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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 phreatic

surface 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;

FLAC Version 6.0

1 - 2 Users Guide

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.

FLAC Version 6.0

INTRODUCTION 1 - 3

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.

FLAC Version 6.0

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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 fa