Legend

0.2
Measured

Ee -0.4 q t= 1.5m, Ef= 124 MPa
S t= 3.0m, e ot -
o ° *
So 06 4 t= 4.5m, €f= 100 MPa Wy
3 0.8 x t= 6.0m, Ef = 69.0 MPa A 2
8 co t= 7.5m, Ef = 1.38 MPa oo
aoa °

1.2

-1.4 4 + + + + + 4

200 300 400 500 600 700 800

Distance from Start of Panel (m)

Figure 3: The measured and fitted longitudinal subsidence for the V-1 panel

calculated curves invariably show the subsidence starting some 20 to 50 m wider that the measured subsidence
with the 1.5 m laminations consistently providing the narrowest profile and closest fit to the measured subsidence

This problem, that the calculated subsidence tends to be wider than the measured subsidence, has been found
throughout the history of subsidence prediction (Heasley, 1988; Kratzsch, 1983). Generally, when using the
empirical, profile or influence-function methods of subsidence prediction, the subsidence trough is narrowed by
functionally limiting the seam convergence at the edge of the panel using various artificial or empirically-derived
parameters. In LAMODEL, where the input material properties are intended to accurately determine the scam
convergence, it is not reasonable to apply some artificial adjustment to the panel edge in order to correct the width
of the subsidence trough. Therefore, in the subsidence calculations presented in this paper, only the given in-mine

geometry was used in the subsidence calculations and only the material properties were adjusted (as described
above) in order to fit the observed subsidence.

If the only goal in this investigation of the subsidence prediction capabilities of LAMODEL was the best fit to the
subsidence profiles in Figure 2, then the 3.0 or 4.5 m laminations would probable provide the best numerical fit.
Also, if the previously determined value (Yang, 1992) of the overburden constant (w — 6.9) was utilized, the
recommended lamination thickness would be 4.2 m. However, the shape of the subsidence trough produced with
the 1.5 m laminations seems to fundamentally fit the measured subsidence better. Specifically, the 1.5 m thickness
provides a flat bottomed trough with steep sides similar to the measured subsidence. Also, for a super-critical
panel, the peak gob stress should essentially be equal to the total overburden load as with the 1.5 m laminations
(Table 1). If the width of the panel in the LAMODEL simulation were artificially narrowed, it is fairly apparent
in Figure 2 that the 1.5 m lamination thickness would provide the best fit to the measured data. But, this empirical
panel narrowing would essentially corrupt the primary in-seam modeling capabilities of LAMODEL

THE D-3 AND D-5 PANELS

The next two panels at which the subsidence was investigated using LAMODEL are known as the D-3 and 0-5
panels, and they are the first and second panels to be extracted at the mine (see Figure 4). The 1-3 panel is 180
m wide and 1250 m long with a coal thickness of 1.8 m and overburden that averages 230 m. The panel was
started on January 22, 1982 and finished on February 26, 1983 in a total of 400 days at an advance rate of 4 m per
work day. The D-5 panel is directly adjacent to the D-3 panel. [tis 168 m wide and 1050 m long with a similar
coal thickness of 1.8 m and overburden of 230 m. The D-5 panel was started on February 28, 1983 and finished
on August 7, 1983 ina total of 160 days at an advance rate of 7 m per work day. Both of these panels advanced
from the northwest towards the southeast, and each panel had its own longitudinal line of subsidence monitoring
stations and a shared transverse line which extends over both the panels and the intervening gate road (see Figure
4). Since these two panels share a gate road, they allow investigating the utility of using LAMODEL to calculate
the interactive subsidence from adjacent panels. Also, because the panels are considerably narrower (< 180m)
and deeper (> 230 m) than the V-1 panel, the surface subsidence is expected to be sub-critical



gob modulus and/or lamination thickness should be researched. More realism could be added to the model by
including the actual variable seam thickness, seam tilt and overburden in the subsidence calculation. In previous
work (Heasley, 1988), this type of realistic detail was shown to significantly increase the accuracy of subsidence
prediction. Also, the tendency of the program to systematically produce subsidence troughs which are wider than
observed needs to be addressed. In the short term, some type of “edge adjustment” might be added to the program
in order to compensate for the tendency towards overly wide subsidence troughs. Finally, additional subsidence
predictive case studies at various sites need to be performed in order to investigate the above items and to
ultimately evaluate the potential of LAMODEL for practical subsidence prediction

REFERENCES

Adamek, V., Jeran, P.W., Trevits, M.A. (1987). Prediction of Surface Deformations over [.ongwall Panels in the
Northern Appalachian Coalfield. USBM, RI 9142, 19 pp

Heasley, K.A. (1998). Numerical Modeling of Coal Mines with a Laminated Displacement-Discontinuity Code.
Ph.D. Thesis. Colorado School of Mines, Golden, Colorado, May. 187 pp.

Heasley, K.A., Salamon, M.D.G. (1996). A New Laminated Displacement-Discontinuity Program: Fundamental
Behavior. Proceedings of the Fifteenth International Conference on Ground Control in Mining, Colorado Schoo}
of Mines, Golden, Colorado, August 13-15, pp. 111-125.

Heasley, K.A. (1988). Computer Modeling of Subsidence and Subsidence-Control Methods. M.S. Thesis. ‘The
Pennsylvania State University, State College, Pennsylvania, August, 203 pp

Heasley, K.A., Saperstein, L.W. (1987). Recent Insight into Longwall Strata Movements Peduced from
Subsidence Analysis. Mining Enginecring, 39:9, pp. 872-876.

Heasley, K.A., Saperstein, L. W. (1986). Practical Subsidence Prediction for the Operating Coal Mine.

Proceedings of the 2nd Workshop on Surface Subsidence Due to Underground Mining. West Virginia University,
Morgantown, West Virginia, pp. 54-67

Jeran, P.W., Barton, T.M. (1985). Comparison of the Subsidence Over Two Different Longwall Panels
Proceedings: Mine Subsidence Control. September 19, USBM, IC 9042, pp. 25-33

Kratzch, H. (1983). Mining Subsidence Engineering. Springer-Verlag, Berlin.

Mark, C., Chase, F.E. (1997). Analysis of Retreat Mining Pillar Stability (ARMPS). Proceedings: New
Technology for Ground Control in Retreat Mining. NIOSH, IC 9446, pp. 17-34

Mark, C. (1987) Analysis of longwall Pillar Stability. Ph.D. Thesis. The Pennsylvania State University, State
College, Pennsylvania, December, 415 pp.

Salamon, M.D.G. (1991). Displacements and Stresses Induced by Longwall Mining in Coal. Proceedings of the
7th Congress of the International Society for Rock Mechanics. A.A. Balkema, Rotterdam, pp. 1199-1202.

Salamon, M.D.G. (1989a). Subsidence Prediction using a Laminated Linear Model. Proceedings of the 30th U.S.
Symposium of Rock Mechanics. A.A. Balkema, Rotterdam, pp. 03-510

Salamon, M.D. G. (1989b). Some Applications of the Frictionless Laminated Model. Proceedings of the 30th
U.S. Symposium of Rock Mechanics. A.A. Balkema, Rotterdam, pp. 891-898

Yang, G. (1992). Numerical Approach to the Prediction of Subsidence due to Longwall Coal Mining using a
Laminated Model. Ph D. Thesis. Colorado School of Mines, Golden, Colorado, 218 pp

Zipf, R.K. (1992a). MULSIM/NL Application and Practitioner's Manual. USBM, IC 9322, 48 pp.

Zipf, R.K. (1992b). MULSIM/NL Theoretical and Programmer's Manual. USBM, IC 9321, 52 pp.



Legend

Subsidence (m

-0.8 + [____ Measured
t= 15m, &f= 124 MPa
—e—t= 3.0m, Ef = 117 MPa
1.2 4 —a—t= 4.5m, Ef = 100 MPa
41 = 6.0 m, Ef = 69.0 MPa
t= 7.5m, Ef= 1.38 MPa
16 + + + +
-200 -100 0 100 200

Distance from Center of Panel (m)

Figure 5: The measured and predicted transverse subsidence for the D-3 panel.

A close exainination of Figures 6 and 7 reveals a number of observations. First, the measured subsidence appears
to be sub-critical as suggested by the panel dimensions and confirmed by the narrow, V-shaped subsidence trough
and the limited amount of subsidence (0.6 m) as compared to the supercritical V-1 panel (1.2 m). Also. as in the
previous measured curves, the subsidence shows various anomalies that are not consistent with a homogeneous
overburden, horizontal seam, constant depth, and constant seam thickness. In particular, the transverse subsidence
in Figure 6 is unsymmetric about the center of the panel and the longitudinal subsidence in Figure 7 shows
considerable variability along the bottom of the subsidence trough. In contrast, the calculated subsidence curves
are symmetric about the panel centerline and very smooth

{n comparing the calculated (or fitted) subsidence with the measured subsidence, a number of observations can
be made. First, it is evident that the maximum subsidence for the calculated curves was calibrated to
approximately 0.63 m. Therefore, all of the calculated curves converge at the center of the subsidence trough at
the same point on the measured subsidence curve. {n general, the thickest 7.5 m lamination appears to pravide
the best fit to the measured subsidence in both the transverse and longitudinal cross-sections (although it is
doubtful that any simplistic subsidence prediction technique can provide a good fit to the highly variable
subsidence along the bottom of the longitudinal profile). In contrast to the measured subsidence, the thinnest
1.5 m laminations generate a transverse subsidence trough which is flat along the bottom and appears super-
critical. At the edges of the subsidence troughs, the calculated curves show the subsidence starting some 20 to
50 m wider than the measured subsidence as was the case with the V-1 panel.

oq Tegend
0.4 Measured
1.5 m, Ef = 380 MPa
— 0.2 + t= 4.5m, Ef= 372 MPa
o t= 7.5 m, Ef = 324 MP;
8 034
c
3
2 04d
3
B 054
0.6 4
-0.7 + —+ —+ + + + +
200-150-100 -60 0 50 100 150 200

Distance from Center of Panel (m)

Figure 6: The measured and fitted transverse subsidence for the D-3 panel


Legend Y

Sortace Survey Staton

Face Advance

Panel 0-5
P

STS ES aOLO eco Hoo SAcCGr Lice

Face Advance ——>-

SECS psn ero aa

Ai tale POS
ial persis)

Pe aararare|
igenclsaisstelelel

a 153
Tereraloitat Reliable cece eiser

Figure 4: Map of the D-3 and D-5 panels.

For the subsidence calculation at these two panels, a single LAMODEL grid 300 elements wide by 300 elements
high with 3 mi elements was created. This grid covered the initial half of both panels. In the model, the
overburden was set at a constant 230 m with a pressure gradient of 0.025 MPa/m. The clastic modulus of the rock
mass was set at 20) GPA and the modulus of the coal was set at 2 GPa. Also, the coal thickness was set al a
constant 1.8 m, and the strength of the coal in the scam was set such that the pillar strengths. ntially followed
the Mark-Bieniawsk1 formula (Mark and Chase, 1997) using an elastic, perfectly-plastic material model (Heasley,
1998). For the subsidence calculation, the off-seam grid capability of LAMODEL was used to calculate the
displacement on the surface every 6 m along lines coincident with the surface survey lines. Once again, the first-

order, free-surface effects were included by simply doubling the surface subsidence as calculated in the infinite
media.

In the first attempt at calculating the subsidence for the D-3 panel, the optimized parameters from the previous
fitted subsidence at the V-1 panel (Table 1) were used. The results of this initial subsidence calculation are shown
in Figure 5, and basically, the V-1 parameters greatly over-predict the amount of subsidence. This result is a little
disturbing. Since these panels are only a few miles apart, it was hoped that the same set of material parameters
would provide reasonable approximations to the subsidence at all of the panels. The observation that the
optimized parameters from the V-| panel do not provide a reasonable fit to the subsidence from the D-3 panel
evokes a couple of possible explanations. first, the geology may have changed between the panels (a reasonable
conclusion since the depth of overburden is so different). And indeed, further investigation indicates that there
is approximately 10% competent rock (sandstone and limestone) over the V-1 panel in contrast to 37% competent
tock over the D-3 and D-5 panels (Mark, 1987; Jeran and Barton, 1985). This increase in the percentage of
competent rock may result in an increase in gob bulking factor and/or overburden stiffness and account for the
reduced subsidence at panel D-3. Also. it must certainly be considered that the mechanical overburden model
used in LAMODEL is not sufficiently realistic for accurate subsidence prediction at sites with widely varying
geometries (widths and depths), but that is the purpose of this case study

Next, in order to optimize the fit of the calculated subsidence to the measured subsidence, the final gob modulus
was increased for three of the lamination thicknesses. The results of this optimization process are shown in
Figures 6 and 7, and the optimized combinations of lamination thickness and final gob modulus are listed in Table
2 [n general, the final gob modulus was increased approximately threefold in order to limit the maximum
calculated subsidence and provide the best fit to the measured data

TABLE 2
CALIBRATED LAMODEI. PARAMETERS FOR PANEL D-3
Lamination Final Gob Peak Gob Average Gob
‘Thickness (m) Modulus (MPa) Stress (MPa) Stress (MPa)
1S 383 5.7 45
— ~ _ _
45 372 5.4 6
7.5 324 43 2.3



Legend
——Measured
Q-t= 15m, Ef= 380 MPa
eh = 45m, Ef 372 MPa
a t= 7.8m, Ef = 324 MPa

Subsidence (m
S
a

-200 -100 0 100 200 300 400 500

Distance from Start of Panel (m)

Figure 9: The measured and fitted longitudinal subsidence for the D-5S panel.

of the calculated subsidence as shown in Figure 8, particulary for the 4.5 and 7.5 m laminations. The left side of
the measured subsidence trough also exhibits a wider profile which is closer to the natural profile calculated by

LAMODEL. The reason that the subsidence at the left side of the measured profile is wider than the previous two
panels is not evident from the available data.

In both figures 8 and 9, as in the figures for pancl D-3, it appears that the 7.5 m laminations provide the best fit
to the measured subsidence in comparison to the thinner laminations. This lamination thickness of 7.5 m
corresponds to a value of 7.2 for the inherent overburden constant, w, proposed by Yang (1992). This value agrees
very well with the average value of 6.9 previously determined by Yang (1992), and supports the premise that the
optimum value of w for subsidence prediction is a constant (or narrow range). By asserting that w is a constant,
it is implied that the best lamination thickness to use for subsidence prediction must increase with increasing
depth. Considering that the laminated overburden model essentially provides a simplified approximation to the
actual bedded behavior of the overburden stratigraphy and that the lamination thickness parameter essentially
functions as a crude measure of the vertical distance between the functional horizontal slip planes in the
overburden, it seems reasonable that as the overburden, or area-of-interest, increases that the effective slip plane
distance and hence the lamination thickness should increase. The same result, that the optimum lamination
thickness is proportional to the area-of-interest, was found for stress modeling where thinner laminations were best
for modeling the small scale inter-seam stresses but thicker laminations were optimum for modeling wide area
longwall abutment stresses (Heasley, 1998). This hypothesis that the lamination thickness needs to increase with
increasing depth or scale seems physically reasonable, however, it is contradictory to the initial hypothesis at the
beginning of this study that the lamination thickness should be an inherent constant of the overburden.

CONCLUSIONS

In this paper, the laminated overburden model with calibrated properties was demonstrated to easily provide fairly
accurate subsidence predictions over several longwall panels. Also, the laminated model demonstrated 4
considerable amount of flexibility for subsidence fitting through varying only two mechanical parameters, the
lamination thickness and the gob modulus. And, since the laminated overburden model in this case study was
implemented as part of a full-featured, displacement-discontinuity program (LAMODEL), the asymmetrical
subsidence associated with multiple panels and yielding gateroads, which is traditionally difficult to predict, was

imulated through realistic failure and yielding of the gate road pillars. This demonstration of the
es of the laminated overburden model is a major step towards the goal of developing a practical,
mechanics-based, subsidence predictive method which would allow the determination of site-specific parameters
from the fundamental properties of the overburden and thereby minimize the amount of required calibration work

However, even though the capabilities of LAMODEL are promising, a number of items, or areas, need to be
investigated before practical subsidence prediction with the program is a reality. The question of whether the
lamination thickness should be an overburden constant or proportional to the depth needs to be further examined
Also, the possibility of a correlation between the amount of competent rock in the overburden and the optimum


PAPER NUMBER: USA-907

SUBSIDENCE PREDICTION USING A
LAMINATED, BOUNDARY-ELEMENT PROGRAM

Keith A. Heasley ' and Timothy M. Barton’

‘ National Institute for Occupational Safety and Stealth, Pittsburgh Research Laboratory,
P.O. Box 18070, Pittsburgh, Pennsylvania, 15236-0070, USA

ABSTRACT

Historically, the surface subsidence over underground coal mines has been predicted using empirical profile or
influence functions which have little or no connection to the actual mechanics of the subsidence. Without a
mechanistic basis, establishing the exact site-specific parameters to use in these empirical methods has been
problematic. A practical subsidence predictive method based on mechanics has the appealing capability of
allowing the determination of site-specific parameters from fundamental properties of the overburden with
minimal field calibration work. This paper presents a case study where a mechanics-based, boundary-element
program is used to calculate the surtace subsidence associated with several panels of a Northern Appalachian
longwail coal mine. The program used in this case study is called LAMODEL, and it incorporates a frictionless,
laminated overburden into a general purpose displacement-discontinuity code primarily designed for calculating
the stresses and displacements in coal mines or other thin seam or vein type deposits. In this paper, the program
is used to calculate both the underground convergence and the resulting surface subsidence at three longwalls
The subsidence results from the model are compared with field measurements and analyzed The results from the
case study in this paper demonstrate that the laminated model with calibrated properties can easily provide fairly
accurate subsidence predictions and is fairly flexible for fitting measured subsidence. However, additional
subsidence predictive case studies are recommended in order to ultimately evaluate the potential of the laminated
overburden model tor practical subsidence prediction

KEYWORDS

Case History, Coal, Computer Program. Design, Discontinuities, Mining, Numerical Analysis, Stress, Subsidence

INTRODUCTION

Historically, the surface subsidence over underground coal mines has been predicted using profile or influence
functions which have little or no connection to the actual mechanics of the ground movement (Heasley, 1988:
Adamek et al., 1987; Kratzch, 1983). Without a mechanistic basis, establishing the exact seam convergence and
function parameters to use in these empirical methods has typically required extensive and expensive field
measurements in order to calibrate the function parameters to a specific mining area. Recently, a laminated
overburden model which is derived from plate mechanics has been used to predict surface subsidence with fairly
good results (Salamon, 199], 1989a. 1989b; Yang. 1992), and has shown the capability of fitting a generic,
empirically-derived subsidence curve for Northern Appalachia (Heasley and Salamon, 1996). This same lammmated
overburden model has currently been coded into a full-featured displacement-discontinuity program, LAMODEL,
for analyzing coal mine stresses and displacements, as well as surface subsidence (Heasley, 1998). In this
program. the various propertics of the seam and gob materials are mechanically combined with the laminated
overburden properties to realistically calculate seam stresses and convergence, This calculated seam convergence
can then be projected to surface subsidence using the laminated overburden mechanics. Since the laminated



0.1 4 Legend
0.2 Measured
“ —g t= 1.5m, Ef= 380 MPa
E 03 T owt? 4.5m, Ef= 372 MPa .
8 04+ > at = 7.5 m, Ef = 324 MPa
o
2-054
a
3 054 by
O74
0.8 4
0.9 —t —t + + + +
-200 -100 0 100 200 300 400 500

Distance from Start of Panel (m)

Figure 7: The measured and fitted longitudinal subsidence for the D-3 pancl

Next, the calibrated parameters from the D-3 panel were used to predict the subsidence at the D-5 panel. In this
final subsidence prediction process with adjacent panels, the strength of the coal in the intervening pate road was
varied in order to help fit the subsidence over the gate road, even though the gob moduli and lamination
thicknesses were held consistent with the calibrated values from the previous D-3 panel. Ultimately, the best fit
was found with coal that yielded at 60% of the nominal Mark-Bieniawski coal strength (Mark and Chase. 1997)

The results of the subsidence calculation for the D-5 panel are shown in Figures 8 and 9, and in general. the
calculated subsidence matches the measured subsidence fairly well. In particular, the calculated subsidence in the
transverse profile in Figure 8 has about the same maximum subsidence as the measured profile, and the sides of
the calculated subsidence trough align well with the measured subsidence. In fact, the calculated subsidence for
the left side of the transverse profile in the D-5 pancl fits better than the original calibrated curves in Figure 6.
Similarly, for the longitudinal profile in Figure 9, the maximum calculated subsidence approximates the maximum
measured subsidence, and the calculated subsidence at the end of the panel aligns well with the measured
subsidence at the end of the panel.-

One of the main reasons that the calculated subsidence fits so well is that the measured transverse subsidence
profile is “wider” than the previous measured profiles. On the right side of the measured profile in Figure 8, the
additional width, or spread, of the trough is attributed to convergence in the gateroad between panel D-3 and D-S
In LAMODEL, this spread of the subsidence profile is realistically modeled by convergence of the gate road
through failure and yielding of the gate road pillars. And indeed, the modeled gateroad failure improves the fit

0 meee — rr “]
Legend
“0.1 Measured
£ -0.2 4
8 -034
€
3
g 044
a
3
nM 05 4+
0.6 +
-0.7 + +— +— +
+200 -100 Q 100 200 300

Distance from Center of Panel (m)

Figure 8: The measured and fitted transverse subsidence for the D-5 panel

ne


TABLE 1!
CALIBRATED LAMODEL PARAMETERS FOR PANEL V-1

Lamination Final Gob Peak Gob | Average Gob
Thickness (m) Modulus (MPa) Stress (MPa) Stress (MPa) 4
1.5 124 3.03 2.05
3 104 2.52 r 56
: 45 100 2.07 1.23
_ 6.0 69.0 131 0.83
1S 1 38 0.48 0.37

subsidence trough is not perfectly flat in the middle as an idealistic super-critical model might sugyest (Kratzch.
1983). Also, in all three measured curves, the subsidence shows anomalies that are not consistent with a
homogeneous overburden, horizontal seam, eonstant depth, and constant seain thickness. In particular, the number
2 transverse line and the longitudinal line show considerable variability along the bottom of the subsidence trough
In a theoretically perfect situation, the subsidence curves for the two transverse lines should be identical, when
in reality, they show considerable differences. In contrast, the calculated subsidence curves in Figures 2 and 3 are
very smooth and consistent. Obviously, in the real world, natural variations in geology, depth, seam thickness,
etc., will cause anomalous variations in the subsidence. However, because LAMODE.1. assumes a constant seam
thickness, a constant depth (for subsidence prediction), a level seam and a homogeneous overburden, the
subsidence curves it produces will generally be very smooth and consistent, and will not exactly match every
anomalous variation in the measured subsidence curves. In general. any idealized subsidence prediction technique
will produce smooth, consistent subsidence and will not exactly match the actual anomalous measured subsidence:
(However, in a previous subsidence prediction study at this site (Heasley, 1988, Heasley and Saperstein, 1987,
1986), the use of more realistic, seam thickness, overburden depth and seam ult was shown to significantly
improve the fit of the calculated subsidence.)

Next, some gencral comparisons between the measured and calculated (or fitted) subsidence can be made. In the
center of the subsidence trough, the maximum subsidence for the calculated curves was calibrated to
approximately 1.2 m. ‘Thus, all of the calculated curves were forced to have the same value of maximum
subsidence, 1,2 m, which appears to be a reasonable compromise between the maximum subsidence values of the
two measured cross-sections. Amongst the various lamination thicknesses, the thinnest 1.5 m laminations appear
to give the best shape for the bottom of the subsidence trough in the transverse profiles (see Figure 2) and provide
the most reasonable gob stress (see Table 1), while the thicker laminations, 6.0 and 7.5 m, appear to provide the
best shape for the bottom of the longitudinal profile (see Figure 3). At the edges of the subsidence troughs, the

Legend
O24 Measured #1
_— — ~Measured #2
is t= 4.5m, Ef=124MPa
2 o6 bf t=30m, Ef= 117 MPa
5 t= 4.5 m, Ef = 100MPa
2 t= 6.0 m, Ef = 69.0 MPa
3 t= 7.5m, Ef = 1.38 MPa
3
a 4
14 + +
-200 -100 0 100 200

Distance from Centerline (m)

Figure 2: The measured and fitted transverse subsidence tor the V-1 panel



subsidence calculation, the off-seam capability of LAMODEL was used to calculate the displacement at the
surface every 6 m along lines coincident with the surface survey lines. The first-order, free-surface effects were

included in this model by simply doubling the surface subsidence as calculated in the infinite media, identical to
the process used in Yang's (1992) influence-function derivation.

igo ar -
(iiss nose
oO

0

ML
Do
lgpe

~t— -Face Advance

Panel 0-5
Toa Wea 1.

Legend }
+ Suitace Survey Station

Liu
° too N

Figure |: Map of the V-1 panel.

The two primary factors which influence the shape and magnitude of the subsidence (particularly in LAMODEL)
are the gob compaction stiffness and the overburden flexural suffness. Therefore, the primary parameters which
are adjusted in LAMODEL for fitting the measured subsidence“re the final gob modulus (E,) which is used to
control the gob stiffness, and the lamination thickness (t) which is used to control the overburden stiffness (as
discussed in Ileasley (1998), the lamination thickness and the overburden modulus affect the overburden behavior
in essentially the same manner; therefore, in order to simplify the calibration process, the overburden modulus was
held constant while only the lamination thickness was varied). The gob material model used in the following
subsidence calculation is the strain-hardening gob as described in Zipf (1992a and 1992b). In all of the
LAMODEL. subsidence runs, the initial gob modulus (E,) is held constant at 0.7 MPa: the virgin vertical stress (0, )
is set at 27.6 MPa; and the gob height factor (n) is set at unity. With these three parameters fixed, raising or
lowering the value of the final gob modulus effectively raises or lowers the modulus of the gob

In this process of analyzing LAMODEL for surtace subsidence calculation, the first panel was used to “calibrate”
the model. This calibration process consisted of an interactive trial-and-error process where: the critical model
parameters (in this case the lamination thickness and the final gob modulus) were initially estimated, the program
was tun to calculate the surface subsidence, the calculated subsidence was compared to the measured subsidence.
the model parameters were adjusted to improve the fit, the program was run again, etc. This cycle continues until
the calculated subsidence fits the measured subsidence as close as desired

For this first calibration process on the V-1 panel. it was found that a wide range of lamination thicknesses and
final gob moduli combinations could be fit equally well to the measured subsidence, A distributed sample of these
parameter combinations ts listed in Table | and shown in Figures 2 and 3. The range of parameters shown in
Table | covers the complete spectrum of reasonable behavior for this panel. For the thinnest laminations (1.5 m),
the peak gob load is essentially equal to the overburden load (see Table |); therefore, at this lamination thickness,
the gob is supporting the total overburden load at the middle of the panel and the flexural stiffness of the
laminations is not effectively supporting any overburden load. On the other end for the spectrum, for the thickest
lamination (7.5 m), the peak gob load is only about 1/6 of the overburden load. and the flexural stiffness of the
laminations is supporting the other 5/6 of the overburden load. Thus, for a given maximum subsidence, the

thinnest, most flexible laminations are associated with the stiffest gob, while the thickest, stiffest laminations are
associated with the softest gob

Looking at Figures 2 and 3, a number of observations can be made. First, the nature of the measured subsidence
is worth noting [n the two measured cross-sections (sce Figure 2), the subsidence flattens considerable in the
middle of the tough and appears to be super-critical as suggested by the panel dimensions Although. the



overburden model has been shown to accurately calculate both underground displacements and stress (Heasley
and Salamon, 1996), and surface subsidence, in separate instances, the combination of these capabilities in the
LAMODEL program gives it the potential to accurately calculate both underground stresses and displacement,
and the associated surface subsidence with the same mechanical model. Using an accurate mechanical basis,
surface subsidence in different mining areas could conceivable be calculated {rom fundamental properties of the
overburden, and would require minimal field calibration work. The following paper relates the application of the
laminated overburden in LAMODEL to subsidence prediction at several longwall panels in Northern Appalachia
and provides an initial evaluation of the program's accuracy and utility for subsidence prediction.

THE LAMODEL PROGRAM

LAMODEL is a PC-based program for calculating the stresses and displacements in coal mines or other thin seam
or vein (ype deposits. It is primarily designed to be utilized by mining cnyineers for investigating and optimizing
pillar sizes and layouts in relation to overburden, abutment and multiple-seam stresses (Heasley, 1998). The
program use a displacement-discontinuity variation of the boundary-clement method and a Successive Over-
Relaxation (SOR) iterative technique for solving the elastic equations of equilibrium around the mine openings
LAMODEL simulates the overburden as a stack of homogeneous isotropic layers with frictionless tuterfaces, and
with each layer having the identical clastic modulus. Poisson's Ratio. and thickness. This “homogeneous
stratification” formulation does not require specific material properties for each individual layer, and yet it still
provides a realistic suppleness to the overburden that is not possible with the classic. homogeneous isotropic
clastic overburden. LAMODEI. was originally derived in 1994 and is written in C++

The LAMODEL program has numerous features including: single and muluple seam simulations, numerous
individual excavation steps: seam level convergence and stress calculations. off-seam convergence and stress
calculations; user-defined overburden properties: up to 26 different in-seam materials from 3 different material
models (elastic. elastic-plastic, strain-softening, bilinear strain-hardening and exponential strain-hardening); user-
defined convergence criteria; and up to a 300 by 300 grid size. Also, LAMODEL can include effects from a
traction-free surface for shallow seams and can include the effects from a variable surface topography

THE MINE

The location of this subsidence case study is a longwall mine in Barbour county in the northwest corner of West
Virginia. This mine started production in 1975 with continuous miners in room-and-pillar sections. [n 1982. the
first longwall was installed and by the me of the final subsidence monitoring in this study (1985) the mine had
successfully completed 5 longwall panels (Heasley. 1988). The mine operates in the Lower Kittanning seam
which averages 1.8 m in thickness and which has an overburden between |20 and 420 m across the property. The
immediate roof of the seam consists of a thinly laminated, sandy-shale overlain with a main roof of interbedded
sandstones, shales and limestones. The mine area is also noted for high horizontal. in situ stresses. At this mune,
the subsidence over the first. second and fifth panels was monitored with surface survey stations

THE V-1 PANEL

The first panel at which the subsidence was investigated using LAMODEL ts called the V-1 panel, and it ts
actually the fifth longwall panel to be extracted at the mine (see Figure 1). The panel is 285 m wide and 640 m
long with a coal thickness of 1.8 m and overburden that averages 120 m. The panel was started on June 15, 1984
and finished on October 19. 1984 ina total of 126 days at an advance rate of 7 m per work day. The panel
advanced from the northwest towards the southeast, and as shown in Figure |, there were two transverse lines and
one longitudinal line of subsidence monitoring stations over the later half of the panel

For this intial subsidence fitting exercise, the entire panel was discretized into a LAMODEL grid 150 elements
wide by 270 elements high using 3 m elements and rigid boundary conditions on all four sides. The overburden
was set ata constant 120 m with a pressure gradient of 0.025 MPa/m, The clastic modulus of the rock mass was
sct at 20 GPA and the modulus of the coal was set at 2 GPa. The coal thickness was set at a constant 1.8 m, and
the strength of the coal in the seam was set such that the pillar strengths essentially followed the Mark-Bieniawskt
formula (Mark and Chase, 1997) using an elastic, perfectly-plastic material model (Heasley, 1998). For the

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