This gob model also requires the gob height factor n.
This factor increases the effective seam thickness for the
element and reduces its stiffness in the BEM program
workings.

Strain Hardening for Gob (Model 5)
This model allows the gob material to increase in stiff-

ness as it consolidates under increasing load. As derived
in the theoretical and programmer’s manual, the stress-

strain relationship is
E, Ep-E

at] POY | Nexp [EFT F] |P |_|, 5)
a |Ep-Ey no, ||t

o=
where _E,_= initial modulus,
Ep = final modulus,
a, = virgin vertical stress,
D = seam closure,
t = seam thickness,
and n = gob height factor.

The parameter (Ep - E,)/(n o,) controls the degree of
nonlinearity in the model. As shown in figure 13, input
parameters are E,, E,, o,, n, and v. As with the prior

models, scaling the above stress-strain relation for the nor-
mal direction of the element by a factor of 1/[2(1 + v)]
provides appropriate stress-strain relations for the tan-
gential directions of the element.

Table 2 summarizes the basic input parameters for
these six material models and the input format required.
For each material, MULSIM/NL reads one record con-
taining the appropriate parameters in the proper format
for that material. The value of the first parameter directs
the program to the proper stress-strain model for each
material defined. For the six models currently permitted,
the assignments are 1—linear elastic coal, 2—strain-
softening coal, 3—elastic-plastic coal, 4—bilinear gob, 5—
strain-hardening gob, and 6—linear clastic gob.

The control parameter example shown in figure 8 uses
five materials. The first, material A, is linear elastic coal
with a Young’s modulus of 500 MPa and a shear modulus
of 200 MPa. Material B is also linear elastic coal, but the
moduli have half the values as material A. In effect,
elements and blocks composed of material B behave as if
they were made of material A at 50% extraction. Mate-
rials C and D are elastic-plastic coal, with yield stresses at
10 and 20 MPa, and yield strains at 0.020 and 0.040,
respectively. Once they yield, the stress cannot increase
further. Poisson’s ratio is 0.25 for both materials. The
initial modulus is 500 MPa for both C and D (10.0/0.020
or 20.0/0.040). Finally, material E is linear elastic gob
with a Young’s modulus and shear modulus of 50 and 20
MPa, respectively. The gob height factor is 4, which
implies that the gob thickness is four times the coal seam
thickness defined later.

Table 2.—Material model parameters and material property array EPROP structure

Model 1 2 3 4 5 6
7... near elastic coal- Young's ‘Shear modulus NAP .....-..-0s NAP seeseee NAD.
(1). modulus (E). _(G).
2... Strain-softening Peak stress .. Peak strain... Residual stress... Residual Poisson's ratio
coal-(2). : strain, W.
3... Elastic plastic coal- do... dO... Plastic modulus .. Poisson's ratio NAp.
@. Ww.
4... Bilinearhardening _—Offset stress... Offset strain .. Hardening modu... do. Gob height fac-
gob-(4). lus. tor (n).
5... Strain hardening Initial modulus Final modulus Final stress (c,) .. Gob height Poisson's ratio
gob-(6). . &). factor (n). W.
6... Linear elastic gob- Young's Shear modulus Gob height factor. NAP ........ Nap.
©. modulus (E). (6). ().
NAp Not applicable.

NOTE.—For these 6 material models, there are no parameters 7 through 10.


USBM MULPLT OF multism.fmi.

MULTIPLE SEAM LONGWALL PANELS

TOTAL NORMAL STRESS-Z DIRECTION MINING STEP 1
xmax= 1882.4
ymax= 1582.4

USBM MULPLT OF multism.fm2
MULTIPLE SEAM LONGWALL PANELS

TOTAL NORMAL STRESS-Z DIRECTION MINING STEP = i
xmin= 382.4 xmax= 1882.4
ymax= 1582.4 ymax= 1582.4

yeni

26.700

24126

21.553

18.980

16.406

13.833

11.260

8.686

64113

3.540

0966

24,600

22.439

19.679

17.219

14.758

12.298

9.838

7.377

4917

2.457

0.003

Figure 32.—Multiple-seam mining example—normal stresses. Top, Upper seam; bot-
tom, lower seam. Stresses are in megapascals. Postprocessor program MULPLT/NL

generates these computer drawn plots.


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Figure 37.-Step 2Fine-mesh section of input file for random room-and-pillar mining example.



fine-mesh boundary. Figure 6 (middle) shows how each
coarse-mesh block is subdivided into a five by five array of
fine-mesh clements. Finally, as shown in figure 6 (bot-
tom), material properties are assigned with a letter code
to each fine-mesh element. As in the coarse-mesh, the
label 1 means an open element, and E represents gob.
Material A is for linear elastic coal, while materials C
and D are for coal materials with a low- and high-yield
strength, respectively. Notice how the model pillars are
constructed with low-yield-strength material in the outer
elements and linear elastic elements in the core.

An important choice in setting up a MULSIM/NL
model is the size of the coarse- and fine-mesh grid areas.
Unfortunately, each problem differs significantly, and no
definite guidelines exist. The fine-mesh should cover the
area of interest so that MULSIM/NL provides stress and
displacement calculations with sufficient detail and accu-
racy. However, the coarse-mesh serves a slightly different
purpose than the fine mesh. In BEM programs like
MULSIM/NL, the in-seam material outside the coarse-
mesh area is completely rigid (i.e., it has infinite stiffness).
Therefore, stress and displacement calculations in blocks
or elements near the external boundary of the model have
very low accuracy due to the effect of the infinitely stiff
external in-seam material. The coarse-mesh blocks act as
a buffer between the infinitely stiff model boundary and

the fine-mesh area where computational accuracy is
desired. Good modeling practice with MULSIM/NL
requires at least three rows (and preferably ten rows) of
coarse-mesh blocks beyond the fine-mesh area to keep the
infinitely stiff external boundary at bay.

To summarize, the basic MULSIM/NL modeling proc-
ess requires the following steps:

Start with an idealized mine plan.
Choose an element and/or block size.
Overlay a coarse-mesh grid.
Assign material properties to coarse-mesh blocks.
Subdivide coarse-mesh blocks within fine-mesh
boundary into elements.

« Assign material properties to fine-mesh elements.

The example problem uses five different in-seam materials
(A through E) whose properties will require definition in
an actual MULSIM/NL input file. These discussions have
illustrated the relationship between an actual mine plan
and the coarse- and fine-mesh boundary-element models
used to approximate it. Knowing something about these
grids and their creation should make the following detailed
discussions of the actual MULSIM/NL input file more
understandable.

INPUT FILE STRUCTURE FOR MULSIM/NL

INPUT FILE SECTIONS

As shown in figure 7, a basic MULSIM/NL input file
has three parts: a control section, the fine-mesh geometry,
and the coarse-mesh geometry. Figure 8 shows an actual
input file for the sample problem discussed in the prior
section that illustrates this basic three-part structure again.
The control section defines all the basic variables for
MULSIM/NL, such as problem size, material properties,
in situ stress fields, and seam orientation. The fine-mesh
section defines geometry and assigns properties to a sub-
array of fine-mesh elements within the coarse-mesh blocks.
The coarse-mesh section defines the mine geometry and
assigns material properties to an array of coarse-mesh
blocks that comprise the overall mine model.

Prior discussions covered the basic modeling process
with MULSIM/NL and the creation of the coarse- and
fine-mesh data arrays. Again, figures 5 and 6 show this
process. The coarse-mesh array shown in figure 5 (bot-
tom) becomes the coarse-mesh section of the input file
shown in figure 8. Similarly, the fine-mesh array shown in
figure 6 (bottom) becomes the fine-mesh section of the
input file.

MULSIM/NL also has multiple mining step and
multiple-seam capabilities. Utilization of these options
changes the input file structure as shown in figures 9, 10,
and 11. Variables within the control section will change in
ways discussed later. Figure 9 shows the input file struc-
ture for a single-seam, multiple mining step problem.
Notice how this input file structure has changed from the
single-seam, single-step input file shown in figure 7. The
fine- and coarse-mesh geometry sections are repeated for
all subsequent mining steps. Each mining step changes the
fine- and/or coarse-mesh geometry array from the prior

CONTROL SECTION

FINE MESH GEOMETRY
SEAM 1 STEP 1

COARSE MESH GEOMETRY
SEAM 1 STEP 1

Figure 7.MULSIM/NL input file structure for single-seam,
single-step problem.


To run MULPLTPC, the user should first change to
the appropriate directory and then type the command
MULPLTPC (return). The rest is self-explanatory. As
with the main program MULNLPC, a small and large ver-
sion exists for use on systems with either 4 or 8 Mb
of RAM. The same limits on the number of fine-mesh

elements apply. To obtain a hardcopy of the color output
from MULPLTPC, the user must first install appropriate
software with a screen capture utility that can drive the
available rasterizing color printer. The previous section on
“"MULSIM/NL PRACTICAL EXAMPLES" shows hard-
copy of output produced by this postprocessor.


APPENDIX.—SPECIAL INSTRUCTIONS FOR PERSONAL COMPUTER
VERSION OF MULSIM/NL

OVERVIEW OF MULSIM/NL ON A PC

This appendix provides additional information necessary
to run MULSIM/NL on a personal computer (PC). The
U.S. Bureau of Mines downloaded this program to the PC
to make it more readily available to the mining industry.
In addition, the Bureau developed preprocessor and post-
processor programs to help create input files and examine
graphical output from MULSIM/NL in a PC environ-
ment. The PC-based version of MULSIM/NL contains
three parts: The main BEM analysis program called
MULNLPC, a simple preprocessor called MULPREPC,
and a graphical postprocessor called MULPLTPC. Func-
tionally and operationally, the PC version of MULSIM/NL
is almost identical with its predecessors that run in a
mainframe or workstation environment. MULNLPC and
MULPLTPC have small and large versions for use on
PC’s with 4 or 8 Mb of random access memory (RAM).
The smaller version can handle a model with 110 by 110
fine-mesh elements, whereas the larger version has
capacity for 150 by 150 fine-mesh elements.

Minimum hardware requirements for the PC version of
MULSIM/NL include (1) a 386 processor with a 387 math
coprocessor, (2) 4 Mb of RAM for the small memory ver-
sion and 8 Mb of RAM for the large memory version, and
(3) a VGA or SVGA color monitor. In addition, if hard-
copies of the color output from the postprocessor
MULPLTPC are desired, software with a screen capture
utility and a rasterizing color printer are required.
Various software vendors market programs with screen
capture utilities, including Pizazz Plus, PC Paintbrush, and
Corel Draw. Similarly, many color raster printers such as
the Hewlett-Packard Paintjet or the Tektronix Color
Image Printers are available.

In developing the PC version of MULSIM/NL, Bureau
researchers used the Microway Inc., Kingston, MA, NDP
FORTRAN Compiler to generate an executable of
MULNLPC, MULPREPC, and MULPLTPC. This com-
piler contains a royalty-free disk operating system (DOS)
memory extender that gives the programs access to mem-
ory beyond the normal 640 Kb. This memory extender is
linked into the executable. Other loaded memory man-
agers, memory extenders, and memory resident programs
will interfere with the Bureau programs! The Microway
compiler also has its own royalty-free graphics library that
was used to generate the graphics in MULPLTPC.

Before using the PC version of MULSIM/NL, the
CONFIG.SYS file may require slight modification to
include these lines.

FILES =30
BUFFERS =32

Make sure that other memory managers, memory extend-
ers, and memory resident programs in the CONFIG.SYS
and/or the AUTOEXECBAT files are disabled. After
making these kinds of modifications, reboot the system,
and then the MULSIM/NL programs are ready to run on
the PC.

CREATING AN INPUT FILE WITH THE PRE-
PROCESSOR PROGRAM MULPREPC

An earlier section of this report, "INPUT FILE
STRUCTURE FOR MULSIM/NL," discusses the three
parts toa MULSIM/NL (or MULNLPC) input file, name-
ly the control section, the fine-mesh geometry, and the
coarse-mesh geometry as shown in figure 7. The preproc-
essor MULPREPC helps generate the control section of
this input file. The control section defines all the basic
variables for MULSIM/NL, such as problem size, material
properties, in situ stress fields, and seam orientation.
MULPREPC creates a MULSIM/NL input file and places
these variables in their proper position, freeing the user
from this tedious task. MULPREPC only makes the con-
trol section of the input file. The user must then use a
text editor or word processor to create the fine-mesh and
coarse-mesh sections of the MULSIM/NL input file.

The PC version of MULSIM/NL has the same input
parameters as described earlier in this report, with two
minor exceptions. First, the PC version is restricted to two
seams. Therefore, the variable NSEAM, defined in record
2 of the input file, must be the integer 1 or 2. Second, the
fine-mesh size is restricted to 110 by 110 fine-mesh ele-
ments (or 22 by 22 fine-mesh blocks) in the small memory
version of the programs. Therefore, the variables IFXS,
IFXE, IFYS, and IFYE must be chosen according to
IFXE - IFXS + 1 < 22 and IFYE - IFYS + 1< 22. The
larger memory version can still handle a fine-mesh size of
150 by 150 elements, as in the workstation or mainframe
versions of the program. In both the small and large
memory versions, maximum coarse-mesh size remains the
same at 50 by 50 blocks.

MULPREPC is run by changing to the appropriate
directory and typing the command MULPREPC followed
by return. At that point, use of the program becomes self-
explanatory. After the user chooses a consistent unit sys-
tem, the program prompts for all the requisite MULSIM/
NL input parameters using typical default values for the


RUNNING MULSIM/NL

The command sequence to actually run MULSIM/NL
depends heavily on the host computer and its operating
system. Subsequent discussions will provide two example
execution command sequences - one for a Hewlett
Packard (HP)? engineering workstation using the UNIX
operating system and another for a VAX minicomputer
using the VMS operating system. In principle, these
examples will apply to other machines and other operating
systems. Prior to presenting these examples though, the
files used by MULSIM/NL require discussion. During its
execution, MULSIM/NL creates and uses files for input,
output, and temporary storage. These discussions will give
the purpose, format, and general contents of those files.
Finally, a chart is presented of actual MULSIM/NL
execution time versus the problem size. This chart
provides the user with a simple means to approximate the
execution time for new problems.

MULSIM/NL FILES

MULSIM/NL uses many files during execution. Ta-
ble 3 lists these files and gives their general content. The
FORTRAN unit name is somewhat generic. The actual
FORTRAN unit name will vary with different computer
systems. Most of the files are binary and unreadable by
the user. Only the input, output, and fine- and coarse-
mesh output data files are formatted American Standard
Code for Information Interchange (ASCII) files and hence
readable by the user.

3Reference to specific products does not imply endorsement by the
US. Bureau of Mines.

Table 3.MULSIM/NL files
FORTRAN Contents
unit name
FOROS.DAT .. Input file
FOROG.DAT .. Out file (printout) .
FORI1.DAT Coarse-mesh element Temporary-delete.
(12, 13, 14). stress and dis-
placement data for
seam 1 (2, 3, 4).
FOR21.DAT Fine-mesh block stress Do.
(22, 23, 24). and displacement
data for seam 1 (2, 3,
4).
FOR31.DAT Coarse-mesh element Save - coarse-mesh
(32, 33, 34). stress, displacement data files.
and energy data for
seam 1 (2, 3, 4).
FOR41.DAT Fine-mesh block Save - fine-mesh
(42, 43, 44). stress, displacement data files.

and energy data for
seam 1 (2, 3, 4).

MULSIM/NL uses FORTRAN unit 05 for input and
unit 06 for printed output. The user must rename and
save these files for subsequent use and inspection. After
MULSIM/NL converges on a sufficiently accurate stress
and displacement solution, it writes the fine- and coarse-
mesh stress and displacement data for each seam to files
in ASCII format. FORTRAN unit 21 (22, 23, 24) stores
the fine-mesh element stress and displacement data for
seam 1 (2, 3,4). Similarly, FORTRAN unit 11 (12, 13, 14)
stores the coarse-mesh block stress and displacement data
for scam 1 (2, 3, 4). Again, the user can opt to delete all
these files after MULSIM/NL finishes.

MULSIM/NL uses the stresses and displacements on
the above files to calculate various energy and energy
change quantities for each mining step. Upon completing
the energy calculation, MULSIM/NL writes the fine- and
coarse-mesh stress, displacement, and energy data to final
output files in ASCII format. FORTRAN unit 41 (42, 43,
44) contains the fine-mesh data for seam 1 (2, 3, 4), and
FORTRAN unit 31 (32, 33, 34) contains the coarse-mesh
data for seam 1 (2, 3, 4). The user must rename and save
these important output data files for subsequent use and
study. To facilitate graphical display of the output data,
MULSIM/NL writes the fine-mesh element data in order.
Starting at the element with the lowest x and y coordinate,
data records are written by increasing x coordinate first,
then by increasing y coordinate. The coarse-mesh data
also follow the same format of increasing x coordinate
first, followed by increasing y coordinate.

MULSIM/NL EXECUTION COMMAND SEQUENCES.

As already stated, the actual commands needed to exe-
cute MULSIM/NL depend heavily on the host computer
and its operating system. Figure 16 shows an example
execution command sequence for a HP engineering work-
station using a UNIX operating system. In this case, these
UNIX commands form a file named “multirun." Submit-
ting this file with "multirun &" causes the following

# Csh Program: multirun

cd /home/zipf/gpanels

mulnl <gpan2.inp >gpan2.prt
mv fort.41 gpan2.f1

mv fort.42 gpan2.f2

mv fort.31 gpan2.cl

mv fort.32 gpan2.c2

rm fort.*

Figure 16.—MULSIM/NL execution command sequence for
Hewlett Packard engineering workstation using UNIX operating
system.


0.324

USBM MULPLT OF multism.fm41 | |
MULTIPLE SEAM LONGWALL PANELS 0.294
TOTAL CLOSURE-Z DIRECTION MINING STEP 1
xmin= 382.4 ies24
ymax: 1582.4 1582.4 0.263
0.232
0.201
O170
"
0139
0208
0.077
0.046
0.015
<min= 382.4
ymin= 382.4
0273
USBM MULPLT OF multism.fm2 |
MULTIPLE SEAM LONGWALL PANELS 0.247
TOTAL CLOSURE-Z DIRECTION MINING STEP a
iss24
1582.4 0.222
ea re a |
onl 0197
One OA74
ahaa &
Z = tt 0146
0121
0.095
0.070
0.045
0,020

Figure 33.—Multiple-seam mining example—normal displacements. Top, Upper seam;
bottom, lower seam. Displacements are in meters. Postprocessor program MULPLT/NL
generates these computer drawn plots.


BRBES cena mayne

15.
16.

17.
18.
19.
20.
21.
22.

25.

27.

29.
30.
31.
32.
33.
34,
35.
36.
37.
38.
39,

41.

yeyenyr

ILLUSTRATIONS

Typical mine layout and boundary element method model
Stress-strain models for MULSIM/NL .
Strain energy relations for various linear and nonlinear backfill or gob behaviors ...
Strain energy relationships for linear and nonlinear material models in MULSIM/NL.
Coarse-mesh generation in basic mine plan
Fine-mesh generation in basic mine plan ....
MULSIM/NL input file structure for single-seam, single-step problem .
MULSIM/NL input file for sample problem shown in figure 1
MULSIM/NL input file structure for single-seam, multiple-step problem . .
MULSIM/NL input file structure for multiple-seam, single-step problem
MULSIM/NL input file structure for multiple-seam, multiple- step problem .
Options for global coordinate system location
Six different stress-strain models available in MULSIM/NL .
Typical direction cosine matrices for orienting local coordinate system telative to global coordinate
SYSEEM eee eee eee rene ee eee eee e ete eb beet b bene tenes
Overrelaxation factor versus computer time and number of iterations per step ............0.000008
MULSIM/NL execution command sequence for Hewlett Packard engineering workstation using UNIX
Operating system 2... cece cee teen e eet e tt eeeeeeeetens
MULSIM/NL execution command sequence for VAX minicomputer using VMS operating system .
Execution time on SUN III workstation versus problem size . eee
Control section of input file for longwall example
Step 1 fine-mesh section of input file for longwall example .
Step 1 coarse-mesh section of input file for longwall example
Step 2 fine-mesh section of input file for longwall example... . .
Step 2 coarse-mesh section of input file for longwall example . . .
Longwall example—normal stresses and normal displacements around headgate during mining step 2.
Longwall example—normal stresses along cross section just ahead of face during mining step 2 .
Longwall example—normal displacements along cross section just behind face during mining step 2
Control section of input file for multiple-seam mining example
Seam 1 (upper seam) fine-mesh section of input file for multiple-seam mining example .
Seam 2 (lower seam) fine-mesh section of input file for multiple-seam mining example .
Seam 1 (upper seam) coarse-mesh section of input file for multiple-seam mining example .
Seam 2 (lower seam) coarse-mesh section of input file for multiple-seam mining example .
Multiple-seam_ mining example—normal stresses ......
Multiple-seam mining example—normal displacements .
Control section of input file for random room-and-pillar mining example
Step 1—Fine-mesh section of input file for random room-and-pillar mining example ..
Step 1—Coarse-mesh section of input file for random room-and-pillar mining example . .
Step 2—Fine-mesh section of input file for random room-and-pillar mining example ... .
Step 2—Coarse-mesh section of input file for random room-and-pillar mining example . .
Step 3Fine-mesh section of input file for random room-and-pillar mining example . ..
Step 3—Coarse-mesh section of input file for random room-and-pillar mining example . .
Random room-and-pillar mining ng example—normal stresses and normal displacements during mining
step 2.

TABLES

MULSIM/NL input and output units for three typical consistent unit systems .
Material model parameters and material property array EPROP structure
MULSIM/NL files
First record variables of coarse- and fine-mesh output data files ....
Variables in coarse- and fine-mesh output data file records

11
14
18

21


USBM MULPLT OF longwall.fmd
PILLAR RECOVERY PANEL
TOTAL CLOSURE-Z DIRECTION MINING STEP 2
SECTION PARALLEL TO X - ROW 61
2.859

2582 4

2.304 4

2.026 4

1.748 4

1.470 4

ai92 4

0.914 4

0.636 4

0.358 4

0.080

xmin= xmax=
8730.0 13470.0

Figure 26.—Longwall example—normal displacements along cross section just behind face during mining step 2.
Displacements are in inches. Postprocessor program MULPLT/NL generates this computer drawn plot.


Record Type 5—Single Record—Format
(6(F6.0, F6.4))

Aq, - normal stress component o,,, at global origin
B,, - normal stress gradient Ao, from global origin
jg ~ shear stress component 7,, at global origin
B,, - shear stress gradient Ar,, from global origin
Ajg - shear stress component 7, at global origin
By, - shear stress gradient Ar,, from global origin
Ag - normal stress component o,, at global origin
Byy - normal stress gradient Ao,, from global origin
Aj - Shear stress component Typ at global origin
Bag - shear stress gradient Ar,, from global origin
Agg - normal stress component ¢,, at global origin
Bag - normal stress gradient Ao,, from global origin.

This record specifies primitive or premining stresses to

MULSIM/ NL. The quantities A,,, B,,, etc,, listed above
form symmetric tensors that look like

An Ap Ap Cn Ty Te
[A] = [Aw Av Asl=|ty %y jl ©
Ay Ag3 Ags Ta Ty Om
By By By] [Acq Aty Ate |-
[B] = | By By By3 | = Aty Aoy, Aty, ©)
By By By | [Arg Aty, doy

[A] contains the primitive stress components at the
global origin, whereas [B] has the stress gradient com-
ponents as a function of vertical distance from the global
origin AZ. Thus, the primitive stress tensor [P] for any
element in the MULSIM/NL model is easily computed
within the program as

(P] = [A] + BAZ. ®

For the input file shown in figure 8, the global origin is
located at seam level similar to figure 12 (right) rather
than on the surface. The ozz (Ay) stress component
equals 10 MPa, and all other stress components and gra-
dients are zero. Therefore, the primitive stress tensor P
for each element in the model has the Pz, component
only, which equals 10 MPa.

Sign conventions for the stress and stress gradient com-
ponents can cause problems. MULSIM/NL uses positive
for compression; therefore, the stress components A at the
global origin are usually all positive. In the global coor-
dinate system, AZ is negative for increasing depths; there-
fore, the stress gradient components B are also negative in
most cases. Negative stress gradients and negative AZ. will
give positive primitive stresses P that increase with depth.

Record Type 6—Single Record—Format
(F8.2, 218, 16X, 418)

BW _ - coarse-mesh block width

NBXI - number of coarse-mesh blocks in x direction
NBET - number of coarse-mesh blocks in y direction
IFXS  - fine-mesh starting block along x axis

IFXE - fine-mesh ending block along x axis

IFYS - fine-mesh starting block along y axis

IFYE - fine-mesh ending block along y axis.

The sixth record defines the coarse-mesh size (NBXI by
NBET) and gives the location of the fine-mesh area within
the coarse-mesh. For the input file example shown in fig-
ure 8, blocks of 7.62 m width comprise the coarse-mesh,
which extends for 12 blocks in the x direction and 11
blocks in the y. The fine-mesh runs from blocks four to
nine along the x axis and from blocks four to eight along
the y. IFXS equals 4; IFXE equals 9; IFYS equals 4; and
IFYE equals 8. A five by five array of fine-mesh elements
subdivides each block within this region. Therefore, the
fine mesh in the example, which covers six by five blocks,
divides into a 30- by 25-element array.

Record Type 7-NSEAM Records—Format (4F8.1)

Xo Yo Ze - global coordinates of the local coordinate
system for the seam

THIKNS  - average scam thickness.


Table 5.—Variables In coarse- and fine-mesh output
data file records

Variable Format Definition
X.....  F7.1 Global X coordinate of element or block
centriod.
F7.1 Global Y coordinate of element or block
centroid.
13(1X) Material code for element or block.

£93 X displacement component—ride 1.

9.3. —_Y displacement component—tide 2.

£93  Z displacement component—normal
closure.

9.3  — X stress component—shear stress 1.

E93 —_Y stress component~shear stress 2.
E93 Z stress component—normal stress.
9.3. Total strain energy into element or block.
E93 Recoverable strain energy from element
or block.
OSE... E93 _Dissipated strain energy in element or

block (DSE = TSE - RSE).

KER... £93 Kinetic energy release for element or
block.

SER .. E9.3 Strain energy release for element or block.

TER .. £9.3 Total energy release for element or block

(TER = KER + SER).

MULPLT/NL is a menu-driven, graphics program that
can display pseudo-three-dimensional plots or two-
dimensional cross sections of the stresses, displacements,
and energies contained in the MULSIM/NL output files.
With MULPLT/NL, the user interactively specifies the
data file name and mining step number to examine. The
user then selects a plot type (three dimensional or two

dimensional) and chooses a quantity from the output file
to display - either stress, displacement, or energy.
MULPLT/NL can also plot changes in these quantities
between any two specified mining steps. This capability
enables direct comparisons between numerical models,
which tend to compute total or absolute stresses and
displacements, and the field programs, which tend to
measure their changes. MULPLT/NL can calculate and
display stress and displacement changes between mining
steps, thus allowing the user to compare numerical results
directly (with due caution) to field measurements of stress
and displacement changes.

MULPLT/NL also permits the user to adjust the scale
on all plot types so that comparisons are not distorted. In
addition, the user can save the raw data comprising any
particular graph created by MULPLT/NL as an ASCII
file. Afterwards, a wide variety of commercially available
software packages, such as a computer-aided-drafting pro-
gram, can import these files and create presentation-
quality graphical displays from these subsets of the
MULSIM/NL output data.

Aside from producing easy-to-read, graphical displays
of MULSIM/NL output data, the real advantage of
MULPLT/NL lies in its speed and simplicity. Experience
seems to show that for every presentation quality graph
created from MULSIM/NL data, at least 100 similar
plots are examined quickly with MULPLT/NL during the
course of numerical experiments. Thus, the simple post-
processor MULPLT/NL serves a vital function in a well-
executed numerical modeling study.

MULSIM/NL PRACTICAL EXAMPLES

Earlier sections of this manual presented the general
capabilities of MULSIM/NL and gave an overview of the
modeling process with this three-dimensional BEM pro-
gram. A later section discussed the input file structure
and all the input variables in great detail. Another section
covered actual execution of MULSIM/NL. The last sec-
tion described the output from the program and discussed
the postprocessor for graphically viewing the output data.

This section provides three detailed examples of
successful MULSIM/NL analyses and includes the actual
input files and sample graphical outputs produced by the
postprocessor MULPLT/NL. Experience shows that
actual examples often provide the best means to illustrate
the use of a program. However, while these examples
stem from current Bureau projects using MULSIM/NL,
they do not represent a complete analysis and solution to
the problems depicted. MULSIM/NL analyses are but a
small part of the overall engineering design process, and

these examples merely seek to illustrate the "how to”
aspect of those analyses.

LONGWALL MINING EXAMPLE

This first example is of a unique longwall panel that
extracts one of the headgate pillars as the panel advances.
Figure 19 shows the input file control section for this two-
step problem. This example illustrates use of the program
with the pound per square inch and inches unit system. All
stress and modulus values have units of pounds per square
inch and all lengths have units of inches. Eight in-seam
materials are defined as follows: A is linear elastic coal at
0% extraction; B is linear elastic gob; C is also linear
elastic coal, but at 45% extraction, and D is elastic-plastic
coal yielding at 500 psi. Materials E, F, G, and H rep-
resent linear elastic coal at 20%, 40%, 60%, and 80%
extraction; however, they remain unused in this model.


NSTEP + mining step number for the first step

MXSTEP —- number of new mining steps in this
problem.

This record specifies the critical MULSIM/NL con-
trol parameters. The first variable, ORF, is an overrelaxa-
tion factor. MULSIM/NL solves the nonlinear system of
boundary-element equations with a Gauss-Seidel iteration
procedure that uses the overrelaxation factor to accelerate
convergence of the stress-displacement solution. (See
Dahlquist and Bjork (9) for further explanation of a
Gauss-Seidel iteration procedure.) ORF can range from
1.00 to about 1.50. Figure 15 shows the effect of ORF on
computation time and number of iterations to solve a
typical MULSIM/NL problem. Both these measures of
equation-solving efficiency decrease as ORF increases to
about 1.45; however, beyond 1.45, the computation time
and number of iterations increases dramatically. No
method exists to tell what the optimum ORF is for any
particular problem. Optimum values for ORF usually
range from 1.25 to 1.45. This example uses 1.35.

SIGACC is a stress convergence criterion used during
the equation-solving process by the nonlinear material
models. MULSIM/NL also has a built-in displacement
convergence criterion computed as the seam thickness
divided by 1,000. When all elements satisfy both the stress
and displacement convergence criteria, then the iterative
equation solver stops. The calculated stresses and dis-
placements did not change significantly from the previous
iteration, and they lie sufficiently close to the prescribed
nonlinear stress-strain relationships. This example spec-
ifies SIGACC as 0.10 MPa (15 psi), which is quite strin-
gent by most practical engineering requirements.

ITMAX places a limit on the number of iterations that
the MULSIM/NL equation solver can use in any one step
to calculate elemental stresses and displacements. Simple
problems that only use MULSIM/NL’s linear capabilities
converge in 15 to 30 iterations. Using the nonlinear
material models may double the number of iterations
required for convergence. Large, well-behaved, nonlinear
problems rarely require more than 100 iterations to

130

PER STEP

COMPUTER TIME
PER STEP, min

NUMBER OF ITERATION

L 1
O11 120° 43 14 18 16
OVERRELAXATION FACTOR, @

Figure 15.—Overrelaxation factor versus computer time and
number of iterations per step.

converge. This example specifies a maximum of 120
iterations per mining step.

The variables NSTEP and MXSTEP control the multi-
ple mining step capabilities in MULSIM/NL. NSTEP
gives the number for the first mining step and MXSTEP
specifies the number of new mining steps in the current
problem. This single-step example starts at mining step 1
(NSTEP) and continues for just 1 step (MXSTEP). The
MULSIM/NL energy calculations performed on the basis
of equation 1 require stress and displacement changes as
input. Therefore, to obtain these energy calculations, the
user must specify at least two mining steps. Energy cal-
culations begin at the second mining step and continue
thereafter.

INPUT SUMMARY

A basic MULSIM/NL input file contains three parts:
a control section, the fine-mesh geometry section, and the
coarse-mesh geometry section. The control section spec-
ifies all the basic parameters for the boundary-element
model, such as problem size, material properties, in situ
stress fields, and seam orientation, The fine-mesh and
coarse-mesh geometry sections define the mine geometry
and material distribution for the model. As shown in the
sample input file (fig. 8), these sections approximate the
actual mine geometry and actual material distribution in
the real seam or vein. As shown in figures 9, 10, and 11,
the fine- and coarse-mesh geometry sections are repeated
in a specific pattern for multiple seam and/or multiple
mining step problems.

INPUT FILE GENERATION WITH
PREPROCESSOR MULPRE/NL

A preprocessor called MULPRE/NL is available to
assist the user generate a MULSIM/NL input file. The
Preprocessor uses various menus and a question and an-
swer format to create the control section of the input file.
Next, MULPRE/NL helps the user build the fine- and
coarse-mesh models with friendly computer graphics. The
MULPRE/NL graphics contain two important functions
for speeding the model building. The first function allows
the user to change the material property code from one
value to another over a user-defined area. The second
function lets the user copy a set of material property codes
from one user-defined area to another. Other functions
also exist, such as a zoom capability, but the change and
copy functions perform the bulk of the model-generation
effort. Subsequent Bureau documents will provide more
complete instructions on the operation and program struc-
ture of the preprocessor MULPRE/NL. New MULSIM/
NL users are advised to use the preprocessor for initial
model generation since accurate model generation is
greatly facilitated.


MULTIPLE SEAM MINING EXAMPLE
0.2500000.200000E+05 2
3

1.00.500E+03.200E+03.000E+00.000E+00.000E+00
1.00.250E+03.100E+03.000E+00.000E+00.000E+00
6.00.500E+02.200E+02.400E+01.000E+00.000E+00

0.0.0000 0.0.0000 0.0.0000 0.0.0000 0.0.0000 0.0.0250
5.00 30 26 6 25 6 21
0.0 0.0 -560.0 2.0

0.0 0.0 -600.0 3.0

1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000
1.35 +20 100 1 1

7

Figure 27.—Control section of input file for multiple-seam mining example.


CONTROL PARAMETER DEFINITION

Prior discussions gave the general three-part structure
of the input file and showed how to create the coarse- and
fine-mesh sections of that file. Knowing something about
the overall input file structure and how it relates to the
mine geometry under consideration will facilitate descrip-
tions of the very important control parameters. Nine
different record types comprise the control section, and
many record types can contain multiple records. The
following discussions will describe each record type and
each variable within that record type. Where necessary,
appropriate ranges are provided for those variables. These
discussions use the control section of the sample problem
input file from figure 8 as an example.

Record Type 1—Single Record—Format (20A4)
TITLE - an arbitrary 80 character title.
The first record gives a descriptive title to the problem.

Record Type 2—Single Record—Format
(F8.2, E12.6, 18)

v = Poisson’s ratio
E - Young’s modulus

NSEAM - Number of seams.

The second record gives the Poisson's ratio and
‘Young’s modulus for the rock mass surrounding the seam.
As in most BEM programs, the rock mass is linear elastic.
In this example, v equals 0.25, which is the common value,
and E equals 20,000 MPa (3,000,000 psi), which is mod-
erately high for most rock, but typical for massive
sandstones. The number of scams, NSEAM, is 1 for this
single-seam example. MULSIM/NL can analyze up to
four scams.

Record Type 3—Single Record—Format (I8)
NMATS - Number of materials.

The third record specifies the number of in-seam mate-
rials. At least one in-seam material is required, and up to
26 materials are allowed (A through Z). This example
uses five materials (A through E) in the fine- and coarse-
mesh geometry as shown in figure 8.

Record Type 4—NMATS Records—Format (10E8.0)

These records define the in-seam material properties
beginning with those for material A, then material B, etc.,
up toNMATS materials. Figure 13 shows the stress-strain
models for MULSIM/NL that include (1) linear elastic for
coal, (2) strain softening, (3) elastic plastic, (4) bilinear
hardening, (5) strain hardening, and (6) linear elastic for
gob. The first three models are for the unmined in-seam
coal material, while the latter are for the broken gob

COAL OR VEIN MATERIAL MODELS

Linear elastic Strain softening

Elastic plastic KEY
‘ a (o,.8,) 3 <Te, £ Young's modulus
A an (, £5) E, Fin! modulus
1 £, Hardening modulus
. (Oy 8) Ey Initiol modulus
~ E, Plastic modulus
8 GOB OR BACKFILL MATERIAL MODELS £) Offset strain
& _Linear elastic Strain hardening Bilinear hardening &) Peak strain
6 4 Eq Residual strain
Jo Offset stress
E Ey O, Peak stress
1 Ooo) / | O, Residual stress
O, Final stress

STRAIN, &

Figure 13.—Six diff

int stress-strain model

wailable in MULSIM/NL.


NONLINEAR MATERIAL PROPERTIES

As with most BEM programs, a linear elastic rock mass
surrounds the seams; however, MULSIM/NL now permits
various nonlinear material models for the in-seam block
and element materials. Prior versions of MULSIM (2-3)
permitted linear stress-strain relations only for in-seam
materials, such as coal or gob. As shown in figure 2,
MULSIM/NL now has six material models from which to
choose including (1) linear elastic for coal, (2) strain
softening, (3) elastic plastic, (4) bilinear hardening, (5)
strain hardening, and (6) linear elastic for gob. The first
three are intended for the unmined in-seam coal material,
while the latter are for the broken gob material left in the
wake of full extraction mining, Model 2 (strain softening)
after Crouch and Fairhurst (4) approximates the yielding
behavior of small-pillars or large-pillar perimeters, while
model 3 (elastic plastic) approximates a pseudoductile
behavior in pillar cores (5). Model 5 (strain hardening)
allows the gob material to increase in stiffness as it
consolidates under increasing load. Model 4 (bilinear
hardening) permits a certain amount of deformation to
occur prior to introducing stiffness. Models 1 and 6 are
basic linear elastic models for coal and gob, respectively.

MULTIPLE MINING STEPS

MULSIM/NL features multiple mining steps to simu-
late various stages of mine development. This feature
enables the user to examine stress and displacement
changes as the mine development advances or retreats.
Such changes more readily compare with field measure-
ment data that tend to measure stress and displacement
(convergence) changes as opposed to total or absolute
stresses and displacements.

ENERGY RELEASE CALCULATIONS

Most important, MULSIM/NL contains an energy sub-
routine that uses the calculated stresses and displacements
at each block and element to evaluate detailed energy
changes for each mining step. This subroutine computes
various ERR quantities for the entire model, as well as
various strain energy values for each element. Cook (6)
developed the original ERR concept, and research found
that ERR correlated well with the incidence of devastat-
ing rock bursts in deep underground South African gold
mines. By analogy, it is hypothesized that the ERR will
also correlate with the incidence of coal mine bumps.

COAL OR VEIN MATERIAL MODELS

Linear elastic

Strain softening

Elastic plastic

1 2

3

Se
Bg GOB OR BACKFILL MATERIAL MODELS
= Linear elastic Strain hardening Bilinear hardening
6 § 4
STRAIN (€)

Figure 2.—Stress-strain models for MULSIM/NL.


USBM MULPLT OF longwall.fma
PILLAR RECOVERY PANEL

TOTAL NORMAL STRESS-Z DIRECTION MINING STEP 2
xmin= . xmax= 13530.0
ymax= 7230.0 ymax= 7230.0

3350.0

3045.0

Ee

2680.0

2345.0

2010.0

1675.0

43404

1008.4

a * 6704

. = 335.4

xmin= 8730.0 xmax= 135300
ymin= 2430.0 ymin= "2430.0

TOTAL CLOSURE-Z DI MINING STEP 2
xnin= 8730.0 xmax= 135300
ymax= 7230.0 7230.0

2.859

2.582

2.304

2.026

1748

1.470

osi4

0.636

0.388

xmin= 8730.0
ymin= 2430.0

Figure 24—Longwall example—normal stresses (top) and normal displace-
ments (bottom) around headgate during mining step 2. Stresses are in pounds
per square inch, and displacements are in inches. Postprocessor program
MULPLT/NL generates these computer drawn plots.


SOSSSOSS9O90909S00: =5 3
SSSSsssosooSSSoSees:
Seescesceescescesses

FrataatuateafestenlealsslenleslaatealeslenlealeslesQealesleclealealealealeatealealselaatea]
‘pena encnen spcocacncncacneAcMcocAmMcocasAcncAMcocasneacoaNt

se

Testes]
enc

Figure 21.—Step 1 coarse-mesh section of input file for long-

wall example.


MULSIM/NL APPLICATION AND PRACTITIONER’S MANUAL

By R. Karl Zipf, Jr."

ABSTRACT

MULSIM/NL (multiple seams, nonlinear) is a new U.S. Bureau of Mines boundary-clement-method
(BEM) program for calculating stresses and displacements (i.e., convergence) in coal mines or thin,
tabular metalliferous veins. This manual gives detailed operating instructions for MULSIM/NL and
illustrates its use with several practical examples. While this manual concentrates on the practical
aspects of actually running and using MULSIM/NL, another companion report titled "MULSIM/NL—
Theoretical and Programmer’s Manual" provides mathematical and programming details to those
engineers and programmers who need to fully understand the FORTRAN program or desire to alter
and enhance it.

MULSIM/NL analyzes one to four parallel seams that have any orientation with respect to the
Earth’s surface. Three main features distinguish MULSIM/NL from its predecessors: (1) nonlinear
material models, (2) multiple mining steps, and (3) comprehensive energy release and strain energy
computations. MULSIM/NL has six material models for the in-seam material including (1) linear elas-
tic for coal, (2) strain softening, (3) elastic plastic, (4) bilinear hardening, (5) strain hardening, and
(6) linear elastic for gob. The multiple mining step capability enables the user to simulate a changing
mine geometry. Finally, MULSIM/NL performs comprehensive energy release rate calculations.

‘Structural engineer, Denver Research Center, U.S. Bureau of Mines, Denver, CO.


ft

Ib/ft2
Ib-ft
Ib-ft/ft?
Ib-ft/ft?
Ib fin?
Ibin

Ibrin /in?

foot

hour

inch

kilobyte

pound

pound per square foot
pound foot

pound foot per square foot
pound foot per cubic foot
pound per square inch
pound inch

pound inch per square inch

Ibrin in?

m

psi
psi/ft

psi/in

UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT

pound inch per cubic inch
meter

megabyte

minute

megajoule

megajoule per square meter
megajoule per cubic meter
megapascal

megapascal per meter
pound per square inch
pound per square inch per foot

pound per square inch per inch

The U.S. Bureau of Mines expressly declares that there are no warranties expressed or implied that apply to the software
contained (or described) herein, By acceptance and use of said software, which is conveyed to the user without
consideration by the Bureau of Mines, the user hercof expressly waives any and all claims for damage and/or suits
including special, consequential, or other similar damages arising out of or in any way connected with the use of the

Disclaimer of Liability

software contained (or described) herein.



material left in the wake of full extraction mining. As will
be discussed later, the distinction between coal material
models and gob material models becomes crucial in the
subsequent energy calculations.

Linear Elastic for Coal (Model 1)

This basic model requires little discussion since it is the
basis for MULSIM/NL’s predecessors MULSIM (3) and
MULSIM/BM (2). The required parameters for the
model are E (Young’s modulus) and G (shear modulus),
which are related by

G Tay" (2)
In the BEM calculations, Young’s modulus E relates the
normal stress to the normal displacement (closure) across
an clement, whereas G relates the associated shear
stresses to the corresponding shear displacements (rides).
As discussed in a related document, the three boundary
conditions applied to each element behave independently
of one another.

With the linear elastic model, MULSIM/NL works
internally with a stiffness K given by

, @)
where t is the seam thickness.

Linear Elastic for Gob (Model 6)

This model is the counterpart to model 1 and is intend-
ed for the gob material left in the wake of mining. Re-
quired parameters are again E and G plus a "gob height
factor," n. The factor n is the ratio between the height
of the zone of broken rotated gob fragments and the un-
mined seam thickness. The factor n typically ranges from
2 to 6 and averages about 4. This material model and
BEM program assume that the rock mass remains linear
elastic beyond a range of “n" seam thicknesses. With
linear elastic gob elements, MULSIM/NL operates with a
stiffness given by

Kk-_=, (4
a

In effect, the factor n accounts for the larger effective
seam thickness present in extracted areas now filled with
gob material. (Another way to consider n is as a modulus
reduction factor as was done by Beckett and Madrid (2).)

Strain Softening for Coal (Model 2)

This model, after Crouch and Fairhurst (4), approxi-
mates the complete stress-strain curve observed during
laboratory strength tests on coal conducted under true
displacement control. In principle, it also describes the
yielding behavior of moderately sized pillars or the
perimeters of large pillars. Field observations by Wang
(7) and Iannacchione (8) support a strain-softening model
for full-scale pillars in many mines.

Required input parameters for this stress-strain model
are a peak stress and peak strain plus a residual stress and
residual strain. As shown in figure 13, these two points
define the strain-softening model. In addition, the model
requires a Poisson’s ratio, v. For the normal components
of stress and displacement, the strain-softening model
works with the peak and residual stress-strain points.
However, for the two shear components, MULSIM/NL
scales the specified peak and residual stresses and strains
by a factor 1/[2(1 + v)]. In the linear elastic portion of
the strain-softening model, MULSIM/NL relates normal
stress and displacement with an clastic modulus computed
as E = o,/€,, where a, is peak stress and ¢, is peak
strain. The shear stresses and displacements also satisfy
a similar relation in the initial linear portion, Shear modu-
lus is computed from elastic modulus using equation 2.

One restriction on the strain-softening model is that
residual strain must exceed peak strain, and peak stress
must exceed residual stress. For strains greater than
residual, stress remains constant at the residual level.

Elastic Plastic for Coal (Model 3)

This stress-strain model, closely akin to the strain-
softening model, approximates a pseudoductile behavior in
pillar cores (5). Required input for the model is again a
peak stress and peak strain, the modulus of the postyield
portion (i.e., its slope) and a Poisson’s ratio, v. As in the
prior model, the factor 1/[2(1 + v)] scales the amplitude
of the normal stress-strain curve to obtain the shear stress-
strain relations. Therefore, E and G satisfy equation 2 in
the initial linear portion.

Bilinear Hardening for Gob (Model 4)

This stress-strain model, analogous to the elastic-plastic
model in certain respects, permits a certain amount of
deformation to occur prior to introducing significant ele-
ment stiffness. Input requirements for the model are
stress and strain at the inflection point, modulus in the
hardening region beyond the inflection point, and Poisson’s
ratio, v. Again, the stress-strain relation for the normal
direction of the element is scaled by 1/2[(1 + v)] to ob-
tain the stress-strain relation for the tangential directions
of the element.


Coarse mesh

Fine mesh

Figure 1.—Typical mine layout and boundary element method model.


to occur. First, the computer changes directory (cd) to
/home/zipf/gpanels. This directory must contain an
executable version of MULSIM/NL, in this case called
“mulnl," and an input file, in this case called "gpan2.inp."
Next, the computer runs "muln!" on input file "gpan2.inp,"
which is equivalent to FORTRAN unit 05 and sends the
printed output to "gpan2.prt," which is equivalent to
FORTRAN unit 06. This example is a multiple-seam
problem. FORTRAN units 41 and 42 contain the fine-
mesh output data, and 31 and 32 contain the coarse-mesh
output data that must be saved for future use. The move
command (mv) renames each of these FORTRAN files
with an appropriate new name. Finally, the remove com-
mand (rm) deletes all other FORTRAN files that this
example chooses not to save including 11, 12, 21, and
22, Upon completion of this command sequence and
MULSIM/NL, the directory "gpanels" will contain five new
output data files including "gpan2.prt,"  "gpan2.fl,"
"gpan2.£2," "gpan2.cl,” and "gpan?.c2,” as well as the input
file "gpan2.inp" and the executable file "mulnl,"

Figure 17 shows another execution command sequence
for a VAX minicomputer using the VMS operating system.
These commands happen to reside in a file called
"SHARP.COM," which upon submission to the computer
causes the following actions to occur. First, the default
directory is set to [ZIPF.SHARP]. That directory con-
tains an input file called "SHARP.INP," which is a single-
seam, multiple-step problem. Next, certain necessary
FORTRAN unit files are set equivalent to other files such
as "005" and the input file "SHARP.INP," "006" and the
printed output file "SHARP.PRT," "041" and the fine-mesh
data file "SHARP.FMD,” and last, "031" and the coarse-
mesh data file "SHARP.CMD." The following command
will run MULSIM/NL, which in this case is the executable
file called "MULNL" that resides in a separate directory
called [ZIPF.MULSIM].. Finally, after, MULSIM/NL
stops, the delete command removes all other FORTRAN
files including 11 and 21.

Again, the actual command sequence needed to run
MULSIM/NL depends on the available computer and its
operating system. These examples, coupled with the prior
explanation of MULSIM/NL’s many operating files,
should provide users with sufficient background infor-
mation to tailor an execution command sequence for their
available hardware.

MULSIM/NL RUNNING TIMES

Execution times for MULSIM/NL will depend on the
particular computer used and the size and complexity of
the problem. Figure 18 shows an approximate relationship
between solution time and problem size. This plot
originates from observed execution times for a large
variety of MULSIM/NL problems. These times only ap-
ply to a SUN If engineering workstation; however, these

SET DEFAULT [ZIPF.SHARP]
DEFINE FOROOS SHARP. INP
DEFINE FOROO6 SHARP.PRT
DEFINE FORO41 SHARP.FMD
DEFINE FORO31 SHARP.CMD
RUN [ZIPF.MULSIM]JMULNL
$ DEL FOR*.*;*

PAAAA

Figure 17.-MULSIM/NL execution command sequence for
VAX minicomputer using VMS operating system.

26 T—1—1—1—

22

20 4

EXECUTION TIME PER MINING STEP, h

es oe ee
0 204 6 8 10 12 14

TOTAL NUMBER OF BLOCKS AND ELEMENTS,

Figure 18.—Execution time on SUN Ill workstation versus
problem size. Shaded area covers approximate possible range
of computing time.

times can be adjusted for other computer systems if the
relative performance of that system to a SUN III is known
approximately. Otherwise, it is extremely easy to generate
another, given any particular system. Knowing the size of
a problem in terms of the total number of elements and
blocks in that problem, figure 18 provides an estimate of
the execution time per mining step. The lower bound time
estimate is for simple, linear elastic problems, whereas the
upper bound time estimate is for highly complex, nonlinear
elastic problems. Again, the user must regard these time
estimates as very approximate, but generally conservative.


IC

9322

BUREAU OF MINES
INFORMATION CIRCULAR/1992

MULSIM/NL Application and
Practitioner’s Manual

By R. Karl Zipf, Jr.

UNITED STATES DEPARTMENT OF THE INTERIOR


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Linear elastic Strain s

‘of tening

Elastic plastic

(Tu),

STRESS (c)

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(Tu)

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is stress-strain state in material.

IN (&)

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rain energy

tionships for linear and nonlinear material models in MULSIM/NL. (T,u)

MULSIM/NL MODELING

Knowing something about basic BEM model generation
will help the novice user understand the input file structure
for MULSIM/NL. BEM modeling starts with an idealized
in-seam mine plan, then overlays a grid work of elements,
and finally assigns material properties to those elements.
This array of material property assignments delivers the
basic model geometry to the BEM program. Coupling this
geometry with material property data, in situ stress data,
and other program controls then forms a basic input file
ready for solution by MULSIM/NL. The following figures
will illustrate this modeling process for the new user.

IDEALIZED MINE PLAN

Modeling begins with an idealized mine plan such as
the example shown in figure 5 (top). This plan shows part
of a retreating room-and-pillar panel. Pillars are 9.1
by 10.7 m with 6.1-m opening widths. The upper area is
mined out and filled with gob, whereas the lower area is
approximately 50% extracted. Mining is about to extract
the point pillar in the area of interest.

COARSE-MESH GENERATION

The first important decision for constructing a
MULSIM/NL model concerns the fine-mesh element
width, which is always one-fifth the coarse-mesh block
width. Typical coal mine models might fix the element
width at a quarter, third, half, or else equal to the entry
width. This example uses a 1.52-m element size, which is
one-quarter of the entry width. Accordingly, the block

width is 7.62 m. (The term block used herein refers to a
modeling block and not to a coal pillar or coal block.)
Figure 5 (middle) shows the basic mine plan again, but
now a 7.62-m coarse-mesh block grid is superimposed.
That grid consists of an array 12 blocks long in the x direc-
tion and 11 blocks wide in the y direction. In addition, a
fine-mesh boundary is defined around the area of interest.
Coarse-mesh blocks that will be divided into fine-mesh ele-
ments extend from four to nine in the x direction and from
four to eight in the y direction. (Note, the coordinate axes
follows normal conventions by starting at the lower left
corner.)

Last, as shown in figure 5 (bottom), each coarse-mesh
block is assigned a letter code representing a particular set
of in-seam material properties. Material B represents lin-
ear elastic coal blocks that are 50% extracted. Material E
is for the gob left in the wake of full extraction mining.
(Note, actual input of properties for materials B and E
occurs later.) The material label 1 signifies an open ele-
ment. Such elements represent entries, crosscuts, and any
other open areas within the seam. In this model, an open
area exists between the gob and the partially mined areas.
Finally, the material label O (zero) represents coarse-mesh
blocks within the fine-mesh boundary.

FINE-MESH GENERATION

With the coarse-mesh grid complete, modeling then
proceeds to the fine-mesh covering the area of interest.
Figure 6 (top) shows a closeup of the mine plan and
the six by five array of coarse-mesh blocks within the


Salamon (J) clarified the original ERR concept and
derived the following relationship implemented in
MULSIM/NL:

Wr

1
Jo, Temes +S Jo,Tre ues

+ 3 Seon t -a)ARAuds, Qa)

where Wa = total energy release during current step,

area mined during current step,

total backfill or gob area,

an

a

5
"

T, = total stress in coal during prior step,

AR = stress change in backfill during current
step,
uy = total displacement during prior step,

Au = displacement change during current
step,

and a = nonlinearity factor.
In this relation, A refers to the change in a field

quantity between mining steps. The first term represents
the strain energy release from the mined-out material.

The second term, called the linear kinetic energy release,
is the change in gravitational potential over the area mined
during this step. The third term, called the nonlinear
kinetic energy release, is an additional energy release (or
sink) arising in the backfill or gob area. This term con-
tains a so-called nonlinearity factor a. Figure 3 illus-
trates the meaning of a and shows how it accounts for the
degree of nonlinearity. Together, the second and third
terms of equation 1 form the kinetic energy release. The
strain energy release, kinetic energy release, and total
energy release terms are computed and written in the
MULSIM/NL output files for all elements within the areas
Sy and Soy. Summing up the elemental energy releases
(ie., carrying out the integrations prescribed by equa-
tion 1) gives the total energy releases for the model during
the current mining step.

The ERR calculations within MULSIM/NL depart
slightly from the original prescription of Salamon (1).
MULSIM/NL evaluates the strain energy release (i.e., the
first term of equation 1) as a "recoverable strain energy" as
shown in figure 4. These calculations assume that the
unloading modulus from the state (T, u) equals the initial
loading modulus. In addition to evaluating recoverable
strain energy as the strain energy release over the current
mined area Sy, MULSIM/NL also evaluates recoverable,
dissipated, and total strain energy for each unmined seam
element with the same scheme as shown in figure 4. The
models shown in figure 4 apply to the unmined seam
material, either coal or rock. The output data files from
MULSIM/NL include these strain energies along with the
stresses and displacements.

(AR, AU)

STRESS CHANGE (AR)

DISPLACEMENT CHANGE (AU)

Figure 3—Strain energy relations for various line:

O0<a<i

Strain energy = '/, a ARAU

1<a<2

ind nonlinear backfill or gob behaviors.


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Figure 22.—Step 2 fine-mesh section of Input file for longwall example.


INTRODUCTION

OBJECTIVES

‘The program described in this U.S. Bureau of Mines
report is part of the MULSIM/NL package, which fea-
tures the actual BEM program described herein, as well
as a preprocessor program called MULPRE/NL and a
plotting postprocessor program called MULPLT/NL. The
preprocessor helps the user generate the requisite input
file for the main program MULSIM/NL, whereas the
postprocessor assists the user in examining the calculated
stresses and displacements in a very rapid graphical
manner.

Documentation and instructions for the MULSIM/NL
package are divided into two related reports with each
providing essential elements toward an understanding of
the whole. The objective of this report "MULSIM/NL—
Application and Practitioner’s Manual’ is to provide users
with detailed operating instructions for MULSIM/NL
along with several practical examples to better illus-
trate the capabilities of the program. A related report
"MULSIM/NL—Theoretical and Programmer’s Manual"
provides certain mathematical and programming details to
those engineers and programmers who need to fully
understand the FORTRAN program or desire to alter and
enhance it.

MULSIM/NL OVERVIEW

MULSIM/NL calculates stresses and displacements
throughout a coarse- and fine-mesh modeling grid used to
approximate an actual mining geometry. It can analyze
one to four parallel seams having any orientation with
respect to the Earth’s surface. Topographic or free sur-
face effects are neglected. MULSIM/NL uses a coarse-
mesh grid (up to 50 by 50) with an embedded fine-mesh
grid (up to 150 by 150) for greater computational detail in

important regions. The material comprising each coarse-
mesh block or fine-mesh element can follow any one of six
linear and nonlinear stress-strain relationships. MULSIM/
NL also performs comprehensive energy release rate
(ERR) calculations for the model based on Salamon’s (1)?
theoretical work. In addition, MULSIM/NL features a
multiple mining step capability. This feature allows the
user to simulate the various temporal stages of mine devel-
opment and examine stress and displacement changes as
the mine advances, These three new capabilities, namely
nonlinear material models, energy calculations, and multi-
ple mining steps, set MULSIM/NL apart from its prede-
cessors, MULSIM/BM, developed by Beckett and Madrid
(2), and the original MULSIM created by Sinha (3).

SCOPE OF MANUAL

This manual provides detailed operating instructions for
MULSIM/NL beginning with the basics of the modeling
process and followed by a full discussion of the input file
giving the meaning, allowable range, and format for each
variable in that file. Basic instructions for operating the
preprocessor MULPRE/NL are also included. This pre-
processor helps the user create a MULSIM/NL input file
in a user-friendly, graphical manner. The next discussion
focuses on actually running MULSIM/NL by giving the
required command sequences for various computer sys-
tems. Subsequent discussions describe the output files,
which include a print file, a coarse-mesh data file, and a
fine-mesh data file. The postprocessor MULPLT/NL,
described next, aids the user in examining these volu-
minous data files in a very simple manner using very fast
graphics routines. Finally, the manual culminates with
several complete examples, including sample input files
and postprocessor plots.

MULSIM/NL CAPABILITIES

MULSIM/NL is a BEM program that calculates three-
dimensional stresses and displacements caused by mining
tabular deposits like coal seams. The BEM model used
for these computations can have one to four parallel seams
at any orientation in the earth. Likewise, the virgin stress
field can also have any orientation. MULSIM/NL as-
sumes that these seams are far below the Earth’s surface,
hence the program does not include the effects of complex
topography.

MULSIM/NL uses a coarse- and fine-mesh modeling
grid to approximate the actual in-seam coal mine geom-
etry. Figure 1 shows a typical coal mine geometry and

illustrates its connection to a MULSIM/NL grid. In this
analysis problem, retreat mining methods will extract the
central pillar in this layout. The coarse-mesh blocks must
cover a sufficiently large section of the actual mine layout,
whereas fine-mesh elements will cover a central region of
interest where greater computational detail is desired.
MULSIM/NL allows up to a 50 by 50 coarse-block array
and up to a 150 by 150 fine-mesh array.

Italic numbers in parentheses refer to items in the list of references
preceding the appendix at the end of this report.


These records specify the location in global coordinates
of the local origin of each seam, as well as the average
seam thickness. This example (fig. 8) assumes a global
coordinate system at the seam level much like figure 12
(right) so the global and local coordinate systems coincide.
Therefore, X,, Y,, and Z, are zero. The seam thickness
in the example is 1.5 m.

The implicit choice of global coordinate system origin
affects not only the local coordinate system definition in
this record but also the primitive stress definition in rec-
ord 5. Placing the global coordinate system origin at seam
level, as in this example (fig. 8) and in figure 12 (right),
requires nonzero terms in the global origin stress compo-
nent tensor A in equation 8. Generally, the stress gradient
tensor B will contain nonzero terms for problems entailing
multiple or inclined seams. The example considered in
figure 8 is a single-horizontal seam. In this special case,
all terms in the stress gradient tensor B are zero. Placing
the global origin on the surface as shown in figure 12 (left)
example requires that all terms in the stress component
tensor A equal zero. Therefore, the stress gradient tensor
B must have nonzero terms to have nonzero primitive
stresses at seam level.

For the special case of horizontal seams (either single
or multiple), all global X,’s must equal one another and
similarly for the Y,’s. MULSIM/NL does not permit rela-
tive rotation or lateral translation of the local coordinate
system of the seam. The local x and y axes must remain
parallel, and the local z axes should remain collinear.
Normally, as shown in the example input file (fig. 8) and
also in figure 12, all X, and Y, equal zero. For a single-
inclined seam, X, and Y, can remain zero. Only in the
special case of inclined, multiple seams does one en-
counter nonzero and nonequal X, and Y,. In this case,
the analyst must use trigonometry to calculate global
coordinates (X,, Y,, Z,) for each seam such that the local
z axes remain collinear.

Record Type 8—Single Record—Format (9F8.5)

EN(1,1), EN(2,1), EN(3,1) - direction cosines of the
local x axis with re-
spect to the global
axes X, Y, and Z.

EN(1,2), EN(2,2), EN(3,2) - direction cosines of the
local y axis with re-
spect to the global
axes X, Y, and Z.

EN(13), EN(2,3), EN(3,3) - direction cosines of the
local z axis with re-
spect to the global
axes X, Y, and Z,

The record specifies the orientation of the local
coordinate system axes with respect to the global axes.
Figure 14 provides several typical examples of different
local coordinate system orientations with respect to the
global system along with the approximate direction cosine
values.

Record Type 9—Single Record—Format
(2F8.2, 18, 24X, 218)

ORF - overrelaxation factor

SIGACC - stress convergence criterion

ITMAX - maximum number of iterations per
mining step

z Horizontal seam

Y 4 0 0
4 EN= {0 1 0
x ) 0 1

Seam dipping 30°
in X direction

0.87 0 - 0.50
EN= (0 1 0
50 0 87

zy
x
“&
y
®
co 300
Sean dipping 30
in Y direction
y 1 0. 0
z EN=(0 .87 50
x 0 ~.50 -.87,
Vertical seam striking
parallel to X

1 0 0
EN={0 0 1
x oO -1 0

Vertical seam striking
parallel to Y

0 o -1
EN= {0 1 0
x 1 0 0

Figure 14.—Typical direction cosine (EN) matrices for orienting
local coordinate system relative to global coordinate system.


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Figure 29.-Seam 2 (lower seam) fine-mesh section of input file for multiple-seam mining example,


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01
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A
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Figure 30.—Seam 1 (upper seam) coarse-
mesh section of input file for multiple-seam

mining example.

been

mmammSSSSSSSSSSSSOSOSa

Figure 31.—Seam 2 (lower seam) coarse-
mesh section of input file for multiple-seam

mining example.


LONGWALL EXAMPLE
0.1500000.900000E+06 1
8

1.00.500E+06.217E+06.000E+00.000E+00.000E+00
6.00.500E+04.179E+04.100E+01.000E+00.000E+00
1.00.275E+06.119E+06.000E+00.000E+00.000E+00
3.00.500E+03.250E-02.000E+00.300E+00.000E+00
1.00.400E+06.174E+06.000E+00.000E+00.000E+00
1.00. 300E+06.130E+06.000E+00.000E+00.000E+00
1.00. 200E+06.870E+05.000E+00.000E+00.000E+00
1.00. 100E+06.430E+05.000E+00.000E+00.000E+00
0.0.0458 0.0.0000

0.0.0000 0.0.0458 0.0.0000 0.0.0917

300.00 50 32

0.0 0.0 -6000.0 72.0

30 45 9 24

1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0. 00000 1.00000
1

1.35 50.00 100

Figure 19.—Control section of input file for longwall example.

Some other noteworthy values include the block width at
300 in (which implies an clement width of 60 in), a seam
thickness of 72 in and a seam depth of -6,000 in (-500 ft).
The scam has a horizontal orientation. Stresses increase
at a rate of 0.0917 psi/in of depth (1.1 psi/ft) vertically
and .0458 psi/in (0.55 psi/ft) horizontally.

Figure 20 shows the fine-mesh for mining step 1. Solid
coal exists on either side of the headgate pillars. This step
serves as the basis from which stress changes are com-
puted as mining extracts the diagonal pillar. Elastic-plastic
coal, which yields at 500 psi, forms the skin of each pillar
while all other coal remains linear elastic. Figure 21
shows the coarse-mesh for this step. The fine-mesh
encompasses the headgate area somewhat right and center
within the coarse-mesh. Solid coal exists on either side of
the headgate, while gob (material B) is on one side of the

tailgate. Material C (linear elastic coal at 45% extraction)
comprises the headgate and tailgate areas.

Figure 22 shows the fine-mesh area for mining step 2,
which has extracted the upper left portion of the model
and replaced it with gob (material B). Figure 23 shows
the coarse-mesh for this step. Note how the longwall
panel has advanced and where gob (material B) has
replaced linear elastic coal (material A).

Running this two-step example consumed about 3 h on
a SUN Engineering workstation. Next, the postprocessor
MULPLT/NL was used to produce the following plots
from the fine-mesh output file. Figure 24 (top) shows
normal stresses in pound per square inch around the

headgate area, while figure 24 (bottom) shows displace-
ments in inches. These are total stresses and displace-
ments and not changes, although the latter can be
requested. Figure 25 is a profile of normal stresses at a
cross section just ahead of the face, while figure 26 shows
displacements along a section just behind the face. Again,
interpretation of these calculations are neither attempted
nor implied in this example.

MULTIPLE-SEAM MINING EXAMPLE

The second example demonstrates an interaction analy-
sis between room-and-pillar mining of an upper seam and
longwall development in a lower seam. Figure 27 shows
the input file control section for this example. Only one
step is considered in what should become a multiple step
problem. This example illustrates use of the program with
the megapascal and meter unit system. Three in-seam
materials are defined as follows: A is linear elastic coal at
0% extraction; B is linear elastic coal at 50% extraction;
and C is linear elastic gob. Vertical stress increases at a
rate of 0.025 MPa/m, while all other stress components
remain zero. The block width is 75 m implying an ele-
ment width of 15 m. Seam thicknesses are 2 m for the
upper seam and 3 m for the lower. The seams are hori-
zontal and lie at depths of -560 and -600 m.

Figure 28 shows the fine-mesh for the upper seam
where partial extraction has occurred. Areas of no extrac-
tion (A) are interlaced with areas of partial extraction (B).


CONTENTS

Abstract
Introduction . .
Objectives .... .
MULSIM/NL overview ..
Scope of manual ...
MULSIM/NL capabilities
Nonlinear material properties
Multiple mining steps ... .
Energy release calculations
MULSIM/NL modeling ... .
Idealized mine plan .....
Coarse-mesh generation . .
Fine-mesh generation . . .
Input file structure for MULSIM/NL .
Input file sections
Units
Global coordinate systes
Control parameter definition .
Record type 1—Single recor format (20A4)
Record type 2—Single record—format (F8.2, E12.
Record type 3Single record—format (18) .
Record type 4-NMATS records—format (10E8.0) .
Linear elastic for coal
Linear elastic for gob
Strain softening for coal
Elastic plastic for coal .......
Bilinear hardening for gob... .
Strain hardening for gob......
Record type 5—Single record—format (6(F6.0, F6.4))
Record type 6—Single record—format (F8.2, 218, 16X, 418)
Record type 7-NSEAM records—format (4F8.1)
Record type 8—Single record—format (9F8.5) . .
Record type 9Single record—format (2F8.2, 18, 24X, 218)
Input summary .
Input file generation with preprocessor 3 MULPRE/NL .
Running MULSIM/NL :
MULSIM/NL files . . .
MULSIM/NL execution comman sequences .
MULSIM/NL running times .
Output files from MULSIM/NL .
Printout file...
Fine- and coarse-mesh output data files
Output file examination with postprocessor MULPLT/NL
MULSIM/NL practical examples .............0005
Longwall mining example . . . .
Multiple-seam mining example
Random room-and-pillar mining example .
Summary .
References .
‘Appendix —Special instructions for personal computer version of MULSIM/NL



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sce

Figure 38.—Step 2—Coarse-mesh section of input
file for random room-and-pillar mining example.


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Figure 36.—Step 1—Coarse-mesh section of input
file for random room-and-pillar mining example.


CUT SEQUENCE MODELS
0.2500000.200000E+05 1

5
0 500.0 200.0

0.0 0.0 0.0 1.5

1.

1.0 250.0 100.0

3.0 10.0 0.020 0.0 0.25

3.0 20.0 0.040 0.0 0.25

6.0 50.0 20.0 4.0
0.0.0000 0.0.0000 0.0.0000 0.0.0000 0.0.0000
7.62 12 11 4 9

1
4

CONTROL
SECTION

0.0.0000
8

1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000

1.35 0.10 120 1
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
1111111111111111111111EEEEEEEE
1111211111111111111111EEEEEEEE
1111111111111111111111EEEEEEEE
11CCCCCC1111CCCCCC1111EEEEEEEE
11CDDDDC1111CDDDDC1111EEEEEEEE
11CDAADC1111CDAADC1111EEEEEEEE
11CDAADC1111CDAADC1111EEEEEEEE
11CDAADC1111CDAADC1111EEEEEEEE
11CDDDDC1111CDDDDC1111EEEEEEEE
11CCCCCC1111CCCCCC1111EEEEEEEE
1111111111111111111111EEEEEEEE
111121111111111111111111111111
111121111111111211111111111111
121111111111111111111111111111
11C0CCCCC1111CCCCCC1111CCCCCC11
11CDDDDC1111CDDDDC1111CDDDDC11
11CDAADC1111CDAADC1111CDAADC11
11CDAADC1111CDAADC1111CDAADC11
11CDAADC1111CDAADC1111CDAADC11
11CDDDDC1111CDDDDC1111CDDDDC11
11C0CCCCC1111CCCCCC1111CCCCCC11
111121111111111111111111111111
111111111111111111111111111111
EEEEEEEEEEEE
EEEEEEEEEEEE
EEEEEEEEEEEE
111000000EEE
BBBOOOOOOEEE
BBB000000111
BBBOOOOOOBBB
BBBOOOOOOBBB
BBBBBBBBBBBB
BBBBBBBBBBBB
BBBBBBBBBBBB

Figure 8.—MULSIM/NL input file for sample problem shown In figure 1.

1

FINE
MESH
GEOMETRY
SECTION

COARSE
MESH
GEOMETRY
SECTION


Table 1._MULSIM/NL input and output units for three typical
consistent unit systems

‘Megapascal- Pound- —-Pound-
Variable meter inch foot
system ‘system system
Input:
Length . m in ft
Stress . MPa Ib/in? Ib/tt?
Modulus . MPa. tb/in? Ib/tt?
Output:
Displacement . m in ft
Stress .. MPa tb/in? Ib/t?
Energy ....... MJ Ibsin Ibett
Energy density . . MJ/m? it Ibsft/#t?
Energy release rate . MJ/m? Ibtt/t

GLOBAL COORDINATE SYSTEM

MULSIM/NL uses a global coordinate system from
which the local origin of each seam is defined. The local
origin for each seam always lies in the lower left corner
of the coarse-mesh geometry for that seam. Both the lo-
cal and the global coordinate systems are right-handed.
The Z axis of the global coordinate system is always

perpendicular to the earth’s surface, while the global X
and Y axes are parallel to that surface. The orientation of
the global coordinate system is therefore fixed with respect
to the earth. However, the local coordinate system can
have any orientation with respect to the global system, i-c.,
the seams can have any orientation relative to the Earth’s
surface.

In the control section of the input file, the user must
define the local origin of each seam relative to a global
coordinate system origin. Implicitly, the user must choose
a location for the global coordinate system. As shown in
figure 12, two logical alternatives exist for this choice: (1)
the actual ground surface, or (2) the lowermost seam. As
discussed later, this choice affects the way primitive or
premining stresses are input. MULSIM/NL does not per-
mit rotation of the seams or their local coordinate systems
with respect to each other. This restriction means that the
local x axes and local y axes shown in figure 12 must re-
main parallel. MULSIM/NL does permit lateral transla-
tion of the seams and their local coordinate systems with
respect to each other. Therefore, the local z axes are not
required to be collinear; however, in most practical appli-
cations, the local z axes are collinear as shown in figure 12.

Figure 12.-Options for global coordinate system location. Left, Global coordinate system located at surface for multiple-seam
problem; right, global coordinate system located at lowermost seam.


Library of Congress Cataloging in Publication Data:

Zipf, R. Karl.
MULSIM/NL application and practitioner’s manual / by R. Karl Zipf, Jr.

p- cm. — (Information circular; 9322)
Includes bibliographical references (p. 45).
Supt. of Docs. no.: I 28.27:9322. *
1. MULSIM/NL. 2. Ground control (Mining)—Computer simulation. I. Title.

II. Series: Information circular (United States. Bureau of Mines); 9322.

TN295.U4 [TN288] 622s—dc20 [622’.28°0113] 91-47134 CIP



The mine geometry lies askew to the grid orientation.
One small area of full extraction (gob - C) appears in the
lower right of the fine-mesh.

Figure 29 shows the fine-mesh for the lower seam
where several longwall panels have been developed. This
model covers a huge seam area, Again, A represents solid
coal whereas B, used to define the gateroad areas, is 50%
extracted coal. Small open areas (1) exist at the ends of
each panel. For the equation solver in MULSIM/NL to
work properly, a small amount of open area (1) must exist
in cach model. Finally, figures 30 and 31 show the coarse
mesh for the upper and lower seams.

Running this example consumed several hours of SUN
III computing time. Next, MULPLT/NL was invoked to
examine the fine-mesh output files for each seam. The
following graphics stem directly from MULPLT/NL. Fig-
ure 32 shows the normal stresses in megapascals on each
seam and clearly illustrates the stress interactions between.
the seams. Similarly, figure 33 shows normal displace-
ments for each seam and the seam interactions. Again,
these calculation results are an example only, and
interpretations are not intended at this time.

RANDOM ROOM-AND-PILLAR MINING EXAMPLE

The third and final example shows a highly irregular
mine geometry. Furthermore, the tabular orebody dips
down the page in the model. Figure 34 shows the input
file control section. This example illustrates use of the
program with the pound per square inch and inches unit
system. Four in-seam materials are defined starting with

A for linear elastic rock at 0% extraction. Materials B, C,
and D are also linear elastic rock, but at 75, 50, and 25%
extraction, respectively. The actual tabular orebody dips
at 20° into a steeply rising hillside. To account for the
orebody dip, the direction cosines specify that the orebody
plane dips about 20° down the page. To account for the
rising hillside, an artificially high stress gradient is used.
Vertical stress increases at 0.2342 psi/in (2.81 psi/ft),
while horizontal stresses increase at one-fourth this
gradient. (If the topography was flat, then the vertical
stress gradient would be about 1.1 psi/ft.) The origin of
the orebody is at a depth of -6,744 in (562 ft), and the
orebody thickness is 240 in. This example has three
mining steps.

Figures 35 and 36 show the fine- and coarse-mesh for
the first step. This step provides calculations of the pre-
mining stress and displacement fields. Figures 37 and 38
show the fine- and coarse-mesh for the mine geometry in
the second mining step. Note the highly irregular mine
geometry undergoing analysis. Finally, figures 39 and 40
show the fine- and coarse-mesh geometry for the third
mining step. In this step, additional extraction has
occurred in the lower, central region of the fine-mesh.

Running this example consumed about 8 h of SUN III
computing time. Figure 41 shows stress and displacement
plots produced by MULPLT/NL for the second mining
step. At the edges of the model, stresses clearly increase
with depth as one moves down the page. As before, these
calculations are for illustrative purposes only and are not
meant for interpretation at this time.


OUTPUT FILES FROM MULSIM/NL

As discussed in the prior section, MULSIM/NL pro-
duces three distinct output file types after a successful
problem run: a printed output file, a coarse-mesh data
file, and a fine-mesh data file. The fine- and coarse-mesh
data files contain the calculated stresses, displacements,
and energies for each element and block and for each
mining step in the problem. However, each seam has its
own fine- and coarse-mesh data files. During execution of
MULSIM/NL, the user should label these output files with
appropriate file name extensions, such as PRT for the
print file, CMD for the coarse-mesh data file, and FMD
for the fine-mesh data file.

PRINTOUT FILE

MULSIM/NL writes a printout file that basically
reflects all the input data and problem control variables.
First, the printout shows the rock mass material prop-
erties, the in-seam material properties, the primitive stress
field, basic model control and model data, location, and
orientation of each seam, and finally the program control
parameters. Next, the fine- and coarse-mesh mine models
are printed for each seam and for the first mining step.
‘These models show the mine geometry and material speci-
fications. After MULSIM/NL finds a stress and displace-
ment solution for the first mining step, it prints out certain
vital statistics on the equation-solving process such as the
number of iterations required for convergence and the
approximate solution accuracy. For each additional mining
step, MULSIM/NL will printout the new mine model and
its solution statistics. Last and most important, the
MULSIM/NL print file provides the energy calculations
for the model. These calculations include various total
energy release quantities and the energy release per unit
area mined (ie., the energy release rate). As mentioned
earlier, the energy calculations require stress and dis-
placement changes as input; therefore, the problem must
have at least two mining steps. MULSIM/NL energy
release calculations begin at the second mining step and
continue thereafter.

FINE- AND COARSE-MESH OUTPUT DATA FILES

The voluminous output data files from MULSIM/NL
contain calculated stresses, displacements, and energies.
Both the coarse- and fine-mesh files have identical struc-
ture so that they are indistinguishable from one another

for subsequent postprocessing purposes. The first record
of these ASCII files specifies five important parameters
that define the rest of the structure of the file. Table 4
shows these variables and gives their meaning. The next
NXY records give the block and/or element output data
for the first mining step followed by additional groups
of NXY records for subsequent mining steps. Thus, the
total size of any output data file is (MXSTEP * NXY + 1)
records.

of coarse- and fine-mesh
output data files

Variable Format Definition

MXxSTEP .. no Number of mining steps (21).

NXY 0... ho Total number of coarse-mesh
blocks or fine-mesh elements in
model (NXY = NX- NY).

F10.2 Block or element width.
110 Number of blocks or elements in X
direction.

NY cee 110 Number of blocks or elements in Y
direction.

Each data record within an output file contains 15 var-
iables displayed in FORTRAN format (2F7.1, 13, 1X,
12E9.3). Table 5 lists these output variables and provides
their meaning, For a more complete discussion of these
variables and in particular the energy quantities, see the
companion volume "MULSIM/NL - Theoretical and Pro-
grammer’s Manual." In essence, the output files store X,
Y, Z triplets ready for graphical display.

OUTPUT FILE EXAMINATION WITH
POSTPROCESSOR MULPLT/NL

When studying various engineering problems with a
numerical analysis program like MULSIM/NL, the pru-
dent user will typically complete many different runs that
systematically vary the problem geometry and material
properties over an expected range. Such parametric stud-
ies will generate many MULSIM/NL output data files.
Examining the numerous output files requires a simple
and fast graphical postprocessor. Ideally, such a postproc-
essor also has a high degree of transportability between
computer platforms, The Bureau developed postprocessor
called MULPLT/NL provides a simple, very fast graphical
means to examine MULSIM/NL output files.


Information Circular 9322

MULSIM/NL Application and
Practitioner’s Manual

By R. Karl Zipf, Jr.

UNITED STATES DEPARTMENT OF THE INTERIOR
Manuel Lujan, Jr., Secretary

BUREAU OF MINES
T S Ary, Director


USBM MULPLT OF _rndrmpt:
RANDOM ROOM AND PILLAR
TOTAL NORMAL STRESS-Z

MINING STEP
xmax= 18060.0
ynax= 18060.0 ymax= 18060.0

6060.0
ymin= 6060.0

USBM_MULPLT OF _rndrmpil.fmd
RANDOM ROOM AND PILLAR MINING

TOTAL CLOSURE-Z DIRECTION MINING STEP 2
xmin= 6060.0 xmax= 18060.0
ymax= 18060.0 ymax= 18060.0

8060.0
6060.0

Figure 41.—Random room-and-

1950.0

1703.2

ose1

0.334

0.287

0.240

o447

0.400

0.083

0.006

- 0.030

- 0.086

mining example—normal stresses (top)

and normal displacements (bottom) during mining step 2. Stresses are in
pounds per square inch, and displacements are in inches. Postprocessor pro-

gram MULPLT/NL generates these computer drawn plots.


USBM MULPLT OF longwall.fmd
PILLAR RECOVERY PANEL
TOTAL NORMAL STRESS-Z DIRECTION MINING STEP 2
SECTION PARALLEL TO X - ROW 45
3350.0

3015.0 4

2680.0 4

2345.0 4

2010.0

1675.0

1340.4 4

1005.1 4

670.1 4

335.4 4

xmin= xmax=
8730.0 13470.0

Figure 25.Longwall example—normal stresses along cross section just ahead of face during mining step 2. Stresses
are in pounds per square inch. Postprocessor program MULPLT/NL generates this computer drawn plot.


RANDOM ROOM AND PILLAR MINING EXAMPLE
0.2500000.600000E+07 1
4

1,00.200E+07.800E+06.000E+00.000E+00.000E+00
1.00.500E+06.200E+06.000E+00.000E+00.000E+00
1.00. 100£+07.400E+06.000E+00.000E+00.000E+00
1.00.150E+07 .600E+06.000E+00.000E+00.000E+00
0.0.0583 0.0.0000 0.0.0000 0.0.0583 0.0.0000 0.0.2342

600.00 40 40 ll 30 11 30
0.0 0.0 -6744.0 240.0
-1.00000 0.00000 0.00000 0.00000-0.92718 0.37461 0.00000 0.37461 0.92718
3

1.35 50.00 100 1

Figure 34.—Control section of input file for random room-and-pillar mining example.


/AAAAAAAAAAAAAAAAAAAAAAAAAAAAL AAI
aaa " Be ee
(ANAAAAAAAAAAAAAAAAAAAAAAAA MAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Al JAAAAAAAAAAl
BAM ANAAAMAAMAAAAAARAAM RAN MAA SA HTT
ARAAAARAAAAAAAAAAAA
AARAAAARAAAARAAAAAAAAAAAAAAAAAADL IIIT T1111 11 1
AARAAAARAAAARAAAAAAAAAAAAAAAAAA 1
ARAARAAAAAAARAAAAAAAAAAAAAAAARA
JAAAAAAAAAAAAAARAAARAAAAAA
AAANAAAAANAAAANAMAAAAAMAAAR Ay rv JAAAAAAAAAAI
AAAARAAAAAAAAAAAAAAAAAAAAAI VAAAAAAAL
ARAAAARAAAAAAAAAAAAAAAAAAAAAARA An IAAAAAAAAAAL
(ARAAAAAAAAAAAAAAAAAAAAAAA| AAAAAAAAAA
AAAAAAAAAAAARAAAAAAAAAAAAAAAAAA\ AA )AAAAAAAAAA
AARAAAARAAAAAAAAAAAAAAAAAAAAAADI 11 1 DAA )AAAAAAAAAA
ARAANAA AAAI Baa AAAAAAAAAA
VAAAAAAAAAAAAAAAAAAAARARY
(AAAAAAAAAAAAAAARAAAAAARAAAAAAAl AAI JAAAAAAAAAAL
AAAARAAAAAAAAAAAAAAAAAAAAAAAAAA| AA JAAAAAAAAAAL
ARAAAAAAAAAAAA AA ARAN AAAAN
VVAAAAAAAAAAAAAAAAAAAA VAAAAAM
ARAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AA JARAAAAAAAAL
AAAAAAAARAAAAAAAAAAAAAAAAAAAAAAD] 11100001111 DDDDDDDODDD!
AAAAARAAAAAARAAAAAAAAAAAAAAAADI ITI 1111 WMT
ANAAAAAAARAAAARAAAAAAAARAAAARAADL T1111 131111
ARAAAARAAAAAAAAAAAAAAAAAAAAAAAA
AANAARRAAAAAAARAABARARAAAAAAAAAD 1 i i 1
AAAAAAARAAARAAAAAAAAARAAAAAA iy i
AAAAAAAARAAAAAAAAAADDDDDDDDDDAAI AAA
ARAAAAAAAAA Hip AA AAAAARAAAA
ARAAAAAAAAAAAAAAAAAI } AA AAAAARAAAA
ARAAAANAAAARAAAA AMA ADL TTT EBAA MRANAAAA
AAAAAAAAARAAAAAN A za ABT IDAMMARAAN
ARAAAAAAAARAARAAAAA ARAM AN ANAANAAAAN
VAAAAAAAAAAA AAAAAAI AA AAAAAAAAAA
ARAARAAAAAARAAAAAAAI AAAAAA AA AAAAAAAARA
ARAAAAAAAAAAARAARAA AAAAAAI A ARANAAAAAA
ABAANAAAANAAARAN NAA AAAAAA iy 00 i
ARAAAAAAAAAAAAAAAAAl AAAAAA
A RRRRARAARRAAAAA Aaa
AAAAAAAAAAARAAAAAAAI AAA
AAAAAAAAAAAAAAAAAAAI 1DAAA iH
ARAAAAAAAAAAAAAAAAAI JAA A
AAAARAAA ARAAA AA ARAAARAAAA
ARAAARAAAAAAAAARAAA {9p AAI AARAAAAAAA
AAAARAAAAAAAAAAAAAAI AA AAAAAAAAAA
EAE TS A
AAAAAAAAA, \AAAAAA 1 AAI \Al
ARAAARAAAAAAAAAAAAA AAARD AA AAAANAAAAN
ARAAARAAAAAARAAAAAA AAAAAA| AA AAAAAAAAAA
AAAAAAARAAAAAAAAAAAI AAAAAA AAI AARAAAAAAA
ARAAAAAAAAAARAAA AAA A ARAAA iv ARAN AAARA
ARAAARAAAAAAAAARAAA AAAAAA iy JAAAAAAAAAAL
AARAAAAAAAAARAAAAAAL AAAAAA AA
ARAAAAAY AAAAAA pDoDD
ARAAARAARAN A MARAAADT LTT Hi
ARAAARAAAAAAAAARAAA }AAAAAAI 1
AARAAAAAAAAARAAAAAA| DAAAAA 1
ARAAAAAAAAAAAAAAAAA| DAAAA
BAAARAAAAAANAAAN NAA A
AARAAAAAAAAA N AA
ARANAARAAAARAAAAAAA Da An JAAAAAAAAAAL
AAAAAAAAAAAAAARAAAA Hn AA JAAAAAAAAAAL
ARARAAAAAAAAAAAAAAA RADA DAA )ARAAAAAAAAL
AARAAAAAAAAAAAAAAAAI Ivy 6 1 JAAAAAAAAAA
AAA AMA f m RAARAANAAA
ARAAAAAAAAAAAAAAAAA )AAAAAA AAI JAAAAAAAAAAL
AAAAAAAAAAAAAAAAAAAI JAAAAAA AA JAAAAAAAAAAI

Figure 20.—Step 1 fine-mesh section of input file for longwall example.


Gob area Area of
interest

50% extraction area
TO) a

is

L
L

Figure 5.—Coarse-mesh generation in basic mine plan. Top,
Idealized plan for retreat room-and-pillar mining; middle, super-
imposed coarse-mesh block grid; bottom, material property
assignments for coarse-mesh grid.

TTT TTT
Fine-mesh boundary
4
Lo =
a ee oe ee ee ee — _
EJEJETEIEIEIEIEIEIEIEIE FEE REE
a
ETETEIE/E(EIEIEIEIEIEIE i
EETELELELELELELELELE IE]. aaa a aa
RE COO a (SHUM HHH SA
BIB|BJO;OFOlOlOlOfElEle 1G RL LA
B/BIByolofolololofii1}1
BIB/BJo/o/0{0lo| ope lB iB : ett
B/B/BfolololololofBlBiB nu SUCHE Mu a
BIBIBIBIBIB18 1818 |B 1B 1B aan aan cals
B/B/B/8/B/8/8/8/B 181818 Saas AE ata
B!B!B!IB/B/B/B/B/BIBIBIB SSUES ES ESOS SES ESS GOGO GEGE EERE FOP

Figure 6.—Fine-mesh generation in basic mine plan. Top,
Closeup of plan and coarse-mesh blocks within fine-mesh
boundary; middle, superimposed fine-mesh grid within fine-mesh
boundary; bottom, material property assignments for fine-mesh
grid.


SUMMARY

This manual describes MULSIM/NL, which is a
boundary-clement program for calculating stresses and
displacements in coal seams or thin tabular vein-like
deposits. The manual gives detailed operating instructions
for MULSIM/NL and then it illustrates its use with
several practical examples. While this manual concen-
trates on the practical aspects of actually running and
using MULSIM/ NL, another related document titled
"MULSIM/NL - Theoretical and Programmer’s Manual"
provides mathematical and programming details to those
engineers and programmers who need to fully understand
the FORTRAN program or desire to alter and enhance it.

MULSIM/NL calculates stresses and displacements
throughout a coarse- and fine-mesh modeling grid. It can
follow any one of six linear and nonlinear stress-strain
relationships. A multiple mining step capability enables
correct simulations of a changing mine geometry. In
addition, MULSIM/NL performs energy release rate cal-
culations that follow Salamon’s (7) theoretical work.

This manual discusses the basic modeling process in
which an actual mine plan is first idealized, then approx-
imated by a coarse- and fine-mesh modeling grid. The in-
seam material that makeup this array of blocks and/or
clements can follow any one of MULSIM/NL’s six differ-
ent stress-strain laws. Understanding the basic modeling
process enables a user to create an input file for program
MULSIM/NL. This input consists of a control section,
fine-mesh geometry sections, and coarse-mesh geometry
sections. The control section defines all the basic model

generation and operating parameters for MULSIM/NL
such as problem size, material properties, in situ stress
fields, and seam orientation. The coarse-mesh section
defines the mine geometry and assigns material properties
in an array of coarse-mesh blocks that comprise the
overall mine model. The fine-mesh section defines geom-
etry and assigns properties to a subarray of fine-mesh
elements within the coarse-mesh.

The command sequence to actually run MULSIM/NL
depends heavily on the host computer and its operating
system. This manual gives example command sequences
for an HP Engineering Workstation with a UNIX oper-
ating system and a VAX computer with the VMS oper-
ating system. Successful execution of MULSIM/NL pro-
duces large output data files containing calculated stresses,
displacements, and energies for each mining step. The
postprocessor MULPLT/NL provides a simple, very fast
graphical means to examine these voluminous MULSIM/
NL output files. MULPLT/NL is a menu-driven, graphics
program that can display pseudo-three-dimensional plots
or two-dimensional cross sections of the calculated
stresses, displacements, and energies.

Last, the manual gives three complete examples that
illustrate how to run MULSIM/NL. These examples show
the complete input file for MULSIM/NL and various sam-
ple plots of the output data generated by the postprocessor
MULPLT/NL. The discussions of the input file and these
examples will provide the potential user with sufficient
instructions to use MULSIM/NL for new purposes.

REFERENCES

1. Salamon, M. D. G. Energy Considerations in Rock Mechanics:
Fundamental Results. J. S. Aft. Inst. Min. Metall., v. 84, No. 8, 1984,
pp. 233-246.

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

3. Sinha, K.P, Displacement Discontinuity Technique for Analyzing
Stresses and Displacements Due to Mining in Seam Deposits. Ph.D.
‘Thesis, Univ. MN, 1979, 311 pp.

4, Crouch, S. L., and C. Fairhurst. The Mechanics of Coal Mine
Bumps and the Interaction Between Coal Pillars, Mine Roof, and Floor
(contract H0101778, Univ. MN). BuMines OFR 53-73, 1973, 88 pp;
NTIS PB 222 898.

5. Heasley, K. A., and K. Barron. A Case Study of Gate Pillar Re-
sponse to Longwall Mining in Bump-Prone Strata. Paper in Proceedings

of Longwall USA, Pittsburgh, PA, 1988, Industrial Presentation, Inc.,
Aurora, CO, 1988, pp. 91-105.

6. Cook, N. G. W., E. Hoek, J. P. G. Pretorius, W. D. Ortlepp, and
M. D. G. Salamon. Rock Mechanics Applied to the Study of Rock
Bursts. J. S. Afr. Inst. Min. Metall., v. 66, No. 10, 1966, pp. 435-528.

7. Wang, F. D., W. A. Skelly, and J. Wolgamott. In Situ Coal Pillar
Strength Study (contract H0242022, CO Sch. Mines). BuMines OFR
107-79, 1976, 243 pp.

8. Iannacchione, A. Behavior of a Coal Pillar Prone to Burst in the
Southern Appalachian Basin of the United States. Paper in Proceedings
of Second International Symposium of Rockbursts and Seismicity in
‘Mines. Univ. MN, June 1988, pp. 427-439,

9. Dahlquist, G., and A. Bjork. Numerical Methods. Prentice-Hall,
1974, S71 pp.


chosen unit system. For a full discussion of the requested
input variables, refer to the section of this report titled
"INPUT FILE STRUCTURE FOR MULSIM/NL."

RUNNING MAIN PROGRAM MULNLPC

An earlier section of this report, "RUNNING
MULSIM/NL," discusses the files used by MULSIM/NL.
and gives examples of the computer operating commands
necessary to run the program in either a mainframe or a
workstation environment. The subsection on "MULSIM/
NL FILES" along with table 3 give details on all input,
printout, coarse-mesh data, and fine-mesh data files used
and created by the main program. MULNLPC uses the
same files as the mainframe and workstation versions with
one minor exception. In the PC version, FORTRAN unit
07 contains the basic program printout as opposed to
FORTRAN unit 06. The PC version also sends some
printed output directly to the computer screen, which is
defined as FORTRAN unit 06. This output consists of a
disclaimer and data for each equation solver iteration as
the program converges on a solution. With these iteration
data, the user can monitor progress of model.

Running MULNLPC requires the following BAT
files. For a single-seam model, create a file called
RUNMULNL.BAT that contains the following DOS
commands:

MULNLPC < %1.INP
REN FORO7.DAT %1.PRT
REN FOR31L.DAT %1.CMD
REN FOR41.DAT %1.FMD
DEL FOR*.*.

Next, create a file called RUNALL.BAT that contains the
following command:

CALL RUNMULNL.BAT TESTA.

Finally, by typing the command RUNALL (return), the PC
will execute the command line in the RUNALL.BAT file,
which in turn executes the RUNMULNL.BAT file with the
argument TESTA substituted for %1. RUNMULNL will
then execute MULNLPC using the file TESTA.INP as
input. After the program has converged to a solution, it
will rename the printed output file TESTA.PRT, the
coarse-mesh data file TESTA.CMD, and the fine-mesh
data file TESTA.FMD. Finally, it will delete any
remaining files of the form FOR*.* before returning
control of the PC back to the user.

With multiple jobs, the file RUNALL.BAT might
contain the following commands:

CALL RUNMULNL.BAT TESTA
CALL RUNMULNL.BAT TESTB
*

*

ete.

With this batch file, the user can solve many MULNLPC
jobs sequentially.

For a two-seam model, the RUNMULNL.BAT file
should contain the following DOS commands:

MULNLPC < %1.INP
REN FORO7.DAT %1.PRT
REN FOR31.DAT %1.CM1
REN FOR32.DAT %1.CM2
REN FOR41.DAT %1.FM1
REN FOR42.DAT %1.FM2
DEL FOR*.*.

For a two-seam job with the argument TEST2, this batch
file will execute MULNLPC using the file TEST2.INP as
input. When it is done, the file TEST2.PRT will con-
tain the printed output, and the files TEST2.CM1,
TEST2.CM2, TEST2.FM1, and TEST2.FM2 will contain
coarse- and fine-mesh data for seams 1 and 2, respectively.
Execution times with MULNLPC depend on many fac-
tors including the machine itself, size of the problem, and
degree of nonlinearity in the model. Typical problems
with a 120 by 120 fine mesh and some nonlinear elements
can require 24 h of computing time with a 386 system.

EXAMINING OUTPUT FILES WITH POST-
PROCESSOR PROGRAM MULPLTPC

‘The program MULPLTPC on a PC operates the same
as MULPLT on a mainframe or workstation; therefore,
the previous subsection on "OUTPUT FILE EXAMINA-
TION WITH THE POSTPROCESSOR MULPLT/NL"
also applies to MULPLTPC. This postprocessor provides
a simple very fast graphical means to examine fine- and
coarse-mesh data files from MULNLPC. It is menu-
driven and can display psuedo-three-dimensional color
plots or two-dimensional cross sections of the calculated
stresses, displacements, and energies. The previously
mentioned subsection provides greater detail on the
capabilities of MULPLTPC.


CONTROL SECTION

CONTROL SECTION

FINE MESH GEOMETRY
SEAM 1 STEP 1

FINE MESH GEOMETRY
SEAM 1 STEP 1

COARSE MESH GEOMETRY
SEAM 1 = STEP 1

FINE MESH GEOMETRY
SEAM 2 STEP 1

FINE MESH GEOMETRY
SEAM 1 STEP 2

COARSE MESH GEOMETRY
SEAM 1 STEP 1

COARSE MESH GEOMETRY
SEAM 1 STEP 2

Figure 9.—MULSIM/NL input file structure for single-seam,
multiple-step problem.

CONTROL SECTION

FINE MESH GEOMETRY
SEAM 1 STEP 1

FINE MESH GEOMETRY
SEAM 2 STEP 1

COARSE MESH GEOMETRY
SEAM 1 = STEP 1

COARSE MESH GEOMETRY
SEAM 2 STEP 1

Figure 10.—MULSIM/NL input file structure for multiple-seam,
single-step problem.

step. By way of example with the mining geometry shown
in figure 8, a second mining step might split the point pil-
lar; a third step could recover the right wing, and finally,
a fourth step would recover the left wing.

Figure 10 shows the input file structure for a multiple-
seam, single-step problem. Variables within the control
section undergoes minor changes as discussed later.
Notice how this input file structure changes from the
single-seam, single-step structure of figure 7, and also note
how it differs from the single-seam, multiple-step structure
of figure 9. In a multiple-seam problem, additional seams

COARSE MESH GEOMETRY
SEAM 2 STEP 1

FINE MESH GEOMETRY
SEAM 1 STEP 2

FINE MESH GEOMETRY
SEAM 2 STEP 2

COARSE MESH GEOMETRY
SEAM 1 STEP 2

COARSE MESH GEOMETRY
SEAM 2 STEP 2

Figure 11.—MULSIM/NL input file structure for multiple-seam,
multiple-step problem.

might lie above and/or below the seam. First, the fine-
mesh geometry is defined for each seam, followed by the
coarse-mesh geometry for each seam.

Finally, figure 11 shows the input file structure for a
multiple-seam, multiple-step problem. Again, compare
how this input file structure changes from the prior struc-
tures shown in figures 7, 9, and 10, The multiple-seam
fine- and coarse-mesh geometry sections are repeated for
each additional mining step.

UNITS

Before moving into discussions on the control param-
eter section of the input file, the important subject of units
requires a few words. MULSIM/NL will work with any
consistent system of units. Table 1 gives examples of three
unit systems for input and the resultant units for the
output.