Stability Modeling with SLOPE/W An Engineering Methodology November 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: [email protected] Web: http://www.geo-slope.com SLOPE/W Table of Contents 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 Page i Table of Contents SLOPE/W 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 ........................................................................