Earth pressures against- and stability of retaining structures Sigurður Már Valsson Faculty of Civil and Environmental Engineering University of Iceland 2011 Earth pressures against- and stability of retaining structures Sigurður Már Valsson 30 ECTS thesis submitted in partial fulfillment of a Magister Scientiarum degree in Civil Engineering Advisors Arne Kavli Dr. Arne Åsmund Skotheim Dr. Sigurður Erlingsson Dr. Torgeir Døssland Faculty Representative Dr. Bjarni Bessason Faculty of Civil and Environmental Engineering School of Engineering and Natural Sciences University of Iceland Molde, June 2011 Earth pressures against- and stability of retaining structures 30 ECTS thesis submitted in partial fulfillment of a Magister Scientiarum degree in Civil Engineering Copyright © 2011 Siguður Már Valsson All rights reserved Faculty of Civil and Environmental Engineering School of Engineering and Natural Sciences University of Iceland Hjarðarhaga 6 107, Reykjavík Iceland Telephone: 525 4000 Bibliographic information: Sigurður Már Valsson, 2011, Earth pressures against- and stability of retaining structures, Master‟s thesis, Faculty of Civil and Environmental Engineering, University of Iceland, pp. 176. Printing: Samskipti Reykjavik, Iceland, June 2011 Abstract The objective of the presented research is to investigate methods used to calculate earth pressures against- and the stability of retaining structures. The classical methods of calculating earth pressures are covered in detail. They are named after their creators Charles-Augustin de Coulomb and William John Macquorn Rankine. A special interest is taken in a variant of Rankine‟s theory developed at Norges teknisk- naturvitenskapelige universitet (NTNU) that incorporates cohesive properties of soils as well as roughness between the structure and the soil material. Both methods are then tested against each other in order to investigate if a clear link exists between the two. The methods are tested against proposed design values of earth pressure coefficients according to the design standard Eurocode 7. Håndbok 016 is a design handbook published by the Norwegian Road Administration (n. Statens vegvesen). In it is a chapter dedicated to the design of retaining structures and bridge abutments. The methods proposed to design retaining structures are used to design cantilevered structures of various heights and with various foundation- and backfill materials based on a few geometrical constraints. The structure designs created with methods in Håndbok 016 are modeled in the finite element program PLAXIS to test if the same material factors of safety could be derived that way. The results from this study are then discussed and commented upon. Table of Contents List of Figures .................................................................................................................... vii List of Tables ..................................................................................................................... xvi Symbols ............................................................................................................................. xvii Abbreviations .................................................................................................................... xix Acknowledgements ........................................................................................................... xxi 1 Introduction ..................................................................................................................... 1 2 Theory .............................................................................................................................. 2 2.1 Vertical pressures .................................................................................................... 2 2.1.1 In situ vertical stresses ................................................................................... 2 2.2 Strength parameters of soil ...................................................................................... 3 2.2.1 Undrained shear strength, Su analysis ............................................................ 3 2.2.2 Drained shear strength, - analysis ............................................................. 5 2.2.3 Deciding when to use which model ............................................................... 7 2.3 Horizontal earth pressures ....................................................................................... 8 2.3.1 At rest horizontal earth pressures ................................................................... 8 2.3.2 Smooth vertical walls and stress fields - Rankine zones ............................... 9 2.3.3 Rough walls and stress fields - Prandtl zones .............................................. 11 2.3.4 Roughness and partially developed stress fields .......................................... 12 2.3.5 Coulomb‟s theory of earth pressures against retaining walls ...................... 19 2.4 Bearing capacity of foundations ............................................................................ 21 2.5 Failure modes of retaining structures .................................................................... 28 3 Comparison of methods used to calculate lateral earth pressures ........................... 30 3.1 Linking the roughness number, , and the roughness angle, . ............................. 30 3.2 Active earth pressures on walls leaning into the backfill ...................................... 37 3.3 Comparison of lateral earth pressures methods to method recommended by Eurocode 7 ............................................................................................................. 41 3.3.1 Active pressures according to Eurocode 7 ................................................... 42 3.3.2 Passive pressures according to Eurocode 7 ................................................. 47 4 Design methods proposed by Håndbok 016 ............................................................... 52 4.1 Requirements ......................................................................................................... 52 4.2 Cantilever walls ..................................................................................................... 59 4.2.1 Calculation procedure .................................................................................. 60 4.2.2 Assumptions and constraints........................................................................ 61 4.2.3 Calculated cases ........................................................................................... 61 4.2.4 Critical base width for L-shaped cantilever wall ......................................... 62 4.2.5 Effect of varying the toe width of cantilever walls ...................................... 65 v 4.2.6 The effect of backfill inclination ................................................................. 73 5 Analysis of stability using PLAXIS .............................................................................. 76 5.1 Finite element method in PLAXIS ......................................................................... 76 5.2 Application of PLAXIS to evaluate method proposed by HB016 ......................... 77 5.2.1 Material models ........................................................................................... 78 5.2.2 The “Phi/c reduction” method in PLAXIS ................................................. 79 5.2.3 Modeling and documenting failures in soil masses ..................................... 80 5.3 Results from PLAXIS simulations ......................................................................... 85 5.3.1 Blasted rock foundation – horizontal terrain ............................................... 85 5.3.2 Gravel foundation – horizontal terrain ........................................................ 87 5.3.3 Clay or clayey silt foundation – horizontal terrain ...................................... 89 5.3.4 Blasted rock foundation – inclined terrain .................................................. 91 5.3.5 Gravel foundation – inclined terrain ............................................................ 93 5.3.6 Clay or clayey silt foundation – inclined terrain ......................................... 94 5.3.7 Summary of PLAXIS simulation results ..................................................... 95 6 Conclusions .................................................................................................................... 97 6.1 Study of earth pressures ......................................................................................... 97 6.2 Structure design with hand calculation methods .................................................... 97 6.3 Evaluation of proposed designs using PLAXIS ..................................................... 98 6.4 Geometry of simulated failure surfaces ............................................................... 100 References ......................................................................................................................... 101 Appendix A: Stress on an arbitrary plane ..................................................................... 103 Appendix B: The MC-failure criterion and the beauty of the attraction ................... 106 Appendix C: Stresses on critical and inclined planes .................................................. 110 Appendix D: The logarithmic spiral .............................................................................. 115 Appendix E: Stressfields in weightless soils