| FLAC3D 6.0 | ||
| Theory and Background | ||
| (an excerpt from FLAC3D Help) | ||
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© 2017 Itasca Consulting Group, Inc.
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First Edition (FLAC3D Version 2.1) April 2002
Second Edition (FLAC3D Version 3.0) September 2005
Third Edition (FLAC3D Version 3.1) December 2006
Fourth Edition (FLAC3D Version 4.0) December 2009
Fifth Edition (FLAC3D Version 5.0) October 2012
Sixth Edition (FLAC3D Version 6.0) April 2017
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Precis
This document is a reproduction of the section “FLAC3D Theory and Background” from the FLAC3D Help. It is provided as a convenience to FLAC3D users who need access to the documentation in easily printable form.
There is no substantial difference between the content presented here and that which appears in the FLAC3D Help. In cases of variance, the difference is either a change made to accommodate format in going from a screen-based media to one intended for paper, or, since the Help is updated concurrent to code revisions, that the Help file content is more up-to-date than this document. In any case of variance between the two, precedence should always be given to the Help.
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This Document and Help Hyperlinks
The FLAC3D Help, from which this document is excerpted and produced, has many cross-reference hyperlinks. These are not reproduced here. Elements in the body-text of the Help that are hyperlinks are colored dark green in this document. This convention has been adopted to allow for link identification within the text of this PDF. To see the matter referenced, however, readers will need to access the equivalent link in the Help file.
FLAC3D Theory and Background: Table of Contents
FLAC3D Theory and Background ……………………………………………………………….. #
THEORETICAL BACKGROUND ………………………………………………………………………… #
Formulation Of A 3d Explicit Finite Volume Model ……………….. #
Mathematical Model Description ……………………………………………… #
Conventions ………………………………………………………………………. #
Stress ……………………………………………………………………………….. #
Rate of Strain and Rate of Rotation ……………………………. #
Equations of Motion and Equilibrium ……………………………. #
Boundary and Initial Conditions …………………………………… #
Constitutive Equations …………………………………………………… #
Numerical Formulation ……………………………………………………………… #
Finite Volume Approximation to Space Derivatives ………. #
Nodal Formulation of the Equations of Motion ……………. #
Explicit Finite Difference Approximation to Time Derivatives …… #
Constitutive Equations in Incremental Form ……………….. #
Large- and Small-Strain Modes ………………………………………. #
Mechanical Timestep Determination for Numerical Stability …… #
Mechanical Damping ………………………………………………………….. #
Grid Discretization ………………………………………………………………………….. #
Mixed Discretization for a Hexahedral Grid ………………………… #
Nodal Mixed Discretization for a Tetrahedral Grid ……………. #
Nodal mixed discretization on strain ………………………….. #
Nodal mixed discretization on stress ………………………….. #
Numerical Implementation …………………………………………………………………. #
Body Discretization …………………………………………………………………. #
Hexahedral Meshing ………………………………………………………….. #
Tetrahedral Meshing ………………………………………………………… #
Initial and Boundary Conditions ……………………………………………. #
Main Calculation Steps ……………………………………………………………. #
Strain-Rate Calculation ………………………………………………………….. #
Stress Calculation …………………………………………………………………… #
Nodal Mass Calculation ……………………………………………………………. #
Out-of-Balance Force and Ratio Calculation ………………………… #
Maximum Out-of-Balance Force ………………………………………… #
Local Maximum Force Ratio ……………………………………………… #
Average Force Ratio ………………………………………………………… #
Maximum Force Ratio ………………………………………………………… #
Velocity and Displacement Calculations ……………………………….. #
Geometry Update Calculation …………………………………………………… #
Energy Calculation in FLAC3D …………………………………………………. #
Energy Dissipation in Zones through Plastic Work …….. #
References ………………………………………………………………………………………….. #
INTERFACES ………………………………………………………………………… #
General Comments ……………………………………………………………………………….. #
Formulation ………………………………………………………………………………………… #
Creation of Interface Geometry ………………………………………………………. #
Choice of Material Properties ………………………………………………………… #
Interface Used to Join Two Sub-grids …………………………………… #
Real Interface — Slip and Separation Only ………………………….. #
All Properties Have Physical Significance ………………………….. #
Modeling Guidelines ………………………………………………………………………….. #
Troubleshooting ………………………………………………………………………… #
Initial Stresses ………………………………………………………………………. #
Interface Corners …………………………………………………………………….. #
Overlapping Interfaces ……………………………………………………………. #
Interfaces and Fluid Flow ………………………………………………………. #
Interfaces and Changing Interacting Objects in Small Strain … #
References ………………………………………………………………………………………….. #
FACTOR OF SAFETY ………………………………………………………………………… #
Introduction ………………………………………………………………………………………. #
Factor of Safety ……………………………………………………………………………….. #
Computational Methods for Factor of Safety Calculation of Slopes … #
Strength Reduction Technique …………………………………………………. #
Limit Analysis ………………………………………………………………………….. #
Limit Equilibrium …………………………………………………………………….. #
Relation of Strength Reduction Method to Limit Equilibrium
and Limit Analysis ……………………………………………………………….. #
Strength Reduction Procedure in FLAC3D ………………………………………… #
Strength Reduction Properties ……………………………………………….. #
Mohr-Coulomb Material …………………………………………………….. #
Ubiquitous-Joint Material ……………………………………………… #
Hoek-Brown Material ………………………………………………………… #
Interfaces ………………………………………………………………………… #
Example Factor of Safety Calculations using
the Strength Reduction Method ………………………………………………………… #
Failure of a Slope with a Complex Surface Profile in a
Mohr-Coulomb Material ………………………………………………………… #
Influence of Slope Curvature on Stability ………………………… #
Simple Slope in Hoek-Brown Material …………………………………… #
Automatic Calculation of a Stable Pit Slope Angle ………….. #
Factor of Safety Contours …………………………………………………….. #
References ………………………………………………………………………………………… #
CONSTITUTIVE MODELS …………………………………………………………………………………. #
Constitutive Models in FLAC3D ………………………………………………………. #
Incremental Formulation …………………………………………………………………. #
Null Model Group ……………………………………………………………………………… #
Null Model ……………………………………………………………………………….. #
Elastic Model Group ………………………………………………………………………… #
Elastic (Isotropic) Model …………………………………………………….. #
Anisotropic (Transversely-Elastic) Model ………………………….. #
Orthotropic Elastic Model …………………………………………………….. #
Plastic Model Group ………………………………………………………………………… #
Drucker-Prager Model ……………………………………………………………… #
Mohr-Coulomb Model …………………………………………………………………. #
Ubiquitous-Joint Model ………………………………………………………….. #
Anisotropic-Elasticity Ubiquitous-Joint Model …………………. #
Strain-Softening/Hardening Mohr-Coulomb Model …………………. #
Bilinear Strain-Softening/Hardening Ubiquitous-Joint Model ….. #
Double-Yield Model …………………………………………………………………. #
Modified Cam-Clay Model ………………………………………………………… #
Hoek-Brown Model …………………………………………………………………….. #
Hoek-Brown-PAC Model ……………………………………………………………… #
Cap-Yield (CYSoil) Model ………………………………………………………. #
Simplified Cap-Yield (CHSoil) Model …………………………………… #
Plastic-Hardening Model ………………………………………………………… #
Swell Model ……………………………………………………………………………… #
Mohr-Coulomb Tension Crack (MohrT) Model ………………………….. #
Model Tests and Examples ……………………………………………………………….. #
Oedometer Test with Mohr-Coulomb Model ……………………………… #
Uniaxial Compressive Strength of a Jointed Material Sample …. #
Isotropic Consolidation Test with Double-Yield Model …….. #
Isotropic Consolidation Test with Modified Cam-Clay Model …. #
Triaxial Compression Test with Hoek-Brown Model ……………… #
Triaxial Compression Test with Hoek-Brown-PAC Model ………. #
Isotropic Compression Test with CYSoil Model …………………… #
Oedometer Test with CYSoil Model ………………………………………… #
Drained Triaxial Test with CYSoil Model — Constant Dilation ….. #
Drained Triaxial Test with CYSoil Model — Dilation Hardening ….. #
Undrained Triaxial Test with CYSoil Model ………………………… #
Drained Triaxial Compression Test with
Simplified Cap-Yield (CHSoil) Model ……………………………….. #
Comparison between Mohr-Coulomb Model and
Plastic-Hardening model …………………………………………………….. #
Isotropic Compression Test with Plastic-Hardening Model ….. #
Drained Triaxial Compression Test with Plastic-Hardening Model ….. #
Undrained Triaxial Compression Test with Plastic-Hardening Model ….. #
Oedometer Test with Plastic-Hardening Model …………………….. #
Single Zone Swell Test ………………………………………………………….. #
Single Zone Loading-Unloading Test with MohrT Model ………… #
References ………………………………………………………………………………………….. #
FLUID-MECHANCIAL INTERACTION ……………………………………………………………… #
FLAC3D Fluid-Thermal-Mechanical-Formulation —
Mathematical Description …………………………………………………………………. #
Conventions and Definitions …………………………………………………… #
Governing Differential Equations ………………………………………….. #
Fluid Flow Boundary and Initial Conditions in FLAC3D ………. #
Numerical Formulation ………………………………………………………………………. #
Saturated Fluid Flow ……………………………………………………………….. #
Finite-Volume Approximation to Space Derivatives ….. #
Nodal Formulation of the Mass Balance Equation ………… #
Explicit Finite-Volume Formulation ………………………. #
Stability Criterion ………………………………………………………… #
Implicit Finite-Volume Formulation ………………………. #
Convergence Criterion …………………………………………………….. #
Saturated/Unsaturated Flow …………………………………………………….. #
Mechanical Timestep and Numerical Stability ………………………. #
Total Stress Correction ………………………………………………………….. #
Fully Saturated Fast Flow ………………………………………………………. #
An Alternative Fast-Flow Algorithm ……………………………… #
Calculation Modes for Fluid-Mechanical Interaction …………………… #
Grid Not Configured for Fluid Flow ………………………………………. #
Grid Configured for Fluid Flow ……………………………………………… #
Properties and Units for Fluid-Flow Analysis ……………………………… #
Permeability Coefficient ………………………………………………………… #
Mass Density ……………………………………………………………………………… #
Fluid Moduli ……………………………………………………………………………… #
Biot Coefficient and Biot Modulus ……………………………….. #
Fluid Bulk Modulus ………………………………………………………….. #
Fluid Moduli and Convergence ………………………………………… #
Fluid Moduli for Drained and Undrained Analyses ………. #
Porosity …………………………………………………………………………………….. #
Saturation …………………………………………………………………………………. #
Undrained Thermal Coefficient ……………………………………………….. #
Fluid Tension Limit …………………………………………………………………. #
Fluid-Flow Boundary Conditions, Initial Conditions, Sources and Sinks ….. #
Solving Flow-Only and Coupled-Flow Problems ……………………………….. #
Time Scales ……………………………………………………………………………….. #
Selection of a Modeling Approach for a Fully Coupled Analysis ….. #
Time Scale ………………………………………………………………………… #
Nature of Imposed Perturbation to the Coupled Process ….. #
Stiffness Ratio ……………………………………………………………….. #
Recommended Procedure to Select a Modeling Approach ….. #
Fixed Pore Pressure (Used in Effective Stress Calculation) ….. #
Flow-Only Calculation to Establish a Pore-Pressure Distribution ….. #
No Flow — Mechanical Generation of Pore Pressure ……………… #
Coupled Flow and Mechanical Calculations ……………………………. #
Verification Examples ………………………………………………………………………. #
Unsteady Groundwater Flow in a Confined Layer …………………… #
One-Dimensional Filling of a Porous Region ………………………… #
Steady-State Fluid Flow with a Free Surface ………………………. #
Spreading of a Groundwater Mound ………………………………………….. #
One-Dimensional Consolidation ……………………………………………….. #
Consolidation Settlement at the Center of a Strip Load ….. #
Transient Fluid Flow to a Well in a Shallow Confined Aquifer ….. #
Pressuremeter Test …………………………………………………………………… #
Semi-confined Aquifer ……………………………………………………………… #
Verification of Concepts, and Modeling Techniques
for Specific Applications ……………………………………………………………….. #
Solid Weight, Buoyancy and Seepage Forces ………………………….. #
A Simple Example Illustrating Solid Weight, Buoyancy and
Seepage Forces …………………………………………………………………. #
Pore Pressure Initialization and Deformation …………………….. #
Heave of a Soil Layer …………………………………………………….. #
Effect of the Biot Coefficient ……………………………………………… #
Undrained Oedometer Test ……………………………………………….. #
Pore Pressure Generation in a Confined Sample ………….. #
Pore Pressure Generation in an Infinite Layer ………….. #
Input Instructions for Fluid-Flow Analysis …………………………………. #
Fluid Commands ………………………………………………………………………….. #
Fluid FISH Variables ……………………………………………………………….. #
Zone-Based Pore Pressure ………………………………………………………… #
References ………………………………………………………………………………………….. #
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