soft spot 71
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FLAC discussionTRANSCRIPT
Soft SpotSoft SpotItasca’s Software Newsletter
VOLUME 7 number 1
February 1999
In the Spotlight
3DEC was developed in 1988 as the three-dimensional
extension of Peter Cundall’s distinct element method.
Initially, the program was used as a research tool to sim-
ulate the progressive, large-scale movements of blocky
rock systems. The first applications were in stability
analyses of rock slopes and
underground excavations. Over
the past ten years, the applica-
tion of 3DEC has expanded to
several other engineering fields,
such as stability assessment of
arch dams on rock foundations,
design of underground power
houses, evaluation of the ulti-
mate capacity of masonry struc-
tures, and seismic studies of
historical columns and arches.
3DEC is now an accepted analy-
sis tool for applications involv-
ing jointed or blocky materials.
This issue of SoftSpot focuses on the recent
advancements and applications of 3DEC. The adjacent
article describes what is new with the December 1998
release of 3DEC Version 2.0. We have asked some of
our 3DEC users to provide examples of recent studies
they have performed. These are presented on page 2; a
list of recent 3DEC-related publications is provided on
page 7. I think you will find that 3DEC offers unique
capabilities in modeling large, complex discontinuous
systems.
—Roger Hart
Director, Software Services
3DEC Version 2.0 Released . . . . . . . . . . . . . . . 1 Modeling Hints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
In the Spotlight . . . . . . . . . . . . . . . . . . . . . 1 Linking Itasca Codes: Interactive
3DEC Applications . . . . . . . . . . . . . . . . . . . 2 Analyses of Coupled 3D Problems . . . . . . . . . . . . . 5
Seismic Response of Stone Masonry Arches Recent 3DEC-Related Publications . . . . . . . . . . . . . . 7
State-of-Stress Determination SoftNotes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3DEC Arch Dam - Safety Analysis of Rock Foundation Training Corner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Soft Spot
3DEC Version 2.0 Released
tasca is pleased to announce the release of 3DEC Version
2.0. The new version of the code is specifically designed
for static, mechanical analyses in rock mechanics—and is
available at a price nearly half that of previous versions.
3DEC was created to model the quasi-static or dynamic
response to loading of rock media
that contain multiple, intersecting
joint structures. 3DEC simulates
large displacements, allows multi-
ple contact modes between blocks,
offers an explicit solution scheme,
provides multiple material models,
and can simulate excavation or
backfilling through the use of
“null blocks.” Tools available in
the code include a preprocessor
that reads AutoCAD files, interac-
tive manipulation of screen
images, mesh-generation tools, a
tunnel generator, and a statistically
based joint-set generator.
Features new to 3DEC with the release of Version 2.0
include the following items.
Built-in Programming Language FISH —The Itasca
programming language, FISH, enables users to define new
variables and functions to customize a numerical model to
suit their particular needs. FISH can vary block and joint
properties within the block structure, define variables for
plotting, implement joint generation schemes, apply a
servo-control of a numerical test, specify different boundary
conditions and automate parameter studies.
(Continued on page 6)
3DEC model of an arch damon a jointed rock foundation
2
3DEC Applications
Seismic Response of Stone MasonryArches
DEC is well suited to perform both static and dynamic
analyses of masonry structures. In this application, 3DEC
is applied to evaluate the seismic behavior of stone masonry
arches. The code performs a detailed simulation of the
architectural components of stone masonry arches under
earthquake loading. Free-standing arches are often found in
partially ruined structures, and their safety is always a cause
for concern. 3DEC models have been created for several
types of arches. A pointed arch model with a T-shape section
is illustrated in Figure 1.
The arch is first subjected to self-weight, and then
dynamic loading is applied in the form of a prescribed
motion at the support blocks. Pointed arches are shown to
withstand a higher loading than circular arches.
Out-of-plane collapse is a predominant failure mode, as
shown in Figure 2. Lemos (1997) provides further informa-
tion on this analysis, including evaluation of other arch
shapes.
The article mentioned above appears in the list of recent
3DEC-related publications that appears on page 7.
1.0 m
0.55 m
7.5 m
5.3 m
Figure 1 Pointed arch model
Figure 2 Failure mode for pointed arch model
State-of-Stress Determination
nowledge of the virgin stress field is obtained from
3DEC analyses in the design for a nuclear-waste reposi-
tory site in Switzerland. The 3DEC model simulates the
topography, complicated geology and applied tectonic forces
at the site. The model is calibrated using hydrofrac stress
measurements, borehole breakout data and geological
indicators.
Figure 3 illustrates the 3DEC model for the repository site.
The different colored blocks in the model correspond to the
various geologic materials at the site. The blocky model con-
sists of approximately 365,000 cubic blocks and is considered
sufficient to evaluate the regional stress state. Figure 4 shows
the inner region of the model in the vicinity of the repository
horizon. The virgin stress field is indicated in Figure 5 by
the plot of principal stress tensors and contours of maximum
principal stress through the repository horizon. Compari-
sons to stress measurements are made at the locations shown
on the figure.
Drs. Heinz Konietzky and Lothar te Kamp of Itasca’s
office in Germany provided this contribution.
3DEC Arch Dam - Safety Analysis ofRock Foundation
he Santa Maria arch dam is located in the eastern Swiss
Alps. It is 117 m high and has a crest length of 650 m.
Due to the wide span, the dam is subjected to large displace-
ments in the center part of the dam foot. The dam survives
these displacements without cracking because several large
joints in the ground open and allow movement. The arrange-
ment of those joints led to the investigation of the safety of
the foundation of the dam. All the major joints down to a
spacing of 15 m were modeled. It can be shown that the
foundation can withstand an increase of the load from full
reservoir by at least a factor of 2. This is much greater than
can be expected due to an earthquake or an overtopping of
the water. Figures 6 and 7 show the components of the arch
dam represented by the 3DEC model.
We thank Mr. Christian Moor of Nordostschweizerische
Kraftwerke (NOK), Baden, Switzerland, for providing this
3DEC application.
For other studies on modeling arch dams with 3DEC, see
Lemos (1996) in the bibliography of recent 3DEC-related
publications that appears on page 7.
3
Figure 3 3DEC model of nuclear-waste repository site
Figure 4 Inner region of model inthe vicinity of the repository S B 1
S B 2
S B 3
S B 4
7 200 0 72 50 0 7 300 0 73 50 0 7 400 0 74 50 0 7 500 0
X (m od el coo r d in a t e )
91 50 0
92 00 0
92 50 0
93 00 0
93 50 0
94 00 0
94 50 0
95 00 0
Z(m
od
el
co
or
din
ate
)
5
1 0
1 5
2 0
2 5
3 0
3 5
4 0
4 5
5 0
5 5
6 0
6 5
7 0
7 5
Figure 5 Plan view of repository region showing principal stresstensors and contours of maximum principal stress (in MPa)
250m
540m
1300 m
1000m
1700 m ü.M.
1400 m ü.M.
AnzahlBlöcke
Volumen[m3]
642'000369
114
178
736
487'000
Total
75
20.5 Mio
715 Mio
737 Mio
Modell-teil
X
Y
Z
model
compo-
nent
number
of
blocks
Volume
[m3]
106
106
106
above sea level
above sea level
Figure 6 3DEC model of Santa Maria arch dam
Figure 7 Arch dam model with addition of major faultsin dam foundation (6700 blocks total)
4
Modeling Hints
Changing the Water Level
Settlement or heave resulting from the lowering or raising
of the groundwater table is a common situation in soil engi-
neering. The analysis of this condition can be conducted
with FLAC for various types of problem settings. When a
fully coupled calculation is performed, the displacement
changes arise automatically as the phreatic surface changes.
However in many cases—for example, in the dewatering of
an excavation—it may often be assumed that the water level
is instantaneously changed; thus, a steady-state flow state is
obtained without performing a fluid-flow calculation. The
pore pressure is then changed to correspond to the change in
the water level.
This simplified analysis may be run either outside the
groundwater configuration or within the groundwater con-
figuration—but with flow turned off. For both approaches,
there is an imposed change in the pore pressures: outside of
CONFIG gw, this can be done with either the WATER table
or INI pp command; within CONFIG gw, it can be done
with the INI pp and INI sat commands.
In addition, for both approaches, there must also be an
adjustment made to the total stresses in zones in which pore
pressures are changed. The total stresses must be corrected
because an imposed instantaneous change in pore pressure in
a material does not affect inter-granular forces; hence, the
effective stress is unchanged in the short term.
The adjustment to total stress can be done conveniently by
subtracting the pore-pressure change from the total stresses
in the affected zones, using the INI sxx add -Dp, INI syy
add -Dp and INI szz add -Dp commands, where Dp is the
change in the pore pressure in the zone affected by the
change in the water level (Dp = p(new) - p(old)).
A simple demonstration of the effect of changing water
level is given by the accompanying data file. A box filled with
soil is initially dry. The soil is instantaneously saturated, and
the soil heaves as indicated in the plot.
Note that gravity is not acting in this example. Saturated
and unsaturated densities must also be adjusted if gravity is
acting and the water level is changed. In CONFIG gw
mode, this is performed automatically for zones in which the
pore pressure is changed; only the unsaturated density needs
to be specified. Outside of the CONFIG gw mode, the
unsaturated density must be assigned by the user to all zones
above the water table and the saturated density to all zones
below, when the water level is changed.
For further discussion and examples on changing the water
level, see Section 6.11.9 of the Theory and Background vol-
ume of the FLAC Manual.
; add water to a box of soil and produce heave
config gw
grid 4 8
m elas
prop dens 1500 sh 1e8 bu 2e8
water dens 1000 bulk 0
set flow off
fix x i 1
fix x i 5
fix x y j 1
ini sxx -1e4
ini szz -1e4
solve ; Initial equilibrium
;
ini pp 1e4 ; Add water
ini sxx add -1e4 ; Adjust total stresses
ini syy add -1e4 ; to account for pore-pressure
ini szz add -1e4 ; change
;
his ydisp i 1 j 9
solve
plot hold bo disp str
FLAC (Ver s io n 3.40)
LEGEND
7-Jan-99 15:01
step 614
-3.333E+00 <x< 7.333E+00
-1.333E+00 <y< 9.333E+00
Boundary plot
0 2E 0
Displacement vectors
Max Vector = 2.390E-04
0 5E -4
Principal stresses
Max. Value = 1.603E+04
0 5E 4
0.000
2.000
4.000
6.000
8.000
-2.000 0.000 2.000 4.000 6.000
JOB TITLE :
Itasca Consulting Group, Inc.
Minneapolis, Minnesota USA
Heave resulting from adding water to a box of soil
End Bearing Piles
Pile elements in FLAC are specifically designed to simulate
the effect of a soil squeezing around a single foundation pile.
The pile element transfers loads to the soil via the coupling
springs connected between the pile nodes and the grid. Pile
elements are thus intended to represent the behavior of fric-
tion piles.
It is possible to also model end-bearing loading with
FLAC’s pile elements. This can be accomplished by neglect-
ing the shear friction along the bottom segment of the pile,
adjusting instead the properties of the corresponding cou-
pling shear spring to account for the pile bearing capacity.
The end-bearing spring can be assigned a limit load evaluated
using an engineering bearing capacity formula. An example
application of this approach is provided in Section 5.4.4.1 in
the Theory and Background volume of the FLAC Manual.
5
Linking Itasca Codes: InteractiveAnalyses of Coupled 3D Problems
s publicized in the last SoftSpot, transfer of information
between Itasca codes is now possible by using FISH.
Recently, this feature was used to couple FLAC3D and PFC3D
to investigate the effects of a coupled mechanical and fluid
flow response. FLAC3D was used to model the fluid flow,
while PFC3D was used to model the porous solid response.
Exchange of necessary information between the two codes
was accomplished by binary file exchange through respective
FISH functions, using a simple DOS batch-file to manage the
sequential execution of the two codes.
The physical scenario is that of fluid flow through a weak
porous medium as a result of a relatively sudden pressure
drop in a local region. The fluid passing through the pore
space imposes drag forces on the solid material that tend to
“push” the material in the direction of flow. Deformation
and break-up of the porous solid occurs as a result of the drag
forces, and affects its local permeability.
Asgian et al. (1995) derived an expression for the drag
force when an assembly of bonded particles represents the
solid material. The pore pressure gradient is part of this
expression and can be obtained from the FLAC3D fluid flow
model. This gradient is output and subsequently used in the
PFC3D model to determine the individual drag force (i.e.,
body force) on each particle.
The permeability associated with any volume in the PFC3D
solid model can be estimated from porosity using the
Kozeny-Carman equation, for example. Updated
permeabilities resulting from deformations of the porous
solid are passed to the FLAC3D model to determine a new
fluid flow state.
Depending on the selected time increment, discrete calcu-
lations of fluid flow and mechanical states can be used in this
manner to simulate a 3D transient dynamic coupled fluid
flow/mechanical response. Figure 1 outlines the approach.
The approach requires a division of the PFC3D model into
a virtual 3D cell space equivalent to that of the FLAC3D
model grid. Information is exchanged between the virtual
cell space in PFC3D and the cell space of the equivalent
FLAC3D grid. Note that,
while the FLAC3D flow
model must encompass the
entire geometric domain of
the PFC3D solid model, the
opposite is not necessary.
Figure 2 shows an example
of volumes occupied by the
two models. As seen in
Figure 2, only the blue vol-
ume in the FLAC3D model
is represented by the
PFC3D model. Figure 2 also
shows a cut through the
models, illustrating the vir-
tual cell space in PFC3D
and the equivalent cell
space in FLAC3D. The
boundary location of low
pressure is also indicated.
Pore pressure contours in
the FLAC3D model and the
corresponding drag forces
Figure 1 Linkage of FLAC3D and PFC3D
Pressurized Medium
Point
5 m
5 m
2 m
1 m3
Low Pressure
Figure 2 Volumes occupied by FLAC3D (left) and PFC3D (right) models
(Continued on page 8)
6
High-Resolution Graphics
—The video card installed in your
computer can be directly accessed
for a high-resolution graphics
screen plot using the SET mode
command in the DOS version of
3DEC 2.0.
Improved Contact Logic
—The contact logic allows large
displacements for deformable as
well as rigid blocks. Every contact
is discretized into sub-contacts,
where interaction forces are
applied. Sub-contacts are updated
to allow a smooth transition of
forces as one block slides over
another block.
New Block Type —A prism-shaped
block is available (command POLY prism).
This type of block can be used, for example, to create blocky
structures such as a masonry wall or arch bridge.
New Block Material Models —Two new material models
are available: an anisotropic elasticity model and a bilinear
plasticity model that incorporates strain-hardening/softening
and ubiquitous jointing for both the matrix and the ubiqui-
tous joints. The anisotropic elasticity model can represent an
orthotropic elastic material and a transversely isotropic elastic
material. Mohr-Coulomb, ubiquitous-joint, and strain hard-
ening/softening behaviors can be obtained as special cases of
the bilinear model.
Pore-Pressure Generation —A pore-pressure gradient can
now be specified for both block zones and joints. This
allows an effective-stress calculation to be performed.
Graphics Enhancements —User-defined graphics can be
added to 3DEC plots via the PLOT label and PLOT overlay
commands. For example, user-defined labels can be added to
the axes of table and history plots. An overlay file contains
(x,y,z) coordinates that define line segments that can be cre-
ated by the user to define an arbitrary shape. The shape can
then be overlaid on the 3DEC plot. The MOVIE facility has
been modified to create much smaller movie files. PCX out-
put of the graphics screen image is available.
Revised User's Manual —The 3DEC Manual has been
revised and expanded to eight volumes. More explanations
are provided for the features in 3DEC, existing examples have
been expanded, and several new examples have been added.
The 3DEC Manual
User's Guide
an introduction to 3DEC and
its capabilities
Command Reference
descriptions of all 3DEC commands
FISH in 3DEC
a complete guide to FISH and FISH functions
Theory and Background
detailed descriptions of the built-in features
Optional Features
detailed descriptions of the optional features
Verification Problems & Example Applications
a collection of verification problems and example
applications
Command and FISH Reference Summary
a quick summary of all 3DEC commands and FISH
statements
Index
a subject index for all volumes of the 3DEC Manual
The entire manual is also provided on CD-ROM. The man-
ual can be viewed with Acrobat Reader, and users can search
for specific topics across all volumes by implementing the
search facility available in Acrobat.
If you are interested in obtaining 3DEC Version 2.0, please
contact your nearest Itasca office or your software agent.
(The information may be obtained from the Itasca web site,
www.itascacg.com.) The bibliography that follows is an
abbreviated version of the full list of 3DEC-related publica-
tions that is also available from the Itasca web site.
3DEC Version 2.0 (Continued from page 1)
7
Recent 3DEC-Related Publications
3DEC has been applied in a wide variety of engineering stud-
ies. The references below describe some of the more recent
applications.
Christianson, M., J. Itoh, and S. Nakaya. “Seismic Analysis
of the 25 Stone Buddhas Group at Hakone, Japan,” in Rock
Mechanics (Proceedings of the 35th U.S. Symposium, Univer-
sity of Nevada, Reno, June 1995), pp. 107-112. J.J.K.
Daemen and R.A. Schultz, Eds. Rotterdam: A.A. Balkema.
Dasgupta, B., and L.J. Lorig. “Numerical Modelling of
Underground Power Houses in India,” in Proceedings of the
International Workshop on Observational Method of Con-
struction of Large Underground Caverns n Difficult Ground
Conditions, (8th ISRM International Congress on Rock
Mechanics, Tokyo, September 1995), pp. 65-74. S. Sakurai,
Ed.
Dasgupta, B., R. Dham, and L.J. Lorig. “Three-Dimensional
Discontinuum Analyses of the Underground Power House
for Sardar Sarovar Project, India,” in Proceedings of the
Eighth International Congress on Rock Mechanics (Tokyo,
Septber 1995), Vol. II, pp. 551-554. T. Fujii, Ed. Rotterdam:
A.A. Balkema, 1995.
Fairhurst, C. “Three Gorges Dam Reservoir, Yangtze River,
China,” Felsbau, 13(6), 390-394 (1995).
Hammer, H., H.C. Siegfried Niedermeyer, and T.
Niedermeyer. “Untersuchen zu Gebrigsspannungen
und-bewegungen in der Schwabischen Alb,” Felsbau, 13(6),
367-373 (1995).
Hella, P., and P. Saksa. “3D Geological Modelling, Model
Transfer and Validation,” in Proceedings of the SCSC ‘95
Conference (Ottawa, July 1995), pp. 967-971. T.I. Oren and
L.G. Birta, Eds. Place: SCS, 1995.
Hökmark, H. “Acceptance of Emplacement Hole Positions -
Stage 1 Thermomechanical Study,” in Preprints of Contribu-
tions to the Workshop on Computational Methods in Engi-
neering Geology (Lund, Sweden, October 1996), pp. 42-51.
R. Pusch and R. Adey, Eds. Lund: Clay Technology AB,
1996.
Hökmark, H. “Numerical Study of the Performance of
Tunnel Plugs,” in Preprints of Contributions to the Workshop
on Computational Methods in Engineering Geology (Lund,
Sweden, October 1996), pp. 212-221. R. Pusch and R. Adey,
Eds. Lund: Clay Technology AB, 1996.
Johansson, E.J.W. “Treating Sewage Underground,” Tunnels
& Tunneling, 21-23 (July 1995).
Johansson, E.J.W., and H. Kuula. “Three-Dimensional
Back-Analysis Calculations of Viikinmaki Underground
Sewage Treatment Plant in Helsinki,” in Proceedings of the
Eighth International Congress on Rock Mechanics (Tokyo,
September 1995), Vol. II, pp. 597-600. T. Fujii, Ed.
Rotterdam: A.A. Balkema, 1995.
Lemos, J.V. “Discrete Element Modelling of the Seismic
Behaviour of Stone Masonry Arches,” Computer Methods in
Structural Masonry – 4 (Proceedings of the 4th International
Symposium Num. Methods in Structural Masonry -
STRUMAS IV, Florence, September 1997), pp. 220-227.
G.N. Pande, J. Middleton, and B. Kralj, Eds. London:
E&FN Spon, 1997.
Lemos, J.V. “Discrete Element Modelling of Historical
Structures,” in Proc. Int. Conf. New Technologies in Struc-
tural Engineering, Lisbon, Vol. 2, pp. 1099-1106. S.P. Santos
and A.M. Baptista, Eds. Lisbon: LNEC, 1996.
Lemos, J.V. “Modelling of Arch Dams on Jointed Rock
Foundations,” in Prediction and Performance in Rock
Mechanics & Rock Engineering (Proc. of ISRM International
Symposium EUROCK ‘96, Turin, September 1996), Vol. 1,
pp. 519-526. G. Barla, Ed. Rotterdam: A.A. Balkema, 1996.
Lemos, J.V. “Assessment of the Ultimate Load of a Masonry
Arch Using Discrete Elements,” in Proc. Int. Conf. Comp.
Meth. in Struct. Masonry, Lisbon, Portugal, April 1995.
Thorval, A., H. Baroudi, J.P. Piguet, E. Vuillod, G. Abdallah,
A. Hosni, and J. Lin. “Couple Thermo-Hydro-Mechanical
Phenomena in Fractured Rocks: Recent Developments in
Modelling Methods and Validation Tests (in French),” in
Proceedings of the 8th International Congress on Rock
Mechanics (Tokyo, September 1995), Vol. 2, pp. 703-706. T.
Fujii, Ed. Rotterdam: A.A. Balkema, 1995.
Tolppanen, P.J., E.J.W. Johansson, and R. Riekkola. “Com-
parison of Vertical and Horizontal Deposition Hole Concept
for Disposal of spent Fuel Based on the Rock Mechanical In
Situ Stress/Strength Analyses,” in Preprints of Contributions
to the Workshop on Computational Methods in Engineering
Geology (Lund, Sweden, October 1996), pp. 230-237. R.
Pusch and R. Adey, Eds. Lund: Clay Technology AB, 1996.
Tolppanen, P.J., E.J.W. Johansson, and J.P. Salo. “Rock
Mechanical Analyses of In-Situ Stress/Strength Ratio at the
Posiva Oy Investigation Sites, Kivetty, Olkiluoto and
Romuvaara” in Prediction and Performance in Rock
Mechanics & Rock Engineering (Proc. of ISRM International
Symposium EUROCK ‘96, Turin, September 1996), Vol. 1,
pp. 435-442. G. Barla, Ed. Rotterdam: A.A. Balkema, 1996.
8
is Itasca’s software
newsletter. It is published twice annu-
ally for clients and friends.
Soft SpotITASCA
Itasca Consulting Group, Inc.
708 South Third Street, Suite 310
Minneapolis, MN 55415 USA
Phone: 612-371-4711 • Fax: 612-371-4717
Email: [email protected] • Web: www.itascacg.com
FLAC Beginners’Course
28 - 30 April 1999
Itasca Consulting Group, Inc.
Minneapolis, Minnesota USA
An introductory course on practical application of FLAC
in geoengineering will be offered at Itasca’s Minneapolis
office. This training is specifically designed to provide
new users with a recommended approach to apply FLAC
most efficiently for geomechanics analysis and design.
Itasca engineers have used FLAC and other Itasca soft-
ware in a wide variety of geoengineering studies. This
experience will guide the teaching and presentations dur-
ing the 3-day course.
One computer will be provided for every two partici-
pants. Topics will include hands-on exercises throughout
the training program. A training notebook will also be
provided for each participant.
The course is restricted to 12 participants, accepted in the
order of the date of payment of the fee ($815). Please
contact Itasca to register or for further information.
Further information and a schedule of the three-day
course is available from Itasca’s web site,
www.itascacg.com.
TrainingCorner
Soft Notes
Printing on Non-PostScript Printers
With the Windows versions of our codes, FLAC 3.4 and
FLAC3D 2.0, plots can be sent directly to the Windows native
printer drivers, when running under Windows 95/98/NT. In
time, all Itasca software will be offered as Windows applica-
tions. Presently, with our DOS codes, plots can be sent
directly to PostScript printers, and there are utilities available
to print these graphics on non-PostScript printers. We have
recently found a shareware program, RoPS, that enables
users to print PostScript graphics files on any Windows com-
patible printer. We find this program easier to install and use
than Ghostview/Ghostscript and recommend it to users. We
now include RoPS on the Itasca CD-ROM, or you can
obtain a copy by visiting the RoPS web page at
www.giant-technologies.com/rops.
Rainbow Keys
We have been pleased so far with our switch from Unikeys
to Rainbow keys. We are not aware of any hardware failures
of the Rainbow keys. We have had some difficulties with
the installation of the software drivers (in WinNT) that were
due to errors in the install scripts for some of the CD-ROMs
(prior to CD-ROM version ITASCA2E).
for particles on the mid- vertical plane
through the PFC3D model appear in Figure 3.
Contact forces between these particles are
also illustrated, with blue indicating com-
pression and red indicating tension. It is seen
that, after some erosion of the porous solid, a
stable state has been achieved.
Asgian, M.I., P.A. Cundall, and B.H.G.
Brady. (1995) “The Mechanical Stability of
Propped Hydraulic Fractures: A Numerical
Study,” in Proceedings of the SPE 69th
Annual Technical Conference and Exhibition
(New Orleans, September 1994), Vol. 1, pp.
475-489. Richardson, Texas: Society of
Petroleum Engineers, 1994; also J. Pet. Tech.,
203-208 (March 1995).
Linking Itasca Codes (Continued from page 5)
Pore Pressure Contours
Pore Pressure Contours
Particle Drag Forces
Contact Forces - Stable
Figure 3 Pore pressure contours (FLAC3D, left), corresponding drag forces (PFC3D, top right),and contact forces from the final stage (PFC3D, bottom right).