1 INTRODUCTION 

Underground limestone mines in the U.S. make use 

of the room and pillar method of mining. Bench 

mining of the floor between the pillars is sometimes 

carried out to improve utilization of the reserves. 

Figure 1 shows an area where bench mining of the 

floor is underway. The benched pillars are in the 

foreground and the original development pillars are 

seen in the background. The National Institute for 

Occupational Safety and Health (NIOSH), 

Pittsburgh Research Laboratory is investigating 

pillar and roof stability in U.S. limestone mines. 

Observations of pillar conditions carried out as part 

of this study revealed that the condition of pillars 

around the perimeter of bench mining operations can 

be worse than elsewhere in the mine. Unstable pillar 

ribs represent a rock fall hazard to mine personnel. 

Over the decade from 1996 through 2005, ground 

falls were the cause of 36% of fatalities and 12% of 

all injury related lost workdays in underground 

limestone mines (Mine Safety and Health 

Administration, 2006). In addition, failure of a 

single pillar can result in overloading of the adjacent 

pillars, possibly resulting in the collapse of multiple 

pillars. 

A total of 31 different mine sites were visited by 

NIOSH researchers. Bench mining of the floor had 

been carried out at 18 of the 31 mine sites visited. 

Evidence of increased instability of the pillars at or 

near the perimeter of the benched areas was 

observed at six of these mines. The observed 

instability was in the form of failure along preexisting geological structures and stress related 

spalling and fracturing of the pillar ribs. 

This paper presents a summary of the 

observations made and the results of numerical 

analyses that were carried out to evaluate the 

changes in loading and pillar strength that occur 

during bench mining. A case study of pillar 

instability associated with bench mining is 

presented. The paper concludes with suggestions for 

identifying situations that are likely to result in 

instability during bench mining and strategies to 

limit the potential for instability. 

Observations and evaluation of floor benching effects on pillar stability

in U.S. limestone mines 

G.S. Esterhuizen, D.R. Dolinar & J.L. Ellenberger. 

National Institute for Occupational Safety and Health, Pittsburgh, USA. 

ABSTRACT: A survey of roof and pillar conditions in underground limestone mines in the United States has 

revealed that bench mining of the floor between pillars can cause instability in the pillars at the perimeter of 

the benched area. Increased loading of these pillars was observed at several mines. Large inclined geological 

structures that are exposed in pillar ribs were observed to contribute to pillar instability. The paper describes a 

study that was carried out using numerical models to assess the effects of bench mining on pillar load and 

stability. It was found that the benched pillars shed load onto the surrounding pillars owing to their reduced 

stiffness. The pillars at the perimeter of the benching area will start shedding load as soon as benching 

increases the height of one side of the pillar. A case study is described which shows the effects of bench 

mining on limestone mine pillars. 

Figure 1. Example of bench mining of the floor between 

pillars in a limestone mine. 
2 FIELD OBSERVATIONS OF BENCH MINING 

IN LIMESTONE MINES 

Field data on roof and pillar conditions were 

collected at 86 different locations in 31 limestone 

mines in Pennsylvania, Virginia, West Virginia, 

Illinois, Kentucky, Tennessee, Missouri and Indiana. 

The data collected at each location included rock 

mass properties, pillar and room dimensions, 

information on roof and pillar stability and rock 

strength properties, (Esterhuizen et al. 2006). The 

rock mass in these limestone mines can be classified 

as “Good” to “Very Good” with rock mass rating 

(RMR) values in the range of 70-85 units, using the 

Bieniawski (1989) method of classification. The 

intact rock strength is in the range of 100-200 MPa. 

Table 1 presents a summary of the dimensions of 

pillars and rooms showing both development and 

benching dimensions at the 31 mines. It can be seen 

that bench mining increases the average pillar height 

from 7.8 to 17.8 m and reduces the average the 

width-to-height (W:H) ratio of the pillars from 1.67 

to 0.95. 

Table 1. Dimensions of room-and-pillar mining layouts. 

Parameter Average Minimum Maximu

m 

Pillar height: development (m) 7.8 4.8 10.7 

Pillar height: benched pillar (m) 17.8 9.9 38.0 

Pillar width (m) 13.9 5.1 28.6 

Pillar W:H: development 1.67 0.93 3.52 

Pillar W:H: benched pillar 0.95 0.29 2.35 

Room width (m) 13.5 9.1 16.8 

Depth of cover (m) 121 23 533 

Local percent extraction (%) 73 54 88 

Observations of pillar conditions at the mines 

revealed several instances where the partially 

benched pillars at the edge of the benching 

operations had become unstable. Table 2 

summarizes the cases in which pillar instability 

associated with bench mining was observed. Case 3 

was evaluated in greater detail and is presented as a 

case study. Benching operations were halted in two 

of the observed cases owing to instability of the 

partially benched pillars. Several cases were 

observed in which the pillars at the perimeter of the 

benching area showed signs of increased loading. In 

addition, instability was observed when bench 

mining exposed large joint structures in the pillar 

ribs. 

It was apparent from the field observations that 

benching not only reduces the pillar strength by 

increasing the pillar height, but also causes an 

increase in pillar load at the perimeter of the 

benched area. The increased pillar load can be 

ascribed to the fact that the benched pillars are taller 

and are consequently less stiff than the surrounding 

development pillars. Stresses are concentrated in the 

stiffer development pillars, which can result in 

instability in these pillars. 

The average pillar stress shown in the table was 

calculated using the tributary area method, which 

does not account for increased loading owing to the 

variable stiffness of the benched and development 

pillars. Numerical model analyses were conducted to 

further quantify the load and strength changes 

caused by benching and evaluate their impact on 

pillar stability. 

3 NUMERICAL ANALYSIS OF THE EFFECT 

OF BENCHING ON PILLAR STRENGTH AND 

LOADING 

The summary of mining dimensions in Table 1 

shows that the average width-to-height (W:H) ratio 

of pillars is reduced by 43% during benching 

operations. The effect of the increased height on 

pillar strength can be estimated using one of the 

published pillar strength equations for hard rock 

mines, such as the equation developed by Hedley 

Table 2. Summary of observed pillar instability associated with bench mining. 

Case W:H 

Develop 

W:H 

Benched 

Average Pillar 

stress (MPa) Instability Observed 

1 1.3 0.59 13.1 Large discontinuities exposed by benching, evidence of high horizontal 

stress, diagonal shearing through pillar. Benching was halted. 

2 1.5 0.73 14.1 Progressive spalling of pillar ribs, pillar width reduced significantly, weak 

bedding infill contributed to spalling. 

3 1.5 0.44 15.0 Spalling of several pillars to hourglass shape. Sloughing from one of the 

pillars caused by a large steeply dipping discontinuity. 

4 1.65 0.61 8.14 Sloughing from pillar ribs as a large discontinuity is exposed at the 

perimeter of benching. 

5 2.0 0.99 19.8 Sloughing from pillar walls at location of a large discontinuity. Benching 

was halted and resumed beyond this area. 

6 1.96 0.92 13.1 Spalling to hourglass shape. Benching halted owing to presence of large 

discontinuities in adjacent pillars. 
and Grant (1972). However, during benching, the 

height of a pillar is progressively increased as each 

side is benched, until all four sides are fully 

benched. The strength of a pillar during these stages 

of bench mining cannot be determined using 

existing pillar strength equations since the equations 

are intended for prism shaped pillars that have equal 

height on all sides. Numerical models were therefore 

used to estimate the strength of the irregular shaped 

pillars formed during benching. Figure 2 shows 

conceptually the stages of benching around a 

limestone pillar that were considered in the models. 

During Stage 1 one side of the pillar has been bench 

mined. At Stage 2, two sides have been benched 

and so on, until the pillar is fully benched in Stage 4. 

Numerical models were also used to investigate the 

changes in average pillar stress at each stage of 

bench mining. 

3.1 Analysis of the Strength of Partially Benched 

Pillars 

The progressive reduction in pillar strength during 

bench mining was assessed using the FLAC3D finite 

difference program (Anon, 2005). Models were set 

up to simulate square pillars with initial W:H ratios 

of 1.0 and 1.5. The benching stages shown in 

Figure 2 were modeled by progressively removing 

the floor rocks on each side of a pillar until it is fully 

benched on all sides. The benching depth was 

selected so that the pillar height was doubled during 

the benching procedure. The model geometry for the 

pillar with initial W:H = 1.0 is shown in Figure 3. 

Model element sizes were kept constant during all 

the runs to avoid element size effects on the results. 

 The mechanical properties that were used to 

simulate the limestone rock mass are summarized in 

Table 3. The properties were selected to model a 

rock mass with an RMR value of 70 and intact rock 

strength of 120 MPa. A bi-linear peak strength 

criterion with strain softening of the failed rock was 

used to capture both brittle spalling and shear failure 

of the limestone, as suggested by Kaiser et al. 

(2000), Martin & Maybee (2000) Diederichs (2002) 

and Diederichs et al. (2002). The brittle rock 

strength was set at 33% of the intact rock strength 

and the Coulomb strength properties of the rock 

mass were based on the Hoek-Brown (1997) 

criterion. Details of the modeling approach and 

selection of input parameters for this model are 

presented in Esterhuizen, (2006). 

 The strength of the modeled pillars was 

determined by gradually increasing the vertical load 

in the models. Failure of the rock in the models was 

allowed to occur in response to the increased 

loading. The loading was increased until the pillar 

started to shed load. The pillar strength was defined 

as the peak vertical load, divided by the horizontal 

cross-sectional area of the pillar. The selected input 

parameters resulted in pillar strength of 48 MPa for 

a square pillar with W:H=1.0, which is 40% of the 

intact rock strength of 120 MPa used in the models. 

The model shows good agreement with the 

Table 3. Input Parameters for the bilinear strength model.

Parameter Value 

Elastic modulus 70 GPa 

Poisson ratio 0.2 

Intact rock strength (UCS) 120 MPa 

First stage (brittle) cohesion 20 MPa 

First stage (brittle) friction angle 0o 

Second stage cohesion 6.5 MPa 

Second stage friction angle 42.7o 

Tensile strength 7 MPa 

Dilation angle 30o 

Figure 3. FLAC3D model of a partially benched pillar 

Velocity applied to 

top of model to 

simulate load 

increase

Developed 

height 8m 

Benched 

height 16m 

Bottom of 

model fixed 

Sides of model 

fixed in 

horizontal 

direction 

Stage 1

Stage 2

Stage 3 Stage 4

Figure 2. Stages of bench mining around a pillar 

considered in the numerical models. 
empirical equation of Hedley and Grant (1972) for 

square pillars with W:H of 0.75 to 2.0. 

Model results for pillar strength at the various 

stages of bench mining are presented in Figure 4, 

which shows how the pillar strength is progressively 

reduced as bench mining is carried out around the 

pillar. The model results show that strength of the 

pillar with W:H=1.0 is reduced by about 16%, from 

its initial value of 48 MPa to a final value of 40 

MPa. The pillar with W:H=1.5 experiences a 

reduction in strength of 37% from the development 

stage to the fully benched stage. 

From a pillar design point of view, it is important 

to also know how bench mining affects the pillar 

loads while the strength reduction is occurring. This 

aspect was assessed using numerical models and is 

discussed below. 

3.2 Analysis of Changes in Pillar Loading During 

Benching 

The examine 3D (Anon, 1998) boundary element 

package was used to determine how the pillar load is 

likely to change in response to benching. The 

program allows an array of pillars to be modeled in 

three dimensions assuming elastic rock properties. 

Benching of the floor can be modeled realistically 

and deflection of the roof over the benched and 

development pillars is simulated. 

The rock mass was modeled with a Young’s 

modulus of 30 GPa, to account for rock mass 

discontinuities, and Poisson’s ratio of 0.2. The field 

stresses were set up to simulate a horizontal to 

vertical stress ratio of 2.0 at a depth of 200 m. The 

models simulated an array of pillars each 12 m wide 

and having W:H ratios of 1.0. The floor of the model 

was removed in stages to simulate benching to W:H 

of 0.5. The rooms were equal in width to the pillars, 

resulting in 75% extraction of the modeled 

limestone. Figure 5 shows a cut-away view of the 

model in which the initial developed pillars, the 

perimeter pillars and the benched pillars can be seen. 

 Figure 6 shows the average stress in the pillars 

obtained from a model in which half of the pillars 

have been benched. The results show that the 

development pillars at the edge of the benched area 

are subjected an increase of about 12% in their 

average stress. The results further show that the 

stress in the partly benched pillar is lower than the 

stress in the adjacent pillar that has not been 

benched yet, indicated as “perimeter pillar” in 

Figures 5 and 6. The lower stress in the partly 

benched pillar can be explained by the fact that its 

stiffness is reduced by the increase in height of one 

of the sides of the pillar, causing the load to be 

transferred to the stiffer development pillars. It can 

clearly be seen that the fully benched pillars are at a 

reduced stress level, owing to their relatively low 

stiffness. As benching continues, the stress in the 

fully benched pillars is expected to gradually 

50%

60%

70%

80%

90%

100%

110%

120%

1 2 3 4 5 6 7 8 9 10

Pillar number

Pillar stress ratio .

Partly benched pillar

Fully benched pillars

Perimeter pillar Development 

pillars 

Figure 6. Results of Examine 3D model showing the 

average pillar stress during bench mining as a ratio of the 

average pillar stress prior to bench mining. 

Figure 4. Results of FLAC3D modeling showing strength 

reduction of pillars with initial W:H=1.0 and 1.5 from initial 

development through various stages of bench mining. Final 

W:H ratios at Stage 4 are 0.5 and 0.75 respectively. 

30

35

40

45

50

55

60

65

70

DevelopStage 1

Stage 2

Stage 3

Stage 4

Pillar Strength (MPa)

Initial W:H = 1.5

Initial W:H = 1.0

Perimeter 

pillar 

Fully benched 

pillar 

Partially benched

pillar

Figure 5. Cutaway view of Examine 3D model showing

development and benched pillars. 
increase back to the tributary stress. 

Further results, showing the changes in the 

average vertical stress in a pillar at the various 

stages of bench mining are presented in Figure 7. 

The figure also shows the associated changes in the 

pillar strength for a pillar with W:H=1.5, as 

previously presented in Figure 4. It can be seen that 

the pillar stress is a maximum just before benching 

starts around the pillar. As soon as one side of the 

pillar has been benched, the average pillar stress 

decreases, owing to the increased height and reduced 

stiffness. The average pillar stress continues to 

decrease as benching progresses, until the pillar is 

fully benched. The stress in the fully benched pillars 

will gradually rise as the benching face moves away. 

Full tributary loading can re-establish in the benched 

pillars if the mined area is sufficiently large. 

These results indicate that bench mining activities 

will result in an increase in the pillar stress around 

the perimeter of the benched area. However, once 

the pillar is partially benched, the average pillar 

stress will decrease. 

3.3 Stress Concentration and Damage 

The numerical models confirm that elevated stresses 

can occur in pillars around the perimeter of a 

benched area. However, the existence of reduced 

stresses in the partially benched pillars seems to be 

in conflict with the field observations, which 

indicate that elevated stresses exist in the partially 

benched pillars. Nearer inspection of the model 

results show that stresses are not symmetrically 

distributed within pillars at the edge of a benched 

area, shown in Figure 8. It can be seen that zones of 

high stress exist within the partially benched pillar 

that are absent in the perimeter pillar, although the 

average vertical stress in the two pillars may be 

similar. The elevated local stresses are likely to 

contribute to the failure observed in the partially 

benched pillars in operating mines. 

4 CASE STUDY OF BENCHING-RELATED 

INSTABILITY 

4.1 Observed Instability 

Pillar instability was observed adjacent to an area of 

bench mining at a mine that is extracting a near 

horizontal limestone bed. Spalling of the pillar ribs, 

resulting in hourglass formation, was observed. In 

the area of concern, the pillars were square with side 

dimensions varying between about 12.2 and 15.2 m 

and were initially benched to 15.8 m high. Further 

benching was carried out, which increased the pillar 

height to 27 m. The room width was measured to be 

about 16.4 m, and the depth of cover is 140 m. The 

average pillar stress is about 15 MPa, based on the 

tributary area method. However, the irregular pillar 

shapes and effects of benching resulted in variable 

stresses in the pillars. The width to height ratio of 

the benched pillars was as low as 0.44 in the 27 m 

high area. Figure 9 shows a plan of the mine 

A

B

C

D

E

F

G

H

J

Key

Pillar

Benching

Large joint

0 100m Scale

Figure 9. Plan view showing layout of pillars and bench 

mining at case study mine as modeled using the Examine 3D 

software. 

Figure 7. Change in the average vertical pillar stress and 

strength during various stages of bench mining, for a pillar 

with W:H=1.5 based on FLAC3D and Examine3D results.

40%

50%

60%

70%

80%

90%

100%

110%

120%

Develop

Perimeter

Stage 1Stage 2Stage 3Stage 4

Ratio

Pillar stress

Pillar strength

Figure 8. Section through the central part of an Examine 3D 

model showing maximum principal stress contours in and 

around pillars at the edge of bench mining. Contours in MPa. 

10

20

30

40

50

60

 Perimeter pillar Partly benched Fully benched

MPa 
workings indicating the area in which benching was 

carried out to a height of 27 m. 

The limestone formation in this mine has uniaxial 

compressive strength in the range of 200-250 MPa. 

Jointing is near vertical with an average spacing of 

about 50 cm. A survey of joint orientations in the 

area showed that the main joint set strikes in the 

North-South direction. A single large, near vertical 

joint, was observed in the roof adjacent to Pillar E, 

and is shown Figure 9. Joint surfaces are rough, and 

the joint continuity is less than 3 m. Bedding joints 

are poorly developed and did not appear to affect the 

pillar stability. The rock mass rating (RMR) for this 

area was determined to be 78 as shown in table 4. 

The initial development mining was carried out 

about 15 years ago, but the final benching stage was 

carried out less than 5 years ago. A number of pillars 

were reported to be progressively spalling to the 

current hourglass shape at the perimeter of the 

benched area. Figure 10 shows the conditions of 

pillars B and E. Evidence of fracture through intact 

rock and slab formation was seen. Pillars A, B, D 

and E showed open vertical fractures and there were 

large slabs lying on the mine floor around the pillars. 

Pillar E was considerably reduced in size, owing to 

the presence of the large joint that intersected one of 

its corners and caused the corner to slough. The 

remaining part of the pillar was in a poor condition, 

containing many stress related fractures and slabs. 

Pillars C, F, H and J were in a relatively good 

condition and did not show any signs of stress 

damage. 

4.2 Analysis and Discussion 

The pillars labeled A, B, D and E in Figure 10 are 

clearly exposed to elevated loading. Spalling to an 

hourglass shape, open fractures and slab formation 

are all well known manifestations of pillar overload. 

A 3D model of the area was set up using the 

Examine 3D software. The model simulated an area 

of about 300x300m with the pillars in question 

located near the center of the model. Two stages 

were modeled. The first stage simulated a condition 

prior to bench mining and the second simulated the 

benched configuration shown in Figure 9. The 

results showed that prior to bench mining, pillars D, 

E and F were slightly more stressed than the 

surrounding pillars owing to their smaller size. The 

stress distribution in the pillars after benching is 

shown in Figure 11. It can be seen that pillars D, E 

and F contain the highest stresses and A, B and C 

have already been partly relieved of stress by the 

bench mining. Pillar E carries the highest stress, 

because it is smaller than the other pillars, and is 

stiffer than the partially benched pillars. The 

relatively lower stresses in pillars A, B and C is 

expected, since their height has been increased by 

benching, and they have shed stress. However, as 

benching approached these pillars, the stresses will 

have been elevated and is likely to have caused the 

observed damage. The benching configuration, 

which forms a protruding right-angle, also 

contributes to the elevated stresses on these pillars. 

5 SUMMARY AND CONCLUSIONS 

Observations show that floor benching can cause 

instability of pillars at the perimeter of bench mining 

operations. Instabilities can be caused by the 

Table 4. Rock Mass Rating parameters in vicinity of unstable pillars 

at case study mine. 

Parameter Value Rating 

Intact rock strength 150 MPa 14 

Joint frequency 2.0 joints/m 21 

Joint condition Rough joints with no infill, poorly

developed bedding, joint walls 

unaltered 

28 

Groundwater Dry 15 

Total: 78 

Scale

0 100m

Legend

(MPa)

1

3

5

7

9

11

13

15

A

B

C

D

E

F

G

H

J

Figure 11. Examine 3D results showing contours of 

maximum principal stress in the pillars. 

Figure 10. View of pillars showing slabbing and rubble from 

rib failure, Pillar B on left and Pillar E on right in photograph. 

B

E

Joint
geological structures in the rock and by an increase 

in pillar loading. 

The presence of large inclined joints or other 

geological discontinuities can cause instability 

because they are more likely to be exposed by the 

increased height of pillars. 

An increase in pillar loading can be explained by 

considering the pillar stiffness. The benched pillars 

have a reduced stiffness and will shed load onto the 

stiffer development pillars. The numerical models 

showed that there was an increase in stress of about 

15% in the pillars around the perimeter of the 

benching operations. 

 The models also showed that the strength of a 

pillar is reduced in a near linear manner as each side 

of the pillar is bench mined. The net effect is that 

partly benched pillars experience a simultaneous 

reduction in strength and load. 

The instability of the partly benched pillar can be 

further ascribed to the uneven distribution of stresses 

within the pillars when they are located at the edge 

of a benching operation. High local stresses near the 

top and bottom of the pillar can initiate stress 

spalling. 

 The case study confirmed that increased stresses 

exist within pillars at the perimeter of the bench 

mining operations. It was further shown that 

irregular sized pillars are more likely to become 

unstable during bench mining. The smaller pillars 

are more susceptible to stress increases as benching 

approaches. The case study also showed that the 

benching should advance in a straight line, to avoid 

lagging corners that will result in elevated stresses in 

the perimeter pillars and degrade their stability. 

 

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