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SLOPE/W 软件是全球最先进的岩土边坡稳定性分析软件之一,它使用极限平衡理论,软件内置多种滑移面搜索方法、孔隙水压力条件、土体强度本构以及加固组件和荷载工况等,可以对简单或复杂的边坡进行稳定性分析,可以进行边坡失效概率分析和参数敏感性分析。SLOPE/W软件还可以应用有限元方法对大部分边坡稳定性问题进行有效计算和分析。 应用SLOPE/W分析程序,可以对岩土工程、水利水电、市政、土木、采矿工程等领域中遇到的几乎所有边坡稳定性问题进行分析评价,是全球应用最广泛的边坡稳定性分析软件。
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Stability Modeling
with SLOPE/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
SLOPE/W Table of Contents
Page i
Table of Contents
1 Introduction ......................................................................................... 1
2 Limit Equilibrium Fundamentals .......................................................... 5
2.1 Introduction ......................................................................................................................... 5
2.2 Background and history ...................................................................................................... 5
2.3 Method basics ..................................................................................................................... 6
2.4 General limit equilibrium formulation ................................................................................... 7
2.5 Interslice force functions ................................................................................................... 11
2.6 Slip surface shapes ........................................................................................................... 11
Circular slip surface .................................................................................................... 11
Planar slip surface ...................................................................................................... 12
Composite slip surface ............................................................................................... 13
Block slip surface ........................................................................................................ 13
Shoring wall ................................................................................................................ 14
2.7 Stress distributions ............................................................................................................ 15
2.8 Limit equilibrium forces and stresses ................................................................................ 20
2.9 Janbu generalized method ................................................................................................ 20
2.10 Missing physics ................................................................................................................. 21
2.11 Other limitations ................................................................................................................ 21
2.12 Slip surface shapes ........................................................................................................... 22
2.13 Seepage forces ................................................................................................................. 23
2.14 Concluding remarks .......................................................................................................... 24
3 Factor of Safety Methods .................................................................. 27
3.1 Introduction ....................................................................................................................... 27
3.2 General limit equilibrium Formulation ............................................................................... 27
3.3 Ordinary or Fellenius method ............................................................................................ 31
3.4 Bishop’s simplified method ............................................................................................... 35
3.5 Janbu’s simplified method ................................................................................................. 37
3.6 Spencer method ................................................................................................................ 38
3.7 Morgenstern-Price method ............................................................................................... 40
3.8 Corps of Engineers method .............................................................................................. 43
Interslice assumption one ........................................................................................... 43
Interslice assumption two ........................................................................................... 44
3.9 Lowe-Karafiath method ..................................................................................................... 46
Table of Contents SLOPE/W
Page ii
3.10
Sarma method ................................................................................................................... 48
3.11 Janbu’s Generalized method ............................................................................................ 49
3.12 Finite element stress-based method ................................................................................. 51
3.13 Commentary on finite element stress-based method ....................................................... 56
3.14 Selecting an appropriate method ...................................................................................... 57
3.15 Rapid Drawdown Analysis Methods ................................................................................. 58
The Simple Effective Strength Method ....................................................................... 59
The Rigorous Effective Strength Method ................................................................... 59
The Staged Undrained Strength Method .................................................................... 60
4 Slip Surface Shapes ......................................................................... 63
4.1 Introduction and background ............................................................................................ 63
4.2 Grid and radius for circular slips ....................................................................................... 63
Single radius point ...................................................................................................... 65
Multiple radius points .................................................................................................. 66
Lateral extent of radius lines....................................................................................... 66
Factor of Safety contours ........................................................................................... 67
4.3 Composite slip surfaces .................................................................................................... 68
4.4 Fully specified slip surfaces .............................................................................................. 71
4.5 Block specified slip surface ............................................................................................... 73
General cross-over form ............................................................................................. 73
Specific parallel form .................................................................................................. 75
4.6 Entry and exit specification ............................................................................................... 77
4.7 Optimization ...................................................................................................................... 79
4.8 Effect of soil strength......................................................................................................... 82
Purely frictional case .................................................................................................. 82
Undrained strength case ............................................................................................ 84
Cause of unrealistic response .................................................................................... 84
Minimum depth ........................................................................................................... 86
Most realistic slip surface position .............................................................................. 86
4.9 Tension cracks and exit projections .................................................................................. 86
Tension crack angle ................................................................................................... 86
Constant tension crack depth ..................................................................................... 87
Tension crack fluid pressures ..................................................................................... 87
Toe projection ............................................................................................................. 87
4.10 Physical admissibility ........................................................................................................ 88
4.11 Invalid slip surfaces and factors of safety ......................................................................... 89
SLOPE/W Table of Contents
Page iii
4.12
Concluding remarks .......................................................................................................... 93
5 Geometry .......................................................................................... 95
5.1 Introduction ....................................................................................................................... 95
5.2 Regions ............................................................................................................................. 95
5.3 Slice discretization ............................................................................................................ 97
5.4 Ground surface line ........................................................................................................... 99
5.5 Tension crack line ........................................................................................................... 100
5.6 Concentrated point loads ................................................................................................ 100
5.7 Ponded water regions ..................................................................................................... 102
5.8 Surface surcharge loads ................................................................................................. 103
6 Functions in GeoStudio .................................................................. 109
6.1 Spline functions ............................................................................................................... 109
Slopes of spline functions ......................................................................................... 110
6.2 Linear functions ............................................................................................................... 111
6.3 Step functions ................................................................................................................. 111
6.4 Closed form curve fits for water content functions .......................................................... 112
6.5 Add-in functions .............................................................................................................. 112
6.6 Spatial functions .............................................................................................................. 112
7 Material Strength ............................................................................ 115
7.1 Introduction ..................................................................................................................... 115
7.2 Mohr-Coulomb ................................................................................................................ 115
7.3 Spatial Mohr-Coulomb model ......................................................................................... 116
7.4 Undrained strength .......................................................................................................... 117
7.5 High strength ................................................................................................................... 117
7.6 Impenetrable (Bedrock) .................................................................................................. 117
7.7 Bilinear ............................................................................................................................ 117
7.8 General data-point strength function ............................................................................... 118
7.9 Anisotropic strength ........................................................................................................ 119
7.10 Strength using an anisotropic function ............................................................................ 120
7.11 Strength as a function of depth ....................................................................................... 121
Relative to top of soil layer ....................................................................................... 121
Relative to specified datum ...................................................................................... 121
7.12 Frictional-undrained combined models ........................................................................... 122
7.13 SHANSEP or strength = f(overburden) model ................................................................ 122
7.14 Hoek and Brown model ................................................................................................... 124
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