Department of Civil Engineering, Faculty of Engineering NUMERICAL MODELLING OF ARCHING IN PILED EMBANKMENTS INCLUDING THE EFFECTS OF REINFORCEMENT AND SUBSOIL Yan Zhuang, BEng, MSc. Thesis submitted to the University of Nottingham for the degree of Doctor of Philosophy September 2009 ABSTRACT Piled embankments provide an economic and effective solution to the problem of constructing embankments over soft soils. This method can reduce settlements, construction time and cost. The performance of piled embankments relies upon the ability of the granular embankment material to arch over the ‘gaps’ between the pile caps. Geogrid or geotextile reinforcement at the base of the embankment is often used to promote this action, although its role in this respect is not completely understood. Design methods which are routinely used in the UK (e.g. BS8006, 1995; Hewlett & Randolph, 1988; the ‘Guido’ method, 1987) estimate the stress which acts on the underlying soft ground completely independently of the properties of the soft ground. This stress is then generally used to design the amount of geogrid or geotextile reinforcement required. However, estimation of this load can vary quite considerably for the various methods. Using finite element modelling the 2D and 3D arching mechanisms in the embankment granular fill has been studied. The results show that the ratio of the embankment height to the centre-to-centre pile spacing is a key parameter, and generic understanding of variation of the behaviour with embankment height has been improved. i These analyses are then extended to include single and multiple layers of reinforcement to establish the amount of vertical load which is carried and the resulting tension, both in 2D and 3D. The contribution to equilibrium of the subsoil beneath the embankment is also considered. Finally the concept of an interaction diagram (and corresponding equation) for use in design is advanced based on the findings. ii ACKNOWLEDGEMENTS Firstly, I would like to thanks my supervisor Dr Ed Ellis, who always provided excellent guidance and patience throughout my research. I have been extremely fortunate to have had a supervisor who always made the time and effort to respond to my queries. He has been more than just a superb supervisor. Not only has he motivated me to become an independent geotechnical engineer but also taught me how to consider my future both in my career and in my life. Secondly I wish to acknowledge the support provided by Professor Hai-Sui Yu. He has always made great efforts to give me help whenever I had difficulties in my work. He has also provided me with great opportunities to extend my knowledge and experience. The opportunity to work with Dr Ed Ellis and Professor Hai-Sui Yu has been the highlight of my professional career and personal experience in my life. I would also like to thank my parents for their continuous encouragement and support. A special thank you to Zhibao Mian for his useful suggestions, help and company. Finally, I am greatly indebted to the financial support provided by a Dorothy Hodgkin Postgraduate Award. This great support enabled me concentrate on the research and provided me with many opportunities to iii extend my knowledge and experience, such as conferences and useful short courses. iv CONTENTS ABSTRACT........................................................................................ i ACKNOWLEDGEMENTS......................................................................iii CONTENTS .......................................................................................v LIST OF FIGURES..............................................................................x LIST OF TABLES..............................................................................xv NOTATION.................................................................................... xvii CHAPTER 1 INTRODUCTION 1.1 Piled embankment................................................................ 1 1.2 Soil arching......................................................................... 3 1.3 Tensile reinforcement ........................................................... 4 1.4 Vertical stress in soft subsoil.................................................. 6 1.5 Aims and objectives.............................................................. 7 1.6 Methodology........................................................................ 7 1.7 Layout of the thesis.............................................................. 8 CHAPTER 2 LITERATURE REVIEW 2.1 Introduction .......................................................................10 2.2 Arching concept..................................................................12 2.2.1 Rectangular prism: Terzaghi (1943) and McKelvey (1994).12 2.2.2 Semicircular arch: Hewlett & Randolph (1988).................18 2.2.3 Positive projecting subsurface conduits: BS8006 (1995) and Marston’s equation.....................................................................23 v 2.2.4 Rectangular pyramid shaped arching: Guido method (1987). ..................................................................................27 2.2.5 Other mechanisms .......................................................31 2.3 Introduction to the Ground Reaction Curve.............................36 2.4 Reinforcement ....................................................................42 2.4.1 Introduction ................................................................42 2.4.2 Methodology................................................................43 2.4.3 ‘Interaction diagram’ ....................................................45 2.5 Key studies ........................................................................47 2.5.1 Numerical and analytical studies ....................................47 2.5.2 Physical modelling........................................................59 2.5.3 Field studies................................................................66 2.6 Finite element analysis.........................................................71 2.6.1 Introduction ................................................................71 2.6.2 Finite element method..................................................72 2.6.3 Basic theories according to ABAQUS/Standard.................74 2.6.3.1 Mesh type.........................................................................................74 2.6.3.2 Contact interaction..........................................................................80 2.6.3.3 Controls...........................................................................................90 2.7 Summary...........................................................................92 CHAPTER 3 GROUND REACTION CURVE IN PLANE STRAIN 3.1 Introduction .......................................................................93 3.2 Analyses presented .............................................................94 3.3 Results ..............................................................................99 3.3.1 Ground Reaction Curves................................................99 3.3.2 Midpoint profile of earth pressure coefficient..................105 vi 3.3.3 Ultimate stress on the subsoil......................................110 3.3.4 Settlement at the subsoil and surface of the embankment.... ................................................................................113 3.4 Summary.........................................................................117 CHAPTER 4 GEOGRID REINFORCED PILED EMBANKMENT IN PLANE STRAIN 4.1 Introduction .....................................................................119 4.2 Analyses presented ...........................................................119 4.3 Results ............................................................................124 4.3.1 Behaviour of reinforced piled embankment....................124 4.3.2 Settlement at the subsoil and surface of the reinforced piled embankment...........................................................................133 4.3.3 Behaviour of geogrid in the piled reinforced embankment .... ................................................................................137 4.4 Summary.........................................................................142 CHAPTER 5 REINFORCED PILED EMBANKMENT WITH SUBSOIL IN PLANE STRAIN 5.1 Introduction .....................................................................143 5.2 Analyses presented ...........................................................143 5.3 Results ............................................................................150 5.4 Summary.........................................................................158 CHAPTER 6 GROUND REACTION CURVE IN THREE-DIMENSIONS 6.1 Introduction .....................................................................159 6.2 Analyses presented ...........................................................161 vii 6.3 Results ............................................................................166 6.3.1 Ground Reaction Curves..............................................166 6.3.2 Midpoint profile of earth pressure coefficient..................170 6.3.3 Ultimate stress on the subsoil......................................174 6.3.4 Settlement at the subsoil and surface of the embankment.... ................................................................................176 6.4 Summary.........................................................................180 CHAPTER 7 GEOGRID REINFORCED PILED EMBANKMENT IN THREE- DIMENSIONS 7.1 Introduction .....................................................................181 7.2 Analyses presented ...........................................................181 7.3 Results ............................................................................186 7.3.1 Behaviour of reinforced piled embankment....................186 7.3.2 Settlement at the subsoil and surface of the reinforced piled embankment...........................................................................193 7.3.3 Behaviour of geogrid in the piled reinforced embankment .... ................................................................................197 7.4 Summary.........................................................................203 CHAPTER 8 REINFORCED PILED EMBANKMENT WITH SUBSOIL IN THREE- DIMENSIONS 8.1 Introduction .....................................................................204 8.2 Analyses presented ...........................................................204 8.3 Results ............................................................................210 8.4 Summary.........................................................................213 viii CHAPTER 9 DISCUSSION OF RESULTS 9.1 Introduction .....................................................................214 9.2 Summary of results...........................................................214 9.2.1 Piled embankment......................................................214 9.2.2 ‘Reinforced’ piled embankment.....................................215 9.2.3 ‘Reinforced’ piled embankment with subsoil...................216 9.3 Comparison of general trends of behaviour as h/(s-a) varies ...217 9.4 Comparison of the value of /(s-a) at the point of maximum s arching for medium height embankments......................................219 9.5 Equation for equilibrium including arching, reinforcement and subsoil ......................................................................................221 9.6 Case studies.....................................................................224 9.6.1 Second Severn Crossing..............................................224 9.6.2 Construction of apartments on a site bordering River Erne, Northern Ireland......................................................................226 9.6.3 A650 Bingley Relief Road ............................................229 9.6.4 A1/N1 Flurry Bog .......................................................230 9.6.5 Case study comparison...............................................231 9.7 Summary.........................................................................240 CHAPTER 10 CONCLUSIONS 10.1 Work reported in the thesis ...............................................242 10.2 Future work.....................................................................245 REFERENCES................................................................................247 ix