ABSTRACT 

 In underground coal mines, concrete block stoppings are widely 

used to control mine ventilation. Although stoppings are not 

intended as roof support, they are subjected to roof to floor 

convergence, and may fail as a result of this loading. Premature 

failure of stoppings can significantly affect mine ventilation, 

limiting the amount of fresh air reaching the working faces and 

increasing the risk for methane explosions. Softening materials are 

often used in stoppings to reduce the damaging effects of roof to 

floor convergence. However, to date, research has not focused on 

the behavior of stopping construction materials subjected to roof or 

floor loading, leaving the design process to trial and error. 

 A combination of numerical simulations and large scale 

physical tests were employed to develop a scientific understanding 

of stopping performance. The first series of physical models were 

constructed using standard CMU (concrete masonry unit) blocks 

and tested in a load frame. The behavior of these walls was 

simulated with a distinct element model. A key finding was that 

very small variations in block size and irregularities in block shape 

significantly affect wall performance. These variations, which are 

inherent to the type of blocks typically used underground, create 

stress concentrations that initiate the failure of stopping walls. A 

second series of models employed concrete stoppings that 

incorporated wood planks, a shredded wood material, and foam 

planks like those commonly used underground. Numerical models 

were again able to match the physical test data. Analysis of the 

softening layers used in stopping construction indicated that the 

strength and stiffness of the material relative to that of the wall is 

crucial in determining the amount of roof to floor convergence the 

wall can withstand prior to failure. 

 The product of this study is a numerical model that can be used 

to evaluate the performance of stopping materials and different wall 

geometries in a controlled environment. Testing was done in a 

laboratory setting with walls constructed on flat, parallel surfaces 

and subjected to uniform loading at a constant rate. Parametric 

studies with the model indicate that in this ideal environment it is 

possible to control the amount of vertical displacement the stopping 

can withstand by adjusting the number of softening layers built into 

the wall and the thickness of the layers. Additionally, under these 

conditions, the position of softening layers within the wall appears 

to have little effect on the amount of displacement walls can 

withstand prior to failure. 

INTRODUCTION 

 Ventilation stoppings, often made of dry-stacked concrete 

blocks, are crucial to maintaining safe, clean air courses in 

underground coal mines. Stoppings are not designed as roof 

support, but are often subjected to vertical loading and may fail 

when roof to floor convergence occurs. Failure of stoppings 

significantly disrupts the mine’s ventilation system and can lead to 

a number of problems, including contaminated air at the working 

faces and increased risk of fire or explosion. In order to increase 

the amount of roof to floor convergence a concrete block stopping 

can withstand prior to failure, softening materials, such as wood or 

foam, can be incorporated into the design of the stopping. 

However, very little research has been done to examine the effects 

of roof to floor convergence on stopping behavior and design of 

these alternative stoppings often consists of trial and error. A 

notable exception is the investigation by Oyler et al., (2001) into 

the response of stoppings subjected to vertical loading from roof 

movements, which concluded that stoppings are able to resist a 

significant amount of roof loading. The study also raised the 

question of softening layers and to what extent a stopping should be 

designed to yield as a means of lengthening its useful life. 

 The goals of this study were to better understand the behavior 

of concrete block walls, evaluate the relative effects of 

incorporating a variety of softening materials into a concrete block 

wall, and to use a numerical model to develop some principles of 

stopping behavior that can serve as guidelines for stopping design. 

In order to achieve these goals, numerical modeling was done in 

conjunction with physical testing in the Mine Roof Simulator 

(MRS) at the Pittsburgh Research Laboratory of the National 

Institute for Occupational Safety and Health (NIOSH). Because of 

its large platen size and high load capacity, the MRS provided a 

unique opportunity to study the complex problem of stopping 

failure in a controlled environment. 

 Development of a numerical model capable of accurately 

simulating the behavior of a concrete block wall began with a study 

into the mechanism by which stopping failure occurs. A 

combination of physical tests and numerical modeling revealed a 

complex failure mechanism. A set of realistic material properties 

for the model were established through a process of literature 

search, physical testing, and numerical modeling of a single 

concrete block. A numerical model was generated in UDEC 

(Itasca, 1985) to simulate the behavior of walls with and without 

NUMERICAL MODELING FOR INCREASED UNDERSTANDING OF THE BEHAVIOR AND 

PERFORMANCE OF COAL MINE STOPPINGS 

Lisa M. Burke, Mining Engineer 

Anthony T. Iannacchione, Senior Scientist 

Thomas M. Barczak, Research Geophysicist 

National Institute for Occupational Safety and Health 

Pittsburgh Research Laboratory 

Pittsburgh, Pennsylvania USA 

Erik Westman, Associate Professor 

Virginia Tech 

Blacksburg, Virginia USA 
softening layers and the output was verified with physical data. 

Finally, the model was used to evaluate the behavior of softening 

materials and to determine three basic principles of stopping 

behavior that can be used in the design of stoppings to withstand 

vertical loading. 

DRY-STACKED BLOCK STOPPING BEHAVIOR 

Failure Mechanism

 Five stopping wall sections with no softening layers were tested 

in the MRS to study the behavior of concrete block walls subjected 

to vertical loading. Each section was made of 21 blocks stacked in 

seven courses approximately 53 inches high, 48 inches wide, and 

6.5 inches thick. The stopping dimensions were chosen with 

enough block interfaces to study the failure mechanism, but with a 

small enough number of blocks so that numerous physical tests 

could be performed and compared with numerical output. Two of 

the walls (noted in figure 1) were made of blocks that came from 

the same manufacturer and were fabricated on the same date. Each 

of the other three walls was constructed using blocks from different 

sources, but within each wall all blocks came from the same source. 

Figure 1 shows the stress-strain curves resulting from the five tests. 

Since all five walls were constructed using standard CMU blocks, 

which are intended to be equivalent in strength, the variability in 

the data is striking. The range of peak stress values is from 

approximately 550 psi to nearly double that at over 1,000 psi. The 

corresponding strain values range from 0.4 to 1.1%. Despite the 

variability in peak strength, the pre- and post-failure moduli are 

consistent at approximately 150,000 and 250,000 psi, respectively. 

 In studying the behavior of these walls, it was determined that 

small variations in block size and shape have a key role in the 

failure of walls subjected to vertical loading (Burke, 2003). When 

adjacent blocks are not the same height, vertical loading results in a 

concentration of stresses in the blocks directly above or below the 

vertical interface, as shown in figure 2. These stress concentrations 

lead to the development of small cracks, which propagate through 

the concrete and into adjacent blocks, ultimately resulting in failure 

of the stopping. In the wall tests discussed above, this failure 

mechanism was observed and cracking occurred in multiple 

locations throughout each wall. Measurements of block height 

recorded prior to testing showed that variations in block size as 

small as 1/16 inch were contributing to this failure mechanism. 

Table 1. Summary of results from property testing of fifteen 

individual standard CMU blocks 

Block Set Test # Modulus 

(psi) 

Peak Stress 

(psi) 

% Strain at 

Peak 

1 1 241,250 1,600 1.11 

1 2 198,125 1,750 1.75 

1 3 149,091 1,409 1.71 

Set 1 Avg 196,155 1,586 1.52 

Set 1 St Dev 46,111 171 0.36 

2 4 262,742 2,968 1.91 

2 5 262,742 2,871 1.96 

2 6 197,778 3,255 2.3 

Set 2 Avg 241,087 3,031 2.06 

Set 2 St Dev 37,507 200 0.21 

3 7 243,125 2,560 1.21 

3 8 226,154 2,192 1.19 

3 9 169,219 1,890 1.58 

3 10 158,548 2,288 1.9 

3 11 262,500 2,463 1.54 

Set 3 Avg 211,909 2,279 1.48 

Set 3 St Dev 45,844 261 0.29 

4 12 213,830 2,234 2.22 

4 13 160,122 2,138 1.81 

4 14 251,200 2,125 2.18 

4 15 219,091 2,384 2.78 

Set 4 Avg 211,061 2,220 2.25 

Set 4 St Dev 37,763 120 0.40 

All Data Avg 214,161 2,272 1.84 

All Data St Dev 40,498 507 0.46 

Material Properties 

 In order to develop a realistic set of material properties, four 

sets of standard CMU blocks from different sources were tested in 

the MRS. Results of these tests are summarized in table 1. 

Although the weight and dimensions of all fifteen blocks were 

nominally the same, a substantial amount of variation in peak stress 

and strain exists within each block set and an even greater amount 

of variation exists between block sets. Among these fifteen 

0

200

400

600

800

1000

1200

0.0 0.5 1.0 1.5 2.0 2.5

% Strain

Vertical Stress (psi)

Two walls from 

the same block 

set

Figure 1. Stress-strain curves resulting from MRS testing of 

seven course standard CMU block walls dry-stacked with no 

softening layers.

Stress 

Concentration 

Figure 2. Difference in height of adjacent blocks causes stress 

concentration, which leads to the formation of tensile cracks in 

blocks above or below the block interface.
samples, the peak stress varied from about 1,400 to 3,300 psi and 

the corresponding strain values varied from approximately 1.1 to 

2.8 %. The amount of variation in modulus of elasticity between 

sets is similar to the amount of variation within each set and the 

average value of all data was selected as numerical model input. 

Unlike material tests meeting ASTM specifications, these tests 

were conducted on full scale samples and much of the variability 

may be due to dimensional differences rather than material 

properties, which should reflect the performance of blocks in the 

walls. 

 Material properties that could not be directly measured from 

physical data were obtained through literature search and FLAC 

(Itasca, 1986) modeling of a single block (Burke, 2003). The 

material properties used in the numerical model are shown in 

table 2. 

Table 2. Material properties used in numerical simulation of wall 

behavior. 

Property Value Units Source 

Density 10.82 lbs/ft3 calculated from block 

measurements 

Modulus of 

elasticity 214,161 psi calculated from MRS data 

Poissons ratio 0.2 American Concrete Institute 

1986 

Internal angle 

of friction 32 degrees determined from numerical 

modeling 

Cohesion 310 psi determined from numerical 

modeling 

Dilation angle 12 degrees Vermeer and de Borst 1984 

Tension limit 100 psi Drysdale and Hamid 1984 

Model Performance 

 A plane stress model was developed using the distinct element 

code, UDEC (Itasca, 1985). Based on the distribution of block 

sizes measured in the five physical wall tests, a set of nonuniformly sized blocks was randomly generated and the cell space 

mapping configuration (Hart, 1993) was used to define the blocks 

in the model. A strain-softening material model was used to 

simulate the behavior of the concrete. 

 A comparison between the numerical model failure mechanism 

and physical test data showed good correlation. Figure 3 shows the 

concentrations of vertical stress in the wall model. The vertical 

stresses are not distributed uniformly, but tend toward two distinct 

columns of high vertical stress. Additionally, two locations of 

particularly high stress, the dark areas in the top two courses of 

blocks, correspond to the interfaces with the largest height 

difference between adjacent blocks. These stress concentrations 

help confirm that the failure mechanism in the model is similar to 

that observed in physical data. Failure of the model occurred at a 

peak stress of approximately 900 psi (figure 4), which is similar to 

the results of the physical wall tests originally shown in figure 1 

and included in figure 4 for comparison. 

SOFTENING MATERIALS 

Physical Testing 

 Four softening materials were tested under vertical loading: 

1.5-inch-thick timber (poplar and pine) planks, Fibroplank, and a 

foam plank. Fibroplank is a 2.5-inch-thick shredded wood and 

Figure 5. Fibroplank and foam materials used in MRS tests of 

block walls incorporating softening materials.

Figure 4. Comparison of stress-strain curves resulting from 

physical testing (MRS) and numerical modeling (UDEC) of a 

seven-course concrete block wall dry-stacked with no 

softening layer.

0

200

400

600

800

1000

1200

0.0 0.5 1.0 1.5 2.0 2.5

% Strain

Vertical Stress (psi)

MRS data

UDEC Model

Figure 3. Non-uniform distribution of vertical stresses in the 

UDEC model of a seven-course concrete block wall drystacked with no softening layers.

Wall stress 
cement product used by some mines as a softening layer in 

stoppings and shown in figure 5. A foam with a density of two 

pounds per cubic foot and a thickness of two inches was chosen for 

the study. The foam plank, also shown in figure 5, had a strength 

of 25 to 33 psi, according to the manufacturer. All four materials 

exhibited strain-hardening behavior and the results from the 

material testing are described in table 3. Of particular importance 

is the significant difference in strength between the pine samples. 

The two samples came from different sources, were not the same 

quality, and had not been subjected to the same drying processes. 

The stronger sample yielded at a peak strength more than double 

that of the weaker sample. 

Table 3. Summary of results from property testing of four 

softening material specimens. 

Yield Stress (psi) at: 

Material Thickness, 

(in) 

Sample 

number Stress 

(psi) 

% 

Strain 

40% 

Strain 

55% 

Strain 

62% 

Strain 

Poplar 1 900 8.5 1,555 2,380 -- 

timber 1.5 

2 900 8.5 1,700 2,715 -- 

Pine 1 1,100 5.0 760 1,080 -- 

timber 1.5 

2 500 8.0 1,555 2,370 3,510 

Fibro- 1 200 6.0 690 -- -- 

plank 2.5 

2 200 5.0 785 2,170 -- 

Foam 2.0 1 0 0.0 42 230 1,400 

 Walls were constructed and tested in the MRS to study the 

impacts on wall behavior of the four softening materials. In each 

case a single softening layer was placed below the top course of 

blocks, as shown in figure 6. The stress-strain curves resulting 

from these tests are given in figure 7. 

 Of the two walls tested with poplar planks, one wall failed at a 

peak stress of 900 psi and the other around 1,000 psi. In the 

softening material tests, the poplar samples yielded around 900 psi. 

In figure 7, the effect of these wood layers can be seen in the 

stiffness change in the stronger wall between 900 psi and 1,000 psi 

when the wall failed. In the weaker wall, the effects of the wood 

are not as prominent because the blocks failed at the point where 

the wood was just beginning to yield (around 900 psi). The 

relatively large difference in strain is thought to be due to the initial 

contact configuration of the wall. The higher strain exhibited a 

very soft initial response which may be caused by the uneven block 

coated with the load frame and of the block-timber interface. 

 Similar results were seen in the walls containing the two types 

of pine discussed previously. As in the poplar wall tests, one wall 

failed around 900 psi while the other failed at approximately 

1,000 psi. In this case, the wall containing the 500 psi pine layer 

clearly shows a substantial change in stiffness at 500 psi as the 

wood begins to yield. The other wall, however, was built using the 

1,100 psi pine and the wall failed at 900 psi. Since the yield 

strength of the wood was higher than that of the wall, the effects of 

the wood on the wall behavior were minimal up to the peak stress 

of the wall. 

 The stress-strain curve from the wall containing Fibroplank 

follows the same trend as that of the walls containing wood. 

Although the change in stiffness is less dramatic in the Fibroplank 

wall, there is a small change around 200 psi, where the Fibroplank 

began to yield. Similar to the wood and Fibroplank, the foam was 

effective in softening the wall and allowing additional convergence 

to occur prior to failure of the wall. The foam, however, had very 

little stiffness initially and began to yield as soon as vertical 

displacement occurred. Thus, the foam allowed a significant 

amount of deformation under a very small load. 

 In analyzing the effects of softening layers on wall 

performance, focus was largely on the elastic portion of the wall 

stress-strain curves, rather than the post-failure behavior of the 

walls. The reason for this lies in the requirements placed on a 

ventilation stopping. In contrast to a roof support structure, where 

it is desirable to load up quickly and maintain the high load as long 

as possible, a stopping is more likely to be successful if it can 

respond to ground movement with minimal load. For example, in 

the test of a wall containing the 1,100 psi pine (shown in figure 7), 

after the peak load was reached, the wood began to split apart, 

deforming only slightly and allowing the wall to maintain a high 

load over 1.5% strain. However, during the time when the load 

was being maintained, the concrete was crumbling to an extent that 

would have impaired its ability to function as a useful ventilation 

Figure 6. Seven-course concrete block wall dry-stacked with 

one layer of wood below the top row of blocks and tested in the 

MRS.

Strain softening layer 

Figure 7. Stress-strain curves resulting from MRS tests of 

seven-course block walls built with one softening layer below 

the top course of blocks.

0

200

400

600

800

1000

1200

1400

1600

0.0 1.0 2.0 3.0 4.0 5.0

% Strain

Vertical Stress (psi)

Poplar

1,100 psi pine

0

200

400

600

800

1000

1200

1400

1600

0.0 1.0 2.0 3.0 4.0 5.0

% Strain

Vertical Stress (psi)

Poplar

1,100 psi pine

Foam

Fibroplank

500 psi pine
structure. In contrast, in the wall with a foam layer, the 

displacement occurred while the stopping was supporting a very 

low load and no significant damage was sustained as the foam 

deformed. The key to extending the life of a stopping, then, is to 

increase the displacement experienced by the wall prior to reaching 

its peak load. 

Model Performance 

 Based on the material tests conducted in the MRS, model walls 

were developed that simulated inclusion of the softening materials 

without changing the previously defined model properties. 

Correlation between the numerical models and physical data was 

remarkably good. Stress-strain curves from the poplar timbers, 

pine timbers, and Fibroplank models are given in figures 8, 9 and 

10, respectively. 

Table 4. Summary of parametric studies conducted with UDEC model. 

Timber Wood yield point 

layer 

description 

Number 

of 

layers 

Position(s) of timber 

layer(s) 

Modulus of 

elasticity (psi) 

before yield 

Stress 

(psi) % Strain 

Modulus of 

elasticity (psi) 

after yield 

Peak stress 

(psi) 

% Strain at 

peak stress 

Displacement 

at peak stress, 

in 

2" Pine 1 below course 1 (top) 85,079 514 0.75 30,522 1,030 2.73 1.49 

2" Pine 2 below courses 1 & 6 60,735 526 0.98 24,338 1,030 4.49 2.54 

2" Pine 3 below courses 1, 5, 6 55,757 522 1.14 17,571 1,030 6.06 3.55 

2" Pine 4 below courses 1, 2, 5, 6 43,175 530 1.37 10,886 1,030 7.66 4.63 

2" Pine 1 below course 1 (top) 85,079 514 0.75 30,522 1,030 2.73 1.49 

2" Pine 1 below course 2 75,539 451 0.70 31,583 1,020 2.69 1.47 

2" Pine 1 below course 3 65,873 543 0.88 32,411 1,010 2.60 1.42 

2" Pine 1 below course 4 72,182 467 0.71 31,983 1,000 2.82 1.54 

2" Pine 1 below course 5 83,657 514 0.76 28,222 1,020 2.69 1.47 

2" Pine 1 below course 6 (bottom) 77,333 513 0.73 24,000 992 2.71 1.48 

2" Pine 1 below course 1 (top) 85,079 514 0.75 30,522 1,030 2.73 1.48 

4" Pine 1 below course 1 (top) 64,204 525 1.13 18,626 1,060 4.70 2.66 

6" Pine 1 below course 1 (top) 50,292 509 1.38 13,558 1,070 6.33 3.70 

Figure 8. Comparison of stress-strain curves from physical 

(MRS) and numerical (UDEC) testing of a seven-course wall 

with one layer of poplar timber below the top row of blocks.

0

200

400

600

800

1000

1200

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

% Strain

Vertical Stress (psi)

MRS walls

UDEC simulation

Figure 9. Comparison of stress-strain curves from physical 

(MRS) and numerical (UDEC) testing of a seven-course wall 

with one layer of 500 psi pine timber below the top row of 

blocks.

0

200

400

600

800

1000

1200

0.0 1.0 2.0 3.0 4.0 5.0

% Strain

Vertical Stress (psi)

MRS wall

UDEC simulations

Figure 10. Comparison of stress-strain curves from physical 

(MRS) and numerical (UDEC) testing of a seven-course wall 

with one layer of Fibroplank below the top row of blocks.

0

200

400

600

800

1000

1200

0.0 1.0 2.0 3.0 4.0 5.0

% Strain

Vertical Stress (psi)

MRS wall

UDEC simulation
PARAMETRIC STUDIES 

 The wall model containing a layer of soft pine most closely 

replicated the physical data and was used as the basis for 

parametric studies examining the behavior of various stopping 

designs. Due to the large amount of variability in block and wall 

behavior, it is very difficult to conduct studies such as these with 

only physical data. The numerical model, however, can be used to 

evaluate the effects of various changes in wall geometry separate 

from the effects of block variability. 

 The first parametric study was conducted to consider the effects 

of adding more than one softening layer to a wall. All layers were 

identical and the layers appeared to have very little effect on one 

another. The model showed that each additional softening layer 

resulted in a slight decrease of the overall stiffness of the wall and 

an increase in displacement approximately one inch, but did not 

appear to have an effect on the peak stress the wall experienced 

prior to failure. These data are shown in table 4. 

 The second parametric study examined the impact on wall 

behavior of moving the softening layer to different locations within 

the wall. Each model had a single pine layer placed in one of six 

possible positions within the wall. The six models indicated that 

the location of the softening layer did not have a significant effect 

on the overall wall behavior. The small amount of variation in 

modulus of elasticity, peak stress, and strain shown in table 4 is 

likely due to local inconsistencies in block size and shape that may 

behave differently when they are placed adjacent to the softening 

layer. 

 The final parametric study considered the effects of increasing 

the thickness of a single softening layer. The results of this study, 

shown in table 4, indicated that the effects of increasing layer 

thickness are similar, although slightly greater in magnitude than 

the effects of incorporating multiple layers. Adding a second two 

inch layer (for a total of four inches of softening material) resulted 

in a 1.05-inch increase in displacement prior to failure and a 

6,184 psi decrease in modulus of elasticity. Similarly, replacing a 

single two inch layer with a four inch layer resulted in a 1.17 inch 

increase in displacement prior to failure and an 11,896 psi decrease 

in modulus of elasticity. 

SUMMARY AND CONCLUSIONS 

 The behavior of dry-stacked concrete block stoppings was 

studied through a combination of physical testing in the MRS and 

numerical modeling. This process led to a number of important 

conclusions. 

• Very small differences in block size and shape have a 

dramatic effect on the behavior of a wall, significantly 

reducing the magnitude of vertical load the wall can 

withstand prior to failure. 

• Softening layers made of a variety of materials, including 

wood, foam, and Fibroplank, can be used to lessen the 

damaging effects of vertical loading due to roof to floor 

convergence. 

• In order to design a stopping that can effectively withstand a 

projected level of roof to floor convergence, it is important to 

consider the relative strength and stiffness of the blocks and 

softening layers and to take into account the variations in 

these material properties that will likely exist. 

 An important output of the study was a set of basic principles 

governing the behavior of stoppings with softening layers under the 

conditions specified in the model. Such principles should be taken 

into account in the design of stoppings that will be subjected to 

vertical loading. Through comparisons of numerical and physical 

data, the model was shown to be capable of accurately simulating 

the behavior of a block stopping with and without softening layers. 

Parametric studies (using pine timber as a softening material) led to 

the development of three principles of stopping behavior. 

• If multiple layers of a pine timber material are used in the 

same wall, each layer will increase the deformation by 

approximately the same amount. 

• Under the test conditions simulated, the location of the 

softening layer within the wall has very little effect on the 

amount of deformation the wall can withstand prior to 

failure. 

• Doubling the thickness of a single softening layer will 

increase the deformation of the wall slightly more than 

incorporating two layers of the original thickness. 

 The model was developed to study a complex problem in a 

controlled environment and has been used to simulate the flat 

surfaces and uniform loading conditions that exist in the MRS. 

Mine conditions will differ to varying extents from those in the 

MRS and for this reason, future studies should include adapting the 

model to replicate key mine conditions, such as an uneven roof and 

floor and non-uniform loading across the width of the wall. 

Stopping construction techniques and dimensions vary as well and 

these factors should be taken into account to facilitate study of 

other and more complex stopping design scenarios. Of course, the 

engineering design process cannot neglect MSHA regulations 

regarding wall strength and fire resistance. In order to develop 

more comprehensive design guidelines, consideration must also be 

given to these factors. 

 In addition to the vertical loading simulated in these models and 

physical tests, stoppings are subjected to transverse loading due to 

air pressure. This additional direction of loading in combination 

with non-uniform vertical loading may produce an out-of-plane 

buckling failure in stoppings that is difficult to reproduce in a twodimensional model. Studying this type of failure is important in the 

development of innovative stopping designs and should be an 

integral part of future studies into stopping behavior. 

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American Concrete Institute (1986). ACI Manual of Concrete 

Practice 1986. Part 1. Detroit, American Concrete Institute. 

Burke, L.M. (2003). Numerical Modeling for Increased 

Understanding of the Behavior and Performance of Coal Mine 

Stoppings. M.S. Thesis, Virginia Polytechnic Institute and State 

University, 114 pp. 

Drysdale, R.G. and Hamid, A.A. (1984). Tensile failure criteria for 

plain concrete masonry. Journal of Structural Engineering. 110.2 

(February), pp. 228-244. 

Hart, R.D. (1993). An Introduction to Distinct Element Modeling 

for Rock Engineering. Proceedings, 7th International Congress on 

Rock Mechanics, Aachen, Germany, September, Vol. 3, pp. 1881-

1891. 

Itasca Consulting Group, Inc. (1986). FLAC, Version 4.0 

Computer Software. Itasca Consulting Group, Inc., PC-WIN, 

35MB, CD-ROM. 
Itasca Consulting Group, Inc. (1985). UDEC, Version 3.1 

Computer software. Itasca Consulting Group, Inc., PC-WIN, 2MB, 

CD-ROM. 

Oyler, D.C., Hasenfus, G. and Molinda, G.M. (2001). Load and 

Deflection Response of Ventilation Stoppings to Longwall 

Abutment Loading – A Case Study. Proceedings, 20th 

International Conference on Ground Control in Mining. 

Morgantown: West Virginia University, Aug. 7-9, pp. 34-14. 

Vermeer, P.A. and De Borst, R. (1984). Non-Associated Plasticity 

for Soils, Concrete and Rock. Heron 29.3, p. 3-64.