GeoStudio SIGMA/W 应力变形有限元分析软件用户手册[英文].pdf

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Stress-Deformation Modeling with SIGMA/W An Engineering Methodology July 2012 Edition GEO-SLOPE International Ltd.

Copyright © 2004-2012 by GEO-SLOPE International, Ltd All rights reserved. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage or retrieval system, without the prior written permission of GEO-SLOPE International, Ltd. Trademarks: GEO-SLOPE, GeoStudio, SLOPE/W, SEEP/W, SIGMA/W, QUAKE/W, CTRAN/W, TEMP/W, AIR/W and VADOSE/W are trademarks or registered trademarks of GEO-SLOPE International Ltd. in Canada and other countries. Other trademarks are the property of their respective owners. GEO-SLOPE International Ltd 1400, 633 – 6th Ave SW Calgary, Alberta, Canada T2P 2Y5 E-mail: info@geo-slope.com Web: http://www.geo-slope.com

SIGMA/W Table of Contents 1 2 3 Table of Contents Introduction ......................................................................................... 1 1.1 Applications ......................................................................................................................... 1 Deformation analysis .................................................................................................... 1 Staged construction ...................................................................................................... 2 Excess pore-water pressures ....................................................................................... 3 Soil-structure interactions ............................................................................................. 4 Consolidation analyses ................................................................................................. 5 Numerical Modeling: What, Why and How ......................................... 7 Introduction ......................................................................................................................... 7 2.1 2.2 What is a numerical model? ................................................................................................ 7 Modeling in geotechnical engineering ................................................................................. 9 2.3 2.4 Why model? ...................................................................................................................... 11 Quantitative predictions .............................................................................................. 11 Compare alternatives ................................................................................................. 13 Identify governing parameters .................................................................................... 14 Discover physical process - train our thinking ............................................................ 15 How to model .................................................................................................................... 18 Make a guess ............................................................................................................. 18 Simplify geometry ....................................................................................................... 20 Start simple ................................................................................................................. 21 Do numerical experiments .......................................................................................... 22 Model only essential components .............................................................................. 23 Start with estimated material properties ..................................................................... 24 Interrogate the results ................................................................................................. 25 Evaluate results in the context of expected results .................................................... 25 Remember the real world ........................................................................................... 25 2.6 How not to model .............................................................................................................. 26 2.7 Closing remarks ................................................................................................................ 27 SIGMA/W: Fundamentals and Practical Modeling Considerations ... 29 Introduction ....................................................................................................................... 29 3.1 Density and unit weight ..................................................................................................... 30 3.2 3.3 Compaction and density ................................................................................................... 31 Compaction and strength ........................................................................................... 32 2.5 Page i

Table of Contents SIGMA/W 4 3.4 3.5 3.6 4.3 3.7 3.8 Plasticity ............................................................................................................................ 33 Volume change ................................................................................................................. 34 Effective and total stress ............................................................................................ 34 Compressibility and consolidation .............................................................................. 35 Zero change in pore-water pressure .......................................................................... 38 Strength parameters ......................................................................................................... 39 Mohr stress circle ....................................................................................................... 39 Mohr Coulomb failure criteria ..................................................................................... 40 Triaxial testing ............................................................................................................ 41 Soil stiffness – Young’s modulus ................................................................................ 42 Total stress, effective stress and pore-water pressures ................................................... 43 Incremental formulation .................................................................................................... 44 Body forces – unit weight ........................................................................................... 44 3.9 Serviceability versus stability ............................................................................................ 45 3.10 Modeling progression ........................................................................................................ 45 3.11 Units .................................................................................................................................. 46 Geometry and Meshing .................................................................... 47 Introduction ....................................................................................................................... 47 4.1 Geometry Objects in GeoStudio ....................................................................................... 48 4.2 Soil regions, points and lines ...................................................................................... 49 Free points .................................................................................................................. 51 Free lines .................................................................................................................... 51 Interface elements on lines ......................................................................................... 52 Circular openings ........................................................................................................ 54 Mesh generation ............................................................................................................... 55 Structured mesh ......................................................................................................... 56 Unstructured quad and triangle mesh ........................................................................ 56 Unstructured triangular mesh ..................................................................................... 56 Triangular grid regions ................................................................................................ 57 Rectangular grid of quads .......................................................................................... 58 Surface layers ................................................................................................................... 58 Joining regions .................................................................................................................. 61 Meshing for transient analyses ......................................................................................... 62 Finite elements .................................................................................................................. 63 Element fundamentals ...................................................................................................... 64 Element nodes ............................................................................................................ 64 4.4 4.5 4.6 4.7 4.8 Page ii

SIGMA/W Table of Contents 4.9 Field variable distribution ............................................................................................ 64 Element and mesh compatibility ................................................................................. 65 Numerical integration .................................................................................................. 67 Secondary variables ................................................................................................... 68 General guidelines for meshing ........................................................................................ 68 Number of elements ................................................................................................... 69 Effect of drawing scale ............................................................................................... 69 Mesh purpose ............................................................................................................. 70 Simplified geometry .................................................................................................... 71 Material Models and Properties ........................................................ 73 Constitutive models overview ........................................................................................... 73 5.1 5.2 Linear-elastic model .......................................................................................................... 75 Anisotropic elastic model .................................................................................................. 76 5.3 Elastic-plastic model ......................................................................................................... 78 5.4 Plastic matrix .............................................................................................................. 79 Yield criterion .............................................................................................................. 80 Negative pore-water pressure .................................................................................... 82 Cam-clay model ................................................................................................................ 83 Soil parameters .......................................................................................................... 84 Yield function .............................................................................................................. 85 Plastic matrix .............................................................................................................. 87 Evaluation of the plastic matrix ................................................................................... 89 Initial condition ............................................................................................................ 91 Soil parameters .......................................................................................................... 93 Modified Cam-clay model ................................................................................................. 94 Initial Conditions ......................................................................................................... 96 Commentary on Cam-Clay Models ................................................................................... 96 Slip surfaces ...................................................................................................................... 96 User Add-in constitutive models ....................................................................................... 96 E-modulus functions.......................................................................................................... 96 Sample functions ........................................................................................................ 98 5.11 Undrained strength functions ............................................................................................ 99 Boundary Conditions ...................................................................... 101 6.1 Multiple boundary condition types ................................................................................... 101 Force or displacement .................................................................................................... 101 6.2 6.3 Body loads ...................................................................................................................... 102 5.7 5.8 5.9 5.10 5.5 5.6 Page iii 5 6

Table of Contents SIGMA/W 7 8 6.4 6.5 6.6 Boundary condition locations .......................................................................................... 103 Nodal boundary conditions ............................................................................................. 104 Edge boundary conditions (pressures or stresses) ........................................................ 105 Converting edge conditions to nodal equivalent forces ............................................ 106 Fluid pressure conditions .......................................................................................... 107 Defining a stress boundary at internal element edges ............................................. 108 Region face boundary conditions ............................................................................. 108 6.7 Transient boundary conditions ........................................................................................ 110 Analysis Types ................................................................................ 113 Problem view ................................................................................................................... 113 7.1 Initial in-situ stresses ....................................................................................................... 113 7.2 Ko procedure ............................................................................................................. 114 Limitations ................................................................................................................ 115 Pore-water pressures ............................................................................................... 115 Unsaturated Soils ..................................................................................................... 116 Example .................................................................................................................... 117 Specifying initial conditions ............................................................................................. 119 Load / deformation analysis ............................................................................................ 119 Dynamic deformation analysis ........................................................................................ 119 Stress redistribution ........................................................................................................ 120 Concept and procedure ............................................................................................ 120 Strength reduction stability ....................................................................................... 121 Permanent deformations .......................................................................................... 122 Limiting equilibrium ................................................................................................... 122 Strain Softening ........................................................................................................ 122 7.7 Staged / multiple analyses .............................................................................................. 123 Coupled Stress-Pore Pressure Analysis ......................................... 125 8.1 Constitutive equation for soil structure ............................................................................ 125 Flow equation for water phase ........................................................................................ 127 8.2 Finite element formulation for coupled analysis .............................................................. 128 8.3 8.4 Computed material parameters ...................................................................................... 131 Pore-pressure response ratio ......................................................................................... 132 8.5 Coupled analysis data ..................................................................................................... 132 8.6 Material properties .................................................................................................... 132 Boundary conditions ................................................................................................. 133 Saturated-only coupled analysis ..................................................................................... 133 7.3 7.4 7.5 7.6 8.7 Page iv

SIGMA/W Table of Contents 9 10.3 10.4 10.5 10.1 10.2 9.2 9.3 9.4 9.5 9.6 8.8 Uncoupled analysis ......................................................................................................... 133 8.9 Time stepping sequence ................................................................................................. 134 8.10 Changes in Conductivity ................................................................................................. 135 8.11 Submerged Deposition ................................................................................................... 136 8.12 Validation ........................................................................................................................ 136 8.13 Coupled analysis examples ............................................................................................ 137 Functions in GeoStudio .................................................................. 139 Spline functions ............................................................................................................... 139 9.1 Slopes of spline functions ......................................................................................... 140 Linear functions ............................................................................................................... 140 Step functions ................................................................................................................. 141 Closed form curve fits for water content functions .......................................................... 142 Add-in functions .............................................................................................................. 142 Spatial functions .............................................................................................................. 144 10 Structural Elements ........................................................................ 145 Introduction ..................................................................................................................... 145 Beam elements ............................................................................................................... 145 Interpolating functions for a beam element .............................................................. 145 Stiffness matrix for a beam element ......................................................................... 146 Beam examples .............................................................................................................. 148 Bar elements ................................................................................................................... 149 Interpolating functions for a bar element .................................................................. 149 Stiffness matrix for a bar element ............................................................................. 149 Bar example .................................................................................................................... 151 11 Staged Construction Sequencing ................................................... 153 Basic concepts ................................................................................................................ 153 11.1 Fill placement example ................................................................................................... 153 11.2 Excavation ....................................................................................................................... 156 11.3 11.4 Braced excavations ......................................................................................................... 157 11.5 Closing remarks .............................................................................................................. 157 12 Numerical Issues ............................................................................ 159 12.1 Nonlinear analysis ........................................................................................................... 159 12.2 Convergence ................................................................................................................... 161 Significant figures ..................................................................................................... 162 Page v

Table of Contents SIGMA/W 12.3 12.4 12.5 Minimum difference .................................................................................................. 162 Maximum number of iterations ................................................................................. 162 Viewing convergence data ....................................................................................... 163 Limiting loads – use incremental loading ........................................................................ 163 Tension zones ................................................................................................................. 164 Equation solvers (direct or parallel direct) ...................................................................... 164 13 Visualization of Results ................................................................... 165 Introduction ..................................................................................................................... 165 13.1 Load steps ....................................................................................................................... 165 13.2 13.3 Types of data available in Contour ................................................................................. 165 13.4 Node and element information ........................................................................................ 168 13.5 Graphing Node and Gauss Data ..................................................................................... 169 Sum(Y) versus average(X) graphs ........................................................................... 171 13.6 “None” values .................................................................................................................. 171 13.7 Isolines ............................................................................................................................ 172 13.8 Mohr circles ..................................................................................................................... 172 13.9 Animation ........................................................................................................................ 173 13.10 Viewing displacements ................................................................................................... 173 13.11 Projecting Gauss point values to nodes ......................................................................... 174 13.12 Contouring data ............................................................................................................... 175 Illustrative Examples ....................................................................... 179 14 15 Theory ............................................................................................. 181 Introduction ..................................................................................................................... 181 15.1 Finite element equations ................................................................................................. 181 15.2 Strain-displacement matrix ....................................................................................... 182 Elastic constitutive relationship ................................................................................ 184 Body forces ............................................................................................................... 184 Forces due to boundary stresses ............................................................................. 185 Nodal forces ............................................................................................................. 186 15.3 Numerical integration ...................................................................................................... 187 15.4 Assembly and solving of global equations ...................................................................... 189 Element stresses ............................................................................................................. 190 15.5 16 Appendix A: Interpolating Functions ............................................... 191 16.1 Coordinate systems ........................................................................................................ 191 Page vi

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