Three-dimensional effects in slope stability for shallow excavations Analyses with the finite element program PLAXIS Niclas Lindberg Master of Science Program in civil engineering Luleå University of Technology Department of Civil, Environmental and Natural resources engineering PREFACE This master thesis is the final part of my five year education in civil engineering at Luleå university of technology. The investigation has been done on behalf of Luleå university with inspiration from Trafikverket. I would like to thank my supervisor Hans Mattsson from Luleå University of technology for all the guidance and inspiration during both the courses and the time doing this investigation. I also want to thank for the possibility to work and learn more about numerical modelling. A special thanks to Per Gunnvard at Luleå university for all the guidance and patience during the time of making this investigation. Finally, thanks to all my friends and family during the years at Luleå university of technology. Luleå, Mars 2018 Niclas Lindberg i ii ABSTRACT The purpose with this study was to investigate the impact of three-dimensional effects in slope stability for three-dimensional excavations and slopes with cohesive soils and compare the results with the method provided by the Swedish commission of slope stability in 1995 regarding three-dimensional effects. Both the factor of safety and the shape of the slip surface was compared between the methods but also the results from their equivalent two- dimensional geometry. The investigation was performed with models created in the finite element software PLAXIS 3D and the limit equilibrium software GeoStudio SLOPE/W. Three-dimensional excavations with varying slope angles, external loads and slope lengths were tested for three different geometry groups in PLAXIS 3D. The equivalent two-dimensional geometries were modeled with SLOPE/W and recalculated with the three-dimensional effect method provided from the Swedish commission of slope stability. The results show that the methods match well for slopes with inclinations 1:2 and 1:1 when an external load is present on the slope edge, and the factor of safety is greater and not close to 1,0. For an excavation with vertical walls or when no external load is present, the methods match poorly. The results also show that for a long and unloaded slope, the factor of safety approaches the value obtained from a simplified two-dimensional analysis. The results imply that the recommendations from the Swedish commission of slope stability are reliable for simple calculations of standard cohesive slopes. Keywords: Slope stability; 3D-effects; FEM iii iv SAMMANFATTNING Syftet med detta examensarbete var att undersöka tredimensionella effekters inverkan vid släntstabilitet hos tredimensionella schakter och slänter av kohesiva jordar och jämföra resultatet med den metod som svenska skredkommissionen rekommenderat år 1995 gällande tredimensionella-effekter. Både säkerhetsfaktorn och formen hos den utbildade glidytan jämfördes mellan metoderna samt resultatet från dess ekvivalenta tvådimensionella geometri. Undersökningen utfördes med hjälp av modellering i det finita elementprogrammet PLAXIS 3D och gränslastanalysprogrammet GeoStudio SLOPE/W. Tredimensionella schakter med varierande släntlutningar, externa laster och släntlängder testades hos tre olika geometrigrupper i PLAXIS 3D. De ekvivalenta tvådimensionella geometrierna modellerades i SLOPE/W och räknades sedan om tredimensionellt enligt den metod som svenska skredkommissionen rekommenderat. Resultatet visar att metoderna överensstämmer väl för schakter med släntlutningen 1:2 och 1:1 där en extern last finns närvarande på släntkrönet och säkerhetsfaktorn är större än och inte nära 1,0. För schakter med vertikala schaktväggar eller schakter där ingen extern last närvarar överensstämmer metoderna inte väl. Resultatet visar också att en långsträckt obelastad slänt har en säkerhetsfaktor som stämmer väl överens med en simplifierad tvådimensionell analys. Resultatet föreslår att rekommendationerna från svenska skredkommissionen är tillförlitliga för enklare beräkningar av normala släntstabilitetsproblem i kohesiva jordar. Nyckelord: Släntstabilitet; 3D-effekter; FEM v vi TABLE OF CONTENTS 1. INTRODUCTION .........................................................................................................1 1.1 Background ..............................................................................................................1 1.2 Purpose and objective ...............................................................................................2 1.3 Limitations ...............................................................................................................3 2. THEORETICAL BACKGROUND ................................................................................5 2.1 Finite element method ..............................................................................................5 2.2 Limit equilibrium method ....................................................................................... 10 2.3 Three-dimensional slope stability ........................................................................... 13 3. SOFTWARE ................................................................................................................ 19 3.1 PLAXIS ................................................................................................................. 19 3.2 GeoStudio, SLOPE/W ............................................................................................ 23 4. NUMERICAL MODELLING WITH PLAXIS 3D....................................................... 25 4.1 Geometries and cases ............................................................................................. 25 4.2 Model specification ................................................................................................ 27 4.3 Phases .................................................................................................................... 29 4.4 Material parameters ................................................................................................ 29 4.5 Mesh and boundaries .............................................................................................. 30 5. SLOPE/W MODELS AND 3D-EFFECT CALCULATIONS ....................................... 31 5.1 SLOPE/W models .................................................................................................. 31 5.2 Calculation of three-dimensional effects ................................................................. 32 6. RESULTS AND ANALYSIS....................................................................................... 33 6.1 Two-dimensional comparison ................................................................................. 35 6.2 Three-dimensional analysis .................................................................................... 36 6.3 3D-effects method compared with PLAXIS 3D models .......................................... 39 6.4 Safety analysis in PLAXIS ..................................................................................... 43 7. DISCUSSION .............................................................................................................. 45 7.1 Suggestions on further studies ................................................................................ 46 REFERENCES ..................................................................................................................... 47 APPENDIX A1 –SFR/DEFORMATION-CURVES, MODEL A ..................................... 51 APPENDIX A2 –SFR/DEFORMATION-CURVES, MODEL B ...................................... 55 vii APPENDIX A3 –SFR/DEFORMATION-CURVES, MODEL C ...................................... 58 APPENDIX B1 – TOTAL DEFORMATIONS, MODEL A ............................................. 59 APPENDIX B2 – TOTAL DEFORMATIONS, MODEL B .............................................. 67 APPENDIX B3 – TOTAL DEFORMATIONS, MODEL C .............................................. 74 APPENDIX C1 –SLOPE/W SLIP SURFACE GROUP A ................................................ 78 APPENDIX C2 –SLOPE/W SLIP SURFACE GROUP B ................................................ 79 APPENDIX C3 –SLOPE/W SLIP SURFACE GROUP C ................................................ 80 viii 1 INTRODUCTION 1.1 Background Slope stability analysis is a branch of geotechnical engineering and concerns the stability for both natural and constructed soil slopes. Many construction projects require excavations in soil to construct pipes and cables, and also foundations for buildings and bridges. Roads and railways are usually built with soil embankments, where stability analysis must be performed to satisfy the safety regulations. Several methods have been developed throughout history to calculate the stability of slopes, which results in a factor of safety. The factor is defined as the ratio of the shear strength available of the soil compared to the necessary strength to maintain equilibrium (Bishop, 1955). The most common approach to calculate the stability of a slope is with the limit equilibrium method (LEM), with an assumption of plane-strain conditions. (Zhang, Guangqi, Zheng, Li, & Zhuang, 2013) With the software and computer power available today, this method can obtain multiple failure surfaces with their factors of safety in a very short time. The finite element method (FEM) is also a popular technique which is a numerical method