approaches 1.4. 

The so called “equivalent-width method,” proposed by Wagner (1992) was selected as a basis for 

calculating the length benefit of rectangular pillars 

in limestone mines. According to this method, the 

length benefit is expressed as an equivalent increase 

in pillar width, which then replaces the true pillar 

width in the pillar strength equation. A modification is made, called the length benefit ratio (LBR), 

which is a factor that increases from zero to 1.0 as the 

width-to-height ratio increases from 0.5 to 1.4. The 

modified form of Wagner’s equivalent-width equation is proposed as follows:

table 3. Discontinuity dip factor (DDf) representing the strength reduction caused by a single 

discontinuity intersecting a pillar at or near its center, used in equation 4

Discontinuity dip 

(deg)

Pillar width-to-height ratio

≤0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 >1.2

30 0.15 0.15 0.15 0.15 0.16 0.16 0.16 0.16 0.16

40 0.23 0.26 0.27 0.27 0.25 0.24 0.23 0.23 0.22

50 0.61 0.65 0.61 0.53 0.44 0.37 0.33 0.30 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

Average frequency of large 

discontinuities per pillar 0.0 0.1 0.2 0.3 0.5 1.0 2.0 3.0 >3.0

Frequency factor (FF) 0.00 0.10 0.18 0.26 0.39 0.63 0.86 0.95 1.00

Width-to-height ratio 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

Length benefit ratio (LBR) 0.00 0.06 0.22 0.50 0.76 0.89 0.96 0.98 0.99 1.00

PiLLar faCtor of SafEty 

ConSiDErationS

Equations 1 to 5 were used to calculate the strength 

and FOS of all the pillars that were recorded in the 

field studies. The results are presented in Figure 5, 

which displays the FOS against the width-to-height 

ratio. Various symbols were used to indicate currently operating and abandoned layouts, failed pillars 

and the approximate number of pillars in the various 

layouts. Abandoned layouts may have been because 

of stability concerns or changes in operating procedures. The axis displaying the FOS was cut-off at 

10.0 causing thirteen cases with FOS values greater 

than 10.0 not to be displayed. 

The results show that the calculated average 

FOS of all the failed pillars is 2.0, which includes 

the cases that were intersected by large angular discontinuities. The average FOS of those pillars that 

are intersected by large discontinuities is 1.5. The 

minimum FOS for the stable layouts is 1.27 which 

is one of the disused layouts. It can also be seen that 

only one of the current pillar layouts has a FOS of 

between 1.0 and 1.8. 

Based on current experience it would appear 

that almost all the stable pillar layouts have FOS 

values of greater than 1.8. Layouts that approach the 

FOS=1.8 line, in Figure 5 are typically deep layouts 

(> 180m (600 ft)) and are subject to relatively high 
average pillar stresses where rib spalling can become 

an issue. Therefore, it would be prudent to design pillars that have safety factors of at least 1.8 to remain 

within the range of known successful layouts. 

PiLLar WiDtH-to-HEiGHt ratio 

ConSiDErationS

Figure 5 shows that there has been a natural tendency 

for mines to avoid slender pillars.

Tens of pillars

Hundreds of pillars

>Thousand pillars

Current pillar layouts

Tens of pillars

Hundreds of pillars

>Thousand pillars

Disused pillar layouts Failed pillars

Failed pillar intersected by 

large angular discontinuity

Failed pillar (not disturbed by 

large angular discontinuity)

Tens of pillars

Hundreds of pillars

>Thousand pillars

Current pillar layouts

Tens of pillars

Hundreds of pillars

>Thousand pillars

Disused pillar layouts Failed pillars

Failed pillar intersected by 

large angular discontinuity

Failed pillar (not disturbed by 

large angular discontinuity)

Width-to-height ratio

Factor of Safety

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Width-to-height ratio = 0.8

Factor of safety = 1.8

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Width-to-height ratio = 0.8

Factor of safety = 1.8

Abandoned pillar layouts 

figure 5. Chart showing the factor of safety against width-to-height ratio using Equation 3. Current 

abandoned pillar layouts are shown as well as single failed pillars. the recommended area for pillar 

design is shaded.

 Nine of the layouts 

that had width-to-height ratios of less than 0.8 are 

no longer in use for various reasons, while only four 

mines are currently operating with these slender pillars. In addition, this study and other investigations 

have shown that slender pillars are more severely 

affected by the presence of discontinuities than 

wider pillars (Esterhuizen, 2000 and 2006). Studies 

have also shown that as the width-to-height ratio 

decreases below 0.8, the confining stresses within a 

pillar approach zero and brittle fracturing can occur 

throughout the unconfined pillar core (Lunder, 1994; 

Martin and Maybee, 2000; Esterhuizen, 2006). The 

confining stress can further be reduced if low friction contact surfaces exist between the pillar and the 

surrounding rock. The fracturing and spalling failure 

mechanism is poorly understood and it seems prudent to avoid designing pillars that might fail in this 

manner. 

Inspection of Figure 5 reveals that a number 

of stable layouts exist that have large safety factors 

(>3.0) and the width-to-height ratios are less than 

0.8. These layouts are mostly at very shallow depths 

of cover, typically less than 60 m (200 ft). These pillars were found to be either very narrow, as little as 

4.5 m (15 ft) wide, or very tall, up to 38 m (125 ft) 
high. The strength and loading of narrow pillars are 

both sensitive to small variations in the over-break, 

blast damage and pillar spacing. Large tall pillars, on 

the other hand, have high ribs which can represent a 

safety hazard and the roof becomes inaccessible and 

poorly visible with increased severity of potential 

rock fall impacts. The strength of these slender pillars is also more adversely impacted by the presence 

of unfavorable discontinuities than wider pillars. 

Therefore, it is not advisable to design layouts with 

such slender pillars, even if the calculated factors of 

safety are high.

PiLLar DESiGn GuiDELinES

The results shown in Figure 5 formed the basis for 

developing the design guidelines that follow. The 

guidelines are empirically based; therefore, their 

validity is restricted to rock conditions, mining 

dimensions and pillar stresses that are similar to 

those included in this study. Therefore, they should 

be applicable to the greater majority of limestone 

mines in the Eastern and Midwestern United States. 

The guidelines for designing stable pillar layouts are 

as follows:

1. Confirm that the rock conditions and the 

rock strength are similar to those observed in 

the stone mines that were part of this study. 

A geotechnical investigation including rock 

mass classification, joint set analysis and rock 

strength testing is recommended. 

2. The pillar strength, loading and safety factor can 

be estimated using equations 1 to 5. The recommended factor of safety against pillar failure is 

1.8 and can be seen in Figure 5 to represent the 

lower bound of current experience. 

3. Pillars having a width-to-height ratio of less 

than 0.8 should be avoided. Slender pillars are 

susceptible to the weakening effect of angular discontinuities and are inherently weaker 

than wider pillars because the pillar core is 

unconfined.

4. The effect of large discontinuities is accounted 

for in the pillar strength equation. Further investigation will be required if more than about 40% 

of the pillars in a layout are likely to be intersected by one or more large discontinuities that 

dip between dip 30 and 70 deg. 

5. Pillars should be designed so that the average 

pillar stress does not exceed 25% of the UCS 

to remain within the limits of past experience. 

The design approach is entirely based on past 

experience; therefore, no comment can be made 

about pillar stability when pillars are loaded 

beyond 25% of the UCS. 

6. Pillar design cannot be carried out without 

considering roof stability. Roof spans directly 

impact the pillar stresses, because wider roof 

spans imply higher stresses in the pillars. As 

part of the pillar design, an evaluation of roof 

span stability and likely maximum stable spans 

should be conducted, as described in the next 

section of this paper. 

The shaded zone in Figure 5 indicates the area in 

which Equation 3 is likely to produce stable pillar 

layouts and coincides with the current experience in 

limestone mines and observations of failed pillars. 

The design recommendations are based entirely on 

the observed performance of stone pillars. Therefore, 

pillars that plot to the left or below the shaded area 

in Figure 5 are beyond the validity of these design 

guidelines and specialist rock engineering advice 

should be sought. 

In room-and-pillar mines, the roof between the pillars is required to remain stable during mining operations for haulage as well as access to the working 

areas. In underground stone mines, the size of the 

rooms is largely dictated by the size of the mining 

equipment. Underground stone mines use large mining equipment to operate economically and require 

openings that are on average 13.5-m (44-ft) wide by 

approximately 7.5 m (25 ft) high to operate effectively. The dimensions of the desired roof spans are 

largely pre-determined and design is focused on optimizing stability under the prevailing rock conditions. 

If the rock mass conditions are such that the desired 

stable spans cannot be achieved cost effectively, it 

is unlikely that underground mining will proceed. 

NIOSH research into stone mine roof stability has 

focused on identifying the causes of instability and 

techniques to optimize stability through design. 

Observations were carried out at 34 operating stone 

mines to identify the factors that contribute to roof 

instability. Data were collected on rock strength, 

jointing and other geological structures, room and 

pillar dimensions, roof stability and pillar performance. Two to five data sets were collected at various locations at each mine site. A data set describes 

the stability of the roof and pillars in an area of 

approximately 100 × 100 m (300 × 300 ft). The range 
of roof spans observed is shown in Figure 6, which 

shows that the 92% of the mine openings are more 

than 10 m (35 ft) wide. 

0 1

6 7

38

25

15

0

0

5

10

15

20

25

30

35

40

45

50

20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60

Roof span (ft)

Frequency

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Cumulative percent

Frequency

Cumulative 

figure 6. Distribution of roof span dimensions measured at 34 different underground stone mines

Of the mines visited, 41% 

were installing support in a regular pattern while the 

remaining 59% did not install any roof support, or 

only rarely installed spot bolting if required. 

All but four of the 34 mines visited had experienced some form of small-scale rock falls or larger 

roof falls. The observed areal extent of smaller scale 

rock falls, less than 1m in length, was as follows: 

• Thin slabs/slivers: 11% of the total roof area

• Joint bounded blocks: 6% of the total roof area

• Bedding defined beams/slabs: 11% of the total 

roof area

In the remaining 72% of roof area observed, the roof 

was stable with no sign of current or past instability. 

Figure 7 shows an example of a 13-m (43-ft) wide, 

naturally stable excavation with excellent roof conditions. Most of the smaller scale instabilities are 

addressed by scaling, rockbolting or screen installation as part of the normal support and rehabilitation 

activities.

In addition to small scale rock falls, large roof 

falls, which typically extend over the full width of 

the opening, were observed at 19 of the 30 mines that 

experienced small scale roof instability. Roof falls 

were categorized by identifying the most significant 

factor contributing to each fall. A summary of these 

factors and the relative frequency of occurrence of 

each are presented below: 

• Stress: Horizontal stress was assessed to be the 

main contributing factor in 36% of all roof falls 

observed. These falls are equally likely to occur 

in shallow or deep cover. A roof fall related to 

stress-induced damage was observed at a depth 

of as little as 50 m (150 ft) in one case. The 

characteristics of stress-related roof falls are 

described in Iannacchione et al. (2003) and 

Esterhuizen et al. (2007). Figure 8 shows a typical ellipsoidal stress related fall and Figure 9 

shows an example of how such a fall progressed 

through the mine workings in a direction perpendicular to the major horizontal stress.

• Beams: The beam of limestone between the 

roof line and some overlying weak band or 

parting plane failed in 28% of all observed large 

roof falls. 

• Blocks: Large discontinuities extending across 

the full width of a room contributed to 21% of 

the roof falls. 

• Caving: The remaining 15% of the roof falls 

was attributed to the collapse of weak shale 

inadvertently exposed in the roof or progressive 

failure of weak roof rocks. 

Although the large roof falls only make up a small 

percentage of the total roof exposure, their potential 

impact on safety and mine operations can be very 

significant. Most cases of large roof falls required 

barricading-off or abandonment of the affected entry. 

When large roof falls occur in critical excavation 

areas, the repair can be very costly.
figure 7. naturally stable 13-m (44-ft) wide 

roof span in a stone mine

figure 8. Example of large elliptical shaped 

roof fall that was related to high horizontal stress 

in the roof

July 14

July 26

Oct. 3 

Pillars 

Major horizontal stress direction 

Prior roof fall

figure 9. Plan view showing the development 

of a stress related roof fall in the direction 

perpendicular to the direction of the major 

horizontal stress, after iannacchione et al. (2003)

MaXiMuM StaBLE roof SPan

The majority of roof spans in operating mines falls 

within a narrow range of 10 m to 17 m (35 ft to 55 ft), 

and is related to the space needed to effectively operate large loaders and haul trucks. Very few of the 

mines used roof spans wider than 15 m (50 ft), so it 

is not clear whether the stability limit is approached 

at 17 m (55 ft) or whether it simply satisfies the practical requirements for equipment operation. Given 

that a large proportion of the mines are able to mine 

without installed support, it seems to indicate that 

wider spans can be achieved if additional supports 

are used. Whether these larger spans would be cost 

effective will of course depend on the support costs.

One way of assessing the potential maximum 

span is to compare the stone mine data to experience in other mine openings around the world. The 

Stability Chart originally developed by Matthews 

et al. (1980), modified after Potvin (1988), Nickson 

(1992) and Hutchinson and Diederichs (1996) was 

used as a basis for comparison. The Stability Chart 

plots a modified Stability Number N ́ which represents the rock mass quality normalized by a stress 

factor, an orientation factor and a gravity adjustment. 

Stability zones have been indicated on the chart 

based on 176 case histories from hard rock mines 

around the world. The following stability zones are 

indicated:

• Stable—support generally not required

• Stable with support—support required for stability, the support type is cable bolting

• Transition—stability not guaranteed, even with 

cable bolt support

• Unsupportable—caving occurs, cannot be supported with cable bolts

Figure 10 shows the stability chart with the stone 

mine case histories and stability categories. In this 

chart the actual heading width is shown instead of 

the “hydraulic radius” which is customarily used. 

The conversion from hydraulic radius to heading 
width assumes the heading is a parallel-sided excavation. The chart also indicates the average Stability 

Number for stone mines as a horizontal dashed line.

It can be seen that the majority of stone mine 

case histories plot in the region of “stable” to “stable 

with support” and only one is located in the transition 

zone. This agrees reasonably well with the observed 

stability and support used in stone mines, although 

stone mines have been able to achieve stability 

with light support compared to cable bolting used 

in the hard rock mine case histories. Based on the 

average Stability Number for stone mines, it would 

appear that stable supported excavations can reliably 

be achieved with spans of up to about 20 m (65 ft) 

using cable bolt supports. Cable bolt lengths in the 

hard rock mines are typically greater than half the 

excavation span, which would imply 10-m (33-ft)-

long or longer cable bolts to achieve stability in a 

20-m (65-ft) wide stone mine entry. Unsupportable 

and caving conditions are indicated when the span 

increases to about 27 m (90 ft). These results are in 

line with current experience. It appears that stone 

mines are working near the span limit that can reliably be achieved using rock bolts as the support 

system. Increasing the spans beyond the 15–17 m 

range (50–55 ft) is likely to incur considerable cost 

and productivity implications as cable bolting would 

become necessary. 

0.1

1.0

10.0

100.0

1000.0

0 10 20 30 40 50 60 70 80

Entry span (ft)

Stability Number N'

No support

Transition zone

Unsupportable - caving

Stable with support

Average Stability Number in 

stone mines 

figure 10. Stability chart showing stone mine case histories and stability zones, modified after 

Matthews et al. (1980), Potvin (1988), nickson (1992) and Hutchinson and Diederichs (1996)

StaBiLity of tHE iMMEDiatE roof 

BEaM

The stability of excavations in bedded deposits is 

closely tied to the composition of the first beam 

of rock in the roof. An assessment of the data collected showed that 25 of 34 mines were attempting 

to maintain a specific thickness of limestone beam in 

the immediate roof. In some cases the upper surface 

of the beam was a pronounced parting plane while 
in others it was a change in lithology, typically when 

the limestone beam is overlain by weaker rocks. A 

constant thickness of roof beam is achieved either 

by probe drilling to determine the thickness of the 

roof beam or by following a known parting plane or 

marker horizon.

The average roof beam thickness in mines 

that were able to mine without regular support was 

2.25 m (7.4 ft), while the average beam thickness in 

the mines that were using regular roof support was 

1.3 m (4.3 ft). Several of the mines that used regular support do so to alleviate the effects of horizontal stress, which is not related to beam thickness. If 

these mines are removed from the data, the average 

beam thickness in mines that use regular support 

drops to 0.8 m (2.6 ft). These results seem to indicate 

that mines with a relatively thin beam of limestone 

in the immediate roof are more likely to encounter 

unstable roof and regular roof bolting becomes necessary. There was no correlation between roof beam 

thickness and excavation span.

The beam thickness is obviously not the only 

factor to consider when deciding on roof reinforcement. Other aspects such as roof jointing, bedding 

breaks, blast damage, groundwater and horizontal 

stress can contribute to roof instability resulting in 

the need for rock bolt support. However, experience 

seems to indicate that a roof beam thickness of less 

than about 1.2 m (4 ft) is highly likely to be unstable 

and a regular pattern of rock bolt supports will be 

required to maintain the roof stability.

HorizontaL StrESS ConSiDErationS

This study showed that horizontal-stress-related roof 

instability can occur at any depth of cover. This is 

not unexpected, given that the horizontal stresses 

are caused by tectonic compression of the limestone 

layers, which is not related to the depth of typical limestone mines (Dolinar, 2003; Iannacchione 

et al., 2003). Observations show that the tectonic 

stresses in limestone formations that outcrop may 

have been released over geologic time by relaxation 

towards the outcrop (Iannacchione and Coyle, 2002). 

Consequently, outcropping mines can have highly 

variable horizontal stress magnitudes which depends 

on the amount of relaxation that occurred over geologic time and the distance from the outcrop. 

A review of horizontal stress measurements in 

limestone and dolomite formations in the Eastern 

and Midwestern US and Eastern Canada, (Dolinar 

2003; Iannacchione et al. 2002) has shown that the 

maximum horizontal stress can be expected to vary 

between 7.6 MPa (1,100 psi) and 26 MPa (3,800 psi) 

up to depths of 300 m (1,000 ft). Limited information 

is available at greater depths. The orientation of 

the maximum horizontal stress is between N60°E 

and N90E in 80% of the sites. This agrees with the 

regional tectonic stress orientation as indicated by 

the World Stress Map Project (2009). The minimum 

horizontal stress is approximately equal to the overburden stress.

An analysis of the impact of horizontal stress 

on beams of rock that may exist in the roof of stone 

mine workings showed that horizontal stress can be 

expected to cause buckling of thinly bedded roof 

strata (Iannacchione et al., 1998). Further analyses 

using numerical models showed that brittle spalling 

(Kaiser et al., 2000) of the roof rocks under nearuniaxial loading conditions can explain roof failure at the stress levels encountered in stone mines 

(Esterhuizen et al., 2008). 

Once a stress-induced roof fall has occurred, it 

can be costly and difficult to arrest the extension of 

the fall into adjacent areas. Avoidance of these falls 

through layout modifications has proved to be very 

successful in several operating mines (Iannacchione 

et al., 2003). It is first necessary to establish the 

direction of the major horizontal stress, which can 

be determined by various stress measurement techniques or can be inferred from stress-related roof 

failures (Mark and Mucho, 1994). The layout is then 

modified so that the main development direction is 

parallel to the maximum horizontal stress and the 

amount of unfavorably oriented cross-cut development is minimized (Parker, 1973). A further modification that has proved to be successful is offsetting 

the cross-cuts and increasing the length of the pillars, 

so that a continuous path does not exist along which 

a roof fall can progress across the layout. Modifying 

a layout in this manner will not necessarily eradicate 

all stress-related problems, but has been shown to 

considerably reduce these problems (Kuhnhein and 

Ramer, 2004). 

Figure 11 shows a mine layout that has been 

optimized for horizontal stress. The main heading direction is parallel to the maximum horizontal stress, pillars are elongated so that unfavorably 

oriented cross-cuts are minimized, the cross-cuts 

are narrower than the headings and the cross-cuts 

are off-set so that potential stress related roof falls 

will abut against solid pillar ribs, rather than snake 

through the layout. 

roof rEinforCEMEnt

The survey of roof support practices showed that 

grouted rock bolts are the most widely used form 

of support. Bolt lengths are typically between 

1.8 m (6 ft) and 2.4 m (8 ft), and where the bolts 
are installed in a regular pattern, the most commonly 

used bolt spacings are either 1.7 m (5 ft) or 1.8 m 

(6 ft). As with most other roof bolting designs in 

strong rocks, high strength and stiff bolts are more 

likely to provide the desired rock reinforcement than 

low strength and low stiffness systems (Iannachione 

et al., 1998). Roof screen or other supplemental supports such as cable bolts are rarely used. 

Roof reinforcement in the relatively strong bedded rock encountered in stone mine can have one or 

more objectives. Depending on the geological conditions the support system can be expected to:

• Provide suspension support for a potentially 

unstable roof beam

• Provide local support to potentially unstable 

blocks in the roof

• Combine thinly laminated roof into a thicker, 

stronger unit

• Provide surface control when progressive spalling and small rock falls occur

The above support functions can usually be achieved 

by the 1.8 m (6 ft) and 2.4 m (8 ft) bolts used in 

the stone mines. When poor ground is encountered 

locally or when horizontal stress related roof failures 

occur, intense bolting, steel straps and cable bolts 

have been used with mixed success to halt the lateral 

extension of these large roof falls. 

From a design point of view, a stone mine is 

unlikely to be economically feasible if heavy support 

such as cable bolts and screen would be required on 

a daily basis. Such rock conditions would probably 

require reduced excavation spans and the support 

costs would be prohibitive. Therefore, the first objective in designing an underground stone mine should 

be to confirm that the rock mass quality is adequate 

for creating the typical 10-m to 17-m (35-ft to 55-ft) 

roof spans without resorting to elaborate support 

systems. 

Heading direction 

parallel to major 

horizontal stress

Cross-cuts are narrower 

than headings

Cross-cuts are offset

Direction of major horizontal stress

Heading direction 

parallel to major 

horizontal stress

Cross-cuts are narrower 

than headings

Cross-cuts are offset

Direction of major horizontal stress

figure 11. Diagram showing room and pillar layout modified to minimize the potential impact of 

horizontal stress related damage

roof SPan DESiGn GuiDELinES 

Designing stable roof spans for underground stone 

mines should be conducted using basic engineering 

principles. Good geotechnical information, combined 

with a pragmatic assessment of the likely modes of 

instability and providing the required support is likely 

to produce a stable initial design. Once an initial 

design has been developed, monitoring of its performance can be carried out to optimize the design. 

Useful information can be obtained from neighboring mines that are operating under similar conditions. A particularly useful piece of information 

would be to identify whether horizontal-stress-related 

roof problems exist and the orientation of the stress 

related damage. This information can go a long way 

in selecting the orientation of the main headings in 

the proposed mine. The following steps should be followed to carry out a mine layout and roof span design:

1. Geotechnical characterization: Designing 

stable roof spans for stone mines can be successfully carried out if adequate geotechnical 
investigations are conducted ahead of the 

design. Such investigations are best conducted 

by experienced ground control specialists and 

are likely to include rock strength testing, core 

logging, bedding layering assessment, joint 

orientation assessment and rock mass classification. If horizontal-stress-related issues are 

expected, stress measurements can assist in 

providing an indication of the orientation and 

magnitude of the maximum horizontal stress. 

2. Confirm rock mass quality: Using the results 

of a rock mass classification or direct inspection of workings, confirm that the rock strength 

and rock mass quality is similar to that found in 

Eastern and Midwestern stone mines. The RMR 

should exceed a value of 60.0 and the rock 

strength should exceed 45 MPa (6,400 psi). 

3. Selection of mining direction: The direction of 

the headings in the production areas should be 

favorably oriented to any expected horizontal 

stress and the prevalent jointing. As with any 

underground excavation layout, it is preferable 

to intersect the main joint strike direction by at 

least 45 degrees. Since room and pillar mines 

have two orthogonal directions of mining, the 

heading direction should be favored over the 

cross-cut direction when selecting the orientation of the layout. If the orientation of the maximum horizontal field stress is known, and stress 

related problems are anticipated, the heading 

direction should be oriented parallel to the 

direction of major horizontal stress, with due 

consideration of joint orientations and cross-cut 

stability. Often it will be a compromise to select 

the final heading orientation. Other modifications to the pillar layout should be considered, 

as discussed below. 

4. Modification of pillar layout: A simple square 

pillar layout with headings and cross-cuts 

of equal width is sufficient in most cases. 

However, if horizontal-stress-related instability 

is expected, the pillar layout can be modified 

in improve the likelihood of success. Possible 

layout modifications were shown in Figure 11.

5. Selection of mining horizon: The location of the 

roof-line relative to pronounced bedding planes 

or lithology changes should be identified next. 

Experience has shown that if the immediate 

roof beam is less than 1.2-m (4-ft) thick, it is 

very likely to be unstable. Thicker roof beams 

may be required if excessive horizontal stresses 

are encountered. Persistent parting planes can 

be selected to form the roof-line if they are 

present at a convenient location in the formation being mined. Using a pre-existing parting 

plane as the roof line helps to act as a marker 

and usually provides a clean breaking surface 

for blasting operations. Many of the mines that 

do not use roof supports have a natural parting 

as the roof line.

6. Selection of roof span: Past experience has 

shown that stable roof spans in the range of 

10 m to 15 m (35 ft to 50 ft) have been regularly achieved in underground stone mines. 

NIOSH studies have shown little correlation 

between mining roof spans and rock quality, 

mainly because there is such a small range of 

rock qualities in operating mines. For an initial design, it might be prudent to design for no 

more than 12 m (40 ft) spans. The spans can be 

increased incrementally, if warranted by monitoring of actual roof performance. There is little 

experience with spans that are greater than 15 m 

(50 ft). 

7. Support considerations: Depending on the characteristics of the immediate roof, basic support in the form of patterned rockbolts may be 

required. The importance of the thickness of the 

first beam in the roof, the orientation of excavations relative to the maximum horizontal stress 

and characteristics of rock joints will determine 

whether and how much support is required. 

Mines that do not use bolting are located in 

formations with a favorable combination of 

geological conditions, and they conduct blasting practices that maintain an unbroken roof 

horizon. 

8. Monitoring and confirmation: Once a roof 

design has been finalized and mining is underway, monitoring should be implemented to verify the stability of the roof. Monitoring results 

can be used to identify potential stability problems before they occur and may indicate that 

a change in the design is required. Monitoring 

technologies that are available include borehole-video logging (Ellenberger, 2009), roof 

deflection monitoring (Marshall et al., 2000), 

roof stability mapping using the Roof Fall 

Risk Index (RFRI), (Iannacchione, et al. 2006) 

and micoseismic monitoring of rock fracture, 

(Iannacchione and Marshall, 2004; Ellenberger 

and Bajpayee, 2007). 

DiSCuSSion anD ConCLuSionS

A study of pillar and roof span performance in stone 

mines that are located in the Eastern and Midwestern 

United States showed that various stability issues can 

be addressed by appropriate design. Pillars can be 

impacted by rock joints, large angular discontinuities 
and can exhibit rib spalling at elevated stresses. Thin 

weak beds in the pillars, although rare, can have a 

significant impact by reducing pillar strength. If the 

roof strata are bedded, beam deflection and buckling can result in roof failure. The roof can also be 

impacted by large discontinuities and the effects of 

horizontal stress. 

A pillar design procedure is proposed that takes 

into consideration the rock strength, pillar dimensions and the potential impact of large angular discontinuities. Based on current performance of pillars 

in stone mines, a safety factor of 1.8 is suggested for 

pillar design with a lower limit, width-to-height ratio 

of 0.8. 

A roof span design procedure is also proposed 

that systematically addresses each of the main stability issues. The procedure focuses on selecting an 

appropriate mining horizon and mining direction. 

The importance of the thickness of the first bed in 

the roof and the likelihood for added rock bolting is 

described. Layout modifications are described that 

can be made to reduce the incidence of horizontalstress-related instability. 

Both the pillar design and roof span guidelines 

require that a good understanding be obtained of the 

geotechnical characteristics of the formation being 

mined. The essential data are the uniaxial compressive strength of the rock, characteristics of the discontinuities and the rock mass classification. Knowledge 

of the magnitude and orientation of the stress field 

can assist in orienting the layout appropriately. 

The design procedures are based on observation 

of the actual performance of pillars and roof spans 

in stone mines within the Eastern and Midwestern 

United States. The guidelines should only be used for 

design under similar geotechnical conditions. 

Disclaimer

The findings and conclusions in this paper have not 

been formally disseminated by the National Institute 

for Occupational Safety and Health and should not 

be construed to represent any agency determination 

or policy.

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