Flac 3D 1

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1 INTRODUCTION 1.1 Overview FLAC 3D is a three-dimensional explicit finite-difference program for engineering mechanics computation. The basis for this program is the well-established numerical formulation used by our two-dimensional program, FLAC.* FLAC 3D extends the analysis capability of FLAC into three dimensions, simulating the behavior of three-dimensional structures built of soil, rock or other materials that undergo plastic flow when their yield limits are reached. Materials are represented by polyhedral elements within a three-dimensional grid that is adjusted by the user to fit the shape of the object to be modeled. Each element behaves according to a prescribed linear or nonlinear stress/strain law in response to applied forces or boundary restraints. The material can yield and flow, and the grid 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 3D ensure that plastic collapse and flow are modeled very accurately. Because no matrices are formed, large three-dimensional calculations can be made without excessive memory requirements. The drawbacks of the explicit formulation (i.e., small timestep limitation and the question of required damping) are overcome by automatic inertia scaling and automatic damping that does not influence the mode of failure. FLAC 3D offers an ideal analysis tool for solution of three-dimensional problems in geotechnical engineering. FLAC 3D is designed specifically to operate on IBM-compatible microcomputers running Windows 98 and later operating systems. Calculations on realistically sized three-dimensional models in geo-engineering can be made in a reasonable time period. For example, models containing up to approximately 140,000 elements can be generated within 128 MB RAM. The runtime to perform 5000 calculation steps for a 10,000 element model of Mohr-Coulomb material is roughly 18 minutes on a 2.4 GHz Pentium IV microcomputer.† The number of calculational steps required to reach a solution state with the explicit-calculation scheme can vary, but a solution typically can be reached within 3000 to 5000 steps for models containing up to 10,000 elements, regardless of material type. (The explicit-solution scheme is explained in Section 1 in Theory and Background.) With the advancements in floating-point operation speed, and the ability to install additional RAM at low cost, it should be possible to solve increasingly larger three-dimensional problems with FLAC 3D. FLAC 3D can be operated from either a command-driven mode or graphics menu-driven mode. The default command-driven mode is very similar to that used by other Itasca software products. You will find that most of the commands are the same as, or three-dimensional extensions of, those in FLAC. A menu-driven, graphical user interface is also available in FLAC 3D for performing plotting, printing and file access. * Itasca Consulting Group, Inc. FLAC (Fast Lagrangian Analysis of Continua.), Version 5.0, 2005. † See Section 5 for a comparison of FLAC 3D runtimes on various computer systems.

FLAC 3D Version 3.0

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User’s Guide

With the graphics facilities* built into FLAC 3D, high-resolution, color-rendered plots are generated quite rapidly. We have developed a graphics screen-plotting facility that allows you to instantly view the model during creation from either command-mode or graphics menu-mode. The model can be translated, rotated and magnified on the screen for better viewing. Color-rendered plots of surfaces showing vectors or contours can be made in 3D, and a two-dimensional plane can be located at any orientation and location in the model for the purpose of viewing vector or contour output on the plane. All output can be directed to a black-and-white or color hardcopy device, to the Windows clipboard, or to a file. You will find that FLAC 3D offers a facility for problem solving similar to that in FLAC. A comparison of FLAC 3D to other numerical methods, a description of general features and updates in FLAC 3D Version 3.0, and a discussion of fields of application are provided in the following sections. If you wish to try FLAC 3D right away, the program installation instructions and a simple tutorial are provided in Section 2.

* The graphics facilities in FLAC 3D utilize the Windows GDI.

FLAC 3D Version 3.0

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1.2 Comparison with Other Methods How does FLAC 3D compare to the more common method of finite elements for numerical modeling? Both methods translate a set of differential equations into matrix equations for each element, relating forces at nodes to displacements at nodes. Although FLAC 3D’s equations are derived by the finite difference method, the resulting element matrices, for an elastic material, are identical to those of the finite element method (for constant-strain tetrahedra). However, FLAC 3D differs in the following respects. 1. The “mixed discretization” scheme (Marti and Cundall, 1982) is used for accurate modeling of plastic collapse loads and plastic flow. This scheme is believed to be physically more justifiable than the “reduced integration” scheme commonly used with finite elements. 2. The full dynamic equations of motion are used, even when modeling systems are essentially static. This enables FLAC 3D to follow physically unstable processes without numerical distress. The approach to provide a time-static solution is discussed in the definition for “Static Solution” given in Section 2.3. 3. An “explicit” solution scheme is used (in contrast to the more usual implicit methods). Explicit schemes can follow arbitrary nonlinearity in stress/strain laws in almost the same computer time as linear laws, whereas implicit solutions can take significantly longer to solve nonlinear problems. Furthermore, it is not necessary to store any matrices, which means: (a) a large number of elements may be modeled with a modest memory requirement; and (b) a large-strain simulation is hardly more time-consuming than a small-strain run, because there is no stiffness matrix to be updated. 4. FLAC 3D is robust in the sense that it can handle any constitutive model with no adjustment to the solution algorithm; many finite element codes need different solution techniques for different constitutive models. These differences are mainly in FLAC 3D’s favor, but there are two disadvantages. 1. Linear simulations run slower with FLAC 3D than with equivalent finite element programs. FLAC 3D is most effective when applied to nonlinear or large-strain problems, or to situations in which physical instability may occur. 2. The solution time with FLAC 3D is determined by the ratio of the longest natural period to the shortest natural period in the system being modeled. This point is discussed in more detail in Section 1 in Theory and Background, but certain problems are very inefficient to model (e.g., beams, represented by solid elements rather than structural elements, or problems that contain large disparities in elastic moduli or element sizes).

FLAC 3D Version 3.0

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User’s Guide

1.3 General Features 1.3.1 Basic Features FLAC 3D offers a wide range of capabilities to solve complex problems in mechanics, and especially in geomechanics. Like FLAC, FLAC 3D embodies special numerical representations for the mechanical response of geologic materials. The program has twelve basic built-in material models: the “null” model; three elasticity models (isotropic, transversely isotropic and orthotropic elasticity); and eight plasticity models (Drucker-Prager, Mohr-Coulomb, strain-hardening/softening, ubiquitous-joint, bilinear strain-hardening/softening ubiquitous-joint, double-yield, modified Camclay and Hoek-Brown). These models are described in detail in Section 2 in Theory and Background. Each zone in a FLAC 3D grid may have a different material model or property, and a continuous gradient or statistical distribution of any property may be specified. Additionally, an interface, or slip-plane, model is available to represent distinct interfaces between two or more portions of the grid. The interfaces are planes upon which slip and/or separation are allowed, thereby simulating the presence of faults, joints or frictional boundaries. The interface model is described in Section 3 in Theory and Background. FLAC 3D contains an automatic 3D grid generator in which grids are created by manipulating and connecting pre-defined shapes.* The generator permits the creation of intersecting internal regions (e.g., intersecting tunnels). The 3D grid is defined by a global x,y,z-coordinate system (rather than in a row-and-column fashion as in FLAC). This provides more flexibility in model creation and definition of parameters in a three-dimensional space. Grid generation procedures are described in Section 1 in the Command Reference under the GENERATE command. Boundary conditions and initial conditions are specified in much the same way as in FLAC. Either velocity (and displacement) boundary conditions, or stress (and force) boundary conditions, may be specified at any boundary orientation. Initial stress conditions, including gravitational loading, may also be given, and a water table may be defined for effective stress calculations. All conditions may be specified with gradients. Boundary conditions are primarily assigned via the APPLY command, and initial conditions via the INITIAL command, as described in Section 1 in the Command Reference. FLAC 3D incorporates the facility to model groundwater flow and pore-pressure dissipation, and the full 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 is assumed to obey either the isotropic or anisotropic form of Darcy’s law. Both the fluid and the grains within the porous solid are deformable. Non-steady flow is modeled, with steady flow treated as an asymptotic case. Fixed pore pressure and constant-flow boundary conditions may be used, and sources and sinks (wells) may be modeled. The flow model can also be run independently from the mechanical calculation, and both confined and unconfined flow can be simulated, with automatic calculation of the phreatic surface. The fluid-flow model is described in Section 1 in Fluid-Mechanical Interaction. * An optional meshing preprocessor is also available, see Section 1.3.2.

FLAC 3D Version 3.0

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Structures, such as tunnel liners, piles, sheet piles, cables, rock bolts or geotextiles, that interact with the surrounding rock or soil, may be modeled with the structural element logic in FLAC 3D. It is possible to either examine the stabilizing effects of supported excavations, or to study the effects of soil or rock instability on surface structures. The different types of structural elements are described in Section 1 in Structural Elements. A factor of safety can be calculated automatically for any FLAC 3D model composed of MohrCoulomb material. The calculation is based on a “strength reduction technique” that performs a series of simulations while changing the strength properties to determine the condition at which an unstable state exists. A factor of safety which corresponds to the point of instability is found, and the critical failure surface is located in the model. The factor-of-safety algorithm is described in Section 3.8. FLAC 3D also contains a powerful built-in programming language, FISH, that enables the user to define new variables and functions. FISH offers a unique capability to users who wish to tailor analyses to suit their specific needs. For example, FISH permits: • user-prescribed property variations in the grid (e.g., nonlinear increase in modulus with depth); • plotting and printing of user-defined variables (i.e., custom-designed plots); • implementation of special grid generators; • servo-control of numerical tests; • specification of unusual boundary conditions; variations in time and space; and • automation of parameter studies. An introduction to FISH is given in Section 4. See Section 2 in the FISH volume for a detailed reference to the FISH language. FLAC 3D contains extensive graphics facilities for generating plots of virtually any problem variable. Three-dimensional graphics rendering is provided in high-resolution video modes. Plotting features include hidden surface plots, surface contour plots and vector plots. Plotted variables can be viewed in front of, behind, or on an arbitrary cross-section plane through, the model. This version of FLAC 3D has been compiled as a native Windows executable using the WIN32 API to support execution under Windows 98 and later operating systems. The program has the look and feel of a typical Windows program; however, most modeling operations are performed in the command-driven mode, while the graphical user interface supports file-handling, model and response visualization (plotting), and printing (using standard Windows file-handling and printing facilities). Plotting operations are described in Section 1 in the Command Reference under the PLOT command.

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User’s Guide

1.3.2 Optional Features Four optional features (for dynamic analysis, thermal analysis, modeling creep-material behavior, and writing user-defined constitutive models) are available as separate modules that can be included in FLAC 3D at an additional cost per module. Also, a fifth optional feature, a hexahedral-meshing preprocessor (3DShop), is available as a separate program.* Dynamic analysis can be performed with FLAC 3D, using the optional dynamic-calculation module. User-specified acceleration, velocity or stress waves can be input directly to the model either as an exterior boundary condition or an interior excitation to the model. FLAC 3D contains absorbing and free-field boundary conditions to simulate the effect of an infinite elastic medium surrounding the model. The dynamic calculation can be coupled to the groundwater flow model; the level of coupling, including dynamic pore-pressure generation (liquefaction), is discussed in Section 1.3.3. The dynamic analysis capability is described in Section 3 in Optional Features. There is a thermal analysis option available as a special module in FLAC 3D. This model simulates the transient 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 pore-pressure calculation, either static or dynamic. (The coupling interactions are described in Section 1.3.3.) The thermal analysis capability is described in Section 1 in Optional Features. There are eight optional material models available that simulate time-dependent (creep) material behavior (All creep models are described in Section 2 in Optional Features.): (1) the classical viscoelastic (Maxwell) model; (2) a Burger’s substance viscoelastic model; (3) a two-component power law; (4) a reference creep formulation (the WIPP model) implemented for nuclear waste isolation studies; (5) a Burger-creep viscoplastic model combining the Burger’s model with the Mohr-Coulomb model; (6) a power-law viscoplastic model combining the two-component power law and the MohrCoulomb model; (7) a WIPP-creep viscoplastic model combining the reference creep formulation with the Drucker-Prager plasticity model; and (8) a “crushed-salt” model that simulates both volumetric and deviatoric creep compaction. * The hexahedral-meshing preprocessor, 3DShop, enables the creation of complex meshes for FLAC 3D. 3DShop can substantially reduce model creation time. See Section 1 in the HexahedralMeshing Preprocessor — 3DShop volume for more information and a tutorial on 3DShop.

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User-defined constitutive models can be written in C++ and compiled as DLL (dynamic link library) files that can be loaded whenever needed with this optional feature. A Visual C++ Version 7.1 compiler is used to compile the DLL files. The procedure to write new constitutive models and create DLLs is described in Section 4 in Optional Features. 1.3.3 Modeling Physical Processes and Interactions The default calculation mode in FLAC 3D is for static mechanical analysis. Alternatively, a groundwater flow analysis or a heat-transfer analysis can be performed, independent of the mechanical calculation. Both the groundwater flow and thermal models may be coupled to the mechanical stress model and to each other. Because the full equations of motion are used in FLAC 3D, the coupling mechanisms operate in dynamic analyses as well as static analyses. The coupling mechanisms are divided into three types of interaction: mechanical and groundwater flow; mechanical and thermal; and thermal and groundwater flow. The level of interaction modeled in FLAC 3D for each type is described below. Mechanical-Groundwater Flow Coupling — Several types of fluid/solid interaction can be specified in FLAC 3D. One type of interaction is consolidation, in which the slow dissipation of pore pressure causes displacements to occur in the solid (e.g., soil). Two mechanical effects are at work in this case: (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 of the solid (e.g., a reduction in effective stress may induce plastic yield). Coupling between fluid and solid due to deformable grains can also be specified. FLAC 3D can calculate pore-pressure effects, with or without pore-pressure dissipation, simply by setting the flow calculation on or off. Also, dynamic pore-pressure generation (e.g., related to liquefaction) can be modeled by accounting for irreversible volume strain in the constitutive model. This is done with two different built-in constitutive models: the “Finn” model, and the “Byrne” model. Both models are provided with the dynamic option. By default, porosity and permeability are assumed constant. However, these properties can be made a function of volumetric strain via a FISH function. As a consequence, two-way coupling of mechanical stress and groundwater flow can be modeled with FLAC 3D. Other types of interaction, such as capillary, electrical or chemical forces between particles of a partially saturated material are not modeled directly by FLAC 3D, but some of the effects may be included by providing suitable FISH functions. Similarly, a FISH function may be used to vary the local fluid modulus as a function of other quantities such as pressure or time. Thermal-Mechanical Coupling — The thermal-mechanical coupling in FLAC 3D is one-way: temperature change may induce a mechanical stress change as a function of the thermal-expansion coefficient. Mechanical changes in the body, however, do not result in temperature change or changes to thermal properties. Additionally, mechanical properties can be made a function of temperature change, since FISH permits access to both temperatures and properties.

FLAC 3D Version 3.0

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User’s Guide

Thermal-Groundwater Flow Coupling — The thermal calculation may be coupled to the groundwater flow calculation by making pore pressures a function of temperature change. Volumetric strain can arise from thermal expansion of both the fluid and the grains within a saturated matrix. Pore pressure 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 of heat 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 temperature change by accessing temperature and property values via FISH.

FLAC 3D Version 3.0

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1.4 Summary of Updates from Version 2.1 FLAC 3D 3.0 contains several improvements; the new features are summarized in the following sections. Existing data files created for Version 2.1 should still operate as before. You should be aware, however, that FLAC 3D 3.0 will not be able to restore files saved by versions earlier than FLAC 3D 2.10. 1.4.1 Hysteretic Damping A new damping facility for dynamic calculations, hysteretic damping, is now available in FLAC 3D Version 3.0. This form of damping allows strain-dependent modulus and damping functions to be incorporated directly into the FLAC 3D simulation. This makes it possible for direct comparisons between calculations with the equivalent-linear method and a fully nonlinear model, without any compromises in the choice of constitutive model. In addition, the need to introduce additional damping, such as Rayleigh damping, is greatly reduced and, consequently, the solution time is substantially reduced, by using hysteretic damping. The new dynamics-analysis chapter provides a detailed description of hysteretic damping, in Section 3.6.5.1 in Optional Features, and a comparison of a FLAC 3D model with hysteretic damping to that using SHAKE91, in Section 3.6.2 in Optional Features. 1.4.2 Hoek-Brown Constitutive Model The Hoek-Brown failure criterion is implemented as a built-in constitutive model in FLAC 3D 3.0. The failure surface is nonlinear and is based on the relation between the major and minor principal stresses. The model incorporates a plasticity flow rule that varies as a function of the confining stress level. The new constitutive models chapter contains further information and examples using the Hoek-Brown model — see Section 2.5.8 in Theory and Background. A verification problem for the case of a cylindrical hole in a Hoek-Brown medium is given in Section 2 in Theory and Background. 1.4.3 Thermal Advection Logic The mechanisms of convective heat transfer (forced convection and free convection) in porous media are now provided with the thermal-analysis option in FLAC 3D Version 3.0. Forced convection can be implemented with or without the fluid-flow configuration; in the latter case, fluid-specific discharge is assigned as a property. Free convection is activated in FLAC 3D zones containing the new isotropic advection/conduction model (MODEL th ac). See Section 1.3.2 in Optional Features for a description of the thermal advection logic, and Section 1.7 in Optional Features for several verification problems.

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User’s Guide

1.4.4 Hydration Models Hydration is defined as the chemical absorption of water into a substance, a process by which heat is generated — the so-called hydration heat. The setting of concrete, which can be considered as a transition from liquid to solid phase, is the most relevant example for the hydration process in the engineering world. FLAC 3D now includes two different thermal hydration models: one for concrete and one more general hydration model. In these models, the thermal capacity, thermal conductivity and the activation energy are dependent on the hydration grade. During the hydration process, the mechanical properties of the material change permanently as a function of the hydration grade. To support this, FLAC 3D incorporates a modified version of the Drucker-Prager constitutive law, in which elastic and strength properties depend on the hydration grade. The hydration models can only be applied with the thermal option. These models are not fully tested and should be used with caution. Documentation on the models is available at the Itasca Constitutive Models web site at www.itasca-udm.com. 1.4.5 Computation Enhancements FLAC 3D Version 3.0 runs approximately 10-20% faster than Version 2.1, as a result of modifications to optimize the calculation cycle and use of an updated optimizing compiler. All calculations and data in FLAC 3D have been converted to double precision floating-point numbers. 1.4.6 Movie Feature FLAC 3D can generate movie files in two industry standard formats: AVI and DCX. The “movie” is a set of AVI or DCX images that are strung together and can then be repeated rapidly as a movie. The MOVIE and SET movie commands are used to invoke the movie feature. 1.4.7 Network Key Facility A network-key version of FLAC 3D 3.0 is available. This version allows a single hardware key to be installed on a central (server) computer for a network. Individual users can then run FLAC 3D from any computer(s) on the network. (The number of instances in which FLAC 3D can be run is limited by the network key.) Network keys require a special licensing arrangement and installation. Contact Itasca for details.

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1.4.8 3DShop Compatibility FLAC 3D Version 3.0 has the ability to import grids generated by 3DShop. 3DShop is a powerful solid modeler and all-hexahedral grid generator that is available through Itasca. 3DShop will greatly simplify the creation of grids for complex geometries. A description of 3DShop and a tutorial are provided in Section 1 in the Hexahedral-Meshing Preprocessor — 3DShop volume. 1.4.9 Fluid-Flow Particle Tracking Particles can now be released into a flow field and their paths can be recorded and plotted. See the TRACK command. 1.4.10 New Features in FISH The following new FISH functions have been added to FLAC 3D 3.0 (see FISH in FLAC3D for more details):

do update

updates all grid-related quantities

gp dynmul

returns the dynamic multi-stepping multiplier to the global timestep

z dynmul

returns the dynamic multi-stepping multiplier to the global timestep

z facenorm

returns area and normal to a zone face

z fri

returns the full rate of rotation increment tensor

z frr

returns the full rate of rotation tensor

z inimodel

initializes all derived model properties for a zone

z pstress

returns the principal stress magnitudes and directions

z sonplane

returns the normal and shear stress on a user specified plane

1.4.11 New Command and Utilities The following new commands have been added to FLAC 3D Version 3.0 (see the Command Reference for more details):

GENERATE separate separates a group of zones from the grid by duplicating gridpoints at shared boundaries

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GENERATE zone uwedge a uniform wedge meshing primitive is now available

GROUP

none unassigns a group name from zones

GROUP

remainder allows assignment of a group name to all zones that belong to the null group

IMPGRID EXPGRID

allows the importing or exporting of 3DShop grid files

INTERFACE wrap simplifies creation of interfaces on group boundaries

MOVIE

allows the creation of AVI or DCX animations

PDELETE

allows deletion of particles in a fluid flow simulation

PLOT

block state state colors are now based on the state flags and no longer change when the view is changed

PLOT

extract allows extraction of numerical values from the grid into a FISH array

SOLVE

fishhalt allows user to specify termination criteria for solving through a FISH function

TRACK

allows particle paths to be traced in a fluid flow simulation

1.4.12 New Example Applications Two new example applications have been added to the Examples volume: Example Application 12 — Embankment Loading on a Cam-Clay Foundation (see Section 12 in the Examples volume); and Example Application 13 — Impermeable Concrete Caisson Wall with Pretensioned Tiebacks (see Section 13 in the Examples volume).

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1.5 Fields of Application FLAC 3D was developed primarily for geotechnical engineering applications. Section 6 contains a bibliography of publications on the application of FLAC 3D to geotechnical problems in the fields of mining, underground engineering, rock mechanics and research. Some possible applications of FLAC 3D are noted below. Because FLAC 3D now has essentially the same capabilities of FLAC, many of the FLAC applications can now be extended into three dimensions with FLAC 3D : • mechanical loading capacity and deformations — in slope stability and foundation design; • evolution of progressive failure and collapse — in hard rock mine and tunnel design; • factor-of-safety calculation — in stability analyses for earth structures, embankments and slopes; • evaluation of the influence of fault structures — in mine design; • restraint provided by cable support on geologic materials — in rock bolting, tiebacks and soil nailing; • fully and partially saturated fluid flow and pore-pressure build-up and dissipation for undrained and drained loading — in groundwater flow and consolidation studies of earthretaining structures; • time-dependent creep behavior of viscous materials — in salt and potash mine design; • dynamic loading on slip-prone geologic structures — in earthquake engineering and mine rockburst studies; • dynamic effects of explosive loading and vibrations — in tunnel driving or in mining operations; • seismic excitation of structures — in earth dam design; • deformation and mechanical instability resulting from thermal-induced loads — in performance assessment of underground repositories of high-level radioactive waste; and • analysis of highly deformable materials — in bulk flow of materials in bins and mine caving.

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1.6 Guide to the FLAC 3D Manual The FLAC 3D Version 3.0 manual consists of eleven documents. This document, the User’s Guide, is the main guide to using FLAC 3D and contains descriptions of the features and capabilities of the program, along with recommendations on the best use of FLAC 3D for problem solving. The remaining documents cover various aspects of FLAC 3D, including theoretical background information, verification testing and example applications. The complete manual is available in electronic format on the FLAC 3D CD-ROM (viewed with Acrobat Reader*), as well as in paper format. Specific topics or keywords can be found across all volumes by implementing the search facility available in Acrobat. The organization of the eleven 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-clicking on 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 3D and its capabilities and features. An overview of the new features in the latest version of FLAC 3D is also provided.

Section 2

Getting Started If you are just beginning to use FLAC 3D, or use it occasionally, we recommend that you read Section 2. This section provides instructions on installation and operation of the program, as well as recommended procedures for running FLAC 3D analyses.

Section 3

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

Section 4

FISH Beginner’s Guide Section 4 provides the new user with an introduction to the FISH programming language in FLAC 3D. This includes a tutorial on the use of the FISH language. FISH is described in detail in Section 2 in the FISH volume.

* “Acrobat(R) Reader copyright (C) 1987-1999, Adobe Systems Incorporated. All rights reserved. Adobe and Acrobat are trademarks of Adobe Systems Incorporated.”

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Miscellaneous Various information is contained in this section, including the FLAC 3D runtime benchmark and procedures for reporting errors and requesting technical support. Descriptions of utility files to assist with FLAC 3D operation are also given.

Section 6

Bibliography This section contains a bibliography of published papers describing some uses of FLAC 3D.

Command Reference Section 1

Command Reference All the commands that can be entered in the command-driven mode in FLAC 3D are described in Section 1 in the Command Reference.

FISH in FLAC 3D Section 1

FISH Beginner’s Guide Section 1 in the FISH volume provides the new user with an introduction to the FISH programming language in FLAC 3D. This includes a tutorial on the use of the FISH 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 in the FISH volume. These functions can assist with various aspects of FLAC 3D model generation and solution.

Theory and Background Section 1

Theoretical Background The theoretical formulation for FLAC 3D is described in detail in Section 1 in Theory and Background. This includes both the description of the mathematical model that describes the mechanics of a system and the numerical implementation.

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Section 2

User’s Guide

Constitutive Models: Theory and Implementation The theoretical formulation and implementation of the various built-in constitutive models are described in Section 2 in Theory and Background.

Section 3

Interfaces The interface logic is described and example applications are given in Section 3 in Theory and Background. A discussion on interface properties is also provided.

Fluid-Mechanical Interaction Section 1

Fluid-Mechanical Interaction The formulation for the fluid-flow model is described, and the various ways to model fluid flow, both with and without solid interaction, are illustrated in Section 1 in Fluid-Mechanical Interaction.

Structural Elements Section 1

Structural Elements Section 1 in Structural Elements describes the various structural element models available in FLAC 3D. These include beams, cables, piles, shells, liners and geogrids.

Optional Features Section 1

Thermal Option Section 1 in Optional Features describes the thermal model option, and presents several verification problems that illustrate its application both with and without interaction with mechanical stress and pore pressure.

Section 2

Creep Material Models The different creep material models available as an option in FLAC 3D are described, and verification and example problems are provided in Section 2 in Optional Features.

Section 3

Dynamic Analysis The dynamic analysis option is described, and considerations for running a dynamic model are provided in Section 3 in Optional Features. Several verification examples are also included in this section.

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Writing New Constitutive Models Users can write their own constitutive models for incorporation into FLAC 3D. The models are written in C++ and compiled as a DLL file (dynamic link library) that can be loaded whenever it is needed. The procedure to create new models is described in Section 4 in Optional Features.

Hexahedral-Meshing Preprocessor — 3DShop Section 1

3DShop 3DShop is a hexahedral-meshing preprocessor that enables the creation of complex meshes for FLAC 3D. 3DShop uncouples the model building from the meshing process. The model is built via a menu-driven graphical interface, and then meshed using a fully automatic all-hexahedral mesh generator. See Section 1 in the HexahedralMeshing Preprocessor — 3DShop volume for details.

Verification Problems This volume contains a collection of FLAC 3D verification problems. These are tests in which a FLAC 3D solution is compared directly to an analytical (i.e., closed-form) solution. See Table 1 in the Verifications volume for a list of the verification problems. Example Applications This volume contains example applications of FLAC 3D that demonstrate the various classes of problems to which FLAC 3D may be applied. See Table 1 in the Examples volume for a list of the example applications. Command and FISH Reference Summary A quick summary of all FLAC 3D commands and FISH statements is contained in the Command and FISH Reference Summary.

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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 and mining 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 50 professionals in offices worldwide. The corporate headquarters for Itasca is located in Minneapolis, Minnesota. Worldwide offices of Itasca are operated as subsidiaries of HCItasca, Inc.: Hydrologic Consultants, Inc. (Denver, Colorado); Itasca Geomekanik AB (Stockholm, Sweden); Itasca Consultants S.A. (Ecully, France); Itasca Consultants GmbH (Gelsenkirchen, Germany); Itasca Consultores S.L. (Llanera, Spain); Itasca S.A. (Santiago, Chile); Itasca Africa (Johannesburg, South Africa); Itasca Consultants Canada Inc. (Sudbury, Canada); and Itasca Consulting China, Ltd. (Wuhan, China). Itasca’s staff members are internationally recognized for their accomplishments in geological, mining and civil engineering projects. Itasca staff consists of geological, mining, hydrological and civil engineers who provide a range of comprehensive services such as (1) computational analysis in support of geo-engineering designs, (2) design and performance of field experiments and demonstrations, (3) laboratory characterization of rock properties, (4) data acquisition, analysis, and system identification, (5) groundwater modeling, and (6) short courses and instruction in the geomechanics application of computational methods. If you should need assistance in any of these areas, we would be glad to offer our services. Itasca Consulting Group is a subsidiary of HCItasca, Inc. HCItasca was formed in 1999 with the merger of Hydrologic Consultants, Inc. (HCI) of Denver, Colorado with Itasca Consulting Group, Inc. of Minneapolis, Minnesota. HCI adds advanced groundwater modeling and dewatering expertise 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 our software. We encourage you to contact us when you have a modeling question. We provide a timely response via telephone, electronic mail or fax. General assistance in the installation of FLAC 3D on your computer, plus answers to questions concerning capabilities of the various features of the code, are provided free of charge. Technical assistance for specific user-defined problems can 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 Place 111 Third Avenue South, Suite 450 Minneapolis, Minnesota 55401 USA Phone: Fax: Email: Web:

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

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

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1.9 References Byrne, P. “A Cyclic Shear-Volume Coupling and Pore-Pressure Model for Sand,” in Proceedings: Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics (St. Louis, Missouri, March, 1991), Paper No. 1.24, 47-55. Marti, J., and P. A. Cundall. “Mixed Discretization Procedure for Accurate Solution of Plasticity Problems,” Int. J. Num. Methods and Anal. Methods in Geomech., 6, 129-139, 1982.

FLAC 3D Version 3.0