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INTRODUCTION 1 - 1

1 INTRODUCTION

1.1 Overview

FLAC is a two-dimensional explicit finite difference program for engineering mechanics compu-tation. This program simulates the behavior of structures built of soil, rock or other materialsthat may undergo plastic flow when their yield limits are reached. Materials are represented byelements, or zones, which form a grid that is adjusted by the user to fit the shape of the object tobe modeled. Each element behaves according to a prescribed linear or nonlinear stress/strain lawin response to the applied forces or boundary restraints. The material can yield and flow, and thegrid can deform (in large-strain mode) and move with the material that is represented. The explicit,Lagrangian calculation scheme and the mixed-discretization zoning technique used in FLAC en-sure that plastic collapse and flow are modeled very accurately. Because no matrices are formed,large two-dimensional calculations can be made without excessive memory requirements. Thedrawbacks of the explicit formulation (i.e., small timestep limitation and the question of requireddamping) are overcome to some extent by automatic inertia scaling and automatic damping that donot influence the mode of failure.

Though FLAC was originally developed for geotechnical and mining engineers, the program offersa wide range of capabilities to solve complex problems in mechanics. Several built-in constitu-tive models that permit the simulation of highly nonlinear, irreversible response representative ofgeologic, or similar, materials are available. In addition, FLAC contains many special features,including:

• interface elements to simulate distinct planes along which slip and/or separa-tion can occur;

• plane-strain, plane-stress and axisymmetric geometry modes;

• groundwater and consolidation (fully coupled) models with automatic phreaticsurface calculation;

• structural element models to simulate structural support (e.g., tunnel liners,rockbolts or foundation piles);

• automatic re-meshing logic to generate a regular mesh, and prevent a badlydistorted grid, during the solution process in large strain simulations;

• “virtual-grid” generation tools available through a graphical-user interface tofacilitate model construction;

• extensive facility for generating plots of virtually any problem variable;

• optional dynamic analysis capability;

• optional viscoelastic and viscoplastic (creep) models;

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• optional thermal (and thermal coupling to mechanical stress and pore pressure)modeling capability;

• optional two-phase flow model to simulate the flow of two immiscible fluids(e.g., water and gas) through a porous medium; and

• optional facility to add new, user-defined constitutive models written in C++and compiled as dynamic link libraries (DLLs) that can be loaded when needed.

FLAC also contains the powerful built-in programming language FISH (short for FLACish). WithFISH, you can write your own functions to extend FLAC ’s usefulness, and even implement yourown constitutive models if so desired. FISH offers a unique capability to FLAC users who wishto tailor analyses to suit specific needs. You will soon see that, with all of these capabilities,FLAC can be an indispensable analysis-and-design tool in a variety of fields in civil and mechanicalengineering.

FLAC can be operated as either a menu-driven or a command-driven computer program. The menu-driven mode provides easy-to-use mouse access to FLAC operation by generating and applying allthe input required for a FLAC simulation, in response to point-and-click operations. This modeallows first-time or occasional users a simple means by which to begin solving problems with FLACimmediately.

The command-driven mode requires knowledge of the word-command “language” used by FLAC,which can be more difficult for new users to master than the menu-driven mode. However, it offersseveral advantages when applied to engineering problems:

1. The input language is based upon recognizable word commands that allow youto identify the application of each command easily and in a logical fashion (e.g.,the APPLY command applies boundary conditions to the model).

2. Engineering simulations usually consist of a lengthy sequence of operations(e.g., establish in-situ stress, apply loads, excavate tunnel, install support,and so on). A series of input commands (from a file or from the keyboard)correspond closely with the physical sequence that it represents.

3. A FLAC data file can easily be modified with a text editor. Several data filescan be linked to run a number of FLAC analyses in sequence. This is ideal forperforming parameter sensitivity studies.

4. The word-oriented input files provide an excellent means of keeping a docu-mented record of the analyses performed for an engineering study. Often, it isconvenient to include these files as an appendix to the engineering report forthe purpose of quality assurance.

5. The command-driven structure allows you to develop pre- and post-processingprograms to manipulate FLAC input/output as desired. For example, you maywish to write a mesh-generation function to create a special grid shape for aseries of FLAC simulations. This can readily be accomplished with the FISHprogramming language, and incorporated directly in the input data file.

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When operated from the menu-driven mode, FLAC commands are created and applied automatically.Also, a record of the commands is kept, and can be saved to provide a documented listing of thecommands used in the analysis. This command record can be used to drive FLAC in command-driven mode.

Dr. Peter Cundall developed FLAC in 1986 specifically to perform engineering analyses on anIBM-compatible microcomputer. The software is designed for high-speed computation of modelscontaining several thousand elements. With the advancements in floating-point operation speed andthe ability to install additional RAM at low cost, increasingly larger problems can be solved withFLAC. For example, FLAC can solve a model containing up to 30,000 elements of Mohr-Coulombmaterial on a microcomputer with 24 MB RAM. The solution speed for a model of this size isroughly 14 calculation steps per second on a 2.4 GHz Pentium IV microcomputer.* The speed isessentially a linear function of the number of elements; a model of 15,000 elements would requirehalf the runtime to process the same number of calculation steps.

For typical models, consisting of 15,000 elements or fewer, the explicit solution scheme in FLACrequires approximately 4000 to 6000 steps to reach a solved state.† Thus, a 15,000 element modelrun on the Pentium described above would require roughly 3 minutes to perform 5000 calculationsteps. Consequently, typical engineering problems involving several thousand elements to model,which once required access to a mainframe computer to solve, can be solved with FLAC on amicrocomputer in a matter of minutes.

A comparison of FLAC to other numerical methods, a description of general features and newupdates in FLAC Version 6.0, and a discussion of fields of application are provided in the followingsections. If you wish to try FLAC right away, the program installation instructions and simplemenu-driven and command-driven tutorials are provided in Section 2.

* See Section 5 for a comparison of FLAC runtimes on various computer systems.

† This can vary but, typically, a problem solution can be reached between 4000 and 6000 steps formodels containing up to 15,000 elements, regardless of material type. The explicit scheme isexplained in Section 1 in Theory and Background.

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1.2 Comparison with Other Methods

How does FLAC compare to the more common method of using finite elements for numericalmodeling? Both methods translate a set of differential equations into matrix equations for eachelement, relating forces at nodes to displacements at nodes. Although FLAC ’s equations are derivedby the finite difference method, the resulting element matrices, for an elastic material, are identicalto those derived by using the finite element method (for constant strain triangles). However, FLACdiffers in the following respects:

1. The “mixed discretization” scheme (Marti and Cundall 1982) is used for ac-curate modeling of plastic collapse loads and plastic flow. This scheme is be-lieved to be physically more justifiable than the “reduced integration” schemecommonly used with finite elements.

2. The full dynamic equations of motion are used, even when modeling sys-tems are essentially static. This enables FLAC to follow physically unstableprocesses without numerical distress.

3. An “explicit” solution scheme is used (in contrast to the more usual implicitmethods). Explicit schemes can follow arbitrary nonlinearity in stress/strainlaws in almost the same computer time as linear laws, whereas implicit solu-tions can take significantly longer to solve nonlinear problems. Furthermore,it is not necessary to store any matrices, which means that: (a) a large numberof elements may be modeled with a modest memory requirement; and (b) alarge-strain simulation is hardly more time-consuming than a small-strain run,because there is no stiffness matrix to be updated.

4. FLAC is robust in the sense that it can handle any constitutive model with noadjustment to the solution algorithm; many finite element codes need differentsolution techniques for different constitutive models.

5. FLAC numbers its elements in a row-and-column fashion rather than in asequential fashion. For many problems, this method makes it easier to identifyelements when specifying properties and interpreting output.

These differences are mainly in FLAC ’s favor, but there are two disadvantages:

1. Linear simulations run slower with FLAC than with equivalent finite elementprograms; FLAC is most effective when applied to nonlinear or large-strainproblems, or to situations in which physical instability may occur.

2. The solution time with FLAC is proportional to the ratio of the longest naturalperiod to the shortest natural period in the system being modeled. This pointis discussed in more detail in Section 1 in Theory and Background, butcertain problems are very inefficient to model (e.g., beams, represented bysolid elements rather than structural elements, or problems that contain largedisparities in elastic moduli or element sizes).

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1.3 General Features

1.3.1 Basic Features

FLAC is primarily intended for geotechnical engineering applications; the code embodies specialnumerical representations for the mechanical response of geologic materials. FLAC has twelve built-in material models: the “null” model, which represents holes (excavations) in the grid; the isotropicelastic model; the transversely isotropic elastic model; and eight plasticity models (Drucker-Prager,Mohr-Coulomb, ubiquitous-joint, strain-hardening/softening, bilinear strain-hardening/softeningubiquitous-joint, double-yield, Hoek-Brown, modified Cam-clay and cap-yield soil model). Youcan also create your own constitutive models by using the FISH programming language. Eachzone in a FLAC grid may have a different material model or property, and a continuous gradient orstatistical distribution of any property may be specified.

Additionally, an interface, or slip-plane, model is available to represent distinct interfaces betweentwo or more portions of the grid. The interfaces are planes upon which slip and/or separation areallowed, thereby simulating the presence of faults, joints or frictional boundaries.

The basic formulation for FLAC is for a two-dimensional plane-strain model. This condition isassociated with long structures or excavations with constant cross-section and acted on by loads inthe plane of the cross section. In addition, FLAC offers a plane-stress option for elastic and Mohr-Coulomb plasticity analysis. In this condition, the stresses normal to the cross section are zero. Thisis encountered, for example, in thin plates loaded only in their plane. Finally, there is also an optionto model axisymmetric geometry. In this case, cylindrical coordinates are used; x = 0 is the axis ofsymmetry, the positive x-direction corresponds to the radial coordinate, the y-direction to the axialcoordinate, and the out-of-plane direction (the z-direction) to the circumferential coordinate. Thisgeometry applies, for example, to problems involving cylindrical test specimens or cylindrical andspherical holes in a continuum. The out-of-plane stress, σzz, is calculated in FLAC for all threesolution conditions, and σzz is taken into account in plastic yield calculations for plane-strain andaxisymmetry conditions.

Either velocity (and displacement) boundary conditions or stress (and force) boundary conditionsmay be specified at any boundary orientation. Initial stress conditions, including gravitationalloading, may be given, and a water table may be defined for effective stress calculations. Allconditions may be specified with gradients.

FLAC incorporates the facility to model groundwater flow and pore pressure dissipation, and thefull coupling between a deformable porous solid and a viscous fluid flowing within the pore space.(The coupled interaction is described further in Section 1.3.3.) The fluid may be assumed to obeyeither the isotropic or anisotropic form of Darcy’s law, and is considered to be deformable. Non-steady flow is modeled, with steady flow treated as an asymptotic case. Fixed pore pressure andconstant-flow boundary conditions may be used, and sources and sinks (wells) may be modeled.The flow model can also be run independent of the mechanical calculation, and both confinedand unconfined flow can be simulated, with automatic calculation of the phreatic surface. Variousfeatures to monitor flow, including streamline plots and fluid-particle tracking, are available inFLAC.

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Structures such as tunnel liners, piles, sheet piles, cables, rockbolts, reinforcing strips or yieldingprops, that interact with the surrounding rock or soil, may be modeled with the structural elementlogic in FLAC. It is possible to examine the stabilizing effects of supported excavations or toexamine the effects of soil or rock instability on surface structures.

FLAC contains a powerful built-in programming language, FISH, which enables the user to definenew variables and functions. FISH is a compiler; programs entered via a FLAC data file aretranslated into a list of instructions stored in FLAC ’s memory space; these are executed whenevera FISH function is invoked. FISH was developed in response to requests from users who wantedto do things with FLAC that were either difficult or impossible with the existing code. Users canwrite their own functions to extend FLAC ’s usefulness. For example, FISH permits:

• user-prescribed property variations in the grid (e.g., nonlinear in-crease in modulus with depth);

• plotting and printing of user-defined variables (custom-designedplots);

• implementation of special grid generators;

• servo-control of numerical tests;

• specification of unusual boundary conditions; variations in time andspace;

• automation of parameter studies; and

• specification of user-defined constitutive models.

An extensive plotting facility is built directly into FLAC. This allows the user to generate plots(either on the screen or to a hardcopy device) of virtually any problem variable in the FLACmodel. Several variables can be plotted as overlays on a plot of the model, or histories of theirchange as a function of calculation step can be plotted. The history plots are especially helpful inascertaining when an equilibrium or failure state has been reached, and for monitoring the changein variables during transient calculations, such as groundwater flow, or dynamic calculations, suchas earthquake motion. As mentioned above, plots can be custom-designed via FISH to meet theuser’s need. Examples are given in Section 3 in the FISH volume.

The basic version of FLAC can be operated in menu-driven or command-driven mode, and the usercan easily switch back and forth between the two modes if desired. The menu-driven (graphical-userinterface) mode is easy to use with point-and-click mouse operation, and is designed to emulateexpected Windows features. This mode provides access to all commands and facilities availablein FLAC. There is also a “virtual-grid” generation mode in the graphical interface to facilitate thecreation of complex model shapes.

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1.3.2 Optional Features

Five optional features (for dynamic analysis, thermal analysis, two-phase flow analysis, modelingcreep material behavior, and adding new constitutive models as dynamic link libraries (DLLs)) areavailable as separate modules that can be included in FLAC at an additional cost per module.

Dynamic analysis can be performed with FLAC, using the optional dynamic calculation module.User-specified acceleration, velocity or stress waves can be input directly to the model either asan exterior boundary condition or an interior excitation to the model. FLAC contains absorbingand free-field boundary conditions to simulate the effect of an infinite elastic medium surroundingthe model. The dynamic calculation can be coupled to the groundwater flow model; the level ofcoupling is discussed in Section 1.3.3.

There is a thermal analysis option available as a special module in FLAC. This model simulates thetransient flux of heat in materials and the subsequent development of thermally induced stresses.The thermal model can be run independently or coupled to the mechanical stress calculation or porepressure calculation, either in static or dynamic mode. (The coupling interactions are described inSection 1.3.3.)

FLAC can perform fluid-flow and fully coupled simulations in which two immiscible fluids (withoptional capillary pressure) are present within a porous medium. This optional feature extends thefacility of the basic groundwater flow model; the components of the formulation are described inSection 1.3.3.

There are six available optional material models that simulate viscoelastic and viscoplastic (creep)behavior: the classical viscoelastic (Maxwell) model; a two-component power law; a referencecreep formulation (the WIPP model) implemented for nuclear waste isolation studies; a Burger-creep viscoplastic model; a WIPP-creep viscoplastic model; and a crushed-salt constitutive model.All six models are available in the creep module. A FLAC grid can be configured for both a creepcalculation and a dynamic calculation. However, both modes cannot be active simultaneouslybecause of the widely different timesteps.

New constitutive models can be added to FLAC as dynamic link libraries (DLLs) that are writtenin C++ and compiled as separate files. The DLLs can be loaded in FLAC whenever needed, via theMODEL load command. By implementing this optional feature, users can access new constitutivemodels from Itasca’s web site. An advantage of these models is that they run at nearly the samespeed as built-in models, and noticeably faster than FISH constitutive models.

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1.3.3 Modeling Physical Processes and Interactions

The default calculation mode in FLAC is for static mechanical analysis. Alternatively, a groundwaterflow analysis or a heat transfer analysis can be performed by itself, independent of the mechanicalcalculation. In addition, both the groundwater flow and thermal models may be coupled to themechanical stress model and to each other. Because the full equations of motion are used in FLAC,the coupling interactions can be applied for dynamic analysis as well as static analysis.

The coupling mechanisms are divided into three types of interaction: mechanical and groundwaterflow; mechanical and thermal; and thermal and groundwater flow. The level of interaction modeledin FLAC for each type is described below.

Mechanical-Groundwater Flow Coupling – Several types of fluid/solid interaction can be specifiedin FLAC. One type of interaction is consolidation, in which the slow dissipation of pore pressurecauses displacements to occur in the solid (e.g., soil). Two mechanical effects are at work in thiscase: (1) the fluid in a zone reacts to mechanical volume changes by a change in the pore pressure;and (2) the pore pressure change causes changes in the effective stress that affect the response ofthe solid (e.g., a reduction in effective stress may induce plastic yield).

FLAC can calculate pore pressure effects, with or without pore pressure dissipation, simply bysetting the flow calculation on or off. Also, dynamic pore pressure generation (e.g., related toliquefaction) can be modeled by accounting for irreversible volume strain in the constitutive model.This can be done with two different built-in constitutive models, the “Finn/Martin” model and the“Finn/Byrne” model, provided with the dynamic option.

By default, porosity is assumed constant; however, porosity can be made a function of volumetricstrain as prescribed by a look-up table. Likewise, permeability is not adjusted by default, but canalso be made a table function of volumetric strain, for inclusion as a coupling mechanism. As aconsequence, two-way coupling of mechanical stress and groundwater flow can be modeled withFLAC.

Two-phase flow processes and capillary effects can be modeled with the optional two-phase flowmodel. With this model, the capillary pressure and relative permeability laws are built-in functionsof the van Genuchten form. The mechanical coupling uses Bishop’s effective stresses, and solidgrains are assumed to be incompressible, as in the basic groundwater formulation.

Other types of interaction, such as electrical or chemical forces between particles of a partiallysaturated material, are not modeled directly by FLAC, but can also be included by writing a suitableFISH function. Similarly, a FISH function may be used to vary the local fluid modulus as a functionof other quantities such as pressure or time.

Thermal-Mechanical Coupling – The thermal-mechanical coupling in FLAC is one-way: tem-perature change may induce a mechanical stress change as a function of the thermal-expansioncoefficient. Mechanical changes in the body, however, do not result in temperature change orchanges to thermal properties.

Additionally, mechanical properties can be made a function of temperature change since FISHpermits access to both temperatures and properties.

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Thermal-Groundwater Flow Coupling – The thermal calculation may be coupled to the groundwaterflow calculation by making pore pressure a function of temperature change. Volumetric strain canarise from thermal expansion of both the fluid and the grains within a saturated matrix. Porepressure change results from this volumetric strain, as well as from mechanical volumetric strain.Groundwater flow can also influence heat transfer; an advection model that takes the transport ofheat by convection into account is provided. The advection model can also simulate temperature-dependent fluid density and thermal advection in the fluid.

As with mechanical properties, groundwater properties can be made a function of temperaturechange by accessing temperature and property values via FISH.

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1.4 Summary of Updates from Version 5.0

FLAC 6.0 contains several improvements; the new features are summarized in the following sections.Existing data files created for Version 5.0 should still operate as before; new commands have beenadded for the updates in Version 6.0. You should be aware, however, that FLAC 6.0 will not be ableto restore files saved by an earlier version of FLAC.

1.4.1 Automatic Rezoning

When FLAC is run in large strain mode, the grid may become sufficiently distorted that the simulationhalts with a “bad geometry” error message. Automatic rezoning logic is now available to generatenew, more regular meshes during the solution process to replace the old, distorted mesh and transfermesh-dependent information from the old mesh to the new mesh. The new command REZONEinitiates the rezoning process. See Section 6 in Theory and Background for a description of therezoning procedure and example applications.

1.4.2 Virtual-Grid Generation Mode

Substantial additions to the grid generation tools in FLAC Version 6.0 make model constructioneasier, faster and tremendously flexible. A new “virtual’grid” mode of grid generation is provided.In this mode, commands are not executed until the grid is completely constructed. When workingin virtual-grid mode, limitless undo/redo operations are possible, which eliminates the extensiveeffort required to correct errors after a grid is created. In addition, the virtual grid is stored withthe model as an object separate from the executed grid. This allows the user to return to the virtualgrid for other purposes, such as to modify the model or use the virtual grid as a basis for a newmodel. The operation of the virtual-grid mode and other new features in the GIIC to facilitate modelcreation are described in the Build Tools section in Section 1.2.1 in the FLAC-GIIC Reference.

1.4.3 Cap-yield Soil (Cysoil) Model

The new Cap-yield soil (Cysoil) material model is a simple strain-hardening/softening constitutivemodel for soils, characterized by a frictional Mohr-Coulomb shear failure envelope (zero cohesion)and a non-linear volumetric cap. The model can be customized to fit different characteristics ofsoil behavior through the selection of hardening laws. These include a cap-hardening power lawthat captures the volumetric behavior observed in isotropic compaction tests, a friction-hardeninglaw that reproduces the hyperbolic stress-strain behavior observed in drained triaxial tests, and acompaction/dilation law that models the irrecoverable volumetric strain taking place as a resultof monotonic soil shearing. The Cysoil model is implemented as a built-in constitutive model inFLAC 6.0. The constitutive models chapter contains further information and examples using theCysoil model (see Section 2.4.9 in Theory and Background). Section 14 in the Examples volumepresents an example application of the Cysoil model and comparison to the Mohr-Coulomb modelfor the case of the dewatered construction of a braced excavation. A comparison of the Cysoilmodel to a benchmark exercise, a triple anchored excavation wall in sand (see Section 18 in the

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Examples volume), is also provided to illustrate the applicability of the Cysoil model. The friction-hardening and cap-hardening laws are used to fit the model to the soil characteristics describedfor the benchmark test. Further, the Cysoil model is calibrated to fit the behavior of the Plaxis“Hardening-Soil” model that has also been compared to the benchmark exercise.

1.4.4 Speed Increase

FLAC Version 6.0 is compiled with a different compiler than that used for FLAC 5.0. The resultis that the (double-precision) code runs significantly faster. (The calculation speed of the single-precision version is not affected.) The speed increase for basic models (without FISH operationsduring cycling) is approximately 35%. For models that include the use of FISH functions duringcycling, an even greater increase in speed is seen. The increase in speed depends on the modeldesign. For this reason, only the double-precision executable is provided with FLAC Version 6.0.It is no longer necessary to provide a single-precision version to increase the calculation speed forsimple models, as was offered with previous versions of FLAC.

1.4.5 New Dynamic Analysis Volume

The dynamic analysis chapter, previously provided in the Optional Features volume, is nowgreatly expanded and available as a separate FLAC volume. New sections have been added toprovide additional guidance and recommendations for dynamic, and especially seismic liquefaction,analysis. Verification and example application problems have also been added to the dynamicanalysis volume. See Section 1 in Dynamic Analysis for an overview of the new volume.

1.4.6 FLAC Manual Restructuring

The thermal analysis and creep material models chapters, previously provided in the OptionalFeatures volume, are now available as separate FLAC volumes. See Section 1 in Thermal Analysisand Section 1 in Creep Material Models. The section describing used-defined constitutive modelswritten in C++ is now part of the Theory and Background volume (see Section 3 in Theory andBackground).

1.4.7 New Features in FISH

The OPT command now works with the FLAC 6.0 double-precision executable. The use of theoptimizer will provide a substantial increase in speed when running FISH constitutive models.

A new FISH function, “MODRED.FIS,” is provided in the Section 3 in the FISH volume. Thisfunction computes the modulus reduction factor and damping ratio in a one-zone model at differentshear strain levels for comparison laboratory measurements.

The intrinsic function rez exe causes commands contained within a given string to be executed. Thefunction is used to facilitate grid regeneration during cycling when the automatic rezoning logic isused. See Section 6 in Theory and Background.

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1.4.8 New Utility Features

A single command input line can now contain up to 200 characters (instead of the 80 character limitin previous versions of FLAC).

Contour plots of zone-based variables can now be extrapolated to gridpoints by using the SETextrap gp command. Either a simple extrapolation procedure or a least-squares extrapolation pro-cedure can be applied. See “EXTRAP.FIS” in Section 3 in the FISH volume for background onthe extrapolation procedure.

New GENERATE commands are available to define grid shapes. The keywords bilinear, column, lineand row are provided to facilitate positioning of gridpoints along different shapes. These are usedprimarily to convert virtual grids to FLAC grids, as discussed in Section 1.2.1 in the FLAC-GIICReference.

The SET rez func command is provided so that the automatic rezoning logic can be invoked whenevera “bad geometry” error is encountered.

1.4.9 New Example Applications and Verification Problems

Two new examples have been added to the Example Applications volume:

Example Application 17 – Rainfall on a SlopeSee Section 17 in the Examples volume.

Example Application 18 – Installation of a Triple Anchored Excavation Wall in SandSee Section 18 in the Examples volume.

One new verification problem has been added to the Verification Problems volume:

Verification Problem 22 – Consolidation Under a Circular FootingSee Section 22 in the Verifications volume.

1.4.10 Compiled HTML Help

The entire Command Reference, FISH in FLAC and Example Applications volumes are includedas an HTML help file for ease of reference. These volumes are accessed through the Help menu inthe GIIC.

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1.5 Fields of Application

FLAC was developed primarily for geotechnical engineering applications. Section 6 contains abibliography of reports published since 1986 on the application of FLAC to geotechnical problemsin the fields of mining, underground engineering, rock mechanics and research. Some exampleapplications are summarized below.

The program has been used primarily for analysis and design in mining engineering and undergroundconstruction. The explicit, time-marching solution of the full equations of motion (including inertialterms) permits the analysis of progressive failure and collapse, which are important phenomena instudies related to mine design.

The interface logic has been used to evaluate the influence of fault structures in mine design.Structural elements have been employed to simulate various rock reinforcement systems, such asgrouted rockbolting and shotcrete. The creep model option in FLAC has been applied for studiesin salt and potash mine design. Through the use of the thermal model option, FLAC has been usedto study the performance of deep underground repositories for high-level radioactive waste.

FLAC has also been used extensively in research areas related to studies of the process of localizationand evolution of shear bands in frictional materials. The results of these studies have helped elucidatethe mechanisms involved in localization, and provide insight into phenomena such as the genesisof fault systems and families of faults.

Additionally, FLAC has potential for application in a variety of fields in civil and mechanical engi-neering. Several applications are described in the following paragraphs and listed in the bibliographyin Section 6.

With the incorporation of groundwater flow logic and coupled mechanical-fluid flow (consolidation)analysis, FLAC offers a robust capability for applications in soil mechanics. Potential applicationsinclude analyses of earth-retaining structures and earthen slopes under drained and undrained load-ing, and calculations of bearing capacity and settlement of foundations. With the axisymmetrygeometry in FLAC, design calculations can be made for cofferdams or caissons, including the ef-fects of layered materials on lateral loading. The structure element logic in FLAC also permits thesimulation of soil reinforcement, such as tiebacks or soil nailing.

With the dynamics analysis option in FLAC, the code can be applied to various engineering dynamicsproblems. Analyses can be performed in earthquake engineering (e.g., studies of dam stability, soil-structure interaction and liquefaction). Calculations can also be made to evaluate effects of explosiveloading, such as underground blasting.

One drawback of early versions of FLAC was the inability to present results from FLAC in theconventional format used in soil mechanics and foundation design. FISH overcomes this problembecause now the user can define the format desired. For example, a p-q diagram can be plottedor factors of safety calculated for a specific design analysis; the factor may be defined by the userin terms of the resistance of the structure to the applied load for the specified problem conditions.These calculations now can be done directly in FLAC (see Section 3 in the FISH volume forexamples).

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It is possible for users to create their own constitutive models via FISH. Researchers can test theirassumptions of material behavior directly in the code, bypassing the effort of writing a separatenumerical program to test their theory. FISH provides the user with great flexibility in designingmodels to represent complex material behavior.

In addition, analyses of highly deformable engineering materials can be made with the large-strainlogic in FLAC. For example, the problem of extrusion of a copper billet through a die has beenstudied using FLAC (see the reference for Cundall and Board 1988, in Section 6).

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1.6 Guide to the FLAC Manual

The FLAC Version 6.0 manual consists of thirteen documents. This document, the User’s Guide,is the main guide to using FLAC and contains descriptions of the features and capabilities ofthe program, along with recommendations on the best use of FLAC for problem solving. Theremaining documents cover various aspects of FLAC, including theoretical background information,verification testing and example applications. The complete manual is available in electronic formaton the FLAC CD-ROM (viewed with Acrobat Reader), as well as in paper format.

The organization of the thirteen documents, and brief summaries of the contents of each section,follows. Please note that if you are viewing the manual in the Acrobat Reader, by double-clickingon a section number given below, you will immediately open that section for viewing.

User’s Guide

Section 1 Introduction

This section introduces you to FLAC and its capabilities and features. An overviewof the new features in the latest version of FLAC is also provided.

Section 2 Getting Started

If you are just beginning to use FLAC, or are only an occasional user, we recommendthat you read Section 2. This section provides instructions on installation and opera-tion of the program, as well as simple tutorials on menu-driven and command-drivenoperation to guide the new user through a FLAC analysis.

Section 3 Problem Solving with FLAC

Section 3 is a guide to practical problem solving. Turn to this section once you arefamiliar with the program operation. Each step in a FLAC analysis is discussed indetail, and advice is given on the most effective procedures to follow when creating,solving and interpreting a FLAC model simulation.

Section 4 FISH Beginner’s Guide

Section 4 provides the new user with an introduction to the FISH programminglanguage in FLAC. This includes a tutorial on the use of the FISH language. FISHis described in detail in Section 2 in the FISH volume.

Section 5 Miscellaneous

Various information is contained in Section 5, including the FLAC runtime bench-mark, and procedures for reporting errors and requesting technical support. Descrip-tions of utility files to assist with FLAC operation are also given.

Section 6 Bibliography

Section 6 contains a bibliography of published papers describing some uses of FLAC.

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Command Reference

Section 1 Command Reference

All of the commands that can be entered in the command-driven mode in FLAC aredescribed in Section 1 in the Command Reference.

FISH in FLAC

Section 1 FISH Beginner’s Guide

Section 1 in the FISH volume provides the new user with an introduction to theFISH programming language in FLAC. This includes a tutorial on the use of theFISH language.

Section 2 FISH Reference

Section 2 in the FISH volume contains a detailed reference to the FISH language.All FISH statements, variables and functions are explained and examples given.

Section 3 Library of FISH Functions

A library of common and general purpose FISH functions is given in Section 3 inthe FISH volume. These functions can assist with various aspects of FLAC modelgeneration and solution.

Section 4 Program Guide

Section 4 in the FISH volume contains a program guide to FLAC ’s linked-list datastructure. This is provided for advanced users to have more direct access to FLACvariables.

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Theory and Background

Section 1 Background – The Explicit Finite Difference Method

The theoretical formulation for FLAC is described in detail in Section 1 in Theoryand Background. A FISH tutorial example of the components of the explicit finitedifference method is also given.

Section 2 Constitutive Models: Theory and Implementation

The theoretical formulation and implementation of the various constitutive modelsare described in Section 2 in Theory and Background.

Section 3 Writing New Constitutive Models

Users can write their own constitutive models for incorporation into FLAC. Themodels are written in C++ and compiled as a DLL file (dynamic link library) thatcan be loaded whenever it is needed. The procedure to create new models is describedin Section 3 in Theory and Background.

Section 4 Grid Generation

Section 4 in Theory and Background presents a general guide to the principles ofgrid generation in FLAC. This includes procedures to adjust and grade the mesh andto attach sub-grids to produce an accurate solution. Several examples are also given.

Section 5 Interfaces

The interface logic is described and example applications are demonstrated in Sec-tion 5 in Theory and Background. A discussion on interface properties is alsoprovided.

Section 6 Automatic Rezoning

This section describes automatic rezoning features, provides input instructions, ex-amples of use and accuracy assessment of the rezoning logic. See Section 6 inTheory and Background.

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Fluid-Mechanical Interaction

Section 1 Fluid-Mechanical Interaction – Single Fluid Phase

The formulation for the groundwater flow model is described, and the various waysto model groundwater flow, both with and without solid interaction, are illustratedin Section 1 in Fluid-Mechanical Interaction.

Section 2 Two-Phase Flow

Section 2 in Fluid-Mechanical Interaction contains a description of the formulationand example applications of the optional two-phase flow model.

Structural Elements

Section 1 Structural Elements

Section 1 in Structural Elements describes the various structural element modelsavailable in FLAC.

Thermal Analysis

Section 1 Thermal Analysis

Section 1 in Thermal Analysis describes the thermal model option, and presentsseveral verification problems that illustrate its application, both with and withoutinteraction with mechanical stress and pore pressure.

Creep Material Models

Section 1 Creep Material Models

The different creep material models available as an option in FLAC are described,and verification and example problems are provided, in Section 1 in Creep MaterialModels.

Dynamic Analysis

Section 1 Dynamic Analysis

The dynamic analysis option is described, and considerations for running a dynamicmodel are provided in Section 1 in Dynamic Analysis. Several verification examplesare also included in this section.

FLAC-GIIC Reference

Section 1 FLAC-GIIC Reference

All of the components of the GIIC (the graphical interface for FLAC) are describedSection 1 in the FLAC-GIIC Reference.

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FLAC/Slope User’s Guide

Section 1 FLAC/Slope

This volume provides a user’s guide to FLAC/Slope, a mini-version of FLAC thatis designed specifically to perform factor-of-safety calculations for slope stabilityanalysis. See Section 1 in the FLAC/Slope User’s Guide.

Verification Problems

This volume contains a collection of FLAC verification problems. These are testsin which a FLAC solution is compared directly to an analytical (i.e., closed-form)solution. See Table 1 in the Verifications volume for a list of the verificationproblems.

Example Applications

This volume contains example applications of FLAC that demonstrate the variousclasses of problems to which FLAC may be applied. See Table 1 in the Examplesvolume for a list of the example applications.

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1.7 Itasca Consulting Group Inc.

Itasca Consulting Group Inc. is more than a developer and distributor of engineering software.Itasca is a consulting and research firm comprised of a specialized team of civil, geotechnical andmining engineers with an established record in solving problems in the areas of:

Civil Engineering

Mining Engineering and Energy Resource Recovery

Nuclear Waste Isolation and Underground Space

Defense Research

Software Engineering

Groundwater Analysis and Dewatering

Itasca was established in 1981 to provide advanced rock mechanics services to the mining industry.Today, Itasca is a multidisciplinary geotechnical firm with 70 professionals in offices worldwide.The corporate headquarters for Itasca is located in Minneapolis, Minnesota. Worldwide officesof Itasca are operated as subsidiaries of HCItasca Inc.: HCItasca Denver (Denver, Colorado);Itasca Geomekanik AB (Stockholm, Sweden); Itasca Consultants S.A.S. (Ecully, France); ItascaConsultants GmbH (Gelsenkirchen, Germany); Itasca Consultores S.L. (Llanera, Spain); Itasca S.A.(Santiago, Chile); Itasca Africa Ltd. (Johannesburg, South Africa); Itasca Consulting Canada Inc.(Sudbury, Canada); Itasca Consulting China Ltd. (Wuhan, China); Itasca Consulting Group Inc.(Japan); Itasca Houston Inc. (Houston, Texas); and Itasca Australia Ltd. (Melbourne, Australia).

Itasca’s staff members are internationally recognized for their accomplishments in geological, min-ing and civil engineering projects. Itasca staff consists of geological, mining, hydrological andcivil engineers who provide a range of comprehensive services such as (1) computational anal-ysis in support of geo-engineering designs, (2) design and performance of field experiments anddemonstrations, (3) laboratory characterization of rock properties, (4) data acquisition, analysisand system identification, (5) groundwater modeling, and (6) short courses and instruction in thegeomechanics application of computational methods. If you should need assistance in any of theseareas, we would be glad to offer our services.

Itasca Consulting Group is a subsidiary of HCItasca Inc. HCItasca was formed in 1999 withthe merger of Hydrologic Consultants Inc. (HCI) of Denver, Colorado with Itasca ConsultingGroup Inc. of Minneapolis, Minnesota. HCI adds advanced groundwater modeling and dewateringexpertise to Itasca.

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1.8 User Support

We believe that the support Itasca provides to code users is a major reason for the popularity of oursoftware. We encourage you to contact us when you have a modeling question. We will providea timely response via telephone, electronic mail or fax. General assistance in the installation ofFLAC on your computer, plus answers to questions concerning capabilities of the various featuresof the code, are provided free of charge. Technical assistance for specific user-defined problemscan be purchased on an as-needed basis.

If you have a question, or desire technical support, please contact us at:

Itasca Consulting Group Inc.Mill Place111 Third Avenue South, Suite 450Minneapolis, Minnesota 55401 USA

Phone: (+1) 612-371-4711Fax: (+1) 612·371·4717Email: [email protected]: www.itascacg.com

We also have a worldwide network of code agents who provide local technical support. Detailsmay be obtained from Itasca.

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1.9 Reference

Marti, J., and P. A. Cundall. “Mixed Discretization Procedure for Accurate Solution of PlasticityProblems,” Int. J. Num. Methods and Anal. Methods in Geomech., 6, 129-139 (1982).

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