14

The void ratio can be determined:

V,
est, 1)
Wy = Vp > Vis ®
0 MY), °

where = void ratio,

Vy = void volume, in’,
V, = test material volume, in’,
and V, = total volume, in’,

The void ratio was determined for each point of dis-
placement using a spreadsheet software program. In addi-
tion, the “bulking factor" (BF) may be determined as the
ratio of the total volume of the broken rock material
(including voids) divided by the volume occupied by the
intact rock, or the void ratio plus 1:

V,
BF=
v,’ (10)
or
W,-V) | Vv,
BR=it of, 1)
v, 'V, ay
BF=e+1. (12)

The bulking factor is often used in the literature to
determine the height of the caving zone (29). Table 4 lists
the bulking factor at the 800-psi stress level.

Particle Breakage

After the test, the rock material was sieved and the
grain size distribution curve was compared with the pretest
gradation curve. Overall particle breakage was quantified
by subtracting the amount of rock particles passing each
sieve before the test from the amount of rock passing after
the test and summing the negative difference according to
the method used by Marsal (30), The appendix lists all of
the pretest and posttest grain size distribution curves
(fig. A-1).

Rock Shape

Zingg’s classification method (25-26) was used to quan-
tify the shape of the rock pieces before and after each test,
as well as to compare shapes of the three different rock
types. For each test, at least eight rocks were sampled
from each sieve size, and the length, width, and thickness
of the rock pieces were measured. The ratio of the thick-
ness to width is plotted on the x-axis, while the ratio of the
width to length is plotted on the y-axis. Figure 15‘Shows
the various classifications by shape (spheroid, blade, roller,
and disk) and the classification of each rock type before
and after the tests.

Contact Points

To evaluate how well the various rock types are able
to transmit an applied load through the skeletal structure
of the granular material, the number of contacts per
particle was determined according to the method used by
Athanasiou-Grivas (3). The number of contact points
was determined by randomly placing test rock material of
a specific gradation into an aquarium equal to the test
chamber in size, shape, and cross-sectional area (160 in’),
The aquarium was then filled with white paint, which was
allowed to drain freely from the bottom and was left to
dry. The points of contact between particles were distin-
guishable by unpainted portions on the rocks or white
splotches due to capillary concentrations of the paint
where the rocks were in contact (fig. 16)"~Approximately
300 rocks were sampled at various levels, and the number
of contact points was counted and averaged. This proce-
dure was repeated for each rock type using the same gra-
dation and quantity of simulated gob material.

, Spheroid
° ‘Weak sandstone,
5 BE od Q 4
é Shelo—g
3 aa Blade Strongserdsions) Rater
rT ¢
3 oat 4
i o 9
- rey
3 2 © Before test
A ftertest
. f f 1
° 02 04 06 os 10

THICKNESS-TO- WIDTH RATIO

Figure 15.—Shape classification chart (25-26).



SIEVE ANALYSIS

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Figure A-1.—Test material gradation curves before and atter test.



16. Su, D. W. Finite Element Modeling of Subsidence Induced by
Underground Coal Mining: The Influence of Material Nonlinearity and
‘Shearing Along Existing Planes of Weakness. Paper in Proceedings of
10th International Conference on Ground Control in Mining. WV
Univ., Morgantown, WV, 1991, pp. 287-300,

17, Heasley, K.A. An Examination of Energy Calculations Applied
to Coal Bump Prediction. Paper in Rock Mechanics as a Multidisci-
plinary Science: Proceedings of the 32nd U.S. Symposium, ed. by
J. Rocgiers (Norman, OK, July 10-12, 1992). A. A. Balkema, 1992,
pp. 481-490.

18, Marachi, N. D., C.K. Chan, H. B. Seed, and J. M. Duncan.
Strength and Deformation Characteristics of Rockfill Materials. Dep.
Civ. Eng,, Univ, CA—Berkeley, Rep. TE-69-5, Sept. 1969, 139 pp.

19. Becker, E., C. K. Chan, and H. B, Seed. Strength and Defor-
mation Characteristics of Rockfill Materials in Plane Strain and Triaxial
Compression Tests, Dep. Civ. Eng, Univ. CA~Berkeley, Rep. TE-72-3,
Oct, 1972, 121 pp.

20. Fumagalli, E, Test on Cohesionless Material for Rockfill Dams,
J. Soil Mech. and Found. Div., Am. Soe. Civ. Eng,, v. 95, No. SM1, Jan,
1969, pp. 313-330,

21, Lowe, J. Shear Strength of Coarse Embankment Dam Materials.
Paper in Proceedings of the 8th International Congress on Large Dams
(Edinburgh, UK, May 4-8, 1964), Publ. Com. Int. Grands Barrages,
1964, pp. 745-761.

22, Franklin, J. A. N. H. Maer, and C. P, Bennett. Rock Mass
Characterization Using Photoanalysis. Int. J. Min. and Geol. Eng.
(UK), v. 6, 1988, pp. 97-112.

23. American Society for Testing and Materials, Standard Method
of Making and Curing Concrete Test Specimens in the Laboratory.
C192-90a in 1991 Annual Book of ASTM Standards: Volume 4.02,
Construction. Philadelphia, PA, 1991, pp. 115-121.

24, Ferm, J.C, and G. C. Smith. A Guide to Cored Rocks in the
Pittsburgh Basin. Dep. Geol., Univ. KY, Lexington, KY; Dep. Geol.,
Univ. SC, Columbia, SC; 1980, 109 pp.

25, Krumbein, W. C., and F. J. Pettijohn. Manual of Sedimentary
Petrography. Appleton-Century, 1938, pp. 288-289.

26. Krumbein, W. C., and L. L. Sloss. Stratigraphy and Sedimen-
tation, Freeman, 24 ed., 1963, pp. 99-108.

31

27. American Society for Testing and Materials. Standard Test Meth-
ods for Absorption and Bulk Specific Gravity of Natural Building Stone.
€97-90 in 1991 Annual Book of ASTM Standards: Volume 4.08, Soil
and Rock; Dimension Stone; Geosynthetics. Philadelphia, PA, 1991,
pp. 1-5.

28, Vallejo, L. EB, R.A. Welsh, and M. K. Robinson, Correlation
Between Unconfined Compressive and Point Load Strengths for Appa-
lachian Rocks. Paper in Rock Mechanics as a Guide for Efficient
Utilization of Natural Resources: Proceedings of the 30th U.S. Sympo-
sium, ed. by W. Khair (Morgantown, WV, June 19-22, 1989). A. A.
Balkema, 1989, pp. 461-468.

29, Peng, S. S. Longwall Mining. Wiley, 1984, 708 pp.

30. Marsal, R J., LR. DeArellano, and A. G. Nunez. Plane Strain
Testing of Rockfill Materials. Paper in Proceedings of Third Pan-
American Conference on Soil Mechanics and Foundation Engineering
(Caracas, Venezuela). 1967, pp. 249-271.

31, Athanasiou-Grivas, D., and M. E. Harr, Particle Contacts in
Discrete Materials. J. Geotech. Eng. Div., Am. Soc. Civ. Eng,, v. 106,
No. GTS, May 1980, pp. 559-564,

32. Doomkamp, J.C, and C. A. M. King. Numerical Analysis in
Geomorphology—An Introduction. St. Martin’s Press (UK), 1971,
372 pp.

33. Ryder, J. A, and H. Wagner. 2D Analysis of Backfill as Means
of Reducing Energy Release Rates at Depth. Chamber of Mines, S,
Afr, Res. Organ,, Res. Rep. 47/78, 22 pp.

34, Salamon, M. D. G. Mechanism of Caving in Longwall Coal
Mining. Paper in Rock Mechanics Contributions and Challenges:
Proceedings of the 3ist U.S. Symposium, ed. by W, A. Hustrulid and
G. A. Johnson (Denver, CO, June 18-20, 1990). A. A. Balkema, 1990,
pp. 161-168,

35. Salamon, M. D. G. (Colorado School of Mines). Private
communication, 1991; available upon request from D. M. Pappas,
Pittsburgh Res. Cent, BuMines, Pittsburgh, PA.

36, Listak, J. M,, J. L. Hill, and J, C, Zelanko. Direct Measurement
of Longwall Strata Behavior. A Case Study. BuMines RI 9040, 1986,
19 pp.


These three rock types were chosen to represent the range
of potential gob materials, The rocks were broken up and
sorted using the following sieve sizes (inches): 3.5, 3.0,
25, 2.0, 1.5, 1.25, 1.0, and 0.75.

The physical characteristics of the source materials
were determined using a number of different methods.
The rock was evaluated based on its appearance, following
the classification method of Ferm (24). Overall shape of
the rock was evaluated using Zingg’s method (as described
in references 25-26), which classifies the rock shape based
on ratios of its dimensions and is discussed in detail in
the section "Rock Shape." Density of the rock was deter-
mined by specific gravity tests following the ASTM guide-
lines (27). Compressive strength of the rock was esti-
mated by a series of point load tests. The point load test
compresses a piece of rock between two points using two
cone-shaped platens. An irregular rock piece is com-
pressed to failure under a point load. From the test re-
sults, a point load index is calculated and standardized
by conversion to a value equivalent to results of testing a
50-mm rock core. The standardized index is averaged,
excluding the two lowest and two highest values. The ay-
erage index value is converted to compressive strength
by using a conversion factor that was recently found by
Vallejo (28) to be dependent upon the rock type (i.e., for
shales the conversion factor is 12.5 times the averaged
index value while for sandstone it is 17.4). Results of the
point load tests are listed in the appendix (tables A-1—
A-3).

Shale

The shale was obtained from a major roof fall in a
southwestern Pennsylvania coal mine located in the Pitts-
burgh Coal Seam. The rock originated between 2.5 and
13 ft above the coal seam. It consisted of dark gray shale
(Ferm No. 124), dark gray shale with sandstone streaks
(Ferm No, 323), and black shale with coal streaks (Ferm
No. 113). From point load test results, the average com-
pressive strength was estimated to be 5,400 psi parallel
to bedding and 10,500 psi perpendicular to bedding. The
shale pieces broke typically into disk shapes with feathered
edges, with an average density of 162.1 Ibf/ft°.

Weak Sandstone

Fresh sandstone was acquired from a southwest-
ern Pennsylvania stone quarry. The rock occurred

SIZE, in
3530 25 20 15125 10 075

N

KEY
Moximum
size, in
_—2

3
35

PERCENT PASSING
8

8

=°

SIZE, mm

Figure 9.—Three gradation curves for laboratory tests with
maximum particle sizes of 3.5, 3.0, and 2.0 In.

approximately 100 ft above the Pittsburgh Coal Seam. The
tock is characterized as a medium-grained, friable, gray
massive sandstone (Ferm No. 544), Point load test results
estimated an average compressive strength of 6,300 psi
parallel to bedding and 6,200 psi perpendicular to bedding.
The sandstone pieces broke into spherical-disk shapes with
less sharp edges than the shale had. Density of the sand-
stone was 157.5 Ibf/ft?.

Strong Sandstone*

Although similar in appearance to the weak sandstone,
the strong sandstone had a compressive strength over
three times as great. Estimated point load results indi-
cated an average compressive strength of 14,200 psi par-
allel to bedding and 18,300 psi perpendicular to bedding.
The rock was obtained by scaling portions of the roof of
a coal mine in southern West Virginia. The strong sand-
stone had a density of 168.4 Ibf/f®, The rock broke into
cubic pieces with well-defined edges. The massive sand-
stone (Ferm No. 564) was located directly above the
Pocahontas No. 3 Seam and ranged in thickness from 10
to 60 ft.

“The authors thank Craig S, Compton, mining engineer technician,
Pittsburgh Research Center, for his diligent efforts in obtaining the
Strong sandstone test material from an underground mine,


18

The equations for these moduli-versus-stress curves
are listed for each individual test in table 5. Inserting
an estimated stress level of 800 psi into these equations
produces moduli values as shown in table 6. These values
seem to compare favorably with the in situ test results and
are somewhat lower than the other laboratory test results
shown in table 1.

Table 6.—Modull
stre

ults at 800-psi
level!

Rock type Modulus, psi

Secant Tangent
2,920 8,820
3,330 9,560
3,760 8,080

70 T T T
op +7
BF Pivotal y i
60F a poin' i] / 4
1 / /
HE /] /
sor ?f, /
if. 1 hn | /
0; 02 04 06708 jo/
i rot
40; / 7

TANGENT MODULUS (E;), 10° psi

30 7
20 7
(]
10 | —— Strong sandstone
| === Weak sandstone
—-— Shale
fl 1
Oo 05 1 2 3 4

STRESS (c),103 psi

Figure 21.—Stress versus tangent modulus for each rock type.
Insert shows pivotal point at 500 ps! where all rock types con-
verge.

In comparing the test results in table 6, the type of rock
tested does not appear to dramatically affect the resulting
moduli values, considering the wide range of rock types
used in the tests. Consequently, a first approximation of
the secant and tangent moduli can be based on the aver-
aged results for all three rock types. Figure 22 shows the
averaged linear curve of the secant modulus and the aver-
aged second-order polynomial curve of the tangent mod-
ulus based on the stress level, as well as the equations and
ranges of these averaged moduli curves. Also evaluated
was the correlation of determination (1°), which measures
the proportion of the variation in the best fit equation that
is explained through knowledge of the actual data. An
1 = 0.95 was determined for the best fit curve for the
secant modulus versus stress, and the best fit curve for the
tangent modulus versus stress resulted in an r? = 0.99,

VOID RATIO

Plotting the secant and tangent moduli versus the void
ratio resulted in the third-order polynomial best fit curves
shown in figure 23. All three rock types produced dis-
tinctly separate curves. Both moduli plots generated con-
sistent curves, with r? = 0.905 to 0.984 for the secant
modulus curves and 1? = 0.969 to 0,979 for the tangent
modulus curves. The strong sandstone curve consistently
produced the highest modulus values, followed by the
weak sandstone and the shale.

60 T T T
KEY /
‘Curve equations:

50 }——Secant modulus, E,' / 4
eg Es = 2.360 +1,360 7
Ly ——Tongent modulus, Et: /
= Ey= 0.00181 o2 + 9.330 +294 7
= MP 1
a /
5 /
wf 0r / 1

/

2)
3 7
3 20 7 |
8 7
Q
= 7

: LT

1 1 1

STRESS (c), 103 psi

Figure 22.—Stress versus secant and tangent modull curves
and equations averaged from all rock types.



36

SIEVE ANALYSIS

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35.

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ILLUSTRATIONS—Continued
Page
Average gradation curve—mean gradation curve determined from photoanalysis of three mine sites .. . 7
Three gradation curves for laboratory tests with maximum particle sizes of 3.5, 3.0, and 2.0 in . 8
Plan and elevation views of test chamber and platens .. 9
Simulated gob in test chamber ............ 9
Test chamber filled with simulated gob and top, 10
Load deformation test setup ..............0005 11
Simulated gob material following completion of test . 1
Shape classification chart ...........+.eeee0e0e 14
Example of contact points identified by white splotches on rock . 15
Examples of secant and tangent moduli determination . 15
Stress-versus-strain results—best fit curves ........ 16
Stress-versus-strain results—actual data for each test . 7
Stress versus secant modulus averaged for each rock type . 17
Stress versus tangent modulus for each rock type ...... 0. sce e cece ea eeeee 18
Stress versus secant and tangent moduli curves and equations averaged from all rock types . 18
Void ratio versus secant and tangent moduli for all rock types ......... 19
Examples of three rock types and distinct shapes used in laboratory tests . bee 22
Multiple regression curves—rock strength versus secant modulus for various thickness-to-width shape
ratios .. 2
Multiple regression curves—rock strength versus tangent modulus for various thickness-to-width shape
ratios 24
Multiple regression curves—rock strength versus bulking factor for various thickness-to-width shape
ratios 25
Comparison of actual and be:
solutions for shale 26
Comparison of actual and best fit stress-versus-strain results with Salamon’s and Terzaghi’s theoretical
solution for weak sandstone . 27
. Comparison of actual and best fit stress-versus-strain results with Salamon’s and Te:
solutions for strong sandstone ....... 06... c cece cece cece eee e ee seneetaneteaneeennees 27
- Comparison of actual and best fit stress-versus-secant-modulus results with Salamon’s and Terzagl
theoretical solutions for shale... 6.66. cece eee e cece tee e eee e ee ee eee eeeneeeeeeeeenas ra
Comparison of actual and best fit stress-versus-secant-modulus results with Salamon’s and Terzaghi’s
theoretical solutions for weak sandstone ....... 06.00 c eee e eee ceeneeee eect eeteteeeeeeees 27
Comparison of actual and best fit stress-versus-secant-modulus results with Salamon’s and Terzaghi’s
theoretical solutions for strong sandstone .......... 0c eee cece ceeeeceeeeteetcenveeannes B
Comparison of actual and best fit stress-versus-tangent-modulus results with Salamon’s and Terzaghi’s
theoretical solutions for shale . .
Comparison of actual and best fit stress-versus-tangent-modulus results with Salamon’s and Terzaghi’s
theoretical solutions for weak sandstone .......... 050 ccc ceseeeeeeeeeeeeeeeeeneeeeeeens
Comparison of actual and best fit stress-versus-tangent-modulus results with Salamon’s and Terzaghi’s
theoretical solutions for strong sandstone . 28
. Test material gradation curves before and after test . 35
TABLES
Comparison of modulus values at a stress level of 800 psi . 3
Range of modulus values used in numerical modeling . . 3
Load deformation test series and parameters varied . 12
Summary of load deformation test results......... 13
Equations of best fit curves for secant and tangent moduli versus stress . 16
Moduli results at 800-psi stress level . . 18


DISCUSSION

The intent of these laboratory tests was to provide a
means for determining the modulus of the simulated gob
materials for use in numerical modeling analysis. The first
approximation used to determine the modulus was found
to be a function of the stress level. The secant modulus
versus stress level consists of the following equation:

E, = 2360 + 1,360, (26) -
where E, = secant modulus, psi,
and a = stress level (due to overburden), psi.

The nonlinear behavior of the tangent modulus versus
stress level is described in the following equation:

E, = 0.001810 + 9.330 + 294, (27)
where E, = tangent modulus, psi,
and @ = stress level (due to overburden), psi.

These equations and the curves are shown in figure 22,

For example, a mine with an overburden stress level
of 680 psi produces a secant modulus of 2,970 psi and a
tangent modulus of 7,410 psi according to the above
equations.

A more exact estimate may be obtained from the mul-
tiple regression analysis of the test data. The multiple
regression analysis produced several predictive curves that
allow the bulking factor, tangent modulus, and secant
modulus to be determined based on the rock strength,
tock shape ratio, and stress level. If the stress level, the
estimated shape ratio of the gob rock, and the compressive
strength of the rock are known, the bulking factor can to
be estimated using figure 27. With the estimated bulking
factor known, the secant and tangent moduli can be deter-
mined from figures 25 and 26,

An example follows, using the data presented in the
longwall caving height study conducted by Listak (36).
The study was conducted in a mine with an overburden of
618 ft, or a stress level of 680 psi. The eventual gob was
composed of the immediate roof, which was black shale
with a compressive strength of 6,500 psi. Although the
thickness-to-width shape ratio was unknown, for shale it
was estimated to be about 0.45. Using figure 27 for a
shape ratio of 0.4 and interpolating between the stress
level curves at the rock strength of 6,500 psi yields a

bulking factor of 1.295. Repeating this procedure for a
shape ratio of 0.5 produces a bulking factor of 1.32,
Averaging the bulking factors for the shape ratio of 0.45
results in an estimated bulking factor of 131. It is
interesting that Listak’s study (36) deduced that the final
caving height occurred approximately 17 ft above the coal-
bed, which implies that the final bulking factor was 1.34,

With the bulking factor determined, the tangent mod-
ulus values can be determined from figure 26 for shape
ratios of 0.4 and 0.5. The tangent modulus is determined
by interpolating between bulking factor curves for a rock
strength of 6,500 psi. Averaging the modulus from both
curves yields a tangent modulus of 5,125 psi. This same
procedure is used to determine the secant modulus of
2,125 psi from figure 25,

Comparing the moduli values obtained from both meth-
ods shows that the second method, using multiple regres-
sion analysis, produces lower values. The moduli values
found using the second method are based mostly on
second-order effects (ie, shape ratio, rock strength),
whereas the first method is based on a first-order effect of
the stress level that directly impacts the behavior of the
gob.

The bulking factor of the actual gob material is prob-
ably dependent upon its position within the gob and the
point in time that it is evaluated during the longwall
Process. For example, immediately after the roof falls,
creating the gob, the bulking factor will start to decrease
as the gob gradually takes on more load and further com-
pacts. Since the behavior of the in situ gob is so complex,
this study assumed that the bulking factor was an average
of the volume monitored during the test with the uniaxial
loading representing the final compaction of the gob.

Although the second method neatly quantifies factors
into the determination of the modulus, the errors of not
including other unknown factors and potential first-order
effects (i.e., bulking factor gradation, caving height, degree
of fracturing of the immediate roof) may only compound
the error involved. Consequently, with so many unknown
gob behavior parameters that were impossible to factor
into the second method, it seems more appropriate to use
the first method to conservatively approximate the behav-
ior of gob.

Most valuable to numerical modelers for estimating the
gob modulus is the first method based directly on the
stress level (fig. 22). These curve equations and ranges
can be implemented into the numerical program to model
the strain-hardening behavior of the gob and thereby
produce more credible results.


Secant and Tangent Moduli
The direct results obtained from these tests are the load

and displacement readings, from which the vertical stress
and strain are determined as follows:

o- +, (13)
7

ez,

(a4)

where @ = vertical stress, psi,

a
a

applied load, Ibf,

4
“

radius of platen applying load, in,
€ = strain, in/in,

D = cumulative displacement of rock material,
in,

and H == initial height of test material, in,

Indirectly from these stress and strain values can be
determined two types of moduli of the simulated gob
material, which give an indication of the stiffness of the
material. Both moduli are obtained from the slope of the
stress-strain curve; the secant modulus is the slope of a
line from a point in question on the stress-strain curve to
the origin, while the tangent modulus is the slope of a line
tangent to that point (fig. 17). The moduli are expressed
as follows:

Figure 16.-Example of contact points Identified by white
splotches on rock.

E,-, (a5)
E+ =, (16)

where E, = secant modulus, psi,

oo)

tangent modulus, psi,
a = cumulative vertical stress, psi,
€ = cumulative strain, in/in,
Ao = change in vertical stress, psi,
and Ae = change in strain, in/in.

A spreadsheet software program was used to calculate
the secant and tangent moduli values at each point. These
moduli values were graphed versus vertical stress and void
ratio, curves were fitted to portions of the curves, and best
fit equations were determined (based on stress level) as
tabulated in table 5.

The tangent modulus versus stress is utilized to define
the parameters used in the numerical model’s stress-strain
equation. According to another theory, the secant modu-
lus versus stress is used to define the parameters of the
stress-versus-strain curve. Consequently, both types of
moduli were determined, and the two different theories
are discussed in the section "Comparison of Theoretical
Solutions With Test Results."

‘STRESS (oc) —»>

Secant. o

fangent
modulus” © Tongen« fe

modulus Ae

—— STRAIN (€) —>

Figure 17.—Examples of secant and tangent modull deter-
mination.



spherical shape, which will pack more tightly together than
will the rectangular-shaped strong sandstone and disk-
shaped shale. However, the weak sandstone exceeded the
shale’s void ratio at 800 psi and the final void ratio, in-
dicating that the thinner, irregularly shaped shale pieces
were breaking more and producing more particle breakage
than the weak sandstone (this point is evident by the
higher particle breakage for shale shown in table 8).
Following completion of the load deformation tests,
the shape ratios were evaluated and compared with the
before-test shape ratios using the ANOVA. Results in the
note under table 7 show that there is a significant differ-
ence in the thickness-to-width shape ratio, but not in the
width-to-length ratio, Apparently, the width and length of

2

the rock particles were breaking proportionally while the
thickness (smallest dimension) of the broken rock pieces
was becoming proportionally larger, indicating a more
spherical-shaped rock following the test. Figure 15 shows
that the strong sandstone changed the most in shape,
starting with a blade-disk shape and ending with a disk-
spherical shape, indicating that the sharply defined edges
of the rectangular pieces were being rounded off. The
high strength of the strong sandstone prevented further
breakage, resulting in less compaction of the material, as
shown in table 9, The shale and the weak sandstone
changed less in shape, but moved toward the spherical
portion of the chart.

Table 8.—Averaged test results
Shale Weak sandstone Strong sandstone
Av Std dev Av Std dev Av Std dev
Void rato:
Initital . 0.7950 0.0714 0.7426 0.0394 0.8667 0.011
At 800 psi 0.2958 0.0443 0.9232 0.0155 0.4877 0.0145,
Final .. 0.1522 0.0514 0.1536 0.00086 0.2524 0.0067
Percent compaction . 36.42 (0.9440 34.30 1,40 33.23 1.84
Particle breakage! 179.0 42.56 163.6 42.92 127.8 9.15
Percent rebound? . 0.85 0.188 1.47 0.0614 1.58 0.158
Shape ratio before:
Thickness-to-width 0.4355 0.0234 0.6302 0.0443 0.5420 0.0362
Width-to-length . . 0.7022 0.0463 (0.7356 0.0439 0.6730 0.0111
Shape ratio after:
Thickness-to-width 0.5295  0,0202 0.6688 0.0098 0.6740 0.0386
Width-to-length? 0.7183 0.0276 (0.7336 0.0262 0.7053 0.0162
Tangent modulus, psi
Stress level . 8,780 554.8 8,133 254.9 7A78 770.3
Bulking factor . 8,363 736.2 7,588 427.3 7,335 585.8
Secant modulus, ps
Stress level . 2,918 367.5 3,334 247.2 3,768 443.8
Bulking factor . . 3,011 385.6 3,154 246.5 3,808 380.0

1Not determined significant

with ANOVA analysis.

2ANOVA was not performed because of small sample size,

Based on modulus values derived from best
directly, the equivalent bulking factor at 800 psi.

t fit curve at a stress level of 800 psi, or, in-

Table @.—Evaluation of maximum size effect on percent
compaction at 500 psl for shale
Maximum size Compaction, pet Maximum size Compaction, pet
2in: 3 in-(cont,):
Test 4. 0.2656 0.2150
Test 9 . 2410 2290
Av 2533 2448 ,
Std 0178 02 NI
Bin:
Test 1. 2310 2880
Test 2. 2350 2080
Test 3. 2490 247
Test 7 . 2690 058
Test 8 . 2860



17

14 1 1 35 1 1
KEY
12 KEY 1 7307 weak sandstone tests |
i dogl —Not J
10 / 7287 Dono i2
420 No. 13 4
8 / 20 No IS
- & 41.5 F =: No. 15 1
g —— Best fit
4 410 curve
m,
Q2 75
:
sO n 0 4
&
Q 6 La 40 a
W ost KEY 35 4
& Shole tests 30 4
M 4b 425 |
3F | 2.0 4
AS 418 |
10 1
1 Ios 4
f 1 A
0 0.05 O10 O15 020 025 030 035 0400450 005 O10 015 020 025 030 035 040 045

STRAIN (e), in/in

Figure 19.—Stress-versus-strain results—actual data for each test.

STRESS LEVEL

Plotting of the secant-modulus-versus-stress level
(fig. 20) produces a perfectly linear curve, while plotting
the tangent-modulus-versus-stress level (fig. 21) results in
a nonlinear, second-order polynomial curve. These curves
replicate the behavioral patterns presented in the pre-
vious paragraph, The secant modulus curves show that the
rock types are clustered; the highest curve is the strong
sandstone, followed by the weak sandstone and the shale.
The rock type curves for the tangent modulus are some-
what clustered, especially between the 0- and 2,000-psi
stress levels, As the insert in figure 21 shows, the strong
sandstone initially produces the highest tangent modulus
values, followed by the shale and weak sandstone, possibly
indicating that the strong sandstone has a stiffer initial
skeletal structure, However, the rock types reverse this
order at a pivotal point of 500 psi.

It is interesting that the equivalent amount of strain that
occurs at the pivotal point on the stress-strain curve in
figure 18 ranges from 0.16 to 0.22 in/in, which is similar to
the 22-pet initial compaction estimated by Su (16).

12-——_

tc)

KEY
—— Strong sandstone
— Weak sandstone
—:— Shale

SECANT MODULUS (€E,), 10° psi
o

od 1 a
ce) 1 2 3

STRESS (0), 10° psi

Figure 20.—Stress versus secant modulus averaged for each
rock type.



CONCLUSIONS AND RECOMMENDATIONS

As table 2 attests, there has been a large range of gob
modulus values used in past numerical modeling of long-
wall panels. From comparing previously determined gob
modulus values in tables 1 and 2, it is apparent that the
results determined in this study (table 6) were most similar
to the in situ tests of caved waste material, somewhat
lower than other laboratory test results, and remarkably
lower than the estimated modulus values used in the nu-
merical modeling (although it is difficult to compare these
values equitably),

The test material used in this study was formulated
to simulate the composition and gradation of actual gob
material. Behavior of the simulated gob material under
uniaxial loading produced a nonlinear stress-strain curve,
linear stress-secant-modulus curve, and a second-order
polynomial stress-tangent-modulus curve. These corre-
lated well with the theoretical solution curves developed by
Ryder (33) and Salamon (34). Although the results of this
study cannot be assumed to duplicate gob moduli of all
mines, they do present two approximation methods for
determining the gob modulus. The first method is based
directly on the stress level, independent of rock type
(equations are shown on figure 22), while the second
method takes into account second-order effects and is
based on the stress level, bulking factor, rock strength,
and the shape ratio of the gob (equations are shown in
table 11). Because of factors unable to be included with

this second method, the first method is recommended to
determine the approximate modulus for modeling pur-
poses. It is hoped that the results presented in this report
will provide a more accurate and consistent means of esti-
mating the gob modulus, which is essential for longwall
numerical modeling.

Caution should be exercised when selecting modulus
values, especially if the gradation is unknown, Gradations
used in this study are based on photographs from mines in
the central Appalachian region. The roof rock in this
tegion is quite competent in strength, which may result in
a different gradation than that found in other coalfields or
seams. Changing the gradation will more likely affect the
bulking factor and, subsequently, the gob modulus. If the
gob is composed of a greater proportion of uniformly sized
tock pieces, the gob will have more void spaces, higher
bulking factor, more deformation, and a lower modulus
value,

If additional research work is conducted on the be-
havior of gob material, the test chamber should be de-
signed to monitor loading at the bottom interface of the
gob and statistical analyses should be conducted to eval-
uate simulated gob material of various gradations, shape
ratios, and rock strengths. Also, gob gradations in various
regions of the United States should be evaluated using
photoanalysis and image enhancement techniques.

REFERENCES

1. Mark, C. Practical Aspects of Longwall Pillar Design. Paper in
Proceedings of 10th International Conference on Ground Control in
Mining, WV Univ., Morgantown, WV, 1991, pp. 1-13.

2. Zip, R.K. MULSIM/NL Theoretical and Programmers Manual.
BuMines IC 9321, 1992, 52 pp.

3. Rice, G. S. Tests of Strength of Roof Supports Used in An-
thracite Mines of Pennsylvania. BuMines B 303, 1929, 44 pp.

4. Peng, S. S. Coal Mine Ground Control. Wiley, 1978, 200 pp.

5. Peng, S. S, K. Matsuki, and W. H. Su. 3-D Structural Analysis
of Longwall Panels. Paper in The State of the Art in Rock Mechanics:
Proceedings of the 21st U.S, Symposium on Rock Mechanics, compiled
by D. A, Summers (Rolla, MO, May 28-30, 1980). Univ. MO, 1980,
pp. 44-56.

6. Bowling, A. J. Investigations Into the Deformability of Rockfill.
Paper in Proceedings of the Third Australian-New Zealand Conference
on Geomechanics (Wellington, N.Z., May 12-16, 1980). N.Z. Inst. Eng,
1980, pp. 1-6.

7. Wardle, L. J., and J. R. Enever. Application of the Displacement
Discontinuity Method to the Planning of Coal Mine Layouts. Paper in
Proceedings of the Sth International Congress on Rock Mechanics
(Melbourne, Aust). A, A. Balkema, 1983, pp. E61-E69.

8. Smart, B, G. D., and S. M. Haley. Further Development of
the Roof Strata Tilt Concept for Pack Design and the Estimation of
Stress Development in a Caved Waste. Min. Sci. & Technol., v. 5, 1987,
pp. 121-130.

9. Trueman, R. A Finite Element Analysis for the Establishment
of Stress Development in a Coal Mine Caved Waste, Min. Sci. &
Technol, v. 10, 1990, pp. 247-252.

10, Hsiung, S.M,, and S. S. Peng. Chain Pillar Design for U.S. Long-
wall Panels, Min, Sci, & Technol, v. 2, 1985, pp. 279-305.

U1. Kripakov, N. P,, L. A. Beckett, D, A. Donato, and J. S, Durr.
Computer-Assisted Mine Design Procedures for Longwall Mining.
BuMines RI 9172, 1988, 38 pp.

12. Beckett, L. A., and R. S. Madrid. MULSIM/BM~A Structural
Analysis Computer Program for Mining Design. BuMines IC 9168, 1988,
302 pp.

13, Hackett, T., and H, Park, Ground Control Analysis of Multi-
Sluice Mining for Thick Western Coal Seams. Soc. Min. Eng. AIME
preprint 87-39, 1987, 8 pp.

14. Maleki, H. N. Development of Modeling Procedures for Coal
Mine Stability Evaluation. Paper in Rock Mechanics Contributions
and Challenges: Proceedings of the 31st U.S. Symposium, ed, by W. A.
Hustrulid and G. A. Johnson (Denver, CO, June 18-20, 1990). A. A.
Balkema, 1990, pp. 85-92.

15, Park, D. W., and V. Gall. Supercomputer Assisted Three-
Dimensional Finite Element Analysis of a Longwall Panel. Paper in
Rock Mechanics as a Guide for Efficient Utilization of Natural Re-
sources: Proceedings of the 30th U.S. Symposium, ed. by W. Khair
(Morgantown, WV, June 19-22, 1989), A.A. Balkema, 1989, pp. 133-140.


n

Table 3.—Load deformation test series and parameters varied

123 4 5 6 7 8 9 10
xX X X X X X X X X X
Weak sandstone
Strong sandstone .
x 0) x
x xX X xX XxX
x x
xX X X X X X X X X
x
x
Xx X X X X
xX X X
x X
1112 13 14 «15 16 17 18 19 2
xX X
X X X X X
xX X X
Maximum size:
2in.. x
3in xX X X xX X X X X
5 In. x
Gradation:
Standard? , x Xx XX X X XX X X
1 size
xX X X X X xX X X X
x
‘Maximum size, 2.5 in,
2890 figure 9,
NOTE.—X Indicates parameter used in test,
Void Ratio W,
H, = <x 23, Q
Indirectly determined is the void ratio, which indicates %s
the amount of void space present in the test material. As aver
pace where H, = layered sand height, in,

the void ratio decreases, the material is more densely
compacted. The void ratio can be determined by using the
rock density, amount of rock in the test chamber, and
cumulative deformation of the simulated gob material.
The formula is somewhat complicated by the layer of sand
on top of the simulated rock material. First, the average
height of the sand layer is determined by dividing the 4
sand’s weight by its density, and dividing by the inside area

of the chamber,

W, = layered sand weight, Ibf,

‘1, = density of the sand, Ibf/ft,

A = inside area of test chamber, in®,


stress level. To account for increasing amount of com-
paction in the direction away from the face, Park (15)
implemented a linear gob model ranging from 2,500 to
20,000 psi depending upon the location. Most recently, Su
(16) chose a very low initial tangent modulus of 1,050 psi,
with a higher modulus of 42,000 psi occurring after a gob
compaction of 22 pet, resulting in the bilinear behavior of
the gob. At the 800-psi stress level, this would result in a

gob secant modulus of 3,420 psi. All of the above gob
moduli values were used for modeling longwall situations;
for comparison purposes, a linear gob modulus value of
7,500 psi was used by Heasley (17) to model pillar retreat

The wide range of reported gob moduli values makes
it imperative that a more accurate and uniform method
of determining moduli values be established.

GOB MATERIAL SIMULATION

The first task in the laboratory tests was to develop
test materials that had properties similar to those of actual
gob material. The characteristics that were considered in-
cluded the tensile and compressive rock strengths, rock
density, surface roughness, rock shape, rock size, and size
gradation, Most of these characteristics would be simu-
lated by broken rock obtained from fresh roof falls. How-
ever, the rock size and gradation needed to be reduced to
a laboratory scale.

SCALED-DOWN GRADATION CURVE

Several articles have been written evaluating scaled-
down gradation curves for determining the stress-strain
Properties of granular materials, Marachi (18), Becker
(19), and Fumagalli (20) determined that the grain size
distribution curves for actual dam rockfill materials could
be proportionally scaled down and accurately represented
for laboratory tests. Marachi provides some theoretical
justification with the observation that with the regular
packing of ideal spheres, the strain and maximum contact
stresses are independent of the particle size. In fact, his
tests found that the difference in strength characteristics
for 2- and 6-in maximum particle size gradations was so
small that for all practical purposes, the strength and
deformation characteristics of the 2-in maximum particle
size materials could be considered the same as those of
the larger particles, Marachi proceeds to describe a meth-
od developed by Lowe (21) to model samples from a pro-
totype material. The gradation curve of the modeled ma-
terial was determined by shifting the gradation curve of
the prototype material, parallel to itself, to the desired
maximum particle size for the laboratory sample.

GRADATION OF GOB MATERIAL

Before Lowe’s method could be used to determine the
gradation curve of the laboratory sample, an approximate
gradation curve of actual gob material needed to be estab-
lished. It has been documented that grain size distribu-
tion curves of rock blast fragments can be estimated from
digitized photographs using photoanalysis software (22).
Although photoanalysis software was not used in the

current study, the basic photoanalysis techniques were
applied to photographs of gob material. Photographs were
taken of several longwall gob sites from the headgate
entries where portions of the gob could be viewed through
the crosscuts. One site was photographed in a Virginia
mine in the Pocahontas Coalbed (fig. 1), and two sites
were photographed in an eastern Kentucky mine in the.
Harlan Coalbed (figs. 2-3).” Only photographs with excel-
lent clarity and lighting can be analyzed. The basic pho-
toanalysis technique involves tracing the outline of the
photographed gob pieces (fig. 4), using a scale in the pho-
tograph to estimate the size of the rock and the frequency
so that a histogram can be compiled, as shown in figure 5.
When the approximate maximum diameter of the rock is
known, the spherical volume of the rock can be estimated
for each rock size grouping. Multiplying the total number
of rock pieces by the estimated volume for each size
grouping produces the total volume of rock for each size
grouping. The total volume is then multiplied by the rock
density to generate the weight of the rock for each size
grouping. Plotting the rock size versus the percent passing
(ie., percentage of rock by weight passing a particular
sieve size) generates the gradation curve of the gob rock.
Figure 6“shows the estimated gradation curves for each
gob site photographed and indicates that the gob gradation
for these three sites may fall within a fairly narrow range.
The roof rock at both mines was relatively strong, so the
actual range of size distribution across the complete spec-
trum of U.S. longwalls may be considerably greater than
is indicated by figure 6. Next, the gradation curves were
corrected to account for rock pieces hidden because of
the two-dimensional effect of the photograph.

The correction factor for the hidden rock was derived
as follows. Mine rock material, with a known gradation
curve, was piled and photographs were taken of the sides.
The resulting photographs were digitized, the rock was
sized, and the volumes were estimated just as they were
for the actual gob photographs. The gradation curves de-
termined from the photoanalysis were then compared with
the known gradation curve. Figure shows that photo-
analysis seemed to accurately estimate the actual grada-
tion curve of the rock material with the exception of the
smaller particle sizes, which it underestimates.


4 4 T T T
T y y KEY Strong sandstone
key
rk
— Laboratory results Weok sandstone Laboratory results U]
—Salamon's curve: —— Salamon's curve:
13406 I _ 3b ., 18906

Br 7 *Treeaan | 7 @ o* e723)
zg ——Terzaghi's curve: / 21 —— Terzaghi's curve:
% 755 iguane -1) / 2 = 208/108);
= o tas ° < 7* o8*
Re 4 be 4
~ n
n n
n Ww
Ww ©
4 E
5 o

1 4 | 7

fe) Ot 02 0.3 04 0 0.1 0.2 0.3 04

STRAIN (e), in/in

Figure 29.—Comparison of actual and best fit stress-versus-
‘strain results with Salamon’s and TerzaghI’s theoretical solution

for weak sandstone,

12 T T T
Shale 4

= a
a 107
0
2
te
g
3
a
fe)
=
~ 4f Laboratory results
2 —— Solamon's curve:
4 Eg? 2.260 +1,110
a 2 —— Terzaghi's curve:
° Mie

s it

1 922

in (1+ 255 0)
1

Figure 30.—Comparison of actual and best fit stress-versus-
strain results with Salamon's and Terzaghl’s theoretical solutions.

STRAIN (e), in/in

for strong sandstone.

SECANT MODULUS (Eg), 10? psi

12 T T T
Weak sandstone 7
10F
st
as
ab — Laboratory results
— Salamon's curve:
E5= 2490 +1,340
= Terzaghi's curve:
2 p 4
1 1

() 1 2 3
STRESS (¢), 103 psi

—__.

Figure 31.—Comparison of actual and best fit stress-versus-
secant-modulus results with Salamon’s and Terzaght’s theoretical

solutions for shale.

STRESS (c), 103 psi

Figure 32.—Comparison of actual and best fit stress-versus-

‘secant-modulus results with Salamon’s and Terzagh’s theoretl-
cal solutions for weak sandstone.



SECANT MODULUS (Eg), 103 psi

Were pty pig
VAN
14F tw=06 YAY

obey
SE eye
F t/w = 05 4
7 o 4
ek & wed
E &

on wo Sd

a
\
33 ee %
Fewer Ouord WO WO War

TANGENT MODULUS (E}), 10% psi

ot ace eee ee ee
16 pet
4F  t/w=04

<°

a

Pee re

fo) 5 10 15 20 25
ROCK STRENGTH, 10° psi

SOE pty

£ ¢
woe oS Pd

fo

Se 8 A

a

SO pyre yt
tw 20.5 2 & v4

80 pg
tw 204 Sf
40F "OS 4

é $ A
3
30F € 4g
“A
A?
&
20F A
ef **
10F ef 21509
f +1604
t wwe eee
° 5 rr

ROCK STRENGTH, 10° psi

Figure 25.—Multiple regression curves—rock strength versus
secant modulus for varlous thickness-to-width shape ratios.

Figure 26.—Multiple regression curves—rock strength versus
tangent modulus for various thickness-to-width shape ratios.



BEHAVIOR OF SIMULATED LONGWALL GOB MATERIAL

By Deno M. Pappas’ and Christopher Mark*

ABSTRACT

This report presents results of a U.S. Bureau of Mines study of longwall gob material. The objective
of this work was to determine material stiffness properties of the gob for use in numerical models
of rock mass response to longwall mining. Photographs of actual mine gob were digitized to obtain
approximate particle size gradations of gob material. The gradation curve was shifted down to a lab-
oratory scale, and 20 uniaxial compression tests were conducted. Varying the maximum particle size
was not found to affect the stress-strain behavior, but changing the gradation appeared to influence the
stress-strain behavior. The stress-strain relationship of the simulated gob material was nonlinear, the
stress-secant-modulus relationship was approximately linear, and the stress-tangent-modulus relationship
was approximately a second-order polynomial function. Equations were generated from these curves,
providing numerical modelers with a means to estimate gob moduli based on the stress level. In addi-
tion, the experimental data were statistically evaluated using multiple regression analyses, producing a
series of equations to predict the secant and tangent moduli from the given stress level, bulking factor,
rock strength, and thickness-to-width shape ratio of the particles.

1Research civil engineer.
2Mining engineer.
Pittsburgh Research Center, U.S. Bureau of Mines, Pittsburgh, PA.


7.

10.
Acl.
A-2.
A-3,

ANOVA test results .........
Averaged test results...

Evaluation of maximum size effect on percent compaction at 500 psi for shale... .
Multiple regression equations for predicting specified parameters
Point load test results used for estimating compressive strength of shale ........
Point load test results used for estimating compressive strength of weak sandstone ...
Point load test results used for estimating compressive strength of strong sandstone... . . wee

TABLES—Continued

UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT

foot

inch

square inch
cubic inch
inch per inch
1,000 pounds

pound

bf
Ibf/fe
Ib/ft

mm

pet

pound (force)

pound (force) per cubic foot
pound per linear foot
millimeter

percent

pound (force) per square inch

second



123

Table 4.-Summary of load deformation test results

Test Maximum Maximum — Compaction, Void ratio! Bulking Modulus? psi Particle
size, In sires, pal Pet Vy ad ¥%; factor? Secant Tangent —_Dreakage
3 700 258 0887 — ~——(0.408 = = = 195.8
3 760 24 780 310 - - - 120.7
3 740 28.3 Bt = 320 - - - 150.4
2 750 28.4 908 373 - - - 898
35 530 29.6 840 - 303 - - - 122.2
325 1,230 48 831 0.189.078 114-2073 9,933 366.3
3 1,250 95.3 855 280210 128-2847 8,921 188.4
3 1,260 36.5 852 253 185 1.25 2,428 9,290 186.0
2 2,790 36.1 802365160 1.36 3,258 7,560 126.4
35 3,130 36.3 679.269 «078 127 -3,231 8,587 242.2
3 6,083, 43.9 76 = 308.002 1.31 3025 7,839 242.5
aeeee 3 2,820 379 7e7 312128 1.31 2917 8,309 182.2
WEAK SANDSTONE
3 3,120 33.1 0701 0311 0.147 1.31 3,404 8,703, 180.1
3 3,150 2 71 343, 163 1.34 3,200 8,820 187.3
3 3,150 344 724 312144 1.31 3,281 9,698, 168.5
2 2,840 96.2 70 313182 1.31 2924 8.584 88.7
35 3,110 329 719.337 _—«162 1.343.573 (9,331 103.4
STRONG SANDSTONE
Bie 3 3,130 348 0.866 0.471 (0.249 147° 3,569 7,251 117.2
19 veesae 3 3,160 31.2 878495 260 1.49 3,829 8,208 132.9
2 wereee 3 3,160 33.7 856.497 248 1.50 4,295 8,826 133.2
No, at z0r0 load; Vagq, at 800 psi; v,, at final load,
2Rt 800 psi.
3 Only 1 particle size used.
NOTE.—Dashes indicate data unavailable because of low stress level of test.
During the test, some sand squeezes out around the where H, = height of test rock material, in,
loading platen and sticks uniformly along the circumfer- . .
ence of the chamber walls, This factor can be accounted HH, = height of test chamber, in,
for by determining the weight of sand sticking to the . *
Fi . " = height of layered sand, in,
chamber walls (per inch of displacement) and subtracting H, ht of lay _
the weight of the wall sand from the layered sand. and D = cumulative displacement, in.

W, - Wee

Vs

8 x 128

A

H, =

, @)

where W,, = sand weight on chamber walls, Ibf,

Subtracting the average height of the layered sand,
minus the amount of cumulative displacement, from the
original height of the chamber (12 in) results in the true
tock material height at that particular point in time during
the test.

H, = H.-H, -D, ®

Multiplying the height of the test material by the area of
the chamber produces the total volume (V,) occupied by
the test material (including voids) at that point in time.

©)

The volume of the rock material (V,) can be determined
» as

V,=H,XA,

W,
V, = —!x 178, ©
1

where W, = weight of test rock material, Ibf,

and y= density of test rock material, Ibf/ft°.


Table 1.—Comparison of modulus values at a stress

level of 800 ps!
Reference Year Rock type Modulus, psi
Tangent Secant
LABORATORY TESTS
Rice (3) ...... 1929 Mine rock 11,900 2,900
(confined).
Mine rock 12,700 2,850
(unconfined).
Mine rock and 18,600 6,600
sand,
Bowling! (6)... 1980 Weathered = 5,400
greywacke.
Greywacke - 7,200
- 12,800
~- 15,500
DRC? ........ + 3,200
Sandstone 4,300
IN SITU TESTS
Wardle (7) .... 1983 Caved waste - 3,100
materis
Smart (8) ..... 1987 ..do. . 3,000
Trueman? (9) .. 1990 ..do. . 3,000

1Used non-coal-measure rocks.
2Bureau’s Denver Research Center.
?Added correction factor to Smart's results,

NOTE.—Dashes Indicate tangent modulus result was not appli-
cable since the stress-strain curves were linear.

Table 2.—Range of modulus values used In numerical modeling

Reference Year Modulus, psi
Tangent Secant
1978 - 14,000- 47,000
1978 - 143,900-139,000
1985 - 250,000- 87,000
1985 - 720,000- 35,000
1987 - 23,600-357,000
Ksipakov (17) . 1988 - 20,000
Park (15) .. 1989 - 32,500- 20,000
Maleki (14) . 1990 188,000 13,200
Su (16) .. 1991 51,050- 42,000 3,420
Heasley (17) 1901 - £7,500

1Based on Rice's test results (3).

?Based on percent of modulus of intact rock.

3Based on location in gob with regard to face.

‘Certain amount of preciosure was allowed before load transfer
‘occurred.

SLow initial modulus at 22-pct compaction,
“Gob modulus selected for room-and-pillar retreat mining
application,

NOTE.—Dashes indicate linear approximations where the tan-
gent modulus cannot be determined.

An examination of British and Australian in-mine tests
of roof fall material revealed some rather startling dif-
ferences in the gob modulus from the results estimated in
the laboratory findings, In 1983, Wardle (7) conducted in
situ tests of caved waste piles resulting from roof failures
in an Australian coal mine. The tests used hydraulic jacks
to apply the load and a displacement transducer to mon-
itor strain. Test results produced approximately linear
behavior of the stress-strain curve, with an estimated de-
formation modulus of 3,100 psi at a maximum stress level
of 200 psi. Meanwhile in the United Kingdom, Smart (8)
evaluated the stress-strain behavior of a stone-built pillar,
using a flatjack to apply the load to the pillar and a con-
vergence strut to monitor displacement. Stress-strain re-
sults show a nonlinear, fourth-order polynomial curve with
a secant modulus of about 3,000 psi at a vertical pressure
of 800 psi. Trueman (9) modified Smart’s stress-strain
curve to take into account ultimate compaction of the ma-
terial. This modification changed the shape of the stress-
strain curve beyond 25 pct compaction because of strain
hardening. With this revised equation for the stress-strain
curve of a material, the secant modulus remains about the
same but the tangent modulus is considerably higher.

A review of the gob moduli used in numerical model
studies found an even wider range of values, as shown in
table 2 (all of these values are based on a linear behavior
of the gob except as noted). In determining the gob se-
cant modulus for use in a finite-element model of a long-
wall panel, Peng (5) estimated that the gob moduli ranged
from 13,900 psi for loosely packed gob to 139,000 psi for
partially failed gob. Using Peng’s rule of thumb for esti-
mating the gob modulus, Hsiung (10) determined the gob
moduli for two different rock types: sandstone ranged
from 50,000 to 87,000 psi, and shale ranged from 20,000
to 35,000 psi, depending upon the gob void ratio. Within
these same ranges, Kripakov (11) and Beckett (12) used a
gob modulus of 20,000 psi to analyze the stress transfer
around longwall panel gob zones using the computer pro-
gram MULSIM/BM. Hackett (13) modified Peng’s rule
of thumb by widening the range of the gob modulus to
0.1, 5, and 10 pet of the intact rock modulus, Hackett
used the gob modulus values of 3,600, 178,000, and
357,000 psi to model stresses in the rock interburden of a
multislice longwall panel using the ADINA finite-element
program. Modeling results were mixed, so that a definite
gob modulus could not be pinpointed. Maleki (14) chose
a model of the gob using an equivalent elastic gob tangent
modulus of 158,000 psi with a certain preclosure allowed
before load transfer could occur, resulting in the bilinear
behavior of the gob. This approach produced a projected
secant modulus of approximately 13,200 psi at the 800-psi


Initial trends of the tangent modulus curve (fig. 23)
show that the modulus stays constant until it reaches avoid
ratio of 0.40 for the shale and weak sandstone and about
0.55 for the strong sandstone. The equivalent strains at
these void ratios range from 0.16 to 0.22, which are similar
to the strains identified on figure 18 using the pivotal point
of 500 psi identified on figure 21. At this initial stage of
the test, the rock modulus is not changing during the
compaction process. This may indicate that the simulated
gob material is maintaining its skeletal stiffness even
though the void ratio is changing because of slippage of
the rock pieces. This same behavior pattern was not as
distinctly identified for the secant modulus curves (fig. 23).

In the later stage of the test, the secant and the tangent
moduli curves for all of the rock types increase expo-
nentially with decreasing void ratio (fig. 23). It is probably
at this stage that strain hardening occurs, when the higher
confinement and normal stresses produce less slippage
(because of higher friction) and more rock breakage,
filling a majority of the voids. The filling and compaction
of the void space increases the stiffness of the rock matrix,
thereby dramatically increasing the modulus of the
material,

The relationship of the moduli to the void ratio appears
to be associated with rock types, whereas the relationship ~
of the moduli to the stress level was not as profoundly
telated to distinct rock types. Consequently, it was deter-
mined to investigate how statistically significant the rock
type and other parameters, such as the particle size, are in

BULKING FACTOR (BF)
1314 15 16 17 1819
TM—1—1— +

KEY
Strong sandstone
Weak sondstone
— Shale

TANGENT MODULUS (Ey),
10° psi

SECANT MODULUS (E,),
108 psi

02 03 04
VOID RATIO (e)

05 06 O07 08 09

Figure 23.—Vold ratio versus secant and tangent modull for all
rock types,

19

affecting the outcome of the test. Two statistical methods
utilized were analysis of variance (ANOVA) and multiple
regression analysis.’

ANALYSIS OF VARIANCE

ANOVA is used to determine whether a set of test
results are statistically different. The ANOVA test, if a
significant difference exists between the sample means
(using the F-ratio), gives an indication if the samples were
drawn from the same population. The null hypothesis for
this test states that the samples have been drawn from the
same population, and the test is applied to see if the null
hypothesis can be rejected at a given significance level
(32). The significance level selected for all tests was 0.05
(ic., probability < 0.05), which is equivalent to a 95-pct
confidence level,

The ANOVA was applied to the test results to deter-
mine if the rock type or maximum particle size signifi-
cantly affects the variables, such as void ratio, particle
breakage, final shape ratio, secant modulus, and tangent
modulus. The null hypothesis for these tests was that
changing the rock type or particle Size does not signifi-
cantly change the variables. Table 7 shows the significance
levels at which the null hypothesis can be rejected, and the
asterisks indicate variables with respective significance
levels less than 0.05 (95-pct confidence interval), The
results suggest that the void ratio, secant modulus, tangent
modulus, and most of the shape ratios are significantly
affected by changing the rock type. On the other hand,
changes in the maximum particle size do not significantly
affect any of the variables. Table 8° ‘displays the averaged
values and standard deviations of the factors that were
determined significant from the ANOVA for results at
equivalent load levels.

Particle Size

As suggested by the ANOVA results in table 7, none of
the factors were significantly affected by the change in
maximum size of the simulated gob material. To verify
this statistical evaluation, the average percent compaction
at a stress level of 500 psi was evaluated for tests using
various maximum particle sizes. Table 9’shows that the
percent compaction is unaffected by varying the maximum
particle size. However, compaction did seem to be af-
fected by the shape of the gob gradation curve. Compac-
tion results for test 6, presented in table 4, appear to be
significantly different from results of other tests. This
difference is attributed to the dissimilar gradation curve

*The authors are grateful to Richard Jones, geologist, Pittsburgh
Research Center, for his assistance with the statistical software program
that evaluated the ANOVA and multiple regression analysis.


RI| 9458 REPORT OF INVESTIGATIONS/1993

Behavior of Simulated Longwall Gob Material

By Deno M. Pappas and Christopher Mark

Bureau of Mines



a Scale, in =

Figure 4.-Sample digitized gob based on Virginia coal mine photograph.



Figure 1.—Gob of a Virginia coal mine.

Figure 2,Gob of an eastern Kentucky coal mine—site 1.


SIEVE ANALYSIS

38

LHSISM AG YASHVOD LNIOY3d

gypr tet seeaet 4 ocesesereg®
3 3
oy oy
Ce 5%
oy js oy 4,
oe oot 8
3% 4. 3% 4
a4 a4
% 2%
°% %
. .
Bu qo jo
B *
"Xo Xo
“S, 8;
B 8 us 8
2 :
2 24g dg
9 #43 9 8
—s & T+ T7145
95
z
ae
js ae js
0%
j- 9%
a4
wy
°y
‘
fo ty
jo 2
we
”
3
Bo
of 3
318%
Fe 8 cD
= 5

4AHSISM AM Y3NIS LNAON3ad

GRAIN SIZE, mm

Figure A-1.—Test material gradation curves before and after test—Continued,



26

Using equation 18 and solving it in terms of the slope
(c/e) defines the secant modulus of the stress-strain
relation

B+2-E+2, (20)

where E, = secant modulus, psi.
This linear equation defines the equation of a line and can
be compared with the best fit equations of the laboratory-
determined secant modulus results shown in table 5.
Therefore, the constants established from the laboratory
secant modulus fitted lines (table 5) can be associated with
the constants in the theoretically determined solutions of
equations 17 and 19, where the intercept defines the initial
secant modulus (E,) and the slope defines the reciprocal
of the maximum strain (1/e,,).
Terzaghi’s Solution

Terzaghi’s approach (35) suggests that the tangent
modulus of granular material is a linear function of the
stress, as expressed by the following equation:

(21)
where E, = tangent modulus, psi,
a = stress, psi,
€ = strain, psi,
Ey = initial tangent modulus,
and a = dimensionless constant.
Expressing equation 21 in terms of strain:

de

Wd  Ejtao’ 2)

and integrating produces the following stress-strain
equation:

es fina + 5” (23)

Solving equation 23 in terms of stress yields:

E)

a= e*-2). (24)

Then, solving equation 24 in terms of the secant modulus

(o/e):

. —-: (25)
Ini + 2
a+ ga)

ol
4
als

Since Terzaghi’s solution is based on the linear fit of the
tangent modulus curve, the laboratory data for the stress-
versus-tangent-modulus curves were fitted to linear curves.
However, these linear fits resulted in negative intercepts,
which required that the intercept be recalculated by
slightly shifting the curve closer to the y-axis. Using the
recalculated intercept, the data curves were refitted and
a new slope was determined. The constants established
from these best fit curves of the stress-versus-tangent-
modulus curves are shown in table 5. As with Salamon’s
solutions, these constants can be associated with Terzaghi’s
equations (equations 24-25), where the intercept defines
the initial tangent modulus (E,) and the slope defines the
constant (a).

Comparing Terzaghi’s and Salamon’s equations with the
actual laboratory data shows that for the stress-versus-
strain results Salamon’s curve closely follows the actual
curve while Terzaghi’s curve is not aligned in two of the
three rock types (figs. 28-30). The stress-versus-secant-
modulus curves show a good linear fit that Salamon’s
equation constants were based upon; however, Terzaghi’s
nonlinear curve is slightly off (figs. 31-33). The stress-
versus-tangent-modulus curves show a fairly close linear fit
that Terzaghi’s equation constants were based upon, and
Salamon’s equations are close to the actual laboratory
results for stress levels less than 2,000 psi (figs. 34-36).
Overall, it appears that both methods model the com-
pressive behavior of granular material, with Salamon’s
method more closely fitting the laboratory data.

5 T T T
KEY Shale
Laboratory results |
47 —-—Best fit curve |
- ——Salamon's curve: |
&é . 1,10 «
% 3b °° ires(ivezen / H
- — —Terzaghi's curve:
3 bee /
oy tele
2 2 13.4 4
WwW
oe
=
o
1
° 0.1 02 03 04

STRAIN (¢), in/in

Figure 28.—Comparison of actual and best fit stress-versus-
Its with Salamon’s and Terzaghi’s theoretical solutions



2.0 TOT TTT

Loe t/w= 06

. .
6 *

J ae

, * 00 o

J ‘00

; g 22s

ob rare eer a

20 pepe
19E t/w 205

BULKING FACTOR (BF)

TUTTI TTT

2.0 pet

1.OE t/w =04

18

1.7 x)

1.6

15 6 9°

14 508
‘00%

13 22

1.2

A

1.0 re rere rere

“Oo 5 10 15 20 25
ROCK STRENGTH, 10° psi

Figure 27.—Multiple regression curves—rock strength versus
bulking factor for various thickness-to-width shape ratios.

25

These plots indicate that as the rock strength and
thickness-to-width shape ratio increases the bulking factor
increases. Also, as the stress levels increase the bulking
factor decreases. These trends seem logical since the
stronger rock remains more intact, resulting in a higher
bulking factor. The thinner and wider disk-shaped rock
has a lower bulking factor; perhaps its fragile shape results
in more breakage and ultimately less void space.

COMPARISON OF THEORETICAL SOLUTIONS
WITH TEST RESULTS

Two theoretical solutions that define the compressive
behavior of granular material were compared with the
actual test results, The stress-strain curves derived from
these theoretical solutions are used in the numerical model
to approximate the strain-hardening behavior of the gob.
The following equations define the stress-strain behavior
of granular materials based on different theories developed
by Ryder (33), Salamon (34), and Terzaghi (as discussed
by Salamon in reference 35).

Salamon’s Solution
According to Salamon (34), the following stress-strain

equation describes the compressive behavior of backfill
material.

Ee
gs, (17)
C= Fen)
Solving this equation for strain:
m7 (8)

where @ = applied stress, psi,
E = initial secant modulus, psi,
€ = strain, in/in,
and €m = maximum strain, in/in.
Differentiating the stress-strain relation (equation 17)

produces the following tangent modulus equation (E, =
da/de):

E, = Ey + 22+
G

im

(19)

where E, = tangent modulus, psi.


INTRODUCTION

In the past 10 years, longwall productivity has broken
records nearly every year. As a result, many large mining
companies have begun to realize that the only way their
mines can stay competitive in the domestic and world
markets is to adopt longwall mining methods. With such
a great interest in longwall mining, there is considerable
need to know the behavior of the underground environ-
ment during the longwall mining process.

While the longwall face moves forward, the shield sup-
ports advance and the roof is allowed to cave behind the
face. As the roof falls, the volume of caved material, re-
ferred to as the "gob,” expands upward until it comes in
contact with the sagging, fractured roof strata. Gradually
the gob consolidates enough to start accepting the large
loads resulting from the overburden weight. The mechan-
ical and physical behavior of the gob material during this
consolidation cycle has received little attention. This is
due to the inaccessibility of the gob, which makes it dif-
ficult to study in situ. The behavior of the gob is very
important in understanding the complex ground response
to longwall mining, in particular for numerical modelers.
With limited data, numerical modelers have in the past
used estimates of gob modulus values that ranged from
1,000 psi to over 300,000 psi. Such wide variations in the
moduli greatly affected the outcome of the numerical
analyses, since the stiffness of the gob is a major com-
ponent in the overall behavior of the model (1)?

The numerical model computer program MULSIM/NL
was recently redesigned to incorporate the nonlinear
stress-strain behavior of the gob that allows for strain
hardening to occur (2). It is hypothesized that the strain-
hardening behavior best models the consolidation of the
gob. As the gob consolidates under increasing strain, the
reduction in the void spaces makes the stress increase at
an exponential rate. This implies that the slope of the gob
stress-strain curve (tangent modulus) increases with in-
creasing stress or strain. Better understanding of the be-
havior of the gob will allow numerical models to be more
accurately applied for simulating longwall mining condi-
tions. Also, better estimates of the gob modulus may find
applications in analysis of stoping in metal and nonmetal
mines, multiple-seam mine design, and surface subsidence.

The U.S. Bureau of Mines goals with this laboratory
study were to estimate the gradation of actual gob mate-
tial, evaluate the stress-strain behavior of simulated gob
material using load deformation tests, and determine the
test parameters that influence the gob modulus. The ulti-
mate goal was to predict the gob modulus of material with
specific attributes based on the test results. This work is
in support of the Bureau’s program to improve the safety
of coal mines, through the development of predictive
methods to identify potential ground control hazards,

BACKGROUND

A review of past research on the load deformation
characteristics of roof fall or gob material found a wide
range of moduli results, as shown in table 1. (The modu-
lus is the slope of the stress-strain curve, which will be
defined in greater detail later.) The earliest study of gob
performance in the United States was reported by Rice
in 1929 (3), He evaluated the strength of cribbing and
roof debris used in anthracite mines and determined the
stress-strain behavior of mine rock material under a uni-
axial load. Based on Rice’s results, the secant modulus
value at the 800-psi stress level for confined mine rock was
2,900 psi, while confined mine rock mixed with sand and
rock debris had a secant modulus of 6,600 psi (table 1).
Also based on Rice’s data, Peng (4) determined a range of
secant modulus values from 1,000 psi for a loosely laid
pyramidal rockpile to a maximum modulus of 47,000 psi

3talic numbers in parentheses refer to items in the list of references
preceding the appendix at the end of this report,

for broken mine rock tested in a steel cylinder (table 2).
The stress-strain curve was found to behave linearly for
the pyramidal rockpile, but nonlinearly for the rock tested
in the steel cylinder, Based on these findings, Peng (5)
used a "rule of thumb" for estimating gob modulus. Gob
modulus was estimated to range from one-hundredth to
one-fifty-seventh of the intact roof rock modulus de-
pending upon on how well the gob was packed. In 1980,
Bowling (6) conducted a series of deformation tests at low
loadings on rockfill material used for civil engineering
application. Because of the low loading, the stress-strain
curve was effectively linear for all of the rock types. Based
on these test results, it was projected that at the 800-psi
stress level the stronger rocks such as quartzite and dol-
erite had a secant modulus of 12,800 to 15,500 psi, where-
as the weaker sedimentary rock had a modulus ranging
from 5,400 to 7,200 psi, depending upon the degree of
weathering (table 1).


16

Table 5.—Equations of best fit curves for secant and tangent modull versus stress

‘Secant modulus versus Tangent modulus versus stress
Test stress Best fit equation, e Best fit equation, second-degree
Best fit equation, Pe linear fit? polynomial fit
linear fit
‘SHALE
2297+ 698 099 10.30 + 975 098 = 0.004450? + G7o + 562 0.99
2270+ 613 99 9.90 + 1,219 99 0038707 + 7.310 + 214 99
2.250 + 1,480 99 Mito + 438 98 0007830? + 9.830 - 124 99
2.360 + 1,350 99 11.70 + 1,160 99 0003060? + 11.60 - 280 99
2.090 + 1,470 99 11.60 + 795 99 0001977 + Ito - 119 99
2.290 + 1,060 99 11.90 + 945 99 00069007 + 10.97 - 13,3 99
2.260 + 1,110 99 40+ 922 99 001720? + 9.600 + 40.0 99
WEAK SANDSTONE
256041470 099 14.70 + 1,017 099 0.002150 + 10.37 - 909 0.99
2.460 + 1,260 99 14.70 + 1,008 99 001620? +1170 - 657 99
2.530 + 1,290 99 15.20 + 850 98 002076? + 10.80 - 91.9 99
2.390 + 1,080 99 15.20 + 344 99 0025607 +10.2c - 259 99
2.530 + 1,600 99 14.304 611 97 002170? +9500 + 136 98
2.490 + 1,340 99 1480+ 765 98 0021107 +1050 - 192 99
STRONG SANDSTONE

2410+ 1,590 0.99 11.00 + 1,620 0.97 0.000978? + 9.10 + 902 0.98
2.960 + 1,850 99 10.90 + 649 98 001710? + 6.260 +1816 89
2.270 + 2,240 99 10.50 + 456 96 001850? + 5.270 + 2,120 98
: 2.340 + 1,890 99 10.87 + 908 a7 001520? + 6.877 +1612 98
Total av .. 2.360 + 1,360 99 1280+ 865 98 001810? + 9.337 + 204 90

? Coefficient of determination.

Used for average stress-secant modulus curve and for Salamon's equation,

2Used for Terzaghi’s equation.
3Used for average stress-tangent modulus curve.

ANALYSIS OF RESULTS

Laboratory test results presented in figure 18 show
that the averaged stress-strain behavior of the simulated
gob material is nonlinear, which compares well with re-
sults of other compression tests of granular material (6).
Figure 19 shows the variability between the actual test
data and the best fit curve. Test results for the strong and
weak sandstone have minimal variability, while the results
for shale are slightly more scattered. It is interesting that
at the lower stress levels the stress-versus-strain curve is
approximately linear, which would explain the linear stress-
strain behavior obtained by Wardle (7).

During the initial portion of the test, the rate of change
of the stress-strain curves (tangent modulus) is greatest
for the strong sandstone, followed by the weak sandstone
and the shale, However, as strain hardening occurs, the
tangent modulus increases more rapidly for the weak sand-
stone, followed by the shale and then the strong sandstone.
Examination of the curves for secant modulus versus stress
show that all stress levels are greatest for strong sand-
stone, followed by the weak sandstone and the shale.
These phenomena are depicted in figure 18 at low and
high stress levels. To better illustrate the stress-strain

behavior of the rock, the individual moduli values were
plotted versus the corresponding stress level and the void
ratio.

4 T T T

KEY
Strong sandstone
Weak sandstone

STRESS (0), 103 psi
y

° on

O16 02 022 03

04
STRAIN (e), in/in

Figure 18.—Stress-versus-strain results—best fit curves. At
500 psi, pivotal stress level corresponds to strain range of 0.16
to 0.22,



Table A-2.—Point load test results used for estimating compressive strength of weak sandstone

TEST_AVGWIDTH DEPTHFAILLD .P  De2 De is _F 1850
(in) (mm) (mm) (kg/cm2) = (KN) (mm2) (mm)
PERPENDICULAR TO BEDDING

1 0.97 24.64 20 9 1.273 627.4 25.05 2.029 0.733 1.487

2 0.68 17.27 20.5 6 0.849 450.82 21.23 1.883 0.68 1.281 XL
3 1 25.4 15.5 17.5 2.476 501.27 22.39 4.939 0.697 3.441
4 1.1 27.94 16 12.5 1.768 569.19 23.86 3.107 0.717 2.227
5 0.8 20.32 14 8.5 1.203 362.21 19.03 3.32 0.647 2.15
6 117 29.72 14.5 12.5 1.768 548.65 23.42 3.223 0.711 2.291

7 1.15 29.21 18 43° 6.083 669.44 25.87 9.087 0.743 6.756 XL

8 1.12 28.45 22 8 1.132 796.86 28.23 1.42 0.773 1.098 XL
9 1.04 26.42 22 18 2547 739.95 27.2 3.442 0.76 2.617
10 0.85 21.59 20.5 16 2,264 563.53 23.74 4.017 0.715 2.873
Ww 15 38.1 14 10.5 1.485 679.15 26.06 2.187 0.746 1.631
12 0.64 16.26 19 10 1.415 393.26 19.83 3.598 0.66 2.373
13 0.35 8.89 12 6 0.849 135.83 11.65 6.249 0.519 3.245

14 0.62 15.75 19.5 21 2.971 390.99 19.77 7.599 0.659 5.005 XL
15 0.78 19.81 13.5 10.5 1.485 340.54 1845 4.362 0.639 2.785
AVG 2.466

COMPRESSIVE STRENGTH 6220 PSI

PARALLEL TO BEDDING

1 0.67 17.02 185 7.5 1.061 400.86 20.02 2647 0.662 1.753 XL
2 0.67 17.02 10 65 0.92 21668 14.72 4.244 0.577 2.448
3 0.62 15.75 cI 13 1,839 621.58 24.93 2.959 0.731 2.163

4 0.88 22.35 35 13° 1.839 996.08 31.56 1.846 0.813 1.501 XL
5 0.86 21.84 15 8 1.132 417.19 20.43 2.713 0.668 1.813
6 0.8 20.32 17 14.5 2.051 439.83 20.97 4.664 0.676 3.155

7 0.55 13.97 8.5 9 1.273 151.19 123 8422 0.532 4.48 XL
8 0.52 13.21 19 75 1.061 319.52 17.88 3,321 0.629 2.09
9 0.82 20.83 19.5 12.3 1.74 517.12 22.74 3.365 0.701 2.361
10 0.34 8.636 20 7.5 1.061 219.91 1483 4.825 0.579 2.792
WY 0.7 17.78 11.5 8 1.132 260.34 16.14 4.347 0.601 2.613

12 0.66 16.76 7 13° 1.839 362.86 19.05 5.069 0.648 3.283 XL
13 0.82 2083 14.5 11° 1,556 384.53 19.61 4.047 0.656 2.656
14 0.4 10.16 9 4 0.566 116.43 10.79 4.861 0.502 2.438
15 0.53 13.46 10 65 092 171.4 13.09 5.365 0.547 2.936
AVG 2.497

COMPRESSIVE STRENGTH _6300 PSI
OVERALL AVG 2.483
COMPRESSIVE STRENGTH = 2.483x145x17.4= 6263 PSI

17.4= CONVER FROM PT LD TO COMPR STR.
FOR SANDSTONE
145= CONVER FROM SI TO ENGL UNITS
XL= EXCLUDE FROM AVG. TOP AND BOTTOM
TWO VALUES:

P = FAILLD/ RAM AREA
De2 = (4x WIDTH x DEPTH)/PI
Is = P/De2

F = (De/50)*.45

1s50 = IisxF

33


Table A-3.—Polnt load test results used for estimating compressive strength of strong sandstone

TEST_AVGWIDTH DEPTHFAILLD P  De2 De  _is _-F 1850
(in) = (mm) (mm) (kg/cm2) (KN) (mm2) (mm)
PERPENDICULAR TO BEDDING
1 0.76 19.3 15 34.5 4.881 368.68 19.2 13.24 0.65 8.606
2 0.71 17.91 8 24.5 9.466 182.4 13.51 19 0,555 10.54 XL
3 0.68 17.27 "W 24 3.395 241.91 15.55 14.04 0.591 8.299
4 0.86 21.84 31 60 8.489 862.19 29.36 9.845 0.787 7.748
5 0.77 19.56 32 55 7.781 796.86 28.23 9.765 0.773 7.55
6 0.35 8.89 10 15.5 2.193 113.19 10.64 19.37 0.498 9.655 XL
7 0.55 13.97 14.5 19 2.688 257.91 16.06 10.42 0.6 6.252
8 0.81 20.57 15 30 4.244 392.93 19.82 10.8 0.659 7.123
9 056 14.22 13.5 17 2.405 244.49 15.64 9.837 0.593 5.83
10 0.95 24.13 15 32.5 4.598 460.85 21.47 9.977 0.684 6.82
11 1.48 3759 | (9.5 24 3.395 454,721.32 7.467 0.681 5.089
12 0.7 17.78 15.5 19 2.688 350.89 18.73 7.661 0.643 4.925 XL
13 0.52 13.21 10 20 «283 168.17 12.97 16.83 0.545 9.167
14 0.91 23.11 13.5 18.5 2617 397.3 19.93 6.588 0.661 4.355 XL
AVG 7.248
COMPRESSIVE STRENGTH 18,287 PSI
PARALLEL TO BEDDING
1 0.86 21.84 17.5 25 3.537 486.72 22.06 7.267 0.692 5.029
2 0.52 13.21 7 22 3.112 285.89 16.91 10.89 0.614 6.684
3 0.77 19.56 20 25.5 3.608 498.04 22.32 7.244 0.696 5.039
4 0.8 20.32 15 20 «283 388.08 19.7 7.201 0.658 4.795 XL
5 0.58 14.73 22 37 6.235 412.66 20.31 12.68 0.667 8.458 XL
6 0.34 8636 10.5 11 1.556 115.45 10.74 13.48 0.501 6.748
7 0.41 10.41 9.5 65 0.92 125.97 11.22 7.3 0.511 3.727 XL
8 0.4 10.16 W 11.5 1.627 142.3 11.93 11.43 0.525 6
9 0.69 17.53 10 18.5 2617 223.15 14.94 11.73 0.581 6.81 XL
10 0.71 18.03 a 24 3.395 482.19 21.96 7.042 0.691 4.863

AVG 5.727
COMPRESSIVE STRENGTH 14,229 PSI

OVERALL AVG 6.487
COMPRESSIVE STRENGTH = 6.487x145x17.4=  16,368PSI

17.4= CONVER FROM PT LD TO COMPR STR.
FOR SANDSTONE

145= CONVER FROM SI TO ENGL UNITS

XL= EXCLUDE FROM AVG. TOP AND BOTTOM
TWO VALUES

P= FAILLD/RAM AREA
De2 = (4x WIDTH x DEPTH)/PI
is = P/De2

F = (De/50)*.45

1950 = IsxF


22

(disk shape), weak sand-

\k-blade shape).

Examples of three rock types and distinct shapes used in laboratory tests, left to right: shale
and strong sandstone (disi

k-spherical shale),

Figure 24,
stone (dis!

lly the rock

types found in most gobs, a means of characterizing the

to the large range of values used
rock types needs to be established.

in comparison

differences among rock type moduli are very small
in past modeling situations (table 2), these minimal dif-

ferences will have a negligible effect on the numerical
model results, For an approximation of a rock modulus
similar to the rock type and gradation used in these tests,

figure 22 is adequate; however, for estimating the modulus

of a rock type different from the laboratory rock, this

figure may not be appropriate. Since the rock types used

in this laboratory study will not match identical

Since
(table 6),

fol-

lowed by shale and strong sandstone with 4.74 and 4.68,
The shale and strong sandstone

had a slightly lower number of contact points, which may
looser packing of the rock and a

Also possibly related to the shape effect was the aver-
age number of contact points prior to testing. Weak sand-

stone had an average number of 5.20 contact points,

respectively. The higher number of contact points for the
weak sandstone may indicate that the more spherical
shape and denser packing resulted in more contact points
relate to the disk and rectangular shapes of the rock

g s
geass
i AS
cst 5

woe
bet
2 33
3 33
gzere
8 g5
Ez 82

22
3 a

MULTIPLE REGRESSION ANALYSIS

Modulus

To evaluate the input parameters that characterize the
rock type and to produce a predictive method of estimat-

1

The ANOVA results in table 7 show that rock
significantly affects the outcome of the secant and tangent

ible

is is al

to evaluate the relationship between one dependent vari-

able and several independent variables.

According to

the modulus, multiple regression analysis was found

to be a useful tool. Multiple regression analy:

ing

moduli values based on both stress level and void ratio,
Therefore, the initial assumption that the secant and
tangent moduli could be estimated based on the stress
level (fig, 22) independent of the rock type may be inexact.


CONTENTS

Abstract .
Introduction .
Background .
Gob material simulation .
Scaled-down gradation curve .
Gradation of gob material
Source material . .
Shale .....,
Weak sandstone .
Strong sandstone
Load deformation test
Test apparatus ...
Test procedure .
Test methodology .
Analysis techniques
Percent compaction
Void ratio .....
Particle breakage
Rock shape ...
Contact points .
Secant and tangent moduli
Analysis of results .
Stress level
Void ratio
Analysis of variance
Particle size .
Rock type ..
Compressibility .
Particle shape
Modulus ......
Multiple regression analysis .
Secant and tangent moduli
Bulking factor .........
Comparison of theoretical solutions with test results
Salamon’s solution .
Terzaghi’s solution .
Discussion ...........
Conclusions and recommendations
References ..........0..055
Appendix.—Additional test data . . .

ILLUSTRATIONS

Gob of a Virginia coal mine ..............005
Gob of an eastern Kentucky coal mine—site 1 .
Gob of an eastern Kentucky coal mine—site 2.
Sample digitized gob based on Virginia coal mine photograph .
Sample histogram of rock size distribution based on photoanalysis of Virgi
Estimated gob gradation of three mine sites based on photoanalysis . .
Comparison of photoanalysis of laboratory rock gradation with actual gradation o:

PAYVAaYNE

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39

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SIEVE ANALYSIS

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Figure A-1.—Test material gradation curves before and after test—Continued.

INT-BU.OF MINES,PGH,,PA 29734


LOAD DEFORMATION TEST

Because there are no published standards for con-
ducting load deformation tests of granular material, and
since several different methods have been employed (as
described in the literature), the apparatus, procedures,
methodology, and analysis techniques required for these
tests were developed,

TEST APPARATUS

The apparatus used for the load deformation tests
is composed of two parts, the chamber and the platen
(fig. 10). The steel chamber is made out of 16-in-OD
(14.31-in-ID) by 12-in ASA 80 pipe with a thickness of
0.843 in; it is bolted and welded to a 20- by 20- by 1-in
base. The chamber has a removable quarter section that

Jevi00 84 80)
843i, 1365 rt

je, 2 by 2°
aN
+-Vo-inrdiam bolt
tt (10 required)

gird out

THT
PLAN
frases
socket heod cop
screws
TI i,
<7 risen platen
F jr]
erin fe
clearance} o)
|}
. 31
12 10}
JO}
° 8
E 7 Seale, in

-

ELEVATION

Figure 10.—Plan and elevation views of test chamber and
platens,

is fastened to the stationary part of the chamber with five
bolts on either side (figs. 10-11). The exterior walls of the
test chamber are instrumented with strain gauges to moni-
tor horizontal and vertical movements.

The upper platen component consists of 14.16-in-
diameter by 2-in-thick steel plate. A 9.5-in-diameter by
S-in-thick spacer is also used to maximize the available
stroke of the test machine. The clearance between the
platen and the inside walls of the chamber is about 0.08 in.

TEST PROCEDURE®

To begin each test, the size-sorted rock is weighed out
according to the proportions indicated by the simulated
gob gradation curves determined previously. Rock from
each size grouping is sampled and measured (length,
width, and thickness) to evaluate shape effect. The rock
is then thoroughly mixed together in a trough to ensure
uniform composition,

The simulated gob for the laboratory tests is shoveled
into the test chamber until it reaches about an inch below
the lip of the chamber top (fig. 11). The weight of the
rock in the test chamber is determined by subtracting the
weight of the gob material remaining in the trough after
filling the chamber from the weight of the original

SThe authors thank Michael DiMartino, electronics technician,
Pittsburgh Research Center, for his input and assistance in conducting
the load deformation tests.

Figure 11.—Simulated gob in test chamber.



Percent Compaction

The amount of strain (€) or percent compaction of the
simulated gob material is defined as follows:

o-F )

where D = cumulative displacement of rock material,
in,

and H = initial height of test material, in.

Although these values are dependent upon the maximum
load applied, the percent compaction does give an indica-
tion of the compressibility of the rock type when eval-
uated at equivalent maximum loadings. During some of
the tests, the axial strain was monitored during the un-
loading of the test material to evaluate the rebound of the
tock. The type of strain shown in equation 1 is known as
the engineering strain and not the true strain, which cor-
rects the initial height for each increment of displacement.

1



Library of Congress Cataloging in Publication Data:

Pappas, Deno M.
Behavior of simulated longwall gob material / by Deno M. Pappas and Christopher
Mark.

P. cm, — (Report of investigations; 9458)
Includes bibliographical references (p. 30).
1. Coal mine waste—Mechanical properties. 2. Soil consolidation—Computer sim-

ulation. 3, Longwail mining. I. Mark, Christopher. I. Title. III. Series: Report
of investigations (United States. Bureau of Mines); 9458.

TN23.U43_ [TN803] 622 s—dc20 [622.334] 92-34621 CIP



32

APPENDIX.—ADDITIONAL TEST DATA

Tables A-1 through A-3 show printouts of point load test data and estimated rock compressive strengths from a
computer spreadsheet program.

Table A-1.—Point load test results used for estimating compressive strength of shale

TEST_AVG WIDTH DEPTH FAIL LD P

De2 De
(in) (mm) (mm) (kg/cm2) (KN) (mm2) (mm)

De _ls F 1850

PERPENDICULAR TO BEDDING

1 1.1 27.94 21.5 48.5 6862 764.85 27.66 8971 0.766 6.873

2 0.85 21.46 21.5 27.5 3.891 587.54 24.24 6622 0.722 4.78

3 0.9 22.86 22 33° 4.669 640.34 25.3 7.291 0.736 5.367

4 1.14 28.96 28 47 6.649 10323 3213 6.441 0.82 5.279

5 0.65 16.51 14 17 2405 294.3 17.16 8.172 0.618 5.05

6 1,76 44.7 19 23 (3.254 1081.5 3289 3,009 0.828 2.492 XL

7 0.55 13.97 10 13° 1.639 177.87 13.34 10.34 0.552 5.705

8 0.85 2159 11.5 25 3.537 316.13 17.78 11.19 0.628 7.026 XL

9 0.58 14.73 "1 17 2405 206.33 14.36 1166 0.57 6.65

10 0.85 2159 16.5 29 4.103 453.57 21.3 9.046 0.681 6.161

1 0.55 13.97 "1 20 «283 195.66 13.99 14.46 0.564 8.152 XL

12 0.65 16.51 10 17 2.405 210.21 14.5 11.44 0.573 6.554

13 1.1 27.94 23 19 2.688 818.21 28.6 3.285 0.778 2.555 XL

14 0.72 18.29 16 23 3.254 37256 19.3 8.734 0.652 5.691

15 1.25 31.75 18.5 37 5.235 747.87 27.35 6.999 0.762 5.335

16 0.9 22.86 12 23 3.254 349.28 18.69 9.316 0.642 5.983
AVG 5.785

COMPRESSIVE STRENGTH 10,486 PSI
PARALLEL TO BEDDING

1 0.86 21.84 18.5 11.5 1.627 514.53 22.68 3.162 0.701 2.216

2 0.96 24.38 7 17 2.405 527.79 22.97 4.557 0.705 3.211

3 0.71 18.03 16 7.5 1.061 367.39 19.17 2.888 0.65 1.876

4 0.58 14.73 22 18 2547 41266 20.31 6.171 0.667 4.115

5 0.86 21.84 20 15 2.122 556.25 23.59 3.815 0.713 2.721

6 0.8 20.32 7 21 2.971 439.83 20.97 6.755 0.676 4.569 XL

7 0.43 10.92 "1 9 1.273 152.97 12.37 8.324 0,533 4.439

8 0.46 11.68 22 14 1.981 327.28 18.09 6.052 0.633 3.83

9 0.75 19.05 22 7 0.99 533.61 23.1 1.856 0.706 1.311 XL

10 0.55 13.97 13.5 5 0.707 240.13 15.5 2.946 0.59 1.739

W 0.73 18.54 18 16 2.264 424.95 20.61 5.327 0.671 3.575

12 0.78 19.81 28 7 0.99 706.31 26.58 1.402 0.752 1.055 XL

13 0.42 10.67 "1 111,556 149.41 12.22 10.42 0.531 5.526 XL

14 0.45 11.43 W 4 0.566 160.08 1265 3.535 0.539 1.905

AVG 2.962
COMPRESSIVE STRENGTH _5,370 PSI

OVERALL AVG 4.374
COMPRESSIVE STRENGTH = 4.374x 145x125 = 7,930 PSI

17.4= CONVER FROM PT LD TO COMPR STR.
FOR SHALE

145= CONVER FROM Si TO ENGL UNITS

XL= EXCLUDE FROM AVG. TOP AND BOTTOM
TWO VALUES

P= FAILLD/RAM AREA

De2 = (4x WIDTH x DEPTH)/PI

Is = P/De2

F = (De/50)~.45

1s50 = IsxF a



20

that was used for test 6, suggesting that the shape of the
grain size distribution curve may affect the compressibility
of the simulated gob material (see appendix figure A-1,
the shape of the gradation curve for test 6 versus the
curves for the other tests). This implies that the test re-
sults are most applicable when the gradation of the actual
gob is similar to the laboratory gradation curve shown in
figure 8

Table 7-ANOVA test results,! showing variables
or parameters significantly affected

Variable or Significance level
Parameter Rock type? Maximum particle size

Void ratio:

Initial. 0.0258" 0.4809

‘At 800 psi 0000" 2201

Final... 0413" 8219
Percent compaction . 0199" 9863
Particle breakage 2345 4084
Shape ratio before:

Thickness to width . . o1e7* NAP

Width to length .... 0243" NAP
Shape ratio after:

Thickness to width... .0000* NAp

Width tolength ..., 3263 NAp
Tangent modulu

Stress level . .0040* 2953

Bulking factor . 0500" .0806
‘Secant modulus:'

‘Stress level . .0079* 2471

Bulking factor. 0187" 1802

NAp Not applicable.

‘includes data from all tests except test 6.

*Asterisk denotes significance level <0.05 (confidence level of
95 pet that the factor significantly affects results).

*Based on data derived from best fit curve at a stress level of
800 psi or, indirectly, the equivalent bulking factor at 800 psi.

NOTE.—ANOVA was also conducted on the shape ratio before
the test versus the shape ratio after the test. Results showed that
the thickness-to-width ratio had a significance level of 0.0167* and
the width-to-ength ratio had a significance level of 0.2630.

Rock Type

Unlike particle size, the rock type was significantly cor-
related with a number of output parameters. The com-
pressibility (percent compaction and void ratio), modulus,
and particle shape were found to be a function of the type
of rock used in the test (table 7). It should be noted that
“rock type" is a more generic term for other parameters
uniquely associated with the rock, such as its composition,
compressive strength, and surface texture.

Compressibility

As the ANOVA results show, the rock type signifi-
cantly affects all of the parameters associated with the

compressibility of the rock. The percent compaction or
strain of the rock at equivalent maximum loads shows that
most of the deformation occurs during the early stage of
the test (fig. 18). The strong sandstone had the highest
initial void ratio, followed by the shale and weak sandstone
(table 8). At a stress level of 800 psi, the void ratio of the
weak sandstone had surpassed that of the shale. The final
void ratio repeated this same trend, indicating that the
shale was the most compressible material, followed by the
weak sandstone and strong sandstone. This trend was
confirmed with the percent compaction, which determined
that the shale had the highest percent compaction with
36 pet, followed by the weak and strong sandstone (34 and
33 pet, respectively), Although the particle breakage was
found not to be a significant factor with the ANOVA
analysis, it displays a similar trend, with shale producing
the highest particle breakage followed by the weak sand-
stone and strong sandstone (table 8).

The rock compressibility may also be affected by the
rock strength, The strong sandstone had an overall com-
pressive strength of 16,400 psi, while shale and weak
sandstone had considerably lower strengths of 8,000 and
6,300 psi, respectively. Therefore, stronger rock can be
associated with less compaction, less particle breakage, and
higher final void ratios, Particle shape may also affect the
degree of compaction; this is discussed in the next section.

Some of the tests evaluated the amount of strain reduc-
tion when the test material was being unloaded (however,
the numbers were too few for statistical analysis), and it
is interesting that under the same maximum loading the
strong sandstone rebounded an average of 1.58 pct while
the shale rebounded only 0.85 pct (table 8). Possibly this
shows that the strong sandstone is more capable of storing
strain energy than are the other rock types.

Particle Shape

The ANOVA analysis in table 7 found that all of the
shape ratios were significantly affected by rock type, with
the exception of the after-test width-to-length shape ratio,
Using Zingg’s method (25-26) for classifying rock shapes,
each rock type, prior to testing, had a slightly different
shape (fig. 15): The shale is a disk shape, the weak sand-
stone borders on disk-spherical shape, and the strong
sandstone borders on disk-blade shape. These shape dif-
ferences are probably due to the unique crystalline struc-
ture of each rock type, which influences the fracturing of
the rock. As figure 24 depicts, the strong sandstone is
rectangular with sharp, defined corners, the weak sand-
stone is slightly more spherical in shape with smooth,
rounded corners, and the shale is flat with feathered edges
and many irregular corners. The average initial void ratio
of each rock type (table 8) shows that the weak sandstone
is the most densely packed, probably because of its


Report of Investigations 9458

Behavior of Simulated Longwall Gob Material

By Deno M. Pappas and Christopher Mark

UNITED STATES DEPARTMENT OF THE INTERIOR
Bruce Babbitt, Secretary

BUREAU OF MINES


12 T T T
Strong sandstone
g OF
a
Ko
<= 8r
°
i]
3
a 6PF
5
a
g KEY
- 4 — Laboratory results J
z — Salamon's curve:
q E,= 2340 +1,890
wW —— Terzaghi's curve: 4
22 «.. ee
s* 108
In(1+ Sogo)
1 L 1
(0) 1 2 3 4

STRESS (c), 10 psi

TANGENT MODULUS (E}), 103 psi

——— Laboratory results

20 ——Salamon's curve: 4
20 @

t*hit0* Tez6) * Trroivener

10 ——Terraghi's curve: |
Eye 922 + Ihe
1 \

te) 1 2 3 4

STRESS (o), 105 psi

Figure 33.-Comparison of actual and best fit stress-versus-
‘secant-modulus results with Salamon’s and Terzaghl’s theoretl-
cal solutions for strong sandstone.

Figure 34.—Comparison of actual and best fit stress-versus-

tangent-modulus results with Salamon’s and Terzaghi’s theoretl-
cal solutions for shale.

60
z Weak sandstone
% 50 “ ]
g J
Q
3 KEY J
2 ——Loboratory results
g | ——Salamon's curve:
5 Eye tao + eee
ir i (172.49) * 7340 (7249)
2 10r —=—Terzaghi's curve:
= 4 E765 +148.

° 1 4

2
STRESS (c, 10° psi

60
KEY ‘Strong sandstone
——Loboratory results
- 50 ——Solamon's curve:
a 2o ot
% Fre 4890 + Ta3qj * 1,890(1/2.34)2
240 ——terzaghi's curve:
g 5+ 9084108 o a
ra
350
5 20
i
@
10
° 1 2 3 4

STRESS (o),10° psi

Figure 35.—Comparison of actual and best fit stress-versus-
tangent-modulus results with Salamon’s and Terzaghi’s theoret!-
cal solutions for weak sandstone.

Figure 36,—Comparison of actual and best fit stress-versus-
tangent-modulus results with Salamon’s and Terzagh!’s theoreti-
cal solutions for strong sandstone.



PERCENT FINER BY WEIGHT

100
90
20]
70)
60)

so

100,
90)

70)
60
50]

SIEVE ANALYSIS

& 98 © PP PPESS
VL LL LESS é

PPeES
SE

Test Il

20

30

50

60

150100 50

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oo © PP PPESS

Test 12

LE LLL LSLSS °

n ran
ry 01 150100 50

GRAIN SIZE, mm

37

PERCENT COARSER BY WEIGHT

Figure A-1.—Test material gradation curves before and after test—Continued.



Doornkamp (32), the purpose of multiple regression is to
discover if variations in values of a particular variable are
accounted for more by its relationship to two or more
other variables taken together than to any one individual
variable, The advantage of multiple regression is that after
it selects the independent variables that best predict the
dependent variable, it produces an equation for predicting
the dependent variable given the independent variables,

Secant and Tangent Moduli

Using a statistical software package, multiple regression
analysis evaluated several independent parameters (i¢.,
rock strength, shape ratios, particle breakage, and initial
void ratio) with respect to the tangent modulus at a wide
range of bulking factor values. This analysis was dupli-
cated using the secant modulus values. Results of the
analysis show that both the secant and tangent moduli are
a function of the rock strength and thickness-to-width
shape ratio with a fairly high degree of correlation (i.e.,
the multiple coefficient of determination or R? = 0.84 to
0.94). Equations were formulated to predict the tangent
modulus and secant modulus at various bulking factors
given the rock strength and thickness-to-width shape ratio,
as shown in table 10. Because of constraints within the
test data, the equations for the very high and very low
bulking factors were extrapolated (BF = 1.15, 1.20, 1.60).
Figures 25 and 26 show the plots of these equations at
several different thickness-to-width shape ratios.

Trends in figures 25 and 26 for both the secant and
tangent moduli analysis show that as the rock strength

23

increases so does the modulus, and as the bulking factor
decreases the modulus values increase. Also, as the shape
ratio increases the modulus increases. The thicker and
narrower rock has a higher modulus factor, perhaps be-
cause its competent shape results in a stiffer rock matrix.

Bulking Factor

Since the modulus was found to be a function of the
rock strength and thickness-to-width shape ratio based on
the bulking factor, a link was needed to connect the
bulking factor to a more obtainable mine parameter such
as the overburden stress level, Toward that end, another
series of multiple regression analyses was conducted to
determine the bulking factor based on the overburden
stress level. The regression analyses evaluated the same
independent variables (i.c., rock strength, shape ratios,
particle breakage, and initial void ratio) with respect to
bulking factors at various stress levels. Results of the
analysis disclosed that the bulking factor is a function of
the rock strength and thickness-to-width shape ratio, the
same two variables found to be a function of the modulus.
Again, the multiple coefficient of determination of the
analysis was high (i.¢., R? = 0.83 to 0.91), Equations were
formulated to predict the bulking factor at various stress
levels given the rock strength and thickness-to-width shape
ratio, as shown in table 10. Figure 27 shows the plot of
these equations graphed with rock strength versus the
bulking factor at various stress intervals, with three plots,
each representing different thickness-to-width shape ratios,

Table 10.—Multiple regression equations for predicting specified parameters

Level Multiple regression equations Fe
BULKING FACTOR (BF) AT VARIOUS STRESS LEVELS (c)

= 400 psi. BF = 0,0000184X1 + 0.267X2 + 1.16 0.828

@ = 600 psi BF = 0,0000203X1 + 0.274X2 + 1.06 875

7 = 800 psi. BF = 0,0000187X1 + 0.262X2 + 1.04 873

@ = 1,000 psi BF = 0,0000185X1 + 0.269X2 + 0.992 892

psi BF = O.0000160X1 + 0.209X2 + 1.00 ‘901

psi BF = O,0000150X1 + 0.221X2 + 0.963 908

psi. «__BF_ = 0,0000136X1 + 0.247%2 + 0.931 894

TANGENT (E) MODULUS AT VARIOUS BULKING FACTORS (BF)

BF = 1.25. E, = 249X1 + 41,200X2 - 24,800
BF = 1.30. E, = 1.76X1 + 23,800x2 - 18,700
BF = 1.35. E, = 1.32X1 + 16,300X2 - 11,400
BF = 1.40. E, = 0.933X1 + 11,300X2 - 7,900
BF = 1.50. E, = 0.568X1 + 6,900X2 - 5,000

AT VARIOUS BULKING FACTORS (BF)

SECANT MODULUS (E,)

BF #125... E, = 0.530X1 + 10,400X2 - 5,340 0.939
BF = 1.30. E, = 0.445X1 + 7,760X2 - 4,160 943
BF = 1.35. E, = 0,348X1 + 5,580X2 - 2,750 906
BF = 1.40, E, = 0,283X1 + 4,900X2 - 2,300 903
BF #150... E, = 0.348X1 + 5,580X2 - 2,750 840

NOTE.—X1 Is the rock strength parameter, X2 Is the thickness-to-width shape ratio, and
FP is the multiple coefficient of determination. The curves shown In figures 25 to 27 are

based on these equations.


50

40

FREQUENCY

APA eno os
123456789 1011 213 415 16 7 16 19 200 22
DIAMETER, in

Figure 5.—Sample histogram of rock size distribution based
on photoanalysis of Virginia coal mine.

SIZE, in

3530 25 20 15 125 1.0 O75

100
@ 80
Zz KEY
8 —# Trial t
a 60 Trial 2
a Actual
FA
iri] 40
$3)
&
a 20

oluti4

100 80 60 40 20 10

SIZE, mm
Ste mm

Figure 7.Comparison of photoanalysis of laboratory rock
gradation with actual gradation of laboratory rock.

SIZE, in SIZE, in
302 20 5 10 5 3 8 1 Os 3025.20 5 10 5 3 2 1 05
100 111 100 4} 7 —+t T 7
KEY \ KEY
g 8 Mine site g 8 Te Averaged 1
Fn a \ ver® Shifted
B 6 8 % Corrected
< 60 4
z < \
bE
E
G 40 2 aok
rs} Ww
g &
a 20 2 ®
a a 2
aw
ols. nae, j
1,000 800 600 400 200 10080 60 40 20 10
SIZE, mm

Figure 6.—Estimated gob gradation of three mine sites based
on photoanalysis.

The gradation curve for the laboratory gob material was
derived by the following procedure. First, the curves in
figure 6 were averaged to obtain the "averaged curve" in
figure 8. The averaged curve was then shifted on the
graph parallel to itself down to a maximum particle size of
3 in (‘shifted curve" of figure 8). Lastly, the shifted curve
of figure 8 was corrected to account for the hidden rock
material in proportion to the adjustment factor determined
previously. This process resulted in the “corrected curve"
of figure 8, which is the simulated gradation curve of
longwall gob from these three mine sites.

Once the standard test gradation curve was obtained,
other curves were developed using various maximum
particle sizes. Since the diameter of the test chamber is
14 in, and it has been determined that the maximum rock
piece should not be more than one-third the diameter of

Figure 8.—Average gradation curve—mean gradation curve
determined from photoanalysis of three mine sites. Shifted curve
Is averaged gradation curve shifted down for laboratory tests.
Corrected curve Is shifted gradation curve adjusted to account
for hidden rock pleces.

the chamber (23), a maximum particle size of 3.5 in was
chosen to be tested with the modeled gob gradation curve
(fig. 9). The curve was also shifted parallel to maximum
rock sizes of 3 in and 2 in to determine if there was any
size effect in these tests (fig. 9).

SOURCE MATERIAL

Three types of rock were obtained for testing. Shale
and strong sandstone were obtained from underground
coal mines where these test rocks were major components
in the gob of each mine’s longwall system. The third rock,
a weak sandstone, was obtained from a stone quarry,


10

material, The weight of the rock in the chamber is needed
to determine the void ratio. Placed on top of the rock is
a layer of cellophane film and moist, uniformly graded
sand. The sand is compacted and leveled with the top
of the chamber (fig. 12).’ The purpose of the sand is to
ensure a smooth testing surface so that load application
of the upper platen is uniformly distributed, while the cel-
lophane film minimizes sand infiltration into the simulated
gob material,

The filled test chamber is moved by forklift into the
laboratory and placed into the 1-million-Ib load frame
(fig. 13). Finally, the top loading surface of the chamber
is aligned with the top of the testing machine’s upper
platen.

Since the vertical displacement of the material exceeds
the stroke of the testing machine, the tests are conducted
in two parts. After 2 in of displacement, the test ma-
chine’s platens are extended, and the test continues for
3 additional inches or until the load reaches 500,000 Ib.
Additional stroke for the second phase of the test is ob-
tained by attaching rods between the base of the chamber
and angle irons placed over the top of the testing machine.
The load on the chamber base is then released, and a 2-in-
thick spacer is placed beneath the suspended chamber.
Finally, the loading platen with the spacer is moved up
against the chamber base, and the test is restarted.

A 458.20 MTS MicroConsole® unit is used to con-
trol the MTS 1,000-kip servocontrolled testing machine
(fig. 13). Initially, the load controller is set to a zero

‘Reference to specific equipment does not imply endorsement by the
U.S. Bureau of Mines,

Figure 12.—Test chamber filled with simulated gob and topped
with layer of sand.

reading. A light preload (<1 pct) is applied to the loading
surface of the simulated gob material to zero the displace-
ment LVDT (linear variable differential transformer) with-
in the load cell. Load is then applied at a preset ramp
rate using a specially designed program created on the
458.91 Microprofiler control unit. The program is set to
provide the desired ramping rate on the test material until
a maximum load of 500 kips is reached or the stroke of
the LVDT is exceeded. A Micromac 4,000 data acquisi-
tion system is used to monitor load, displacement, and
chamber strains, Readings are taken at 4-s intervals, with
data stored on a personal computer. Raw data are later
transferred to a Vax mainframe computer for data reduc-
tion and analysis using the RS/1 software package.

Upon completion of the load deformation test, the
chamber is removed from the testing machine and the
quarter panel of the chamber is detached. Figure 14
shows that the simulated gob material compresses about
3.5 to 4 in after a maximum load of 500,000 Ibf. The test
remains are sieved to determine particle breakage, and
various sizes of rock pieces are sampled and measured to
determine changes in particle shape.

TEST METHODOLOGY

The goal of the laboratory tests was to determine how
maximum particle size, particle shape, particle breakage,
void ratio, and rock strength affect the stress-strain be-
havior (i.e., the secant and tangent moduli) of the sim-
ulated gob material. The ultimate goal of the tests was
to develop an equation for predicting the moduli.

Table 3 shows the individual tests that were run and
the parameters that were varied. Each rock type varied in
overall particle shape and strength (see "Source Material,"
which defines these characteristics for each rock type).
Maximum size of the test material ranged from 2 to 3.5 in.
The gradation curve used for the test material was the
curve shown in figure 9, except that one test used a
uniform-size rock. The maximum load applied to the sim-
ulated gob material increased as the test series progressed
and as additional stroke capability of the test machine was
made available.

ANALYSIS TECHNIQUES

The data from the load deformation tests were analyzed
to determine several parameters, as summarized below
and in table 4.’ Some of these parameters were evaluated
at the initiation and conclusion of the test (zero and maxi-
mum load of the test) and/or at a stress level of 800 psi.
The stress level of 800 psi represents 730 ft of overburden,
which is typical of many U.S. longwalls.