《Flac3D manual》Flac3D 手册（英文版）Fast Lagrangian Analysis of Continua in 3 Dimensions

Online Contents-I FLAc3D fast lagrangian Analysis of Continua in 3 Dimensions Online Manual Table of Contents USER’ S GUIDE Frontispiece Terms and conditions Pr Table of Contents Section 1: Introduction Section 2: Getting Started Section 3: Problem Solving with FLAC3D Section 4: FISH Beginner's Guide Section 5: Miscellaneous Section 6: Bibliograph COMMAND REFERENCE Frontispiece Table of contents Section 1: Command Reference FLAC3D Version 3. I

Online Contents - 1 FLAC3D Fast Lagrangian Analysis of Continua in 3 Dimensions Online Manual Table of Contents USER’S GUIDE Frontispiece Terms and Conditions Precis Table of Contents Section 1 : Introduction Section 2 : Getting Started Section 3 : Problem Solving with FLAC3D Section 4 : FISH Beginner’s Guide Section 5 : Miscellaneous Section 6 : Bibliography COMMAND REFERENCE Frontispiece Table of Contents Section 1 : Command Reference FLAC3D Version 3.1

Online Contents-2 FISH IN FLAC3D Frontispiece Precis Table of Contents Section 1: FISH Beginner's Guide Section 2: FISH Reference Section 3: Library of FISH Functions THEORY AND BACKGROUND Frontispiece Pr Table of Contents Section 1: Theoretical Background Section 2: Constitutive Models: Theory and Implementation Section 3: Interfaces FLUID-MECHANICAL INTERACTION Frontispiece Table of contents Section 1: Fluid-Mechanical Interaction- Single Phase Fluid STRUCTURAL ELEMENTS Frontispiece Table of Contents Section 1: Structural elements FLAC3D Version 3. 1

Online Contents - 2 FISH IN FLAC3D Frontispiece Precis Table of Contents Section 1 : FISH Beginner’s Guide Section 2 : FISH Reference Section 3 : Library of FISH Functions THEORY AND BACKGROUND Frontispiece Precis Table of Contents Section 1 : Theoretical Background Section 2 : Constitutive Models: Theory and Implementation Section 3 : Interfaces FLUID-MECHANICAL INTERACTION Frontispiece Table of Contents Section 1 : Fluid-Mechanical Interaction — Single Phase Fluid STRUCTURAL ELEMENTS Frontispiece Table of Contents Section 1 : Structural Elements FLAC3D Version 3.1

Online Contents-3 OPTIONAL FEATURES Frontispiece Precis Table of Contents Section 1: Thermal Option Section 2: Creep material Models Section 3: Dynamic Analysis Section 4: Writing New Constitutive Models HEXAHEDRAL-MESHING PREPROCESSOR- 3D Shop Frontispiece Table of Contents Section 1: Hexahedral-Meshing Preprocessor--3DShop FLAC3D Version 3. I

Online Contents - 3 OPTIONAL FEATURES Frontispiece Precis Table of Contents Section 1 : Thermal Option Section 2 : Creep Material Models Section 3 : Dynamic Analysis Section 4 : Writing New Constitutive Models HEXAHEDRAL-MESHING PREPROCESSOR — 3DShop Frontispiece Table of Contents Section 1 : Hexahedral-Meshing Preprocessor — 3DShop FLAC3D Version 3.1

Online Contents-4 VERIFICATION PROBLEMS Frontispiece Precis Table of Contents Cylindrical Hole in an Infinite Mohr-Coulomb Material Cylindrical Hole in an Infinite Hoek-Brown Medium Rough Strip Footing on a Cohesive Frictionless Material Smooth Circular Footing on an Associated Mohr-Coulomb Material Smooth Square Footing on a Cohesive Frictionless Material Uniaxial Compressive Strength of a Jointed Material Sample Drained and Undrained Triaxial Compression Test on a Cam-Clay Sample Lined Circular Tunnel in an Elastic Medium with Anisotropic Stresses Development of Plastic Hinges in a Statically Loaded Beam Cylindrical Concrete Vault Simply Supported Orthotropic Plate Simply Supported Isotropic Rectangular Plate under Combined Lateral and Direct Loads FLAC3D Version 3. 1

Online Contents - 4 VERIFICATION PROBLEMS Frontispiece Precis Table of Contents Cylindrical Hole in an Infinite Mohr-Coulomb Material Cylindrical Hole in an Infinite Hoek-Brown Medium Rough Strip Footing on a Cohesive Frictionless Material Smooth Circular Footing on an Associated Mohr-Coulomb Material Smooth Square Footing on a Cohesive Frictionless Material Uniaxial Compressive Strength of a Jointed Material Sample Drained and Undrained Triaxial Compression Test on a Cam-Clay Sample Lined Circular Tunnel in an Elastic Medium with Anisotropic Stresses Development of Plastic Hinges in a Statically Loaded Beam Cylindrical Concrete Vault Simply Supported Orthotropic Plate Simply Supported Isotropic Rectangular Plate under Combined Lateral and Direct Loads FLAC3D Version 3.1

Online contents -5 EXAMPLE APPLICATIONS Frontispiece Precis Table of Contents Influence of Slope Curvature on Stability Pillar loads at Intersecting Tunnels Excavation in a Saturated Soil Excavation and Support for a Shallow tunnel Grid Generation for Intersecting Tunnels Pressurized Cylindrical Cavern Prediction of Borehole closure in a salt formation Axial and Lateral Loading of a Concrete Pile Undrained Cylindrical Cavity Expansion in a Cam-Clay Medium Simulation of Pull-Tests for Fully Bonded Rock reinforcement Wheel Load over a Buried Pipe Embankment Loading on a Cam-Clay Foundation Impermeable Concrete Caisson Wall with Pretensioned Tiebacks FLAC3D Version 3. I

Online Contents - 5 EXAMPLE APPLICATIONS Frontispiece Precis Table of Contents Influence of Slope Curvature on Stability Pillar Loads at Intersecting Tunnels Excavation in a Saturated Soil Excavation and Support for a Shallow Tunnel Grid Generation for Intersecting Tunnels Pressurized Cylindrical Cavern Prediction of Borehole Closure in a Salt Formation Axial and Lateral Loading of a Concrete Pile Undrained Cylindrical Cavity Expansion in a Cam-Clay Medium Simulation of Pull-Tests for Fully Bonded Rock Reinforcement Wheel Load over a Buried Pipe Embankment Loading on a Cam-Clay Foundation Impermeable Concrete Caisson Wall with Pretensioned Tiebacks FLAC3D Version 3.1

INTRODUCTION 1 INTRODUCTION 1.1 Overview FLAC3D is a three-dimensional explicit finite-difference program for engineering mechanics com putation. The basis for this program is the well-established numerical formulation used by our two-dimensional program, FLAC. FLAC3D 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 FLaC3D 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 require ments. 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 FLAC3D offers an ideal anal ysis tool for solution of three-dimensional problems in geotechnical engineering FLAC3D is designed specifically to operate on Microsoft Windows systems, and is currently sup- ported on Windows 2000 and Windows XP (including XP64). Itanium-based systems are not supported. Calculations on realistically sized three-dimensional models in geo-engineering can be made in a reasonable time period. For example, a model containing 125,000 zones of a Mohr Coulomb material can be generated within 350 MB RAM. The runtime to perform 5000 calculation steps for a 10,000 zone model of Mohr-Coulomb material is roughly 12 minutes on a 2.8 GHz Pentium IV microcomputer. i The number of calculation steps required to reach a solution state with the explicit-calculation scheme can vary, but a solution typically can be reached within 3000 to 6000 steps for models containing up to 10,000 elements, regardless of material type. (The explicit- olution scheme is explained in Section I 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 FLAC3D FLAC3D can be operated from either a command-driven mode or a 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 FLAC3D for performing plotting, printing and file access Itasca Consulting Group, Inc. FLAC (Fast Lagrangian Analysis of Continua ) Version 5.0, 2005 i See Section 5 for a comparison of FLaC 3D runtimes on various computer systems FLAC3D Version 3.1

INTRODUCTION 1-1 1 INTRODUCTION 1.1 Overview FLAC3D is a three-dimensional explicit finite-difference program for engineering mechanics com￾putation. The basis for this program is the well-established numerical formulation used by our two-dimensional program, FLAC.* FLAC3D 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 FLAC3D 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 require￾ments. 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. FLAC3D offers an ideal analysis tool for solution of three-dimensional problems in geotechnical engineering. FLAC3D is designed specifically to operate on Microsoft Windows systems, and is currently sup￾ported on Windows 2000 and Windows XP (including XP64). Itanium-based systems are not supported. Calculations on realistically sized three-dimensional models in geo-engineering can be made in a reasonable time period. For example, a model containing 125,000 zones of a Mohr￾Coulomb material can be generated within 350 MB RAM. The runtime to perform 5000 calculation steps for a 10,000 zone model of Mohr-Coulomb material is roughly 12 minutes on a 2.8 GHz Pentium IV microcomputer.† The number of calculation 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 FLAC3D. FLAC3D can be operated from either a command-driven mode or a 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 FLAC3D 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 FLAC3D runtimes on various computer systems. FLAC3D Version 3.1

User's guide With the graphics facilities* built into FLAC3D, high-resolution, color-rendered plots are generated quite rapidly. We have developed a graphics screen-plotting facility that allows you to instantly w the model during creation from either command-mode or graphics menu-mode. The model 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 Flac3d offers a facility for problem solving similar to the one in FLAC.A comparison of FLAC3D to other numerical methods, a description of general features and updates in FLAC3D Version 3. 1, and a discussion of fields of application are provided in the following sections If you wish to try FLAC3D right away, the program installation instructions and a simple tutorial are provided in Section 2 The graphics facilities in FLAC3D utilize the Windows GDI FLAC3D Version 3.1

1-2 User’s Guide With the graphics facilities* built into FLAC3D, 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 FLAC3D offers a facility for problem solving similar to the one in FLAC. A comparison of FLAC3D to other numerical methods, a description of general features and updates in FLAC3D Version 3.1, and a discussion of fields of application are provided in the following sections. If you wish to try FLAC3D right away, the program installation instructions and a simple tutorial are provided in Section 2. * The graphics facilities in FLAC3D utilize the Windows GDI. FLAC3D Version 3.1

INTRODUCTION 13 1. 2 Comparison with Other Methods How does FLAC3D compare to the more common method of using 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 FLAC3D'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, FLAC3D differs in the following respect 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 sys- tems are essentially static. This enables FLAC3D 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 solu- tions 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. FLAC3D is robust in the sense that it can handle any constitutive model with no solution techniques for different constitutive models ent codes need different adjustment to the solution algorithm; many finite elem These differences are mainly in FLAC3D's favor, but there are two disadvantages Linear simulations run more slowly with FLAC3D than with equivalent finite element programs. FLAC3D 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 FLAC3D 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 elastic moduli or element sizes) FLAC3D Version 3.1

INTRODUCTION 1-3 1.2 Comparison with Other Methods How does FLAC3D compare to the more common method of using 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 FLAC3D’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, FLAC3D 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 sys￾tems are essentially static. This enables FLAC3D 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 solu￾tions 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. FLAC3D 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 FLAC3D’s favor, but there are two disadvantages: 1. Linear simulations run more slowly with FLAC3D than with equivalent finite element programs. FLAC3D 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 FLAC3D 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). FLAC3D Version 3.1

User's guide 1.3 General Features 13. Basic features FLAC3D offers a wide range of capabilities to solve complex problems in mechanics, and espe cially in geomechanics. Like FLAC, FLAC3D 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 elaS- ticity); and eight plasticity models(Drucker-Prager, Mohr-Coulomb, strain-hardening/softening, ubiquitous-joint, bilinear strain-hardening/softening ubiquitous-joint, double-yield, modified Cam clay and Hoek-Brown). These models are described in detail in Section 2 in Theory and back- ground. Each zone in a FLaC3D grid may have a different material model or property, and 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 FLAC3D contains an automatic 3D grid generator in which grids are created by manipulating and (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 com mand. and initial conditions via the INITIAL command as described in Section 1 in the Command Reference FLAC3D 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 fuid 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 fow 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 independent of 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 s An optional meshing preprocessor is also available-see Section 1.3.2 FLAC3D Version 3.1

1-4 User’s Guide 1.3 General Features 1.3.1 Basic Features FLAC3D offers a wide range of capabilities to solve complex problems in mechanics, and espe￾cially in geomechanics. Like FLAC, FLAC3D 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 elas￾ticity); and eight plasticity models (Drucker-Prager, Mohr-Coulomb, strain-hardening/softening, ubiquitous-joint, bilinear strain-hardening/softening ubiquitous-joint, double-yield, modified Cam￾clay and Hoek-Brown). These models are described in detail in Section 2 in Theory and Back￾ground. Each zone in a FLAC3D 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. FLAC3D 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 com￾mand, and initial conditions via the INITIAL command, as described in Section 1 in the Command Reference. FLAC3D 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 independent of 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. FLAC3D Version 3.1

INTRODUCTION 5 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 FLAC3D. 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 I in Structural Elements A factor of safety can be calculated automatically for any FLAC3D model composed of Mohr Coulomb 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 FLAC3D 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 FLAC3D 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 FLAC3D 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 FLAC3D Version 3.1

INTRODUCTION 1-5 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 FLAC3D. 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 FLAC3D model composed of Mohr￾Coulomb 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. FLAC3D 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. FLAC3D 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 ofFLAC3D 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. FLAC3D Version 3.1