FIELD OBSERVATIONS AND NUMERICAL STUDIES OF 


HORIZONTAL STRESS EFFECTS ON ROOF STABILITY IN 


U.S. LIMESTONE MINES 


G. S. Esterhuizen 


D. R. Dolinar 


A. T. Iannacchione 


National Institute for Occupational Safety and Health 


Abstract 

Limestone formations in the United States can be subject to relatively high horizontal 

stresses owing 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 rock fall hazard. Rock falls 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 has an effect on the horizontal stress distribution within the roof. The 

effects of high horizontal stresses can be mitigated by orienting the heading 

development direction parallel to the maximum horizontal stress, reducing the number 

of cross-cuts and off-setting 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. 

1.1 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 mines [1]. Owing 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. Hasenfus [2] summarized the historical 

development of an understanding of horizontal stress issues and mitigation techniques 

in coal mines, dating back to the 1950’s. In hard rock mines horizontal stress induced 

stability problems have been identified and documented since the 1960’s [3, 4]. 
Horizontal stress related stability issues in U.S. limestone mines and techniques to 

improve stability by support and changes in mine layout have been well documented in 

the literature [5, 6, 7, 8, 9, 10, 11]. This paper provides a review of the horizontal 

stresses and related roof stability issues in U.S. 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. 

2.1 	 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 U.S. can be much higher than 

the overburden stress. Horizontal stresses in limestone formations have been measured 

in limestone mines [7] and in many of the area’s coal mines [12]. Research has shown 

that the horizontal stress may be explained by the effect of plate tectonics [7, 13]. 

Tectonic loading is related to the movement of the North American plate as it is pushed 

away from the Mid-Atlantic ridge. A constant strain field of between 0.45 and 0.90 

millistrains is associated with the tectonic loading, which 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 time [8, 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 U.S. and Eastern Canada [13] 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: 

σ 0.041h + 9.51 (MPa) (1) h max

where: h is the depth in meters. 

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 Project [15]. The magnitude of the minimum horizontal stress is 

approximately one half the maximum horizontal stress. 
y = 0.0407x + 9.5082 

R 2

 = 0.3337 

0.00 

10.00 

20.00 

30.00 

40.00 

50.00 

60.00 

Stress (MPa) 

0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 

Depth (m) 

Figure 1. Maximum horizontal stress measurements in limestone and dolomite 

formations in the Eastern and Midwest U.S. and Eastern Canada, showing a fitted 

straight line and equation. 

3.1 Roof Stability and Horizontal Stress Related Damage 

3.1.1 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 instability [16]. 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 

Bieniawski [17]. 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 meter 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 meters. 

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. 

3.1.2 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 strata [6, 12, 18]. Stress mapping 

techniques were used to identify the occurrence of horizontal stress related instability 

[18]. Various forms of roof damage were observed and are described below. 

3.1.2.1 Roof Guttering 

Horizontal stress related damage can manifest itself as guttering along the pillar-roof 

contact area [6, 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. 

3.1.2.2 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 occur [5, 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. 
Figure 2. Roof guttering at the pillar-roof contact. 

3.1.2.3 Oval Shaped Falls 

Another common manifestation of horizontal stress is large oval-shaped falls, with the 

long axis oriented approximately perpendicular to the major horizontal stress [6], 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 roof [9]. 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. 

3.1.2.4 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 meters, 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 direction [6]. 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 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 over lying strata in a limestone mine. 
 

 

July 26 

5

1

2

3

0

4

July 14 

July 26 

Oct. 3 

Roof Fall - Oct. 3 

Lower Roof Beam 

Began to Fail 

Pillars 

Roof Monitor 

Roof sag (cm) 

0 25m 

0 70 Days

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]. 

3.2 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. Re-orienting the excavations and modifications of mine 

layouts have been successful in improving roof conditions in several cases [8, 10, 11, 

20]. The method includes re-orienting the mining layout so that the main direction of 

development is parallel to the direction of maximum horizontal stress and limiting the 

number of cross-cuts. 

4.1 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 model [21, 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 software [23] was used to assess roof stability for the 

typical stress conditions and mining dimensions that are found in U.S. 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 modeled. 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. 

4.1.1 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 modeled. 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. 

The rock failure criterion was based on a two-stage failure process consisting of brittle 

fracturing and frictional shearing [24, 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 strength 

[25, 26, 27] and has frequently been observed in limestone mine workings [26, 27, 28]. 
Pillar Pillar

Pillar Pillar

A

A

on of 

um 

al 

15-20

20-25

25-30

35

40

Bedding discontinuities were modeled 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. 

4.1.2 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 re-distribute the stress in 

these models. Some stress re-distribution did occur, however, when bedding 

discontinuities were modeled. 

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. 

Directi

maxim

horizont

stress

30-

35-

Stress

(MPa)

Pillar Pillar 

Pillar Pillar 

A 

A 

Direction of 

maximum 

horizontal 

stress 

15-20 

20-25 

25-30 

30-35 

35-40 

Stress 

(MPa) 

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. 

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 
0 5m

Roof line

>1.5

1.0 1.5

0.5 1.0

0.0 0.5

Key

Room

Bedding 

discontinuities

0 5m

>1.5

1.0 1.5

0.5 1.0

0.0 0.5

Key

0 5m 

Roof line 

>1.5 

1.0 1.5 

0.5 1.0 

0.0 0.5 

Key 

a)

>1.5

1.0 1.5

0.5 1.0

0.0 0.5

Key 

Bedding 

discontinuities 

Room 

0 5m b)

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. 


Roof line

a) 0 5m

>1.5

1.0-1.5

0.5-1.0

0.0-0.5

Key

0 5m 

Roof line 

>1.5 

1.0-1.5 

0.5-1.0 

0.0-0.5 

Key Bedding 

discontinuity 

0 5m

Room

>1.5

1.0-1.5

0.5-1.0

0.0-0.5

Key

b)

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. 

some slip occurs along the bedding discontinuities. Separation of up to 2 mm occurs 


across the bedding discontinuity near the center 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 modeled 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. 
4.1.3 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 Coulomb-based 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 re-distributed in response to the initial failure which causes 

further failure to occur. The models were allowed to run until no more failure growth 

occurred. 

4.1.3.1 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 behavior 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. 

Pillar

Pillar Pillar

Pillar Pillar

Pillar Pillar

Pillar

a) b)

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. 
 

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. 

4.1.3.2 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 crosscuts 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 crosscuts are located opposite the center 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 crosscut. 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. 

Pillar

Pillar

Pillar

Pillar

Offset

Pillar

Pillar

Pillar

Offset

a) b) 0 10m 0 10m 

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. 
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. 

5.1 Conclusions 

This review and study of horizontal stress related stability issues in U.S. limestone 

mines has shown that: 

a) 	 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. 

b) 	 About 20% of the mines surveyed by NIOSH researchers experienced 

horizontal stress related roof damage. 

c) 	 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. 

d) 	 Numerical analyses using a two-stage brittle/shearing failure criterion appears 

to capture the essence of roof instability in hard and brittle limestone 

formations. 

e) 	 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. 

f) 	 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 crosscuts so that lateral growth of roof failures is restricted. 

g) 	 The numerical modeling 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. 

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