3DEC 3 Dimensional Distinct Element Code User’s Guide
©2003 Itasca Consulting Group, Inc. Mill Place 111 Third Avenue South, Suite 450 Minneapolis, Minnesota 55401 USA
Phone: Fax: E-Mail: Web:
(1) 612-371-4711 (1) 612·371·4717
[email protected] www.itascacg.com
First Edition December 1998 First Revision May 1999 Second Revision September 1999 Second Edition January 2003
Terms - 1
Terms and Conditions for Licensing 3DEC YOU SHOULD READ THE FOLLOWING TERMS AND CONDITIONS CAREFULLY BEFORE USING THE 3DEC PROGRAM. INSTALLATION OF THE 3DEC PROGRAM INTO YOUR COMPUTER INDICATES YOUR ACCEPTANCE OF THESE TERMS AND CONDITIONS. IF YOU DO NOT AGREE WITH THEM, YOU SHOULD RETURN THE PACKAGE PROMPTLY AND YOUR MONEY WILL BE REFUNDED. This program is provided by Itasca Consulting Group, Inc. Title to the media on which the program is recorded and to the documentation in support thereof is transferred to the customer, but title to the program is retained by Itasca. You assume responsibility for the selection of the program to achieve your intended results and for the installation of the program, the use of and the results obtained from the program. LICENSE • You may use the program on only one machine at any one time. • You may copy the program for back-up only in support of such use. • You may not use, copy, modify, or transfer the program, or any copy, in whole or part, except as expressly provided in this document. • You may not sell, sub-license, rent, or lease this program. TERMS The license is effective until terminated. You may terminate it any time by destroying the program together with any back-up copies and returning the hardware lock. It will also terminate if you fail to comply with any term or condition of this agreement. You agree upon such termination to destroy the program together with any back-up copies, modifications, and/or merged portions in any form and return the hardware lock to Itasca. WARRANTY Itasca will correct any errors in the code at no charge for twelve (12) months after the purchase date of the code. Notification of a suspected error must be made in writing, with a complete listing of the input and output files and description of the error. If, in the judgment of Itasca, the code does contain an error, Itasca will (at its option) correct or replace the copy at no cost to the user or refund the initial purchase price of the code.
3DEC Version 3.0
Terms - 2
User’s Guide
LIMITATION OF LIABILITY Itasca assumes no liability whatsoever with respect to any use of 3DEC or any portion thereof or with respect to any damages or losses that may result from such use, including (without limitation) loss of time, money or goodwill that may arise from the use of 3DEC (including any modifications or updates that may follow). In no event shall Itasca be responsible for any indirect, special, incidental or consequential damages arising from use of 3DEC. CODE SUPPORT Itasca will provide telephone support, at no charge, to assist the code owner in the installation of the 3DEC code on his or her computer system. Additionally, general assistance may be provided in aiding the owner in understanding the capabilities of the various features of the code. However, no-cost assistance is not provided for help in applying 3DEC to specific user-defined problems. Technical support can be purchased on an as-needed basis. For users who envisage the need for substantial amounts of assistance, consulting support is available. In all instances, the user is encouraged to send the problem description to Itasca by electronic mail in order to minimize the amount of time spent trying to define the problem. See Section 6 in the User’s Guide for details.
3DEC Version 3.0
User’s Guide
1
PRECIS This volume is the user’s guide to 3DEC. This guide contains general information on the operation of 3DEC for engineering mechanics computation. Section 1 gives an introduction to the capabilities and applications of 3DEC. An overview of the new features in the latest version of 3DEC is also provided. The first-time user should consult Section 2 for an introduction to the operation of 3DEC. The installation and operation procedures are given along with a simple tutorial to guide the new user through a 3DEC analysis. Section 3 provides general guidance in the use of 3DEC in problem solving for static mechanical analysis for geotechnical engineering. An introduction to the built-in programming language, FISH, is given in Section 4. This includes a tutorial on the use of the FISH language. Note that no programming experience is assumed. 3DEC contains a graphical interface to assist with model creation and presentation of results. The graphical interface is described in Section 5. Various items of interest to 3DEC users are contained in Section 6, including a 3DEC runtime benchmark on several different types of computers, and procedures for reporting errors and requesting technical assistance. Section 7 contains a bibliography of published papers describing some applications of 3DEC in different fields of engineering. The 3DEC Manual consists of seven documents. The following volumes, which comprise the 3DEC Manual, are available. (The titles in parentheses below are the names used to refer to the volumes in the text.) USER’S GUIDE — (User’s Guide) — an introduction to 3DEC and its capabilities COMMAND REFERENCE — (Command Reference) — descriptions of all 3DEC commands FISH in 3DEC — (FISH volume) — a complete guide to FISH as applied in 3DEC THEORY AND BACKGROUND — (Theory and Background) — thorough discussions of the built-in features in 3DEC OPTIONAL FEATURES — (Optional Features) — detailed descriptions of the optional features: thermal analysis, dynamic analysis, and the surface support (liner) model VERIFICATION PROBLEMS (Verifications volume) and EXAMPLE APPLICATIONS (Examples volume) — a collection of verification problems and example applications COMMAND AND FISH REFERENCE SUMMARY — (Command and FISH Reference Summary) — a quick summary of all 3DEC commands and FISH statements
3DEC Version 3.0
2
3DEC Version 3.0
User’s Guide
User’s Guide
Contents - 1
TABLE OF CONTENTS 1 INTRODUCTION 1.1 1.2 1.3
1.4
1.5 1.6 1.7 1.8 1.9
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison with Other Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Basic Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Optional Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary of Updates from Version 2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Automatic Topographic Stress Initialization . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 User-Defined Models (UDM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3 Additional Constitutive Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.4 Double Precision Version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.5 Dynamic Free Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.6 Partial Density Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.7 Higher Order Tetrahedral Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.8 Improved Bitmap and Printer Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.9 Poly Cube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.10 Structural Beam Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.11 Surface Stress Plotting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.12 Generalized Boundary Histories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.13 Joint Fluid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.14 New Mouse Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.15 User-Controlled Colors for Contours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.16 User-Defined Stress Plot Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fields of Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Guide to the 3DEC Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Itasca Consulting Group, Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . User Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-1 1-4 1-6 1-6 1-8 1-9 1-9 1-9 1-9 1-9 1-9 1 - 10 1 - 10 1 - 10 1 - 10 1 - 10 1 - 10 1 - 11 1 - 11 1 - 11 1 - 11 1 - 11 1 - 12 1 - 13 1 - 17 1 - 18 1 - 19
3DEC Version 3.0
Contents - 2
User’s Guide
2 GETTING STARTED Installation and Start-up Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Installation of 3DEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 System Requirements for Windows 95/98/ME/NT/2000/XP . . . . . . . . . 2.1.3 Windows-Console Version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Utility Software and Graphics Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.5 Version Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.6 Start-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.7 Program Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.8 Running 3DEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.9 Installation Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 A Simple Tutorial — Use of Common Commands . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 The 3DEC Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Command Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Mechanics of Using 3DEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Model Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Assigning Material Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2.1 Block Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2.2 Joint Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.3 Applying Boundary and Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.4 Stepping to Initial Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.5 Performing Alterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.6 Saving/Restoring Problem State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.7 Summary of Commands for Simple Analyses . . . . . . . . . . . . . . . . . . . . . . 2.7 Sign Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Systems of Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1
2-2 2-2 2-3 2-3 2-4 2-5 2-6 2-6 2-6 2-7 2 - 10 2 - 18 2 - 21 2 - 24 2 - 26 2 - 28 2 - 31 2 - 31 2 - 34 2 - 35 2 - 37 2 - 39 2 - 42 2 - 44 2 - 45 2 - 47 2 - 48 2 - 50
3 PROBLEM SOLVING WITH 3DEC 3.1
General Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Step 1: Define the Objectives for the Model Analysis . . . . . . . . . . . . . . . 3.1.2 Step 2: Create a Conceptual Picture of the Physical System . . . . . . . . . . 3.1.3 Step 3: Construct and Run Simple Idealized Models . . . . . . . . . . . . . . . . 3.1.4 Step 4: Assemble Problem-Specific Data . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.5 Step 5: Prepare a Series of Detailed Model Runs . . . . . . . . . . . . . . . . . . . 3.1.6 Step 6: Perform the Model Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.7 Step 7: Present Results for Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . .
3DEC Version 3.0
3-2 3-3 3-3 3-4 3-5 3-5 3-6 3-6
User’s Guide
3.2
3.3
3.4
3.5
3.6 3.7
Contents - 3
Model Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Fitting the 3DEC Model to a Problem Region . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Joint Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Creating Internal Boundary Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3.1 Tunnel Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3.2 POLY cube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Selecting the Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Orientation of Geologic Features to the Model Axes . . . . . . . . . . . . . . . . 3.2.6 Choice of Model Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.7 Incorporation of Discontinuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selection of Deformable versus Rigid Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Poisson’s Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Zoning for Deformable Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Stress Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1.1 Applied Stress Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1.2 Changing Boundary Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1.3 Checking the Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1.4 Cautions and Advice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Displacement Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Real Boundaries — Choosing the Right Type . . . . . . . . . . . . . . . . . . . . . . . 3.4.4 Artificial Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.4.1 Symmetry Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.4.2 Boundary Truncation — Location of the Far-Field Boundary . Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Uniform Stresses in an Unjointed Medium: No Gravity . . . . . . . . . . . . . 3.5.2 Stresses with Gradients in an Unjointed Medium: Uniform Material . . 3.5.3 Stresses with Gradients in a Nonuniform Material . . . . . . . . . . . . . . . . . . 3.5.4 Compaction within a Model with Nonuniform Zoning . . . . . . . . . . . . . . . 3.5.5 Initial Stresses following a Model Change . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.6 Stresses in a Jointed Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.7 Determination of the In-situ Stress State . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.8 Transferring Field Stresses to Model Stresses . . . . . . . . . . . . . . . . . . . . . . . 3.5.9 Topographical Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Loading and Sequential Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Choice of Constitutive Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.1 Deformable-Block Material Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.2 Joint Material Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.3 Selection of an Appropriate Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-7 3-7 3 - 12 3 - 17 3 - 18 3 - 19 3 - 22 3 - 22 3 - 23 3 - 24 3 - 26 3 - 26 3 - 31 3 - 32 3 - 32 3 - 33 3 - 34 3 - 35 3 - 35 3 - 38 3 - 38 3 - 39 3 - 39 3 - 39 3 - 42 3 - 42 3 - 43 3 - 44 3 - 46 3 - 48 3 - 49 3 - 51 3 - 53 3 - 54 3 - 55 3 - 76 3 - 76 3 - 78 3 - 79
3DEC Version 3.0
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User’s Guide
Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.1 Block Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.1.1 Mass Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.1.2 Intrinsic Deformability Properties . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.1.3 Intrinsic Strength Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.1.4 Post-Failure Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.1.5 Extrapolation to Field-Scale Properties . . . . . . . . . . . . . . . . . . . . . 3.8.2 Joint Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Tips and Advice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10.1 Unbalanced Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10.2 Block/Gridpoint Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10.3 Plastic Indicators for Block Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10.4 Histories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11 Modeling Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.1 Modeling of Data-Limited Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.2 Modeling of Chaotic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.3 Localization, Physical Instability and Path-Dependence . . . . . . . . . . . . . 3.12 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8
3 - 86 3 - 86 3 - 86 3 - 86 3 - 87 3 - 89 3 - 96 3 - 100 3 - 102 3 - 108 3 - 108 3 - 108 3 - 109 3 - 110 3 - 111 3 - 111 3 - 111 3 - 113 3 - 115
4 FISH BEGINNER’S GUIDE 4.1 4.2
Introduction and Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 1 Tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 2
5 GRAPHICAL INTERFACE 5.1 5.2
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Menus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Main Menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Select Color Mode Menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Select Joint Mode Menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.4 Target Active Menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.5 Structure Menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.6 Special Options Menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.7 Stresses Menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.8 Vectors (and Contours) Menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3DEC Version 3.0
5-2 5-4 5-4 5 - 10 5 - 11 5 - 12 5 - 17 5 - 18 5 - 20 5 - 24
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Contents - 5
6 MISCELLANEOUS 6.1 6.2
6.3
3DEC Runtime Benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Error Reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Reporting via Internet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Reporting via Fax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Technical Support Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-1 6-3 6-3 6-3 6-3
7 BIBLIOGRAPHY
3DEC Version 3.0
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User’s Guide
TABLES Table 2.1 Table 2.2 Table 2.3 Table 2.4 Table 2.5 Table 3.1 Table 3.2 Table 3.3 Table 3.4 Table 3.5 Table 3.6 Table 4.1 Table 6.1
Maximum number of 3DEC blocks in available RAM . . . . . . . . . . . . . . . . . . . . . Typographical conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boundary condition command summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic commands for simple analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Systems of units — mechanical parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Recommended steps for numerical analysis in geomechanics . . . . . . . . . . . . . . . 3DEC block constitutive models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3DEC joint constitutive models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selected elastic constants (laboratory-scale) for rocks (adapted from Goodman 1980) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selected strength properties (laboratory-scale) for rocks (adapted from Goodman 1980) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical values for Hoek-Brown rock-mass strength parameters (adapted from Hoek and Brown (1988)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Commands that directly refer to FISH names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3DEC runtime calculation rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3DEC Version 3.0
2-4 2 - 25 2 - 35 2 - 44 2 - 47 3-3 3 - 77 3 - 79 3 - 87 3 - 88 3 - 99 4-4 6-1
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Contents - 7
FIGURES Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Figure 2.6 Figure 2.7 Figure 2.8 Figure 2.9 Figure 2.10 Figure 2.11 Figure 2.12 Figure 2.13 Figure 2.14 Figure 2.15 Figure 2.16 Figure 2.17 Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5
Figure 3.6 Figure 3.7 Figure 3.8 Figure 3.9 Figure 3.10 Figure 3.11 Figure 3.12 Figure 3.13 Figure 3.14 Figure 3.15 Figure 3.16
PostScript plot from “TEST3.DAT” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3DEC model of a rock slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . History of y-velocity for initial rock slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rock slope failure in progress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vertical cross-section through wedge showing displacement vectors . . . . . . . Example of a 3DEC model (not to scale) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3DEC model block divided into two blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General solution procedure for static analysis in geomechanics . . . . . . . . . . . . Block model with three intersecting joint planes . . . . . . . . . . . . . . . . . . . . . . . . . Tunnel in jointed rock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tunnel in jointed rock — excavation and joint structure . . . . . . . . . . . . . . . . . . Maximum unbalanced force history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y-displacement history at (.3, .3, 0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sliding wedge in tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y-displacement history at (.3, .3, -0.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y-displacement history at (.3, .3, -0.1) — wedge is stable . . . . . . . . . . . . . . . . . Sign convention for positive stress components . . . . . . . . . . . . . . . . . . . . . . . . . . Spectrum of modeling situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cubic model created with the POLY face command . . . . . . . . . . . . . . . . . . . . . . An octahedral-shaped prism generated with the POLY prism command . . . . . Tunnel model created with the POLY tunnel command . . . . . . . . . . . . . . . . . . . . Terms describing the attitude of an inclined plane: dip angle, α, is positive measured downward from the horizontal (xz) plane; dip direction, β, is positive measured clockwise from north (z) . . . . . . . . . Model created with the JSET and HIDE commands . . . . . . . . . . . . . . . . . . . . . . . Concave block created with the JOIN command . . . . . . . . . . . . . . . . . . . . . . . . . Rock slope containing continuous and noncontinuous joints . . . . . . . . . . . . . . Tunnel created with TUNNEL command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elements of the POLY cube command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Resultant geometry from example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orientation of 3DEC model axes (x,y,z) relative to north-east-up reference axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stereonet plot of fault relative to model axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stereonet plot of pole to fault and model reference axes relative to problem north-east axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Model for Poisson’s effect in rock with vertical and horizontal jointing . . . . Poisson’s effect for vertically-jointed rock (ν = 0.3 for intact rock) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-9 2 - 12 2 - 15 2 - 17 2 - 17 2 - 18 2 - 22 2 - 27 2 - 29 2 - 30 2 - 31 2 - 38 2 - 39 2 - 41 2 - 41 2 - 43 2 - 45 3-2 3-9 3 - 10 3 - 11 3 - 12 3 - 14 3 - 15 3 - 16 3 - 19 3 - 20 3 - 21 3 - 23 3 - 25 3 - 25 3 - 27 3 - 28
3DEC Version 3.0
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Figure 3.17 Figure 3.18 Figure 3.19 Figure 3.20 Figure 3.21 Figure 3.22 Figure 3.23 Figure 3.24 Figure 3.25 Figure 3.26 Figure 3.27 Figure 3.28 Figure 3.29 Figure 3.30 Figure 3.31 Figure 3.32 Figure 3.33 Figure 3.34 Figure 3.35 Figure 3.36 Figure 3.37 Figure 3.38 Figure 3.39 Figure 3.40 Figure 3.41 Figure 3.42 Figure 3.43 Figure 3.44 Figure 3.45 Figure 3.46 Figure 3.47 Figure 3.48 Figure 3.49
User’s Guide
Model for Poisson’s effect in rock with joints dipping at angle θ from the horizontal and with spacing S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Poisson’s effect for jointed rock at various joint angles (blocks are rigid) . . . Poisson’s effect for rock with two equally spaced joint sets with θ = 45◦ (blocks are deformable with ν = 0.2) . . . . . . . . . . . . . . . . . . . . Uplift when material is removed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixing stress and velocity boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . Models used to transfer stress boundary conditions . . . . . . . . . . . . . . . . . . . . . . Nonuniform stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Uniform stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Slip of a confined joint; plot shows shear stress contours . . . . . . . . . . . . . . . . . 3DEC model of tunnel region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Displacement histories at top of model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y-displacement history at tunnel roof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Close-up view of wedge in roof (surrounding blocks hidden) . . . . . . . . . . . . . Cable bolts positioned around tunnel excavation . . . . . . . . . . . . . . . . . . . . . . . . . y-displacement history at tunnel roof — reinforcement element support . . . . y-displacement history at tunnel roof — cable support . . . . . . . . . . . . . . . . . . . Axial forces in reinforcement elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Axial forces in cable elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thick concrete liner support — liner blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y-displacement history at tunnel roof — tunnel liner added after tractions reduced by 50% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thick concrete liner support — prism-shaped liner blocks . . . . . . . . . . . . . . . . Thick concrete liner support — mixed-discretization zoning in liner blocks . y-displacement history at tunnel roof — support by prism-shaped liner blocks Principal stress distribution in top section of liner . . . . . . . . . . . . . . . . . . . . . . . . Direct shear test model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Average shear stress versus shear displacement — Coulomb slip model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Average normal displacement versus shear displacement — Coulomb slip model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Average shear stress versus shear displacement — Coulomb slip model with peak and residual strength . . . . . . . . . . . . . . . Average normal displacement versus shear displacement — Coulomb slip model with peak and residual strength . . . . . . . . . . . . . . . Idealized relation for dilation angle, ψ, from triaxial test results (Vermeer and de Borst 1984) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . σyy stress versus yy-strain for tension test with cons 2 model . . . . . . . . . . . . . σyy stress versus yy-strain for tension test with cons 6 model and tensilesoftening table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx-strain versus yy-strain for tension test with cons 2 model . . . . . . . . . . . . . .
3DEC Version 3.0
3 - 29 3 - 29 3 - 30 3 - 36 3 - 37 3 - 40 3 - 47 3 - 48 3 - 51 3 - 58 3 - 61 3 - 62 3 - 62 3 - 63 3 - 66 3 - 66 3 - 67 3 - 67 3 - 70 3 - 70 3 - 73 3 - 74 3 - 75 3 - 75 3 - 80 3 - 83 3 - 83 3 - 84 3 - 85 3 - 89 3 - 93 3 - 94 3 - 95
User’s Guide
Figure 3.50 Figure 3.51 Figure 5.1 Figure 5.2 Figure 5.3 Figure 5.4 Figure 5.5
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xx-strain versus yy-strain for tension test with cons 6 model and tensilesoftening table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A small portion of a jointed rock mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3DEC graphical interface (DOS version) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3DEC menu guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Location of viewing plane in terms of dip, dip direction and center distance from model axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example interrogate block menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Symbols identifying failure mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 - 95 3 - 112 5-1 5-3 5-9 5 - 13 5 - 22
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EXAMPLES Example 2.1 Example 2.2 Example 2.3 Example 2.4 Example 2.5 Example 2.6 Example 2.7 Example 2.8 Example 2.9 Example 3.1 Example 3.2 Example 3.3 Example 3.4 Example 3.5 Example 3.6 Example 3.7 Example 3.8 Example 3.9 Example 3.10 Example 3.11 Example 3.12 Example 3.13 Example 3.14 Example 3.15 Example 3.16 Example 3.17 Example 3.18 Example 3.19 Example 3.20 Example 3.21 Example 3.22 Example 3.23 Example 3.24 Example 3.25 Example 4.1
3DEC output from “TEST1.DAT” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3DEC model block divided into two blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . Block model with three intersecting joint planes . . . . . . . . . . . . . . . . . . . . . . . Tunnel in jointed rock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Assigning material models and properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applying boundary and initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stepping to initial equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reduce the strength of the joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stabilize roof block with a cable bolt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A cube generated with the POLY face command . . . . . . . . . . . . . . . . . . . . . . . . A cube generated with the POLY brick command . . . . . . . . . . . . . . . . . . . . . . . An octahedral-shaped prism generated with the POLY prism command . . . A tunnel model generated with the POLY tunnel command . . . . . . . . . . . . . . Creation of a noncontinuous vertical joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rock slope containing continuous and noncontinuous joints . . . . . . . . . . . . . Tunnel created with the TUNNEL command . . . . . . . . . . . . . . . . . . . . . . . . . . . . Data file which generates a model using POLY cube command . . . . . . . . . . . Uplift when material is removed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixing stress and velocity boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . Initial and boundary stresses in equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . Initial stress state with gravitational gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . Initial stress gradient in a nonuniform material . . . . . . . . . . . . . . . . . . . . . . . . . Nonuniform stress initialized in a model with nonuniform zoning . . . . . . . . Initial stresses following a model change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Slip of a confined joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability analysis of an underground excavation — initial model . . . . . . . . . Stability analysis of an underground excavation — initial equilibrium stress state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability analysis of an underground excavation — unsupported tunnel . . . Stability analysis of an underground excavation — local reinforcement support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability analysis of an underground excavation — fully grouted cable support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability analysis of an underground excavation — reduce tunnel tractions by 50% and install liner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability analysis of an underground excavation — liner with m-d zoning . Direct shear test with Coulomb slip model . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tension test on tensile-softening material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Defining a FISH function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3DEC Version 3.0
2-8 2 - 21 2 - 28 2 - 29 2 - 34 2 - 36 2 - 38 2 - 40 2 - 42 3-8 3-9 3 - 10 3 - 11 3 - 13 3 - 16 3 - 18 3 - 21 3 - 35 3 - 36 3 - 43 3 - 44 3 - 45 3 - 46 3 - 49 3 - 50 3 - 56 3 - 59 3 - 61 3 - 63 3 - 64 3 - 68 3 - 71 3 - 80 3 - 91 4-2
User’s Guide
Example 4.2 Example 4.3 Example 4.4 Example 4.5 Example 4.6 Example 4.7 Example 4.8 Example 4.9 Example 4.10 Example 4.11 Example 4.12 Example 6.1
Contents - 11
Using a variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SETting variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test your understanding of function and variable names . . . . . . . . . . . . . . . . Capturing the history of a FISH variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FISH functions to calculate bulk and shear moduli . . . . . . . . . . . . . . . . . . . . . Using symbolic variables in 3DEC input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Controlled loop in FISH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applying a nonlinear initial distribution of moduli . . . . . . . . . . . . . . . . . . . . . Splitting lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Action of the IF ELSE ENDIF construct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Benchmark data file — “TIMING.DAT” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-3 4-3 4-4 4-4 4-6 4-6 4-7 4-8 4-9 4-9 4 - 11 6-2
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3DEC Version 3.0
User’s Guide
INTRODUCTION
1-1
1 INTRODUCTION 1.1 Overview 3DEC is a three-dimensional numerical program based on the distinct element method for discontinuum modeling. The basis for this program is the extensively tested numerical formulation used by the two-dimensional version, UDEC (Itasca 1996). 3DEC simulates the response of discontinuous media (such as a jointed rock mass) subjected to either static or dynamic loading. The discontinuous medium is represented as an assemblage of discrete blocks. The discontinuities are treated as boundary conditions between blocks; large displacements along discontinuities and rotations of blocks are allowed. Individual blocks behave as either rigid or deformable material. Deformable blocks are subdivided into a mesh of finite difference elements, and each element responds according to a prescribed linear or nonlinear stress-strain law. The relative motion of the discontinuities is also governed by linear or nonlinear force-displacement relations for movement in both the normal and shear directions. 3DEC has several built-in material behavior models, for both the intact blocks and the discontinuities, that permit the simulation of response representative of discontinuous geologic, or similar, materials. 3DEC is based on a “Lagrangian” calculation scheme that is well-suited to model the large movements and deformations of a blocky system. The distinguishing features of 3DEC are summarized below. • The rock mass is modeled as a 3D assemblage of rigid or deformable blocks. • Discontinuities are regarded as distinct boundary interactions between these blocks; joint behavior is prescribed for these interactions. • Continuous and discontinuous joint patterns can be generated on a statistical basis. A joint structure can be built into the model directly from the geologic mapping. • 3DEC employs an explicit in-time solution algorithm that accommodates both large displacement and rotation and permits time domain calculations. • The graphics facility permits interactive manipulation of 3D objects. In the graphics screen mode, the user can “move” into the model and make regions invisible for better viewing purposes. This allows the user to build the model for a geotechnical analysis and instantly view the 3D representation. This greatly facilitates the generation of 3D models and interpretation of results. 3DEC also contains the powerful built-in programming language FISH (short for FLACish; FISH was originally developed for our two-dimensional, finite-difference, continuum program FLAC). With FISH, you can write your own functions to extend 3DEC ’s usefulness. FISH offers a unique capability to 3DEC users who wish to tailor analyses to suit specific needs.
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With the exception of the graphics mode, 3DEC is a command-driven (rather than menu-driven) computer program. Although a menu-driven program is easier to learn for the first time, the command-driven structure in 3DEC offers several advantages when applied in engineering studies. 1. The input “language” is based upon recognizable word commands that allow you to identify the application of each command easily and in a logical fashion (e.g., the BOUNDARY 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) corresponds closely with the physical sequence that it represents. 3. A 3DEC data file can easily be modified with a text editor. Several data files can be linked to run a number of 3DEC analyses in sequence. This is ideal for performing parameter sensitivity studies. 4. The word-oriented input files provide an excellent means to keep a documented record of the analyses performed for an engineering study. Often, it is convenient to include these files as an appendix to the engineering report for the purpose of quality assurance. 5. The command-driven structure allows you to develop pre- and post-processing programs to manipulate 3DEC input/output as desired. For example, you may wish to write a joint-generation function to create a special joint structure for a series of 3DEC simulations. This can readily be accomplished with the FISH programming language and incorporated directly in the input data file. The formulation and development of the distinct element method embodied in 3DEC has progressed for a period of over 25 years, beginning with the initial presentation by Cundall (1971). In 1988, Dr. Cundall and Itasca staff adapted 3DEC specifically to perform engineering calculations on a PC. The software is designed for high-speed computation of models containing several thousand blocks. With the advancements in floating-point operation speed and the ability to install additional RAM at low cost, increasingly larger problems can be solved with 3DEC. For example, 3DEC can solve a model containing up to 7500 rigid blocks (or 3000 deformable blocks with 24 degrees-of-freedom per block) on a microcomputer using 32 MB RAM. The solution speed for a model of this size is roughly 125 calculation steps per minute (or 200 calculation steps per minute for the 3000 deformable block model) on a 2.23 GHz Pentium 4 microcomputer.* The calculation speed is essentially a linear function of the number of blocks in a model, and the number of blocks is a linear function of the available RAM on the computer (see Table 2.1 in Section 2.1.3). For typical models, consisting of roughly 2000 rigid blocks (or 1000 deformable blocks) or fewer, the explicit solution scheme in 3DEC requires approximately 2000 to 4000 steps to reach a solved * See Section 6 for a comparison of 3DEC runtimes on various computer systems.
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state.* For example, a 1000 deformable block model run on the Pentium computer described above would require roughly 6 minutes to perform 4000 calculation steps. Consequently, typical engineering problems involving several hundred blocks and multiple solution stages can be solved with 3DEC on a microcomputer in a matter of minutes or a few hours. A comparison of 3DEC to other numerical methods, a description of general features and new updates in 3DEC Version 3.0, and a discussion of fields of application are provided in the following sections. If you wish to try 3DEC right away, the program installation instructions and a simple tutorial are provided in Section 2.2.
* This will vary depending on the amount of relative motion that occurs between blocks. The explicit solution scheme is explained in Section 1.2.2 in Theory and Background.
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1.2 Comparison with Other Methods Some common questions asked about 3DEC are: “Is 3DEC a distinct element or discrete element program? What is the difference, and what is 3DEC ’s relation to other programs?” We provide a definition here which we hope will clarify these matters. Many finite element, boundary element and Lagrangian finite difference programs have interface elements or “slide lines” that enable them to model a discontinuous material to some extent. However, their formulation is usually restricted in one or more of the following ways. First, the logic may break down when many intersecting interfaces are used; second, there may not be an automatic scheme for recognizing new contacts; and third, the formulation may be limited to small displacements and/or rotation. Such programs are usually adapted from existing continuum programs. The name discrete element method applies to a computer program only if it: (a) allows finite displacements and rotations of discrete bodies, including complete detachment; and (b) recognizes new contacts automatically as the calculation progresses. Without the first attribute, a program cannot reproduce some important mechanisms in a discontinuous medium; without the second, the program is limited to small numbers of bodies for which the interactions are known in advance. The term distinct element method was coined by Cundall and Strack (1979) to refer to the particular discrete element scheme that uses deformable contacts and an explicit, time-domain solution of the original equations of motion (not the transformed, modal equations). There are four main classes of computer programs that conform to the proposed definition of a discrete element method. (The classes and representative programs are discussed further in Section 1.1.1 in Theory and Background.) 1. Distinct Element Programs — These programs use explicit time-marching to solve the equations of motion directly. Bodies may be rigid or deformable (by subdivision into elements); contacts are deformable. 3DEC falls in this category. 2. Modal Methods — The method is similar to the distinct element method in the case of rigid bodies but, for deformable bodies, modal superposition is used. 3. Discontinuous Deformation Analysis — Contacts are rigid, and bodies may be rigid or deformable. The condition of no-interpenetration is achieved by an iteration scheme; the body deformability comes from superposition of strain modes. 4. Momentum-Exchange Methods — Both the contacts and the bodies are rigid: momentum is exchanged between two contacting bodies during an instantaneous collision. Frictional sliding can be represented.
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There are several published schemes that appear to resemble discrete element methods, but which are different in character or are lacking one or more essential ingredients. For example, many publications are concerned with the stability of one or more rigid bodies, using the limit equilibrium method (Hoek (1973); Warburton (1981); Goodman and Shi (1985); Lin and Fairhurst (1988)). This method computes the static force equilibrium of the bodies and does not address the changes in force distribution that accompany displacements of the bodies.
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1.3 General Features 1.3.1 Basic Features 3DEC is primarily intended for analysis in rock engineering projects, ranging from studies of the progressive failure of rock slopes to evaluations of the influence of rock joints, faults, bedding planes, etc. on underground excavations and rock foundations. 3DEC is ideally suited to study potential modes of failure directly related to the presence of discontinuous features. The program can best be used when the geologic structure is fairly well-defined — for example, from observation or geologic mapping. Both a manual and automatic joint generator are built into 3DEC to create individual, and sets of, discontinuities which represent jointed structure in a rock mass. A wide variety of joint patterns can be generated in the model. There are also two tunnel generators to set up models with long regularly-shaped excavations. A pre-processor program (PGEN) is provided for reading AutoCad DXF files of section views of a body that can be manipulated to provide a 3DEC data file to generate polyhedra which define a model’s block structure. This program is particularly useful for defining complex excavations or geologic shapes. Different representations of joint material behavior are available. The basic model is the Coulomb slip criterion, which assigns elastic stiffness, frictional, cohesive and tensile strengths and dilation characteristics to a joint. A modification to this model is the inclusion of displacement weakening as a result of loss in cohesive and tensile strength at the onset of shear failure. A more complex model, the continuously yielding joint model, is also available and simulates continuous weakening behavior as a function of accumulated plastic shear displacement. Joint models and properties can be assigned separately to individual or sets of discontinuities in a 3DEC model. It should be noted that the geometric roughness of a joint is represented via the joint material model, even though the plot of discontinuities shows the joint as a planar segment. Blocks in 3DEC can be either rigid or deformable. There are five built-in (19 with the userdefined/extended models option (UDM)) material models for deformable blocks, ranging from the “null” block material, which represents holes (excavations), to the shear yielding models, which include strain-hardening/softening behavior and represent nonlinear, irreversible shear failure. Thus, blocks can be used to simulate backfill and soil materials as well as intact rock. (Purchasers of the UDM option may write their own models.) An effective-stress analysis can be performed by assigning a pore-pressure distribution that acts on both the blocks and the contacts. The automatic zone generator in 3DEC allows the user to divide deformable blocks into finite difference tetrahedral zones. A single command allows the user to specify as fine a discretization as needed, and to vary the discretization throughout the model. Thus, a fine tetrahedral mesh can be prescribed for blocks in the region of interest, and a coarser mesh can be used for blocks farther out. 3DEC also has “inner/outer region” coupling and automatic radially-graded mesh generation within polyhedra for modeling “infinite domain” problems. For block plasticity analysis, a special zone generator can be used to create “mixed-discretization” blocks for improved accuracy when
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modeling plastic collapse. The user may also use high order tetrahedral elements for plasticity problems. The explicit solution algorithm in 3DEC permits either static or dynamic analysis. Static analysis is the default solution mode. Dynamic analysis is provided as an optional feature and is discussed below, in Section 1.3.2. Both stress (force) and fixed displacement (zero velocity) boundary conditions are available for static analysis. Boundary conditions may be different at different locations. 3DEC includes the ability to model steady state or transient fracture fluid flow. The flow logic includes a system of flow planes, flow pipes and flow knots. Structural element logic is implemented to simulate rock reinforcement. Reinforcement includes point-anchored and fully-grouted cables and bolts. An optional surface support/liner model is also available and is described in Section 1.3.2. 3DEC contains a powerful built-in programming language, FISH, that enables the user to define new variables and functions. FISH is a compiler; programs entered via a 3DEC data file are translated into a list of instructions stored in 3DEC ’s memory space; these are executed whenever a FISH function is invoked. FISH permits: • user-prescribed property variations in the block structure (e.g., nonlinear increase in modulus with depth); • plotting and printing of user-defined variables (custom-designed plots); • implementation of special joint generators; • servo-control of numerical tests; • specification of unusual boundary conditions; variations in time and space; and • automation of parameter studies. Interactive manipulation of screen images is built directly into 3DEC. This allows the user to generate shaded perspective views, wire-frames, vectors, tensors, contours, time histories, etc. The history plots are especially helpful to ascertain when an equilibrium state or failure state has been reached. 3DEC also has the facility to create two-dimensional “windows” through the 3D model. On these windows, output can be presented in the form of principal stress plots, stress contour plots, relative shear plots, and vector plots. All plots can be created in screen mode by single keystrokes that move and rotate the 3D model, orient the window, and produce the required output (vectors, contours, etc.). The output can then be directed to a hardcopy device for incorporation into reports.
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1.3.2 Optional Features Four optional features (for dynamic analysis, thermal analysis, user-defined models (UDM) and modeling surface support) are available as separate modules that can be included in 3DEC at an additional cost per module. Dynamic analysis can be performed with 3DEC, using the optional dynamic calculation module. User-specified velocity or stress waves can be input directly to the model either as an exterior boundary condition or an interior excitation to the model. A library of simple dynamic wave forms is also available for input. 3DEC contains absorbing boundary conditions to simulate the effect of an infinite elastic medium surrounding the model. The dynamic analysis option is described in Section 2 in Optional Features. There is a limited thermal analysis option available as a special module in 3DEC. This model simulates the transient conduction of heat in materials and the subsequent development of thermallyinduced stresses. Heat sources can be added and can be made to decay exponentially with time. The thermal option is described in Section 1 in Optional Features. The user-defined model (UDM) option provides the capability for the user to write their own block material models. The models are compiled as a DLL and are linked when requested by the user. As part of the UDM option, an additional 14 block constitutive models are available. This includes 8 viscous models, two non-isotropic elastic models and 4 plasticity models. A surface-support model is available to simulate structures such as concrete linings, shotcrete and other forms of tunnel support, and stabilizing lining for open cuts or natural slopes. The optional surface-support model is described in Section 3 in Optional Features.
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1.4 Summary of Updates from Version 2.0 3DEC 3.00 contains several improvements. The new features are summarized in the following sections. Please note that, due to these changes, existing data files created for 2.00 may not operate correctly. Data files that contain memory addressees or indices must be modified. 3DEC 3.00 will not restart save files from 3DEC 2.00 1.4.1 Automatic Topographic Stress Initialization This feature is used to calculate gravity-induced stresses in models that have a large topological variation on the free surface. Previously, the models had to be cycled to equilibrate the gravity loads. In some cases, cycling to equilibrium induced unwanted shear displacements and stresses. This is a new keyword under the INSITU command. Some cycling will still be required, but this will be less than without the topographical stress initialization. 1.4.2 User-Defined Models (UDM) Purchasers of the UDM option will have the ability to write their own block constitutive models. The models are then compiled as a DLL file and are linked during runtime (see Section 4 in Optional Features and the ZONE command in the Command Reference) as requested by the user. Instructions and examples on how to write these models are included. 1.4.3 Additional Constitutive Models Purchasers of the UDM option will also have access to several new block constitutive models. These models include: anisotropic, cam-clay, double-yield, drucker, mohr, orthotropic, ss, subiquitous, ubiquitous and creep models (burger, cpower, cvisc, cwipp, power, pwipp, viscous, wipp). 1.4.4 Double Precision Version 3DEC now includes a separate executable that is written entirely in double precision. The double precision version requires three times the amount of memory required by the single precision version. The double precision version is useful in models where critical information is lost because of the dimension of the models. This can occur in fluid flow models and also in creep modes where more than 1,000,000 cycles may be executed. 1.4.5 Dynamic Free Field A dynamic free field logic has been added to 3DEC. The free field logic allows the lateral boundaries of a model to be closer to the area of interest without causing unwanted side effects.
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1.4.6 Partial Density Scaling Normally, the timestep in 3DEC is controlled by the smallest gridpoint masses in the model. In dynamic simulations, this can produce a timestep which results in unacceptable solution times. Density scaling is not usually used in dynamic problems since the true gridpoint masses are important to the solution. However, in many models the timestep is controlled by a few very tiny zones that do not contribute significantly to the overall solution. Partial density scaling allows 3DEC to eliminate the effect of these few small zones without affecting the rest of the model. 1.4.7 Higher Order Tetrahedral Elements The normal tetrahedral zoning in 3DEC can be relatively inaccurate in models with a high degree of plastic strain (depending on loading conditions). The mixed discretization zoning solves this inaccuracy but is limited to six-sided blocks. The higher order elements are more accurate in plasticity than the normal tetrahedral elements and do not have the shape restriction of the mixed discretized zones. 1.4.8 Improved Bitmap and Printer Output Several improvements have been made to make the legends, colors, backgrounds, fill shading, and line typing better-suited for printing and output to bitmap files. This makes inclusion of 3DEC graphics directly into report documents much easier. 1.4.9 Poly Cube Poly cube is new model building tool which can be used to generate a complex geometry in 3DEC. This is provided as an alternative to the PGEN pre-processor. Either user-defined outlines or extractions from AutoCAD DXF files can be used to generate the geometry. The blocks generated using poly cube are easier to zone than those generated by PGEN. 1.4.10 Structural Beam Elements Structural beam elements have been added to allow the simulation of spaced support such as steel ribs. 1.4.11 Surface Stress Plotting Filled stress plots can now be generated on the surface of the 3D bodies (as opposed to cross sections). These plots are currently limited to stresses and appear as block filled plots.
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1.4.12 Generalized Boundary Histories The boundary logic has been modified to allow the use of multiple boundary histories. Previously, only one history could be defined in each of the 3 axes. Each gridpoint may now have its own history terms in each of the 3 axes. 1.4.13 Joint Fluid Flow 3DEC now has the capability to calculate fluid flow in joints. The flow logic is set up to use flow planes, flow pipes, and flow knots. These objects represent the joint surfaces, intersections of joints, and meeting at block corners. 1.4.14 New Mouse Controls In graphics mode, the left mouse button may be used in place of the arrow keys to translate or rotate the model. The right mouse button can be used to center the model on the centroid of the selected block. The model will then rotate about the center of that block. 1.4.15 User-Controlled Colors for Contours By specifying colors in a contour plot command the user can select the color filling. For example, plot xsec syy red green
will use a red to green variation for the contour colors. 1.4.16 User-Defined Stress Plot Planes The user can define arbitrary planes in space to plot stresses. The planes are 3D objects and can be rotated along with visible blocks or excavated blocks. This improves the visualization of the stresses around an opening.
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1.5 Fields of Application 3DEC was originally developed to perform stability analysis of jointed rock slopes. The discontinuum formulation for rigid blocks and the explicit time-marching solution of the full equations of motion (including inertial terms) facilitate the analysis of progressive, large-scale movements of slopes in blocky rock. 3DEC has been applied most often in studies related to mining engineering. Both static and dynamic analyses for deep underground mine openings have been performed. Fault-slip induced failure around excavations is one example of analyses conducted with 3DEC. Blasting effects have been studied by applying dynamic stress or velocity waves at model boundaries. Research in the area of fault-slip induced seismicity has also been conducted by use of the continuously-yielding joint model. Structural elements have been employed to simulate various rock reinforcement systems such as grouted rockbolting. 3DEC has also been applied in the fields of underground construction and deep underground storage of high-level radioactive waste. Through the use of the optional thermal model, 3DEC has been used to simulate effects of thermal loading in connection with buried nuclear waste. 3DEC has been used to a limited extent as a computational design tool. However, the program is better-suited to investigate potential failure mechanisms associated with the response of a jointed rock mass. The nature of a jointed rock mass is that it is a “data-limited” system — i.e., the internal structure and stress state are, in large part, unknown and unknowable. Thus, it is impossible, in principle, to make a complete model of a rock mass system. Nevertheless, an understanding of the response of underground openings in jointed rock can be achieved at a phenomenological level using 3DEC. This methodology seeks to improve the engineering understanding of the relative impact of various phenomena on the rock mechanics design. In this way, the engineer can anticipate potential problem areas by identifying mechanisms that may lead to unacceptable states of deformation/loading (or failure) of the underground opening. The paper by Starfield and Cundall (1988) is recommended as a guide for using 3DEC in rock engineering projects. Section 7 presents a bibliography of published reports on the application of 3DEC in the fields of mining and underground engineering. Additionally, 3DEC has potential for application in other fields of engineering, as discussed below and listed in Section 7. 3DEC has the potential for application in studies related to earthquake engineering. For example, the program may be used to provide explanations of phenomena related to fault movement. 3DEC is particularly well-suited to simulate blocky structures, such as stone masonry arches. Example studies are the assessment of safety conditions of old masonry bridges (see Lemos 1997 in Section 7) and the seismic behavior of stone masonry arches (see Lemos 1995 in Section 7). 3DEC has also been used to simulate the behavior of a concrete arch dam constructed on a jointed rock foundation (see Lemos 1996 in Section 7) and the stability condition of underground power stations (see Dasgupta and Lorig 1995 and Dasgupta et al. 1995 in Section 7).
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1.6 Guide to the 3DEC Manual The 3DEC Version 3.0 manual consists of eight documents. This document, the User’s Guide, is the main guide to using 3DEC and contains descriptions of the features and capabilities of the program along with recommendations on the best use of 3DEC for problem solving. The remaining documents cover various aspects of 3DEC, including theoretical background information, verification testing and example applications. The complete manual is available in electronic format on the Itasca software CD-ROM (viewed with Acrobat Reader), as well as in paper format. The organization of the eight documents and brief summaries of the contents of each section follows. Please note that if you are viewing the manual in the Acrobat Reader, double-clicking on a section number given below will immediately open that section for viewing. User’s Guide Section 1
Introduction This section introduces you to 3DEC and its capabilities and features. An overview of the new features in the latest version of 3DEC is also provided.
Section 2
Getting Started If you are just beginning to use 3DEC or are only an occasional user, we recommend that you read Section 2. This section provides instructions on installation and operation of the program as well as a simple tutorial to guide the new user through a 3DEC analysis.
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 3DEC analysis is discussed in detail, and advice is given on the most effective procedures to follow when creating, solving and interpreting a 3DEC model simulation.
Section 4
FISH Beginner’s Guide Section 4 provides the new user with an introduction to the FISH programming language in 3DEC. This includes a tutorial on the use of the FISH language. FISH is described in detail in Section 2 in the FISH volume.
Section 5
Graphical Interface 3DEC contains a graphical interface to facilitate both model creation and presentation of results. Section 5 describes the features of this interface.
Section 6
Miscellaneous Various information is contained in Section 6, including the 3DEC runtime benchmark and procedures for reporting errors and requesting technical support.
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Section 7
User’s Guide
Bibliography Section 7 contains a bibliography of published papers describing some uses of 3DEC.
Command Reference Section 1
Command Reference All the commands that can be entered in the command-driven mode in 3DEC are described in Section 1 in the Command Reference.
Section 2
Error Messages Section 2 in the Command Reference lists all the error messages and their meanings.
FISH in 3DEC 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 3DEC. 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 3DEC model generation and solution.
Section 4
Program Guide Section 4 in the FISH volume contains a program guide to 3DEC ’s linked-list data structure. This is provided for advanced users to have more direct access to 3DEC variables.
Section 5
FISH Error Messages A complete list of FISH error messages is given in Section 5 in the FISH volume.
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Theory and Background Section 1
Background — The Distinct Element Method The theoretical formulation for 3DEC is described in detail in Section 1 in Theory and Background.
Section 2
Block Constitutive Models The theoretical formulation and implementation of the various block constitutive models are described in Section 2 in Theory and Background.
Section 3
Continuously-Yielding Joint Model Section 3 in Theory and Background describes the formulation for the continuously yielding joint model. A simulation of a direct shear test with the model is also given.
Section 4
Structural Elements Section 4 in Theory and Background describes the structural element reinforcement models available in 3DEC.
Section 5
Polygon Generator The pre-processor program, PGEN, that assists with the creation of complex models is described in Section 5 in Theory and Background.
Section 6
Joint Fluid Flow Section 6 in Theory and Background describes the implementation of joint fluid flow in 3DEC.
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.
Section 2
Dynamic Analysis The dynamic analysis option is described and considerations for running a dynamic model are provided in Section 2 in Optional Features. Several verification examples are also included in this section.
Section 3
Surface Support Model A surface support model option is provided to simulate tunnel lining and slope stabilizing lining. Section 3 in Optional Features describes the surface support model.
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Section 4
User’s Guide
User-Defined Models and Extended Constitutive Models Section 4 in Optional Features contains theoretical descriptions of several material constitutive models and instructions needed to write new models which can be used by 3DEC.
Verification Problems and Example Applications This volume is divided into two sections. The first section contains a collection of 3DEC verification problems. These are tests in which a 3DEC solution is compared directly to an analytical (i.e., closed-form) solution. See Table 1 in the Verification and Examples volume for a list of the verification problems. The second section contains example applications of 3DEC that demonstrate the various classes of problems to which 3DEC may be applied. See Table 2 in the Verification and Examples volume for a list of the example applications. Command and FISH Reference Summary A quick summary of all 3DEC 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 53 professionals and 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); and Itasca Consultants Canada Inc. (Sudbury, Canada). 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 that 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 3DEC 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 Cundall, P. A. “A Computer Model for Simulating Progressive Large Scale Movements in Blocky Rock Systems,” in Proceedings of the Symposium of the International Society for Rock Mechanics (Nancy, France, 1971), Vol. 1, Paper No. II-8, 1971. Cundall, P. A., and O. D. L. Strack. “A Discrete Numerical Model for Granular Assemblies,” Geotechnique, 29, 47-65 (1979). Goodman, R. E., and G.-H. Shi. Block Theory and Its Application to Rock Engineering. New Jersey: Prentice Hall, 1985. Hoek, E. “Methods for the Rapid Assessment of the Stability of Three-Dimensional Rock Slopes,” Quarterly J. Eng. Geol., 6, 3 (1973). Itasca Consulting Group, Inc. UDEC (Universal Distinct Element Code), Version 3.0. Minneapolis: ICG, 1996. Lin, D., and C. Fairhurst. “Static Analysis of the Stability of Three-Dimensional Blocky Systems around Excavations in Rock,” Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 25(3), 138-147 (1988). Starfield, A. M., and P. A. Cundall. “Towards a Methodology for Rock Mechanics Modelling,” Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 25, 99-106 (1988). Warburton, P. M. “Vector Stability Analysis of an Arbitrary Polyhedral Rock Block with any Number of Free Faces,” Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 18, 415-427 (1981).
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2 GETTING STARTED This section provides the first-time user with an introduction to 3DEC. If you are familiar with the program but only use it occasionally, you may find this section (in particular, Section 2.6) helpful in refreshing your memory on the mechanics of running 3DEC. Getting Started provides instructions for program installation and start-up on your computer. It also outlines the recommended procedure for applying 3DEC to problems in geo-engineering and includes simple examples that demonstrate each step of this procedure. More complete information on problem solving is provided in Section 3. 3DEC is a command-driven code. This is an important distinction, especially if you are used to using menu-driven software. As explained previously in Section 1.1, the command-driven structure allows 3DEC to be a very versatile tool for use in engineering analysis. However, this structure can present difficulties for new, or occasional, users. Command lines must be entered as input to 3DEC, either interactively via the keyboard or from a remote data file, in order for the code to operate. There are over 40 main commands and nearly 400 command modifiers (called keywords) which are recognized by 3DEC. To the new user, it may seem an insurmountable task to wade through all the commands to select those necessary for a desired analysis. This difficulty is not as formidable as it first appears if the user recognizes that only a very few commands are actually needed to perform simple analyses. As the user becomes more comfortable with 3DEC and uses the code regularly, more commands can be applied and more complex analyses performed. In this section, we provide a primer on the few basic commands the new (or occasional) user needs to perform simple 3DEC calculations. This section contains the following information. A step-by-step procedure is given in Section 2.1 to install, load and test the operation of 3DEC on your computer. This is followed by a tutorial example (Section 2.2) which demonstrates the use of common input commands to execute a 3DEC model. There are a few things that you will need to know before creating and running your own 3DEC model — i.e., you need to know the 3DEC terminology. The nomenclature used for this program is described in Section 2.3. The definition of a 3DEC finite difference grid is given in Section 2.4. You should also know the syntax for the 3DEC input language when running in command-driven mode; an overview is provided in Section 2.5. The mechanics of running a 3DEC model are described in separate steps; in Section 2.6, each step is discussed separately and simple examples are provided. The sign conventions and systems of units used in the program appear in Sections 2.7 and 2.8, respectively. The different types of files used and created by 3DEC are described in Section 2.9.
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2.1 Installation and Start-up Procedures 2.1.1 Installation of 3DEC The 3DEC package, which includes a Windows95/98/ME/NT/2000/XP-console version (see Section 2.1.3 for a description), is installed in Windows from a CD-ROM using standard Windows procedures. The code installation, including the executables, utilities, data files and manual, requires approximately 24 MB of disk space. A default installation of 3DEC from the CD-ROM will install the program, its example files, and the complete 3DEC manual. The Adobe Acrobat Reader is necessary for viewing the manual; an installation for the Reader is also included on the CD-ROM for users who wish to install it. To begin installation, insert the CD-ROM into the appropriate drive. If the autorun feature for the CD drive is enabled, a menu providing options for using the CD will appear automatically. If this menu does not appear, at the command line ( START –> RUN in Windows) type “[cd drive]:\start.exe” to access the CD-ROM menu. The option to install 3DEC may be selected from this menu. The installation program will guide you through installation. When the installation is finished, a file named “INSTNOTE.PDF” will be found in the program sub-folder (“3DEC”) that resides in the main installation folder. (This is the folder that is specified during the installation process as the location to which files will be copied; by default, this is “\ITASCA.”) The “INSTNOTE.PDF” file provides a listing of the directory structure that is created on installation and a description of the actions that have been performed as part of the installation. This information may be used, in the unlikely event it is necessary or desirable, to either manually install or manually uninstall 3DEC. The recommended method for uninstalling 3DEC is to use the Windows “Add/Remove Programs” applet ( START –> SETTINGS –> CONTROL PANEL –> ADD/REMOVE PROGRAMS ). Please note that references made in the 3DEC manual to files presume the default directory structure described in “INSTNOTE.PDF”; all data files described in the manual are contained in these folders. The first time you load 3DEC you will be asked to enter a customer title. This title will appear on graphics screen plots and hardcopy plots. The title can be changed by using the SET cust1 command. After installing the software, connect the 3DEC hardware key to the LPT1 port on the computer before using the code. The executable file for 3DEC is “3DEC.EXE,” which is stored in the “\ITASCA\3DEC” directory. In addition to the executable code, two sets of dynamic linked libraries (DLLs) are provided. One set of DLLs is used to access the various graphics formats in 3DEC. The other set corresponds to the optional user-defined constitutive models available with 3DEC. All of these DLLs are located in the “\ITASCA\3DEC” directory.
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2.1.2 System Requirements for Windows 95/98/ME/NT/2000/XP 3DEC for Windows 95/98/ME/NT/2000/XP is a 32-bit Windows-console application. Any computer capable of running Win95/98/ME/NT/2000/XP is suitable for use with this version of 3DEC. The minimum hardware specifications to operate Windows 95 are adequate for the Windows-console version of 3DEC. This code will not run on 16-bit systems such as Win3.x. The executable file is “3DEC.EXE.” 2.1.3 Windows-Console Version The Windows-console version of 3DEC operates in text mode in Windows. Plots can be sent directly to Windows native printers (using the SET plot windows command). Plots can also be directed to the Windows clipboard (using the SET plot clipboard command), to an Enhanced Metafile format (using the SET plot emf command), and to PCX, BMP, or JPEG bitmap files. See Section 2.1.4 for details. The Windows-console version of 3DEC is compiled with the Absoft Fortran compiler. The Windows-console executable program will operate under Windows 95, 98, ME, Windows NT 4.0, Win2000 or XP. Multitasking — You may find yourself switching constantly between your favorite text editor and 3DEC while developing a model. Task switching or multitasking software helps considerably in this process. Multitasking with the Windows-console version of 3DEC operates in the same manner as other native Windows applications. There is no difficulty with task switching even with a 3DEC plot displayed. Please note that you cannot edit and save a data file while it is open in 3DEC. Type to close the data file in 3DEC. Memory Allocation — Automatic memory allocation logic has been implemented in 3DEC. When loaded, 3DEC will automatically attempt to allocate 16 MB of RAM. You can change the memory allocation for 3DEC by typing the following when loading 3DEC from a DOS shell or Windows shortcut; type 3dec
m
m is the amount of RAM, in MB, that will be made available for a 3DEC model. For example, if you wish to allocate 30 MB for a model, type 3dec 30
After loading 3DEC, type print mem
for a listing of the total memory available and the amount of memory, and percentage, currently used for the model. If the amount of memory requested is more than that available, Windows will swap memory onto the hard drive. This will slow execution considerably, and is not recommended. Note that 3DEC
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requires approximately 3.0 MB to load. You must account for this memory in the total memory requested. As a guide, Table 2.1 summarizes the approximate maximum numbers of rigid or deformable blocks that can be created for different sizes of available RAM. Table 2.1
Maximum number of 3DEC blocks in available RAM
Available RAM (MB)
Maximum number of rigid blocks
Maximum number of deformable blocks∗
8 16 32 64
2,000 4,500 7,500 15,000
1,000 2,000 3,000 7,000
* Assumes 24 translational degrees-of-freedom per block. Maximum number of blocks will be reduced for more degrees-of-freedom.
2.1.4 Utility Software and Graphics Devices Several types of utility software and graphics devices are available that can be of great help while operating 3DEC. Editors — A text editor is used to create 3DEC input data files. Any text editor that produces standard ASCII text files may be used. Care must be taken if more “advanced” word-processing software (e.g., WordPerfect, Word) is used: this software typically encodes format descriptions into the standard output format; these descriptions are not recognized by 3DEC and will cause an error. 3DEC input files must be in standard ASCII format. Graphic Output — 3DEC supports all Windows-compatible printers. Also, black-and-white or color output may be written to a file that can be read by some graphics programs, such as CorelDraw. In addition, a PCX-format screen dump can be imported into other applications, such as Paintbrush for Windows (see the SET pcx command in Section 1 in the Command Reference). NOTE: The screen dump file generated by the key in graphics mode is in the resolution of the screen. The PCX files generated by the SET plot PCX and PLOT pen commands may be in a user-specified resolution. (default = 1024 × 768) 3DEC also supports EMF, BMP and JPEG file formats and can export graphics to the Windows clipboard. 3DEC offers several options to access Windows output. 1. By specifying the SET plot windows command, plots generated with the PLOT pen or COPY command will be directed to a Windows printer. Note that the current printer is used when plots are generated from data files and must be changed outside 3DEC using the Printers folder in the My Computer object.
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2. The command SET plot clipboard directs all hardcopy output to the Windows clipboard (no file is generated). The image is in Enhanced Metafile format and subsequently may be pasted into any other Windows application that is compatible with that format. 3. The SET plot emf command directs output to an Enhanced Metafile format file on disk, where it may be saved for reference or later embedded in a Windows document. It is the user’s responsibility to see that the SET output command has been used to set the output filename to one with an “.EMF” extension. 4. The SET plot BMP, PCX, or JPG directs output to bitmap format files which are saved on disk. Use the SET plot resolution command to specify the resolution of the bitmap file (default = 1024 × 768). Use the SET out command to specify the name of the file. Screen Capture — Graphics software can assist in the production/presentation of 3DEC results. 3DEC ’s MOVIE option allows graphics images to be stored and later displayed in series. A movie viewer is contained in the “\ITASCA\Utility” directory. 2.1.5 Version Identification The version number of 3DEC follows a simple numbering system that identifies the level of updates in the program. There are three numerical identifiers in the version number — that is, Version I.JK
where I
is an integer starting with 1 that identifies a major release of the code;
J
is an integer that is incremented whenever a modification is made that requires a major change to the code structure for a supplemental upgrade release of 3DEC; and
K
is an integer that is incremented when minor modifications are officially released as an update to the current version.
In addition to the version number, sub-version numbers are also used to identify minor changes to 3DEC that have been made since the official version was released. Users may access the latest sub-version of the current version of 3DEC on our website at http://www.itascacg.com. (Contact Itasca for further information.) However, 3DEC with a sub-version number greater than that of the officially-released version should be used with caution, because not all features have been fully tested. By typing the command print version
the complete version number, including the sub-version number, can be obtained.
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2.1.6 Start-up The default installation procedure creates an “Itasca Codes” group with icons for 3DEC. An environment variable pointing at the “\ITASCA\System” directory is created. The necessary drivers for the hardware key are also installed — be sure that the 3DEC hardware key is attached to the LPT1 port on your computer. To load 3DEC, simply click the appropriate icon in the Itasca Codes group. Use the Properties option in Win95 to identify a working directory — in fact, create as many icons as needed to identify a number of individual project directories. Double-click the appropriate icon. Alternatively, the 3DEC executable can be started in an existing DOS session in the standard DOS manner, if so desired. For example, to load 3DEC type 3dec
at the DOS prompt while in the directory where the file “3DEC.EXE” resides. In order to facilitate the running of the data files contained in the 3DEC manual, a batch file, “3DEC.BAT,” is provided in every sub-directory described in “INSTNOTE.PDF.” By doubleclicking on “3DEC.BAT” in a specific directory from the Windows Explorer, the user can start up 3DEC to execute the data files in that directory. 2.1.7 Program Initialization On start-up, 3DEC will look for the file named “3DEC.INI” in the current directory and then, if not found, in the directory pointed to by the ITASCA environment variable. (By default, this is the “\ITASCA\System” directory.) The “3DEC.INI” file can contain any 3DEC commands that preset attributes of the program that you may wish to apply every time 3DEC is used. If the file “3DEC.INI” does not exist, 3DEC simply continues without error. Note that some commands in a “3DEC.INI” file may result in an error message. 2.1.8 Running 3DEC 3DEC can be run interactively or from an input data file in command-driven mode. If you wish to run the code interactively, just begin typing in commands. 3DEC will execute each command as the key is pressed. If an error arises, an error message will be written to the screen. (See Section 2 in the Command Reference for explanations of error messages.) As an alternative, an input data file may be created using a text editor (see Section 2.1.4). This file contains a set of commands just as they would be entered in the interactive mode. Although the data file may have any name, a common identifying extension (e.g., “.DAT”) will help to distinguish it from other 3DEC files (see Section 2.9).
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The data file can be read into 3DEC by typing the command call
file.dat
on the command line, in which “FILE.DAT” is the user-assigned name for the data file. You will see the data entries scroll up the screen as 3DEC reads each line. 2.1.9 Installation Tests Three simple data files, “TEST1.DAT,” “TEST2.DAT” and “TEST3.DAT,” are included in the “\Tutorial\Beginner” directory so that you can test that 3DEC is installed properly on your computer. These files test the calculation kernel, the graphics screen plotting, and the hardcopy plotting facilities for your computer. In order to run the third test, a Windows-compatible printer must be installed as your default printer. To run these tests, double-click on “3DEC.BAT” in the “\Tutorial\Beginner” directory. The code will load, and the 3DEC start-up heading will appear on your screen. At the 3dec> prompt, type call test1.dat
and press . Several data entries should scroll up the screen, and a simple model will be executed for 1000 calculation steps. Example 2.1 contains the results of a successful “TEST1.DAT” run. The output in this figure summarizes information on the model. Now enter the command call test2.dat
A screen plot of this model should appear. The plot is a block plot of the model showing the top block sliding down the fixed bottom block. Press the key to close the plot window and return to the 3dec> prompt. If a Windows-compatible printer is installed, type call test3.dat
and the plot shown in Figure 2.1 should be sent to your printer. If you do not have a printer connected, type quit
to stop the installation testing.
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Example 2.1 3DEC output from “TEST1.DAT” >pri max No. No. No. No. No.
Cycles = 2000 MFREE of blocks (total) of blocks (visible) of vertices of zones
block vol. block mass zone vol. zone mass zone stress s11 s22 s33 s12 s13 s23 grid-point x-vel y-vel z-vel fx fy fz x-dis y-dis z-dis No. of contacts No. of sub-contacts
= 27571 2 2 154 399
min 2.887E+02 5.774E+05 6.659E-01 1.332E+03 min -2.210E+04 -1.273E+05 -2.104E+04 -4.905E+03 -1.111E+04 -4.386E+03
MTOP =
max 7.113E+02 1.423E+06 6.841E+00 1.368E+04 max 2.365E+04 0.000E+00 1.896E+04 3.180E+04 8.867E+03 5.525E+03 5.424E-01 3.139E-01 1.488E-03 1.613E+05 1.302E+06 2.333E+03 2.862E-01 1.753E-01 8.237E-04
1250000
ISMAX = 249999
average 5.000E+02 1.000E+06 2.506E+00 5.013E+03 average -1.479E+03 -4.358E+04 -5.028E+00 8.059E+03 1.665E+01 1.671E+01 3.478E-01 2.011E-01 3.512E-04 2.956E+04 1.299E+05 2.786E+02 1.833E-01 1.118E-01 1.929E-04
total 1.000E+03 2.000E+06 1.000E+03 2.000E+06 s.dev. 7.536E+03 3.975E+04 6.906E+03 8.208E+03 1.704E+03 1.449E+03
1 58
If you are not able to reproduce the results of any or all of these three tests, you should review the system requirements and installation steps in Sections 2.1 through 2.1.7. If you are still having difficulty, we recommend that you contact Itasca and describe the problem you have encountered and the type of computer you are using (see Section 6.2 for error-reporting procedures).
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3DEC (Version 3.00) 12-Aug-02
16:01
dip= 70.00 above dd = 200.00 center 5.000E+00 5.000E+00 5.000E+00 cut-pl. 0.000E+00 mag = 1.00 cycle 2000
Itasca Consulting Group, Inc.
Figure 2.1
PostScript plot from “TEST3.DAT”
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2.2 A Simple Tutorial — Use of Common Commands This section is provided for the new user who wishes to begin experimenting with 3DEC right away. A simple example is presented to help you learn some of the basic aspects of solving problems with 3DEC. The example is a three-dimensional model of a sedimentary rock slope. This is a cut slope in rock with steeply dipping foliation planes and is based on an actual problem described by Starfield and Cundall, 1988. A rotational failure was found to occur with simultaneous sliding along both the foliation planes and shallow-dipping fracture planes. The rotational failure mode was identified by two-dimensional distinct element analysis as the principal mechanism for the slope collapse. The three-dimensional model contains two intersecting discontinuities in the slope, forming a wedge. We will evaluate the stability of the slope for different values of joint friction. (The data file, “TUT.DAT,” included in the “\Tutorial\Beginner” directory, contains all the commands we are about to enter interactively.) We run this problem interactively (i.e., by typing the commands from the keyboard, pressing at the end of each command line, and seeing the results directly). To begin, load 3DEC by double-clicking on “3DEC.BAT” in the “\Tutorial\Beginner” directory. Your computer will load the program and display the initial heading followed by the interactive prompt 3dec>. We begin by specifying a single polyhedral block using the POLY brick command.* Type poly brick
(0,80)
(0,50)
(-30,80)
and press to continue. This command creates a brick-shaped polyhedron which extends from coordinates 0 to 80 units in the x-direction, from 0 to 50 units in the y-direction, and from -30 units to 80 units in the z-direction. To see the polyhedron, type plot
A perspective view of the polyhedron will appear on the screen. The model is viewed from a viewing plane which is defined as being oriented parallel to and coincident with the graphics screen. The model view is defined in terms of the position of the viewing plane relative to the model reference axes. The model axes are a left-handed set (x,y,z) oriented, by default, as x (east), y (vertically up) and z (north). The default view of the model is from the viewing plane oriented parallel to the xy-plane of the model, with the centroid of the model positioned at the center of the screen. The model can be moved and rotated by pressing selected keys on the keyboard. For example, to rotate the model about the x- or y-axes of the viewing plane, press the key and then the arrow keys on the numeric keypad (up/down arrow keys cause rotation about an axis pointing to the right in the viewing plane, left/right arrow keys cause rotation about an axis pointing upward in the viewing plane). The user should turn to Section 5 for a full description of the facilities available in the graphical interface. * See the command reference list in Section 1.2 in the Command Reference for further details. Note that command words can be abbreviated (see Section 2.5).
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To continue the problem and return to the 3dec> prompt, strike the key. The polyhedron is now split into separate polyhedra by using the JSET command. First, we create boundary blocks that will confine the slope blocks. Enter the commands jset jset
dip 90 dip 90
dd 180 dd 180
origin 0,0,0 origin 0,0,50
These commands create two joint planes through the model at locations defined by a dip angle (dip), a dip direction (dd), and a location on the plane (origin). The dip angle and dip direction are oriented relative to the model axes. (See Section 3.2.2 for further information on locating joint planes in the model.) The bounding blocks are then hidden from view before we introduce joint planes that represent the actual joint structure in the slope. (Note that blocks hidden from view will not be cut by the JSET command.) To hide the bounding blocks, type hide 0,80 0,50 hide 0,80 0,50 mark region 1
-30,0 50,80
Blocks located in the range 0
