Introduction

The room and pillar method of mining is used

to recover flat lying limestone deposits in the

Eastern and Midwestern United States. The

production excavations are 12 to 18 m wide to

allow efficient operation of the large

underground production equipment. The

rooms are typically about 8 m high on initial

development and the floor is bench mined in

about 30% of the operations to produce a

typical final excavation height of about 15 m.

The stability of these relatively wide and high

excavations must be assured to provide a safe

and productive work environment. Fall of

ground injuries account for about 15% of lost

work days in underground limestone mines1.

Due to the large excavation dimensions and

the height of the workings, falls of ground can

have a devastating effect when they occur. 

Horizontal stresses have long been

recognized as a source of excavation instability

in underground coal and hard rock mines.

Hasenfus2 summarized the historical

development of an understanding of horizontal

stress issues and mitigation techniques in coal

mines, dating back to the 1950s. In hard rock

mines horizontal stress induced stability

problems have been identified and documented

since the 1960s3,4. Horizontal stress related

stability issues in US limestone mines and

techniques to improve stability by support and

changes in mine layout have been well

documented in the literature5–11. This paper

provides a review of the horizontal stresses

and related roof stability issues in US

limestone mines, and presents the results of

recent three-dimensional numerical analyses

that were carried out at the National Institute

for Occupational Safety and Health (NIOSH),

Pittsburgh Research Laboratory, to assess the

stress and rock failure distribution for various

geological and mine layout scenarios.

Horizontal stress in limestone formations

in the Eastern and Midwestern United

States 

Stress measurements and field observations

have shown that the horizontal stresses in the

limestone formations of the Eastern and

Midwestern US can be much higher than the

overburden stress. Horizontal stresses in

limestone formations have been measured in

limestone mines7 and in many of the area’s

coal mines12. Research has shown that the

horizontal stress may be explained by the

effect of plate tectonics7,13. Tectonic loading is

related to the movement of the North American

plate as it is pushed away from the MidAtlantic ridge. A constant strain field of

between 0.45 and 0.90 millistrains is

associated with the tectonic loading, which

Field observations and numerical

studies of horizontal stress effects on

roof stability in US limestone mines

by G.S. Esterhuizen*, D.R. Dolinar*, and A.T. Iannacchione*

Synopsis

Limestone formations in the United States can be subject to

relatively high horizontal stresses due to the existence of tectonic

loading of the limestone strata. Underground limestone mines use

the room-and-pillar method, in which 12- to 18-m-wide rooms are

typically excavated. The stability of these excavations can be

compromised by the horizontal stress, resulting in a rockfall hazard.

Rockfalls are the cause of 15% of all reportable injuries in

underground limestone mines. Horizontal stress related damage can

occur in the form of guttering along one or more sides of an

excavation, roof beam buckling or oval shaped roof falls, with the

long axis perpendicular to the major horizontal stress. Numerical

analyses show that the pillar layout and orientation of the mine

workings have an effect on the horizontal stress distribution within

the roof. The effects of high horizontal stresses can be mitigated by

orientating the heading development direction parallel to the

maximum horizontal stress, reducing the number of cross-cuts and

offsetting the cross-cuts to limit the potential lateral extent of

horizontal stress related roof falls. The modeling approach described

in this paper can be used as a tool to evaluate potential roof failure

and optimize the stability of room and pillar layouts.

* National Institute for Occupational Safety and

Health, USA.
induces higher horizontal stresses in the stiff limestone

strata. The induced stress magnitude is not necessarily

related to the cover depth for depths encountered in limestone

mining operations, but rather to the stiffness of the strata.

The typical elastic modulus of the limestones varies from 35

to 65 GPa. High horizontal stresses are not present in all the

limestone formations because local features such as

outcropping and folding may have relieved the stresses over

geological time8,14. Consequently, outcropping mines can

have highly variable horizontal stress magnitudes, which

depend on the amount of relief that occurred 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 Canada13 shows that the maximum horizontal

stress can vary between 4.1 MPa and 47.6 MPa up to depths

of 300 m, shown in Figure 1. Limited information is available

at greater depths. A linear equation fitted to the maximum

horizontal stress data produces the following:

[1]

where: h is the depth in metres.

The orientation of the maximum horizontal stress is

between N60°E and N90°E in 80% of the sites. This agrees

with the regional tectonic stress orientation as indicated by

the World Stress Map Project15. The magnitude of the

minimum horizontal stress is approximately one half the

maximum horizontal stress. 

Roof stability and horizontal stress related damage

Survey of roof stability in limestone mines 

NIOSH researchers recently conducted a survey of roof

conditions in 34 underground limestone mines to identify the

factors contributing to roof instability16. The survey included

conducting rock mass rating and laboratory strength testing

of the intact limestone. 

Rock mass rating (RMR) results showed that the

limestone formations that are being mined fall in the range of

60–85 using the 1989 version of the classification system of

Bieniawski17. The results of laboratory testing showed that

68% of average rock strength values for mine sites lie in the

range of 120 MPa to 180 MPa. Joint frequency is on the order

of 3 joints per metre and typically consist of two or more

steeply dipping joint sets plus bedding. The steeper joints are

typically rough and discontinuous while the bedding joints

can be continuous over several tens of metres. 

The survey further showed that about 46% of the mines

regularly use roof reinforcement, while the remainder of the

mines rely on the natural stability of the surrounding rock

mass and may occasionally use rock reinforcement. Roof

reinforcement was typically mechanical anchored or grouted

rock bolts that are 1.8 to 2.4 m long. 

It was found that horizontal stress contributed to roof

damage at seven of the 34 mines visited during the survey. 

A review of the geological and mine layout parameters at

these mines showed that they were not significantly different

from the mines that did not experience horizontal stress

related instability. For example, the depth of cover at the

locations of stress related damage varied from 40 m up to

300 m, similar to that of the entire dataset. The average

uniaxial compressive strength (UCS) of the limestone rocks 

at these mines was 188 MPa, which is not exceptional. The

laboratory-determined elastic modulus of the rocks at the

mines having horizontal stress stability problems was 63.8

GPa, while it was 52.3 GPa at the remaining mines, which

seems to indicate that high elastic modulus might be used 

as an indicator of potential roof stability problems. However,

the data also showed that mines with higher elastic modulus

values were not necessarily all subject to horizontal stress

related instability. On the contrary, mines where the elastic

modulus of the limestone was less than about 50 GPa were

all free of horizontal stress related problems.

Observed roof damage related to horizontal stress 

Stress induced roof damage in limestone mines is similar in

appearance to that seen in other bedded deposits such as coal

mine roof strata6,12,18. Stress mapping techniques were used

to identify the occurrence of horizontal stress related

instability18. Various forms of roof damage were observed

and are described below.

Figure 1—Maximum horizontal stress measurements in limestone and dolomite formations in the Eastern and Midwest US and Eastern Canada, showing a

fitted straight line and equation
Roof guttering

Horizontal stress related damage can manifest itself as

guttering along the pillar-roof contact area6,19 as seen in

Figure 2. This is very similar to ‘cutter roof’ seen in coal

mines that are subject to high horizontal stresses. Once the

roof has been damaged at the pillar contacts, the confining

stresses are relieved and the immediate roof layers can fail.

The failure can extend across the width of the excavation if it

is not well supported. This type of failure has been observed

in mines located in both inclined and flat lying limestone

formations. 

Beam instability

The bedded rock in the roof of limestone mines can behave

as individual beams or plates that can fail under gravity

loading or as a result of the horizontal stress. In high

horizontal stress conditions, buckling of the rock beds, stress

fracturing and shearing of the beds can occur5,6,16,19. Stepped

roof and brows are signs of beam type failure. Mining under

a thinly bedded roof usually requires regular support, such as

patterned rock bolts, because the individual beds are unable

to sustain their integrity over the span of the excavation.

When mining under a more massive roof, the thicker roof

beds may be naturally stable. However, when mining under

an apparently massive roof, it becomes important to know

the location of any weak bedding discontinuities so that

thinner roof beds can be identified and appropriately

supported. 

Oval shaped falls

Another common manifestation of horizontal stress is large

oval-shaped falls, with the long axis orientated approximately perpendicular to the major horizontal stress6, as

shown in Figure 3. These falls typically initiate by failure of

the lower roof bed and can progress upwards to form an

arch-shaped cavity in the roof, as seen in Figure 4. The

mechanism of failure may be described as progressive

shearing and buckling of the individual rock layers in the

roof9. The failures are often preceded by excessive deflection

of the roof beams, which may be associated with

microseismic emissions. Collapse of the roof beams is

progressive in the vertical direction, with individual beds

failing from the bottom up. These falls are often seen to

initiate in the roof between two pillars. 

Failure propagation

Oval-shaped roof falls have been observed to gradually

propagate in the lateral direction, perpendicular to the

direction of the maximum horizontal stress. They can extend

for several tens of metres, and can extend well over 100 m.

Once an oval-shaped cavity is formed, the stress concentrations at the ends of the oval appear to cause further rock

failure and growth of the failed zone in the lateral direction6.

The propagation of the failure appears to be associated with

relatively large roof deflections ahead of the failed cavity. An

example of roof deflection and propagation of the roof fall

cavity is shown in Figure 5, after Iannacchione et al.5. In this

case, the roof collapsed when the roof sag exceeded 5 cm at

the indicated roof monitor location.

Figure 2—Roof guttering at the pillar-roof contact

Figure 3—Horizontal stress induced roof failure that initiated between

two pillars. Arrows show direction of maximum horizontal stress

Figure 4—Large-oval shaped fall that has propagated upwards into

weaker overlying strata in a limestone mine
Mitigation alternatives

High horizontal stresses pre-exist mining and little can be

done to completely avoid these stresses. Techniques that

have been developed to alleviate the effects of horizontal

stress in limestone mines include the selection of a stable

roof line, favorable orientation of mine workings relative to

the stress field, pillar layout modifications, and installation of

regular roof reinforcement. Reorienting the excavations and

modifications of mine layouts have been successful in

improving roof conditions in several cases8,10,11,20. The

method includes reorienting the mining layout so that the

main direction of development is parallel to the direction of

maximum horizontal stress and limiting the number of crosscuts. 

Analysis of bedded roof stability in high horizontal

stress conditions

Roof bed stability in a three-dimensional mining layout can

readily be assessed using numerical models, overcoming

some of the limitations of analytical procedures such as

classical beam theory or the ‘voussoir’ beam model21,22.

Numerical models allow the effect of initial horizontal

stresses, complex excavation layouts, support elements and

progressive rock failure to be simulated. 

The FLAC 3D finite difference software23 was used to

assess roof stability for the typical stress conditions and

mining dimensions that are found in US limestone mines. For

these analyses, the rock material was assumed to be elastic

and bedding joints were introduced in the models using the

interface and ubiquitous joint logic in the FLAC 3D software.

Various combinations of roof bed thickness and location of

bedding discontinuities were modelled. The results were

evaluated by reviewing the stress distributions and applying

a rock failure criterion to the elastic stress results to identify

potential zones of failure.

Model design

A model was initially developed to evaluate the stress distribution and potential failure in the roof for various depths of

cover, horizontal stress scenarios and various roof bed

geometries. The model simulated an array of 14-m-wide

rooms and pillars, which is representative of the excavations

in limestone mining operations. Symmetry of the layout

allowed only a quarter of a pillar and the adjacent rooms to

be modelled. Interface elements were used to explicitly

simulate roof bed discontinuities at various locations above

the rooms. 

A second, larger model, was set up to simulate an array

of sixteen pillars and the surrounding rooms, which allowed

various pillar configurations and loading conditions to be

assessed. In order to avoid model edge effects, results were

evaluated only in the central part of this model.

The models were set up to simulate workings at 100, 200,

and 300-m depth. Only the 300-m depth results are

presented here. The maximum horizontal stress at 300-m

depth was set at 21.8 MPa, based on Equation [1]. The

minimum horizontal stress was set equal to one half the

maximum horizontal stress, while the vertical stress was 

7.8 MPa, representing the cover loading. 

The rock material properties were based on laboratory

test results, the limestone having an elastic modulus of 

50 GPa and Poisson’s ratio of 0.2. The uniaxial compressive

strength of the rock was set to 63 MPa, which is low relative

to the typical strength values found in limestone mines. The

rock strength was deliberately chosen to be low, so that the

differences between the models would be more evident than

when using a higher, more representative strength. The

extent of failure is indicated by a failure index, which is

calculated as the ratio of the rock strength to the maximum

principal stress. A failure index of less than 1.0 can be

interpreted as fractured rock that can potentially become

unstable in the absence of support. 

Figure 5—Progressive roof failure associated with high horizontal stress, showing roof sag measured at roof monitor ahead of the initial fall, after

Iannacchione et al.5
The rock failure criterion was based on a two-stage

failure process consisting of brittle fracturing and frictional

shearing24,25. This failure process simulates the failure of

hard brittle rocks in which extensional fractures develop

parallel to the direction of the maximum principal stress at

low confinement. At higher confinement values, the friction

is mobilized in the rock, allowing the classical Coulomb

failure criterion to be used. The brittle fracturing mode of

failure can occur when the maximum principal stress is

between 10% and 30% of the laboratory-scale uniaxial

compressive strength25–27 and has frequently been observed

in limestone mine workings26–28. 

Bedding discontinuities were modelled with friction angle

of 30° and cohesion of 1.0 MPa. The normal and shear

stiffness of the bedding discontinuities were both set at 

10 GPa.

Bedding discontinuity effects on roof stability 

The first set of models was run to determine how the

presence of bedding discontinuities affects the stress distribution and potential rock failure in the roof. The rock was

assumed to be elastic and potential failure was identified by

calculating the failure index. The intact rock was not

permitted to fail and redistribute the stress in these models.

Some stress redistribution did occur, however, when bedding

discontinuities were modelled.

The results presented in Figure 6 show the stress distribution in the immediate roof for a case without any bedding

joints in the roof. It can be seen that the immediate roof is

subject to elevated horizontal stresses in the rooms that are

perpendicular to the major horizontal stress. The roof of the

intersection area and rooms parallel to the major horizontal

stress are subject to lower stresses. This indicates that if the

stresses are sufficiently high to cause compressive failure of

the roof, the area between pillars is more likely to fail than

the intersections, which is consistent with observations. 

The failure index results in Figure 7a show that, in the

absence of bedding discontinuities, rock failure potential is a

maximum at the pillar-roof contact and can extend over the

room to form an arch of potential failure up to about 3 m

above the roof line. If a single bedding discontinuity is

introduced 1 m above the roof line, see Figure 7b, the

stresses are re-distributed by the presence of the discontinuity. A reduction occurs in the horizontal stress in the 

1-m-thick roof beam as it deflects downwards and some slip

Figure 6—Plan view of numerical model results showing contours of horizontal stress 1 m above the roof of a room and pillar layout located at 300 m

depth subject to a maximum horizontal stress magnitude of 21.8 MPa

Figure 7—Vertical section along A-A in figure 5 showing rock failure index values (a) without bedding discontinuities and (b) with a bedding discontinuity 

1 m above the roof line
occurs along the bedding discontinuities. Separation of up to

2 mm occurs across the bedding discontinuity near the centre

of the room. The beam deflection causes an increase in

horizontal stress as well as a reduction in confining stress in

the overlying roof, which causes the potential rock failure to

extend to 4 m above the roof line.

A third model was set up in which three bedding discontinuities 1 m apart were introduced above the roof line, shown

in Figure 8a. The potential failure now extends up to 5 m

above the roof line as beam deflection and stress redistribution continues further into the roof. 

In the final case the roof is modelled as a thinly bedded

rock using the ubiquitous joint logic in FLAC 3D. This

assumed that each element in the model contains horizontal

planes of weakness that can shear. The strength of these

ubiquitous weaknesses was set equal to that of the bedding

discontinuities described above. The stability index results

are shown in Figure 8b, which showed the extent of potential

failure is much greater, now extending about 10 m above the

roof line. Inspection of the results showed that slip along the

roof beds allowed more roof deflection to occur, which

reduced the confinement in the roof. 

Assessment of room and pillar layout alternatives

The larger FLAC 3D model was first used to compare

potential roof failure in a regular room and pillar layout using

square pillars. A second assessment was made of a layout

containing rectangular, offset pillars.

For these models, it was assumed that a 5-m-thick

limestone layer was present in the roof of the excavations.

Failure of the roof was again determined using a relatively

low strength of the limestone to highlight the differences

between the layouts. Initial rock failure was determined in

the models from the elastic stress distribution. Potential

failure growth was determined by invoking the Coulombbased strain softening logic in FLAC 3D. A special function

was developed using the internal programming language of

FLAC 3D to simulate the brittle/shearing failure mode

described earlier. Using this approach, stresses are redistributed in response to the initial failure, which causes

further failure to occur. The models were allowed to run until

no more failure growth occurred.

Assessment of a square pillar layout

Figure 9 shows the initial failure and failure growth in the

roof for a layout of square pillars that is (a) aligned with the

direction of maximum horizontal stress and (b) the stress is

rotated through 45°. These results show that for the first

case, failure is likely to initiate between pillars and will grow

in the direction perpendicular to the maximum horizontal

stress, similar to the behaviour observed in limestone mines.

A practical issue with this type of failure is that once failure

starts, it is free to extend laterally across the width of the

mine until a solid abutment or barrier pillar is encountered. 

Figure 9—Plan view showing effect of a change in the orientation of the maximum horizontal stress potential roof failure in a room and pillar layout

consisting of square pillars. Darker shading indicates initial failure and lighter shading indicates potential failure growth. The arrow indicates the direction

of maximum horizontal stress

Figure 8—Vertical section along A-A in Figure 5 showing rock failure index values (a) with three 1-m-thick bedding discontinuities in the roof and (b) thinly

laminated roof
The results for the 45° case show that roof failure is

likely to snake through the pillars, similar to the failure seen

in the field study presented in Figure 5. Again, this type of

failure can continue to extend laterally until a barrier or

abutment is encountered. The model showed that ultimate

roof failure can encircle the pillars, which was observed in

one location at the mine site as shown in Figure 5.

Assessment of a rectangular pillar layout

The practice of aligning pillars and heading development

parallel to the direction of maximum horizontal stress was

simulated to determine whether the models would reflect the

improved stability of this type of layout. The model was set

up to simulate rooms and pillars that were the same width as

those shown in Figure 9, except that the pillar length in the

direction parallel to the maximum horizontal stress was

doubled. In addition, the cross-cuts were offset, a common

practice in the limestone mines, so that the lateral growth of

roof failure is restricted. The results shown in Figure 10a,

presents a case where the cross-cuts are located opposite the

centre of the adjacent pillar, that is, the offset is a maximum.

It can be seen that potential failure initiation is very similar to

that shown in Figure 9a for the square pillar layout.

However, failure growth is restricted to the vicinity of the

cross-cut. Should the failure extend across the adjacent

rooms, it will encounter the adjacent pillar, which will halt its

growth. Figure 10b shows a case where the cross-cut offset

has been reduced. Here, it can be seen that the initial failure

is again similar to the previous case, but the failure growth

cuts across the headings into the adjacent cross-cuts,

resulting in the potential for a continuous band of failures

across the width of the mined area.

Operating limestone mines that have adopted a

rectangular pillar layout aligned with the maximum

horizontal stress typically reduce the cross-cut width to

reduce the exposure to potentially unstable roof. In some

cases, the cross-cut roof is lowered and arched so that it is

not exposed to the horizontal stresses in the main roof.

Conclusions

This review and study of horizontal stress related stability

issues in US limestone mines has shown that:

➤ Horizontal stresses in limestone formations in the

Eastern and Midwestern United States are the result of

plate tectonics and can result in roof damage in

limestone mines 

➤ About 20% of the mines surveyed by NIOSH

researchers experienced horizontal stress related roof

damage

➤ Large oval shaped stress induced rock falls represent a

significant safety and operational hazard. These falls

can extend for many tens of meters across a mined

area, blocking access to mine workings beyond 

➤ Numerical analyses using a two-stage brittle/shearing

failure criterion appears to capture the essence of roof

instability in hard and brittle limestone formations 

➤ The model studies showed that bedding discontinuities

in the immediate roof can exacerbate the depth and

extent of rock failure in the roof. Roof stability is

further degraded by increased deflection and separation

of the bedded roof

➤ The models and mine experience both show that there

is great advantage in aligning the pillar layout parallel

to the direction of maximum horizontal stress and

offsetting cross-cuts so that lateral growth of roof

failures is restricted 

➤ The numerical modelling approach presented in this

paper can be used to assist in limestone mine layout

design when confronted with horizontal stress related

stability problems. 

Disclaimer

The findings and conclusions in this report 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.

Figure 10—Plan view showing effect of a change in the pillar offset on potential roof failure in a room and pillar layout consisting of rectangular pillars.

Darker shading indicates initial failure and lighter shading indicates potential failure growth. The arrow indicates the direction of maximum horizontal

stress
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