THE INFLUENCE OF GEOMETRY ON THE PERFORMANCE OF BREAKWATER ARMOUR UNITS A thesis submitted for the degree of Doctor of Philosophy of the University of London S.S.L. Hettiarachchi, B.Sc. (Eng.) Hydraulics Section, Department of Civil Engineering, Imperial College of Science and Technology. May 1987 TO MY PARENTS 3 ABSTRACT This study is mainly concerned with the influence of voids and geometry of armour on the performance of breakwaters and other coastal structures used in port construction and for sea defence purposes. In particular, attention is focused on armour units of a hollow-block form used for breakwater construction. Wave action on coastal structures is investigated from a viewpoint of the hydraulics of flow through porous media. Extensive experimental investigations were performed on a variety of porous media under steady flow, oscillatory flow and unidirectional accelerated flow conditions to study the influence of the geometry of the voids matrix on overall hydraulic behaviour. The different structures investigated were broadly classified into vertical-faced rectangular structures and sloping structures, both containing homogeneous fill, conventional trapezoidal breakwaters with layered fill and armoured with hollow block armour units, and vertical pile structures. By varying the external configuration and internal material layout it was possible to generate a wide spectrum of porous coastal structures of practical interest. The study identified both geometric and hydraulic governing parameters to classify porous media in general and hollow-block armour units in particular. The importance of area blockage at the wave-structure interface, volumetric porosity and tortuosity of the structure, dimension and shape of voids was established in relation to the performance of different porous media. Investigations were conducted on both permeability characteristics and force coefficients to study their behaviour as the flow was changed from steady to accelerated conditions including both unidirectional and oscillatory flow regimes. The study provides extensive information on wave reflection, wave transmission and energy loss coefficients for a wide range of structures, thus providing a base for their performance to be assessed. Wave steepness, front slope and overall effective length of the structure and the degree of submergence were found to be important parameters which had to be considered together with the material layout of a porous structure. Reflection, run-up and run-down coefficients were found for breakwaters armoured with different types of hollow block armour unit and measurements were made of along-slope and lift forces acting on a single unit. The upward along-slope force associated with wave impact was found to be the 4 dominant loading mechanism and the positive lift force - tending to extract an armour unit from the slope - was found to be within acceptable limits, not endangering the stability of the structure. Analytical and numerical techniques were developed to predict reflection and transmission coefficients and to monitor internal wave decay in porous structures consisting of homogeneous fill. Because of the complexity of the problem, the study was limited to small-amplitude long waves normally incident to the structure. The respective coefficients were predicted in terms of the incident wave conditions and the hydraulic and geometric properties of the porous medium. The Forchheimer equation was used for the hydraulic gradient - velocity relationship. An assessment was also made of interface losses and scale effects on wave transmission through porous structures. The analysis of sloping embankments is performed by transforming them to an equivalent rectangular section and the physical significance of this concept was investigated experimentally. Satisfactory agreement was obtained between experimental and predicted values. The study was relatively fundamental in nature but the results obtained are relevant to practical problems of breakwater design and also provide a basis for further work on this topic. 5 ACKNOWLEDGEMENTS I wish to express my thanks to Professor P. Holmes for his supervision, encouragement and guidance provided during the course of the research study. My thanks are also due to the members of the academic staff and colleagues of the Hydraulics Section for their advice and cooperation. I am grateful to Dr. R. Wing for his assistance with instrumentation and to Mr. N.W.H. Allsop of Hydraulics Research Ltd. for his keen interest and assistance. Assistance given to me in laboratory work by Geoff Thomas, John Audsley, members of the technical staff and colleagues, Robert Shih and Y. Yang, is greatly appreciated. I am thankful to Patricia O'Connell for typing the manuscript and for her assistance. I am very grateful to my parents for their constant encouragement and for providing funds for my studies. I acknowledge with thanks the financial assistance given to me from the Mountbatten Memorial Trust and the Leche Trust. I am also thankful to Hydraulics Research Ltd. for providing a bursary. My sincere thanks are also due to Mildred and Arthur Madanayake and Dr. Priyan Dias for their invaluable support during my stay in U.K. Finally, I wish to express my gratitude to Premini, my wife, for her assistance at all times. In spite of being busy with her own studies, she always found time to help me. 6 CONTENTS P age ABSTRACT 3 ACKNOWLEDGEMENTS 5 LIST OF TABLES 9 LIST OF FIGURES 11 LIST OF PLATES 25 LIST OF SYMBOLS 26 CHAPTER 1 - INTRODUCTION 28 CHAPTER 2 - REVIEW OF PREVIOUS INVESTIGATIONS 44 2.1. Introduction 44 2.2. Flow through porous media 46 2.3. Hydraulic gradient - velocity relationships for steady 53 non-Darcy flow in porous media 2.4. Time dependent flow in porous media 57 2.5. Wave action on porous structures 62 CHAPTER 3 - APPROACH TO THE PROBLEM 92 3.1. Introduction 92 3.2. Relevant conclusions from the literature review 92 3.3. Governing parameters for porous media and hollow 94 block units 3.4. Selection of experimental media 97 3.5. Type of tests and experimental techniques 103 3.6. Theoretical considerations 113 CHAPTER 4 - EXPERIMENTAL APPARATUS, FLOW ENVIRONMENT AND 127 PROCEDURES 4.1. Introduction 127 4.2. Steady flow tests 127 4.3. Oscillatory flow tests 131 4.4. Unidirectional acceleration tests 140 4.5. Tests on a model breakwater section 146 7 Page 4.6. Measurement of physical properties of random porous 151 media CHAPTER 5 - THEORETICAL DEVELOPMENTS 164 5.1. Introduction 164 5.2. Governing equations 164 5.3. Analytical developments 166 5.4. Numerical developments 177 5.5. Properties of finite difference schemes 185 CHAPTER 6 - STEADY FLOW PERMEABILITY TESTS AND OSCILLATORY 194 FLOW TESTS 6.1. Introduction 194 6.2. Physical properties of porous media 195 6.3. Steady flow permeability tests 196 6.4. Oscillatory flow tests 202 6.5. Tests to determine interface losses 212 6.6. Evaluation of the theoretical analyses 213 CHAPTER 7 - CONSTANT ACCELERATION AND VELOCITY TESTS FOR 269 MOVING POROUS BLOCK 7.1. Int roduct i on 269 7.2. Method of analysis 271 7.3. Discussion of results 274 7.4. Concluding remarks 279 CHAPTER 8 - ADDITIONAL TESTS UNDER OSCILLATORY FLOW 309 CONDITIONS 8.1. Introduction 309 8.2. Performance of closed block structures (porous 309 wave absorbers) 8.3. Performance of porous submerged structures 318 8.4. Performance of an open block structure with a 319 sloping front 8 Page 8.5. Performance of a porous trapezoidal structure 323 8.6. Influence of length of open and closed block 324 structures in relation to their overall performance 8.7. Evaluation of the theoretical analyses 326 CHAPTER 9 - TESTS ON A BREAKWATER SLOPING SECTION 363 9.1. Introduction 363 9.2. Reflection, run-up and run-down studies 363 9.3. Measurement of lift and along-slope forces 374 CHAPTER 10 - SCALE EFFECTS IN MODELS OF POROUS COASTAL 435 STRUCTURES 10.1. Introduction 435 10.2. Modelling for transmission and reflection on 435 undistorted scale 10.3. Methods of determining the scale ratio for particle 437 size 10.4. Objectives of the present study 438 10.5. Analytical development, its application and 439 discussion 10.6. Scale effect tests on wave transmission and 447 reflect ion CHAPTER 11 - SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 462 11.1. Summary 462 11.2. Conclusions 463 11.3. Recommendations 467 REFERENCES 469 9 LIST OF TABLES PaSe Table 1.1 - Classification of breakwater armour units 37 Table 2.1 - Structure of the literature survey 45 Table 2.2 - Flow coefficients for Engelund's (1953) 54 equat ion Table 2.3 - Comparison of Engelund's (1953) and LeMehaute's 84 (1957) equations Table 2.4 - Wave action on porous structures 85 Table 3.1 - Experimental techniques 115 Table 6.1 - Summary of the experimental programme 222 Table 6.2 - Physical properties of experimental media 223 Table 6.3 - Results from steady flow permeability tests 225 Table 6.4 - Results from selected investigations on steady 226 flow permeability tests Table 6.5 - Results from oscillatory flow tests 227 Relative magnitude of transmission (Kt), reflection (Kr) and energy loss (K^) coefficients Table 6.6 - Cross-comparison studies with experimental 228 media Table 7.1 - Results from unidirectional constant 282 acceleration tests Table 7.2 - Results from constant velocity tests 283 Table 8.1 - Numerical solution for the internal transmission 333 coefficients for different porous media Table 8.2 - Response of the numerical solution to variations 334 in laminar and turbulent flow coefficients Table 8.3 - Sensitivity