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vanes" 4 Scale (m)
t) 150

Figure 9 — Map of the E-1 and E-2 panels.

seam consists of limestone overlain with a main roof of
interbedded shales, sandstones, limestones and coal (Moebs
and Barton, 1985).

The E-1 and E-2 panels. The two panels at Mine 2, where
LAMODEL was used to investigate the subsidence, are
known as the E-I and E-2 panels. These are the first and

&

‘Subsidence (m)
oe e¢ & &
a 2 B

-200 -100 ° 100 200
Distance from Center of Panel (m)

Figure 10 — The measured and fitted subsidence for the
E-1 Panel.

‘Subsidence (m)
S
Py

4124
200-150-100 50,0 $0 400150200
Distance from Center of Panel (m)

Figure 11 — The measured and fitted subsidence for the
E-2 Panel.

second panels to be extracted at the mine (see Fig. 9 and Table
1). Both of these panels advanced from the northwest towards
the southeast, and each panel had its own longitudinal line of
subsidence-monitoring stations and shared three transverse
lines that extended over both the panels and the intervening
gate road (see Fig. 9). Because these two panels share a gate
road similar to panels D-3 and D-S5, they also allow/require
the subsidence over the gate road to be adjusted by varying
the coal strength (see Table 2).

For the subsidence calculation at these two panels, a single
LAMODEL grid covered the initial half of both panels
centering on the transverse profile line closest to the start of
the panels. In the model, as in all the models in this paper, the
elastic modulus of the rock mass was set at 20 GPa and the
modulus of the coal was set at 2 GPa. The calibrated subsid-
ence for these panels is shown in Figs. 10 and 11, and the
associated calibrated parameters are given in Table 2.

Discussion

In this paper, surface subsidence from five northern Appa-
lachian longwall panels and a room-and-pillar section was
calculated in the process of evaluating the utility of using the
LAMODEL program for subsidence calculation. This num-
ber of case studies provides a fairly substantial basis for
understanding the subsidence predictive capabilities of the
program, and the evaluation process has highlighted a num-
ber of characteristics and peculiarities of subsidence predic-
tion with LAMODEL. First, it appears that the LAMODEL
subsidence calculation is not as accurate as available empiri-
cal subsidence predictive methods. The program systemati-


Legend

aa esr
Tote ysmEt=300 He
itdsmeteara
2 sete rm etenae
z
a+
Bos
3
os
os
a7
200-150-100 «5O S100 150200

Distance from Center of Panel (m)

Figure 5 — The measured and fitted subsidence for the
D-3 Panel.

Subsidence (m)
2 6 @

e

&

200 100 0 100 200 300
Distance from Center of Panel (m)

Figure 6 — The measured and fitted subsidence for the
D-5 Panel.

OOOOOoOOOOIoIt
DOOOOoOOOoo

O
O
OOOOOoOWoooo
HCG ea

Pulled Pillars

Figure 7 — Map of the C-3 panel.

subsidence were increased by decreasing the gate road coal
strength. Typically, the coal strength is initially set at 100%
of the strength determined by the Bieniawski pillar formula
(Heasley, 1998). When more subsidence is needed over the
gate roads for better calibration, the coal strength is lowered
to some percentage of the recommended Bieniawski pillar
strength (see Table 2). The calibrated subsidence for the D-
3 and D-5 panels is shown in Figs. 5 and 6, respectively.

The C-3 panel. The next panel where the measured subsid-
ence was calibrated using LAMODEL is called the C-3 panel,
which is a room-and-pillar retreat section at Mine | (see Fig.
7 and Table 1). The chain pillars in the section were typically
driven 13-m (43-ft) wide by 22-m (72-ft) long, with 5-m- (16-
ft-) wide rooms and crosscuts. The overall retreat line moved
from the southwest towards the northeast, with pillars being
extracted systematically row by row, west to east using the
split-and-fender cut sequence on a single pair of pillars at one
time. On the surface above this section, the subsidence was
‘monitored with two longitudinal survey lines and one doglegged
transverse survey line of subsidence monitoring stations (see
Fig. 7). For the subsidence calibration of this panel, the elastic
modulus of the overburden and coal were set to the same
values as previous LAMODEL runs at this mine. The cali-
brated subsidence for this panel is shown in Fig. 8 and the
associated LAMODEL parameters are given in Table 2.

on
Lagend
004
ev)
Tete a0met2 340 mre
ot Me-teasm ete zamre
Enz Tetecomerer2ure
8
503
z
B04
a
05
08
07
10 «500-0 80 100 450200280

Distance from Edge of Panel (m)

Figure 8 — The measured and fitted subsidence for the
C-3 Panel.

Mine 2

The second case study mine in this paper is a longwall
mine in Greene County in the southwest corner of Pennsyl-
vania (see Fig. 1). The mine operates in the Pittsburgh seam,
which averages 1.8-m (6-ft) in thickness and which has an
overburden between 230 and 300 m (750 and 1,000 ft) across
the property. In the study area, the immediate roof of the


cally produced subsidence troughs that were wider than
observed. Also, the initial hope that one set of regional input
parameters would be determined that would provide reason-
able subsidence prediction throughout the given area was not
achieved. The expected correlation between the geology and
the optimum input parameters was not evident in this work.
However, for a mechanics-based program, LAMODEL does
provide moderately accurate subsidence calculations. Also,
the laminated model demonstrated a considerable amount of
flexibility for subsidence fitting through varying only two
mechanical parameters, the lamination thickness and the gob
modulus. LAMODEL is one of a few programs that can even
attempt to calculate both underground stress and conver-
gence and the resulting surface subsidence.

References

Adamek, V., Jeran, P.W., and Trevits, M.A., 1987, “Prediction of
Surface Deformations over Longwall Panels in the Northern
Appalachian Coalfield,” US Bureau of Mines, 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, CO, May, 187 pp.

Heasley, K.A., and Salamon, M.D.G., 1996. “A new laminated
displacement-discontinuity program: fundamental behavior,” Pro-
ceedings of the Fifteenth International Conference on Ground
Controlin Mining, Colorado Schoo! of Mines, Golden, CO, August
43-15, pp. 111-125.

Heasley, K.A., 1988, “Computer Modeling of Subsidence and Sub-
sidence-Control Methods,” M.S. Thesis, The Pennsylvania State
University, State College, PA, August, 203 pp.

Jeran, P.W., and Barton, T.M., 1985, "Comparison of the subsidence
over two different longwall panels,” Proceedings: Mine Subsid-
ence Control, September 19, US Bureau of Mines, IC 9042, pp.
25-33.

Kratzch, H., 1983, Mining Subsidence Engineering, Springer-Veriag,
Berlin.

Moebs, N.N., and Barton, T.M., 1985, “Short-term effects of longwall
mining on shallow water sources,” Proceedings: Mine Subsid-
ence Control, September 19, US Bureau of Mines, IC 9042, pp.
13-24.

Salamon, M.D.G., 1991, “Displacements and stresses induced by
tongwall 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. 503-510.

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 Subsid-
ence due to Longwall Coal Mining using a Laminated Model,"
Ph.D. Thesis, Colorado School of Mines, Golden, CO, 218 pp.



Coal mine subsidence prediction
using a boundary-element program

K.A. Heasley and T.M. Barton

Abstract

This paper presents several case studies in which a me-
chanics-based boundary-element program is used to back-
calculate the surface subsidence associated with various
panels at several northern Appalachian coal mines. The
program used in this case study is called LAMODEL, which
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 five
longwall panels and a room-and-pillar section. The fitted
subsidence from the model is compared with the field mea-
surements and analyzed. The results from this work show that
the LAMODEL program is not as accurate as available
empirical subsidence-predictive methods; the expected cor-
relation between the geology and the optimum input param-
eters is not evident. However, for a mechanics-based pro-
gram, LAMODEL does provide moderately accurate subsid-
ence calculations, and it is one of a few programs that can
even attempt to practically calculate both underground stress
and convergence and the resulting surface subsidence.

Introduction

Historically, the surface subsidence above underground
coal mines has been predicted using profile or influence
functions that use little or no mechanics to calculate the
ground movement (Kratzch, 1983; Adamek et al., 1987;
Heasley, 1988). Without a mechanistic input, establishing
the exact seam convergence and function parameters to use in
these empirical methods has typically required extensive and
expensive field measurements to calibrate the function pa-
fameters to a specific mining area. 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.

Recently, a laminated overburden model derived from
plate mechanics was used to predict surface subsidence with
fairly good results (Salamon, 1989a, 1989b, 1991; Yang,
1992). The model has shown the capability of fitting a generic,
empirically derived subsidence curve for northern Appala-
chia (Heasley and Salamon, 1996). The combination of both
of these capabilities in a single mathematical model gives it

the potential to accurately calculate both underground stresses
and displacement and the associated surface subsidence with
the same mechanical basis. This laminated overburden model
has now been coded into a full-featured displacement-discon-
tinuity program, LAMODEL, for analyzing coal mine stresses
and displacements, as well as surface subsidence (Heasley,
1998). in this program, the various properties 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 over-
burden mechanics.

‘This paper relates the application of the laminated over-
burden in LAMODEL to subsidence prediction at several
longwall panels and a room-and-pillar section 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-type deposits. Itis primarily designed to be utilized by
mining engineers for investigating and optimizing pillar
sizes and layouts in relation to overburden, abutment and
multiple-seam stresses (Heasley, 1998). The program uses a
displacement-discontinuity variation of the boundary-ele-
ment method for determining and solving the elastic equa-
tions of equilibrium around the mine openings. LAMODEL
simulates the overburden as a stack of homogeneous isotro-
pic layers with frictionless interfaces and with each layer
having the identical elastic modulus, Poisson’s Ratio and
thickness. This “homogeneous stratification” formulation
does not require (or allow) specific material properties for
each individual layer. Yet it still provides a realistic supple-
ness to the overburden that is not possible with the classic,
homogeneous isotropic elastic overburden.

The two primary factors that influence the shape and
magnitude of the subsidence (particularly in LAMODEL) are
the gob compaction stiffness and the overburden flexural
stiffness. Therefore, the primary parameters that are adjusted
in LAMODEL for fitting the measured subsidence are 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. In the process of analyzing
the potential of LAMODEL for surface subsidence calcula-

K.A. Heasley, member SME, and T.M. Barton are mining engineers with the National Institute for Occupational Safety
and Heaith, Pittsburgh Research Laboratory, Pittsburgh, PA. Preprint number 99-181, presented at the SME Annual
Meeting, March 9-11, 1998, Orlando, FL. Revised manuscript accepted for publication November 1999. Discussion of
this peer-reviewed and approved paper is invited and must be submitted to SME prior to Sept. 30, 2000.


Sf
““*" WEST VIRGINIA

Figure 1 — Location map of the case study mines.

Sessa ga
wpa oobecssd)S:
oo

i » lag

Panel V-1
jm)
co

[ul
Oo
—~<— Face Advance

1

SstipsenesessZ
SoSSSSRnEeEe7
mene
Legend Scale (m)
+ Surface Survey Station —a|
0 100

Figure 2 — Map of the V-1 panel.

tion presented in this paper, the measured subsidence is used
to “calibrate” the model. This calibration process consists of
aninteractive trial-and-error process where the critical mode!
parameters (in this case the lamination thickness and the final
gob modulus) are initially estimated. The program is run to
Calculate the surface subsidence, the calculated subsidence is

Table 1 — Panel dimensions used in the calibration

models.
Seam
Length, Width, thickness, Depth,
Panel m m m m
vA 640 285 18 120
D3 1,250 180 18 230
os 1,050 168 18 230
C3 256 168 17 180
e1 1,430 194 18 277
E2 1,730 194 18 247

compared to the measured subsidence, the model parameters
are adjusted to improve the fit and, then, the program is run
again. This cycle continues until the calculated subsidence
fits the measured subsidence as close as desired. The result-
ing values of the critical model parameters are considered to
be “calibrated” to the given site conditions.

Mine 1

The location of the first subsidence-prediction case study
in this paper is a longwall mine in Barbour County in the
northwest corner of West Virginia (see Fig. 1). This mine
started production in 1975 with continuous miners in room-
and-pillar sections. In 1982, the first longwall was installed
and, by the time of the final subsidence monitoring in this
study (1985), the mine had successfully completed five
longwall panels (Jeran and Barton, 1985; Heasley, 1988).
The mine operates in the Lower Kittanning seam that aver-
ages 1.8 m (5.9 ft) in thickness and has an overburden
between 120 and 420 m (390 and 1,380 ft) 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.

The V-1 panel. The first panel at which the subsidence
was investigated using LAMODEL is called the V-1 panel. It
is actually the fifth longwall panel to be extracted at the mine
(see Fig. 2 and Table 1.). The panel advanced from the
northwest towards the southeast, and, as shown in Fig. 2,
there were two transverse lines and one longitudinal line of
subsidence monitoring stations over the later half of the
panel. For this initial subsidence-fitting exercise, the entire
panel was discretized into LAMODEL. The overburden was
set ata constant 120 m (390 ft), the elastic modulus of the rock
mass was set at 20 GPa, the modulus of the coal was set at 2
GPa and the coal thickness was set at a constant 1.8 m (5.9 ft).

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 param-
eter combinations is listed in Table 2 and shown in Fig. 3. The
range of parameters shown in Table 2 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 2). Therefore, at this
lamination thickness, the gob is supporting the total overbur-
den load at the middle of the panel and the flexural stiffness
of the laminations is not effectively supporting any overbur-
den load. On the other end of the spectrum, for the thickest
lamination (7.5 m), the peak gob load is only about one-si sth
of the overburden load, and the flexural stiffness of the


Table 2 — Calibrated LAMODEL parameters.
Final Peak == Average Coal strength,
Lamination gob gob gob percent of
thickness, modulus, stress, stress, Bieniawski
m MPa MPa MPa strength
Panel V-1
15 124 3.0 20 100
45 100 25 16 100
75 13805 0.4 100
Panel 0-3
15 383 57 45 100
45 372 5.4 3.6 100
75 324 43 23 100
Panel D-5
15 383 57 45 60
45 372 5.4 3.6 60
75 324 43 23 60
Panel C-3
3.0 340 42 - 100
45 293 3.3 - 100
6.0 212 1.8 - 100
Panel E-1
3.0 203 67 - 100
6.0 179 54 - 100
9.0 144 32 - 100
Panel E-2
3.0 170 5.9 - 55
6.0 149 42 - 75
9.0 84 Ww - 95

Legend

Measured #1
Measured 02

ot 15m, Ef 124 MPa
ot 4.5m, Ef= 100 MPa

at 7.5m, EF= 138 MPa

Subsidence (m)

-200 -100 O 100 200
Distance from Center of Panel {m)

Figure 3 — The measured and fitted subsidence for the
V-1 Panel

ome doovegooos9s09
Saoue Se Seeseqcesceoo09
QU [ata

Panel D-5
Panel D-3

Face Advance ——>—

Face Advance ——>-

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

laminations is supporting the other five-sixths of the overbur-
den load. Thus, for fitting LAMODEL to a given maximum
subsidence, the thinnest, most flexible laminations require
the stiffest gob, while the thickest, stiffest laminations man-
date a softer gob.

‘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 D-5 panels, and they are the first and second
panels to be extracted at Mine I (see Fig. 4 and Table 1). 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
that extends over both the panels and the intervening gate
road (see Fig. 4). Because these panels are considerably
narrower ($180 m) and deeper (>230 m) than the V-I panel,
the surface subsidence is expected to be subcritical.

For the subsidence calculation at these two panels, a single
LAMODEL grid was created that covered the initial half of
both panels. The elastic modulus of the overburden and coal
were set to the same values as used for the V-I panel.
However, the input coal strength was varied to fit the subsid-
ence over the intervening gate roads. Essentially, both the
convergence in the gate road and the associated overlying