mechanics of interseam failure in multiple · ‘ mechanics of interseam failure in multiple...
TRANSCRIPT
‘ MECHANICS OF INTERSEAM FAILURE IN MULTIPLEHORIZON MINING/
byEddie N. =BarkQ
Thesis submitted to the Faculty of the
Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
in _· Mining Engineering
APPROVED: /’/ — „ . __,ii CET; ig
C. Haygbcks, Chairmanl
Karmis’/;/E/„’
J. R. Lucas, Dept. Head R. Krebs „C//
June, 1982
Blacksburg, Virginia
ii
TABLE OF CONTENTS
.?2S.<2ACKNOWLEDGMENTS ......................... ii
LIST OF FIGURES ......................... vi
LIST OF TABLES ......................... x
CHAPTER
I. INTRODUCTION ....................... l
II. LITERATURE REVIEW ..................... 3
2.1 General ....................... 3
2.2 Geological Factors .................. 24
2.3 Stability Analysis .................. 27
2.3.1 Mohr-Coulomb Criterion ............ 29V
2.3.2 Finite Element Method ............. 31
2.3.2.1 Advantages of the Finite ElementMethod ................ 34
2.3.2.2 Modeling Criteria for the FiniteElement Me¤h¤d ............ 35
2.4 Brittle Model .................... 39
2.4.1 Comparison of Model Material and NaturalRock ..................... 43
2.4.2 Properties of Model Material ......... 44
III. CASE STUDIES ....................... 47
3.1 Case Study No. 1 ................... 47
3.2 Case Study No. 2 ................... 49
3.3 Case Study No. 3 ................... 49
3.4 Case Study No. 4 ................... 52
3.5 Case Study No. 5 ................... 52
iiih
Chapter Pägg
3.6 Case Study No. 6 ................... S5
IV. PHYSICAL MODELING . . .".................. 58
4.1 Description of Test Equipment ............ 58
4.2 Design of Loading Frame ............... 63
4.3 Instrumentation ................... 66
4.4 Developing a Model Material ............. 66
4.4.1 Laboratory Testing .............. 70
4.5 Procedure ...................... 72
V. COMPUTER MODELING .................... 75
5.1 Finite Element Mesh Generation ............ 78
5.1.1 Model I ................... 81
Model II ................... 84
5.1.3 Model III ................... 84
5.1.4 Model IV ................... 87
5.1.5 Model V ................... 87
5.2 Computer Codes Used in the Analysis ......... 90
5.2.1 The Mesh-plot Program ............. 90
5.2.2 The Finite Element Computer Code ....... 90
- 5.2.3 The General Purpose Contouring Program(GPCP) .................... 91
5.3 Procedure ...................... 92
VI. RESULTS .......................... 95
6.1 Computer Modeling .................. 95
6.1.1 Model I .................... 95
6.1.1.1 Effect of Modulus .......... 990
iv
Chapter Page6.1.1.2 Effect of Poisson's Ratio ...... 102
6.1.1.3 Effect of Density .......... 103
6.1.1.4 Effect of Cohesion .......... 109
6.1.1.5 Effect of Angle of Internal Friction . 111
6.1.1.6 Effect of Proximity of Seams ..... 115
6.1.2 Model II ................... 122
6.1.3 Model III ................... 123
6.1.4 Model IV ........... _........ 126
6.1.5 Model V 128
6.2 Physical Model .................... 128
VII. SUMMARY .......................... 132
VIII. CONCLUSIONS AND RECOMMENDATIONS .............. 135
8.1 Conclusions ..................... 135
8.2 Recommendations ................... 136
REFERENCES ........................ 138
APPENDICES ........................ 145
Appendix A Modified Finite Element Program Used inthe Computer Analysis .......... 145
Appendix B Safety Factor Contours Obtained from theAnalysis ................. 171
VITA ........................... 196
v
LIST OF FIGURES
Figure Page
1. Massive Interseam Failure Caused by Removal of theUnderlying Pillars (after Stemple, 1956) ....... 4
2. Shear Failure in Redstone Seam Over Robbed LowerSeam (after Holland, 1951) .............. 6
3. Bending, Shearing and Readjustment of Level Causedby Subsidence in the Lower Seam (after Holland, 1951) . 7
4. Bending in Humph Coal After Mining a Lower Seam(after Holland, 1951) ................. 8
5. Model of Strata Disturbance Above a Fully ExtractedUnderlying Panel (after Peng and Chandra, 1980) .... 9
6. Relationship Between Interseam Thickness and Widthof Opening (after Hedley, 1978) ............ ll
7 . Relationship of Innerburden Thickness and Z Sandstonefor Room and Pillar System in the Appalachian CoalRegion (after Haycocks and Karmis, 1981) ....... 13
8. Damage in Upper Coal Seams (after Stemple, 1956) . . . 16
9. Shearing Action in the Gob Region of a Longwall Panel(after Engineers International, 1981) ......... 18
10. Effect of Parting Thickness on Extraction When MiningAbove a Worked—Out Seam (after Engineers International,1980) ......................... 19
11. Typical Failure of a Bolted Mine Roof (after Cox, 1974) 21
12. Stages of Roof Failure Showing the Shearing Action WhenMbderately Transverse Jointing are Encountered (afterAdler, 1973) ..................... 22
13. Stages of Roof Failure Showing the Shearing Action WhenSevere Transverse Jointing are Encountered (after Adler,1973) ......................... 23
14, Mohr—Coulomb Failure Criterion (after Desai andSiriwardane, 1981) .................. 32
vi
Figure Page
15. Numbering of Nodes—to Reduce Band Width (after DesaiI I I I I I I I I I I I I I I I I I II16.
Inaccuracy of Solution as a Function of Aspect Ratio(after Desai and Abel, 1972) ............. 38
17. Effect of External Boundary Location on Accuracy ofFinite Element Method Solution (after Kulhawy, 1974). . 40
18. Geological Column of Case Study No. 1 ......... 48
19. Geological Column of Case Study No. 2 ......... 50
20. Geological Column of the Central Pennsylvania CoalArea, Cambria County (after Hasler, 1951) ....... 51
21. Geological Column of Case Study No. 4 ......... 53
22. Geological Column of Case Study No. 5 ......... 54
23. Geological Column of Case Study No. 6 (after Peng andI I I I I I I I I I I I I I I I I I I
I24.Loading Frame Used in the Physical Modeling ...... 59
25. Design and Construction of the Loading Bracket and itsRelation to the Loading Frame ............. 65
26. Classification of Modeling Materials (after Stimpson,I I I I I I I I I I I I I I I I I I I I I I II27.
Relation Between Compressive Strength and CylinderLength (after Hobbs, 1967) .............. 71
28. Stress at a Point on a Fracture Surface (after Wang,E I I I I I I I I I I I I I I I I I I I I I
I29.Simplified Geological Column Used in the Analysis . . . 79
3OI I I I I I I I I I I III
I I I I I I I I I I I
I3lII I I I I I I I I I I I I I I I I I I I I I
I32II I I I I I I I I I I I I I I I I I I I I I
I33II I I I I I I I I I I I I I I I I I I I I I
I34II I I I I I I I I I I I I I I I I I I I I I I
Ivii
Figure Page
35. Safety Factor Contour Plot of Model I ..... . . . . 97
36. Effect of Modulus of the Interseam on Failure in theUpper Seam ...................... 100
37. Critical Fracture Surfaces for Varying Modulus ofthe Innerburden .................... 101
38. Effect of Poisson Ratio of the Interseam on Failurein the Upper Seam ................... 104
39. Critical Fracture Surfaces for Varying Poisson Ratioof the Innerburden .................. 105
40. Effect of Density of the Interseam on Failure in theUpper Seam ...................... 107
41. Critical Failure Surfaces for Varying Density of theInnerburden ...................... 108
42. Effect of Cohesion in the Interseam on Failure in theUpper Seam ...................... 110
43. Critical Fracture Surfaces for Varying Cohesion ofthe Innerburden .................... 112
44. Effect of Angle of Internal Friction of the Interseamon Failure in the Upper Seam ............. 113
45. Critical Failure Surfaces for Varying Angle of InternalFriction of the Innerburden ............. 114
46. Effect of Proximity of Two Seams on Interseam Failure . 117
47. Critical Failure Surface (Interseam Distance = 49.5 ft) 118
48. Critical Failure Surface (Interseam Distance = 69.5 ft) 119
49. Critical Failure Surface (Interseam Distance = 89.5 ft) 120
50. Critical Failure Surface (Interseam Distance = 119.5 ft) 121
51. Critical Failure Surface-—Model II .... „ ..... 124
52. Critical Failure Surface——Model III .......... 125
53. Critical Failure Surface——Model IV .......... 127
viii
Figure Page54. Critical Failure Surface——Model V........... 12955. Initial Fracture Pattern of Model Test........ 131
ix
LIST OF TABLES
Table Page
1. Some Physical Parameters, Their Dimensions andModel Scale Factors (after Hobbs, 1967) ........ 45
2. Rated Delivery of ENERPAC EEM 435L Pump ........ 61
3. Rated Delivery of ENERPAC PEM 3022C Pump ....... 62
4. Test Results of Uniaxial Compressive Strength ofDifferent Mixtures of Sand and POR-ROK Cement ..... 73
S. Material Parameters Used in the Analysis (afterAgbabian, 1978; Obert and Duvall, 1969). ....... 82
x
CHAPTER I
V INTRODUCTION
There are many mineable, contiguously placed coal seams in the
Appalachian Coalfields. Historically, the selection of the mining
sequence has been based primarily on seam ownership, availability and
economics. However, the mining of any seam without consideration for
the ground control problems that can occur may seriously affect subse-
quent operations in the coal seams above and below the mined area. Such
practices are often reflected in the recovery, cost and safety hazards
in the mining of subsequent seams.
The ground control mechanisms controlling mu1ti—seam mining in the
Appalachian Coalfields has been isolated into these four areas:—— massive interseam failure
-- pillar load transferV
—— subsidence-— arching
The objective in this study is to determine the factors controlling the
massive interseam failure in the Appalachian Coalfields and to produce
firm mining guidelines that will facilitate optimum seam extraction,
safety and minimum mining costs (Haycocks and Karmis, 1981).
Interseam failure might occur in a multiple horizon mine as an
alternative to the formation of a subsidence trough over an excavation.
Highly inclined shear or shear tensile failures may develop which
usually results in block movement of the ground into the lower
l
2
excavations. This phenomenon has been recorded by several observers
(Barrientos and Parker, 1974; Holland, 1951; and Stemple, 1956).
In order to understand the mechanisms involved in the interseam
failure of a contiguous seam operation, the following parameters will
be considered in this research:
i) The effect of horizontal to vertical load ratio.
ii) The effect of relative stiffness of the layers.
iii) The effect of changing other rock properties.
iv) The effect of proximity of other seams.
CHAPTER II
LITERATURE REVIEW
2.1 GeneralU
Multi—seam mining problems have existed for a very long time.
British mines have been operating in multi-seam conditions for a con-
siderable period of time (Finlay, et al, 1933; Dunham, et al, 1978; and
Spedding, 1976). Quoting Dunham and Stace (1978):
"In the British Coalfields, it is becomingincreasingly uncomon to mine in virgin areasand it has been estimated that every working i
face will be affected by interaction effects —from previous workings at least once duringits life."
Multi-seam mining problems are not limited to Britain but are
experienced world wide, and the United States is experiencing these
problems in many regions.
Holland (1951) lists the following factors below as being of para-
mount importance in the solution of problems of the stability of lower
or upper beds after the main bed is mined:
i) Mining methods in extracting the beds.
ii) Extraction ratio and uniformity of beds concerned.
iii) The intervals between the beds under consideration.
iv) Thickness of beds.
v) Nature of strata between beds.
Further, Holland (1951) observed that in 38 case studies undertaken in
the Appalachian Coal region, about 75% of them had a shear or shear
tensile failure after an underlying bed had been mined. Figure 1 is an
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example of massive interseam failure caused by removal of underlying
pillars. Some of these case studies had water and air entering the
cracks allowing the shales in the imediate roof of the underlying bed
to weaken. Other problems which may be encountered when an underlying
bed is mined first are as shown in Figures 2, 3 and 4. To explain the
phenomena, Peng and Chandra (1980) proposed the idea of a dome shape to
describe the zone of caving--the zone in which failure by shear and
block movement occurs. The maximum height of this dome was empirically
assumed to be 30 to 50 times the mining height.
In observations carried out on the multi-seam mines of the Pocahon-
tas Coalfields in Southern West Virginia, which applies to coalfields in
Virginia and Kentucky, Lazer (1965) concluded that, when the lower seam
is mined first prior to mining the upper seam, interaction between beds
is almost non existent if the interval between workings are greater
than 50 feet. He further observed that, within the normal limits, the
thickness of the lower mined out seam has no effect on the upper seam
mining and the interval between seams may be as little as 50 feet. The
paper by Hasler (1951) also supports these observations.
The complexity of interaction due to seam interval is manifested
in the paper by Dunham and Stace (1978) where they noted that in Brit-
ish Coalfields maximum seam interval beyond which interactive effects
are no longer felt is quoted from 210 feet to 750 feet. Dunham and
Stace (1978) also emphasize that the influence of seam interval in
multi-seam for any given situation is very much complicated by a
variety of other considerations.
6
Goal 8"-l2"
Bone 6"-8"Fireclay '
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Goal Grade Normal4'—4'l0"‘ Grade
Coal crushedalong this line
Figure 2.r Shear Failure in Redstone Seam Over Robbed LowerSeam (after Holland,l951)
7
Figure 3. Bending, Shearing and Readjustment of LeveliCaused by Subsidence in the Lower Seam (afterHolland,l95l)
8
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Soft Fireclay with Fakey Bands I
1 /I Q II
IFireclayI
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Figure 4. Bending in Humph Coal After Mining a Lower Seam(after Holland,195l)
9
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Hasler (1951) studied the multiple seams of the Central Pennsyl-
vania bituminous coal region, especially in the Cambria County. He
observed that in the cases of the lower of the two or more beds of coal
in vertically adjacent areas which was mined before the extraction of
the upper bed, the problems encountered are:
i) Unavoidable damage to the upper bed--and the causes
of these damage are subsidence, fracture, and parting_
of the overlying strata and beds of coal withinvarying ranges.
ii) Damage to overlying bed due to large and extensive
pillars of coal left in the lower worked out bed.
The effects are listed as bumps in the floor,
crushing of the coal in the upper bed, undue
fractures in the coal.
The discussion above has been centered on coal, but it should be
emphasized that multiple seam mining is not restricted to coal but to
metal mining and other minerals as well. Hedley (1974) in the analysis
of multi-seam mining at Elliot Lake uranium mines, lists the causes of
the failure in the interseams as, buckling due to high horizontal
forces, tensile failure at the center of the roof in the lower bed, and
the shear or tensile failure in the interseam (usually occurring at the
edge of the pillar). According to the observation made at these mines,
the latter cause was the major mechanism of failure in the Elliot Lake
uranium mines. A graph of parting thickness (interseam thickness)
against stope span (width of opening) was plotted from observations of
Elliot Lake uranium mines as in Figure 6. From the graph, Hedley
11
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Figure 6. Relationship Between Interseam '1'hickness and Width ofOpening (after Hedley,l978)
12
Elliot Lake uraniu mines as in Figure 6. From the graph, Hedley
(1954) postulates the formula below as a rule of thumb in the designing
of the multiple seam mines at Elliot Lake.
L _g 51:2 (1)
where L = maximum width of opening, ft.
tz = interseam interval, ft.In reviewing most of the literature on multi-seam mining, it imme-
diately becomes obvious that the character of the beds between the coal
seams is very important in any evaluation of the problems attached to
them. Figure 7 illustrates the importance of the character of the
innerburden to the stability of the other seams. There are four se-
quences in which multi-seam mines can be worked and they are
(King, et al, 1972):
i) The lower seam is mined out first prior to mining
the superincumbent seams.
ii) Simultaneous mining of upper and lower seams.
iii) The upper seam is mined prior to mining the
underlying seam.
iv) Combinations of the above (Hasler, 1951; Stemple, 1956;
and Lazer, 1965).
The sequence of mining to be considered in this study is the
situation where the lower seam is mined prior to the extraction in the
upper seam.
Many of the published works available on multiple seam mining,
depending on which part of the world the investigation was made, con-
13
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0 10 20 30 $0 50 60 70 80 90 100Z Sandscone in lnnerburden
Figure 7. Relationship of Innerburden Thickness and Z Sandscone forRoom and Pillar System in the Appalachian Coal Region(after Haycocks and Karmis, 1981)
14
tain some recommendations in extraction of these contiguous beds. The
author will summarize these suggestions of mining in an upper bed after
the extraction of the lower seam as below:
i) Extraction in the lower seam should be complete with
no pillars or large remnants left in place (Holland,
1971).
ii) Pillar lines should be kept long and straight to
reduce shearing of the overlying strata at the edges
of the barrier pillar (Holland, 1951).
iii) As in (i) above if pillars are to be kept in the
lower seam, it is advisable to columnize them,
especially for developments and long-life entries.
lt is also recommended that whatever remnant pillars
are left should be uniformly distributed (Peng and
Chandra, 1980).
Reporting of observations in a mine is very important in studies
of this kind; bearing in mind the above statement, King, et al, (1972)
in their survey of the interaction of several workings on each other in
the Midland Coalfields in Great Britain listed these conditions as the
result of the phenomenon:
i) increased closure of mine openings due to the inter-
action producing an increase in the intensity of the
force field surrounding the opening;
ii) deterioration in the natural strength of the strata
surrounding the opening owing to the effects of the
15
increased rock pressures and/or lateral strain;
iii) increased roof control difficulties on working faces
and roadway closure arising from interaction of
subsidence of a lower working face; this is referred
to as "live" interaction and is comon in multi—seam
workings.
Stemple (1956) in his report of the observations in coalfields of
Eastern United States, stated that the damage that can be expected in
the upper seam because of previous excavation in a lower one depends on
the thickness of the underlying bed, the method of mining and the thick-
ness of the innerburden. Shearing of the upper coal bed was also ob-
served and is thought to occasionally facilitate the extraction of that
seam (Figure 8). The recommendation for the limitation of excessive
damage in the upper bed in this case was the complete mining of the
lower seam prior to the extraction of the overlying bed.
The most common phenomena observed in Stemple's study were:
—— cracking or horizontal parting in the overlying strata.
—— vertical displacement of the upper seam which usually
translates into separation of the bed.
—- roof falls, floor heaves and pillar crushing or squeezing.
Maximum disturbance in the upper seam was generally observed
when isolated, groups of pillars, or solid coal (barrier
pillars, chain pillars) were left in the lower seam. This
caused the upper seam to shear along the coal line in the
lower seam.
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—- less disturbance is caused when the lower seam is thin rather
than thick. The nature of the strata between seams has an
influence on failure too.
Further observation in the longwall method of mining in contiguous
seams shows the shearing action in the gob region. If longwall mining
system is used, an isolated pillar left in the lower seam acts as an
unsupported cantilever beam and thus can bend 100 to 300 feet before
fracturing (Figure 9). The severity of the disturbance, however,
depends on the nature and thickness of strata in between the beds and
thickness of the coal (Engineers International, 1981).
Various factors are involved in the failure mechanism of an under-
ground excavation and more so in practical experience. Most of these
factors which have been mentioned earlier, however, complicate the
analysis of examples of actual cases in the field. Engineers Inter-
national, Inc. (1981) collected some data from mine visits and litera-
ture review, mostly from the Appalachia, and presented them in a graph
(Figure 10) comparing mining of both top and bottom seams. Figure 10
shows the relationship of extraction ratio to the interseam distance
(parting thickness). Data points from each mining operation were
connected vertically to facilitate interpretation.
Interseam distance is basically the underlying parameter in any
study of multi-seam mining for the causes of structural problems. The
extraction ratio decreases as the height of the interseam becomes
smaller or if the nature of the parting is weak (Engineers Internation-
al, 1981). Fracturing of the upper seam and bumps created by pillars
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left in the lower seam--due to high stresses induced and shearing of
the intact and the bedding interface--are the major causes of lower
extraction ratios in the upper seam.
There are many examples in which the shearing mechanism of the
innerburden affects the successful mining of contiguous beds. As has
been mentioned earlier in the observations made of the problems encoun-
tered in multiple-seam mining, roof falls are one of the major diffi-
culties encoutered in the excavation process. Cox (1974) observed
. that most of the major roof failures are associated with structural
fracture zones, massive shale beds of lenticular structure or thinly
laminated sand-shales. Apart from the obvious weakness presented by
jointing and faulting, massive shales and laminated sandy shales create
a low shear strength roof structure suggesting mostly shearing mechan-
ism in its failure. The conclusions in this paper suggest that shear
failures of the rock are possible if short bolts are used in roofs of
low shear strength as shown in Figure 11. The potential of shear fail-
ure along vertical fracture planes (joints, etc.) are also stated (Cox,
1974). The stages of failure in the roof showing the shearing action
when a moderate and severe transverse jointing are encountered as in
Figures 12 and 13.
An example of positive use of the shearing mechanism of failure in
mining has been in the excavation of ore using the block caving tech-
nique. This method of mining entails the induction of caving to facili-
tate the recovery of the ore. The caving is induced by undercutting the
ore and thus allowing shearing from both ends of the opening. To limit
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Figure 12. Stages of Roof Failure Showing the ShearingAction When Moderate Transverse Jointing areEncountered (after Adler, 1973)
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g ‘°o goir; ;.'-Q; tg»~}_
-' .„,_-..
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1-1 w ^—;—Ä+‘6+=:i”¢* . ·;·_g;ä<;j;;. ~«-1ä 3 ¤«°T‘Öl‘$€Y.‘‘‘·T.
ä·—•¥Ü6Ü:..=a-'
f--;·‘?"·€·"‘ *4-IO . P’ · G ,2 2 *63;\
GS I-I• ¤-1 $4 'U. o H <¤IIcn-0. <‘
co 0 I-I.gg ;> L1-1‘ u 0 0< U1 U1 V
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_ 1-I
GJI"'‘533 ·‘ L=4
24
greater dilution the deposit must be massive, it must have strong walls
from which ore can part easily. Planes of weakness in the ore can help
greatly in this method. The size of the undercut depends on factors
such as the planes of weakness in the ore, the height of the ore avail-
able for extraction and the output of the mine.
2.2 Geological Factors
As usually happens in most ground control problems, geology of the
area under consideration plays a major role in its analysis. The geo-
logical factors very much dictate the extent of failure in the inter-
seam of any multiple horizon mine.
Massive shear failures have been postulated to be the mechanism of
failure in the interseam of two or more vertically adjacent beds when
the lower one is mined first (Holland, 1951; Stemple, 1956). In the
study of taphrogenesis, a term formulated by KRENKEL to define the
formation of Grabensl, it was found that the massive shear failures and
tensile failures are the most predominant means of formation of the
world's rifts.
The geological history of most of the world's rifts is still
clouded in controversy; there is no agreement over how the rifts
evolved, nevertheless most of the parties involved in the controversy
acknowledge the fact that somewhere along the history of the formation
of the rifts, massive shear and tensile failure occurred to cause the
rifts.
lGrabens in German means ditch and is used frequently in geologyto mean rifts.
25
Studying the rifting process really gives an insight into the
phenomenon of massive shear failures and their relation to interseam
failure. Burek (1981), in writing about warping in the rifts of
Arabia, North East Africa and the continents which surround the North
Atlantic rifts, noted that continental warping and shearing are due to
horizontal, compressional stresses caused by the injection and spread-
ing of mantle derived--new oceanic crust (mantle diapirism, ocean-floor
spreading). Burek (1981) also found that lateral movements along diag-
onally arranged shear zones apart from causing compressional shield
folding also causes major faults and fault systems. Evidence of large
tectonic forces (or stresses) was observed in most of these regions.
Confirmation of the above findings has been made by other workers in
this field (Illies, 1968; 1972).
Large tectonic stresses (lateral) have been postulated to be a _
factor in the formation of massive shear failure. This has been true
in the formation of rifts, especially after the idea of plate tectonics
was introduced as the fundamental explanation of the world in its pres-
ent state. D'elia, et al, (1971) made a study of the mechanical behav-
ior or a highly metamorphosed Miocenic mudstone and found that areas of
high tectonic activity produced much sheared material. Their discovery
was rationalized thus, that the tectonic compression, which in this
region is East-West in direction, causes the mudstone to undergo large
shear deformations which gave rise to the faults and the shear zones.
Mohr (1972) in his studies on the rifts in East Africa (Afar, Ethiopia)
confirms the fact that tectonic activity in the region is a factor in
26
the rifting process.
Chang, et al, (1977) described the modes in which fractures in a
rock occur; and in their determination of the factors involved stressed
the importance of the influence of the change in the temperature and
pressure inside the earth caused by tectonic movement in faulting. The
five modes of fracturing were: shear-tension, shear-compression, uni-
form compression, uniform tension and uniform shear.
The influence of local geology in massive shear failure is further
detailed in the report on massive rock failure at the Bautsch Mine,
Galena, Illinois to the United States Bureau of Mines by Touseull and
Rick (1974). The report concedes that unequal compression of the clay
seam between areas closer and farther from the free face did increase
the amout of load on supports in the area and thus might have caused
the initial failures in pillars experienced. Another mechanics which
they reported was the loss of cohesion and the bedding planes in the
bentonite seam, which might have been the major factor in many of the
small roof failures that occurred. The wall rock alteration that ·
occurred near the mineralized zone was also a factor in most of the
failures.
In discussing some of the pertinent questions pertaining to multi-
seam mining, Stemple (1956) mentioned the importance of the strata in
the roof of the upper seam when the underlying bed has been mined. It
has been suggested then that less trouble will be experienced for a
hard sandstone roof than a soft shale roof. The importance of the
character of the intervening formation (interseam strata) was also
27
stressed in his study.
2.3 Stability Analysis
There are many types of stability analysis which can be applied to
excavations in a massive rock. The majority of these methods evolved
from techniques evolved for pit slopes and so a brief discussion of the
pit slope stability analysis will be undertaken.
Slope stability analysis is usually treated as a limiting equilib-
rium mechanics problem. A failure surface is assumed and a free body
is sliced from the slope. With known or assumed values of the forces
acting upon the free body, the shear resistance of the soil or rock
needed for equilibrium can be calculated. A factor of safety can then
be determined by comparing the shear resistance to the estimated shear
strength (Whitman and Bailey, 1967).
From this basis many methods have been developed, for example the
Friction Circle method, Fellenius or Simplified Bishop methods, Morgen-
stern-Price method and the wedge method. The details in these analyses
are beyond the scope of this study and will not be elaborated on
_ further.A new approach of stability analysis, which has been successfully
used for openings in massive rocks, was developed by the United States
Bureau of Mines (Wang and Sun, 1970). The accuracy of most of the con-
ventional slope stability analyses mentioned earlier has become ques-
tionable because of the assumptions made in the calculations. The
Fellenius method assumes each slice to be in equilibrium without forces
acting on the sides, whilst the Bishop method assumes each slice to be
28
in equilibrium, with horizontal resultant forces acting on the sides
(Whitman and Bailey, 1967). Static equilibrium, however, is not satis-
fied completely in any of these two methods and thus causes errors in
the magnitude of 60 percent and 7 percent in the Fellenius and the
Bishop methods, respectively.
The Bureau of Mines method of stability analysis was also treated
as a limiting equilibrium problem. The method uses the finite element
and Mohr—Coulomb failure criteria in the analysis (Wang and Sun, 1970;
Wang, et al, 1971). The procedure usually employed in limiting
equilibrium methods are that (Scott, 1980):
i) Failure occurs as a result of shear on a surface in
the geological material and the failure condition is
assumed to be satisfied on that surface.f
ii) The failure surface is assumed and a number of
surfaces are examined.
iii) For each surface, the failure load (or stress which
will just cause the shear failure) is computed.
Safety factors can also be computed.
iv) A systematic search is then made to find the particular
surface for which the safety factor is the least.
The stress field of the structure under consideration can be ob-
tained using the finite element method of stress analysis. Then, a-
long a possible fracture surface, the normal and shear stresses at
every point is computed using the basic strength of material equations.
The resisting strength is then calculated for the Mohr-Coulomb equation,
29
knowing the normal and shear strengths. To calculate the factor of
safety for all the points on the possible failure surface, the ratio of
the resisting strength to the total shear force is evaluated. The
total shear force is obtained by integrating the shear stresses along
the failure surface (Wang and Sun, 1970).
The usual method of stability analysis of an underground structure
has been based on the critical stress concept based on the maximum com-
pressive and tensile stresses determined to exist around an excavation
(Obert and Duvall, 1967). In this method, the check for stability is
for the rock strength to be equal to or greater than the product of the
appropriate critical stress and the safety factor. This system of
stability analysis although widely used has been found inacceptable as
a criteria for structural failure, that involves a separation of mater-
ial from walls of an excavation. The critical stress method of stabil-
ity analysis, however, works for initiation of cracks on the periphery
of the excavation (Wang, et al, 1971). This new method of stability
analysis has been used in a single opening in massive rocks and has
been found to be consistent with the field observations of rib slabbingn
and roof arching (Wang, et al, 1971).
This type of analysis has been investigated for a single opening
(Wang, et al, 1971) but it has also been shown that it can be applied
to an advancing longwall face (Kidybinski and Babcock, 1973).
2.3.1 Mohr—Coulomb Failure Criterion
The clear definition of failure in rock mechanics studies is sur-
rounded by controversy, but Silverman (1957) defines it in a way that
30
will be acceptable to all parties:
"Failure may be defined in several ways: as theattainment of the yield point; the appearance of
_ the slip on the external surface of the specimen;or in the case of the so-called brittle materials,it may coincide with actual rupture. For materialswhich do not have a definite yield point, a certainpercentage of residual deformation may be definedas failure."
To predict failure of rock many theories have been propounded and
they are usually based on the following simple assumptions (Lundborg,
1968):
i) Maximum principal stress.
ii) Maximum principal strain.
iii) Maximum shear stress.
iv) Maximum shear strain.
v) Maximum strain energy.
vi) Maximum distortional strain energy
or maximum octahedral shear stress.
The Mohr-Coulomb failure criteria is based on the assumption of
maximum shear stress. The theory postulates that the shear strength
increases with increasing normal stress on the failure plane (Desai and
Siriwardane, 1981). For a two-dimensional case, the theory stipulates
that failure will occur in a material along a surface element when the
magnitude of the shear stress becomes equal to the sum of the resist-
ances due to cohesion and friction (Wang, et al, 1971).
T = c + uou (2)
Where on is the normal stress acting on the surface
element.
31
u is the coefficient of internal friction.
T is the shear stress acting on the surface element.
u = tan ¢Where ¢ is the angle of internal friction.
To express the Mohr—Coulomb failure criterion in terms of princi-
pal stresses, reference will be made to Figure 14. From Figure 14,
(01 - 03)/2 = AB + BF (3)
Rewriting,
(01 - 03)/2 = 0Asin¢ + Ccos¢ ~ (4)
hence,
(läé)= sin¢ + Ccos¢ (5)
The failure criteria ignores the effects of intermediate principal
stress and does not allow for hardening behavior. This theory, how-
ever, takes into account the frictional aspects of the rock.
The Mohr—Coulomb failure criteria appears to be attractive to the
engineer because it considers the actual behavior of materials includ-
ing its inhomogeneity and anisotropy (Silverman, 1957).
2.3.2 Finite Element Me¤h¤d
The basic concept of the finite element method is the idealiza—
tion of an elastic continuum as an assemblage of discrete elements
interconnected at their nodal points (Wang and Sun, 1970). As usual,
the force-deflection or stress-strain relationship and the requirement
for compatibility and equilibrium are used in obtaining the stiffness
properties of the elements (Wang and Sun, 1970). The basic element
32
T
..•lII* A
Tf ____;____________ P
E9 ¤> ga °z A °1 °
Figure 14. Mohr-Coulomb Failure Criterion (after Desai andSiriwardane,198l)
33
(equilibrium) equation used for the finite element analysis is
(Desai and Abel, 1972),
{B1 {6} =° {Q} (6)where [k] is the element property matrix,
is the vector of nodal displacements,
{Q} is the vector of element nodal forcing parameters.
The element equations are then assembled to obtain a relationship
of the form (Desai and Abel, 1972),
[1<]'{r} = {R} (7)where [K] is the assemblage property matrix,
is the assemblage vector of nodal displacements
is the assemblage vector of nodal forcing parameters.
The boundary conditions, surface traction and specific loading
conditions on any point can be incorporated into the analysis for
solutions of displacements. Secondary quantities such as strains and
stresses in an element can then be calculated using a transformation
matrix as shown below (Desai and Abel, 1972):
{6} = [c] [B] {q} (8)
where {o} is the stress in an element
[C] is the stress--strain matrix (might be Hooke's Law
if linear elastic constitutive law is to be used).
[B] is the transformation matrix.
Complete discussion of the finite element method is beyond the
scope of this thesis. Further reference to this method of analysis can
be obtained from Desai and Abel, 1972, and Zienkiewicz, 1977, and all
34
such programs are computerized.
The output from most programs are in the form of displacements at
nodes, the vertical and horizontal stresses, the principal stresses and
the angles they make and the shear stress involved in an element.
Thus, with such an array of stress components given, the finite element
method is important for many uses other than analysis of stresses.
2.3.2.1 Advantages of the Finite Element Method
Before the discussion on finite element method is ended as such,
it will be expedient to state the advantages it has over other methods
of stress analyses (Wilson, 1965).
i) The method is completely general with respect to
geometry and material properties.
ii) Complex bodies composed of many different materials
are easily represented.
iii) Anisotropic materials are automatically included in the
formulation and thus allows filament structures to be
handled easily.
iv) Displacement or stress boundary conditions may be
specified at any nodal point within the finite element
system.
v) Arbitrary thermal, mechanical and accelerated loads
can be specified too.
vi) Precision wise, it has been shown mathematically that
the method converges to the exact solution as the
number of elements is increased. Thus, the desired
35
degree of accuracy can be obtained.
vii) In the formulation of the finite element method,
symmetric, positive--definite matrix which usually
occurs in a banded form is usually obtained and thus
can be solved with a minimum of computer storage
and time.
2.3.2.2 Modeling Criteria for the Finite Element Method
The most important aspect of the finite element method is the dis-
cretization of the model body. This process is essentially an engineer-
ing judgment exercise and the importance of it cannot be overemphasized.
The decision on the number, shape, size and configuration of the ele-
ments should be made in such a way as to simulate as closely as possible
the original body (Desai and Abel, 1972).
Although it has been mentioned that engineering judgment is needed
in the discretization process, some guidelines are, nevertheless, sug-
gested to facilitate the decision-making process (Desai and Abel, 1972).
i) In the location of nodes, subdivision lines and planes
are usually placed where abrupt changes in geometry,
loading and material properties occur.
ii) A finer subdivision is necessary in regions where
stress concentrations are expected.
iii) Curved boundaries can be approximated as piecewise
linear by the sides of the elements adjacent to the
boundary, if straight—sided elements are to be employed.
Isoparametric elements with curved sides can be used.
36
iv) To minimize the solution time and the storage require-
ment for the overall stiffness matrix, the band width
is made as small as possible. The band width is given
as,
B=(1>+1)£ (9)
where B is semi band width.
D is the maximum largest difference occurring for
all elements of the assemblage.
f is the number of degrees of freedom at each node.
. In this case the numbering system is very important in
terms of computer time and storage requirements.
Figure 15 (b) shows the right way to number the nodes
and elements.
v) The aspect ratio of the elements affects the finite
element solution. The aspect ratio is defined as the
ratio of the largest dimension of the element to the
smallest dimension. Long, narrow elements are usually
avoided when drawing a mesh for a body. The graph in
Figure 16 shows the inaccuracy of solutions as a
function of the aspect ratio.
vi) For a body of infinite lateral dimensions, side bounda-
ries can be assumed and side nodes restrained to move
only in the vertical direction and not horizontally.
Kulhawy (1974) showed that for geotechnical problems, such as are
being considered in this study, arbitrary, linear strain quadrilateral
37
lv
I I I I I I I II
I II I I I17 I I I I I I9 1OI 11I 12I 13I 141 15I 16I I I I I II 2 3 4 6 6 7 8 X
(a)
Iv6 10 I6I zo I I II I I I I I I4 9I 14 19I I I I II I I I I I I3 BI I3I ISI I I
I II27 I 12 17I I I I
‘I I I I II 6 11 16 21 X I. Ib)
Figure 15. Numbering of Nodes to Reduce Band Width(after Desai and Abel,1972)
38
lexact solution
<
ä ‘5"‘* " \ä \\ä \\§ \> Va 40% ‘~\_‘=\ä .
\\\ I\¤l 1 1 11 2 3 4 6 6 7 8 9
. g lonuest dimensionAspect Rano SFIQYIESI dl|'T1€¤SlOl’I
Figurelö, Innaccuracy of Solution as a Function of AspectRatio (after Desai and Abel,l972)
39
elements are the most appropriate. His paper recommends a minimum of
125-150 elements for the analysis of simple structures in homogeneous
rock and that the boundaries of the finite element mesh should be
located at least six radii away from the center of the opening to
minimize the boundary effects. (Figure 17).
2.4 Brittle Model
Physical modeling is slowly gaining popularity in the solution of
very complex rock mechanics problems. Theoretical and field-measure-
ment approaches have been used extensively in the solution of ground
control problems, but these approaches have their limitations. The
theoretical studies are based on the theories of elasticity and plas-
ticity, which sometimes do not apply directly to a particular problem,
because of the simplifying assumptions that must be made to obtain a
solution (Barron and Larocque, 1963). Field measurements adapt the
theory to the ground conditions, but the interpretation of the measure-
ments is complicated because of the unknown and often uncontrollable
variables which influence the measured phenomena. The inaccessibility
of most of the structure for measurement purposes also is a problem
(Barron and Larocque, 1963).
Although physical models have some limitations, it nevertheless
allows for realistic empirical and theoretical equations to be deduced.
It also allows for all variables which influence the phenomena to be
measured. The main attractions of physical models are convenience,
speed and low expense in the investigation of complex engineering
problems (Whittaker, 1974).
40
1.1
1 O Theoretical
013. H 0.9ut>
ß O 8 /9 ¤ Y and X displacement atO
ä4/
nodal points.2 I 0 cy and Ox in elements.E\
O•7 //V Txy ill €lEII1€I1CS•
m I0):3•-6§ 0.6äFu
0.5 _3R SR 7R 9R llR 13R
Location of Boundary of FEM Mesh
Figure17. Effect of External Boundary Location on Accuracyof Finite Element Method Solution (after Kulhawy,l974)
41
Various physical models have been built to simulate diverse rock
mechanics problems. Everling (1964) performed experiments to simulate
the behavior of the ground surrounding a roadway, the support charac-
teristics of different systems in a roadway, and to investigate the
break phenomena and deformation processes in the ground responsible for
the changes in the cross-section of the roadway. Model dimension was
6.6 feet by 6.6 feet by 1.3 feet and five hydraulic props on each of
the four narrow sides were used to apply the required load. Each of
the props has its own pup capable of exerting 60 tons of force. The
top cover of this model, which was constructed at the Mining Research
Station at Essen—Kray in West Germany, was stressed against the model
by four props-which helped to achieve the plane strain conditions ex-4
perienced underground. Geometrical scale of 1/10 was used and the
strengths of coal, shale and sandstone were modeled on a strength scale
of 1/10 using variations in mix of Portland cement, fused alumina
cement and quartz powder.
Hobbs (1966) also performed a series of experiments using scale
models to determine the movement of strata in the vicinity of mine
roadways underground, controlling such factors as rock strength, pres-
sure, roadway size, roadway shape, support design, packing system de-
sign, pack width and ribside position. The facility designed for this
case at the National Coal Board Mining Research Establishment at Isle-
worth in England could test models of dimensions 2 feet by 2 feet by
5 inches. The model was loaded using 12 rams, 3 on each side. Each of
the rams had a capacity of 3.14 tons and were all powered by an elec-
42
tric pup and relief valves system. Preliminary tests on the rams
showed that there was little variation between the applied ram loads at
the same ram pressure for individual cylinders. A geometrical scale
factor of 1/50 was used. The model material is a mixture of sand,
plaster and water.
The profile measuring head (N.C.B., M.R.E. Isleworth type no. 943)
was used in most of the measurements in Hobbs's (1966) physical model.
Everling (1964), however, used distance measuring devices and permanent
photographic records in the test on the physical model.
Barron and Larocque (1963) reports on a physical model design to
simulate a vertical section taken through the orebody bounded by the
opposite faces of the pillar in the Wabana Iron 0re Mine in Newfound—
land, Canada. The main objective was to investigate the following
problems:
i) The stress distributions in the model under various
conditions, as the rooms are developed.
ii) The effects of discontinuities in the ground.
The dimensions of the Wabana Mine model were 6 feet by 6 feet by 1 foot
and had three 50-ton capacity rams to apply load on each side of the
model. Four 2-ton rams were used to apply restraining load to the face
of the model-—to simulate plane strain conditions. The geometrical
scale factor for the model was 1/70 and the materials used here were a
variation of the water and plaster using retarders and fillers to
achieve the required physical properties.
Rosenblad (1969) reported on the use of a model of approximately
43
22 inches by 22 inches by 6 inches to investigate the behavior of
jointed rocks. The equipment developed, the materials used and the
instrumentation used are all obtained in detail in the papers by
Rosenblad (1968, 1969).
Sandbox models have been used successfully to simulate the pos-
sible distribution of stress in the region of coal-mine face workings
. as described by Harris (1974).
2.4.1 Comparison of Model Material and Natural Rock
To carry out any model study it is very important to scale the
geometrical factors as well as the mechanical properties of the mate-
rials and loads involved (Barron and Larocque, 1963). The technique of
dimensional analysis is usually used to specify the requirements for
similitude between the model and the prototype. The basis of this
technique is to collect all the physical quantities, constants, and
characteristics pertaining to the problem and applying certain rules,
usually the Buckingham-H theorem, to form dimensionless parameters.
The dimensionless parameters for the model must have the same value as
the prototype according to the similitude condition (Barron and
Larocque, 1963).
It must be emphasized here that it is usually very difficult to
obtain a perfect similitude between physical models and mining condi-
tions, although such models can achieve sufficient accuracy to contrib-
ute qualitatively and quantitatively to the solution of rock mechanics
problems. Usually, some of the independent dimensionless variables,
which have less significant influence on the test results, are allowed
44
to deviate from the correct values (Rosenblad, 1968).
Mandel (1963) describes an equivalent material as the softer model
material, chosen in such a way that its mechanical properties of elas-
tic, plastic and viscous deformation may be deduced from those of the
material of the structure by a change in the scales of the stresses,
times and deformations. The paper goes on to classify similitude into
simple and extended types. Simple similitude is when the scale of the
displacements is that of lengths, so that the deformations are equal at
two homologous points in the structure and in the model. When the dis-
placement is small a scale different from lengths can be adopted--
extended type of similitude.
Hobbs (1966) after going through the dimensional analysis drew up
a table to indicate the scale factors used in those model tests and
also to show how other parameters are related to the basic scale fac-
tors of length, mass and time. Thakur (1968) proposed that the time
scale factor for equivalent materials is equal to the square root of
the geometrical scale factor under both elastic and plastic conditions.
T =/V <1o>The above conclusion is in agreement with the work of Hobbs (1966).
2.4.2 Properties of Model Material
Some general guidelines are given in the literature as to the
properties of model materials needed in any study (Rosenblad, 1968).
i) The material should be economical, costwise.
ii) lt should be easily obtainable.
iii) It should be reproducible from one batch to the next.
45
Tab le 1
Some Physical Parameters, Their
Dimensions and Model Scale Factors
(after Hobbs, 1967)
Physical Scale FactorParameter Dimension (a) (b)
Length L'
A 1/50
Mass M p 11/25x10·5
Time T 1 1/JE0
. -3 -3Density ML uA = 11/20
Strength 1/90
StressM_lT_2 uA—l1_2
1/90Young'sModulus M-1T-2 uA-11-2 1/90
. -2 -2Acceleration LT A1 = 1
Poisson Ratio 0 1 1
Angle of Internal Friction 0 1 1
46
iv) The material should be similar to rock in all its
pertinent properties.
v) Its static properties should not change with time.
vi) Its deformability should be sufficiently large to cause
adequate response in displacement and strain measuring
instruments.
vii) It should be possible for measuring instruments to be
easily fixed to or embedded in the material.
Further requirements enumerated by Rowe and Base (1966) list these
requirements below as very important in model material properties:
i) That there should be an affinity between the
stress/strain relations of model material and that
of the prototype.
ii) The value of Poisson's ratio and angle of internal °
friction for both the model and prototype materials
should be the same.
iii) The model material should be capable of easy fabrication
to the required form, preferably without inducing
internal stress.
iv) The material strength should be such that a loading
frame could be built to fail the model.
CHAPTER III
CASE STUDIES
Specific examples of multi-seam mines and their mechanism of fail-
ure are enuerated below. Six examples of cases in which the under-
lying seam was mined first are described in this chapter. All these
examples were collected from the literature.
3.1 Case Study No. 1
This mine is located in McDowell County in West Virginia (Stemple,
1956). Two seams are worked in the mine--Pocahontas No. 6 and Pocahon-
tas No. 3--in the upper and lower tiers. The method of mining is the
room and pillar technique with 90% planned extraction ratio in the up-
per bed and 92.4% in the lower seam. The thickness of the upper and
lower seams are 46 inches and 54 inches, respectively. The interval
between the seams is between 140 and 150 feet, and it consists of
shales and sandstones in basically the same proportions. Figure 18
shows the geological column in the mining area.
The observations made after the lower seam was mined were very
favorable—-the disturbance in the upper seam was minimal although a
sizeable pillar was left in the lower seam. Surface subsidence in this
mine was also very minimal-—some cracks showing up but not significant.
The relative stability experienced in this case might be due to thicker
interseam and the sandstones involved in the innerburden. The same
reasoning can also be espoused for the minimal surface subsidence
experienced.
47
48
LOCATION: McDowell Co., W. Va.
— ::_—-:_
T : r
* ··· SMM — — __;5: ,
CQDGL:; :‘:. SM-ke: 1 "-—:'-"-‘-Y
J lg! °;· · °· *-'°:i ",’j· l-' ·:·‘.·Z·>.¢1·:‘-_*-:Ü- ZIII' .IT“.;?‘ .Z?' II; "L;".I”.. PKÜJEÜ—: ;" §g~¤·U?«_.." "“ °‘ "_“'_" Z
•: •: :'Z
°• _ 2., • ·:•:2:lz
IÜ} ·°I l'. ··‘-S Ä: Ä' ·l Ü °Ü-Z Ä ’. zi l:_°=}-E ·i'-'Ä: Ä'-;
-::5 zi-:§l¤I@«5 5 :5 5 5 5-:-5-
äsMiningMethod:
Upper seam--room and pillarExtraction 90%Lower seam——room and pillarExtraction 92.4%
Figure 18. Geological Columm of Case Study No. 1
49
3.2 Case Study No. 2
The location of the mine is in Mercer County in West Virginia
(Stemple, 1956). The mine is serviced by two seams——the Pocahontas
No. 11 and Pocahontas No. 3. The seams have thicknesses of 54 inches
and 68 inches in the lower and upper beds, respectively. The interval
between the two seams is approximately 510 feet. The geological forma-
tion in the innerburden is composed of shales and sandstones with the
coal seam Pocahontas No. 6 in it (Figure 19).
Observations of disturbance is similar to that in Example 1--minimal disturbance in the upper seam and minimal surface subsidence.
The greater thickness of the innerburden might be the clue to the insig-
nificant disturbance in the upper seam.
3.3 Case Study No. 3
The mine under consideration is located in Cambria County in the
state of Pennsylvania (Hasler, 1951). The geological column of the area
as given by the U.S. Geological Survey is shown in Figure 20. The seams
uder consideration here are the lower Kittanning and the Upper Freeport
for the lower and upper beds. The bed thicknesses for the lower and the
upper seams are 42 inches with an interval of approximately 180 feet.
The room and pillar method of mining is used in this case.
There was not a marked disturbance in the upper bed after two years
had elapsed from the time of the mining of the lower seam. Significant
disturbance was, however, experienced in the upper bed in the area where
pillars in the underlying seam has been extracted. It should, however,
be noted that the pillars in the upper bed were columnized to that in
50
LOCATION: Mercer Co., W. Va.
_”l—II I 426 .
_ I I$h¤l2„—— —- — _;
Pomkmhs C·>¢° ^°· " ég: *:1 7-.—§h¤.J&·-7...1. 1 1-.
,:‘• °• Z
2.,:-: xl': Z.•• • •• ••••
I5lO
-—_———§|¤ql2.-— ————— —
Mining Method:
Upper seem--room and pillarExtraction 74%
Lower seam—-room and pillarExtraction 80%
Figure 19. Ceological Column of Case Study No. 2
51
Scale, 1 inch = 150 feet Willmore Sandstone memberSummerhill Sands tone member
Morgantown ("Ebensburg")Sandstone member
. REC} ShaleCcmemaugh Saltzburg Sandstone member1Formation
= Buffalo Sandstone member
Red Shale
-
Sandstone member
I Upper Freeport CoalLower Freeport Coal
Allegheny
-
Upper Kittanning CoalFormationMiddle Kittanning CoalLower Kittanning Coal
——— Brookville or Clarion CoalFigure 20. Geological Column of the Central Pennsylvania Co.al
Area, Cambria County (after Hasler, 1951)
52
the lower seam. A combination of factors can be used to explain why
there is some stability in the upper bed in this case--the greater seam
interval, the good planning reflected in the columnization of the
pillars in the two seams and the hitherto unmentioned time factor.
3.4 Case Study No. 4
McDowell County, in West Virginia, figures again in the discussion
of the examples of failures in the multi-seam mines (Stemple, 1956).
The seams being worked in this mine are the Pocahontas No. ll and
Pocahontas No. 3 with seam thickness of 36 inches and an average of
90 inches, respectively. 75% and 90% are the extraction ratios for the
upper and lower beds, respectively. The seam interval in this mine is
about 470 feet and is composed of shales, coal seams, fireclays and
several sandstone beds (Figure 21).
Disturbances observed in the upper bed are very significant with
cracks which stretch to the lower seam. The roof and the coal in the
upper seam were also observed to be fractured. These observations point
to shear failure. Surface subsidence, which is in the form of wide
cracks and the settlements, were also observed. The predominance of
shales in the innerburden and also the high extraction ratio in the
lower seam might account for the instability and the subsidence in the
upper seam.
3.5 Case Study No. 5
Consideration of shear and shear tensile failure is made in this
example. The location of the mine is in Raleigh County in West Virginia
53
LOCATION: McDowell Co. , W. Va.'·_·:•··_· •_
.• I
‘·.;.j ·— :. '· . '_„.·—· Cggß ng,;· :·.;- :5qns na ·.- : ;=
476—..—-—·... ··..— .·.. ·$h¤*¤- : E EE?
Mining Method:
Upper seam- room and pillarExtraction 75 percent
Lower seam- room and pillarExtraction 90 percent
Figure 21. Geological Column of Case Study No. 4
54
LOCATION: Raleigh Co., W. Va.
,4 ,Savvlslbna 300
I· \‘-ml SkalaIIsaaamt aaa: **8
SkalaSanalslona
[ /Skala Sao-53¤
Skala
Sanalslvna
II.. näsau aa: 33 '
Mining Method:
Upper seam-—room and pillarExtraction 92%
Lower seam——room and pillarExtraction 80%
Figure 22. Geological Column of Case Study No. 5
55
(Stemple, 1956). The mine has two seams, Sewell and Beckley in the
upper and lower beds, respectively. These coal seams have thicknesses
of 48 inches in the upper and between 33 to 165 inches in the latter
and they are mined at 92% and 80% extraction ratios. The interval
between the seams is also variable between 260 to 330 feet with mostly
shales and sandstones in its geological formation. Figure 22 depicts
the geological colum of the mining area.
Significant damage was experienced in the upper bed even in the
virgin areas. The damage is intensified in the development work of the
upper seam. Breaks to the surface from the lower seam are essentially
vertical at first, but later show slight positive inclination estimated
at 10 degrees maximum--shear and shear tensile type failure and subsid-
ence. The low interseam height is the greatest factor in the damage
done in the upper seam.
3.6 Case·Study No. 6
All the mines in the examples above have been using the room and
pillar method of mining. The discussion in this example is, however,
concerned with the failure mechanism experienced when longwall method
of mining is used in multi—seam mines. The mine under consideration
has two seams, the Upper Campbell Creek and the Eagle (Peng and Chandra,
1980). Mostly shales and sandstones form the interval between the seam
and has a height of approximately 190 feet (Figure 23). The lower seam
was mined using the longwall method, the upper bed was basically mined
by the room and pillar method with some longwall practiced in some few
areas.
56
LOCATION: W. Va. Cover consists ofmainly sandstone· um and shale
4 l5· M.6'6" Campbell Coal7'l" Shale
Sandstone_ 1'4" Powelton Coal14'l" Shale2'5" Powelton CoalEEG 3'3" shaie
I IIMining Method: 42 4 SandstoneUpper seam——room andpillarLower
seam--longwall \88 '2 I 16' ll" _Shale3' Coal and Shalell'7" Shale
4'5' Sandstone9'll" shaie7' Eagle Coal3'lO" shaieSandstone
Figure 23. Geological Column of Case Study No. 6(after Peng and Chandra, 1980)
57
The panel entries of the upper seam were located directly above
the gob areas left by the longwall panels in the lower bed. Fewer
maintenance problems occurred because of the location of the panels in
the upper seam in the de—stressed zone created by the mining of the
lower bed. However, as the upper seam was advanced towards the limit
of mining in the lower seam, greater roof control problems at the face
started. Cracks left in the roof were as high as 20 feet. Severity of
the problem kept increasing even after the face moved beyond the mining
limit of the lower seam.
CHAPTER IV
PHYSICAL MODELING
Physical models have been used quite extensively to study various
problems in rock mechanics; and for the purpose of this study this type
of models are being used primarily to investigate the failure patterns
that occur in multi—seam mining and to corroborate the results obtained
with the computers.
This chapter will, therefore, describe in detail all the test
equipment, the development of the model material and the procedure
adopted in the tests.
4.1 Description of Test Equipment
The model appaIatuS is shown in Figure 24.
The model to be tested has a dimension of 24 inches by 24 inches
by 6 inches and is boud on the four thinner sides by l inch thick
steel. This arrangement around the model is to achieve the uniform
loading conditions in the vertical and horizontal directions. The type
of steel used in all these arrangements is the ASTM A36 type structural
steel.
To apply the load on the model a hydraulic system was chosen be-
cause of convenience in its usage. The load is applied directly using
twelve hydraulic cylinders manufactured by Applied Power, Inc. Three
rams were placed on each side of the model, so that the uniform loading
conditions on the sides can be simulated close enough. Each of these
rams has a capacity of 25 tons and stroke of 4 inches.
58
59
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60
Two hydraulic pumps were used in this assembly for easy manipula-
tion of the pressure (or load) in the horizontal and the vertical sec-
tions of the model. It was also found that to use only one hydraulic
pup for this assembly will amount to maintaining equal pressures (or
load) on the vertical and horizontal sections of the model which will
seriously limit the objectives of the experiment.
Although the two electric powered hydraulic pups used in the
model tests are physically different, they seem to have the same basic
output specifications. The pump that controls the cylinders acting
vertically has a rated delivery as shown in Table 2.
This pump has a three-way valving with an "on—off-jog" switch, it
is also fitted with two safety relief valves--one factory set at 10,000
psi and the other is adjustable for pre-setting maximum operating pres-
sures.
The rated delivery of the pump that controls the cylinders acting
horizontally is as shown in Table 3. A two-way manual valve is a
standard attachment to this hydraulic pump and has the usual two safety
relief valves also incorporated. The motor specifications in this pump
reads a bit different from the previous pump described-—it is rated at
1% horsepower to 8,000 psi for continuous operation and to 10,000 psi
for intermittent use. A special electrical wiring was required, how-
ever, for the 3 phase, 230 volts with 60 Hz electrical specification on
this motor. A full load rated current is 10 Amperes and it has a speed
of 1725 revolutions per minute.
Rigid steel tubing was chosen in the connections around the cylin-
4 61
Table 2
Rated Delivery of ENERPAC EEM 435L Pump
Flow Rate Pressure(Cu.i¤./min.) (psi)
280 O
195 500
42 10,000
62
Table 3
Rated Delivery of ENERPAC PEM 3022C Pump
Flow Rate Pressure(Cu.in./min.) (psi)
700 0
60 10,000
63
ders to reduce the occurrence of damaged hoses and the subsequent re-
placements that might accompany the experiment if rubber tubing were
used throughout the assembly. High pressure 316 stainless steel tubing
of 3/8 inch outside diameter and 1/4 inch inside diameter with a work-
ing pressure of up to 10,000 psi was used. Rubber hoses capable of
10,000 psi were used for the flexibility needed in the connection of
the pressure gages and the pressure relief valves around the area of
the pump.
An arrangement to reduce the time taken to extend the pistons of
the vertical or horizontal cylinders was incorporated in the assembly.
Lines coming from cylinders acting in the same direction were connected
from both sides by a tee fitting. The other side of the tee fitting
then connects the pump with all the necessary arrangement for the hy-
draulic gage and relief valve connection. It is assumed that there is
no significant loss of pressure in the lines and so the pressure read-
ings obtained from the lines--by the gages--are the same as that
applied on individual cylinders.
4.2 Desigg of Loading Frame
The following factors were considered in the design of the loading
frame, which obviously is the most important apparatus in the model
tests:
i) The stability of the frame itself in terms of toppling
during the tests.
ii) That the frame should be able to sustain the maximum
load that could be applied without failing.
64
iii) That enough space could be left after construction for
a reasonable model to be tested.
iv) The frame should be simple in design, economical with
materials for its construction being readily available.
Structural steel I-beams Wl8 x 50 of ASTM No. A36 specifications
were recomended for the basic frame using the guidelines above. The
loading frame was designed to 81 inches high so that it can be moved
into position in the laboratory. Another restriction imposed on the
design of the frame was the choice of the capacity of the cylinders to
be used. The choice of 25 ton cylinders was to allow reasonable loads
to be applied to the model. The regulation of the load was another
factor in the choice of these rams. These hydraulic cylinders were
mounted on the loading frame by bolts through holes previously drilled
on the latter.
The basic design of the frame as shown in Figure 24 was checked
for maximum deflection, moment, maximum shear force and reactions for
each beam. A fillet weld of at least l/4 inch using E6OXX electrodes
and an electric arc of length of at least 24% inches was recommended
for the joints in this design to ensure stability of the frame.
An additional feature was added to the design of the loading
frame. This feature which was designed to sit at the four corners of
the model is shown in Figure 25. The basic function of these features
which will be referred to simply as brackets were:—— to support the model initially in the test position before
any load can be applied.
65
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66
-- to serve as the holder of the steel plates which are needed
for the uniform loading required in the test.
-- to allow for some movement in the piston action of the
cylinders before the test begins.
4.3 Instrumentation
The load on the model can be read off the hydraulic gages connect-
ed to the lines that feed the cylinders. However, the most important
instrumentation in these tests are the permanent photographie records
kept for the various experiments. Photographie records are very impor-
tant in a study like this because of the fact that similitude of the
model material to the prototype is not perfect. The imperfeetions in
the similitude mean that measurements made on a physical model could
not be assued absolute. However, the incorporation of photographie
records and the hydraulic gages in this work makes for a realistie
qualitative analysis.
Two hydraulic gages which are capable of measuring up to 50,000
lbs. were connected to the hydraulic lines linking the cylinders aeting
horizontally or vertieally. The gages are mounted in the lines using
gage adaptors and auto-damper valves. This additional equipment added
to the gage is to prevent any damaging dial snap—back if a sudden load
release occurs.
4.4 Developing A Model Material
Wide varieties of materials have been used in physical models to
quantitatively and qualitatively study assorted rock mechanies problems.
67
Stimpson (1970) reviews most of the up-to-date information on modeling
materials. Sugar cubes have been used by Trollope in modeling of a
trapezoidal opening in block-jointed media.
Hobbs (1966) used various mixes of sand, plaster and water as the
model material for the tests he carried out. Cement paste in this case
was rejected because of the difficulty experienced in maintaining a
constant strength and the brittle behavior or a weak model material
made with this type of mortar. Although the compressive strengths of
the plaster—water mixes were found to be of the correct order, dis-
advantages were noticed in them, viz;
i) Shrinkage during the setting and hydration process.‘ ii) Excessive compaction when the compressive strength of
the plaster was exceeded.
iii) Low density.
Fine-grained silver sand filler was used to reduce the above disadvan-
tages for strengths of up to 150 psi.
Various mixture ratio of Portland cement, fused alumina cement and
quartz powder were used by Everling (1964) to simulate the 1/10
strength ratio of coal, shale and sandstone which was used in the model
study. Paraffin layers were incorporated in both the roof and the
floor to simulate bedding planes.
Rosenblad (1968) reported on the development of a model material
for the study of the failure modes in intact and jointed rock masses.
The material used was the rounded Valley, Nebraska river sand, hydrocal
B-11 gypsum cement, and water in 7.6:1:1.4 proportions by weight,
68
respectively. This material had an unconfined compressive strength of
610 psi and a direct tensile strength of about 85 psi, it has a void
ratio of 0.6 and a dry unit weight of 120 lb. per cu. ft.
For the simulation of the Wabana Iron Ore Mine in Canada, Barron
and Larocque (1963) used some variation of the water/plaster of Paris
ratio and some retarders and fillers. The geometrical scaling factor
for this material was 70 and that of the force is 13.7.
Barton (1970) developed a model material of red 1ead-sand/
ballotini-plaster-water to study rock slope failure. The model material
here had an unconfined compressive strength as low as 5 lbf/inz and
Young's moduli ranged between 350 and 560 lbf/inz.
Stimpson (1970) attempted to classify in a simplified way the
modeling materials which can or have been used for rock and soil mechan-
ics problems. This classification is as in Figure 26; the fact that the
mechanisms of rock and rock-like material deformation in compression
showed that dilation was important was used in this classification.
Close scrutiny of the classification in Figure 26 shows the
variety of model materials which could have been used for this study.
The basic factors that prevailed finally for the choice of the material
in this study was:
i) The ability to satisfy the similitude conditions.
ii) The ease of fabrication of the model.
iii) The ability of the material to set reasonably fast.
iv) The availability and the relatively quick delivery
of the material.
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70
v) The workability of the material.
vi) The ability to use fillers to make a weak model which
will fail under test.
The material chosen for this study was a commercial c€m€ut——
POR-ROK cement, manufactured by Hallemite, Lehn & Fink Industrial
Products Division of Sterling Drugs, Inc. and ordinary building sand as
the filler material. This cement sets in about 15 minutes and approxi—
mates various rock properties by the addition or exclusion of various
proportions of sand. The more sand is added the lower the strength of
the model material. Less water is also needed for this type of
cement——3 oz. of water for every 1 lb. of POR-ROK used.
4.4.1 Laboratory Testing
The choice of the mix proportions and the method of mixing was
achieved by laboratory testing-—unconfined compression tests. For a
model of dimensions 24 inches by 24 inches by 6 inches, with three
25 ton cylinders acting uniformly on the sides, 350 psi is the maximum
stress that can be applied on it. Thus, to achieve failure of the
model, the strength of the models to be tested should be below 350 psi.
Cylindrical specimens of the different proportions of the cement
and the filler chosen were tested. The length to diameter ratio for
all the samples tested was made to be about 2.0 (Hobbs, 1967).
Figure 27 shows the relationship between the uniaxial compressive
strength and the cylinder length for cylinders of 2.5 cm diameter
(Hobbs, 1967). Figure 27 proves the necessity of using the length/
diameter ratio of 2, if the inevitable increase in strength of cylin-
71
Ö Pennant Sandstone
38000 I Kirkby Siltstone
A Massive Ormonde Sandstone34000
NZ·-• 30000\¤-1.¤3 26000 Oä os-« 22000uU:Q)-5 18000 ·cnrnGJÄ 14000§ IU
10000
60001 2 3 4
Cylinder Length (in)
Figure 27. Relation Between Compressive Strength andCylinder Length (after Hobbs, 1967)
72
ders of L/D ratio less than 2 is to_be avoided. Hobbs (1967) attrib-
utes the increase in strength in the shorter samples to the influence
of the end restraint, which causes the stress system to be essentially
triaxial throughout the whole volume of the rock specimen. The lesser
probability of a gross weakness being present in the shorter specimen
is also cited as a factor.
Uniaxial compressive strength tests were conducted on the speci-
mens of sand and POR-ROK cement with different proportions of mix. The
results of those mixtures after 28 days of curing under room temperature
conditions are sumarized in Table 5.
Three samples of each type of mixture were tested and averaged out
for the uniaxial compressive strength. All the testing was done using
the million pound capacity M.T.S. stiff testing machine at the MiningQ
Department of Virginia Polytechnic Institute and State University,
Blacksburg, Virginia.
4.5 Procedure
A mold of inside dimensions of 24 inches by 24 inches by 6 inches
was constructed with wood to make the concrete models for these tests.
The concrete models had a composition of 70% by weight sand and 30%
by weight POR-ROK cement. A block of wood 9 inches by 6 inches by
1% inches was placed in the mold 7% inches from one end before the
pouring of the concrete was done. This block of wood created a hole to
simulate a mined area.
The concrete was mixed by hand and left under room conditions to
cure (Table 4). The tests were carried out with the side with shorter
73
Table 4
Test Results of Uniaxial Compressive
Strength of Different Mixtures of Sand
and POReROK Cement
Z Sand Diameter Length Failure Displacement FailureLoad Pressure
_______ (in.) _jQglL) (lb.) (in.) (psi)
10 2.699 4.426 22,500 0.01575 3932.7
20 2.695 4.262 23.500 0.01550 4119.6
30 2.686 4.213 24,500 0.01650 4323.8
40 2.690 4.187 18,750 0.0154 3299.2
50 2.693 4.149 13,250 0.0150 2326.2
60 3.334 6.346 16,770 0.0130 1920.5
70* 3.330 6.324 4,000 459.3
80* 3.298 6.572 1,600 187.3
90* 3.330 6.380 1,000 114.8
* 3 days curing at room temperature.
74
distance to the hole on the bottom cylinders and the reverse carried
out with the second model. The cylinders acting horizontally were
first activated up to a maintained load of 2000 lb. (387.82 psi); and
the cylinders which act in the vertical direction are advanced until
model failure. Photographs are taken at the beginning and end of the
tests.
CHAPTER V
COMPUTER MODELING ·
The limiting equilibrium approach as published by Wang, et al,
(1971) was used in the analysis. This method of stability analysis as
has been stated earlier has the great advantage of the versatility of
the finite element method to achieve realistic solutions to ground con-
trol problems. Plane stress and plane strain two-dimensional finite
element analysis can be made for an underground structure of given
geometry, loading and material properties. Usually in practice, plane
strain analysis is done assuming that the length in the third plane is
infinite. The basis of the finite element method has been discussed in
a preceding chapter.
The stress field around the underground structure under consider-
ation can be determined from the finite element analysis. A possible
fracture surface can then be calculated from the principal stress di-
rections obtained from the finite element method, using the linear
Mohr-Coulomb failure criterion. The possible fracture surface is com-
puted bearing in mind that at any point, the tangent to the surface is
oriented such that the quantity (lr| + uou) is a maximum at an angle 6,
from the maximum principal stress direction. 9, however, is related to
the coefficient of internal friction as shown below (Obert and Duvall,
1967; Wang, et al, 1971)
tan2S =·% (11)
Smooth curves to connect the tangents will produce a pattern of
75
76
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77
the possible failure surfaces over the entire structure. Two families
of fracture surfaces intersect each other at an angle of 26 or
180° - 29 (Wang, et al, 1971).
A typical fracture surface and the definition of the parameters is
as shown in Figure 28. The equations used in this analysis are as
. below (Wang, et al, 1971):
Normal stress,
0 = Ä-(0 + 0 ) --l (0 - 0 ) cos2¢ + 1 sin2¢ (12)n 2 x y 2 x y xy
Shear stress,
rnm = 1Xycos2¢ (ox - 0y) sin2¢ (13)” Where ox, oy, 1Xy are the horizontal, vertical and shear stresses,
respectively. (They are obtained from the
finite element stress analysis).
0u, rnm are the normal and shear stresses acting onthe fracture surface (Figure 28).
and ¢ is the fracture surface orientation (Figure 28).
The above two equations are used in the calculation of safety
factor of the fracture surface at a point. Integrating over all the
points along the fracture surface, the safety factor relationship
becomes (Wang, et al, 1971),Z (c + u0 )
Factor of safety = ——E?jF—-—Jl— (14)nm
This factor is the stability index; the higher it is the more stable
the structure becomes (Wang, et al, 1971).
78
The procedure detailed above was all incorporated into the two-
dimensional finite element computer program developed by C. S. Desai
and J. F. Abel (1972). See Appendix A. Some assumptions were made in
the algorithm in the modification of the finite element program to in-
corporate the stability analysis. The analysis was made for each ele-
ment of the mesh. Only one point on the possible fracture surface was
considered and this point was assued to be at the centroid of the
element. The fracture surface orientation, which is the tangent to the
surface or the tangent from the vertical axis (Figure 28), is calcu-
lated accurately using the principal stress orientation and the angle
given by the coefficient of internal friction. Factors of safety are
calculated for each element. These factors of safety are then cOutOuI—
ed using the General Purpose Contouring Program (GPCP) developed by
Batten and made available by the California Computer Products, Inc. .
5.1 Finite Element Mesh Generation
Five standard models were analyzed in this as shown in Figures 13,
14, 15, 16 and 17. These models were constructed bearing in mind the
modeling criteria for the finite element as described earlier and also
documented by Kulhawy (1974). The initial model (Model I) shown in
Figure 13 was to simulate the situation in the Pittsburgh or Big Vein
seam at Georges Creek Region, Maryland as reported by Stemple (1956)
and Holland (1951) and illustrated in Figure 1.
The geological columnar stratigraphic section used in the modeling
procedure was simplified. The column is shown in Figure 29. Shorter
computer time and reduced modeling complexity was the main aim of the
79
l2' I SaudstoneC°al
29 . 5 Shales5 Cm
-„•¥ we '~ $+2*QV9
. S Coal (miued)~_ M T.
l5' Shales
Figure 29 . S implified C-eo logical Coluum Used in the Analys is
80
simplification. The Pittsburgh or Big Vein seam used in the analysiswas 14% feet thick with an overlying Redstone seam of 4 feet. The
innerburden consisted mainly of shales with some intercalations of
sandstones. The innerburden was, however. modeled as shalesaloneLflßwith
material properties modified to allow for thedsandstone 1gt;£§Ql$§1Ä;;T
incorporated*and_aMshale floor to the underlying coal seam was also
aafédieféntly Älgllwéxfigäqpthe opening to minimize the boundary effects of the model%whighmcan
\§E§ÄIEIÄÄÄÄ1;-Äf§;;;—ÄÄÄ—ÄÄE§§§Z§“EE”EEÄ”Ä;;;i;5 obtained from the
finite element method.
To extend the studies on Model I a second model with an opening in
the upper bed of the same length as the lower seam was constructed--
Model II. Model III was constructed to simulate room and pillar mining
which is very prevalent in this area of the Appalachian Coalfields to
allow some practical recommendations to be made. The pillars in this
latter model were columnized——the pillars in the lower layer were placed
exactly below the upper layer. The last two models were Variations of
the staggered pillars that could be expected in practice.
These meshes for the finite element program were 240 feet in length
and 75 feet high. A Vertical stress of 1000 psi was loaded on the top
of the model to simulate ¤heWÄ$ħE§§ä§§”§ÄħSure (cover load). No Ver-
tiEa1ad;sp1gcemeQQ_iE_Ehe_nodes_at_Ehemlower_bgunga£y of the model_wasw———permitted. The side nodes of the model were restricted in their move-ment-in”;he horixontal direction. All the other nodes in the model
81
were free to move in all directions.
The numbering system used here was quite contrary to that espoused
in an earlier discussion. The band width in the finite element method
using Equation 9 should be minimized as far as possible as recommended
by Desai and Abel (1972). The nodes and elements are, however, number-
ed laterally, although numbering vertically would have produced a
smaller band width. The meshes were numbered this way to take some
advantage of the automatic generation of nodal and element data by the
computer code being used. Numbering laterally also makes it easy to
remove elements to simulate excavation.
The material properties used in this study were taken from the
literature (Agbabian,~19Z8i_0bertmand Duvall, 1969) and they are asshown in Table 5.
ewlffwh 1 HHHMWAWMMM
5.1.1. Model I
As has been mentioned earlier, Model I was to simulate the situa-
tion in the Pittsburgh or Big Vein seam at Georges Creek Region, Mary-
land as shown in Figure 1. The situation was, however, simplified to
the mesh shown in Figure 30. The model has an overall dimension of
240 feet by 75 feet with an 80 feet by 9.5 feet opening in the lower
coal seam (See Figure 30). Shales make up the floor of the opening,
with coal roof. The shale floor is 15 feet thick and an interseam of
shale of 29.5 feet. Five feet of coal was left on top of the opening--
roof of opening.
The coal seam in the upper bed is 4 feet thick, 12 feet from thetop. 1000 psi pressure was applied to the top of the model. This
82
Table 5
Material Parameters Used in the Analysis(after Agbabian, 1978; Obert and Duvall, 1969)
Rock Modulus Poisson Density Cohesion Angle ofType (E)x108psi Ratio (v) (p) pc8· (C) psi Internal Friction
Q degrees
Shale 1.61 0.10 158.4 167040.0 55.0Coal 0.72 0.23 128.2 61200.0 15.0
Sandstone 2.97 0.13 144.8 819360.0 43.23
83
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84
pressure had to be converted to concentrated loads at the nodes at thetop of the mesh. To achieve the concentrated loads at these nodes, the
principle of equal influence of loads at nodes was used. The idea of
equal influence area is to assume that the load at each node on top of
the model acts halfway to the left and also to the right of the node
in question.
This model contained 574 nodal points and 504 elements.
5.1.2 Model II
Model II was similar to Model I except for the addition of an open-
ing in the upper seam with a dimension of 80 feet by 4 feet. The mesh-
plot of this model is as shown in Figure 31. The geology of Model II
was the same as Model I. The assumption of 1000 psi pressure on top
of the model is also used in this case.
574 nodal points and 487 elements were under consideration in this
model.
5.1.3 Model III
This model has an overall dimension of 240 feet by 75 feet and has
four openings in the two coal seams (See Figure 32). The two openings
in the lower seam have dimensions of 20 feet by 9.5 feet each with a
60 foot pillar in between the two openings. The other two openings in
the upper coal seam were constructed so as to produce a columnized pil-
lar system as in practice. The openings are each of dimensions 20 feet
by 4 feet. This model is similar to Model I in the case of the geology,
except that there are two openings in the lower seam and upper seam as
85
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87
opposed to only one opening in the lower one. Two upper seam openings
are also incorporated to simulate room and pillar situations.
This model had 574 nodal points and 504 elements.
5.1.4 Model IV
Model IV has the same dimension and geology as Model I and was
aimed at simulating room and pillar system as it applies to multi—seam
mining. Staggered pillars were considered with its center to center
dimensions of rooms as 80 feet. This means that pillars are 60 feet
and openings are 20 feet in length which is the usual dimensions used
in mines in the Appalachian Region. Two openings were located in the
lower seam and three in the upper bed.
Using the same numbering system as before, a mesh of 574 nodal
points and 500 elements were considered. The loading and boundary
conditions were as previously used for the three models mentioned
earlier. The mesh for Model IV is as in Figure 33.
5.1.5 Model V
Model V is similar to Model IV except that the locations of the
openings were somehow reversed. Two openings were located in the
upper seam and three in the lower one. 574 nodal points and 500
elements were under consideration.
The meshplot of Model V is shown in Figure 34.
88
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90
5.2 Computer Codes Used in the Analysis
Three sets of computer programs were used in the present study,
viz,
i) The Mesh-plot program.
ii) The Finite Element program.
iii) The General Purpose Contouring program.
5.2.1 The Mesh-plot Program
Apart from using the Mesh-plot program in this analysis as a pic-
torial view of the mass of data input to the computer, this program
was also used as the only check on the input data errors. The finite
element code used in this analysis, which has been listed in Appendix
A, has its own internal data error checks. The Mesh-plot program,
however, allows one to spot the errors in the computer plot that is
generated easily.•
This program is written in FORTRAN IV with packaged plotting sub-
routines available at the Virginia Tech Computing Center. Two plotters
can be used with this program--the Versatec 1200 electrostatic plotter
and the Calcomp 1051 dru plotter. The input data to this program is
in the same format as that of the finite element program, thus its use-
fulness as a check on the input data of the latter program which is
bigger and expensive to use.
5.2.2 The Finite Element Computer Code
There are lots of computer codes used for the finite element
analysis, but the code selected for this study is that developed and
91
published by Desai and Abel (1972). This code is relatively simple
and because of its simple and generalized nature is not very efficient
for large-scale problems. The code is limited to linear, elastic,
plane strain or plane stress analysis of isotropic bodies. Only one
loading case may be accomodated for each problem. Notwithstanding
all these limitations, the program has been successfully applied to
many solid mechanics problems.
The elements used are 4-Constant strain triangle quadrilaterals
and/or constant strain triangles. Various subroutines are employed in
this code to carry out most of the computational steps. These sub-
routines are controlled by the main routine which reads the title of
the problem, computes the semi-band width, solves the overall equilib—
rium equations and prints the displacements.
5.2.3 The General Purpose Contouring Program (GPCP)
The General Purpose Contouring Program (GPCP) is capable of repre-
senting graphically the functions of two independent variables as con-
tour diagrams. GPCP was originally developed by George W. Batten, Jr.
of the University of Houston, Texas and is available on the Versatec
1200 electrostatic and the Calcomp 1051 plotters.
The program can be used in a wide variety of applications ranging
from the generation of contour maps of gravitational fields and strata
depths in the realm of geophysics to the depiction of temperature and
barometric pressure in the field of meteorology. GPCP has been used in
the depiction of contour maps of stress around an opening,
(Bhattacharya, 1980).
92
There are two basic modes in which data could be input into GPCP:—— data consist of the function values at the mesh
points of a rectangular array (gridded data).
-- function data at arbitrary points within the
region of interest (irregular data).
In the case of the random data points, GPCP generates gridded data by
analytically constructing a smooth surface passing through every data
point. Gradient information can also be specified to facilitate the
determination of the mesh point estimates derived from the random data.
GPCP is very flexible in that the user could specify the manner in
which the contour lines generated could be plotted-—bold lines, dash
lines, lines with or without labels, etc. Areas could be blanked out
so that no contours are plotted in those regions. Annotations, in the
form of lines and alphameric symbols can also be included in the
plotted maps.
GPCP was made available as a proprietory package program from the
Virginia Tech Computing Center, therefore a listing of the program was
not available.
5.3 Procedure
The finite element mesh which has been discussed earlier is ob-
viously very important in this analysis. After a reasonable mesh has
been conceived, the whole formulation is digitized and input into the
computer. The nodes were numbered from left to right——the reasons for
that are given in an earlier section. The number of node, its coordi-nates and the boundary conditions are all input together. The element
93
data describes the location of each element with respect to the nodal
points which had been supplied earlier. The material type of which the
element is part is also included in the data cards describing the
element.
To facilitate the input procedure, the computer automatically
generates the nodal point data if the intermediate nodal points fall
on a straight line and are equidistant. The first and last points on
the line, however, will have to be specified. The computer code used
in this case will assume automatically KODE = O (boudary condition,
where loading conditions in the x and y directions are prescribed).
Automatic generation of element data also exist for elements which are
on a line in such a way that their corner node indices each increase by
one compared to the previous element. The computer code will, however,
assume the same material type in its automatic generation.
Material properties used in this analysis which has been stated in
Table 5 will have to be specified even before the digitization process
of the nodal and element data. The boundary conditions for the modeli
are also incorporated in the data fed into the computer.
The output from the modified finite element method of analysis
gives us an array of stresses ranging from the vertical stresses to the
angle of the principal stresses. The safety factor in every element
(occurring at the centroid of the element) is also calculated. How-
ever, for easy access to the part of the output concerning the safety
factors at the centroid of the elements, the values of the coordinates
and their corresponding safety factors and displacement are stored on a
disk.
94
The data stored on disk is fed into GPCP to produce contours ofthe safety factors. The data which is stored on the disk are preparedto make it easier for the input process into the contouring program.This means that the data is stored in the same format as that for GPCP.
CHAPTER VI
RESULTS
6.1 Computer Modeling
The results obtained from the stability analysis done on the com-
puter is in the form of contour maps and thus the interpretation of
them is very important in this study. From the theory of the technique
implemented in this study, fracture will be most likely to occur first
along the surface that has the lowest factor of safety, which will be
referred to herein as the critical fracture surface (Wang, et al, 1971).
This technique does not, however, use the absolute values of the safety
factors, but gives a good exhibit of the trend of the shear failure in
a structure.
Observation from the results from all the models described earlier
will be undertaken in this chapter. Tests carried out especially with
Model I will be explained and observationamade from the results obtain-
ed will be stated. It should be emphasized, however, that the observa-
tions stated in this text are valid for the material properties and
constitutive law of rocks (which, in this case, is linear elastic)
used.
6.1.1 Model I
The description of the model has been stated before in Section
5.1.1. The model basically has one opening of 80 feet by 9.5 feet in
the lower coal seam. The main objective for the construction of this
model was to simulate the effect of mining the lower coal seam on the
95
96
umined upper coal bed. Figure 35 shows the safety factor contours
obtained using the material properties tabulated in Table 5. Further
experiments (or tests) on modulus, Poisson ratio, density, angle of
internal friction and cohesion were undertaken to investigate the
mechanism of failure in the interseam. The sensitivity of the material
properties used in this analysis was tested to fully understand the
failure mechanism in the interseam. The observations in these tests
will be discussed later on in the chapter.
The critical failure surface, which is the lowest safety factor
contour line, is the 20 contour line in this case (Figure 35). It must,
however, be borne in mind that a lower safety factor contour other than
the chosen contour could be obtained from Figure 35 but for the fact
that the contouring program is very efficient with this contour
interval--20.
The approximate angle the shear failure line makes with the hori-
zontal is about 700. Field observations have confirmed this angle as
very common in cases as that being considered in this model. As com-
monly observed underground, the critical failure surface as it is in
this contour plot occurs at the edge of the opening. This phenomena
has been observed by workers like Aggson (1979).
Observing closely the contour plot obtained from Model I, higher
safety factors tend to be experienced in the middle portion of the
interseam. As in almost all the cases the critical fracture surface
around the opening is neither the nearest nor the most distant of all
possible fracture surfaces that begin and end on the boundary of the
97
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98
excavation (Wang, et al, 1971). Illustrating how useful this method of
analysis is, safety factor values obtained in the center of the imedi-
ate roof of the opening were very small indeed, thus strengthening the
fact that tensile failures could occur in those areas.
It is noticeable that the contours at the boundary of this model
and many other contour plots in this study are not uniform (i.e.,
almost vertically straight contours) contour lines. This is because of
the limitation on the storage capacity of GPCP, very large values of
safety factors had to be removed from all the data sets for the program
to work. Most of the large values, incidentally, were at the bounda—
ries, as expected, thus the non—uniformity of the boundary contours.
The region of high safety factors is very extensive in the middle
part of the interseam layer although the initial failure at the edge of
the opening is the most critical of all the failure regions. The
extent of the predicted failure in the upper seam for this model was
judged to be an important determination especially in checking the
interactive effects of seams. To determine the extent of this failure,
the distance between the 20 safety factor contour at the floor of the
upper bed was measured, bearing in mind the scale factors used in the
drawing of the contours. It was especially important in the tests car-
ried out and described in later sections that some consistency in the
determination of the extent of the predicted failure in the upper seam
was established. This, therefore, explains the use of the floor of the
upper coal seam as the reference.
99
6.1.1.1 Effect of Modulus
This test on Model I was undertaken to evaluate the effect ofmodulus changes on the mechanism of failure in this study. To achievethis objective, the ratio of the modulus of the shales to that of thecoal (Eshale/Ecoal) wäs varied and the effects studie;( The moduli ofthe coal seams_gg;?@however, kept constant and that of the shales
varied. This was undertaken with the understanding that the shaleswere the most important geological formation in the study because of
its predominance in the interseam.
The rationale behind the use of the ratio of the modulus was fora simplified analysis, that is, the use of simple integers in the graphplots and description. Eshale/Ecoal ratios of 2, 4, 8 and 10 were„«undertakenin this study. „„ l' ‘* *« 7
The plot on Figure 36 is a clear indication as to the trend gf
fheextentof failure in the upper seam when the lower seam is mined, as
the interseam modulus is increased. It is noticeable that a change in
the ratio of the modulus of the rocks in the model affects the extentof failure in the overlying seam. As the modulus of the shale in the
interseam is increased the extent of failure in the upper seam generally
increases as well.
Figure 37 shows the critical fracture surfaces which occur withchanges in the modulus of the innerburden.
Individual contour plots for the changes in modulus made in this
analysis are shown in Appendix B. As the modulus of the interseam
increases, the failure surface in the middle portion of the shales in
100
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Figure 36. Effect of Modulus of the Interseam on Failurein the Upper Seam
101
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102
this region becomes thinner. The thinning effect in the middle region
of the interseam can be explained by the brittle nature which the shale
assues as modulus increases. The brittle nature of the interseam also
explains the expansion of the angle of fracture in the interseam; the
angle increases from 70° to Eshale/Ecoal ratio of 2 to 90° when theratio is 10.
Observing the middle of the imediate roof of the excavation in
the lower seam, it can be noticed that as the Eshale value increasesthe values of the safety factor contours also increase.
6.1.1.2 Effect of Poisson's Ratio
Poisson's ratio plays an important role in the solution of the fi-
nite element method of stress analysis, especially in the consideration
of lateral stresses which have been found to be very important in this
case (shear failure). It was, therefore, of great interest to try andO
evaluate the effect of changes in the Poisson's ratio in the interseam
on the stability in the interseam.
For easy analysis, the Poisson's ratios of the coal seams was kept
constant and that of the shales which dominates the interseam was
varied. The ratio of the Poisson's ratio of the shales to that of the
coal seams were used for the same reasons as mentioned in the previous
section. The ratios used in this analysis were 0.3, 0.5, 1.0 and 1.5.
It was not possible to increase the ratio beyond 1.5 as the maximum
Poisson's ratio of 0.5 was being approached and the degree of plastici-
ty after that point will be too high, thus unrealistic for any practi-
cal purpose.
103
Figure 38 shows the relationship between the extent of the pre-
dicted failure in the upper seam when the lower bed is mined and the
gradual increase in the Poisson's ratio of the interseam as in Model I.
Generally from the graph, there is an increase in the lateral extent
of failure in the upper seam as the Poisson's ratio of the interseam is
increased.
Figure 39 shows the critical fracture surface plots obtained for
changes in the Poisson's ratio of the interseam. The thinning out of
the middle section of the interseam encountered in the previous section
on the incremental modulus effect does not occur in these contour plots.
Actually, the middle region of the interseam bloats out from 700 to
about 900 failure angle as the Poisson's ratio in the interseam in-
creases. The higher degree of plasticity as the Poisson's ratio is
increased may account for this bloating effect in the middle section of
the interseam experienced in this case.
The middle of the immediate roof of the opening appears much
"safer" as the Poisson's ratio of the interseam is increased. This
means that as Poisson's ratio of the interseam is increased the immedi-
ate roof of the opening assues higher values of safety factors. The
increase in plasticity may also account for this favorable region in
the immediate roof.
6.1.1.3 Effect of Density
The weight of the rocks above an opening is very vital to the
stability of the excavation. This factor was studied varying the
density of the shale in the interseam of Model I. For the use of
104
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Vshale/vcoal
Figure 33. Effect of Poissor1's Ratio of the Iuterseam onFailure in the Upper Seam
105
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106
simple integers in the analysis of this factor the ratio of density ofm„z%
shale to that of coal (ps/pc) were used. The ratios considered in
this analysis are 0.5, 1.0, 1.5 and 2.0. To achieve these ratios the
density of coal was constant and the density of shale
varied.
The plot on Figure 40 shows the relationship between the lateral
extent of the predicted failure in the upper seam when the lower bed
is excavated and the ratio of the density of shales to that of coal in
Model I. The plot obtained in this exercise shows that as the density
in the interseam is increased, the lateral extent of the failure in
the upper seam decreases until ps/pc = 1.4 then it starts to increase.
After the ps/pc = 1.4 has been reached, it can safely be inferred
that the weight of the interseam plays a greater role on the failure
pattern which occurs. Other factors such as the stiffness of the mate-
rial and the lateral stresses must have had a lot more influence on the
interseam failure before this ratio of densities was reached.
Safety factor contour plots of the various ratios are as shown in
Appendix B. Figure 41, however, shows the critical failure surfaces of
the model when the density of the innerburden is changed. In a general
observation of the contour plots obtained from this computer analysis,
it can be noticed that there is not much difference in the basic fail-
ure pattern for ps/pc ratio of 0.5 and 1.0. The angle of failure as
obtained for both contour plots is approximately the same. The only
significant difference that is apparent in the two plots is the lateral
extent of the failure in the upper seam which is shown in Figure 40.
107
100.0
EV 80.0äQ1cn1-4GJOeD-•
° 60.0:2·«-•GJE 0 °E °~¤€¢/lr-•
u-4 40.004.1C2G.)4.1Nkl'34.1 20.0u•«-1’U
8¤-•
0.5 1.0 1.5 2.0 2.5D shale/D coal
Figure 40 . Effect of Density of the Interseam on Failure in the' Upper Seam
108
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109
Dramatic differences in the contour plot of ps/pc ratio of 1.5
and 2.0 are experienced, nevertheless. Apart from the appazent large
differences in the lateral extent of the failure in the upper seam, the
middle section of the upper seam which usually has a series of high
safety factor contours in all the plots a;% different. Those high
safety factor contour areas in the upper seam seems/to flatten out in
structure until the ps/pc ratio gets to 2.0 when the values get lower
and flatter.
It should be realized that the area between the critical failure
surfaces containüéome competent rocks. This is to say that the mechan-
ism of this massive failure which happens in the interseam in the multi-
ple horizon mining is mainly shear in nature, and this is justified by
the high values of safety factors encountered in between the failure
surface.
6.1.1.4 Effect of Cohesion
The parameter cohesion plays an important role in the calculation
of shear stresses. It is also one of the important parameters consider-
ed in the linear Mohr-Coulomb failure criteria. Cohesion, therefore,
was considered a very vital parameter to study. The values of cohesion
in the interseam were varied with that of the other seams or materials
kept constant. The usual ratio of cohesion of shales to that of coal
was used in this analysis in a bid to simplify the interpretation of
the results. The ratios used were 1.0, 2.0 and 3.0.
The results obtained from this analysis have been summarily plotted
in Figure 42. This plot shows the trend of the lateral extent of
110
100.0
73EJä 80.0<Urn$-401CL¤«ZD3 60.0aß$-4:3--4EFr-« ————O—————-Ol-———O————-———-·"6‘ 40.0uC-'0uN$:1'¤3 20.0"UGJ$-•¤-4
1.0 2.0 3.0 4.0 5.0
Cshale/Ccoal
Figure 42. Effect of Cohesiou in the Interseam cn Failurein the Upper Seam
111
failure in the upper seam when the lower bed is mined as cohesion in
the interseam is increased. Actual safety factor contours are shown in
Appendix B. The four figures shown in this case gives the impression
that the parameter cohesion (of the interseam layer) has no effect on
the manner in which the whole structure fails. Figure 43 shows thecritical failure surface for changes in the cohesion of the innerburden.It was suspected, however, that the cohesion factor in the calculation
of the safety factor was insignificant as compared to the normal stress-es (Equations 2 and 14). All observations mentioned under Section 6.1.1(on Model I) apply in this case. In fact, both of the exercises have
identical safety factor contour plots.
6.1.1.5 Effect of Angle of Internal Friction
The linear Mohr-Coulomb equation and the safety factor equation
in Equations 2 and 14 show that the angle of internal friction (¢) is
one of the factors which needs consideration in any stability analysis
like in this study. As usual, ¢ of the interseam layer which is predom-
inantly of the rock type shales was varied keeping that of the coal con-
stant. The usual ratio of ¢Shale/¢COal were considered; in this case,1.0, 2.0, 3.0, 4.0 and 5.0.
The results obtained in this exercise are summarized in Figure 44.
The other contour plots were ignored because they were all identical to
that shown in Figure 45. The graph on Figure 44 also depicts the rela-
tionship between the angle of internal friction (¢) of interseam layer
and the lateral extent of failure in the upper layer, when the lower bed
is mined. There seems to be no apparent relationship, that is, ¢ of the
112
GJSU¤-rOßO•v-4U!dlSOUGDß•v-4>~•HCU>HO
*4-1U)UUQ
*4-IH5VJGIHI3UUaßPHG)"Uu-{HQ2!US•1-OHUG)HßHßUI-4
05Q
GJH300••-4PH
113
,„100.0U33EQGJU1H2, 80.0G-•
IDGJ„-CUC1••-4
Q 60.0I!
•v-4<¤ .In
"5 ‘ -—-o————-—o—-———o——————c>—-————-0U5 40.0UX .Lü'UGJUO••·•'5 20.0$-4G-•
1.0 2.0 3.0 4.0 5.0¢shale/¢coal
Figure 44.. Effect of Angle ef Internal Friction of theInterseam on Failure in the Upper Seam
114
--4QG$-40)UG
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115
interseam has no effect on the failure pattern experienced in the model
studies.
In leaving this discussion on the effect of ¢ on interseam failure,
it will be expedient to mention that the contour plots of Model I
(using the material properties in Table 5) is identical to the plots
obtained in this exercise.
6.1.1.6 Effect of Proximity of Seams
Hasler (1951) and Lazer (1965) observed in the coal mines in the
Pocahontas Coalfields that interactions were non-existent when inter-
vals between seams are greater than 50 feet. Other intervals have been
observed in other coalfields which might imply that the geology of the
area might be a factor in the interaction of the contiguous seams.
With these observations in mind, Model I was expanded vertically
in the interseam to study the effect of the bed interval. Various
meshplots were drawn to accomodate seam intervals of 29.5 feet (which
is the standard Model I), 49.5 feet, 69.5 feet, 89.5 feet and 119.5
feet. These meshplots were designed on the same basis and guidelines
as mentioned earlier. They all had an opening of 80 feet by 9.5 feet
in the lower seam with 5 feet of coal as the immediate roof. The upper
seam was unmined. The horizontal lengths of all the meshes were 240
feet, although the vertical lengths for them varied in each case. The
29.5 feet interval had 75 feet vertical length as against 165 feet for
119.5 feet seam interval.
The boundary conditions used in all these cases were the same as
that described before. This means that a 1000 psi pressure was applied
116
on the top of each of the mesh created and distributed uniformly on the
top. There was no vertical displacement allowed in the nodes at the
lower boundary of each mesh in this case. The nodes at the side bound-
aries of the meshes were only allowed to move vertically and not hori-
zontally, all other nodes were, however, allowed to move freely in any
direction.
The same numbering system as described under Model I was used and
the material properties previously specified in Table 5 were used in
this analysis.
Safety factor contours obtained after the finite element analysis
are shown in Appendix B. The trend of the lateral extent of failure in
the upper seam when the lower bed is mined, as the seam interval in-
creases is depicted in Figure 46. Figures 47, 48, 49 and 50 show the
critical failure surfaces which have been isolated from the safety fac-
tor contours. The critical failure surfaces could not be superimposed
because of differing scales. The usual safety factor contour assumed
for the critical failure surface could not be applied in this case be-
cause in most of the cases, the 20 contour line did not run into the
upper seam. The lowest safety factor contour that could reach into the
upper seam and still show the trend of failure in it as the bed inter-
val was increased was found to be the 60 contour line.
An interesting observation was made from Figure 46, that the later-
al extent of the failure predicted by this method in the upper seam de-
creases as the distance between the bed increases until the interval
reaches about 52 feet, then it starts to increase. It was believed
117
120.0
II ?1
I I100.02 V 12: I /5 I·’
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II
20.0 20.0 60.0 60.0 100.0 120.0Interseam Distance (ft)
Figure 46 . Effect of Proximity of Two Seams on Interseam Failure
118
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from studying the graph and the safety factor contour plots that the
mined lower bed ceases to be a greater factor in the failure of the
upper seam after the interval between the two seams is beyond about
52 feet. Consistent reduction in the lateral length of the failure inthe upper seam when increasing the interval between the beds until the
52 foot mark gave rise to the above inferences. Gradual increment of
the failure region after the 52 foot interval was also observed; but to
make the inference more justifiable, a rapid increment in failure in
this region after the 90 foot interval was experienced showing that
there was more than the mined lower seam involved in the cause of the
failure and that its involvement was dimishing rapidly as the interval
between the beds increases.
The boundary contours in the contour plots shown in Appendix B
show clearly the uniformity of safety factors at the boundary of the
area of analysis. The uniformity of the safety factor contours show
that boundary effects in this finite element model is almost non—exist—
ent. It can also be noticed that the high safety factor region in the
middle of the interseam which is to be expected gets thinner with every
increase in the seam interval. The low safety factors, which occur at
the edges of the opening, is also a manifestation of the high stress
concentrations around that region which contribute greatly toward shear
failure in that region.
6.1.2 Model II
This model has an 80 feet by 9.5 feet opening in the lower seamand alsg$80 feet by 4 feet opening in the upper one. Basically, this
123
model was to simulate the simultaneous mining of contiguous seams and
for a check on the failure patterns. The critical failure surface of
this model is as shown in Figure 51. The critical failure surface hereis indicated by the 20 safety factor contour line.
The critical failure surface in this case is clearly manifested
in that//the break from the lower seam to the upper seam can be noticed
easily. The failure angle obtained is about 80° to the horizontal.
The volume of rock involved in the failure region in this case is quite
greater than that shown in Model I. The slabbing of the rib of theopening in the lower seam is also noticed.
The boundaries to this model have fairly high safety factor values
except that they are not uiformly looking contours as usually expected.
That may be due to stress redistribution, with higher stresses occur-
ring in the areas of the opening.
6.1.3 Model III
This model was constructed to investigate the many recommendations
made by workers like, Peng and Chandra (1980), Hasler (1951) and Zachar
(1952) that any pillars left in a multi-seam mine should be columnized.
The critical failure surface obtained from this model is shown in
Figure 52. The 100 safety factor contour is shown to illustrate fur-
ther the fracture pattern.
The plot obtained from the model justifies the rationale behind
the recommendation of columnization of pillars in a multi—seam mine.
Due to the many high safety factors encountered in this model study, the
contour interval was increased to 50 and thus the lowest safety factor
124
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126
contour encountered is 50. It can be realized from the plot that the
failure region in this model is very much confined to where the open-
ings are and that pillars left are almost intact in terms of failure.
The pillars in the lower seam seem almost intact and although the
pillars left in the upper one tend to be smaller than the original, it
has some stability as against those to be described in Models IV and V.
Observing carefully the failure that might occur around the openings it
can be noticed that there are some high safety factor areas in the
middle of any two openings vertically adjacent.
6.1.4 Model IV
Staggered pillars in multi-seam mining was modeled in the remain-
ing meshes to investigate the possibility of leaving the pillars in a
·staggered formation. It was noted that in the literature these pillar
formations had been discouraged (Stemple, 1956), although it was con-
ceivable that the staggered pillars could be stable and not cause much
ground control problems if enough time could elapse after the complete
excavation of the lower seam before the upper one is mined.
The meshplot for this model has been discussed in Section 5.1.4
and shown in Figure 33. The critical failure surface obtained for this
model, however, is shown in Figure 53. The 40 safety factor contour
has been added to clearly define the failure surface. 7The contour plots obtained in this model analysis confirmf/the
fact that there has been no recommendation for staggered pillar system
for multi-seam mining. The critical failure surface, which in this
case is the 20 safety factor contour, runs from an upper opening into
127
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128
a lower one making both openings unstable. Some very undesirable
ground control problems can also be noticed quite clearly in this case,
the critical failure surface which forms on the ribside of the lower
opening can also be a sign of rib slabbing. The kind of stability ex-
perienced when the pillars were columized in the previous test could
not be attested to in this model.
6.1.5 Model V
This model which is described in Section 5.1.5 and with its mesh-plot shown in Figure 34, was constructed to observe the differences in
the kind of ground control problems it poses as compared to Model IV.
The same rationale as described in the previous section was also behind
this model's construction. _Observation of the contour plot obtained working with this model,
which is shown in Figure 54, shows that ground control problems associ-
ated with this model is identical to those experienced with Model IV.
6.2 Physical Model
Two tests were done in this analysis, because of the technical dif-
ficulties experienced in the preparation of the models, especially in
the creation of layered blocks. These tests and other tests carried out,
however, suggest that the design and construction of the loading frame
and all the accessories are in good condition and conforming to the a
design criteria mentioned in Chapter 4.
The two tests showed that when a load of 2000 lb. (387.82 psi) was
applied in the horizontal direction a similar load (i.e., 2000 lb.) in
129
(rl,.Il :
Ep 4"E?‘
130
the vertical direction was needed to break the model. The model also
broke initially in the vertical direction in the end with.the shorter
distance to the hole in the pattern expected from the computer and
literature study (Figure 55 and Figure 1). A photograph could not be
taken in the initial stages of the model failure but Figure 55
represents what happened initially.
131
•-4OOON
2000lb
Figure 55. Initial Fracture Pattern of Model Test
CHAPTER VII
SUMMARY
The case studies carried out in this investigation prove that^when pillars of the upper seam are superimposed on the pillars left in
the lower seam, greater stability in the overlying seam is achieved.
Investigating cases where the underlying seam has been mined prior to
mining the upper seam, it was found that less disturbance occurs in the
upper seam when the innerburden is thick. It was also found that the
extraction ratio has to be small when the innerburden is not thick or
when the nature of the interseam is weak, if stability in both seams is
to be maintained. The case studies also revealed that isolated pillars
left in the lower seam act as an unsupported cantilever beam which can
bend 100 to 300 feet before fracturing in longwall mining.
Most of the energy and time of this research have been devoted to
the design and construction of a loading frame for the physical model-
ing aspect of this study. Two samples were tested and they exhibited
the same shearing pattern as was found from the literature and the
computer model studies. A loading frame capable of testing a model
block of 24 inches by 24 inches by 6 inches, with a maximum pressure of
10,000 psi, was however, designed and constructed.· Computer analysis was performed on a multi-seam mine modeled to
simulate as closely as possible the situation experienced in Figure 1.
Five different models were constructed ;ä;a;;empt to study all the con-
ditions to be expected in a multi-seam mine with the underlying seam
132
133
mined first prior to the extraction in the overlying seam. Different
tests were also carried out on the first model (Model I) such as the
investigation of the effect of modulus, Poisson's ratio, density, cohe-
sion and the angle of internal friction of the innerburden on its fail-
ure. The critical failure surface obtained using the lowest safety
factor contour shows a shear failure line approximately 70° to the
horizontal, which confirms what has been observed in the field.
When the modulus of the innerburden was increased systematically
it was found that failure in the upper seam also increases. Increasing
the Poisson's ratio of the innerburden also increased the extent of the
failure in the upper seam significantly. There was a cluster of high
safety factors in the middle section of the innerburden when increasing
the Poisson's ratio and this was attributed to the high degree of plas-
ticity and the high lateral stresses which come into effect in this
test. The density of the innerburden also has an effect on the failure
in the upper seam. It was inferred from the tests that the weight of
the innerburden comes into play in the failure of the upper seam after
pshale/pcoal is greater than 1.4. The frictional factors--cohesion andangle of internal friction-—were found to have no significant effect on
the failure in the upper seam when the lower seam is mined first.
The effect of proximity of seams on the failure in the upper seam
was investigated using innerburden thicknesses of 29.5 feet, 49.5 feet,
69.5 feet, 89.5 feet and 119.5 feet (Model I was used in all these
cases). The computer analysis showed that the mined lower seam ceases
to be a significant factor in the failure of the upper seam after the
134
innerburden thickness exceeds 52 feet.
When an opening was constructed in the upper seam, it was found
from the computer analysis that the critical failure surface ran from
the lower seam into the upper one; and also slabbing of the ribs of the
openings w;;ééäoticed. Colummization of pillars in a multi—seam mining
has been recommended by many workers and it was found in this study the
best way to leave pillars in a multi—seam mining. The pillars in the
lower seam seems almost intact with slight robbing of pillars in the
upper seam; the relative stability experienced superimposing pillars in
multi—seam mines explains why it is recomended by most workers in this
area. Instability in the pillars left in both seams was experienced
when staggered pillars were modeled and analyzed using the computer.
CHAPTER VIII
CONCLUSIONS AND RECOMENDATIONS
8.1 Conclusions
Three methods of analysis have been used in the study of the
mechanics of interseam failure when a lower seam is mined first prior
to the mining of the upper seam. The three methods are: computer
modeling, case studies from the literature and physical modeling. The
following conclusions were drawn from the above methods of analysis:
1. Using the material parameters in Table 5, which are very real-
istic for mines in the Appalachian Coalfields, the finite element
method used suggests that shear failure is most likely when the inner-
burden is less than 52 feet. This conclusion is also consistent with
what has been observed in the Appalachian Coal region (Hasler, 1951;
Lazer, 1965).
2. As the modulus of the innerburden increases, the tendency to
fracture through to the upper seam becomes greater. This finding im-
plies that, although massive formations such as sandstones are pre-
ferred in the innerburden, these may result in extensive fracture planes
under some mining conditions.
3. The computer analysis also shows that as the Poisson's ratio of
the innerburden increases the failure in the upper seam also increases.
Thus, shear failure through to the upper seam is dependent on the later-
al stresses and some degree of plasticity of the innerburden.
135
136
4. Increase in the density of the innerburden greatly increases
the innerburden instability due to shear failure. This was expressed
in the computer analysis when density was varied.
5. Cohesion and angle of internal friction (frictional factors)
in the innerburden have no significant effect on the stability of the
upper seam.
6. When a room and pillar method of mining is used in the extrac-
tion of the seams in a multiple seam mine, the pillars in the upper
seam should be superimposed on the pillars left in the lower seam. The
investigations in the field and the computer analysis have found this
consideration to be very important for stability in the upper seam in
this case. Thus, staggering of pillars should be discouraged.
7. Longwall panels in the upper seam when placed in the
de-stressedzones created by the mining of the lower seam minimize;/damage
in the overlying bed.
8.2 Recomendations
More tests on the physical model with a particular mine and its
conditions in mind would be very helpful to this study. This will
invariably include a study of similitude conditions and all the
different scale factors pertaining to the mine.
Further measurements on the physical model such as displacements
(convergence) in the openings will also be very helpful if complete
study is to be achieved in the laboratory. Linear Variable Differen-
tial Transformers (LVDT) in conjunction with the Data Acquisition
System already acquired could be used to monitor the displacements in
137
the model during the tests.
Further work on making the POR-ROK Cement/sand model into layers
for close modeling of situations in the field needs to be done. This
might be achieved by making the model in slabs and placing them in the
frame with an adhesive.
Finally, further field studies can be conducted to study the
effect of time on the interseam failure.
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APPENDIX A
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SAFETY FACTOR CONTOURS OBTAINED FROM
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MECHANICS OF INTERSEAM FAILURE IN
MULTIPLE HORIZON MINING
byEddie N. Barko
(ABSTRACT)
The mechanics of massive interseam failure in a multiple seam mine
was investigated using three approaches: case studies, physical models
and computer analysis. Specific examples of multi—seam mines with the
underlying seam mined first prior to the mining of the overlying seam
were studied with some design guidelines drawn from them. A loading
frame capable of testing model blocks of 24 inches by 24 inches by
6 inches and also capable of applying up to a maximum of 10,000 psi of
pressure on the models was designed and built.
In this investigation, factors that affect the stability of the
overlying seam when the underlying seam is mined first were studied
using the finite element method and the Mohr-Coulomb failure criteria.
Critical failure surfaces obtained from the computer analysis were
analyzed for columnized and staggered pillars in room and pillar mining
with the columnized pillars favored over the staggered ones.