Experimental study of local scour around complex bridge piers

EXPERIMENTAL STUDY OF LOCAL SCOUR AROUND COMPLEX BRIDGE PIERS MARIO ENRIQUE MORENO CASTIBLANCO Thesis submitted for the fulfilment of the requirements for the degree of Doctoral Program in Civil Engineering ____________________________________________________ Supervisor: Professor Doctor Rodrigo Jorge Fonseca de Oliveira Maia ____________________________________________________ Co-Supervisor: Doctor Lúcia Teixeira Couto JULY 2016 Experimental Study of Local Scour around Complex Bridge Piers i ACKNOWLEDGEMENTS Since I started working as an undergraduate student in the area of water resources and hydraulics at Los Andes University in Colombia 14 years ago, I decided that the ultimate goal of my educational process should be to pursue a Ph.D. in Civil Engineering. This document includes the results of the Ph.D. research project that I conducted during the last six years in Portugal. This period of time was some of the richest and most exciting years of my life. In this big journey, literally from South America to Europe, I met many people with whom I learned a lot and who I will never forget. The following lines are dedicated to thank the ones that in one way or another contributed to my stay in Portugal as well as in the completion of this research. First I would like to thank my supervisors, Professor Rodrigo Maia and Dr. Lúcia Couto, for their unconditional support and encouragement throughout my research work. I must also acknowledge all their availability, dedication, guidance and feedback on the papers, for conferences and journals, which we co-authored with other colleagues during my Ph.D. studies. I also appreciate their availability in reviewing this document. I also thank Professor Maia for his guidance and supervision of the tests performed at the hydraulics laboratory of the Faculty of Engineering of the University of Porto (FEUP). I appreciate the discussion moments we have about the political and economic situation of Colombia and the success of soccer Colombian players in the Porto team. Chiefly, I cherish the friendship that has grown among us through these years. I want to thank his for providing comfortable conditions at FEUP during the last two years of my Ph.D. studies. I also owe a debt of gratitude to Mrs. Lúcia, for her constant support, great advice and comments, direction and assistance during the performance of the experimental campaign performed at the National Laboratory for Civil Engineering (LNEC). I appreciate her experience in physical modelling of hydraulic structures as it allowed discussing and decision making regarding the experimental results obtained in this research. I want to thank her specially for providing all necessary conditions at LNEC so I could work comfortably during the first four years of my Ph.D. studies. She definitely played a very important role in my adaptation to this new country (e.g. culture, customs and food). Sometimes, her personal advice, recommendations and protective attitude reminded me of my mom. I would also like to thank my committee members, professor Vitor Abrantes Almeida, professor Francesco Ballio, professor António H. Cardoso, professor Fernando Veloso Gomes and professor Francisco Taveira Pinto for serving as my committee members. I also want to thank you for letting my defence be an enjoyable moment, and for your brilliant comments and suggestions, thanks to you. I also met other inspiring people working as part of the research project denominated "Experimental study of local scour at complex bridge piers" with which I had the pleasure to participate in enriching discussions as well as had their valuable feedback on my own research project. I also want to thank Professors João P. Pêgo, Cristina Fael and Rui Lança, senior researcher João Rocha and also to the consultants Roger Bettess, Juan P. Martín-Vide, Roberto Gaudio and Luís Texeira; each one, in their own way, helped me to pursue and to refine my research goals. I am grateful for all the discussion to clarify the physics underlying scouring process at bridge piers. I also would like to thank João Manuel and his team for the adequacy and preparation of the experimental facility at LNEC, as well as António Muralha for the help in some measurements of tests performed at LNEC. I am also grateful to students Luís Brito and Pedro Ramos for assisting me with the test measurements carried out at FEUP; and to Cristina Silva for the continuous support in the affairs of the university. During the four years that I was at LNEC, I had the opportunity and pleasure to meet other researchers that made my experience even more enriching. I want to thank my colleagues of the Department of Experimental Study of Local Scour around Complex Bridge Piers ii Hydraulics and Environment Teresa Viseu, Elsa Alves, Ana Estela Barbosa, José Melo, Leandro Valente, Mateus Mendoça, Natália Lopes, João Fernandes, Sílvia Amaral, Rute Viera, Gonçalo Jesus, Adelaide Gonçalves, Ricardo Rossato, Fernando Pereira, Pedro Massa, Ana Mendoça, Diogo Neves, Lourenço Sasseti, Paula García, Ricardo Jónatas, João Rogeiro, João Gomes, João Pedro, Inês Reis and Jorge Gadelho for welcoming a foreigner. I will always remember the interesting discussions we usually had at lunch time as well as the meetings and activities outside of LNEC with some of you. I acknowledge those days I worked in the same office at LNEC with Ricardo, my first Italian friend. I want to thank him for all the good moments we spent together and to introduce me to his friends, Italians of course, who are now my new friends. During the four years that I was in Lisbon I met a little more than 200 Italians that I hope to see again in Italy or anywhere in the world. I would like to express my special appreciation to my Italian housemates Federico, Chiara, Silvia, Beatrice, Giorgio, Ylenia, Consuelo and Teo for their friendship and support in my Ph.D. I will always remember the good dinners at our house as well as at Ti Natércia restaurant - Tina thanks for being my favourite chef. I also regard the many visits of Lavinia. Besides, I want to thank them for the good times both in Portugal and in Italy. Grazie mille amici! In life, it is always good to find people with similar interests; Ruben Silva “my new brother” is one of them. Besides sharing a house during my first year in Lisbon we both are sports fans. I remember the good times when we attended to different sport competitions in Portugal (e.g., MotoGP race, Le Mans Series race, Tennis tournament, Surf championship, Cycling race) and of course a lot of soccer matches at different stadiums of the country (supporting Porto, Benfica, Sporting and the National team). I will never forget our big trip to Barcelona to celebrate the fifth Champions League won by the Barcelona team as well as our weekend trips to explore amazing places found in Portugal. I would like to express my special appreciation to him for his friendship during these six years and I am very grateful for letting me share four Christmas with his family. Até breve meu caro amigo! It was a pleasure to meet other Ph.D. students in Portugal with whom I could share experiences and support to finish my thesis. I want to thank Ana Ricardo, Helena Nogeira, Sebastián Guillén and David Ferrás for his friendship and advice. I want to thank my compatriot Diana Díaz by ringing a visit to Lisbon and for the good times we had together at December of 2013. I also want to thank my old Colombian friends Jenny, Susana, Santana, Chicho and Gustavo for their continuous support. I would also like to express my sincere gratitude to my two mentors at Los Andes University, Professors Juan Saldarriaga and José “Pepe” Rengifo, for the unconditional support in my academic and research activities in Colombia: they were the ones that encouraged me to make this journey. I owe Juan a debt of gratitude for motivating me as well as providing an immense knowledge that was conveyed to me when we worked together for nine years at the Aqueduct and Sewage Research Centre at the Universidad de Los Andes. A special thanks to Pepe, who I consider my grandfather, for his enthusiasm, motivation, patience and advice during the last fourteen years of my life. Por último, quiero dedicar esta tesis a mi familia, lo más valioso de mi vida! Mis padres, Mario y Elvira, merecen una mención especial por su inseparable apoyo, paciencia y amor. Les transmito un reconocimiento especial a mi hermano, Maicol, y su señora, Maritza, por su continuo apoyo. Me gustaría agradecer inmensamente el apoyo amoroso de mis encantadoras sobrinas, a pesar de la distancia, Mabelita, la más bella violinista, y Manuelita, loquilla preciosa. También agradezco a mis otros dos hermanos, Maher y Marlon, por su continuo ánimo y apoyo. Agradezco inmensamente los buenos deseos de mis abuelos, tíos, primos y demás familiares. This research was supported by the Portuguese Foundation for Science and Technology with the research grant SFRH/BD/76396/2011 and the research project PTDC/ECM/101353/2008. Experimental Study of Local Scour around Complex Bridge Piers iii ABSTRACT Due to physical, geotechnical and economic considerations, bridges are frequently built with foundations of complex geometries. Currently, two types of pier-foundations are used in new largespan bridges: (1) common complex piers (also named as pile-supported piers), which consist of a column founded on a pile cap supported by an array of piles; and (2) special complex piers, which are characterized by non-conventional column and pile-cap geometries (e.g., pile-supported piers with multi-columns). In this study, the term “complex piers” applies to pier geometries characterized by a column founded on a pile cap supported by an array of piles. Local scour is a complex phenomenon involving three-dimensional flow structures, typically developed around piers and bridge abutments founded in movable bed rivers. Local scour can lead to partial failure or to collapse of bridge piers and decks. The cost of large bridges, with common and/or special complex piers, justifies carrying out an accurate prediction of scour depth, for both economic and safety reasons, which in turn leads to the interest of hydraulic engineers in predicting the equilibrium scour depth at complex piers. However, it is known that, despite the studies conducted in the past for pile-supported piers, the scour predictors do not reproduce adequately the measured scour values, as suggested by Ferraro et al. (2013). This derives from the fact that there are many factors influencing the phenomenon. Presently, three methods to predict equilibrium scour depth at complex piers can be considered as consolidated: the Auckland method (Coleman, 2005), the FDOT method (Sheppard and Renna, 2010) and the HEC-18 method (Arneson et al., 2012). The present study develops an extensive research to systematically map equilibrium scour at complex piers and relate the observations with the characteristic variables of the tests. A total of eighty-four long-duration tests with seven complex pier models, aligned with the approach flow under clear-water flow conditions, were performed. Six of the complex piers models were analysed at the flume of the Hydraulics and Environment Department, National Laboratory for Civil Engineering (LNEC) while the remaining one was evaluated at the flume of the Faculty of Engineering of the University of Porto (FEUP). Forty-eight out of the total number of tests were used to quantify the influence of the complex-pier position and geometry on the scour depth time evolution. The following combined effects were analysed: (1) the relative column width, 𝐷𝑐/𝐷𝑝𝑐 (𝐷𝑐= column width; 𝐷𝑝𝑐= pile-cap width), and the relative pile-cap position, 𝐻𝑐/ℎ (𝐻𝑐= distance from the initial bed level to the top surface of the pile cap; ℎ= approach flow depth); (2) the relative pile-cap thickness, 𝑇/ℎ (𝑇= pile-cap thickness), and 𝐻𝑐/ℎ; and (3) the pile-group configuration (characterized by the number of alignments in the group, 𝑛) and 𝐻𝑐/ℎ. The experimental results were classified according to three pile-cap situations: (i) Situation 1, characterized by the bottom of the pile cap being above the initial bed level; (ii) Situation 2, characterized by the pile cap being partially buried in the initial bed configuration; and (iii) Situation 3, characterized by the pile cap being initially completely buried in the bed. The common criterion to stop experimental tests on complex piers was analysed, and a new criterion was introduced. In these forty-eight tests, the equilibrium scour depth was calculated by extrapolation of data series. The results are used to evaluate the three specified influences (𝐷𝑐/𝐷𝑝𝑐 and 𝐻𝑐/ℎ; 𝑇/ℎ and 𝐻𝑐/ℎ; 𝑛 and 𝐻𝑐/ℎ) on the equilibrium scour depth for the three mentioned situations. The analysis includes the definition of the pile-cap position at which the maximum equilibrium scour depth occurs. Some of the methods most commonly used to predict equilibrium scour depth around complex piers are based on tests carried out, separately, for their individual components: the column, the pile cap and the pile group. In some of those methods, the scour depth at complex piers is estimated by adding the Experimental Study of Local Scour around Complex Bridge Piers iv contributions of the isolated components, ignoring the non-linear interaction between them. In the present study, a new, physically sounder approach to experimentally assess the contribution of complex piers’ components to scouring is presented and discussed. The new approach takes into account the interactions of the different aspects of the flow field and their impact on the local scour depth. Seventy out of the total number of tests performed in this study were used to estimate the complex pier components’ contributions on equilibrium scour depth according to the new approach. Results showed that the contribution of each component is highly dependent on its position (relative to the initial bed level), and also depends on: (1) 𝐷𝑐/𝐷𝑝𝑐; (2) 𝑇/ℎ; and (3) 𝑓𝑐/𝐷𝑝 (𝑓𝑐= longitudinal extension of the pile cap out from the upstream pile front; 𝐷𝑝= pile width). A comparison of the results of this approach with the corresponding contributions based on tests with isolated components was also performed. Finally, forty-eight out of the total number of tests carried out in this study were used to evaluate the performance of the three mentioned predictors, concluding that: (1) the Auckland predictor gives more acceptable values of equilibrium scour depth; (2) the FDOT predictor gives conservative values of the equilibrium scour depth; and (3) the HEC-18 predictor systematically tends to underestimate equilibrium scour depth values. Based on the experimental results of the present study and on the conceptual approaches of Auckland and FDOT methods, an alternative formulation for a predictor of equilibrium scour depth at complex piers is suggested and validated. This new formulation performed better than the other three methods (in terms of accuracy). KEYWORDS Local scour, complex pier, bridge foundations, equilibrium scour depth, laboratory tests. Experimental Study of Local Scour around Complex Bridge Piers v RESUMO Considerações de ordem física, geotécnica e económica têm levado a que, cada vez mais, as fundações de pontes sejam construídas com geometrias complexas. Atualmente, dois tipos de pilar-fundação são usados nos novos projetos de grandes pontes: (1) pilares complexos comuns (igualmente designados por pilares suportados por estacas), constituídos por uma coluna fundada em um maciço de encabeçamento e suportado por um grupo de estacas; e (2) pilares complexos especiais, que são caracterizados por geometrias não convencionais do pilar e do maciço de encabeçamento. Em este estudo, o termo “pilares complexos” aplica-se a geometrias constituídas por colunas fundadas em maciços de encabeçamento suportados por estacas. As erosões localizadas podem ser entendidas como processos complexos associados a estruturas tridimensionais do escoamento que se observam junto de obstruções ao mesmo. De entre essas obstruções destaca-se os pilares (simples ou complexos) ou encontros de pontes, atentas as correspondentes erosões localizadas, que podem conduzir à rotura parcial ou ao colapso de pontes. O custo de grandes pontes, com pilares complexos comuns e/ou especiais, justifica uma previsão rigorosa das profundidades de erosão, tanto por razões económicas como de segurança. Porém, é sabido que, apesar dos numerosos estudos conduzidos no passado, ainda não se atingiu sucesso pleno nas propostas e métodos para prever a profundidade máxima das cavidades de erosão, como sugere Ferraro et al. (2013). Nos últimos anos têm vindo a ser considerados, como referência, três métodos de previsão da profundidade de equilíbrio desenvolvida junto de pilares complexos: método de Auckland (Coleman, 2005), método do FDOT (Sheppard and Renna, 2010) e método do HEC-18 (Arneson et al., 2012). O presente estudo apresenta uma extensa campanha experimental que caracteriza sistematicamente as profundidades de equilíbrio da cavidade de erosão em pilares complexos, relacionando as observações com as variáveis características dos ensaios. Um total de oitenta e quatro ensaios de longa duração foi realizado com sete modelos de pilares complexos, alinhados com o escoamento de aproximação em condições de escoamento sem transporte sólido generalizado. Seis dos modelos de pilares complexos foram analisados no canal do Departamento de Hidráulica e Ambiente, Laboratório Nacional de Engenharia Civil (LNEC) enquanto o restante modelo foi analisado no canal da Faculdade de Engenharia da Universidade do Porto (FEUP). Quarenta e oito do número total de ensaios realizados neste estudo foram usados para quantificar a influência da posição e geometria do pilar complexo na evolução temporal da profundidade de erosão. Os seguintes efeitos combinados foram analisados: (1) a largura relativa da coluna, 𝐷𝑐/𝐷𝑝𝑐 (𝐷𝑐= largura da coluna; 𝐷𝑝𝑐= largura do maciço), e a posição relativa do maciço, 𝐻𝑐/ℎ (𝐻𝑐= distância desde o nível inicial do leito à parte superior do maciço; ℎ= profundidade do escoamento de aproximação); (2) a espessura relativa do maciço, 𝑇/ℎ (𝑇= espessura do maciço), e 𝐻𝑐/ℎ; e (3) a configuração do grupo de estacas (caracterizada pelo número de alinhamentos no grupo, 𝑛) e 𝐻𝑐/ℎ. Os resultados experimentais foram enquadráveis em três situações tipificadas: (i) Situação 1, caracterizada pelo facto de o maciço estar acima do nível inicial do leito; (ii) Situação 2, caracterizada pelo facto de o maciço se encontrar parcialmente enterrado no leito inicial; e (iii) Situação 3, caracterizada pelo facto de o maciço estar completamente enterrado no leito inicial. Os ensaios conduzidos permitiram também avaliar o critério comumente usado para estimar o tempo de duração adequado para pilares complexos. Foi introduzido um critério para finalizar os ensaios de pilares complexos. Nestes quarenta e oito ensaios, as profundidades de equilíbrio da cavidade de erosão foram calculadas por extrapolação de cada uma das séries de dados. Os resultados são utilizados para avaliar Experimental Study of Local Scour around Complex Bridge Piers xii Figure 2.18 – Scheme of flow structure and local scour around pile groups ........................................ 32 Figure 2.19 – Flow structure around: (a) a rectangular debris cluster (adapted from Pagliara and Carnacina 2011) and (b) pier with caisson (adapted from Veerappadevaru et al. 2011) .................................................................................................................................. 32 Figure 2.20 – Scheme of the flow structure around complex piers ....................................................... 33 Figure 2.21 – Scheme of complex pier geometry .................................................................................. 34 Figure 2.22 – Complex pier situations as a function of the relative pile-cap position ........................... 35 Figure 2.23 – Temporal evolution of scour depth at pile groups, adapted from Lança et al. (2013a) ............................................................................................................................... 36 Figure 2.24 – Temporal variation of scour depth at complex piers in position (3), adapted from Sousa (2007) ...................................................................................................................... 36 Figure 2.25 – Scour depth time evolution at complex piers in position (4), adapted from Ferraro et al. (2013) ............................................................................................................................ 37 Figure 2.26 – Scour depth time evolution at complex piers in position (6), adapted from Ferraro et al. (2013) ............................................................................................................................ 37 Figure 2.27 – Dimensions of complex pier models used in the five studies from literature .................. 39 Figure 2.28 – Scour depth as function of the relative column position .................................................. 41 Figure 2.29 – Effect of the relative column width on scour depth as function of the relative column position, based on Melville and Raudkivi (1996) data ....................................................... 42 Figure 2.30 – Effect of the pile-cap thickness on scour depth: (a) complex pier models and (b) scour depth variation as function of the relative column position, adapted from Ferraro et al. (2013) ........................................................................................................... 43 Figure 2.31 – Effect of the relative pile spacing on the relative scour depth for pile groups with: (a) a single row (m = 1) and (b) a single column (n = 1) ......................................................... 44 Figure 2.32 – (a) variation of dspg/ds with Sp/Dp and 𝜃, adapted from Lança et al. (2013a) and (b) system of wake vortices at an alignment of piles, adapted from Lança et al. (2012) ........ 45 Figure 2.33 – Conceptual variation of equivalent diameter with column position, adapted from Coleman (2005) ................................................................................................................. 46 Figure 2.34 – Conceptual hypothesis for superimposing scour components, adapted from Jones and Sheppard (2000a) ....................................................................................................... 47 Figure 2.35 – Projected width of piles, adapted from Richardson and Davis (2001) ............................ 50 Figure 2.36 – Conceptual hypothesis of summing equivalent diameters, adapted from Sheppard and Renna (2010) .............................................................................................................. 51 Figure 3.1 – Dimensions of complex pier models analysed at (units in millimetres): (a) LNEC’s flume and (b) FEUP’s flume ............................................................................................... 59 Figure 3.2 – Complex pier configurations .............................................................................................. 60 Figure 3.3 – Grading curve of the sand used in the experiments ......................................................... 61 Experimental Study of Local Scour around Complex Bridge Piers xiii Figure 3.4 – Scheme of the pile-cap positions associated with the study of the three typical situations for: (a) Models 1 and 4, (b) Models 2, 3 and 5, (c) Model 6 and (d) Model 7 .... 63 Figure 3.5 – Scheme and photographs of LNEC’s flume, based on the scheme by Cardoso (1982) ................................................................................................................................. 65 Figure 3.6 – Surge tank operation ......................................................................................................... 66 Figure 3.7 – Scheme and photographs of the tilting flume ................................................................... 67 Figure 3.8 – Scheme of FEUP’s flume .................................................................................................. 68 Figure 3.9 – Step 1 of the experimental procedure: (a) LNEC’s flume and (b) FEUP’s flume ............. 70 Figure 3.10 – Step 2 of the experimental procedure: (a) LNEC’s flume and (b) FEUP’s flume ........... 71 Figure 3.11 – Step 3 of the experimental procedure: (a) LNEC’s flume and (b) FEUP’s flume ........... 72 Figure 3.12 – Step 4 of the experimental procedure: (a) LNEC’s flume and (b) FEUP’s flume ........... 73 Figure 3.13 – Typical scour patterns at the end of the test: (a) LNEC’s flume and (b) FEUP’s flume .................................................................................................................................. 74 Figure 4.1 – Situation 1: (a) scheme of the temporal evolution of the scour depth (time on linear and logarithmic scales) and (b) photographs of scour hole evolution ............................... 76 Figure 4.2 – Situation 2: (a) scheme of the temporal evolution of the scour depth (time on linear and logarithmic scales) and (b) photographs of scour hole evolution ............................... 77 Figure 4.3 – Situation 3: (a) scheme of the temporal evolution of the scour depth (time on linear and logarithmic scales) and (b) photographs of scour hole evolution ............................... 77 Figure 4.4 – Influence of Dc/Dpc on the temporal evolution of the scour depth for Situation 1: (a) Positions A to D and (b) Position E .................................................................................... 78 Figure 4.5 – Influence of Dc/Dpc on the temporal evolution of the scour depth for Situation 2 (pile cap slightly buried): (a) Position F and (b) Position G ....................................................... 79 Figure 4.6 – Influence of Dc/Dpc on the temporal evolution of the scour depth for Situation 2 (pile cap almost buried): (a) Position H and (b) Position I ......................................................... 80 Figure 4.7 – Photos of the scour hole evolution in test M5I1 ................................................................ 80 Figure 4.8 – Influence of Dc/Dpc on the temporal evolution of the scour depth for Situation 3: (a) Position J and (b) Position K .............................................................................................. 81 Figure 4.9 – Influence of Dc/Dpc on the temporal evolution of the scour depth for Situation 3 (Position L) ......................................................................................................................... 81 Figure 4.10 – Influence of T/h on the temporal evolution of the scour depth for Situation 1: (a) Position D and (b) Position E ............................................................................................. 82 Figure 4.11 – Influence of T/h on the temporal evolution of the scour depth for Position F: (a) test in Situation 1 and (b) tests in Situation 2 ........................................................................... 83 Figure 4.12 – Influence of T/h on the temporal evolution of the scour depth for Situation 2: (a) Position G, (b) Position H and (c) Position I ...................................................................... 83 Figure 4.13 – Influence of T/h on the temporal evolution of the scour depth for Situation 3 ................ 84 Experimental Study of Local Scour around Complex Bridge Piers xiv Figure 4.14 – Influence of the pile-cap elevation on the temporal evolution of the scour depth for: (a) Situation 1 (Positions M to O), (b) Situation 2 (Positions P to R) and (c) Situation 3 (Positions S and T) .......................................................................................................... 86 Figure 4.15 – Experiment M2H1: (a) scour rate evolution and (b) temporal evolution of the scour depth .................................................................................................................................. 88 Figure 5.1 – Effect of the relative column width on the equilibrium scour depth as a function of the relative column position ...................................................................................................... 94 Figure 5.2 – Interpretation of the flow structure in the cases in which the maximum equilibrium scour depth occurred (Situation 2) for: (a) Model 2, (b) Model 3 and (c) Model 5 ............. 95 Figure 5.3 – (a) Scheme with dimensions of Model Mu (Moreno et al., 2015a) (units in millimetres) and (b) equilibrium scour depth as a function of the relative column position observed with Models 5 and Mu ........................................................................... 96 Figure 5.4 – Scour hole in test 4 with Model Mu (a) downstream scour hole and (b) lateral scour hole ..................................................................................................................................... 97 Figure 5.5 – Effect of the relative pile-cap thickness on the equilibrium scour depth as a function of the relative column position for: (a) Models 4, 5 and 6 and (b) Models 1 and 2 ............ 97 Figure 5.6 –Equilibrium scour depth as a function of the relative column position for models with: (a) two alignments of piles (Model 3) and (b) one alignment of piles (Model 7) ................ 99 Figure 5.7 – Scheme of (a) complex pier obstruction area (Model Fe1) and (b) equivalent obstruction width of the complex pier ............................................................................... 101 Figure 5.8 – Effect of the relative pile-cap thickness on the relative maximum scour depth .............. 102 Figure 5.9 – dsm/Dpc as function of Hc/T for Situation 2: (a) rectangular pile-cap shape and (b) circular and rectangular round-nose pile-cap shapes ...................................................... 103 Figure 5.10 – Effect of the relative column width and column/pile-cap shapes on dsm/dsecu as function of Hc/dsecu for Situation 3 ..................................................................................... 105 Figure 6.1 – Scheme of the subtraction approach (contribution of the complex pier components on scour depth) ................................................................................................................ 109 Figure 6.2 – Scour depth time evolution in tests with Model 3 for: (a) Configuration C2 and (b) Configuration C3 .............................................................................................................. 112 Figure 6.3 – Scour depth time evolution and final scour hole in Configurations C1, C2 and C3 for: (a) Model 4 (Position E) and (b) Model 7 (Position Q) ..................................................... 113 Figure 6.4 – Variation of factor Khc with the relative position of the base of the column ..................... 115 Figure 6.5 – Variation of factor Khpg with the relative position of the top of the pile group .................. 116 Figure 6.6 – Variation of factor Khpc with the relative position of the base of the pile cap: (a) Models 1 to 6 and (b) Model 7 ......................................................................................... 117 Figure 6.7 – Scheme of the geometry of complex pier components ................................................... 118 Figure 6.8 – Comparison of Khc obtained through subtraction with Khc obtained from tests with isolated columns .............................................................................................................. 121 Experimental Study of Local Scour around Complex Bridge Piers xv Figure 6.9 – Comparison of Khpc obtained through subtraction with Khpc obtained from tests with isolated pile caps: (a) T/h ≈ 0.30, (b) T/h ≈ 0.45 and (c) T/h ≈ 0.60 ................................ 122 Figure 6.10 – Comparison of Khpg obtained through subtraction with Khpg obtained from tests with pile groups ....................................................................................................................... 122 Figure 6.11 – Comparison of factors Khc , Khpc and Khpg obtained by the subtraction concept with the corresponding values predicted by FDOT and HEC-18 methods: (a) variation of factor Khc; (b) variation of factor Khpc; and (c) variation of factor Khpg .............................. 124 Figure 7.1 – Comparison of observed and predicted equilibrium scour depths, for the methods of: (a) Auckland, (b) HEC-18 and (c) FDOT ......................................................................... 128 Figure 7.2 – Conceptual variation of: (a) dse with Hc and (b) De with Hc ............................................. 131 Figure 7.3 – Longitudinal extension length of the pile cap out from the upstream piles front ............. 133 Figure 7.4 – Predicted versus observed scour depths at complex piers by: (a) suggested formulation, (b) FDOT predictor, (c) Auckland predictor and (d) HEC-18 predictor ........ 137 Figure 7.5 – Equilibrium scour depths as a function of column position with: (a) model by Grimaldi and Cardoso (2010) and (b) models by Ferraro et al. (2013) .......................................... 138 Experimental Study of Local Scour around Complex Bridge Piers xvi Experimental Study of Local Scour around Complex Bridge Piers xvii LIST OF TABLES Table 2.1 – Bed condition factors .......................................................................................................... 30 Table 2.2 – Experimental models: flow parameters, bed granulometry parameters and duration of the tests ............................................................................................................................. 38 Table 3.1 – Geometric characteristics of the complex pier models of the experimental campaign ...... 61 Table 3.2 – Designation of the tests performed with Configuration C1 (Models 1 to 6) ....................... 63 Table 3.3 – Designation of the tests performed with Configuration C2 (Models 1 to 6) ....................... 64 Table 3.4 – Designation of the tests performed with Configuration C3 (Models 1 to 6) ....................... 64 Table 3.5 – Designation of the tests performed with Model 7 ............................................................... 64 Table 4.1 – Relative column position, test duration and maximum scour depth for Models 1 to 3 ....... 85 Table 4.2 – Relative column position, test duration and maximum scour depth for Models 4 to 6 ....... 85 Table 4.3 – Relative column position, test duration and maximum scour depth for Model 7 ............... 87 Table 4.4 – Relative column position, equivalent diameter of the complex pier, test duration and scour depth with 5% criterion for Models 1, 2 and 3 .......................................................... 88 Table 4.5 – Relative column position, equivalent diameter of the complex pier, test duration and scour depth with 5% criterion for Models 4, 5 and 6 .......................................................... 89 Table 4.6 – Relative column position, equivalent diameter of the complex pier, test duration and scour depth with 5% criterion for Model 7.......................................................................... 89 Table 5.1 – Equilibrium scour depths (extrapolated values) with Models 1 to 6 ................................... 93 Table 5.2 – Equilibrium scour depths (extrapolated values) with Model 7 ............................................ 93 Table 5.3 – Experimental models: flow parameters, model geometry parameters and test durations .......................................................................................................................... 100 Table 5.4 – Values of (Hc/T)max as function of relative column width .................................................. 103 Table 6.1 – Relative column position, test duration, maximum and equilibrium scour depth values for tests with Configurations C2 and C3 .......................................................................... 110 Table 6.2 – Equilibrium scour depths of the reference tests ............................................................... 111 Table 6.3 – Equilibrium scour depths associated to each complex pier component .......................... 114 Table 6.4 – Characteristic control variables and non-dimensional parameters of studies on suspended columns ......................................................................................................... 119 Table 6.5 – Characteristic control variables and non-dimensional parameters of studies on suspended pile caps ........................................................................................................ 119 Table 6.6 – Characteristic control variables and non-dimensional parameters of studies on submerged pile groups .................................................................................................... 120 Table 7.1 – Control variables and non-dimensional parameters for specific pier foundations’ studies .............................................................................................................................. 132 Experimental Study of Local Scour around Complex Bridge Piers xviii Table 7.2 – Control variables and non-dimensional parameters for single piers’ studies with longduration tests .................................................................................................................... 136 Table 7.3 – Control variables and non-dimensional parameters for pile groups’ studies with longduration tests .................................................................................................................... 136 Experimental Study of Local Scour around Complex Bridge Piers xix LIST OF SYMBOLS 𝑎1,𝑎2 = parameters obtained by regression analysis; 𝐵 = channel width; 𝐵′ = constant of integration; 𝑐1,𝑐2,𝑐3 = parameters obtained by regression analysis; 𝐷 = pier width; 𝐷𝑐 = column width; 𝐷𝑒 = equivalent pier diameter; 𝐷𝑒𝑐 = equivalent diameter of the column; 𝐷𝑒𝑐(min) = equivalent diameter of a single pier that lead to a scour depth equal to |𝐻𝑐|; 𝐷𝑒𝑝𝑐 = equivalent diameter of the pile cap; 𝐷𝑒𝑝𝑔 = equivalent diameter of the pile group; 𝐷𝑒∗ = maximum equivalent diameter of the complex pier; 𝐷𝑝 = pile width; 𝐷𝑝𝑐 = pile-cap width; 𝐷𝑝𝑐 = diameter of cylindrical foundation; 𝑑𝑠 = scour depth; 𝑑𝑠𝑐(max) = maximum column scour depth; 𝑑𝑠𝑐𝑝𝑐 = scour depth produced by the combination of the column and pile cap; 𝑑𝑠𝑒 = equilibrium scour depth; 𝑑𝑠𝑒𝑐 = column contribution to the local scour depth; 𝑑𝑠𝑒𝑐𝑢 = equilibrium scour depth for an uniform single pier with the same geometrical definition of the complex pier column; 𝑑𝑠𝑒𝐶1 = equilibrium scour depth due to Configuration C1 of the complex pier; 𝑑𝑠𝑒𝐶2 = equilibrium scour depth due to Configuration C2 of the complex pier; 𝑑𝑠𝑒𝐶3 = equilibrium scour depth due to Configuration C3 of the complex pier; 𝑑𝑠𝑒𝑝𝑐 = pile cap contribution to the local scour depth; 𝑑𝑠𝑒𝑝𝑐𝑢 = equilibrium scour depth for an uniform single pier with the same geometrical definition of the complex pier pile-cap; 𝑑𝑠𝑒𝑝𝑔 = pile group contribution to the local scour depth; 𝑑𝑠𝑒𝑝𝑔𝑢 = equilibrium scour depth developed for a an unsubmerged pile group; 𝑑𝑠𝑚 = maximum scour depth; Experimental Study of Local Scour around Complex Bridge Piers xx 𝑑𝑠𝑚 = scour depth measured at the end of the tests; 𝑑𝑠𝑚𝑀𝑆 = scour depth measured at time defined according to equation (4.1); 𝑑𝑠𝑝 = scour depth at an individual pile in the same bed and approach flow conditions of the pile group; 𝑑𝑠𝑝𝑐(max) = maximum pile cap scour depth; 𝑑𝑠𝑝𝑔 = maximum scour depth observed at pile group; 𝑑𝑠5% = scour depth obtained by criterion of 5%; 𝑑1,𝑑2,𝑑3 = parameters obtained by regression analysis; 𝑑16 = sediment size which 16% of sediment is finer; 𝑑50 = median size of sediment particle size distribution; 𝑑84 = sediment size which 84% of sediment is finer; 𝑓 = weighted average of the pile-cap front and side extensions beyond the column; 𝑓𝑙 = extension length of pile cap face out from column face; 𝑓𝑝 = longitudinal extension length of pile cap face out from the nearest pile front face; 𝑓𝑡 = extension width of pile cap face out from column face; Fr = Froude number; Fr𝑑 = densimetric Froude number; 𝑔 = gravitational acceleration; ℎ = approach flow depth; 𝐻𝑏 = pile-cap position below the initial bed level at which occurs the minimum scour depth when the pile cap is completely buried in the bed; 𝐻𝑐 = column position (distance from the initial bed level to the bottom surface of the column); ℎ𝑐(max) = limiting water depth at which the flow influences the scouring process around the column; (𝐻𝑐/𝑇)max = pile-cap position at which the maximum equilibrium scour depth can be obtained; 𝐻𝑑 = dune height; 𝐻𝑝𝑐 = pile-cap position (distance from the initial bed level to the bottom of the pile-cap); ℎ𝑝𝑐(max) = limiting water depth at which the flow influences the scouring process around the pile cap; 𝐻𝑝𝑔 = pile-group position (distance from the initial bed level to the top of the pile group); ℎ𝑝𝑔(max) = limiting water depth at which the flow influences the scouring process around the pile group; 𝐻𝑐∗ = distance from the bed to the top of the footing after column scour component has been computed; 𝐻𝑝𝑐 ∗ = distance between the bed and the bottom of the pile cap after column scour component has been computed; 𝐻𝑝𝑔 ∗ = distance between the bed and the top of the pile group after pile cap scour component has Experimental Study of Local Scour around Complex Bridge Piers xxi been computed; 𝐻𝑥 = pile-cap position at which occurs the maximum scour depth; ℎ1 = adjusted flow depth for pile cap computations; ℎ2 = adjusted flow depth for pile group computations; 𝐾𝐴 = pile group factor; 𝐾𝑏𝑐 = correction factor for bed forms; 𝐾𝑏𝑝𝑐 = factor that accounts for the dependence of the pile-cap position on the scour hole; 𝐾𝑏𝑝𝑔 = buried pile group attenuation factor; 𝐾𝑑 = sediment coarseness factor; 𝐾𝑓 = pile cap extension factor; 𝐾𝑔 = factor describing the geometry of the channel cross-section; 𝐾ℎ𝑐 = factor to account for the position of the bottom of the column relative to the initial bed level; 𝐾ℎ𝐷 = flow depth-pier size factor; 𝐾ℎ𝐷𝑒 = flow shallowness factor; 𝐾ℎ𝑝𝑐 = factor to account for the position of the bottom of the pile cap relative to the initial bed level; 𝐾ℎ𝑝𝑔 = factor to account for the position of the top of the pile group relative to the initial bed level; 𝐾𝐼 = flow intensity factor; 𝐾𝑚 = factor to account for the aligned rows; 𝑘𝑠 = height of grain roughness of the bed; 𝐾𝑆 = factor describing the shape of the pier; 𝐾𝑆𝑐 = column shape factor; 𝐾𝑠𝑝 = pile spacing factor; 𝐾𝑆𝑝 = pile shape factor; 𝐾𝑆𝑝𝑐 = pile-cap shape factor; 𝐾𝑆𝑝𝑔 = factor to account for the shape of the pile group; 𝐾𝑆(pg) = pile-group configuration factor; 𝐾𝑠𝑝𝑚 = factor to account for the pile spacing length (𝑆𝑚) and the number of piles in line with flow (𝑚); 𝐾𝑠𝑝𝑛 = factor to account for the pile spacing width (𝑆𝑛) and the number of piles normal to the flow (𝑛); 𝐾𝑤 = correction factor for wide piers; 𝐾𝜃 = factor describing the alignment of the pier; 𝐿 = pier length; 𝐿𝑐 = column length; Experimental Study of Local Scour around Complex Bridge Piers 4 Fael et al., 2014). During the recent years, three methods have been consolidated and have been used to predict the equilibrium scour depth at single piers as well as complex piers: Auckland method (Melville and Coleman, 2000), FDOT method (Sheppard and Renna, 2010) and HEC-18 method (Arneson et al., 2012). Those three scour predictors were established on the basis of data obtained in hundreds of experiments run all over the world; still, both Auckland and HEC-18 methods are frequently claimed to over-predict the scour depth in natural conditions. According to Sheppard et al. (2004), over-prediction is due to the incorrect consideration of the effect of the sediment size factor. Figure 1.4 – Photographs of local scour experiments at (a) single piers (Sheppard, 2003), (b) pile groups (Lança, 2013) and (c) complex piers (Sousa, 2007) Local scouring at complex piers requires and deserves additional research work since few experimental studies are reported in the literature by comparison with local scour studies at single piers. Those few that exist, authored by Martin-Vide et al. (1998), Jones and Sheppard (2000a), Sheppard and Glasser (2004), Coleman (2005), Ataie-Ashtiani et al. (2010), Grimaldi and Cardoso (2010), Ferraro et al. (2013) and Amini et al. (2014), some of which report on short-duration scour tests. Some studies concerning local scour at pile groups, corresponding to the case of complex piers caped above the water surface, are reported in the literature. They include those of Hannah (1978), Elliott and Baker (1985), Salim and Jones (1996), Smith (1999), Zhao and Sheppard (1999), Sumer and Fredsøe (2002), Ataie-Ashtiani and Beheshti (2006), Amini et al. (2012) and Lança et al. (2013a) some of which report on short-duration scour tests. The rigorous prediction of local scour depth around complex piers may not be guaranteed by the three consolidated predictors, i.e., Auckland, FDOT and HEC-18 methods. In spite of the complexity of the scour phenomena at complex piers, the three predictors were derived from limited experimental evidence. FDOT method, being the most comprehensive and using the most robust data basis, relies on the results of only 49 tests, while the possible combinations of column, pile cap and pile group geometries are infinite. It is, thus, with no surprise that the predictions of existing methods lead to erroneous results (e.g., Ferraro et al., 2013), justifying a strong research commitment and effort. 1.2. OBJECTIVES The general objective of this study is to contribute to the understanding and characterization of local scour around complex bridge piers aligned with the approach flow under clear-water conditions. This objective is detailed as follows: 1. Production of extensive data on clear-water local scour at complex piers; Experimental Study of Local Scour around Complex Bridge Piers 5 2. Description of the different stages of the time evolution in scour depth at complex piers depending on the pile-cap position relative to initial bed level; 3. Evaluation of the common criterion to stop experimental tests on complex piers (onset of the equilibrium phase of scour process); 4. Characterization and description of the effects of the pile-cap position, the relative column width, the relative pile-cap thickness and the pile-group configuration on the maximum scour depth at complex piers; 5. Estimation of the complex pier components’ contribution on the total local scour depth through a new experimental approach; 6. Revision and evaluation of the three consolidated predictors of the scour depth at complex piers; 7. Proposal of a new set of equations to predict the equilibrium scour depth at complex piers. 1.3. LIST OF PUBLICATIONS WITH RESULTS FROM THE PRESENT STUDY A number of contributions emerged during these five years of research, either by papers published (or submitted) in peer-reviewed journals or by papers published in conference proceedings. These are listed below together with the indication of the chapter that presents the published results and conclusions of each paper. 1. Moreno, M., Maia, R., Couto, L. and Cardoso, A. H. (2016). Subtraction approach to experimentally assess the contribution of the complex pier components to the local scour depth. Manuscript submitted to the Journal of Hydraulic Engineering. (Chapter 6); 2. Moreno, M., Maia, R. and Couto, L. (2016). Prediction of equilibrium local scour depth at complex bridge piers. Journal of Hydraulic Engineering. 10.1061/(ASCE)HY.19437900.0001153, 04016045. (Chapters 5 and 7); 3. Moreno, M., Maia, R. and Couto, L. (2015). Effects of relative column width and pile-cap elevation on local scour depth around complex piers. Journal of Hydraulic Engineering. 10.1061/(ASCE)HY.1943-7900.000108, 04015051. (Chapters 4 and 5); 4. Moreno, M., Muralha, A., Couto, L., Maia, R. and Cardoso, A. H. (2015). Influence of column width on the equilibrium scour depth at a complex pier. Proceeding of 36th IAHR World Congress, Delft – The Hague, the Netherlands, 28 June – 3 July. (Chapter 5); 5. Moreno, M., Maia, R., Pêgo, J. P., Couto, L. and Cardoso, A. H. (2014). Contribuição das componentes de um pilar complexo na profundidade de erosão localizada (in Portuguese). Proceedings 9as Jornadas de Hidráulica, Recursos Hídricos e Ambiente do Departamento de Engenharia Civil da FEUP, Porto, Portugal, 31 October. (Chapter 6); 6. Moreno, M., Couto, L., Maia, R. and Cardoso, A. (2014). Erosões localizadas em pilares complexos de pontes: desempenho de modelos de previsão existentes (in Portuguese). Revista Recursos Hídricos, 35(1), 5-22. (Chapters 2, 3 and 7); 7. Moreno, M., Maia, R., Couto, L. and Cardoso, A. (2014). Contribution of complex pier components on local scour depth. Proceeding of 3rd IAHR Europe Congress, Porto, Portugal, 14-16 April. (Chapter 6); 8. Moreno, M., Couto, L. and Maia, R. (2012). Evolución temporal de la profundidad de erosión local junto de pilas de puentes de geometría compleja (in Spanish). Proceeding of XXV Congreso Latinoamericano de Hidráulica, San José, Costa Rica, 9-12 September. (Chapters 3 and 4); Experimental Study of Local Scour around Complex Bridge Piers 6 9. Moreno, M., Maia, R., Couto, L. and Cardoso, A. (2012). Evaluation of local scour depth around complex bridge piers. Proceeding of River Flow 2012, San José, Costa Rica, 5-7 April. (Chapters 3, 4 and 7); 10. Moreno, M., Couto, L. and Maia, R. (2012). Evolução temporal da profundidade de erosão localizada junto de pilares complexos (in Portuguese). Proceeding of 11º Congresso da Água, Porto, Portugal, 6-8 February. (Chapters 3 and 4). 1.4. THESIS STRUCTURE The thesis is organized in eight chapters and one appendix. In this first chapter, a brief overview of the history of bridges development, definition of the geometry of foundation aimed at this study, and some examples of bridge failures that highlight the relevance of the research are provided. The main motivation and objectives of the work are presented. A list of the publications that emerged from this research is also included. Chapter 2 (Literature review) is a state of the art on local scour around single and complex piers, with special emphasis on the flow structure and the mechanisms involved in the scour process, the temporal evolution of maximum scour depth, the non-dimensional parameters affecting local scouring and the equilibrium scour depth prediction at single and complex piers. In the last topic, only Auckland method (Melville and Coleman, 2000; Coleman, 2005), FDOT method (Sheppard and Renna, 2010) and HEC-18 method (Arneson et al., 2012) are taken into account since these three predictors are considered as consolidated. These three methods present both equations for single and complex piers. Chapter 3 (Experimental setup) describes the two experimental facilities used in the present study to assess and characterize local scour at complex piers. It also includes the description of the experimental campaigns and of the procedures adopted in both facilities. Seven different complex pier models were tested, six of them in the flume at the National Laboratory for Civil Engineering (LNEC) and the other one in the flume at the Faculty of Engineering of the University of Porto (FEUP). The geometric variables of the complex pier models, the flow control variables and the sediment characteristics are summarized for all the experimental tests. Chapter 4 (Temporal evolution of the scour depth at complex piers) presents the results of the scour depth time evolution observed in the tests performed with the seven complex piers, identifying the different stages that occur in the scour process. The influences of the pile-cap position, of the relative column width, of the relative pile-cap thickness and of the pile-group configuration are analysed. The common criterion to stop experimental tests on complex piers is analysed, and a new stop criterion is introduced. The chapter is based on the paper Moreno et al. (2015b) (i.e., item (3) from the list of publications in section 1.3) and on the preliminary results presented in Moreno et al. (2012a, 2012b, 2012c) (i.e., items (10), (9) and (8) in section 1.3, respectively). Chapter 5 (Effect of complex pier geometry on equilibrium scour depth) presents the results that enhance the quantification of the influence of complex pier geometry on the equilibrium scour depth. The effects of the pile-cap position, the relative column width, the relative pile-cap thickness and the pile-group configuration are analysed. The equilibrium scour depths are obtained by extrapolation of the scour depth records. Comparison of those effects with the corresponding results obtained through other complex pier models published in literature is also performed. The chapter is based on the papers Moreno et al. (2015b, 2016a) (i.e., items (3) and (2) from the list of publications in section 1.3) and on Experimental Study of Local Scour around Complex Bridge Piers 7 the preliminary results presented in Moreno et al. (2012b, 2015a) (i.e., items (9) and (4) in section 1.3, respectively). In Chapter 6 (Complex pier components’ contribution on the equilibrium scour depth) a new, physically sounder approach to experimentally assess the contribution of complex piers’ components on scouring is presented and discussed. According to the new approach, the scour depth at a given component is calculated by subtracting the scour depth at two contiguous piers’ components from the scour depth at the corresponding complete complex pier, this way keeping the prevailing interactions. A comparison of the results of this approach with the corresponding contributions based on tests with isolated components is also presented. The chapter is based on the paper Moreno et al. (2016b) (i.e., item (1) from the list of publications in section 1.3) and on the preliminary results presented in Moreno et al. (2014a, 2014c) (i.e., items (7) and (5) in section 1.3, respectively). In Chapter 7 (Prediction of equilibrium scour depth around complex piers) the performance of the three most consolidated methods to predict the equilibrium scour depth at complex piers is analysed and discussed. Based on the experimental results of the present study (i.e., Chapters 5 and 6) and on the conceptual approaches of Auckland and FDOT methods, an alternative formulation for a predictor of equilibrium scour depth is suggested and validated. This chapter is based on the papers Moreno et al. (2014b, 2016a) (i.e., items (6) and (2) from the list of publications in section 1.3, respectively) and on the preliminary results presented in Moreno et al. (2012b) (i.e., item (9) in section 1.3). In Chapter 8 (Conclusions and future research) the main conclusions of the present research are drawn and suggestions and recommendations for future works are given. An appendix is included at the end of the thesis, presenting the scour data obtained for the full set of tests performed in this study. For each test, the geometric variables of the complex pier models, the flow control variables, the equilibrium scour depth, the scour depth time evolution records, a chart of the scour depth evolution and photos of the scour hole development are reported. Experimental Study of Local Scour around Complex Bridge Piers 8 Experimental Study of Local Scour around Complex Bridge Piers 9 2. LITERATURE REVIEW 2.1. INTRODUCTION The process of scouring in rivers and streams can result from natural phenomena or from man-made alterations (building of structures in the riverbed); both can produce effects over long reaches of the river or only locally. According to Breusers and Raudkivi (1991), the river scour can be divided into general, constriction and local scour. General scour occurs in a river or stream as the result of natural processes irrespective of whether a structure is located there. Constriction scour occurs if a structure causes narrowing the water course or flood plain rechannelling. Local scour results directly from the impact of a structure on the flow. This scour, which is a function of the type of structure, is superimposed on the general scour and on the constriction scour. For river bridges, these structures refer to abutments and pier-foundations (that include the case of the single piers, compound piers, complex piers among others). Scour may occur for two distinct sediment transport conditions: (1) under clear-water, i.e., in the absence of sediment movement in the bed of the approach channel; and (2) under live-bed, i.e., when generalized movement of the bed sediment occurs in the approach flow. The first condition corresponds to the bed shear stress being smaller or, at most, equal to the critical bed shear stress to beginning of sediment motion whereas for the second condition the bed shear stress is higher than the critical bed shear stress. Many researchers have attempted to understand and evaluate the process of local scour around bridge piers. Typically, the investigations have been made through either laboratory model studies or field investigations, with some disparities between them, the values obtained through laboratory tests tending to over-estimate the field values. One possible reason is that most of the design relationship for local scour depths were based on limited range of experiments and/or did not consider the various factors affecting scour process. As a result of these investigations, a large number of equations has been proposed for estimating equilibrium scour depth at bridge piers (see Sheppard et al., 2011). In this chapter, only the Auckland method (Melville and Coleman, 2000; Coleman, 2005), the FDOT method (Sheppard and Renna, 2010) and the HEC-18 method (Arneson et al., 2012) are taken into account since these three predictors are considered consolidated and applicable to complex bridge piers. These three methods present both equations for single and complex piers. This chapter is a review of the available and most relevant literature on the subject of local scour around bridge piers with non-cohesive material, where the clear-water condition is emphasized. The local scour around bridge piers depends strongly on the geometry of the pier. This reason is one that justifies the chapter being divided in local scour around single piers (section 2.2) and local scour around complex piers (section 2.3). The characteristic flow structure around those structures and the different mechanisms involved in the local scour phenomena caused are described in sections 2.2.1 and 2.3.1. Dimensional analyses are formulated in sections 2.2.2 and 2.3.2. Some aspects of the time dependent development phase of the scour process are treated in sections 2.2.3 and 2.3.3. The criteria used to stop the experimental tests are described in sections 2.2.4 and 2.3.4. According to dimensional Experimental Study of Local Scour around Complex Bridge Piers 10 analysis, the various dimensionless parameters that influence the scour process are discussed in sections 2.2.5 and 2.3.5. Those parameters are associated with the flow, the bed material and the pier geometry. And finally, the methods that engineers actually use for estimating the maximum scour depth at bridge piers are presented in sections 2.2.6 and 2.3.6. When presenting the methods, the symbols of some variables are changed and harmonized with the purpose of their comparison. 2.2. LOCAL SCOUR AROUND SINGLE PIERS 2.2.1 FLOW STRUCTURE Local scour at a single pier is attributable to the forces exerted on the bed by the complex, highly three-dimensional and unsteady flow field generated by the pier. The flow field is marked by turbulence structures with a wide range of scales, and by a pronounced downflow at the pier’s leading edge (Kirkil et al., 2009). The flow field in the scour hole around single piers has been studied in the last four decades, with a higher incidence in the last two. Research has been made mostly through experimentation with different techniques, e.g., flow visualization techniques (hydrogen-bubble, dyes, bentonite solution), Acoustic Doppler Velocimetry (ADV), Acoustic Doppler Velocity Profilers (ADVP) and Particle Image Velocimetry (PIV) in both plane and scoured beds under clear-water and live-bed conditions at cylindrical piers (reference obstacle). Numerical techniques like Large-Eddy Simulation (LES), Reynolds-Averaged Navier–Stokes (RANS), Detached-Eddy Simulation (DES) or hybrid RANS-LES can be used to reveal the flow field, its structures and interactions. The most relevant studies on flow field around cylindrical piers include the ones of Melville (1975), Melville and Raudkivi (1977), Morton and Evans-Lopez (1986), Dargahi (1989, 1990), Ahmed and Rajaratnam (1997, 1998), Graf and Istiarto (2002), Muzzammil and Gangadhariah (2003), Rao et al. (2004), Ettema et al. (2006), Zhao and Huhe (2006), Dey and Raikar (2007), Unger and Hager (2007), Link et al. (2008), Nogueira et al. (2008), Sadeque et al. (2008), Kirkil et al. (2008, 2009), Diab (2011), Khosronejad et al. (2012) and Radice and Tran (2012). The flow field at a single pier is a complex three-dimensional turbulent phenomenon resulting from strong flow-pier-sediment interaction, which increases with the development of the scour hole. According to the results of these studies, the basic mechanisms that cause local scour at cylindrical piers may be summarized as: 1. In the proximity of the pier, the flow velocity goes to zero on the upstream face of the pier. Due to the stagnation pressure in front of the pier, the water surface is raised, forming a surface roller, called bow wave, as shown in Figure 2.1. The particular pressure gradient produces descending trajectories (downflow) on the pier face. From those, the ones more close to the front face pier edges are deviated laterally. The resulting downflow acts like a vertical jet eroding a groove in front of the pier base and undermining the scour hole slope formed above, as shown in Figure 2.1. 2. The downflow rolls up again as it continues to create a hole and by interaction with the incoming flow forms a complex vortex system, called horseshoe vortex, as shown in Figure 2.2. This develops as a result of flow separation at the upstream face of the scour hole. The horseshoe vortex carries out the transport of eroded particles away past the pier. As the scour depth increases, the strength of the horseshoe vortex weakens, leading to a reduction of the scouring rate. The horseshoe vortex is part of a system of structures of turbulence that, together with the downflow and the flow acceleration close to the sides of the pier, are the prime erosive flow mechanisms. The turbulence structures (e.g., coherent structures in the Experimental Study of Local Scour around Complex Bridge Piers 11 form of necklace vortices, eddies shed in the separated shear layers, large-scale wake rollers) are not isolated from each other. They are intrinsically connected within the flow field. According to Zhao and Huhe (2006), the horseshoe vortex system contains a primary horseshoe vortex (1), a horseshoe vortex close to the pier base (2), and the secondary horseshoe vortices (3 to 6), as outlined in Figure 2.2(c). The scale of the horseshoe vortices increase with increasing scouring depth. 3. At the downstream face of the pier wake vortices appear by the separation of the flow at the sides of the pier and that are moved downstream by the approach flow. Both the horseshoe and the wake vortices erode sediment from the base region around the pier. The wake vortices work as miniature tornados lifting sediment from the bed and transporting it downstream by the flow. Figure 2.3 displays the wake vortex system at the downstream face of the pier observed in different pier studies. Figure 2.1 – Streamline plots of the flow at various times, adapted from Unger and Hager (2007) Figure 2.2 – (a) visualization of the vortex system inside the scour hole, adapted from Kirkil et al. (2008), (b) visualization of transverse section of the vorticity map, adapted from Nogueira et al. (2008) and (c) visualization of the horseshoe vortex system in a transversal section, adapted from Zhao and Huhe (2006) Experimental Study of Local Scour around Complex Bridge Piers 12 Figure 2.3 – Visualization of wake vortices at downstream of the pier made by: (a) Rao et al. (2004), (b) Ettema et al. (2006), (c) Sadeque et al. (2008) and (d) Kirkil et al. (2008) Figure 2.4 shows a present author interpretation of the flow structure around a single cylindrical pier, taking into account the previous description of the different components. Figure 2.4 – Flow structure around cylindrical bridge piers Few studies have been performed in recent years to evaluate the flow structure around non-circular piers. Those include the ones of Raikar and Dey (2008) and Diab et al. (2009, 2010). They carried out tests with square piers in order to characterize the development of the turbulent horseshoe vortex Experimental Study of Local Scour around Complex Bridge Piers 13 system flow in different stages of the scour process (including the equilibrium). The measurements were performed through an ADV. They analysed the size of the horseshoe vortex, the turbulence intensities and Reynolds stresses at different azimuthal planes. Additionally, Chang et al. (2010) described the main features of the flow field and turbulence structure in the vicinity of a rectangular pier at a small angle of attack. 2.2.2 DIMENSIONAL ANALYSIS As defined in many studies, as for example in Lança (2013), the maximum scour depth around single piers, 𝑑𝑠, at a given instant, 𝑡, can be described by the following set of independent variables and parameters: 𝑑𝑠=𝑓[flow (ℎ,𝑆𝑒,𝑔), fluid (𝜌,𝜇), bed material (𝑑50,𝜎𝑔,𝜌𝑠) pier (𝐷,𝐿,𝐾𝑆,𝜃), channel (𝐵,𝑆𝑜,𝐾𝑔), time (𝑡)] (2.1) where, ℎ = approach flow depth; 𝑆𝑒 = slope of energy line; 𝑔 = gravitational acceleration; 𝜌 = fluid density; 𝜇 = fluid dynamic viscosity; 𝑑50 = median size of sediment particle size distribution (such that 50% by weight are smaller); 𝜎𝑔 = geometric standard deviation of the sediment particle size distribution; 𝜌𝑠 = sediment density; 𝐷 = pier width; 𝐿 = pier length; 𝐾𝑆 = factor describing the shape of the pier; 𝜃 = pier alignment angle; 𝐵 = channel width; 𝑆𝑜 = channel bottom slope; 𝐾𝑔 = factor describing the geometry of the channel cross-section; 𝑡 = time. Figure 2.5 shows the scheme of a single pier with the respective variables described above. Figure 2.5 – Set of variables describing the scour process with influence in the scour depth at a single pier It should be noted that the critical velocity for sediment entrainment, 𝑈𝑐, is not considered since it is fully defined by ℎ, 𝑆𝑒, 𝑔, 𝜌, 𝜇, 𝑑50 and 𝜌𝑠. For uniform flows, 𝑆𝑒=𝑆𝑜, the friction velocity, 𝑢∗, is given by 𝑢∗=√𝑔𝑅𝑆𝑒=√𝑔𝑅𝑆𝑜, where 𝑅=𝜑(𝐵,ℎ,𝐾𝑔) is the hydraulic radius of the flow crosssection and 𝜑 stands for functional relationship. Since the sediment submerged density of the flow is given by Δ=(𝜌𝑠−𝜌)𝜌 ⁄, equation (2.1) can be written as 𝑑𝑠=𝜑(𝜎𝑔,Δ,𝐾𝑆,𝜃,𝐾𝑔,ℎ,𝑑50,𝐷,𝐿,𝐵,𝑢∗,𝑔,𝜌,𝜇,𝑡) (2.2) Choosing 𝐷, 𝑢∗ and 𝜇 for basic variables and applying the Vaschy-Buckingham theorem, equation (2.2) becomes Experimental Study of Local Scour around Complex Bridge Piers 20 uniform material (𝜎𝑔≤1.50), 30≤𝐷𝑑50 ⁄≤100 and ℎ/𝐷≥2. The data with these experimental conditions were selected in order to minimize the influence of other effects. The figure includes data by Ettema (1976, 1980), Jain and Fischer (1979), Chee (1982), Chiew (1984), Melville (1984), Ettema et al. (1998a), Melville and Chiew (1999), Lee and Sturm (2009), Simarro et al. (2011), Lança et al. (2013b), Lopez et al. (2014) and unpublished data by Jones (reported by Sheppard et al., 2011). Figure 2.8 – Equilibrium scour depth as a function of velocity, for comparatively coarse uniform bed sediment For very low velocities, scour does not develop around obstacles and the bed behaves as if it was fixed. According to Melville and Chiew (1999), the scouring process begins long before the approach velocity is strong enough to initiate sediment transport, at about 40% of the threshold velocity of the bed sediment, as shown in Figure 2.8. In clear-water conditions, the relative scour depth, 𝑑𝑠𝑒/𝐷, increases as the relative approach velocity, 𝑈/𝑈𝑐, is increased until the former reaches a maximum of about 2.6 times the pier diameter at critical velocity, i.e., 𝑈/𝑈𝑐=1. The maximum scour depth is called the threshold peak. According to Melville (2008), in live-bed conditions, after 𝑈/𝑈𝑐>1, 𝑑𝑠𝑒/𝐷 first decreases with the relative approach velocity and then increases again to a second peak, these changes being relatively small, but the threshold peak is not exceeded providing the sediment is uniform. The second peak occurs at about the transition flatbed stage of sediment transport on the channel bed and is termed the live-bed peak, as shown in Figure 2.8 (represented by the envelope curve in the range 1<𝑈/𝑈𝑐<5). The scour depth variations under live-bed conditions are a consequence of the size and steepness of the bed features occurring at particular flow velocities (Chee, 1982; Chiew, 1984; Melville, 1984). The steeper and higher the bed forms, the lesser the observed scour depth because the sediment supplied with the passage of a given bed form is not fully removed from the scour hole prior to the arrival of the next bed form. The live-bed peak occurs at about the transition flatbed condition when the bed forms are very long and of negligible height. Antidunes dissipate some energy at higher velocities and the local scour depth appears to decrease again. The magnitude of the scour depth fluctuations due to bed-form migration is approximately equal to the half-amplitude of the bed forms, indicating that the scour depth due to bed forms is about one-half the bed-form height (Chee, 1982; Chiew, 1984). The higher values of 𝑑𝑠𝑒/𝐷 obtained by Jain and Fischer (1979) for the range 2.0<𝑈/𝑈𝑐<3.5 in comparison to the corresponding values for the other three live-bed studies considered (Chee, 1982; Chiew, 1984; Melville, 1984) (Figure 2.8) may be associated to differences in the scour measuring technique used in the studies. Experimental Study of Local Scour around Complex Bridge Piers 21 2.2.5.3 Sediment grading effect Variations of the particle size distribution of the bed sediment (i.e., 𝜎𝑔=√𝑑84/𝑑16) can have a significant influence on equilibrium scour depths around bridge piers. Ettema (1976) and Chiew (1984) carried out tests under clear-water conditions for different values of 𝜎𝑔 in order to evaluate the effect of nonuniform sediments on 𝑑𝑠𝑒/𝐷. Both researchers observed a decrease in 𝑑𝑠𝑒/𝐷 values with increasing values of 𝜎𝑔. The reduction in scour depths is attributed to armouring of the scour hole by coarser particles in the original bed mixture. Figure 2.9(a) plots 𝑑𝑠𝑒/𝐷 as a function of 𝜎𝑔 for laboratory data obtained from some researchers with cylindrical piers, 𝑑50≥0.6 mm, ℎ/𝐷≥2, 0.8≤𝑈/𝑈𝑐≤1.0 and 30≤𝐷𝑑50 ⁄≤100. The data with these experimental conditions were selected in order to minimize the influence of other effects. The figure includes data by Ettema (1976, 1980), Chiew (1984), Melville and Chiew (1999), Lee and Sturm (2009), Simarro et al. (2011) and Lança et al. (2013b). According to Figure 2.9(a), 𝑑𝑠𝑒 𝐷 ⁄ decreases with 𝜎𝑔 for 𝜎𝑔>1.50 until a minimum value of approximately 0.48 for 𝜎𝑔=5.5. The relative equilibrium scour depth, 𝑑𝑠𝑒 𝐷 ⁄, may be considered constant for 𝜎𝑔≤1.50. For nonuniform bed mixtures (𝜎𝑔>1.50), selective sediment transport of the finer particles typically occurs for flow velocities smaller than the critical velocity of beginning of motion associated with 𝑑50. The selective sediment transport leads to the formation of a superficial armour layer composed of the courser grains that finally inhibits sediment transport as well as the formation of scour holes (at least partly). Consequently, the maximum scour depth is not observed for 𝑈≈𝑈𝑐, where 𝑈𝑐 is the critical velocity associated with the median size grains, 𝑑50, of the mixture. In those cases, the maximum scour depth is observed for the live-bed peak (Figure 2.8), where the velocity triggers the rupture of the armour layer guaranteeing the displacement of the coarse grains. Figure 2.9 – Equilibrium scour depth as a function of the geometric standard deviation of sediment sizes for tests under: (a) clear-water conditions and (b) live-bed conditions Figure 2.9(b) shows the results of the studies conducted by Chiew (1984) and Baker (1986) under livebed conditions. The values of 𝑑𝑠𝑒/𝐷 plotted in the figure correspond to values observed at the live-bed peak. In the figure a decrease in 𝑑𝑠𝑒/𝐷 values with increasing values of 𝜎𝑔 is again observed; however, this effect is not as marked as in the case of clear-water conditions, represented by the envelope curve of Figure 2.9(a). Experimental Study of Local Scour around Complex Bridge Piers 22 2.2.5.4 Sediment coarseness effect The effect of relative sediment size (defined by the ratio 𝐷𝑑50 ⁄) on the equilibrium scour depth is also reported as “sediment coarseness effect”. For several decades, most researchers (e.g., Raudkivi and Ettema, 1983; Melville and Sutherland, 1988; Melville and Coleman, 2000) have successively assumed that 𝑑𝑠𝑒/𝐷 would be unaffected by 𝐷𝑑50 ⁄ for values of 𝐷𝑑50 ⁄>100. This may be justified by the fact that the tests in these studies were performed for a narrow range of 𝐷𝑑50 ⁄. In the last decade, studies by Sheppard et al. (2004, 2014), Lee and Sturm (2009), Sheppard and Renna (2010) and Lança et al. (2011, 2013b) have shown that the relative sediment size can significantly affect the scour depth even for 𝐷𝑑50 ⁄>100. The tests of these studies were performed for large values of 𝐷𝑑50 ⁄ (up to 4168). According to these studies, 𝑑𝑠𝑒/𝐷 decreases with increasing 𝐷𝑑50 ⁄, for 𝐷𝑑50 ⁄>100, as shown in Figure 2.10. This figure plots 𝑑𝑠𝑒/𝐷 as a function of 𝐷𝑑50 ⁄ for laboratory data with cylindrical piers, 𝜎𝑔≤1.50, 0.8≤𝑈/𝑈𝑐≤1.0 and ℎ/𝐷≥2. The data with these experimental conditions were selected in order to minimize the influence of other effects. The figure includes data by Ettema (1976, 1980), Chiew (1984), Ettema et al. (1998a), Sheppard et al. (2004), Lee and Sturm (2009), Simarro et al. (2011) and Lança et al. (2013b). Due to experimental limitations, i.e., dimensions of laboratory facilities, a small number of tests that comply with the mentioned experimental conditions for 𝐷𝑑50 ⁄>300 can be observed. For this reason, in this range, experimental data with fine sands (𝑑50<0.6 𝑚𝑚) and coarse sands with 1.0≤ℎ/𝐷≤1.5 are also included in the figure for completeness (pointed out by two ellipses, respectively). Figure 2.10 – Equilibrium scour depth as a function of bed material size Figure 2.10 shows that the maximum scour depth occurs in the range of 30<𝐷𝑑50 ⁄<100 in which the material size does not influence the scour depth. According to the envelope curve of the scour data plotted in Figure 2.10, the effect of 𝐷𝑑50 ⁄ on local scour depth can be identified and separated in three zones. In Zone 1 (𝐷𝑑50 ⁄<30) the sediment is coarse relative to pier diameter. A significant proportion of the energy of the downflow is dissipated in the coarse bed material at the base of the scour hole. In Zone 2 (100>𝐷𝑑50 ⁄>30) the sediment is of an intermediate size. The sediment is entrained mainly from the groove with only a limited entrainment under the horseshoe vortex. The supply of sediment to the groove is accomplished by sliding down the lateral slope in the hole. In Zone 3 (𝐷𝑑50 ⁄>100) the sediment is fine relative to pier diameter. The sediment is entrained from the groove by the downflow and from the hole slope by the horseshoe vortex until equilibrium is reached. These definitions were based on zone descriptions by Raudkivi and Ettema (1983). Experimental Study of Local Scour around Complex Bridge Piers 23 2.2.5.5 Flow shallowness effect The effect of the approach flow depth in relation to the pier size (defined by the ratio ℎ/𝐷) on the equilibrium scour depth is also reported as “flow shallowness effect”. Melville and Coleman (2000) compiled the experimental data of several researchers (some of these data for short durations) to study the effect of ℎ/𝐷 on 𝑑𝑠𝑒/𝐷. According to results of those studies, Melville and Coleman (2000) suggest that for shallow flows compared to the pier size (wide piers), the scour depth increases proportionately with the flow depth and is independent of the pier size. Conversely, for deep flows compared to the pier size (narrow piers), the scour depth increases proportionately with pier size and is independent of the flow depth; while for intermediate depth flows, the scour depth depends on both flow depth and pier size. These three trends are clearly defined by the envelope curve of the experimental data in Figure 2.11, where wide piers are characterized by ℎ𝐷 ⁄<0.2 while narrow piers are associated to ℎ𝐷 ⁄>2.0. The figure plots 𝑑𝑠𝑒/𝐷 as a function of ℎ/𝐷 for laboratory data with cylindrical piers, 𝑑50≥0.6 mm, 𝜎𝑔≤1.50, 0.8≤𝑈/𝑈𝑐≤1.0 and 30≤𝐷𝑑50 ⁄≤100. The data with those experimental conditions were selected in order to minimize the influence of other effects. The figure includes data by Ettema (1980), Chiew (1984), Graff (1995), Ettema et al. (1998a), Melville and Chiew (1999), Sheppard et al. (2004), Lee and Sturm (2009), Simarro et al. (2011), Lança et al. (2013b) and unpublished data by Coleman (reported by Sheppard et al., 2011). Due to the limited number of tests that comply with the mentioned conditions for ℎ𝐷 ⁄<0.5, tests with coarse sands and 𝐷𝑑50 ⁄>300 are also included in the figure for completeness (pointed out by an ellipse). Figure 2.11 – The influence of flow shallowness on equilibrium scour depth According to Melville (2008), the scour process at wide piers features a zone of slow moving fluid existing ahead of the pier on the line of symmetry. In this zone, scour activity is reduced and the central portion of the width of the pier is ineffective in generating scour. In deeper flows, the strength of the horseshoe vortex and associated downflow is related to the transverse size of the pier. For intermediate size piers (or intermediate flow depths), flow depth influences local scour depth when the horseshoe vortex is affected by the formation of the surface roller. The two vortices have opposite directions of rotation. In principle, so long as they do not interfere with each other, the local scour depth is independent of flow depth, which is the case of narrow piers. With decreasing flow depth, the surface roller becomes more dominant and renders the horseshoe vortices less capable of entraining sediment. Thus, the local scour depth is reduced for shallower flows. Experimental Study of Local Scour around Complex Bridge Piers 24 2.2.5.6 Viscosity effect Most of the important works on local scouring at single piers (e.g., Ettema, 1980; Chiew, 1984; Melville and Chiew, 1999; Oliveto and Hager, 2002; Sheppard et al., 2004; Lança et al., 2013b) do not consider the influence of viscosity on their experiments. The assumption seems to be that the flow is fully rough turbulent inside the scour hole, i.e., free of viscous effects, due to the presence of highly turbulent flow structures irrespective of the approach flow regime. In contrast, few studies (Shen et al., 1969; Nicollet and Ramette, 1971; Lança et al., 2015) indicate that the equilibrium scour depth depends on the pier Reynolds number, 𝑈𝐷/𝜐, or on the sediment Reynolds number, 𝑈𝑑50/𝜐, parameters that consider the effect of viscosity. Figure 2.12 plots 𝑑𝑠𝑒/𝐷 as a function of 𝑈𝑑50/𝜐 for laboratory data obtained by Nicollet and Ramette (1971) and Lança et al. (2013b, 2015) with cylindrical piers, 𝑑50≥0.6 mm, ℎ/𝐷≥1.5 and 30≤ 𝐷𝑑50 ⁄≤100. The data with these experimental conditions were selected in order to minimize the influence of other effects. The data obtained by Shen et al. (1969) were not considered by the fact that these have a strong influence of sediment coarseness parameter, since 𝐷𝑑50 ⁄=633. The figure shows (1) that scouring is independent of the sediment Reynolds number for 200<𝑈𝑑50/𝜐<300 and (2) a slight decrease of the dimensionless scour depth as the sediment Reynolds number increases for 𝑈𝑑50/𝜐>300. In turn, a slight increase of 𝑑𝑠𝑒/𝐷 with increase ℎ/𝐷 is observed. Figure 2.12 – Equilibrium scour depth as a function of the sediment Reynolds number 2.2.5.7 Pier shape effect The shape effect is usually accounted for through the coefficient 𝐾𝑆 that is the ratio between the maximum scour depth at a pier of a given shape and the maximum scour depth at the cylindrical pier (standard obstacle) for otherwise equal conditions of the approach flow and bed material. Figure 2.13 shows the comparison of the scour holes around two piers, each with different shape, measured in tests with the same bed granulometry and flow conditions. Figure 2.13(a) corresponds to the case of a cylindrical pier and Figure 2.13(b) corresponds to the case of a square pier. According to those results, both the area of the scour hole and the maximum scour depth have higher values for the square pier compared to the cylindrical pier. This is due to the fact that the square pier shape: (1) alters significantly more the surrounding streamlines of the flow around the obstacle; and (2) slightly increases the magnitude of the downflow, the size of the horseshoe vortex and the vorticity, as compared with the cylindrical pier shape. The maximum scour depth observed at the square pier (Figure 2.13(a)) is approximately 1.23 times the corresponding depth at the cylindrical pier (Figure 2.13(b)). Experimental Study of Local Scour around Complex Bridge Piers 25 Figure 2.13 – Scour holes around different pier shapes: (a) cylindrical pier (adapted from Rey and Raikar, 2007) and (b) square pier (adapted from Raikar and Dey, 2008) Factors to account for pier shapes other than cylindrical have been published by many researchers (e.g., Tison, 1940; Chabert and Engeldinger, 1956; Laursen and Toch, 1956; Dietz, 1972; Diab, 2011; Fael et al., 2014). Figure 2.14 shows the variation of shape factors 𝐾𝑆 with the relation 𝐿/𝐷 (𝐿= pier length) for four common pier shapes: (1) rectangular (Figure 2.14(a)); (2) rectangular round-nose or oblong (Figure 2.14(b)); (3) lenticular (Figure 2.14(c)); and (4) elliptic (Figure 2.14(d)). Figure 2.14 – Shape factor (KS) as a function of L/D for: (a) rectangular piers, (b) rectangular round-nose or oblong piers, (c) lenticular piers and (b) elliptic piers The values apply to piers aligned with the flow and are referenced to a value of 𝐾𝑆=1.0 for cylindrical piers. The curve fit of the experimental data is also included in each figure. It is clear that the influence of 𝐿/𝐷 on the estimation of factor 𝐾𝑆 is minor for rectangular (square-nose) and Experimental Study of Local Scour around Complex Bridge Piers 26 rectangular round-nose pier shapes and is higher for lenticular and elliptic pier shapes. Values of the factor 𝐾𝑆 for other shape piers (not so common) were compiled by Melville and Coleman (2000). 2.2.5.8 Pier alignment effect The effect of pier alignment is important when the shape of the pier is different from cylindrical. The alignment angle, 𝜃, corresponds to the angle defined between the pier axis and the flow direction at a plane parallel to the channel bottom, as shown in Figure 2.5. The two schemes in Figure 2.15 represent the scour hole formed around one rectangular pier aligned to the same direction of the flow and another scour hole formed around the same pier but oriented in an angle 𝜃 with the flow direction. Figure 2.15 – Schemes of the scour hole in relation with the pier alignment angle Figure 2.16 shows diagrams of scour hole around rectangular piers oriented in different angles to flow direction. The shape of the hole is a function of pier orientation angle and 𝐿/𝐷 ratio. The point of maximum depth changes with the variation of the pier orientation angle. According to Ettema et al. (1998b) the scour process starts at locations of greatest velocity and vorticity at the pier corners, and then envelops the entire pier. Figure 2.16 – Diagrams of scour hole around rectangular piers oriented in different angles to flow direction The effect of the alignment angle of bridge piers in the scour depth developed around those piers has been initially evaluated by Laursen and Toch (1956). This effect is considered through the alignment factor, 𝐾𝜃. This factor relates the scour depth associated to a given 𝜃 with the scour depth at the same pier for 𝜃 = 0º. The pier alignment factors (𝐾𝜃) obtained by Ettema et al. (1998b) and Fael et al. (2014), for rectangular piers with different angles and 𝐿/𝐷 ratios, are presented in Figure 2.17. Experimental Study of Local Scour around Complex Bridge Piers 27 Figure 2.17 – Local scour depth variation with pier alignment (rectangular piers) From Figure 2.17, it is evident that 𝐾𝜃 increases when 𝐿/𝐷 increases. This may be justified by the fact that the area of the pier exposed to the flow, for a particular angle, increases for larger 𝐿/𝐷 ratios. In turn, for each 𝐿/𝐷 ratio, the factor 𝐾𝜃 increases with increasing 𝜃 until 𝐾𝜃 attains a maximum value. According to Ettema et al. (1998b), a maximum occurs when the projected width of the pier is largest, which occurs when 𝜃=𝑡𝑎𝑛−1(𝐿/𝐷) for a skewed rectangular pier. 2.2.6 METHODS FOR ESTIMATION OF LOCAL SCOUR DEPTHS 2.2.6.1 Auckland Method Melville and Coleman (2000) compiled the information of some researchers, most of those from the Auckland University (e.g., Ettema, 1976; Raudkivi and Ettema, 1977; Breusers et al., 1977; Ettema, 1980; Raudkivi and Sutherland, 1981; Chee, 1982; Chiew, 1984; Raudkivi, 1986), and formulated a method to predict the maximum scour depth at pier foundations (i.e. abutments, single piers, nonuniform piers). The method is based in the design method proposed by Melville and Sutherland (1988), established on the basis of a large set of experimental data that included wide variations in flow velocity and depth, sediment size and gradation, and pier size, shape, and alignment. According to Melville and Coleman (2000) the design method is supported on the following relation for the equilibrium depth of local scour: 𝑑𝑠𝑒=𝐾ℎ𝐷𝐾𝐼𝐾𝑑𝐾𝑆𝐾𝜃 (2.20) where 𝑑𝑠𝑒 = equilibrium scour depth; 𝐾ℎ𝐷, 𝐾𝐼, 𝐾𝑑, 𝐾𝑆 and 𝐾𝜃 are the factors that account for the depth-pier size, flow intensity, sediment coarseness, pier shape, and pier alignment, respectively. Variables 𝑑𝑠𝑒 and 𝐾ℎ𝐷 correspond dimensionally to a length, while the other 𝐾’s are dimensionless. The depth-pier size factor can be expressed by the following expression: 𝐾ℎ𝐷= { 2.4𝐷 for ℎ𝐷>1.43 2√𝐷×ℎ for 0.2<ℎ𝐷<1.43 4.5ℎ for ℎ𝐷<0.2 (2.21) Experimental Study of Local Scour around Complex Bridge Piers 28 where 𝐷 = single pier width; ℎ = flow depth directly upstream of the pier. The flow intensity factor can be expressed by the following equation: 𝐾𝐼= { 𝑈 𝑈𝑐 for 𝑈 𝑈𝑐<1 1.0 for 𝑈 𝑈𝑐≥1 (2.22) where 𝑈 = mean velocity of flow directly upstream of the pier; 𝑈𝑐 = critical flow velocity. The sediment coarseness factor can be expressed by the following equation: 𝐾𝑑= { 0.57𝑙𝑜𝑔(2.24𝐷 𝑑50) for 𝐷 𝑑50≤25 1.0 for 𝐷 𝑑50>25 (2.23) where 𝑑50 = median size of sediment particle size distribution. The pier shape factor should be estimated according to Figure 2.14 for rectangular, oblong, rectangular round-nose, lenticular and elliptic shapes. For cylindrical shape, 𝐾𝑆 should be considered as 1.0. The pier alignment factor can be calculated by: 𝐾𝜃=(𝐿𝐷𝑠𝑖𝑛𝜃+𝑐𝑜𝑠𝜃)0.65 (2.24) where 𝜃 = pier alignment angle; 𝐿 and 𝐷 are the dimensions of the pier. For circular piers, 𝐾𝜃=1.0. If 𝐿/𝐷 is larger than 12, the value of 𝐿/𝐷 = 12 should be used in equation (2.24). According to experimental data reported in section 2.2.5, the Auckland method provides higher values of factor 𝐾𝐼 for clear-water conditions and it does not consider the reduction effect on factor 𝐾𝑑 for 𝐷/𝑑50>100. 2.2.6.2 FDOT Method Sheppard and Renna (2010) presented a method to predict the maximum scour depth at single piers for the Florida Department of Transportation (FDOT). This method is based on different studies developed by Sheppard at Florida University since 1995 (e.g., Sheppard, 1999; Pritsivelis, 1999; Jones and Sheppard, 2000b; Sheppard et al., 2000, 2004). These studies were performed with experimental tests in four different Laboratories (three in US: University of Florida in Gainesville, Florida, Colorado State University in Fort Collins, Colorado, and the Conte USGS-BRD Laboratory in Turners Falls, Massachusetts; the fourth, University of Auckland in Auckland, New Zealand). According to Sheppard et al., (2014), the scour depth predictor in clear-water conditions is: 𝑑𝑠𝑒 𝐷𝑒=2.5𝐾ℎ𝐷𝑒𝐾𝐼𝐾𝑑 (2.25) Experimental Study of Local Scour around Complex Bridge Piers 29 where 𝑑𝑠𝑒 = equilibrium scour depth; 𝐷𝑒 = equivalent diameter of the pier; 𝐾ℎ𝐷𝑒 = flow shallowness factor; 𝐾𝐼 = flow intensity factor; 𝐾𝑑 = sediment size factor. The scour at single structures with shapes different from the circular can be analysed using their “equivalent diameter”, 𝐷𝑒. The equivalent diameter is the diameter of a circular pier that will experience the same equilibrium scour depth of the single pier in study under the same sediment and flow conditions. This is defined as: 𝐷𝑒=𝐾𝑆𝑊𝑝 (2.26) where 𝐾𝑆 = pier shape factor; 𝑊𝑝 = projected width of the pier. The variable 𝐾𝑆 can be calculated by 𝐾𝑆={1 for circular piers 0.86+0.97(|𝜃−𝜋4|)4 for rectangular piers (2.27) where 𝜃 = flow skew angle in radians. The flow shallowness factor can be expressed by the following expression 𝐾ℎ𝐷𝑒=tanh[(ℎ 𝐷𝑒)0.4] (2.28) where ℎ = flow depth directly upstream of the pier. The flow intensity factor can be expressed by the following expression 𝐾𝐼=1−1.2[ln(𝑈 𝑈𝑐)]2 for 0.4<𝑈 𝑈𝑐≤1 (2.29) where 𝑈 = mean velocity of the flow directly upstream of the pier; 𝑈𝑐 = critical flow velocity. The sediment coarseness factor can be expressed by the following equation 𝐾𝑑=(𝐷𝑒 𝑑50) 0.4(𝐷𝑒 𝑑50)1.2+10.6(𝐷𝑒 𝑑50)−0.13 (2.30) where 𝑑50 = median size of sediment particle size distribution. 2.2.6.3 HEC-18 Method The HEC-18 method was developed by the Hydrologic Engineering Center of the Federal Highway Administration (FHWA) in the United States of America. This method is based on the laboratory data of circular piers by Chabert and Engeldinger (1956) and Shen et al. (1969). HEC-18 method has been modified by Richardson and Davis (1995, 2001) and Arneson et al. (2012). The equation for Experimental Study of Local Scour around Complex Bridge Piers 36 In position (1), characterized by the bottom of the pile cap being out of the water, the scour depth time evolution at complex piers corresponds to the temporal evolution observed around pile groups, as shown in Figure 2.23. Figure 2.23 – Temporal evolution of scour depth at pile groups, adapted from Lança et al. (2013a) According to Lança et al. (2013a), when the pile group is aligned to the flow, the scour process begins in front of each pile, with individual holes, until they merge into one single global scour hole due to interaction of the flow structure around the piles (with the presence of the four mechanisms before mentioned – scour reinforcement, sheltering, wake vortices interaction and compressed horse-shoe vortices). The maximum scour depth is located in front of the upstream pile of the group. On the contrary, the maximum scour depth can be located in the middle or the downstream piles, when the pile group is not aligned with the flow. In position (2), characterized by the pile cap being partially immersed in the water, the scour depth evolution is similar to that observed in the position (1), in which the scour process occurs in front of the piles. In position (3), characterized by the pile cap under the water and above the bed, the trend of the temporal evolution of the sour depth is similar to that observed in the first two positions, as shown in Figure 2.24. According to Sousa (2007), the presence of the three components of the complex pier in the flow leads to an increase of the scour rate and of the respective scour depth. The maximum scour depth is identified in front of the upstream piles. Figure 2.24 – Temporal variation of scour depth at complex piers in position (3), adapted from Sousa (2007) Experimental Study of Local Scour around Complex Bridge Piers 37 In position (4), characterized by the pile cap being partially buried in the bed, the scour process starts at the front of the pile cap, and depending of the pile cap thickness and the partially buried depth, the scour may migrate below the pile cap towards the frontal piles (Ferraro et al. 2013), as shown in Figure 2.25. According to Ataie-Ashtiani et al. (2010) and Ferraro et al. (2013), for complex pier where the top of the pile cap is close to the initial bed level, i.e., position (5), the scour process is similar to the above described for position (4). Figure 2.25 – Scour depth time evolution at complex piers in position (4), adapted from Ferraro et al. (2013) According to Ferraro et al. (2013), once the pile cap is entirely buried, i.e., position (6) of Figure 2.22, the scour starts at the column side or in front of the column until the scour hole partly uncovers the top of the pile cap. Next, the scour depth remains unchanged for a while, with a value equal to the depth of the top of the pile cap below the initial bed level. That stage ends with the scour process continuing in front of the pile cap, as shown in Figure 2.26. This description of the scour depth evolution is in accordance with the results obtained by various researchers in studies of cylindrical columns founded on cylindrical caissons (e.g., Melville and Raudkivi, 1996; Umeda et al., 2010; Lu et al., 2011; Kothyari and Kumar, 2012). Figure 2.26 – Scour depth time evolution at complex piers in position (6), adapted from Ferraro et al. (2013) In position (7), characterized by the pile cap remaining buried below the bottom of the scour hole, the scour depth time evolution is similar to the one observed for single piers, as shown in Figure 2.7. Experimental Study of Local Scour around Complex Bridge Piers 38 2.3.4 EQUILIBRIUM SCOUR DEPTH IN LABORATORY TESTS As mentioned in section 2.2.4 for single piers, it can be assumed that the equilibrium scour exists and it is achieved in infinite time. Again the question is which should be the minimum duration of the experimental tests, with complex piers, to achieve equilibrium conditions. In this regard, some authors (e.g., Coleman, 2005; Melville et al., 2006; Ataie-Ashtiani et al., 2010) suggest the same criterion proposed by Melville and Chiew (1999) for experimental tests with single piers, as was described in section 2.2.4. The mentioned authors use, as reference, the smaller value of 5% of the complex pier characteristic length (e.g., its equivalent pier diameter) and of the flow depth. In the case of pile groups, Lança et al. (2013a) suggest that the duration of scour tests should be more than 7 days, which is the duration considered adequate for single cylindrical piers (according to Simarro et al., 2011), since the scouring process can be expected to be more complex and slower. 2.3.5 EFFECTS OF SPECIFIC PARAMETERS ON MAXIMUM LOCAL SCOUR DEPTH 2.3.5.1 Framework As mentioned in section 1.1, few studies on scouring at complex piers under clear-water conditions were performed in recent years. The next five were identified: (1) Coleman (2005); (2) Ataie-Ashtiani et al. (2010); (3) Grimaldi and Cardoso (2010); (4) Ferraro et al. (2013); and (5) Amini et al. (2014). A total of thirteen complex pier models were analysed in these five studies, as shown in Table 2.2. The values of the most important control variables characterizing the set of tests performed with those models are summarized in Table 2.2. For each model the number of tests (each corresponding to a pile-cap position in relation to the initial bed level) and the test durations, 𝑡𝑑, are also included. In all the thirteen experimental models coarse sand (𝑑50≥0.6 mm) was used, accounted for being insusceptible to the formation of ripples in the approach flow reach. Table 2.2 – Experimental models: flow parameters, bed granulometry parameters and duration of the tests Study Model Nº tests 𝑩 (m) 𝑼 (m/s) 𝑼𝒄 (m/s) 𝒉 (m) 𝒅𝟓𝟎 (mm) 𝒕𝒅 (days) Coleman (2005) Co1 11 1.50 0.33 0.44 0.60 0.84 NS Co2 11 1.50 0.37 0.44 0.60 0.84 NS Co3 8 1.50 0.34 0.41 0.33 0.84 NS Ataie-Ashtiani et al. (2010) AA1 39 0.60 0.22-0.26 0.30-0.31 0.13-0.16 0.60 0.4-3.1 AA2 22 0.60 0.23-0.26 0.30-0.34 0.14-0.16 0.60 0.4-2.1 Grimaldi and Cardoso (2010) GC 12 0.70 0.28 0.30 0.10 0.83 4.8-18.1 Ferraro et al. (2013) Fe1 10 0.70 0.27 0.30 0.10 0.83 8.3-37.0 Fe2 11 0.70 0.27 0.30 0.10 0.83 3.2-41.2 Amini et al. (2014) A1 7 1.52 0.36 0.38 0.24 0.80 1.0 A2 7 1.52 0.36 0.38 0.24 0.80 1.0 A3 13 1.52 0.36 0.38 0.24 0.80 1.0 A4 13 1.52 0.36 0.38 0.24 0.80 1.0 A5 16 1.52 0.36 0.38 0.24 0.80 1.0 Note: NS = not specified. Experimental Study of Local Scour around Complex Bridge Piers 39 Figure 2.27 shows the dimensions of the thirteen complex pier models identified in the literature. Figure 2.27 – Dimensions of complex pier models used in the five studies from literature Experimental Study of Local Scour around Complex Bridge Piers 40 2.3.5.2 Relative column position The experimental range of all thirteen models reported in the literature (Table 2.2) covered the three pile-cap situations (see Figure 2.22) by considering different values of 𝐻𝑐/ℎ. The measured scour depth values, 𝑑𝑠, are plotted against 𝐻𝑐/ℎ (considered negative when the top of the pile cap is below the initial bed level) in Figure 2.28 for the test series in the mentioned thirteen models. Each chart of the figure includes: (1) two vertical lines at 𝐻𝑐/ℎ=0 and 𝐻𝑐/ℎ=𝑇/ℎ, which are used to delimit the regions associated to the three mentioned situations; and (2) the envelope curve of the experimental scour data. Although some of the tests performed with the thirteen models analysed were of short duration, those allowed to characterize qualitatively the variation of the scour depth with the relative column position. Figure 2.28(a) shows a schematic conceptual variation of 𝑑𝑠 with 𝐻𝑐/ℎ, distinguishing five different defining zones and stages: (1) the scour depth is only influenced by the pile group; (2) the increment of the scour depth is associated with the presence of the column and pile cap in the flow (increasing the area exposed to the flow); (3) the reduction in the scour depth, from the maximum value, is due to the pile cap overhang dimension tendency to weaken the flow structure (e.g., downflow, horseshoe vortices); (4) the increment in the scour depth values is due to this depth being controlled by the position of the top of the pile cap (on decreasing 𝐻𝑐/ℎ ratio); and (5) the scour depth is only influenced by the column. Analysing the Figure 2.28, it could be concluded that the 𝑑𝑠 variation in ten of the thirteen models is analogous of that Figure 2.28(a), i.e., being possible to identify the five stages with exception of Model Fe2 (Figure 2.28(i)), Model A1 (Figure 2.28(j)) and Model A2 (Figure 2.28(k)). This may be justified by the fact that: (1) the Model Fe2 has a thin pile-cap thickness, implying no contribution of the pile cap on the scour depth; (2) the Model A1 has a column width close to the pile cap width (𝐷𝑐/𝐷𝑝𝑐=0.80), in which the 𝑑𝑠 variation is similar to that observed by Martin-Vide et al. (1998) in a pier founded on an alignment of piles; and (3) the Model A2 has also a large 𝐷𝑐/𝐷𝑝𝑐 ratio (0.73). From the results of Figure 2.28 it can be concluded that the 𝑑𝑠 variation with 𝐻𝑐/ℎ depends also on the parameters 𝐷𝑐/𝐷𝑝𝑐 and 𝑇/ℎ as well as the shape of the three complex pier components. The comparison of the envelope curves in Models GC (Figure 2.28(g)) and Fe1 (Figure 2.28(h)) suggests that similar column and pile-cap configuration sets with circular or round-nose rectangular shape are leading to similar scour depth values since the widths of these two components are equal, as shown in Figure 2.27. These findings are in agreement with those obtained in Figure 2.14 for single piers. Experimental Study of Local Scour around Complex Bridge Piers 41 Figure 2.28 – Scour depth as function of the relative column position Experimental Study of Local Scour around Complex Bridge Piers 42 2.3.5.3 Relative column width Few studies have been performed to evaluate the effect of the relative column width, 𝐷𝑐/𝐷𝑝𝑐 (relation between the column and the pile cap widths), on the maximum scour depth. This effect has been studied in compound foundations: (1) rectangular columns founded on rectangular caissons (e.g. Jones et al., 1992; Parola et al., 1996); and (2) cylindrical columns founded on cylindrical caissons (e.g., Melville and Raudkivi, 1996; Umeda et al., 2010; Lu et al., 2011). These authors concluded that the scour depth depends on the caisson extension lengths beyond the external face of the column (represented in the correspondent studies geometries by 𝐷𝑐/𝐷𝑝𝑐) and the relative column position, 𝐻𝑐/ℎ. Data obtained by Melville and Raudkivi (1996) were selected and the representation of their results was rearranged with the purpose of highlighting the effect of 𝐷𝑐/𝐷𝑝𝑐, as shown in Figure 2.29. It is clear that the scour depth increases with the increment of the ratio 𝐷𝑐/𝐷𝑝𝑐. Regarding studies on complex piers, the effect of 𝐷𝑐/𝐷𝑝𝑐 on 𝑑𝑠 has been analysed in the work of Coleman (2005), Sheppard and Renna (2010), Ataie-Ashtiani et al. (2010) and Arneson et al. (2012). Coleman (2005) used the results of Melville and Raudkivi (1996), in relation to the effect of 𝐷𝑐/𝐷𝑝𝑐 and 𝐻𝑐 on 𝑑𝑠, to suggest a predictor to calculate the local scour at complex piers when the pile cap is partially buried in the bed. Comparing the scouring results obtained by Coleman (2005) for two of the models used, Co1 and Co2 (see Figure 2.27) – presented in Figure 2.28(b) for Model Co1 and in Figure 2.28(c) for Model Co2 –, it can be concluded that the higher scour depth values of Model Co1 over the full 𝐻𝑐/ℎ range is due to the fact that, in this model (where 𝑓𝑙/𝑓𝑡=0), the downflow in front of the column is not affected by the upstream pile-cap extension. Figure 2.29 – Effect of the relative column width on scour depth as function of the relative column position, based on Melville and Raudkivi (1996) data Results of experimental tests carried out by Jones (1989), Salim and Jones (1996) and Jones and Sheppard (2000a) were considered in the development of the FDOT predictor (Sheppard and Renna, 2010) and of the HEC-18 predictor (Arneson et al., 2012). These tests were performed to evaluate the effect of the pile-cap front and side extension lengths beyond the column external face on the maximum scour depth. Jones (1989) observed that when the top of the pile cap was placed at or below the initial bed level, maximum local scour was 20% less than for the different tested conditions with the pile cap above the bed. Jones and Sheppard (2000a) carried out experiments on suspended columns with a thin plate attached to the bottom, positioned above the stream bed, to create and study the overhang length effect. Ataie-Ashtiani et al. (2010) considered that, in complex piers with rectangular Experimental Study of Local Scour around Complex Bridge Piers 43 shapes, the upstream and lateral overhang distances from the corresponding column faces has an important effect on scour depth in the cases where the pile cap is partially or completely buried. AtaieAshtiani et al. (2010) established a new expression to calculate the equivalent diameter suggested by Coleman (2005) by taking into account the results of their rectangular complex piers studies. 2.3.5.4 Pile-cap thickness Ferraro et al. (2013) carried out experiments with two complex pier models (Fe1 and Fe2, Table 2.2) to study the effect of the relative pile-cap thickness, 𝑇/ℎ, on the maximum scour depth as a function of the relative column position, 𝐻𝑐/ℎ. In these two models only the pile-cap thickness was changed, as shown in Figure 2.27. Model Fe1 corresponds to a thick pile cap case whereas Model Fe2 represents a case with a thin pile cap, as shown in Figure 2.30(a). The variation of maximum scour depth with 𝐻𝑐/ℎ for the two mentioned models is presented in Figure 2.30(b). The results of 𝑑𝑠𝑒 variation with 𝐻𝑐/ℎ (Figure 2.30(b)) show that, in general, the complex pier with the thicker pile cap generates deeper scour holes. The increase in scour depth values from the test with Model Fe2 (𝑇/ℎ=0.01) to the test with Model Fe1 (𝑇/ℎ=0.50) is justified by the larger area exposed frontal to the flow due to the pile cap front in Model Fe1 compared to Model Fe2. For the thicker pile cap case (Model Fe1) the maximum scour depth occurred when the pile cap was partially buried in the initial bed level. In this condition, the thicker pile cap intercepted a greater flow portion and diverted it towards the bed, that increasing the strength of the erosive agents (downflow and horseshoe vortex). Figure 2.30 – Effect of the pile-cap thickness on scour depth: (a) complex pier models and (b) scour depth variation as function of the relative column position, adapted from Ferraro et al. (2013) 2.3.5.5 Pile-group configuration Knowledge of local scouring at pile groups is not extensive, with small number of studies reported in the literature. They include those of Hannah (1978), Elliott and Baker (1985), Salim and Jones (1996), Zhao and Sheppard (1999), Smith (1999), Sumer and Fredsøe (2002), Ataie-Ashtiani and Beheshti (2006), Amini et al. (2012) and Lança et al. (2013a). Excepting the studies of Smith (1999) and Lança et al. (2013a), the tests were performed for short durations. These studies focus on the effect of pile spacing, 𝑆𝑛/𝐷𝑝 and 𝑆𝑚/𝐷𝑝, skew-angle, 𝜃, as well as number of columns and number of rows of the pile group, 𝑛 and 𝑚 respectively. Figure 2.31 shows the effect of the relative pile spacing (𝑆𝑛/𝐷𝑝 or 𝑆𝑚/𝐷𝑝) on the relative pile group scour depth, 𝑑𝑠𝑝𝑔/𝑑𝑠𝑝 (𝑑𝑠𝑝𝑔 = maximum scour depth observed at pile group and 𝑑𝑠𝑝 = scour depth observed at an individual pile in the same bed and approach flow conditions), for different Experimental Study of Local Scour around Complex Bridge Piers 44 configurations of the pile group, all aligned with the approach flow. The figure includes the experimental data obtained by Hannah (1978), Ataie-Ashtiani and Beheshti (2006) and Lança et al. (2013a). Even though the corresponding tests of the first two studies were carried out with short durations, it can be assumed that the corresponding ratio 𝑑𝑠𝑝𝑔/𝑑𝑠𝑝 approaches to that which would be obtained with tests of longer durations. Figure 2.31 – Effect of the relative pile spacing on the relative scour depth for pile groups with: (a) a single row (m = 1) and (b) a single column (n = 1) Figure 2.31(a) displays 𝑑𝑠𝑝𝑔/𝑑𝑠𝑝 as a function of the relative spacing perpendicular to the flow, 𝑆𝑛/𝐷𝑝. This figure includes tests with pile groups of a single row (one transverse alignment), i.e., 𝑚 = 1 (see Figure 2.21). The results shows that the maximum scour depth occurs for 𝑆𝑛/𝐷𝑝 = 1 and gradually diminishes with the increase of the relative pile spacing. This may explained by the fact that the interference between adjacent piles diminishes leading to incipient individual scour holes. Further increase on 𝑆𝑛/𝐷𝑝 shows that the individual scour holes tend to separate and, for 𝑆𝑛/𝐷𝑝≥ 7, a clear and individual scour hole corresponds to each pile. Figure 2.31(b) shows 𝑑𝑠𝑝𝑔/𝑑𝑠𝑝 as function of the relative spacing in the direction of the flow, 𝑆𝑚/𝐷𝑝. This figure includes tests with pile groups of a single column (one longitudinal alignment), i.e., 𝑛 = 1 (see Figure 2.21). For 𝑆𝑚/𝐷𝑝 = 1, the piles touch each other and the scour depth at the front of the pile group for 𝑚 = 2 would be practically equal to the one obtained at a single pile (𝑑𝑠𝑝𝑔/𝑑𝑠𝑝=1); whereas, for that same case (𝑆𝑚/𝐷𝑝 = 1) increasing the number of pile rows (𝑚 higher than 2) it will only lead to a slight increase of 𝑑𝑠𝑝𝑔/𝑑𝑠𝑝. The maximum scour depth at a pile group (irrespective of 𝑚) is obtained for 𝑆𝑚/𝐷𝑝 between 2 to 3. This may be associated to the scour reinforcement mechanism described in section 2.3.1. Then, the interaction between piles reduces gradually until 𝑆𝑚/𝐷𝑝 = 12. For 𝑆𝑚/𝐷𝑝 > 12, the scour depth in the upstream pile would be again the same as the one corresponding to an isolated pile. In Figure 2.32(a), the values of relative scour depths of the pile group, 𝑑𝑠𝑝𝑔/𝑑𝑠𝑝, are plotted against the pile spacing, 𝑆𝑝/𝐷𝑝 (𝑆𝑝 representing longitudinal and transverse pile spacing, since it is considered that 𝑆𝑚 = 𝑆𝑛), and 𝜃. This figure is a representation of the results obtained by Lança et al. (2013a) for a pile group with 𝑚 = 4 and 𝑛 = 2 and cylindrical piles. According to Salim and Jones (1996), collapsed pile groups (i.e., 𝑆𝑝/𝐷𝑝 = 1) tend to behave as single piers whose dimensions are the sum of the dimensions of the individual piles, wherein the variation with skew-angle is similar to the observed in Figure 2.17. Experimental Study of Local Scour around Complex Bridge Piers 45 Figure 2.32 – (a) variation of dspg/ds with Sp/Dp and 𝜃, adapted from Lança et al. (2013a) and (b) system of wake vortices at an alignment of piles, adapted from Lança et al. (2012) In Figure 2.32(a), with the exception of 𝑆𝑝/𝐷𝑝 = 1, the maximum scour depth occurs for 𝜃= 30°. For this configuration (𝜃= 30°), the maxima scour depths tend to occur at the rear piles of the first column, which may be interpreted as an indication that such piles are located in the path of the most energetic wake vortices generated upstream, as illustrated in Figure 2.32(b). In pile groups with cylindrical piles, other studies (e.g., Hannah, 1978; Zhao and Sheppard, 1999) concluded that the maximum scour depth is observed for 25º and 40º respectively. The difference of results between the study by Lança et al. (2013a) and the studies by Hannah (1978) and Zhao and Sheppard (1999) may be associated to the short test durations in the last studies. 2.3.6 METHODS FOR ESTIMATION OF LOCAL SCOUR DEPTHS 2.3.6.1 Auckland Method The Auckland design method for complex piers was initially proposed by Melville and Coleman (2000) based on the concept of the equivalent pier diameter, 𝐷𝑒, introduced by Melville and Raudkivi (1996) (on a study of cylindrical columns founded on cylindrical caissons). These authors defined 𝐷𝑒 as the diameter of a single pier that would induce the same scour depth as the actual nonuniform pier, for the same flow and sediment. Melville and Coleman (2000) suggest that the equilibrium scour depth at complex piers may be calculated using the equation developed by the same authors for single piers (section 2.2.6.1), which reads, 𝑑𝑠𝑒=𝐾ℎ𝐷𝐾𝐼𝐾𝑑𝐾𝑆𝐾𝜃 (2.38) where 𝐾𝑆 = foundation shape factor. In the expressions for the factors 𝐾ℎ𝐷, 𝐾𝑑 and 𝐾𝜃 (i.e., equations (2.21), (2.23) and (2.24), respectively) 𝐷𝑒 is used instead of 𝐷. Coleman (2005) reformulated the initial procedure by considering that 𝐷𝑒 depends on the column position relative to the initial bed level, 𝐻𝑐. This author uses expressions previously published in the literature for piers with different types of foundations (e.g., pile groups, pile groups with a floating debris raft, piers founded on caissons or pile caps) to calculate the corresponding value of 𝐷𝑒. Experimental Study of Local Scour around Complex Bridge Piers 52 initial bed level (Case 1), the second configuration corresponds to the pile cap being partially buried in the bed (Case 2) and the third configuration is represented by the pile cap completely buried in the bed (Case 3). Scour depth prediction for Case 1: The equivalent diameter of the column, 𝐷𝑒𝑐, can be computed by 𝐷𝑒𝑐={𝐾𝑠𝐾𝜃𝐾𝑓𝐾ℎ𝑐𝐷𝑐for 𝐻𝑐<ℎ𝑐(max) 0for 𝐻𝑐≥ℎ𝑐(max) (2.65) where 𝐾𝑠 = column shape factor; 𝐾𝜃 = column skew factor; 𝐾𝑓 = pile cap extension factor; 𝐾ℎ𝑐 = factor to account for the position of the bottom of the column relative to the initial bed level and ℎ𝑐(max) = limiting water depth at which the flow influences the scouring process around the column. The limiting variable ℎ𝑐(max) and those factors are estimated by the following expressions: ℎ𝑐(max)={3𝐾𝑠𝐾𝜃𝐷𝑐for ℎ≥3𝐾𝑠𝐾𝜃𝐷𝑐 ℎfor ℎ<3𝐾𝑠𝐾𝜃𝐷𝑐 (2.66) 𝐾𝑠={0.86+0.97|𝜃 𝜋 180°−𝜋4|4for rectangular columns 1for circular columns (2.67) 𝐾𝜃=𝐷𝑐∙𝑐𝑜𝑠𝜃+𝐿𝑐∙𝑠𝑖𝑛𝜃 𝐷𝑐 (2.68) 𝐾𝑓= { 1for 𝑓 𝐷𝑐<1 0.75+0.5(𝑓 𝐷𝑐)−0.25(𝑓 𝐷𝑐)2 for 1≤𝑓 𝐷𝑐≤3 0for 𝑓 𝐷𝑐>3 (2.69) where 𝑓 is the weighted average of the pile cap front and side extensions beyond the corresponding column faces. This is computed by the following equation 𝑓= { 3𝑓𝑙+𝑓𝑡 4for 𝜃≤45° 𝑓𝑙+3𝑓𝑡 4for 𝜃>45° (2.70) Experimental Study of Local Scour around Complex Bridge Piers 53 𝐾ℎ𝑐= { 0.41−1.34[𝐻𝑐 ℎ𝑐(max)+𝑑𝑠𝑐(max)]+0.86[𝐻𝑐 ℎ𝑐(max)+𝑑𝑠𝑐(max)]2 +1.40[𝐻𝑐 ℎ𝑐(max)+𝑑𝑠𝑐(max)]3−1.65[𝐻𝑐 ℎ𝑐(max)+𝑑𝑠𝑐(max)]4 } (2.71) where 𝑑𝑠𝑐(max) = maximum column scour depth, which is calculated using 𝐷=𝐾𝑠𝐾𝜃𝐷𝑐 in the single pier equations (section 2.2.6.2). The equivalent diameter of the pile cap, 𝐷𝑒𝑝𝑐, can be computed by 𝐷𝑒𝑝𝑐={𝐾𝑠𝐾𝜃𝐾ℎ𝑝𝑐𝐷𝑝𝑐 for 𝐻𝑝𝑐<ℎ𝑝𝑐(max) 0for 𝐻𝑝𝑐≥ℎ𝑝𝑐(max) (2.72) where 𝐾𝑠 = pile cap shape factor; 𝐾𝜃 = pile cap skew factor; 𝐾ℎ𝑝𝑐 = factor to account for the position of the bottom of the pile cap relative to the initial bed level and ℎ𝑝𝑐(max) = limiting water depth at which the flow influences the scouring process around the pile cap. The limiting variable ℎ𝑝𝑐(max) and those factors are estimated by the following equation ℎ𝑝𝑐(max)={𝐷𝑒𝑐+1.5𝐾𝑠𝐾𝜃𝐷𝑝𝑐 for ℎ≥(𝐷𝑒𝑐+1.5𝐾𝑠𝐾𝜃𝐷𝑝𝑐) ℎfor ℎ<(𝐷𝑒𝑐+1.5𝐾𝑠𝐾𝜃𝐷𝑝𝑐) (2.73) 𝐾𝑠={0.86+0.97|𝜃 𝜋 180°−𝜋4|4for rectangular pile caps 1for circular pile caps (2.74) 𝐾𝜃=𝐷𝑝𝑐∙𝑐𝑜𝑠𝜃+𝐿𝑝𝑐∙𝑠𝑖𝑛𝜃 𝐷𝑝𝑐 (2.75) 𝐾ℎ𝑝𝑐= ( −1.34{[ 𝐻𝑝𝑐 ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]−[ 𝐻𝑐 ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]} +0.86{[ 𝐻𝑝𝑐 ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]2−[ 𝐻𝑐 ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]2} +1.40{[ 𝐻𝑝𝑐 ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]3−[ 𝐻𝑐 ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]3} −1.65{[ 𝐻𝑝𝑐 ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]4−[ 𝐻𝑐 ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]4} ) (2.76) Experimental Study of Local Scour around Complex Bridge Piers 54 where 𝑑𝑠𝑝𝑐(max) = maximum pile cap scour depth, which is calculated using 𝐷=𝐾𝑠𝐾𝜃𝐷𝑝𝑐 in the single pier equations (section 2.2.6.2). In the equation (2.76), if 𝐻𝑐>ℎ𝑝𝑐(max), then 𝐻𝑐=ℎ𝑝𝑐(max). The equivalent diameter of the pile group, 𝐷𝑒𝑝𝑔, can be computed by 𝐷𝑒𝑝𝑔=𝐾𝑆𝑝𝑔𝐾𝑠𝑝𝐾𝑚𝐾ℎ𝑝𝑔𝑊𝑝𝑔 (2.77) where 𝐾𝑆𝑝𝑔 = pile group shape factor; 𝐾𝑠𝑝 = pile spacing factor; 𝐾𝑚 = factor for number of aligned rows; 𝐾ℎ𝑝𝑔 = factor to account for the height of the pile group relative to the initial bed level and 𝑊𝑝𝑔= sum of the non-overlapping individual pile widths projected on a plane normal to the approach flow, calculated according to Figure 2.35. The shape factor for the pile group can be estimated by the following equation 𝐾𝑆𝑝𝑔=𝐾𝑆𝑝−𝐾𝑆(𝑝𝑔) 9(𝑆𝑝 𝑤𝑝𝑖)+𝐾𝑆𝑝−10 9(𝐾𝑆𝑝−𝐾𝑆(𝑝𝑔)) (2.78) where 𝐾𝑆𝑝 = pile shape factor and 𝐾𝑆(𝑝𝑔) = pile group configuration factor. The variable 𝑤𝑝𝑖 can be calculated by equation (2.62) while these two factors can be determined by 𝐾𝑆𝑝={0.86+0.97|𝜃 𝜋 180°−𝜋4|4for rectangular piles 1for circular piles (2.79) 𝐾𝑆(𝑝𝑔)= { 0.86+0.97|𝜃 𝜋 180°−𝜋4|4for pile groups with 𝑆𝑝 𝐷𝑝≤3 and 𝑛>1 1for pile groups with 𝑆𝑝 𝐷𝑝>3 or 𝑛=1 (2.80) where 𝑆𝑝 = smaller distance of 𝑆𝑚 and 𝑆𝑛 of Figure 2.35. The factor for pile spacing can be calculated by equation (2.61). The factor for number of aligned rows can be estimated by the following expression 𝐾𝑚= { 1 for |𝜃|≥5° or 𝑆𝑝 𝐷𝑝>7, or 𝑚=1 0.98+0.017𝑚 for |𝜃|<5°,𝑆𝑝 𝐷𝑝≤6 and 𝑚<8 (2.81) Equation (2.81) was provided by Sheppard (personal communication) to correct the original equation (Sheppard and Renna 2010). The factor that accounts for the location of the top of the group can be calculated by the following equation Experimental Study of Local Scour around Complex Bridge Piers 55 𝐾ℎ𝑝𝑔= { (𝐻𝑝𝑔+𝑑𝑠𝑐𝑝𝑐 ℎ𝑝𝑔(max))0.1 for (𝐻𝑝𝑔+𝑑𝑠𝑐𝑝𝑐 ℎ𝑝𝑔(max))≤1 1for (𝐻𝑝𝑔+𝑑𝑠𝑐𝑝𝑐 ℎ𝑝𝑔(max))>1 (2.82) where 𝑑𝑠𝑐𝑝𝑐 = scour depth produced by the combination of the column and pile cap using 𝐷=𝐷𝑒𝑐+ 𝐷𝑒𝑝𝑐 in the single pier equations (section 2.2.6.2) and ℎ𝑝𝑔(max) = limiting water depth at which the flow influences the scouring process around the pile group, which it is estimated by ℎ𝑝𝑔(max)={𝐾𝑆𝑝𝑔𝐾𝑠𝑝𝐾𝑚𝑊𝑝𝑔 for ℎ+𝑑𝑠𝑐𝑝𝑐>𝐾𝑆𝑝𝑔𝐾𝑠𝑝𝐾𝑚𝑊𝑝𝑔 ℎ+𝑑𝑠𝑐𝑝𝑐 for ℎ+𝑑𝑠𝑐𝑝𝑐≤𝐾𝑆𝑝𝑔𝐾𝑠𝑝𝐾𝑚𝑊𝑝𝑔 (2.83) Scour depth prediction for Case 2: Since the bottom of the column is above the bed for Case 2, the procedure for computing 𝐷𝑒𝑐 is the same as for Case 1, thus 𝐷𝑒𝑐=𝐾𝑠𝐾𝜃𝐾𝑓𝐾ℎ𝑐𝐷𝑐for 𝐻𝑐<ℎ𝑐(max) (2.84) The respective factors can be calculated using the set of equations (2.66) to (2.71). In this case, the procedure for computing 𝐷𝑒𝑝𝑐 requires iterative calculations since the shape and size of the structure exposed to the flow can change with the progress of the local scour. The procedure is, according to Sheppard and Renna (2010): (1) set 𝑖=0; (2) estimate 𝑑𝑠[𝑐+𝑝𝑐(0)]=𝑑𝑠𝑐 using the 𝐷𝑒𝑐 calculated by equation (2.84) in the single pier equations (section 2.2.6.2); (3) calculate the distance from the pre-locally scoured bed to the bottom of the scour hole until an equilibrium scour is reached or the pile cap is uncovered, 𝐻𝑝𝑐 ∗, by equation (2.85); (4) compute the equivalent diameter of the pile cap 𝐷𝑒𝑝𝑐(𝑖) by equation (2.86), in this equation if 𝐻𝑐>ℎ𝑝𝑐(max) set 𝐻𝑐=ℎ𝑝𝑐(max); (5) compute the scour depth due to the column and the portion of the pile cap that is exposed, 𝑑𝑠[𝑐+𝑝𝑐(𝑖)], using the single piers equations (section 2.2.6.2) with a 𝐷=𝐷𝑒𝑐+𝐷𝑒𝑝𝑐(𝑖); and (6) check for convergence using equation (2.88), if Δ≤0.05 the procedure ends, otherwise set 𝑖=𝑖+1 and return to step (3) of the procedure. 𝐻𝑝𝑐 ∗={𝐻𝑝𝑐 for 𝑑𝑠[𝑐+𝑝𝑐(𝑖)]≥|𝐻𝑝𝑐| −𝑑𝑠[𝑐+𝑝𝑐(𝑖)] for 𝑑𝑠[𝑐+𝑝𝑐(𝑖)]<|𝐻𝑝𝑐| (2.85) 𝐷𝑒𝑝𝑐(𝑖)=𝐾𝑠𝐾𝜃𝐾ℎ𝑝𝑐𝐷𝑝𝑐 for 𝐻𝑝𝑐<ℎ𝑝𝑐(max) (2.86) where ℎ𝑝𝑐(max), 𝐾𝑠 and 𝐾𝜃 can be estimated by equations (2.73), (2.74) and (2.75) respectively, while 𝐾ℎ𝑝𝑐 is estimated by Experimental Study of Local Scour around Complex Bridge Piers 56 𝐾ℎ𝑝𝑐= ( −1.34{[ 𝐻𝑝𝑐 ∗ ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]−[ 𝐻𝑐 ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]} +0.86{[ 𝐻𝑝𝑐 ∗ ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]2−[ 𝐻𝑐 ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]2} +1.40{[ 𝐻𝑝𝑐 ∗ ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]3−[ 𝐻𝑐 ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]3} −1.65{[ 𝐻𝑝𝑐 ∗ ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]4−[ 𝐻𝑐 ℎ𝑝𝑐(max)+𝑑𝑠𝑝𝑐(max)]4} ) (2.87) where 𝑑𝑠𝑝𝑐(max) = maximum pile cap scour depth, which is calculated using 𝐷=𝐾𝑠𝐾𝜃𝐷𝑝𝑐 in the single pier equations (section 2.2.6.2). Δ=|𝑑𝑠[𝑐+𝑝𝑐(𝑖)]−𝑑𝑠[𝑐+𝑝𝑐(𝑖−1)] 𝑑𝑠[𝑐+𝑝𝑐(𝑖−1)] | (2.88) In this case, 𝐷𝑒𝑝𝑔 is calculated depending if the pile group is exposed in the scour hole, thus 𝐷𝑒𝑝𝑔=𝐾𝑆𝑝𝑔𝐾𝑠𝑝𝐾𝑚𝐾ℎ𝑝𝑔𝑊𝑝𝑔 for 𝑑𝑠𝑐𝑝𝑐>|𝐻𝑝𝑔| 𝐷𝑒𝑝𝑔=0 for 𝑑𝑠𝑐𝑝𝑐≤|𝐻𝑝𝑔| (2.89) where 𝑑𝑠𝑐𝑝𝑐 = scour depth produced by the combination of the column and pile cap using a diameter 𝐷=𝐷𝑒𝑐+𝐷𝑒𝑝𝑐 in the single pier equations (section 2.2.6.2). 𝐾𝑆𝑝𝑔, 𝐾𝑠𝑝 and 𝐾𝑚 can be estimated by equations (2.78), (2.61) and (2.81) respectively. The variable 𝑊𝑝𝑔 can be calculated according to Figure 2.35 while 𝐾ℎ𝑝𝑔 is estimated by the following equation 𝐾ℎ𝑝𝑔= { (𝐻𝑝𝑔+𝑑𝑠𝑐𝑝𝑐 ℎ𝑝𝑔(max))0.1 for (𝐻𝑝𝑔+𝑑𝑠𝑐𝑝𝑐 ℎ𝑝𝑔(max))≤1 1for (𝐻𝑝𝑔+𝑑𝑠𝑐𝑝𝑐 ℎ𝑝𝑔(max))>1 (2.90) where ℎ𝑝𝑔(max) = limiting water depth at which the flow influences the scouring process around the pile group, which is estimated by ℎ𝑝𝑔(max)={𝐾𝑆𝑝𝑔𝐾𝑠𝑝𝐾𝑚𝑊𝑝𝑔 for ℎ+𝑑𝑠𝑐𝑝𝑐>𝐾𝑆𝑝𝑔𝐾𝑠𝑝𝐾𝑚𝑊𝑝𝑔 ℎ+𝑑𝑠𝑐𝑝𝑐 for ℎ+𝑑𝑠𝑐𝑝𝑐≤𝐾𝑆𝑝𝑔𝐾𝑠𝑝𝐾𝑚𝑊𝑝𝑔 (2.91) Scour depth prediction for Case 3: The equivalent diameter of the column, 𝐷𝑒𝑐, can be computed by Experimental Study of Local Scour around Complex Bridge Piers 57 𝐷𝑒𝑐={𝐾𝑠𝐾𝜃𝐾𝑓𝐾ℎ𝑐𝐷𝑐for 𝑑𝑠𝑐(max)>|𝐻𝑐| 𝐾𝑠𝐾𝜃𝐷𝑐for 𝑑𝑠𝑐(max)≤|𝐻𝑐| (2.92) where 𝑑𝑠𝑐(max) = maximum column scour depth, which is calculated using 𝐷=𝐾𝑠𝐾𝜃𝐷𝑐 in the single pier equations (section 2.2.6.2). The factors can be calculated through equations (2.66) to (2.71). If the scour depth due to the column enables the top of the pile cap to be reached, i.e., 𝑑𝑠𝑐(max)>|𝐻𝑐|, and 𝐷𝑒𝑐 calculated by equation (2.92) is smaller than 𝐷𝑒𝑐(min) (equivalent diameter of a single pier that leads to a scour depth equal to |𝐻𝑐|), 𝐷𝑒𝑐= 𝐷𝑒𝑐(min). In this case, in the procedure for computing 𝐷𝑒𝑝𝑐 iterative calculations is necessary as mentioned for Case 2. According to Sheppard and Renna (2010), the procedure is: (1) set 𝑖=0; (2) estimate 𝑑𝑠[𝑐+𝑝𝑐(0)]=𝑑𝑠𝑐 using the 𝐷𝑒𝑐 calculated by equation (2.84) in the single pier equations (section 2.2.6.2); (3) calculate 𝐻𝑝𝑐 ∗ by equation (2.85); (4) compute 𝐷𝑒𝑝𝑐(𝑖) by equation (2.93), in this equation if 𝐻𝑐>ℎ𝑝𝑐(max) set 𝐻𝑐=ℎ𝑝𝑐(max); (5) compute the scour depth due to the column and the portion of the pile cap that is exposed, 𝑑𝑠[𝑐+𝑝𝑐(𝑖)], using the single piers equations (section 2.2.6.2) with a 𝐷=𝐷𝑒𝑐+𝐷𝑒𝑝𝑐(𝑖); and (6) check for convergence using equation (2.88), if Δ≤0.05 the procedure ends, otherwise set 𝑖=𝑖+1 and return to step (3) of the procedure. 𝐷𝑒𝑝𝑐(𝑖)=𝐾𝑠𝐾𝜃𝐾ℎ𝑝𝑐𝐾𝑏𝑝𝑐𝐷𝑝𝑐 for 𝐻𝑝𝑐<ℎ𝑝𝑐(max) (2.93) where 𝐾𝑏𝑝𝑐 = factor that accounts for the dependence of the pile-cap position on the scour hole. ℎ𝑝𝑐(max), 𝐾𝑠, 𝐾𝜃 and 𝐾ℎ𝑝𝑐 can be estimated by equations (2.73), (2.74), (2.75) and (2.87) respectively, while 𝐾𝑏𝑝𝑐 is estimated by 𝐾𝑏𝑝𝑐= { 0.93(𝐻𝑐 𝑑𝑠𝑐(max))2+1.93(𝐻𝑐 𝑑𝑠𝑐(max))+1 for −𝑑𝑠𝑐𝑝𝑐≤𝐻𝑐 0for −𝑑𝑠𝑐𝑝𝑐>𝐻𝑐 (2.94) where 𝑑𝑠𝑐(max) = maximum column scour depth, which is calculated using 𝐷=𝐾𝑠𝐾𝜃𝐷𝑐 in the single pier equations (section 2.2.6.2). In this case, 𝐷𝑒𝑝𝑔 is calculated depending if the pile group is exposed in the scour hole, thus 𝐷𝑒𝑝𝑔={𝐾𝑆𝑝𝑔𝐾𝑠𝑝𝐾𝑚𝐾ℎ𝑝𝑔𝐾𝑏𝑝𝑔𝑊𝑝𝑔 for 𝑑𝑠𝑐𝑝𝑐>|𝐻𝑝𝑔| 0for 𝑑𝑠𝑐𝑝𝑐≤|𝐻𝑝𝑔| (2.95) where 𝐾𝑏𝑝𝑔= buried pile group attenuation factor and 𝑑𝑠𝑐𝑝𝑐 = scour depth produced by the combination of the column and pile cap using 𝐷=𝐷𝑒𝑐+𝐷𝑒𝑝𝑐 in the single pier equations (section 2.2.6.2). 𝐾𝑆𝑝𝑔, 𝐾𝑠𝑝 and 𝐾𝑚 can be estimated by equations (2.78), (2.61) and (2.81) respectively. 𝑊𝑝𝑔 can be calculated according to Figure 2.35 while 𝐾ℎ𝑝𝑔 is estimated by the following equation Experimental Study of Local Scour around Complex Bridge Piers 58 𝐾ℎ𝑝𝑔= { (𝐻𝑝𝑔+𝑑𝑠𝑐𝑝𝑐 ℎ𝑝𝑔(max))0.1 for (𝐻𝑝𝑔+𝑑𝑠𝑐𝑝𝑐 ℎ𝑝𝑔(max))≤1 1for (𝐻𝑝𝑔+𝑑𝑠𝑐𝑝𝑐 ℎ𝑝𝑔(max))>1 (2.96) where ℎ𝑝𝑔(max) = limiting water depth at which the flow influences the scouring process around the pile group, which is estimated by ℎ𝑝𝑔(max)=𝐾𝑆𝑝𝑔𝐾𝑠𝑝𝐾𝑚𝑊𝑝𝑔 for ℎ+𝑑𝑠𝑐𝑝𝑐>𝐾𝑆𝑝𝑔𝐾𝑠𝑝𝐾𝑚𝑊𝑝𝑔 ℎ𝑝𝑔(max)=ℎ+𝑑𝑠𝑐𝑝𝑐 for ℎ+𝑑𝑠𝑐𝑝𝑐≤𝐾𝑆𝑝𝑔𝐾𝑠𝑝𝐾𝑚𝑊𝑝𝑔 (2.97) 𝐾𝑏𝑝𝑔 can be calculated as 𝐾𝑏𝑝𝑔=𝐻𝑝𝑔+𝑑𝑠𝑐𝑝𝑐 𝑑𝑠𝑐𝑝𝑐 (2.98) Experimental Study of Local Scour around Complex Bridge Piers 59 3. EXPERIMENTAL SETUP 3.1. INTRODUCTION Details for the experimental campaign performed in the present study are provided in this chapter. The experimental work planned in this study to understand and characterize pier’s local scour was carried out in two flumes located, respectively, at the Hydraulics and Environment Department, National Laboratory for Civil Engineering (LNEC) and at the Faculty of Engineering of the University of Porto (FEUP). A total of 92 tests were performed using seven different complex pier models. Six of them were analysed at LNEC’s flume, i.e., Model 1 to Model 6 in Figure 3.1(a), while the remaining one was evaluated at FEUP’s flume, i.e., Model 7 in Figure 3.1(b). The dimensions of the seven pier models analysed in the present study are considerably higher than the pier models used in the five studies from literature (see Figure 2.27). The experimental setup includes: (1) the description of the experimental campaign; (2) the description of the laboratory facilities (two flumes); and finally (3) the experimental procedures in both flumes. Figure 3.1 – Dimensions of complex pier models analysed at (units in millimetres): (a) LNEC’s flume and (b) FEUP’s flume In the experimental campaign three configurations of the complex pier models were considered, as shown in Figure 3.2. The Configuration C1 corresponds to the complete complex pier structure (i.e., complex pier with the three components) while the Configuration C2 corresponds to the mentioned Experimental Study of Local Scour around Complex Bridge Piers 60 complete structure without the column and the Configuration C3 corresponds to the complete structure without the pile group. Figure 3.2 – Complex pier configurations A total of 48 tests were performed for Configuration C1 in order to quantify the influence of the complex pier position (relative to the initial bed level) and complex pier geometry on the temporal evolution of the scour depth (results and discussion presented in Chapter 4) and on the equilibrium scour depth (results and discussion presented in Chapter 5). The results of these 48 tests were also used to evaluate the three mentioned methods to predict equilibrium scour depths (results and discussion presented in Chapter 7). The following effects on the equilibrium scour depth were analysed: 1. The combined effects of the relative column width, 𝐷𝑐/𝐷𝑝𝑐, and the relative column position, 𝐻𝑐/ℎ, were evaluated on the basis of the results obtained with Model 2 (𝐷𝑐/𝐷𝑝𝑐= 0.85), Model 3 (𝐷𝑐/𝐷𝑝𝑐= 0.70) and Model 5 (𝐷𝑐/𝐷𝑝𝑐= 0.55). In the tests with these three different models only the column dimensions (width and length) were changed, as shown in Figure 3.1(a). 2. The combined effects of the relative pile-cap thickness, 𝑇/ℎ, and the relative column position, 𝐻𝑐/ℎ, were analysed on the basis of the results obtained with Model 4 (𝑇/ℎ= 0.60), Model 5 (𝑇/ℎ= 0.45) and Model 6 (𝑇/ℎ= 0.30). For these three models (4, 5 and 6, all of them with 𝐷𝑐/𝐷𝑝𝑐= 0.55), only the pile cap thickness was changed, as shown in Figure 3.1(a). 3. The effect of the pile-group configuration (characterized by the number of pile columns, 𝑛) was evaluated on the basis of the results obtained with Model 3 (𝑛= 2, Figure 3.1(a)) and Model 7 (𝑛= 1, Figure 3.1(b)). A total of 44 tests were performed for Configurations C2 and C3. The results of these tests as well as the results of some tests with Configuration C1 were used to quantify the contribution of the complex pier components on the total equilibrium scour depth (results and discussion presented in Chapter 6). 3.2. EXPERIMENTAL CAMPAIGN 3.2.1 COMPLEX PIER MODELS As mentioned above, seven complex pier models were built in order to assess the influence of its geometry on the development of the scour hole. These models were designed with a rectangular round-nose column founded on a rectangular round-nose pile cap, supported by a pile group. The arrangement of this last component consists of: two alignments of four cylindrical piles in the case of Experimental Study of Local Scour around Complex Bridge Piers 61 Models 1 to 6 (Figure 3.1(a)) and one alignment of four cylindrical piles for Model 7 (Figure 3.1(b)). The longitudinal axis of the complex pier models was aligned with the approach flow, i.e., 𝜃=0°. The geometric characteristics of the seven models are summarized in Table 3.1. Table 3.1 – Geometric characteristics of the complex pier models of the experimental campaign Variable Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 𝐷𝑐 (m) 0.170 0.170 0.140 0.110 0.110 0.110 0.089 𝐿𝑐 (m) 0.493 0.493 0.463 0.433 0.433 0.433 0.465 𝑓𝑙 (m) 0.015 0.015 0.030 0.045 0.045 0.045 0.015 𝑓𝑡 (m) 0.015 0.015 0.030 0.045 0.045 0.045 0.015 𝐷𝑝𝑐 (m) 0.200 0.200 0.200 0.200 0.200 0.200 0.120 𝐿𝑝𝑐 (m) 0.523 0.523 0.523 0.523 0.523 0.523 0.495 𝑇 (m) 0.120 0.090 0.090 0.120 0.090 0.060 0.058 𝐷𝑝 (m) 0.050 0.050 0.050 0.050 0.050 0.050 0.050 𝑓𝑝 (m) 0.030 0.030 0.030 0.030 0.030 0.030 0.035 𝑚 4 4 4 4 4 4 4 𝑛 2 2 2 2 2 2 1 𝑆𝑚 (m) 0.125 0.125 0.125 0.125 0.125 0.125 0.125 𝑆𝑛 (m) 0.125 0.125 0.125 0.125 0.125 0.125 - 3.2.2 EXPERIMENTAL CONDITIONS In both flumes, the recess boxes – where the test models were installed – were filled with quartz sand so that a corresponding scour hole would develop. A uniform sediment and coarse material was used in the bed with the purpose of preventing ripples formation. Figure 3.3 shows the grading curve of the sand obtained by mechanical sieving. According to the grading curve, the median particle size (𝑑50) was 0.86 mm corresponding to coarse sand (defined by 𝑑50≥ 0.6 mm). The geometric standard deviation of the grain-size distribution (𝜎𝑔=√𝑑84/𝑑16) was 1.28. This confirms that the sediment is uniform and therefore the bed material gradation effect on 𝑑𝑠𝑒 is avoided, according to section 2.2.5.4. Figure 3.3 – Grading curve of the sand used in the experiments Experimental Study of Local Scour around Complex Bridge Piers 68 Figure 3.8 – Scheme of FEUP’s flume The flow discharge is measured by two electromagnetic flow-meters [5] installed at pipes situated between the constant head reservoir and the settling chamber [7]. The maximum flow discharge is 90 l/s. The transition from the constant head reservoir to the channel fixed bed [10] is made by a free fall and ascending ramps [8]. These ramps promote the uniform flow distribution at the entrance of the Experimental Study of Local Scour around Complex Bridge Piers 69 channel. At that entrance, immediately after the downstream ramp, a 3.0 m long bed reach was covered with small gravel [9] to provide proper roughness and guarantee fully developed flow. The flume is 33.15-m-long, 1.00-m-wide and 1.00-m-deep. The central bed recess box starts at 16.00 m from the entrance; the length of the recess box [13] is 3.20 m and its depth is 0.35 m. The hopper [14] collects the entrained sediments and the downstream gate [16] allows the water level regulation inside the channel. The complex pier model [12] was built in two different materials: PVC pipes for the pile group and perspex for the column and the pile cap. The piles were designed with pieces of different lengths to permit obtaining the different positions of the piles (Figure 3.4(d)). The flume is equipped with a moving platform supported in its lateral walls. The platform, located over the recess box was used to fix a point gauge [11] to measure scour depths. The flow depth was measured by using a point gauge [15] located at the downstream part of the flume. 3.5. EXPERIMENTAL PROCEDURES The procedures of the tests carried out at the LNEC’s and the FEUP’s flumes were based on the procedure followed by Grimaldi (2005), on a study which included tests on local scour around cylindrical single piers with countermeasures at LNEC’s facility. The procedures include the following five steps: (1) complex piers preparation and fixation, (2) preparation of the sand bed, (3) flow-discharge and flow-depth stabilization, (4) scour depth measurement, and (5) end of the experiment. 3.5.1 COMPLEX PIERS PREPARATION AND FIXATION The components of the complex piers models were built separately in order to perform tests in the three mentioned configurations (Figure 3.2). The complex pier models analysed at LNEC’s flume were built in two different materials: aluminium for the pile group and concrete for the column and pile cap, as shown in Figure 3.9(a), whereas, the complex pier model analysed at FEUP’s flume was also built in two different materials: PVC pipes for the pile group and Perspex for the column and the pile cap, as shown in Figure 3.9(b). The procedures of complex pier fixation on the bed were different in both flumes. The procedure at the LNEC’s flume for tests with Configuration C1 (full complex pier) was: (a) 8 piles of 0.18-m-height were placed and fixed to the two recess boxes floor; (b) other pieces of piles, with the same diameter and different heights, were screwed to the fixed piles to obtain the required pile height; (c) the pile cap was joined to the piles through eight screws (one for each pile); and finally (d) the column was placed above the pile cap and assembled through two long screws, as shown in Figure 3.9(a). For tests with Configuration C2 (complex pier without the column) steps (a) to (c) were followed whereas for tests with Configuration C3 (complex pier with no pile group), the column and the pile cap were suspended by a metallic structure that includes one vertical screw passing through the two elements welded to a thin plate, as shown in Figure 3.9(a). The procedure at the FEUP’s flume for tests with Configuration C1 was: (e) an acrylic board with four stoppers was placed and fixed to the recess box floor; (f) the four PVC piles were fixed to the board placing them in the respective stoppers (50-mm-height perspex cylinders with diameters equal to the inside pile diameter); (g) the pile cap was assembled in the PVC piles through four orifices on the bottom of the pile cap with dimensions equal to the outside pile diameter; and finally (h) the column Experimental Study of Local Scour around Complex Bridge Piers 70 was placed above the pile cap and assembled through six pins. For tests with Configuration C2, steps (e) to (g) were followed whereas for tests with Configuration C3, the column and the pile cap were assembled through six pins and the two elements were suspended by a metallic structure that includes two vertical screws passing through the pile cap and column, as shown in Figure 3.9(b). Figure 3.9 – Step 1 of the experimental procedure: (a) LNEC’s flume and (b) FEUP’s flume 3.5.2 PREPARATION OF THE SAND BED First, the sand bed was accommodated in the flume recess box(es) (two for LNEC’s flume). Then, the sand bed was completely saturated with water and drained at least once to guarantee the adequate sand compaction. An aluminium bar was used to level the sand bed surface with the adjacent concrete bed. Adjustments of the lateral edges and of the zone around the complex pier were done manually. The sand zone around the model configuration was covered with thin metallic plates (filter fabric combined with a thin metallic grid in the case of FEUP’s tests) to avoid uncontrolled scour at the beginning of each test, as shown in Figure 3.10. Experimental Study of Local Scour around Complex Bridge Piers 71 Figure 3.10 – Step 2 of the experimental procedure: (a) LNEC’s flume and (b) FEUP’s flume 3.5.3 FLOW-DISCHARGE AND FLOW-DEPTH STABILIZATION The flumes were slowly filled with water to allow air entrapped in the sediment to escape. For this purpose a discharge of approximately 3 l/s was used in both flumes. When the flow depth in the flumes was about 5 cm, the flow-rate was increased gradually, imposing a high water depth and low flow velocity, as shown in Figure 3.11. The flow depths were regulated by adjusting the downstream sluice gates, as shown in [7] of Figure 3.7 (LNEC’s flume) and in [16] of Figure 3.8 (FEUP’s flume). Discharges were measured by electromagnetic flow meters, as shown in [8] of Figure 3.5 (LNEC’s flume) and in [5] of Figure 3.8 (FEUP’s flume). In each test carried out at LNEC’s flume, the flow discharge values were recorded approximately every 5 minutes through a computer and those were verified, at least, twice a day in the monitor, as shown in Figure 3.11(a). Whereas, the approach flow depth was verified, at least, twice a day by hydrometers located at upstream and downstream sections of the channel, as shown in [8] and [11] of Figure 3.7. In each test performed at FEUP’s flume, the flow discharge and the approach flow depth were verified twice a day in the flow-meter display (Figure 3.11(b)) and by a hydrometer located downstream part of the channel, respectively. Experimental Study of Local Scour around Complex Bridge Piers 72 Figure 3.11 – Step 3 of the experimental procedure: (a) LNEC’s flume and (b) FEUP’s flume 3.5.4 SCOUR DEPTH MEASUREMENT Once the flow depth and the discharge were established, the thin plates were carefully removed ant the tests started. Scour process was immediately initiated and the scour depth was measured every ≈ 10 minutes during the first hour to the accuracy of ± 0.1 mm with an adapted point gauge. Afterwards, the intervals between measurements increased and, after the first day, two or three measurements were carried out per day. Depending on the test and scour time evolution, one, two or the three complex pier elements were in contact with the bed surface. For this reason, the point gauges were adapted to measure the scour depth in front of: (1) the column; (2) the pile cap; and (3) one of the upstream piles, as shown in Figure 3.12(a) for Models 1 to 6 and in Figure 3.12(b) for Model 7. In the case of measurements in front of the piles, the point gauge was inserted in a small hole drilled through the pile cap for Models 1 to 6 while in the case of Model 7 a metric tape glued in front of the upstream pile was used. Experimental Study of Local Scour around Complex Bridge Piers 73 Figure 3.12 – Step 4 of the experimental procedure: (a) LNEC’s flume and (b) FEUP’s flume 3.5.5 END OF THE EXPERIMENT In the particular case of scour around complex piers equilibrium criterion has not yet been established as mentioned in section 2.3.4. As explained in that section, some authors suggest the use of the same criterion proposed by Melville and Chiew (1999) for tests with single piers. The analysis performed with the results of preliminary tests showed that the application of the criterion of Melville and Chiew (1999) to complex piers would imply test durations much smaller than those required to obtain the different scouring phases detected. For this reason, in the present study minimal durations depending of the pile-cap positon (and larger than the ones obtained by the Melville and Chiew (1999) criterion) were established. In the case of tests with Models 1 to 6 (analysed at LNEC’s flume) and for Configuration C1, the minimum durations were 14, 17 and 20 days, respectively when (1) the pile cap is above the bed, (2) is partially buried or (3) completely buried in the bed. In the other two configurations a minimum duration of 14 days was considered. In the case of Model 7 (analysed at FEUP’s flume) a minimum duration of 7 days was established for the three configurations. The difference of the minimum durations between the tests at FEUP’s and at LNEC’s flumes is due to fact that the geometry of Model 7 resembles a single pier and in tests with such piers at least 7 days duration is required, as suggested by Lança et al. (2013b). Once a given experiment was stopped, the flume was slowly drained. After that, the scour hole pattern was photographed. Figure 3.13 shows the Experimental Study of Local Scour around Complex Bridge Piers 74 recess box, the complex piers and the scour hole at the end of the tests, after flume’s depletion, for the three mentioned pile-cap positions, i.e., pile cap above the initial bed level, pile cap partially buried in the bed and pile cap completely buried in the bed. Figure 3.13 – Typical scour patterns at the end of the test: (a) LNEC’s flume and (b) FEUP’s flume It should be stressed that the approach reach located upstream of the piers remained undisturbed along the entire duration of the experiments, for all test model configurations; this long term stability could ensure that local scour hole development and depths were not affected by upstream bed degradation that could potentially occur otherwise. Experimental Study of Local Scour around Complex Bridge Piers 75 4. TEMPORAL EVOLUTION OF THE SCOUR DEPTH AT COMPLEX PIERS 4.1. INTRODUCTION The temporal evolution of the scour depth at single piers under clear-water flow conditions follows a logarithmic trend and three phases of the scour process may be identified: initial phase, principal phase and equilibrium phase (e.g., Ettema, 1980; Couto and Cardoso, 2001) as discussed in section 2.2.3. The principal phase of the scouring process at complex bridge piers can display different stages, depending on the pile-cap position relative to the initial bed level as described in section 2.3.3. In accordance with experimental results of Ataie-Ashtiani et al. (2010) and Ferraro et al. (2013), these stages are associated with the progressive physical presence in the scour hole developed of one, two, or the three structural components of the complex pier. As mentioned in section 2.3.3, the temporal evolution of the scour depth observed at pile groups (e.g., Hannah, 1978; Lança et al., 2013a) can be adopted to the case of complex piers when the pile cap is out of the water as well as the scour depth time evolution observed at pier-caissons (e.g., Melville and Raudkivi, 1996; Lu et al., 2011; Kothyari and Kumar, 2012) can be adopted to the case of complex piers when the pile cap is completely buried in the bed. From the five studies identified on scouring at complex piers (Table 2.2) only the studies of Ataie-Ashtiani et al. (2010) and Ferraro et al. (2013) included the analysis of the effect of the pile-cap position on the temporal evolution of the scour depth. Ferraro et al. (2013) investigated also the effect of the pile-cap thickness on the temporal evolution of the scour depth by means of results obtained with two models (Fe1 and Fe2 in Figure 2.27). Due to the limited number of studies in this topic, as only two studies could be reported, 48 longduration tests were performed in the present work in order to quantify the influence of the complex pier position (relative to the initial bed level) and complex pier geometry on the temporal evolution of the scour depth. Those 48 tests correspond to tests carried out with the seven complex pier models studied (Figure 3.1) for Configuration C1 (complete complex pier). The results of the tests performed at LNEC’s flume (i.e., with Models 1 to 6) were used to analyse: (1) the combined effects of the relative column width, 𝐷𝑐/𝐷𝑝𝑐, and the relative column position, 𝐻𝑐/ℎ, on the scour depth time evolution (presented in section 4.2.2); and (2) the combined effects of the relative pile-cap thickness, 𝑇/ℎ, and the relative column position, 𝐻𝑐/ℎ, on the temporal evolution of the scour depth (presented in section 4.2.3). The results of the tests performed at FEUP’s flume (i.e., with Model 7) were used to analyse: (1) the effect of the relative column position, 𝐻𝑐/ℎ, on the temporal evolution of the scour depth (presented in section 4.3.1); and (2) the influence of the pile-group configuration. As mentioned in section 2.3.4, some authors (e.g., Coleman, 2005; Ataie-Ashtiani et al., 2010) use as a criterion to stop laboratory tests on complex piers (equilibrium scour stage) the same criterion proposed by Melville and Chiew (1999) for tests with single piers. The results of the 48 tests were also used to evaluate the referred criterion applicability, as presented in section 4.4. Experimental Study of Local Scour around Complex Bridge Piers 76 4.2. SCOUR DEPTH TIME EVOLUTION IN TESTS WITH MODELS 1 TO 6 (LNEC’S MODELS) 4.2.1 GENERAL APPROACH According to results of tests carried out for Models 1 to 6 (at LNEC’s flume), the scour process in the three clear and distinguished situations considered (Figure 2.22) may be typically described as follows: 1. In Situation 1, characterized by the fact that the bottom of the pile cap is above the initial bed level, the temporal evolution of the maximum scour depth is similar to that of the single pier case, following a unique stage, as illustrated in Figure 4.1(a) (curve S1-A). In this situation, the scour process initiates in front of each of the upstream piles, with individual holes, until they merge into one single scour hole; the maximum scour depth is located in front of the upstream piles of the group. Figure 4.1(b) shows photos of the referred scour hole development. Figure 4.1 – Situation 1: (a) scheme of the temporal evolution of the scour depth (time on linear and logarithmic scales) and (b) photographs of scour hole evolution 2. In Situation 2, corresponding to the case where the pile cap is partially buried in the bed, the scour depth evolution does not follow a unique trend, as identified in Situation 1, but has rather different stages. Three stages are typically identified (Figure 4.2(a)): (i) initially, the scour process develops in front of the pile cap (curve S2-A); (ii) after a lapse of time, which depends on the pile-cap position and thickness, the scour process progresses below the pile cap (curve S2-B); and (iii) finally the scour process continues underneath the pile cap, in front of the upstream piles (curve S2-C). Figure 4.2(b) shows the scour hole development associated with those three stages. 3. In Situation 3, when the pile cap is completely buried in the bed, the scour depth record also displays different stages depending on the top of the pile-cap position below the initial bed level. Three stages are also typically identified (Figure 4.3(a)): (j) initially, the scour process develops in front of the column until the scour hole partly uncovers the top of the pile cap Experimental Study of Local Scour around Complex Bridge Piers 77 (curve S3-A); (jj) that period is followed by a stage (curve S3-B) when the scour depth does not evolve during a (more or less significant, depending of 𝐷𝑐/𝐷𝑝𝑐 ratio) lapse of time and the maximum scour depth is equal to the distance from the initial bed level to the top of the pile cap; and (jjj) on the following stage, the scour process continues in front of the pile cap (curve S3-C). Figure 4.3(b) shows the scour hole development associated with those three stages. Figure 4.2 – Situation 2: (a) scheme of the temporal evolution of the scour depth (time on linear and logarithmic scales) and (b) photographs of scour hole evolution Figure 4.3 – Situation 3: (a) scheme of the temporal evolution of the scour depth (time on linear and logarithmic scales) and (b) photographs of scour hole evolution Experimental Study of Local Scour around Complex Bridge Piers 84 In the three positions of Situation 3 (J, K and L), characterized by the pile cap being initially completely buried in the bed, the temporal evolution of the scour depth does not depend on the pilecap thickness, due to the fact that the scour hole does not reach the bottom of the pile cap in any of the models analysed (4 to 6). Figure 4.13 shows the scour depth time evolution obtained in tests with Model 4, in which those temporal evolutions apply to the other two models. Figure 4.13 – Influence of T/h on the temporal evolution of the scour depth for Situation 3 In Positions J and K, the scour depth temporal evolution curves (Figure 4.13) display a similar trend, with three stages, as described for the general case of tests in this situation (Figure 4.3), while in Position L, characterized by the top of the pile cap remaining below the base of the scour hole, only the first stage was observed. 4.2.4 MAXIMUM SCOUR DEPTHS Table 4.1 (Models 1 to 3) and Table 4.2 (Models 4 to 6) summarize the values of the relative column position, 𝐻𝑐/ℎ, test duration, 𝑡𝑑, and deepest scour depth measured at the end of the tests, 𝑑𝑠𝑚, of the 40 tests reported in sections 4.2.2 and 4.2.3 (all tests with Configuration C1). Experimental Study of Local Scour around Complex Bridge Piers 85 Table 4.1 – Relative column position, test duration and maximum scour depth for Models 1 to 3 Model 1 Model 2 Model 3 𝑯𝒄/𝒉 𝒕𝒅 (h) 𝒅𝒔𝒎 (m) 𝒕𝒅 (h) 𝒅𝒔𝒎 (m) 𝒕𝒅 (h) 𝒅𝒔𝒎 (m) 1.700 310.0 0.114 310.0 0.114 310.0 0.114 1.300 405.8 0.126 - - - - 1.150 412.7 0.139 405.8 0.126 405.8 0.126 1.000 428.1 0.142 412.7 0.139 412.7 0.139 0.667 452.9 0.154 411.7 0.145 675.0 0.141 0.333 551.8 0.148 599.4 0.133 646.3 0.141 0.050 596.7 0.195 593.0 0.169 350.8 0.127 0.000 525.5 0.183 670.9 0.200 594.3 0.185 −0.235 - - 526.6 0.190 576.3 0.121 −0.500 1125.8 0.199 1125.8 0.199 599.6 0.126 −1.500 647.5 0.193 647.5 0.193 696.1 0.166 Table 4.2 – Relative column position, test duration and maximum scour depth for Models 4 to 6 Model 4 Model 5 Model 6 𝑯𝒄/𝒉 𝒕𝒅 (h) 𝒅𝒔𝒎 (m) 𝒕𝒅 (h) 𝒅𝒔𝒎 (m) 𝒕𝒅 (h) 𝒅𝒔𝒎 (m) 1.700 310.0 0.114 310.0 0.114 310.0 0.114 1.300 405.8 0.126 - - - - 1.150 412.7 0.139 405.8 0.126 - - 1.000 428.1 0.142 412.7 0.139 405.8 0.126 0.667 405.8 0.136 310.6 0.123 428.2 0.118 0.333 674.9 0.127 430.8 0.116 453.0 0.106 0.185 478.5 0.172 576.6 0.145 481.1 0.171 0.050 696.2 0.153 671.1 0.095 576.6 0.145 0.000 593.0 0.077 646.5 0.079 647.4 0.130 −0.250 1126.0 0.089 1126.0 0.089 1126.0 0.089 −0.500 594.6 0.115 594.6 0.115 594.6 0.115 −1.500 596.8 0.155 596.8 0.155 596.8 0.155 4.3. SCOUR DEPTH TIME EVOLUTION IN TESTS WITH MODEL 7 (FEUP’S MODEL) 4.3.1 INFLUENCE OF THE PILE-CAP POSITION Eight tests with different pile-cap position were performed with Model 7. Those tests include: three to Situation 1, three to Situation 2 and two to Situation 3, as shown in Figure 3.4(d). Figure 4.14(a) shows the temporal evolution of the scour depth for the three tests of Situation 1 (Positions M, N and O), all the corresponding curves showing similar trends to curve S1-A (Figure 4.1). The slight increment in the scour depth values from Position M to Position O may be justified by the corresponding small increment of the area exposed to the flow. For the three tests of Situation 2 Experimental Study of Local Scour around Complex Bridge Piers 86 (Positions P, Q and R), the three characteristic stages described for Models 1 to 6 (curve S2 of Figure 4.2) were also observed. However, the scour depth evolution trend in these tests is more similar to the typical one obtained for tests of Situation 1, as shown in Figure 4.14(b). This may be justified by the fact that the longitudinal axis of the pile cap overlaps that of the alignment of piles (Figure 3.1), this enabling the upstream pile to contribute to the scour process immediately after the entire front of the pile cap is exposed in the scour hole. Figure 4.14(c) shows the scour depth time evolution for the two tests of Situation 3 (Positions S and T), where once again, due to the particular complex pier geometry, the trend of the curves obtained is similar to that observed for Models 1 and 2. In test M7S1 the three characteristic stages of curve S3 (Figure 4.3) were observed, where the duration of the intermediate stage (S3-B) was short as observed in tests M2J1 and M2K1 of Model 2. In test M7T1, characterized by the top of the pile cap remaining below the base of the scour hole, only the first stage was observed, as expected. Figure 4.14 – Influence of the pile-cap elevation on the temporal evolution of the scour depth for: (a) Situation 1 (Positions M to O), (b) Situation 2 (Positions P to R) and (c) Situation 3 (Positions S and T) Experimental Study of Local Scour around Complex Bridge Piers 87 4.3.2 MAXIMUM SCOUR DEPTHS Table 4.3 summarizes the values of the relative column position, 𝐻𝑐/ℎ, test duration, 𝑡𝑑, and deepest scour depth measured at the end of the tests, 𝑑𝑠𝑚, of the 8 tests reported in the previous section (all tests with Configuration C1). Table 4.3 – Relative column position, test duration and maximum scour depth for Model 7 𝑯𝒄/𝒉 𝒕𝒅 (h) 𝒅𝒔𝒎 (m) 1.500 264.5 0.134 1.000 166.5 0.135 0.667 245.2 0.141 0.322 291.0 0.178 0.161 273.0 0.213 0.000 299.2 0.178 −0.333 360.0 0.151 −1.500 334.7 0.167 4.4. CRITERION TO STOP LABORATORY EXPERIMENTS As mentioned in section 2.3.4, some authors (e.g., Coleman, 2005; Melville et al., 2006; AtaieAshtiani et al., 2010) use as a criterion to stop laboratory tests with complex piers (equilibrium scour stage) the same criterion proposed by Melville and Chiew (1999) for tests with single piers. Thus, the time needed to develop equilibrium scour depth, 𝑡𝑒, is defined as the time at which the scour hole develops to a depth at which the rate of increase in scour does not exceed 5% of the pier diameter in the subsequent 24 h period. In complex piers, the mentioned authors use, as reference, the smaller value of 5% of the complex pier characteristic length (e.g., its equivalent pier diameter, 𝐷𝑒) and of the flow depth (ℎ). In all 48 tests performed in this study for Configuration C1 (i.e., complete complex pier), the equivalent pier diameter (according to equations suggested by Coleman 2005, presented in detail in section 2.3.6.1) was used as the smaller dimension length of the complex pier for the evaluation of Melville and Chiew (1999) criterion. The scour depth evolution recorded in test M2H1 was selected here to exemplify this criterion. Figure 4.15(a) shows the temporal variation of the relative scouring rate (∆𝑑𝑠/𝐷𝑒) in 24 hours associated to the scour depth evolution for that test. According to this figure, the time to obtain a scouring rate of 5% (mentioned criterion) is approximately 3.9 days. For this duration, the experimental scour depth was 0.115 m as shown in Figure 4.15(b). Hence, if hypothetically, test M2H1 had been finished immediately after 3.9 days (regarding the mentioned 5% criterion) the bottom of the scour hole developed would not have reached the pile group. In fact, in this experiment, the scour process began in front of the upstream piles after approximately 14 days (Figure 4.15(b)), when the rate of scour depth evolution increased very rapidly, higher than 5%, as shown in Figure 4.15(a). After the test duration of 24.7 days, a scour depth of 0.169 m was achieved, which is 47% higher than the scour depth obtained by the 5% criterion. Experimental Study of Local Scour around Complex Bridge Piers 88 Figure 4.15 – Experiment M2H1: (a) scour rate evolution and (b) temporal evolution of the scour depth Table 4.4 (Models 1 to 3), Table 4.5 (Models 4 to 6) and Table 4.6 (Model 7) summarize the minimum test duration, 𝑡𝑑5%, in which the scour rate fulfils the criterion of 5% suggested by Melville and Chiew (1999) and the corresponding scour depths, 𝑑𝑠5%, for all experiments of Configuration C1 with the seven models. The equivalent diameter of the complex pier, 𝐷𝑒, used in the analyses is also included. As mentioned in section 3.2.3, some tests were used to cover the same pile-cap position in different models; therefore, the results of one test in those pile-cap positions were only included in the tables. Table 4.4 – Relative column position, equivalent diameter of the complex pier, test duration and scour depth with 5% criterion for Models 1, 2 and 3 Model 1 Model 2 Model 3 𝑯𝒄/𝒉 𝑫𝒆 (m) 𝒕𝒅𝟓% (h) 𝒅𝒔𝟓% (m) 𝑫𝒆 (m) 𝒕𝒅𝟓% (h) 𝒅𝒔𝟓% (m) 𝑫𝒆 (m) 𝒕𝒅𝟓% (h) 𝒅𝒔𝟓% (m) 1.700 0.089 71.9 0.096 1.000 0.124 93.4 0.109 0.667 0.143 115.0 0.111 0.136 123.3 0.119 0.127 94.2 0.102 0.333 0.162 46.6 0.087 0.157 78.6 0.080 0.138 74.3 0.064 0.050 0.162 188.5 0.158 0.162 93.7 0.115 0.139 99.7 0.102 0.000 0.162 172.6 0.154 0.162 117.3 0.129 0.138 103.7 0.128 −0.235 0.164 97.6 0.140 0.139 72.2 0.070 −0.500 0.167 93.9 0.114 0.139 97.5 0.100 −1.500 0.170 104.0 0.141 0.140 103.7 0.113 Experimental Study of Local Scour around Complex Bridge Piers 89 Table 4.5 – Relative column position, equivalent diameter of the complex pier, test duration and scour depth with 5% criterion for Models 4, 5 and 6 Model 4 Model 5 Model 6 𝑯𝒄/𝒉 𝑫𝒆 (m) 𝒕𝒅𝟓% (h) 𝒅𝒔𝟓% (m) 𝑫𝒆 (m) 𝒕𝒅𝟓% (h) 𝒅𝒔𝟓% (m) 𝑫𝒆 (m) 𝒕𝒅𝟓% (h) 𝒅𝒔𝟓% (m) 1.000 0.115 127.8 0.120 0.106 94.7 0.103 0.667 0.126 52.3 0.090 0.120 72.4 0.086 0.114 100.2 0.094 0.333 0.129 78.8 0.088 0.125 76.6 0.068 0.121 89.0 0.082 0.185 0.126 175.0 0.128 0.126 104.0 0.087 0.124 173.1 0.123 0.050 0.121 55.3 0.008 0.121 54.1 0.002 0.121 121.0 0.091 0.000 0.120 47.6 0.006 0.120 51.5 0.003 0.120 54.5 0.019 −0.250 0.115 52.4 0.050 −0.500 0.111 76.0 0.100 −1.500 0.110 163.2 0.114 Table 4.6 – Relative column position, equivalent diameter of the complex pier, test duration and scour depth with 5% criterion for Model 7 𝑯𝒄/𝒉 𝑫𝒆 (m) 𝒕𝒅𝟓% (h) 𝒅𝒔𝟓% (m) 1.500 0.050 154.5 0.130 1.000 0.061 118.5 0.133 0.667 0.072 123.5 0.131 0.322 0.083 171.0 0.169 0.161 0.088 196.1 0.209 0.000 0.086 176.0 0.162 −0.333 0.088 164.0 0.145 −1.500 0.089 150.3 0.156 According to the results of Table 4.4, Table 4.5 and Table 4.6, it can be concluded that the relation between the scour depth obtained with the 5% criterion, 𝑑𝑠5%, and the ending scour depth measured in the tests, 𝑑𝑠𝑚, was on average 81.2%, 72.3% and 74.1% for Situations 1 to 3, respectively. In fact, these values exclude tests with Models 4, 5 and 6 for positions 𝐻𝑐/ℎ=[0.05,0.0] in which the correspondent relations (𝑑𝑠5%/𝑑𝑠𝑚) obtained were abnormally lower than 15%; the considerable discrepancy in these cases may be explained by the fact that scour rate values less than the 5% criterion limit have been achieved quite early in the development of the scouring process. On the other hand, the time duration to reach the equilibrium condition should be on average 102, 109 and 107 hours for Situations 1, 2 and 3 respectively (𝑡𝑑5% in Table 4.4, Table 4.5 and Table 4.6). Nevertheless, those time durations were smaller than those required to obtain the different scouring phases detected (namely, stages B and C in Situations 2 and 3). It is assumed herein that the expressions developed by Sheppard et al. (2011), taking into account the findings of Melville and Chiew (1999), for estimating the time to reach 90% of 𝑑𝑠𝑒 are adequate to estimate test durations at complex piers. In accordance, the test duration, 𝑡𝑑𝑀𝑆, is evaluated by Experimental Study of Local Scour around Complex Bridge Piers 90 𝑡𝑑𝑀𝑆(days)= { 200𝐷𝑒 𝑈(𝑈 𝑈𝑐−0.4)𝑒−1.83𝑈 𝑈𝑐 for ℎ 𝐷𝑒>6 127.8𝐷𝑒 𝑈(𝑈 𝑈𝑐−0.4)(ℎ 𝐷𝑒)0.25𝑒−1.83𝑈 𝑈𝑐 for ℎ 𝐷𝑒≤6 (4.1) Equation (4.1) is valid for 0.4<𝑈/𝑈𝑐<1.0. In this equation, the pier width of the original expression (Sheppard et al., 2011) was replaced by an equivalent diameter 𝐷𝑒 of the complex pier. The application to the tests of this study (Configuration C1) enabled to obtain the scour depth (𝑑𝑠𝑚𝑀𝑆) measured at the time duration defined (240 hours <𝑡𝑑𝑀𝑆< 390 hours) according to equation (4.1) and the corresponding ratio 𝑑𝑠𝑚𝑀𝑆/𝑑𝑠𝑚≈[0.95,0.81,0.87] for Situations 1 to 3, respectively. These results confirm that equation (4.1) is a good approximation to estimate a priori the time duration of the scour tests to be performed. In these calculations, the equivalent diameters, 𝐷𝑒, were calculated with the expressions suggested by Coleman (2005) (presented in detail in section 2.3.6.1). As one of the objectives of this study is to present a method to predict the equilibrium scour at complex piers (Chapter 7), the present author recommends using equations (7.7) to (7.17) to estimate 𝐷𝑒 in future application of equation (4.1). 4.5. CONCLUSIONS From the previous discussion, the most important conclusions of this chapter can be drawn: 1. Seven complex pier models, characterized in Table 3.1, were used to quantify the influence of the complex pier position and geometry on the scour depth time evolution. The experimental results were classified according to three pile cap situations: (i) Situation 1, characterized by the bottom of the pile cap being above the initial bed level; (ii) Situation 2, characterized by the pile cap being partially buried in the initial bed configuration; and (iii) Situation 3, characterized by the pile cap being initially completely buried in the bed. In Situation 1, the pile group is the main component of the complex pier to contribute to the scour process while in Situation 2, most of the scour process is associated to the column and the pile cap. In Situation 3, the column is the main component to contribute to the scour process; 2. The temporal evolution of scour depth at complex piers is generally influenced by the relative column position (𝐻𝑐/ℎ), by the relative column width (𝐷𝑐/𝐷𝑝𝑐), by the relative pile-cap thickness (𝑇/ℎ) and by the pile-group configuration. The different stages in the scour depth time evolution are associated with the number of structural elements of the complex pier that are exposed to the flow inside the scour hole developed along the scouring process; and 3. The criterion established to stop the tests by Melville and Chiew (1999) for single piers, also commonly used in complex piers, was evaluated. This criterion seems to no longer have such a good performance when more than one component of the complex pier is exposed to the flow in the scour hole. In general, the application of this criterion would imply much smaller experiment running times than those required for the different scouring phases (e.g., the different stages presented in sections 4.2 and 4.3 for the complex pier models of this study). Equation (4.1), based on Sheppard et al. (2011), can be used to estimate the time recommended to stop the tests with complex piers. Experimental Study of Local Scour around Complex Bridge Piers 91 5. EFFECT OF COMPLEX PIER GEOMETRY ON EQUILIBRIUM SCOUR DEPTH 5.1. INTRODUCTION According to the dimensional analysis performed in section 2.3.2, the equilibrium scour depth at complex piers, 𝑑𝑠𝑒, may depend of the following non-dimensional parameters 𝑑𝑠𝑒 𝐷𝑐=𝜑 ( 𝜎𝑔,𝐾𝑆𝑐,𝐾𝜃,ℎ 𝐷𝑐,𝐷𝑐 𝑑50,𝑈 𝑈𝑐,𝑢∗𝑑50 𝜐,𝑢∗𝑡 𝐷𝑐, 𝐾𝑆𝑝𝑐,𝐷𝑐 𝐷𝑝𝑐,𝑇ℎ,𝐻𝑐 ℎ,𝑓𝑙 𝑓𝑡,𝑓𝑝 𝐷𝑝,𝐾𝑆𝑝,𝑚,𝑆𝑚 𝐷𝑝,𝑛,𝑆𝑛 𝐷𝑝 ) (2.37) It should be recalled that: (1) the first seven non-dimensional parameters of the upper-line in equation (2.37) have been extensively studied for single piers (see section 2.2.5); (2) the last non-dimensional parameter of the upper-line in equation (2.37) – that corresponds to the temporal evolution of the scour depth at complex piers – (or similar form of this relationship depending on pier width adopted) was described and discussed in Chapter 4; and (3) the last five non-dimensional parameters of the lowerline in equation (2.37) have been extensively studied for pile groups (see section 2.3.5.5). As mentioned in section 2.3.5, the five studies identified as relevant on scouring at complex piers are focused on characterizing and quantifying the influence of the relative column position, 𝐻𝑐/ℎ (𝐻𝑐= distance from the initial bed level to the top of the pile cap; ℎ= approach flow depth), on 𝑑𝑠𝑒. The results of those studies indicate that 𝑑𝑠𝑒 depends directly on 𝐻𝑐/ℎ and that the maximum scour depth occurs when the pile cap is partially buried in the bed. Additionally, Ferraro et al. (2013) studied the effect of the relative pile-cap thickness, 𝑇/ℎ (𝑇= pile-cap thickness), on 𝑑𝑠𝑒. They concluded that, in general, the maximum scour depth values measured on complex piers increase with increasing pilecap thickness. Furthermore, the effect of the relative column width, 𝐷𝑐/𝐷𝑝𝑐 (𝐷𝑐= column width; 𝐷𝑝𝑐= pile-cap width), on 𝑑𝑠𝑒 has been extensively studied for different geometries of the complex piers (i.e., at columns founded on caissons, section 2.3.5.3). Sheppard and Renna (2010) and Arneson et al. (2012) presented a design chart to account for the shielding effect due to the pile-cap extension (from column faces) lengths as function of 𝐻𝑐/ℎ. The chart was obtained based on tests with column/pile-cap sets suspended on the approach flow. In the present study, the availability of two comparatively large flumes (sections 3.3 and 3.4) rendered possible to generate additional scour data at complex piers, i.e., 48 long-duration (7 to 47 days) tests obtained from seven different complex pier geometries (Figure 3.1). All 48 tests were performed with Configuration C1 (i.e., complex pier with the three elements, Figure 3.2). The aim of this chapter is to: (1) investigate the influence of the relative column position, the relative column width, the relative Experimental Study of Local Scour around Complex Bridge Piers 92 pile-cap thickness and the pile-group configuration on the maximum local scour depth with the results of the 48 tests performed; and (2) compare the results of the present experimental study with the results of studies performed up to the present date on complex pier models (i.e., the thirteen models in Table 2.2). Within the first objective the combined effects of the different parameters mentioned before were analysed, namely: (a) 𝐷𝑐/𝐷𝑝𝑐 and 𝐻𝑐/ℎ on 𝑑𝑠𝑒 on the basis of the results obtained with Model 2 (𝐷𝑐/𝐷𝑝𝑐= 0.85), Model 3 (𝐷𝑐/𝐷𝑝𝑐= 0.70) and Model 5 (𝐷𝑐/𝐷𝑝𝑐= 0.55), in which only the column dimensions (width and length) were changed (Table 3.1); (b) 𝑇/ℎ and 𝐻𝑐/ℎ on 𝑑𝑠𝑒 by means of the results obtained with Model 4 (𝑇/ℎ= 0.60), Model 5 (𝑇/ℎ= 0.45) and Model 6 (𝑇/ℎ= 0.30), in which only the pile-cap thickness was changed (Table 3.1); and (c) the pile-group configuration (characterized by the number of alignments, 𝑛) and 𝐻𝑐/ℎ on 𝑑𝑠𝑒 on the basis of the results obtained with Model 3 (𝑛= 2) and Model 7 (𝑛= 1). The current chapter is organized as follows: a brief introduction was presented in the current section (5.1); equilibrium scour depths obtained for the 48 tests performed in this study are summarized in section 5.2; main results concerning the influences of 𝐻𝑐/ℎ, 𝐷𝑐/𝐷𝑝𝑐 and 𝑇/ℎ on 𝑑𝑠𝑒 based on the tests performed in this work are presented and discussed in sections 5.3 to 5.5; section 5.6 discusses the comparison of the main results obtained in the present experimental data with the published experimental data; and section 5.7 is dedicated to the related main conclusions. 5.2. EQUILIBRIUM SCOUR DEPTHS According to the early work of Chabert and Engeldinger (1956) and latter works such as Ettema (1980), it can be assumed that, for clear-water conditions, the equilibrium stage in the scour evolution is attained asymptotically, as discussed in sections 2.2.4. Hence, in order to estimate the equilibrium scour depth, 𝑑𝑠𝑒, the recorded experimental scour depth values, summarized in the Appendix, were extrapolated to time infinite by means of the following equation: 𝑑𝑠=𝑑𝑠𝑒[1−𝑒−𝑎(𝑈𝑡 𝐷𝑒)𝑏] (5.1) where, 𝑑𝑠 = the scour depth at time 𝑡; 𝑈 = the mean velocity of the approach flow; 𝐷𝑒 = the equivalent diameter of the complex pier; and 𝑎 and 𝑏 = parameters obtained by regression analysis. Equation (5.1) is a modification of the Franzetti et al. (1982) equation, in which the single cylindrical pier diameter of the original expression was replaced by the parameter 𝐷𝑒. This change is due to the fact that the complex pier has three structural components, each with a different width. The equivalent diameter, 𝐷𝑒, was calculated with the equations suggested by Coleman (2005) (see section 2.3.6.1). Equation (5.1) was fitted to the experimental data obtained from the 48 tests performed with Configuration C1. In tests in which the scour depth time evolution presented a unique trend (e.g., all tests of Situation 1) the adjustment was applied using all experimental data. In the other experiments, which showed two or more scour depth time evolution stage trends, the adjustment was carried out taking into account only the experimental data associated to the ultimate stage of the scour depth time evolution curve. The equilibrium scour depth values obtained by extrapolation for all experiments with equation (5.1) are summarised in Table 5.1 for Models 1 to 6 and in Table 5.2 for Model 7. Experimental Study of Local Scour around Complex Bridge Piers 93 Table 5.1 – Equilibrium scour depths (extrapolated values) with Models 1 to 6 Pile-cap position 𝑯𝒄 𝒉 Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 𝒅𝒔𝒆 (m) 𝒅𝒔𝒆 (m) 𝒅𝒔𝒆 (m) 𝒅𝒔𝒆 (m) 𝒅𝒔𝒆 (m) 𝒅𝒔𝒆 (m) A 1.700 0.123 0.123 0.123 0.123 0.123 0.123 B 1.300 0.144 0.144 C 1.150 0.156 0.144 0.144 0.156 0.144 D 1.000 0.168 0.156 0.156 0.168 0.156 0.144 E 0.667 0.193 0.185 0.175 0.173 0.161 0.141 F 0.333 0.199 0.192 0.177 0.160 0.159 0.136 G 0.185 0.201 0.168 0.195 H 0.050 0.218 0.189 0.175 0.184 0.118 0.176 I 0.000 0.223 0.245 0.225 0.113 0.112 0.157 J −0.235 0.212 0.162 J −0.250 0.103 0.103 0.103 K −0.500 0.228 0.228 0.184 0.148 0.148 0.148 L −1.500 0.240 0.240 0.218 0.178 0.178 0.178 Table 5.2 – Equilibrium scour depths (extrapolated values) with Model 7 Pile-cap position 𝑯𝒄/𝒉 𝒅𝒔𝒆 (m) M 1.500 0.139 N 1.000 0.141 O 0.667 0.150 P 0.322 0.188 Q 0.161 0.230 R 0.000 0.188 S −0.333 0.168 T −1.500 0.176 5.3. COMBINED EFFECTS OF RELATIVE COLUMN WIDTH AND POSITION The combined effects of the relative column with, 𝐷𝑐/𝐷𝑝𝑐, and the relative column position, 𝐻𝑐/ℎ, on the equilibrium scour depth, 𝑑𝑠𝑒, were evaluated on the basis of the results obtained with Models 2, 3 and 5 (Figure 3.1). By considering those three models, four recognized parameters that influence 𝑑𝑠𝑒 could change: (1) the width of the column (𝐷𝑐); (2) the pile-cap front and side overhang length (𝑓𝑙 and 𝑓𝑡 in Figure 2.21); (3) the sediment coarseness ratio (expressed by 𝐷𝑒/𝑑50); and (4) the flow shallowness ratio (expressed by ℎ/𝐷𝑒). Nevertheless, it can be considered that the effects of sediment coarseness and flow shallowness are practically the same for all the three models (2, 3 and 5) and the corresponding 𝐻𝑐/ℎ positions. These two effects were calculated by the equations suggested by Sheppard et al. (2014), i.e., equations (2.28) and (2.30). Taking that into account, in this study the 𝑑𝑠𝑒 variations in the three models are associated only with the ratio 𝐷𝑐/𝐷𝑝𝑐 and the pile-cap overhang length. Experimental Study of Local Scour around Complex Bridge Piers 100 5.6. COMPARISON OF THE PRESENT EXPERIMENTAL STUDY WITH RESULTS REPORTED IN LITERATURE 5.6.1 ASSESSMENT OF EXPERIMENTAL DATA This section includes the comparison of the results obtained from the thirteen models reported in the literature (see Table 2.2) with the results obtained in the present study (from seven models) and extensively described and discussed in the previous sections of this chapter. Table 5.3 summarizes the most relevant flow characteristics and geometry parameters of those twenty complex pier models. The table includes also the duration of the reported tests. The same model designations used in Table 2.2 are used in Table 5.3 for the models from literature. Table 5.3 – Experimental models: flow parameters, model geometry parameters and test durations Model 𝑼/𝑼𝒄 𝑩/𝒉 𝑾𝒐/𝑩 𝑫𝒄/𝑫𝒑𝒄 𝒇𝒍/𝒇𝒕 𝑻/𝒉 𝒉/𝑫𝒆∗ 𝑫𝒆∗/𝒅𝟓𝟎 𝒕𝒅 (days) Co1 0.75 2.5 0.07 0.25 0.00 0.10 9.92 72 NS Co2 0.85 2.5 0.07 0.25 1.11 0.10 9.92 72 NS Co3 0.83 4.5 0.10 0.53 0.89 0.24 1.97 141 NS AA1 0.72-0.85 3.9-4.5 0.07 0.24 0.44 ≈0.22 ≈3.50 70 0.4-3.1 AA2 0.74-0.80 3.9-4.3 0.09 0.47 0.96 ≈0.28 ≈3.00 83 0.4-2.1 GC 0.92 7.0 0.14 0.34 1.00 0.50 0.91 92 4.8-18.1 Fe1 0.92 7.0 0.14 0.33 1.00 0.50 0.93 90 8.3-37.0 Fe2 0.92 7.0 0.13 0.33 1.00 0.01 0.98 87 3.2-41.2 A1 0.95 6.3 0.12 0.80 1.00 0.13 1.32 225 1.0 A2 0.95 6.3 0.10 0.73 1.00 0.13 1.84 172 1.0 A3 0.95 6.3 0.11 0.38 1.71 0.46 1.69 179 1.0 A4 0.95 6.3 0.05 0.39 0.85 0.15 4.32 65 1.0 A5 0.95 6.3 0.08 0.49 3.93 0.32 2.39 126 1.0 1 (PS) 0.80 10.0 0.09 0.85 1.00 0.60 1.22 191 12.9-46.9 2 (PS) 0.80 10.0 0.09 0.85 1.00 0.45 1.22 190 12.9-46.9 3 (PS) 0.80 10.0 0.08 0.70 1.00 0.45 1.41 165 12.9-29.0 4 (PS) 0.80 10.0 0.08 0.55 1.00 0.60 1.55 150 12.9-46.9 5 (PS) 0.80 10.0 0.08 0.55 1.00 0.45 1.58 148 12.9-46.9 6 (PS) 0.80 10.0 0.07 0.55 1.00 0.30 1.60 145 12.9-46.9 7 (PS) 0.97 5.6 0.10 0.74 1.00 0.32 2.03 103 6.9-15.0 Note: Co = Coleman (2005); AA = Ataie-Ashtiani et al. (2010); GC = Grimaldi and Cardoso (2010); Fe = Ferraro et al. (2013); A = Amini et al. (2014); PS = Present study; 𝑊𝑜 = equivalent width of obstruction of the pier; 𝐷𝑒∗= maximum equivalent diameter (calculated according to Coleman 2005); NS = not specified. The wall effect is negligible when 𝐵/ℎ>5 (𝐵 = flume width) in which the velocity field is twodimensional at the central section of the channel, in line with Yalin (1971). According to that criterion and to the values in Table 5.3, tests with Models Co1 and Co2 may be markedly reflecting wall effects while tests with Models Co3, AA1 and AA2 may have a slight influence of wall effects. Experimental Study of Local Scour around Complex Bridge Piers 101 In fact, in the specific case of complex piers, there are no studies that define the equivalent obstruction width of the pier, 𝑊𝑜, for the calculation of the effect of horizontal contraction. The author of the present study considers that the contraction effect may be calculated taking into account the ratio 𝑊𝑜/𝐵. In studies of single piers (e.g., Chiew and Melville, 1987), the contraction effect is negligible when 𝑊𝑜/𝐵<0.10, in which 𝑊𝑜 is equal to the single pier width. In the present study, the 𝑊𝑜 values of the twenty models were calculated as the ratio between the maximum obstruction area of the pier (in a cross section perpendicular to the channel walls) and the flow depth. The maximum area of obstruction was obtained after analysing different positions of the complex pier relative to the initial bed level, as illustrated in Figure 5.7. According to Table 5.3, tests with Models GC, Fe1, Fe2, A1 and A3 may have a slight influence of the contraction effect since 𝑊𝑜/𝐵>0.10 Figure 5.7 – Scheme of (a) complex pier obstruction area (Model Fe1) and (b) equivalent obstruction width of the complex pier As presented in Table 5.3, all tests performed by Ataie-Ashtiani et al. (2010) and by Amini et al. (2014) were carried out with short durations (between 0.4 and 3.1 days) in comparison with the minimum duration suggested by several authors, i.e., 7 days (see section 2.3.4). In accordance, it is possible that the equilibrium scour depth has not been reached in the tests of those five models (AA1, AA2, A1, A2, A3, A4 and A5). Given that the scour depth data reported by each of the mentioned authors was not extrapolated – and most of the scour depth records were not available, not allowing the required extrapolation of 𝑑𝑠𝑒 values – the comparative analysis of the literature and the present study results was performed and will be described by taking into account the scour depth values measured at the end of the tests, 𝑑𝑠𝑚. Similar behaviour could be identified in the equilibrium scour depth variation as a function of 𝐻𝑐/ℎ obtained by considering the extrapolated values and the measured values for the models where the time series are available (Models of Fe1, Fe2, GC and of the present study). The corresponding extrapolated values did show a shift of 10-20% (depending on the complex pier models) to the measured values. As the experimental tests were not performed under the same conditions (see Table 5.3), the measured scour depth values were adjusted taking into account the influence of flow shallowness, ℎ/𝐷𝑒, of flow intensity, 𝑈/𝑈𝑐, and of sediment coarseness, 𝐷𝑒/𝑑50. The adjustment process was accomplished through equations (2.28) to (2.30), using the 𝐷𝑒 values previously calculated in section 4.4. In the following paragraphs the comparison of the scour depth results is performed for the three situations previously discussed, i.e., pile cap above the initial bed level (Situation 1), pile cap partially buried (Situation 2) and pile cap completely buried in the bed (Situation 3). The results of Model Fe2 – due to the particular dimension of the pile-cap thickness – and the results of all models by Amini et al. (2014) Experimental Study of Local Scour around Complex Bridge Piers 102 (Models A1–A5 in Table 5.3) – due to the extremely short durations of the tests – were excluded from that analysis. 5.6.2 COMPARISON IN SITUATION 1 The evaluation of the effect of 𝑇/ℎ on 𝑑𝑠𝑚 was performed only for Situation 1 (where the pile cap is above the initial bed level) and particularly for the position where the pile cap is completely immersed in the flow, with the column out of the flow. The values of 𝑑𝑠𝑚/𝑑𝑠𝑝𝑔 (𝑑𝑠𝑝𝑔= maximum scour depth of the pile group, i.e., complex pier with the bottom of the pile cap out of the water) are plotted against 𝑇/ℎ in Figure 5.8. It is clear that the parameter 𝑇/ℎ influences 𝑑𝑠𝑚/𝑑𝑠𝑝𝑔, leading to increasing normalized scour depth as 𝑇/ℎ increases, as observed for the envelope curve of experimental data. This result corroborates the findings of Melville and Dongol (1992) and Lagasse et al. (2010) on experimental tests for piers with idealized debris rafts at the water surface. Melville and Dongol (1992) tested cylindrical shapes while Lagasse et al. (2010) tested rectangular shapes of the idealized debris (component which can resemble the pile cap of the complex pier). Figure 5.8 – Effect of the relative pile-cap thickness on the relative maximum scour depth According to Figure 5.8, it may be concluded that other parameters than 𝑇/ℎ affect 𝑑𝑠𝑚/𝑑𝑠𝑝𝑔, and those can be the main factors that varied from the different studies, namely the shape of the pile cap, the number of pile alignments and the ratio 𝑓𝑝/𝐷𝑝 (𝑓𝑝 = longitudinal extension length of the pile cap out from the upstream pile front; 𝐷𝑝= pile width). 5.6.3 COMPARISON IN SITUATION 2 For a comparative analysis of complex pier models under Situation 2 (i.e., 0≤𝐻𝑐≤𝑇), 𝑑𝑠𝑚 and 𝐻𝑐 values were normalized, respectively, by 𝐷𝑝𝑐 (as the pile cap is the main component to contribute to the scour process in that situation) and by 𝑇 (parameter that defines the upper limit of 𝐻𝑐 for that situation). The adjusted values of 𝑑𝑠𝑚/𝐷𝑝𝑐 are plotted against 𝐻𝑐/𝑇 in Figure 5.9. In the left plot, Figure 5.9(a) corresponds to models with rectangular pile caps whereas Figure 5.9(b) relates to models with circular and rectangular round-nose pile caps. The analysis highlights that in general, the relative difference in 𝑑𝑠𝑚 values may be associated with the effect of the relative column width, 𝐷𝑐/𝐷𝑝𝑐; the effect of the pile-cap extensions symmetry, 𝑓𝑙/𝑓𝑡; the pile-cap shape; the relative pile-cap thickness, 𝑇/ℎ; and the test duration, 𝑡𝑑. As mentioned in section 2.3.5.2, similar column/pile-cap configuration Experimental Study of Local Scour around Complex Bridge Piers 103 sets with circular or round-nose rectangular shapes (i.e., with identical component’s widths) lead to similar scour depth values, as shown in Figure 5.9(b) for Models GC and Fe1. The reduction in 𝑑𝑠𝑚/𝐷𝑝𝑐 values from Model Co1 to Model Co2, as shown in Figure 5.9(a), is mostly associated with the increment of the pile-cap front extension length (i.e., increase of 𝑓𝑙/𝑓𝑡 ratio), as previously explained in section 2.3.5.3. Figure 5.9 – dsm/Dpc as function of Hc/T for Situation 2: (a) rectangular pile-cap shape and (b) circular and rectangular round-nose pile-cap shapes The assessment of the critical relative column position at which the maximum scour depth can occur, (𝐻𝑐/𝑇)max, is important in terms of complex pier design. The experimental fitting curves presented for the different models on Figure 5.9 do enable to obtain the corresponding values of (𝐻𝑐/𝑇)max, included in Table 5.4. Table 5.4 – Values of (Hc/T)max as function of relative column width Models from Literature 𝑫𝒄 𝑫𝒑𝒄 (𝑯𝒄 𝑻)𝒎𝒂𝒙 Models of present study 𝑫𝒄 𝑫𝒑𝒄 (𝑯𝒄 𝑻)𝒎𝒂𝒙 Model AA1 0.24 0.83 Model 4 0.55 0.26 Model Co1 0.25 0.75 Model 5 0.55 0.39 Model Co2 0.25 0.66 Model 6 0.55 0.37 Model Fe1 0.33 0.62 Model 3 0.70 0.00 Model GC 0.34 0.58 Model 7 0.74 0.50 Model AA2 0.47 0.47 Model 1 0.85 0.00 Model Co3 0.53 0.28 Model 2 0.85 0.00 Experimental Study of Local Scour around Complex Bridge Piers 104 It is clear that (𝐻𝑐/𝑇)max decreases with increasing 𝐷𝑐/𝐷𝑝𝑐 ratio for the models from literature. In the three models of the present study with 𝐷𝑐/𝐷𝑝𝑐=0.55 (Models 4, 5 and 6) the values of (𝐻𝑐/𝑇)max obtained fit into a narrow range, where the corresponding value for Model Co3 does also fit. Whereas, in three models of the present study with 𝐷𝑐/𝐷𝑝𝑐≥0.70 (Models 3, 1 and 2) (𝐻𝑐/𝑇)max is null (= 0). In accordance, it can be assumed (by extrapolation of the trend line associated to (𝐻𝑐/𝑇)max values in the range 𝐷𝑐/𝐷𝑝𝑐≤0.55) that the ratio 𝐷𝑐/𝐷𝑝𝑐= 0.65 is the minimum value for which the maximum scour depth occurs at position 𝐻𝑐=0. Taking into account that the value of (𝐻𝑐/𝑇)max observed for Model 7 of the present study is atypical, what may be justified by the fact that this model is the only one with a sole alignment of piles. As explained in section 5.5, Model 7 presents different characteristics of the scour process, in particular on the contribution of the pile group when the complex pier is positioned in Situation 2 (for which the maximum scour depth occurs). The analysis of results reveals that the column position is directly influenced by 𝐷𝑐/𝐷𝑝𝑐. Nevertheless, that position may also be influenced by the flow shallowness, ℎ/𝐷𝑝𝑐, and by the symmetry of the pilecap extensions, 𝑓𝑙/𝑓𝑡. The following regression equation takes the full parameters’ dependence in due account, excluding the value of Model 7. (𝐻𝑐 𝑇)max= { 0 for 𝐷𝑐 𝐷𝑝𝑐>0.65 [0.9+0.1(𝑓𝑙 𝑓𝑡)0.4][0.84−3.1(𝐷𝑐 𝐷𝑝𝑐)3.1] 𝐾𝑠𝑝𝑐[tanh(ℎ 𝐷𝑝𝑐 1 √𝐷𝑐/𝐷𝑝𝑐)]0.2 for 0.15≤𝐷𝑐 𝐷𝑝𝑐≤0.65 (5.2) where 𝐾𝑠𝑝𝑐= pile-cap shape factor (1.04 for rectangular shape and 1.0 for circular or round-nose rectangular shapes). In the range 0.15<𝐷𝑐/𝐷𝑝𝑐<0.65, the determination coefficient is 𝑟2=0.76 and the root mean square error is RMSE = 0.12. The lower limit of the range was fixed at 0.15, as this value corresponds to a complex pier configuration with 𝑓𝑙≈3𝐷𝑐 (with 𝑓𝑙/𝑓𝑡≈1), a value that may be considered as a maximum practical ratio in engineering terms. 5.6.4 COMPARISON IN SITUATION 3 For a comparative analysis of the complex pier models under Situation 3 (i.e., 𝐻𝑐<0), the 𝑑𝑠𝑚 and 𝐻𝑐 values were both normalized by 𝑑𝑠𝑒𝑐𝑢 (depth of local scour for a uniform single pier with the same geometrical definition of the complex pier column). The variable 𝑑𝑠𝑒𝑐𝑢 was selected as the normalization factor since the column is the main component to contribute to the scour process in this situation. Figure 5.10 displays the effect of 𝐷𝑐/𝐷𝑝𝑐 and of the column/pile-cap shapes on 𝑑𝑠𝑚/𝑑𝑠𝑒𝑐𝑢 as function of 𝐻𝑐/𝑑𝑠𝑒𝑐𝑢, where each 𝐷𝑐/𝐷𝑝𝑐 ratio is included in brackets on the model’s legend. Similarly to what was mentioned for Situation 2, the Models CG (circular column/pile-cap shapes) and Fe1 (round-nose rectangular column/pile-cap shapes) do show an analogous scour depth variation, as shown in Figure 5.10(a), where these results are compared with the ones obtained by Melville and Raudkivi (1996) for a cylindrical column-caisson model with 𝐷𝑐/𝐷𝑝𝑐=0.37 (represented by MR). The apparent reduction of 𝑑𝑠𝑚 in Models CG and Fe1 compared to Model MR is due to the smaller scour rate that occurs for −0.3<𝐻𝑐/𝑑𝑠𝑐<0, where the scour process is developing below the pile Experimental Study of Local Scour around Complex Bridge Piers 105 cap. This may be due to the discontinuity between the pile cap’s front and the scour hole’s bottom, that leads to a reduction of the strength of the downflow and horseshoe vortices for Models CG and Fe1. Figure 5.10 – Effect of the relative column width and column/pile-cap shapes on dsm/dsecu as function of Hc/dsecu for Situation 3 Figure 5.10(b) shows the comparison of 𝑑𝑠𝑚/𝑑𝑠𝑒𝑐𝑢 for a complex pier with rectangular column/pilecap shapes (Model AA2) and a cylindrical column-caisson model (Model MR for 𝐷𝑐/𝐷𝑝𝑐=0.48). The increment on 𝑑𝑠𝑚 values of Model AA2 relative to Model MR, approximately 8–10% on average, may be associated with the pile-cap shape, since results in rectangular piers reflect higher magnitudes of the flow structure (e.g., downflow, horseshoe vortex, vortices and turbulence intensity) when compared to circular piers, as referred by Dey and Raikar (2007). Figure 5.10(c) displays the comparison of Model Co3 (rectangular column/pile-cap shapes) with Models 4, 5 and 6 of the present study (round-nose rectangular column/pile-cap shapes), where a relevant increase of 𝑑𝑠𝑚 values is observed in the Model Co3 compared to the other three models for the range −0.5<𝐻𝑐/𝑑𝑠𝑒𝑐𝑢<0. This increment can be associated mainly to geometry definitions of Model Co3, namely: the relative thinner pile cap (𝑇/𝑑𝑠𝑒𝑐𝑢≈0.37); the asymmetry of the pile-cap extension lengths (𝑓𝑙/𝑓𝑡=0.89); and the rectangular shape of both the column and pile cap. 5.7. CONCLUSIONS The most important conclusions of this chapter, relative to the experiments performed in this study with Configuration C1, can be summarized as follows: Experimental Study of Local Scour around Complex Bridge Piers 106 1. Seven complex pier models, characterized in Table 3.1, were used to quantify the influence of the complex pier position and geometry on the equilibrium scour depth. The experimental results were classified according to three pile-cap situations: (i) Situation 1, characterized by the bottom of the pile cap being above the initial bed level; (ii) Situation 2, characterized by the pile cap being partially buried in the initial bed configuration; and (iii) Situation 3, characterized by the pile cap being initially completely buried in the bed; 2. The equilibrium scour depth, 𝑑𝑠𝑒, at complex piers is generally influenced by the relative column position (𝐻𝑐/ℎ), by the relative column width (expressed by 𝐷𝑐/𝐷𝑝𝑐 and 𝑓𝑙/𝑓𝑡), by the relative pile-cap thickness (𝑇/ℎ), by the pile-group configuration and by the shape of the complex pier components (i.e., column, pile cap and piles). The equilibrium scour depth at these piers is also influenced by the effects of flow intensity, flow shallowness and sediment coarseness widely characterized for single piers; 3. The combined effect of 𝐷𝑐/𝐷𝑝𝑐 and 𝐻𝑐/ℎ on 𝑑𝑠𝑒 was evaluated for Models 2, 3 and 5. In general, the differences in 𝑑𝑠𝑒 values range from minimal to relevant with decreasing 𝐻𝑐/ℎ ratio, due to the corresponding increasing influence of the column on the scour process. For a specific 𝐻𝑐/ℎ position, the increment in 𝑑𝑠𝑒 values is directly associated with the increment in the column width and also with the corresponding reduction in the pile-cap front and side extension lengths. For the lower relative column-width values, i.e., 𝐷𝑐/𝐷𝑝𝑐<0.6, it could be concluded that the pile cap overhang from the column face plays the role of an obstruction to the downflow adjacent to the column, reducing the vortex system and hence the scour depth. This reduction is most evident in the cases when the top of the pile cap is close to the initial bed level, for which the flow behaviour is similar to collars in single piers. For larger relative column-width values, i.e., 𝐷𝑐/𝐷𝑝𝑐≥0.6, the influence of the pile cap overhang is negligible; 4. The combined effect of 𝑇/ℎ and 𝐻𝑐/ℎ on 𝑑𝑠𝑒 was also evaluated for two sets of complex pier models (i.e., Models 4, 5 and 6 on a set and Models 1 and 2 on another set). In both sets and for Situation 1, the increment in 𝑑𝑠𝑒 values is related to the increment in 𝑇/ℎ, while, in Situation 2, the 𝑑𝑠𝑒 behaviour with 𝐻𝑐/ℎ depends not only on 𝑇/ℎ ratio but also on the pilegroup contribution to the scour process. When the pile cap is completely buried (Situation 3), the effect of 𝑇/ℎ in 𝑑𝑠𝑒 showed to be negligible; and 5. The effect of the pile-group configuration (represented by the number of alignments, 𝑛) on 𝑑𝑠𝑒 was also assessed. This effect is more evident in Situations 1, in which the pile group is the main component contributing to the scour process, whereas in Situation 2, this effect occurs when the piles are exposed to the flow along the scouring process. In these situations and for the piles separation used in the experimental tests, the increment in the number of alignments (𝑛) of the pile group implies an increase in the scour depth. On the comparison of the present experimental study with the results of studies performed to date, it was concluded that: 1. In seven out of the thirteen complex pier models analysed in studies from literature (presented in Table 2.2), the tests were carried out for short durations, i.e., least than four days. That fact may lead to relevant inaccuracy on evaluation of the equilibrium scour depth. Additionally, some of the tests performed with the thirteen models may also be slightly reflecting wall and contraction effects; and 2. The experimental data of seven reported models in addition to the data from the present study were used to evaluate the critical relative column position at which the maximum equilibrium scour depth is achieved, (𝐻𝑐/𝑇)max. The results reveal that (𝐻𝑐/𝑇)max decreases with increasing 𝐷𝑐/𝐷𝑝𝑐 ratio. For practical applications, the relative position (𝐻𝑐/𝑇)max can be obtained through equation (5.2). Experimental Study of Local Scour around Complex Bridge Piers 107 6. COMPLEX PIER COMPONENTS CONTRIBUTIONS ON THE EQUILIBRIUM SCOUR DEPTH 6.1. INTRODUCTION The most commonly used methods to predict the equilibrium scour depth at complex piers, 𝑑𝑠𝑒, are (1) Auckland method (Coleman, 2005), (2) FDOT method (Sheppard and Renna, 2010) and (3) HEC-18 method (Arneson et al., 2012), as presented in section 2.3.6. The last two and most recent methods were developed through quantifying the contribution of each structural pier component to the total scour depth, justifying that these two methods will be retained in the present analysis. The HEC-18 method calculates the total equilibrium scour depth by adding the scour depth assumed to be produced separately by each pier component, as illustrated in Figure 2.34, somehow adopting the superposition concept suggested earlier by Sheppard and Jones (1998). The FDOT method also adopts the superposition concept since the equilibrium scour depth is calculated at one hypothetically equivalent cylindrical pier whose diameter is the sum of the equivalent diameters of the column, the pile cap and the pile group, as shown in Figure 2.36. A key idea to be retained herein is that the HEC-18 and FDOT methods were developed on the basis of experiments performed on isolated components of the complex pier by authors such as Salim and Jones (1996), Sheppard and Jones (1998), Smith (1999) or Jones and Sheppard (2000a). Another important fact is that most of those experiments were of short duration and so do not provide an accurate basis for predicting equilibrium scour depths. More recently, Dey et al. (2008), Muto (2008) and Amini et al. (2011, 2012, 2014) carried out work on scour at complex piers exploiting the superposition concept, but their work also suffers from being based on experiments with rather short durations. Local scour experiments performed for isolated components necessarily ignore the interactions and joint effects of the different components of the complex piers on the near-field flow structure, namely the most obvious: (1) the deflection of the downflow generated along the upstream face of the column by pile cap overhang (characterized by 𝑓𝑙 and 𝑓𝑡, see Figure 2.21); (2) the interactions of the downflow generated by the upstream face of the pile cap and the vortical structures occurring around the piles; and (3) the interactions of the internal boundary layer created along the bottom face of the pile cap and those vortical structures. Such interactions depend on the position of the base of the column relative to the initial bed level, the pile-cap thickness, the longitudinal projection of the pile cap beyond the front of the pile group (see 𝑓𝑝 in Figure 2.21), 𝑓𝑙 and 𝑓𝑡 lengths, and other geometrical pier characteristic dimensions. Considering the scour at a complex pier to be the sum of the scour at the individual components as if they were in isolation ignores the interaction between the constituent components and hence can lead to inaccurate predictions. Indeed, this is probably the reason why existing methods, based upon the superposition concept, do not properly predict the equilibrium scour depth, as stated by, e.g., Ataie-Ashtiani et al. (2010) or Ferraro et al. (2013). Experimental Study of Local Scour around Complex Bridge Piers 108 Since the non-linear interaction between the different components seems to be an important issue, a new approach is attempted in this study to experimentally assess the contribution of each complex pier component to the total equilibrium scour depth. The basic idea behind this new approach can be illustrated with a particular case: for the same approach flow, bed sediment and pier geometry and alignment, the scour depth directly ascribable to the column can be unambiguously evaluated by subtracting the scour depth at an incomplete “pier”, without the particular column, from the scour depth at the equivalent complete pier; it is reasonable to assume that, by putting back the column into the incomplete “pier”, the scour depth would correspond again to the scour depth at the complete pier. The same applies to the other pier components. Accordingly, the scour depth at three different configurations, defined by three different combinations of complex pier components (see Figure 3.2), was experimentally obtained for each position of the base of the column relative to the initial bed level, as defined by 𝐻𝑐. Those were Configuration C1, corresponding to the complete pier, Configuration C2, without the column, and Configuration C3, without the pile group. Configurations C2 and C3 do not represent real complex piers; instead, they are experimental configurations used to calculate, through subtraction, the contribution of the missing complex pier component to the total scour depth, as follows: 𝑑𝑠𝑒𝑐=𝑑𝑠𝑒𝐶1−𝑑𝑠𝑒𝐶2 (6.1) 𝑑𝑠𝑒𝑝𝑔=𝑑𝑠𝑒𝐶1−𝑑𝑠𝑒𝐶3 (6.2) 𝑑𝑠𝑒𝑝𝑐=𝑑𝑠𝑒𝐶1−𝑑𝑠𝑒𝑐−𝑑𝑠𝑝𝑔 (6.3) where 𝑑𝑠𝑒𝑐, 𝑑𝑠𝑒𝑝𝑐 and 𝑑𝑠𝑒𝑝𝑔 are, respectively, the equilibrium scour depths associated with the column, the pile cap and the pile group; and 𝑑𝑠𝑒𝐶1, 𝑑𝑠𝑒𝐶2 and 𝑑𝑠𝑒𝐶3 represent the equilibrium scour depths at Configurations C1, C2 and C3, respectively. From equations (6.1) to (6.3), it is clear that 𝑑𝑠𝑒𝑐 and 𝑑𝑠𝑒𝑝𝑔 can be obtained directly subtracting experimental values, while 𝑑𝑠𝑒𝑝𝑐 requires the previous knowledge of 𝑑𝑠𝑒𝑐 and 𝑑𝑠𝑒𝑝𝑔, as illustrated in Figure 6.1. The subtraction approach has some physical limitations. In fact, tests with Configuration C2, i.e., the complex pier without the column, cannot be performed when the top of the pile cap is below the initial bed level. For this reason, the contributions of the column and the pile cap to the local scour depth may only be obtained when the bottom of the column is above the initial bed level. It should, though, be noticed here that the experiments underlying the existing superposition methods also suffer from the same sort of physical limitations: experiments with completely buried isolated pile cap or pile group are also not feasible. Experimental Study of Local Scour around Complex Bridge Piers 109 Figure 6.1 – Scheme of the subtraction approach (contribution of the complex pier components on scour depth) In the present study, it is assumed that the scour depth associated to the column, 𝑑𝑠𝑒𝑐, the pile group, 𝑑𝑠𝑒𝑝𝑔, and the pile cap, 𝑑𝑠𝑒𝑝𝑐, can be assessed by the following expressions included in or inspired by the HEC-18 method (Arneson et al., 2012): 𝑑𝑠𝑒𝑐=𝐾ℎ𝑐𝑑𝑠𝑒𝑐𝑢 (6.4) 𝑑𝑠𝑒𝑝𝑔=𝐾ℎ𝑝𝑔𝑑𝑠𝑒𝑝𝑔𝑢 (6.5) 𝑑𝑠𝑒𝑝𝑐=𝐾ℎ𝑝𝑐𝑑𝑠𝑒𝑝𝑐𝑢 (6.6) Here, the factor 𝐾ℎ𝑐 accounts for the influence of the position of the base of the column, 𝐻𝑐 (see Figure 2.21); 𝑑𝑠𝑒𝑐𝑢 is the equilibrium scour depth developed at a single pier with the same dimensions as the column; 𝐾ℎ𝑝𝑔 is the factor accounting for the influence of the position of the top of the pile group, 𝐻𝑝𝑔 (see Figure 2.21); 𝑑𝑠𝑒𝑝𝑔𝑢 is the equilibrium scour depth developed at an unsubmerged pile group; 𝐾ℎ𝑝𝑐 is the factor accounting for the influence of the position of the base of the pile cap, 𝐻𝑝𝑐 (see Figure 2.21); 𝑑𝑠𝑒𝑝𝑐𝑢 is the equilibrium scour depth developed at a single pier with the same dimensions as the pile cap. A total of 70 tests performed in this study was used to: (1) describe the temporal evolution of the scour depth for Configurations C2 and C3 of the complex pier (section 6.3); (2) estimate the contribution of complex pier components on equilibrium scour depth according to the subtraction approach, by Experimental Study of Local Scour around Complex Bridge Piers 116 the case where the top of the pile group is below the initial bed level (𝐻𝑝𝑔<0), 𝐻𝑝𝑔 is normalized by the pile-cap width, 𝐷𝑝𝑐, since 𝐷𝑝𝑐 mostly embodies the influence of the pile cap on the exposition of the upstream piles to the flow within the scour hole. No data are available for Model 1 because Configuration C3 was not tested. Figure 6.5 shows the decrease of 𝐾ℎ𝑝𝑔 as 𝐻𝑝𝑔/ℎ decreases, for 𝐻𝑝𝑔>0. This can be explained by the decrease of the flow obstruction resulting from the corresponding decrease of the frontal area of the upstream piles, which in turn leads to the reduction of the scour depth. The factor 𝐾ℎ𝑝𝑔 also slightly depends on the relation 𝑓𝑝/𝐷𝑝; the lower values of 𝐾ℎ𝑝𝑔 correspond to the higher 𝑓𝑝/𝐷𝑝 ratios, observed in Model 7, where 𝑓𝑝/𝐷𝑝=0.6. This finding is consistent with the results of Lagasse et al. (2010) on scouring at debris-laden piles, according to which the scour depth at the pile face is strongly dependent on the upstream debris length in front of the pile face. The interactions of the downflow generated by the upstream face of the pile cap and the vortical structures occurring around the piles can be captured by the influence of 𝑓𝑝/𝐷𝑝 on the factor 𝐾ℎ𝑝𝑔. When the top of the pile group is below the initial bed level, i.e., for 𝐻𝑝𝑔<0, a similar trend is observed: 𝐾ℎ𝑝𝑔 decreases as 𝐻𝑝𝑔/𝐷𝑝𝑐 decreases. In this range, corresponding to situations where the pile cap is partially or completely buried in the bed, the contribution of the pile group to scouring is highly dependent on the joint action of the column and the pile cap on the process. This joint action, captured by the ratio of column width to pile-cap width, 𝐷𝑐/𝐷𝑝𝑐, contributes to the exposition of the upstream piles to the flow inside the scour hole. As 𝐷𝑐/𝐷𝑝𝑐 increases, the scour protection resulting from the collar effect inherent to the pile cap (effect due to pier collars used as bridge scour countermeasure) decreases and the scour depth tends to increase as well, as shown in Figure 6.5. The distance from the pile-cap bottom to the initial bed level at which the pile group contributes to the scouring process decreases with decreasing 𝐷𝑐/𝐷𝑝𝑐, as discussed in section 5.3. Figure 6.5 – Variation of factor Khpg with the relative position of the top of the pile group Figure 6.6 provides the variation of 𝐾ℎ𝑝𝑐 with the relative position of the base of the pile cap, 𝐻𝑝𝑐/ℎ or (𝐻𝑝𝑐/𝑇). In the case where the bottom of the pile cap is above the bed level (𝐻𝑝𝑐≥0), 𝐻𝑝𝑐 is normalized by the approach flow depth, ℎ, to represent the pile cap suspension in the flow, whereas, in the case where the bottom of the pile cap is below the initial bed level (𝐻𝑝𝑐<0), 𝐻𝑝𝑐 is normalized by the pile-cap thickness, 𝑇, since 𝑇 defines the lower value of 𝐻𝑝𝑐 where the pile cap is completely buried in the bed. No data are available for 𝐻𝑝𝑐/𝑇<−1 due to physical limitation previously identified on the experimental exploitation of Configuration C2 (complex pier without the column). Again, no data on 𝐾ℎ𝑝𝑐 exist for Model 1, since Configuration C3 was not tested for this model. Experimental Study of Local Scour around Complex Bridge Piers 117 From Figure 6.6, it can be concluded that, when the pile cap is partially buried in the bed, i.e., for 𝐻𝑝𝑐/𝑇>−1, 𝐾ℎ𝑝𝑐 tends to increase with 𝐻𝑝𝑐/𝑇 and, except for Model 2, 𝐾ℎ𝑝𝑐 reaches a maximum in the range −0.6≤𝐻𝑝𝑐/𝑇≤0. This trend can be ascribed to the pile cap protrusion from the undisturbed initial bed since the strength of the downflow generated in the upstream face of the pile cap, as well as of the associated vortical flow structure, increase with 𝐻𝑝𝑐/𝑇, leading to deeper scour holes. When the base of the pile cap is above the initial bed level, i.e., for 𝐻𝑝𝑐>0, 𝐾ℎ𝑝𝑐 tends to decrease with 𝐻𝑝𝑐/ℎ; this indicates that the effect of the flow structures associated with the pile cap tends to decrease as the pile cap is placed higher in the water column. In other words, the pile cap contributes most scouring when it is close to the initial bed level. Figure 6.6 – Variation of factor Khpc with the relative position of the base of the pile cap: (a) Models 1 to 6 and (b) Model 7 From the data on Models 2, 3 and 5 (all with 𝑇/ℎ=0.45), it can be concluded that the variation of 𝐾ℎ𝑝𝑐 with the relative position of the base of the pile cap is also dependent of the relative column width, 𝐷𝑐/𝐷𝑝𝑐, as illustrated in Figure 6.6(a). Since Models 4 to 6 only differ in the pile-cap thickness, 𝑇, the scouring results at these models clearly indicate that 𝑇 plays a key role on scouring: the equilibrium scour increases with 𝑇/ℎ, corroborating the results of Ferraro et al. (2013). For essentially the same value of 𝑇/ℎ, for example Model 6 (𝑇/ℎ=0.30, Figure 6.6(a)) and Model 7 (𝑇/ℎ=0.32, Figure 6.6(b)), different values of 𝐾ℎ𝑝𝑐 arise as a result of different 𝐷𝑐/𝐷𝑝𝑐 ratios as well as of different pile-group configurations (characterized by 𝑛 and 𝑓𝑝, see Table 3.1). When the base of the pile cap is close to the initial bed level, either above or below, the greater contribution of the pile cap for Model 7, where 𝐷𝑐/𝐷𝑝𝑐=0.74, can be explained by (1) the preservation of the downflow jet formed along the upstream face of the column, that is only negligibly affected by the reduced pile-cap overhang and (2) the different interaction of the internal boundary layer created along the surface of Experimental Study of Local Scour around Complex Bridge Piers 118 the base of the pile cap with the vortical structures due to the piles. The boundary layer is differently disrupted by the two pile groups, influencing differently the flow acceleration otherwise created underneath the pile cap. 6.5. COMPARISON OF SUBTRACTION AND SUPERPOSITION APPROACHES 6.5.1 EXPERIMENTAL DATA FROM STUDIES WITH ISOLATED COMPONENTS As previously mentioned, studies on local scouring at isolated components of complex piers were mostly carried out during the last decades with the purpose of characterizing the contribution of each complex pier component on the equilibrium scour depth, 𝑑𝑠𝑒, following the superposition concept (Sheppard and Jones, 1998). In order to compare the results of the previous section, relative to the contribution of the complex pier components on 𝑑𝑠𝑒 obtained through subtraction (i.e., factors 𝐾ℎ𝑐, 𝐾ℎ𝑝𝑔 and 𝐾ℎ𝑝𝑐 represented in Figure 6.4 to Figure 6.6, respectively), experimental data from isolated components (superposition concept) were considered. Those included: (a) (Jones and Sheppard, 2000; Amini et al., 2014) for isolated columns; (b) (Jones and Sheppard, 2000; Amini et al., 2011) for isolated pile caps; and (c) (Salim and Jones, 1996; Smith, 1999; Dey et al., 2008; Muto, 2008; Amini et al., 2012) for isolated pile groups. Figure 6.7 shows the geometric characteristics of the three complex pier components. Figure 6.7 – Scheme of the geometry of complex pier components The values of the most important control variables and non-dimensional parameters characterizing the set of tests with isolated components performed by those researchers are summarized in Table 6.4 for studies with isolated columns, in Table 6.5 for studies with isolated pile caps and in Table 6.6 for studies with isolated pile groups. Each isolated complex pier component model was evaluated for different positions in relation to the initial bed level (Figure 6.7), those referenced by: (1) 𝐻𝑐 for isolated columns (distance from the initial bed level to the column bottom surface); (2) 𝐻𝑝𝑐 for isolated pile caps (distance from the initial bed level to the pile cap bottom surface); and (3) 𝐻𝑝𝑔 for submerged pile groups (distance from the initial bed level to the top of the pile group). For each model of isolated component the number of tests (each corresponding to one specific position of the component in relation to the initial bed level), the component shape and the test durations, 𝑡𝑑, are also included in Table 6.4, Table 6.5 and Table 6.6. Experimental Study of Local Scour around Complex Bridge Piers 119 Table 6.4 – Characteristic control variables and non-dimensional parameters of studies on suspended columns Study Model Shape Number of tests 𝑫𝒄 (m) 𝒉 𝑫𝒄 𝑳𝒄 𝑫𝒄 𝑼 𝑼𝒄 𝑫𝒄 𝒅𝟓𝟎 𝒕𝒅 (h) Jones and Sheppard (2000a) JSc1 R 10 0.152 2.0 NS ≈0.94 152 >46 Amini et al. (2014) Ac1 S 7 0.160 1.5 1.0 0.95 200 24a Ac2 R 6 0.110 2.2 2.4 0.95 138 24a Ac3 C 6 0.067 3.6 1.0 0.95 84 24a Ac4 R 6 0.030 8.0 2.3 0.95 38 24a Ac5 R 9 0.060 4.0 1.3 0.95 75 24a Note: R = rectangular; S = square; C = circular; NS = not specified. a most of the tests were carried out with durations of 8 hours; nevertheless scour depths were adjusted to a 24 hours duration taking into account that in each model a reference test with duration of 24 hours was performed Table 6.5 – Characteristic control variables and non-dimensional parameters of studies on suspended pile caps Study Model Shape Number of tests 𝑫𝒑𝒄 (m) 𝒉 𝑫𝒑𝒄 𝑳𝒑𝒄 𝑫𝒑𝒄 𝑼 𝑼𝒄 𝑫𝒑𝒄 𝒅𝟓𝟎 𝑻𝒉 𝒕𝒅 (h) Jones and Sheppard (2000a) JSpc1 R 6 0.305 1.0 NS ≈0.94 305 0.10 >46 JSpc2 R 7 0.305 1.0 NS ≈0.94 305 0.20 >46 JSpc3 R 5 0.305 1.0 NS ≈0.94 305 0.30 >46 JSpc4 R 6 0.305 1.0 NS ≈0.94 305 0.40 >46 JSpc5 R 3 0.305 1.0 NS ≈0.94 1694 0.60 >46 JSpc6 R 3 0.305 1.0 NS 0.92 1694 0.80 >46 Amini et al. (2011) Apc1 S 9 0.200 1.2 1.0 0.95 250 0.13 24a Apc2 S 9 0.200 1.2 1.0 0.95 250 0.21 24a Apc3 R 8 0.150 1.6 2.0 0.95 188 0.13 24a Apc4 R 11 0.177 1.4 1.4 0.95 221 0.46 24a Apc5 R 10 0.175 1.4 2.1 0.95 219 0.25 24a Apc6 Ch 7 0.137 1.8 5.5 0.95 171 0.21 24a Apc7 R 7 0.077 3.1 1.6 0.95 96 0.15 24a Apc8 R 6 0.123 2.0 2.4 0.95 154 0.31 24a Note: R = rectangular; S = square; C = circular; Ch = chamfered; NS = not specified. a most of the tests were carried out with durations of 8 hours; nevertheless scour depths were adjusted to a 24 hours duration taking into account that in each model a reference test with duration of 24 hours was performed Experimental Study of Local Scour around Complex Bridge Piers 120 Table 6.6 – Characteristic control variables and non-dimensional parameters of studies on submerged pile groups Study Model Pile shape Number of tests 𝑫𝒑 (m) Array (𝒏×𝒎) 𝑺𝒑 𝑫𝒑 𝒉 𝑫𝒑 𝑼 𝑼𝒄 𝑫𝒑 𝒅𝟓𝟎 𝒕𝒅 (h) Salim and Jones (1996) SJ1 S 6 NS 3 × 3 NS NS ≈1.00 NS 4-24 Smith (1999) Sm1 S 3 0.032 3 × 8 3.0 ≈11.7 ≈0.90 169-185 39-96 Sm2 S 3 0.032 8 × 3 3.0 ≈11.7 ≈0.90 169-185 58-115 Dey et al. (2008) Dey1 C 9 0.030 1 × 1 NA 8.3 ≈0.90 10-37 48 Dey2 C 9 0.060 1 × 1 NA 4.2 ≈0.90 20-74 48 Dey3 C 16 0.080 1 × 1 NA 3.1 ≈0.90 27-99 48 Muto (2008) Mu1 C 5 0.050 1 × 1 NA ≈1.2 ≈0.95 35 NS Amini et al. (2012) Apg1 C 6 0.060 2 × 2 2.0 4.0 ≈0.95 75 24a Apg2 C 7 0.042 2 × 4 2.0 5.7 ≈0.96 53 24a Apg3 C 7 0.060 3 × 3 2.0 4.0 ≈0.97 75 24a Apg4 C 6 0.042 4 × 4 1.9 5.7 ≈0.96 53 24a Apg5 C 7 0.042 4 × 5 2.0 5.7 ≈0.96 53 24a Note: R = rectangular; S = square; C = circular; Ch = chamfered; NS = not specified; NA = not applicable. a most of the tests were carried out with durations of 8 hours; nevertheless scour depths were adjusted to a 24 hours duration taking into account that in each model a reference test with duration of 24 hours was performed In the calculation of factors 𝐾ℎ𝑐=𝑑𝑠𝑒𝑐/𝑑𝑠𝑒𝑐𝑢, 𝐾ℎ𝑝𝑐=𝑑𝑠𝑒𝑝𝑐/𝑑𝑠𝑒𝑝𝑐𝑢 and 𝐾ℎ𝑝𝑔=𝑑𝑠𝑒𝑝𝑔/𝑑𝑠𝑒𝑝𝑔𝑢 for the experimental data with isolated components, the values of the variables 𝑑𝑠𝑒𝑐, 𝑑𝑠𝑒𝑝𝑐 and 𝑑𝑠𝑒𝑝𝑔 correspond to the maximum scour depth measured in each of the tests performed for each of the isolated component geometries considered (Table 6.4, Table 6.5 and Table 6.6). For the case of pile groups (Table 6.6), the values of the variable 𝑑𝑠𝑒𝑝𝑔𝑢 correspond to the maximum scour depth measured in the tests with unsubmerged pile groups. For the other cases, the values of the variables 𝑑𝑠𝑒𝑐𝑢 and 𝑑𝑠𝑒𝑝𝑐𝑢 were obtained through the predictor suggested by Lança et al. (2013b) considering a flow intensity factor (𝐾𝐼) as defined by Sheppard et al. (2014) and a shape factor (𝐾𝑆) as defined by Fael et al. (2014). In the calculation of those values, the same geometric configuration of each component (i.e., width, length and shape), bed granulometry and flow conditions used in each set of tests were considered. 6.5.2 COMPARISON OF THE CONTRIBUTIONS OF COMPLEX PIER COMPONENTS FROM BOTH APPROACHES Figure 6.8 refers to the values of the column factor, 𝐾ℎ𝑐, obtained through both approaches. This figure is the equivalent to Figure 6.4, now extended to negative values of 𝐻𝑐. In this range, 𝐻𝑐 is rendered non-dimensional through 𝑑𝑠𝑒𝑐𝑢. The dashed line is the envelope curve of the literature data. The figure highlights the systematic increase of 𝐾ℎ𝑐 as 𝐻𝑐/ℎ and 𝐻𝑐/𝑑𝑠𝑒𝑐𝑢 decrease, reflecting the increment of the column frontal area exposed to the flow above or inside the scour hole as submergence increases. More importantly, Figure 6.8 shows that the data obtained in the present study tend to plot above the data from the literature, mostly for 0<𝐻𝑐/ℎ<0.2. For 𝐻𝑐/ℎ>0, the smaller values of 𝐾ℎ𝑐 obtained from the data reported by Jones and Sheppard (2000) and Amini et al. (2014) can be partly attributed to the short duration of their tests. Independent of this effect, the values of 𝐾ℎ𝑐 Experimental Study of Local Scour around Complex Bridge Piers 121 obtained through subtraction seem physically sounder, in particular, for the relative position of the base of the column 𝐻𝑐/ℎ=[0.05,0.18]. In fact, when the top of the pile cap or the column-bottom approach the initial bed, the scour depth induced by the pile cap as measured for Configuration C2 tends to be comparatively small (see tests M4F2, M4H2 and equivalent for different models). This implies that most of the scour depth at complete complex piers is mostly driven by the column when the top of the pile cap is near to the initial bed. It seems that the excavation power of the downflow, horseshoe vortex and wake vortices directly induced by the pile cap do not add much to the power of the equivalent flow structures created by the column in spite of the protecting collar effect mobilized by the top surface of the pile cap. This explanation deserves to be further investigated through detailed flow mapping. Figure 6.8 – Comparison of Khc obtained through subtraction with Khc obtained from tests with isolated columns Figure 6.9 shows the values of factor 𝐾ℎ𝑝𝑐 as a function of the relative position of the base of the pile cap, 𝐻𝑝𝑐/ℎ and 𝐻𝑝𝑐/𝑇. It compares the results of this study with those of Jones and Sheppard (2000) and Amini et al. (2011) for three ranges of the relative pile-cap thickness, 𝑇/ℎ: (1) 0.30≤𝑇/ℎ≤ 0.32 in Figure 6.9(a); (2) 0.40≤𝑇/ℎ≤0.46 in Figure 6.9(b); and (3) 𝑇/ℎ=0.60 in Figure 6.9(c). The data of Jones and Sheppard (2000) cover the range 𝐻𝑝𝑐> 0, whereas the data by Amini et al. (2011) cover practically the same range as the present study. With few exceptions, the present values of 𝐾ℎ𝑝𝑐 are of the same order of magnitude and follow the same trend as those of Jones and Sheppard (2000), whereas higher values were obtained from the data reported by Amini et al. (2011). These discrepancies mostly likely result from the different relative flow depth, ℎ/𝐷𝑝𝑐, values and range covered by the three studies: ℎ/𝐷𝑝𝑐= [2.0; 1.4] in the study of Amini et al. (2011), Figure 6.9(a) and Figure 6.9(b), respectively; ℎ/𝐷𝑝𝑐= 1.0 in the study of Jones and Sheppard (2000); and ℎ/𝐷𝑝𝑐= [1.0; 1.5] in the present study, Models 1 to 6 and Model 7 respectively. It is worth noting that the maxima values of 𝐾ℎ𝑝𝑐 are significantly smaller than the maxima 𝐾ℎ𝑝𝑐. Experimental Study of Local Scour around Complex Bridge Piers 122 Figure 6.9 – Comparison of Khpc obtained through subtraction with Khpc obtained from tests with isolated pile caps: (a) T/h ≈ 0.30, (b) T/h ≈ 0.45 and (c) T/h ≈ 0.60 The values of the factor 𝐾ℎ𝑝𝑔 obtained through subtraction and from experimental data on isolated pile groups are plotted in Figure 6.10 as a function of the relative position of the top of the pile group, 𝐻𝑝𝑔/ℎ and 𝐻𝑝𝑔/𝐷𝑝𝑐, the scaling length depending on whether 𝐻𝑝𝑔< 0 or 𝐻𝑝𝑔> 0, as before. The data gathered from the literature include those reported by Salim and Jones (1996), Smith (1999), Dey et al. (2008), Muto (2008) and Amini et al. (2012). Figure 6.10 – Comparison of Khpg obtained through subtraction with Khpg obtained from tests with pile groups Experimental Study of Local Scour around Complex Bridge Piers 123 These literature data are somewhat scattered, possibly due to different pile-group arrangements, to different time effects associated to different durations of the experiments as well as to different relative grain sizes, 𝐷𝑝/𝑑50, as reported in Table 6.6. To reduce uncertainty in the comparison, the literature data are enveloped by a dashed line in Figure 6.10. According to the figure, it can be concluded that the contribution of the pile groups obtained through the subtraction approach leads to values of 𝐾ℎ𝑝𝑔 clearly larger than those obtained for isolated pile groups. It should be stressed here that the data obtained in this study seem physically more robust. Pile groups cannot trigger scouring when 𝐻𝑝𝑔< 0 but this does not mean that they do not contribute to the process once they become exposed to the flow, as implied by the results of previous studies. On the contrary, pile groups contribute significantly to scouring even for 𝐻𝑝𝑔< 0, and this behaviour is captured by the subtraction approach. 6.6. FURTHER DISCUSSION The contributions of the complex pier components to the equilibrium scour depth discussed in section 6.4 were finally compared with the predictions of methods based on the superposition concept, i.e., FDOT and HEC-18 methods. The comparison focused on the factors 𝐾ℎ𝑐, 𝐾ℎ𝑝𝑐 and 𝐾ℎ𝑝𝑔, as shown in Figure 6.11, where the same non-dimensional positions as in Figure 6.8 to Figure 6.10 were adopted. The results obtained for Model 5 are showed in Figure 6.11. From Figure 6.11(a) it can be concluded that the data on the column contribution practically coincide with the prediction curves produced through the FDOT and the HEC-18 methods. Figure 6.11(b) shows that the pile-cap contributions obtained in the present study follow a trend similar to the predictions obtained by means of FDOT and HEC-18 methods when the bottom of the pile cap is above the initial bed level, i.e., for 𝐻𝑝𝑐>0. On the contrary, if the pile cap is partially buried in the bed, i.e., for 𝐻𝑝𝑐<0, the results obtained through both predictors and the data of the present study are far apart, particularly for HEC-18. The significant overestimation of 𝐾ℎ𝑝𝑐 by the HEC-18 method can be attributable to the fact that, in this situation (𝐻𝑝𝑐<0), the method considers a pile cap foundation deeper than the expected scour depth (see section 2.3.6.2). Finally, the data on the contribution of the pile groups, as represented by 𝐾ℎ𝑝𝑔, follow the same trend as the results obtained through both FDOT and HEC-18 methods but the values are rather different, as shown in Figure 6.11(c). Indeed, the HEC-18 method tends to underestimate the values of 𝐾ℎ𝑝𝑔 whereas the FDOT method produces conservative values of 𝐾ℎ𝑝𝑔. The behaviour of the HEC-18 method is directly associated to the fact that it was derived from the results of isolated pile groups by Salim and Jones (1996), and which are represented by equation (2.59). As mentioned previously, tests with submerged pile groups ignored the interactions of the downflow generated by the upstream face of the pile cap and the vortical structures occurring around the piles, reducing the local scour. The overestimation in the FDOT method can, in turn, be attributed to conservative values for the factor ℎ𝑝𝑔(max) (see equation (2.83)) used in the contribution of the pile group by Sheppard and Renna (2010). That factor accounts for a limiting water depth at which the flow influences the scouring process around the pile group. It should be mentioned here that none of the two predictors considers the influence of 𝑓𝑝/𝐷𝑝 on the pile-group contribution, while this effect was identified to be important in the present study. Similar results and relative variations of the three factors described in Figure 6.11 – for Model 5 – could be observed for the other six pier models tested in this study. Experimental Study of Local Scour around Complex Bridge Piers 124 Figure 6.11 – Comparison of factors Khc , Khpc and Khpg obtained by the subtraction concept with the corresponding values predicted by FDOT and HEC-18 methods: (a) variation of factor Khc; (b) variation of factor Khpc; and (c) variation of factor Khpg 6.7. CONCLUSIONS A new experimental approach to assess the contribution of each component of the complex pier (column, pile cap and pile group) to the total equilibrium local scour depth has been proposed in this chapter. This approach takes account the interactions of the different aspects of the flow field and their impact on the local scour depth since the experimental contribution of a given component is derived by subtracting the scour depth generated at a configuration without that component from the scour depth at the complete complex pier. The most important conclusions of this study can be summarized as follows: Experimental Study of Local Scour around Complex Bridge Piers 125 1. The column contribution increases as the position of its base relative to the initial bed level, 𝐻𝑐/ℎ, decreases; it also depends on the ratio of the column-width to the width of the pile cap, 𝐷𝑐/𝐷𝑝𝑐. The subtraction approach provides values of the column contribution larger than those obtained for isolated columns for small values of 𝐻𝑐/ℎ; 2. The largest values of the pile-cap contribution were obtained for pile caps which were partially buried in the bed, where the subtraction approach provides smaller values than experiments with isolated pile caps. Similar to the column contribution, the pile-cap contribution also depends on the ratio 𝐷𝑐/𝐷𝑝𝑐; 3. The most marked differences between the data obtained through subtraction and those measured at isolated pier components was identified for the pile groups, where the subtraction approach leads to significantly higher scour values. The pile-group contribution decreases with decreasing the position of its top relative to the initial bed level. When the top of the piles is above the initial bed level, this contribution also depends on the relation 𝑓𝑝/𝐷𝑝, whereas, when the top of the piles is below the initial bed level, this contribution is highly dependent on 𝐷𝑐/𝐷𝑝𝑐; 4. Both the HEC-18 and the FDOT methods seem to properly predict the contributions of the column and the pile cap to the overall scour when these pier components are suspended above the initial bed; both methods, however, over-predict the contribution of the scour depth induced by the pile cap, the over-prediction being particularly marked in the case of HEC-18; the FDOT method produces conservative scour depth values due to the pile group whereas the HEC-18 method tends to underestimate these values. Experimental Study of Local Scour around Complex Bridge Piers 228 Test M5D3 𝑑50 ℎ 𝑈 𝑈𝑐 𝑈/𝑈𝑐 𝐵/𝐷𝑝𝑐 𝐵/ℎ ℎ/𝐷𝑝𝑐 0.086 mm 0.20 m 0.258 m/s 0.322 m/s 0.80 10.0 10.0 1.0 Scour depth measurements in the test M5D3 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 0.00 0.0000 95.32 0.0000 196.10 0.0047 341.07 0.0140 7.35 0.0000 103.77 0.0000 218.68 0.0051 363.63 0.0160 22.52 0.0000 122.27 0.0000 266.12 0.0066 431.27 0.0170 30.52 0.0000 147.70 0.0010 290.90 0.0087 74.77 0.0000 171.25 0.0044 316.70 0.0119 0.00 0.04 0.08 0.12 0.16 0.20 0.24 072 144 216 288 360 432 504 576 648 720 ds (m) t(h) Experimental Study of Local Scour around Complex Bridge Piers 229 Test M5E3 𝑑50 ℎ 𝑈 𝑈𝑐 𝑈/𝑈𝑐 𝐵/𝐷𝑝𝑐 𝐵/ℎ ℎ/𝐷𝑝𝑐 0.086 mm 0.20 m 0.258 m/s 0.322 m/s 0.80 10.0 10.0 1.0 Scour depth measurements in the test M5E3 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 0.00 0.0000 8.55 0.0004 285.12 0.0179 357.30 0.0286 0.32 0.0000 30.17 0.0042 295.02 0.0191 408.13 0.0338 1.13 0.0000 45.68 0.0050 309.30 0.0213 480.52 0.0447 3.28 0.0000 54.10 0.0059 319.27 0.0226 5.35 0.0000 118.42 0.0098 333.20 0.0264 7.05 0.0002 141.90 0.0121 342.28 0.0270 0.00 0.04 0.08 0.12 0.16 0.20 0.24 072 144 216 288 360 432 504 576 648 720 ds (m) t(h) Experimental Study of Local Scour around Complex Bridge Piers 230 Test M5F3 𝑑50 ℎ 𝑈 𝑈𝑐 𝑈/𝑈𝑐 𝐵/𝐷𝑝𝑐 𝐵/ℎ ℎ/𝐷𝑝𝑐 0.086 mm 0.20 m 0.258 m/s 0.322 m/s 0.80 10.0 10.0 1.0 Scour depth measurements in the test M5F3 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 0.00 0.0000 3.08 0.0268 46.13 0.0474 166.98 0.0644 0.13 0.0073 4.82 0.0296 52.22 0.0494 192.42 0.0677 0.38 0.0149 6.22 0.0299 71.60 0.0522 215.95 0.0698 0.80 0.0210 21.77 0.0391 98.33 0.0560 259.82 0.0719 1.30 0.0226 24.90 0.0416 119.23 0.0590 2.00 0.0254 29.37 0.0429 141.67 0.0618 0.00 0.04 0.08 0.12 0.16 0.20 0.24 072 144 216 288 360 432 504 576 648 720 ds (m) t(h) Experimental Study of Local Scour around Complex Bridge Piers 231 Test M5G3 𝑑50 ℎ 𝑈 𝑈𝑐 𝑈/𝑈𝑐 𝐵/𝐷𝑝𝑐 𝐵/ℎ ℎ/𝐷𝑝𝑐 0.086 mm 0.20 m 0.258 m/s 0.322 m/s 0.80 10.0 10.0 1.0 Scour depth measurements in the test M5G3 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 0.00 0.0000 7.73 0.0299 100.65 0.0827 289.37 0.1217 0.22 0.0000 22.77 0.0432 119.87 0.0882 314.93 0.1241 0.57 0.0026 27.07 0.0480 126.12 0.0895 358.67 0.1296 1.78 0.0137 31.07 0.0497 146.10 0.0932 389.92 0.1310 2.43 0.0167 49.02 0.0629 169.38 0.1029 458.68 0.1384 3.90 0.0203 54.88 0.0647 194.85 0.1088 5.57 0.0256 76.73 0.0760 217.63 0.1126 0.00 0.04 0.08 0.12 0.16 0.20 0.24 072 144 216 288 360 432 504 576 648 720 ds (m) t(h) Experimental Study of Local Scour around Complex Bridge Piers 232 Test M6E3 𝑑50 ℎ 𝑈 𝑈𝑐 𝑈/𝑈𝑐 𝐵/𝐷𝑝𝑐 𝐵/ℎ ℎ/𝐷𝑝𝑐 0.086 mm 0.20 m 0.258 m/s 0.322 m/s 0.80 10.0 10.0 1.0 Scour depth measurements in the test M6E3 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 0.00 0.0000 51.38 0.0000 170.93 0.0000 436.57 0.0283 2.68 0.0000 77.53 0.0000 198.85 0.0000 464.17 0.0323 4.33 0.0000 97.60 0.0000 249.72 0.0000 488.03 0.0338 6.22 0.0000 106.05 0.0000 267.10 0.0013 501.18 0.0342 7.75 0.0000 120.03 0.0000 292.57 0.0091 25.72 0.0000 127.58 0.0000 318.47 0.0159 32.77 0.0000 148.48 0.0000 364.95 0.0208 0.00 0.04 0.08 0.12 0.16 0.20 0.24 072 144 216 288 360 432 504 576 648 720 ds (m) t(h) Experimental Study of Local Scour around Complex Bridge Piers 233 Test M6F3 𝑑50 ℎ 𝑈 𝑈𝑐 𝑈/𝑈𝑐 𝐵/𝐷𝑝𝑐 𝐵/ℎ ℎ/𝐷𝑝𝑐 0.086 mm 0.20 m 0.258 m/s 0.322 m/s 0.80 10.0 10.0 1.0 Scour depth measurements in the test M6F3 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 0.00 0.0000 5.13 0.0044 71.73 0.0136 265.63 0.0259 0.17 0.0000 7.38 0.0051 79.05 0.0142 338.47 0.0291 0.58 0.0000 22.37 0.0077 99.80 0.0159 365.18 0.0299 0.83 0.0000 26.52 0.0086 127.88 0.0180 410.88 0.0324 1.88 0.0000 30.63 0.0089 172.22 0.0207 440.10 0.0361 2.67 0.0009 48.17 0.0106 197.10 0.0225 484.63 0.0420 3.78 0.0016 55.08 0.0124 222.05 0.0236 0.00 0.04 0.08 0.12 0.16 0.20 0.24 072 144 216 288 360 432 504 576 648 720 ds (m) t(h) Experimental Study of Local Scour around Complex Bridge Piers 234 Test M6G3 𝑑50 ℎ 𝑈 𝑈𝑐 𝑈/𝑈𝑐 𝐵/𝐷𝑝𝑐 𝐵/ℎ ℎ/𝐷𝑝𝑐 0.086 mm 0.20 m 0.258 m/s 0.322 m/s 0.80 10.0 10.0 1.0 Scour depth measurements in the test M6G3 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 0.00 0.0000 2.97 0.0065 31.63 0.0434 200.52 0.0577 0.22 0.0000 3.87 0.0090 49.15 0.0487 237.38 0.0600 0.35 0.0004 5.43 0.0138 55.80 0.0497 269.72 0.0617 0.63 0.0006 6.68 0.0190 76.22 0.0520 318.85 0.0626 1.00 0.0010 8.22 0.0247 124.53 0.0544 364.55 0.0648 1.63 0.0018 24.67 0.0406 149.83 0.0550 411.72 0.0670 2.28 0.0036 28.47 0.0427 173.90 0.0575 0.00 0.04 0.08 0.12 0.16 0.20 0.24 072 144 216 288 360 432 504 576 648 720 ds (m) t(h) Experimental Study of Local Scour around Complex Bridge Piers 235 Test M7N3 𝑑50 ℎ 𝑈 𝑈𝑐 𝑈/𝑈𝑐 𝐵/𝐷𝑝𝑐 𝐵/ℎ ℎ/𝐷𝑝𝑐 0.086 mm 0.18 m 0.315 m/s 0.322 m/s 0.80 8.3 5.6 1.5 Scour depth measurements in the test M7N3 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 0.00 0.0000 60.00 0.0000 120.00 0.0000 240.00 0.0000 12.00 0.0000 72.00 0.0000 144.00 0.0000 264.00 0.0000 24.00 0.0000 84.00 0.0000 168.00 0.0000 288.00 0.0000 36.00 0.0000 96.00 0.0000 192.00 0.0000 48.00 0.0000 108.00 0.0000 216.00 0.0000 0.00 0.04 0.08 0.12 0.16 0.20 0.24 072 144 216 288 360 ds (m) t(h) Experimental Study of Local Scour around Complex Bridge Piers 236 Test M7O3 𝑑50 ℎ 𝑈 𝑈𝑐 𝑈/𝑈𝑐 𝐵/𝐷𝑝𝑐 𝐵/ℎ ℎ/𝐷𝑝𝑐 0.086 mm 0.18 m 0.315 m/s 0.322 m/s 0.80 8.3 5.6 1.5 Scour depth measurements in the test M7O3 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 0.00 0.0000 20.75 0.0072 114.75 0.0111 211.00 0.0142 0.25 0.0003 26.75 0.0078 121.50 0.0112 258.92 0.0170 0.75 0.0008 42.92 0.0090 141.00 0.0120 287.75 0.0171 1.75 0.0014 66.75 0.0094 148.00 0.0123 311.75 0.0174 2.75 0.0019 72.75 0.0095 162.93 0.0130 335.75 0.0175 18.75 0.0069 91.00 0.0105 186.75 0.0132 0.00 0.04 0.08 0.12 0.16 0.20 0.24 072 144 216 288 360 ds (m) t(h) Experimental Study of Local Scour around Complex Bridge Piers 237 Test M7P3 𝑑50 ℎ 𝑈 𝑈𝑐 𝑈/𝑈𝑐 𝐵/𝐷𝑝𝑐 𝐵/ℎ ℎ/𝐷𝑝𝑐 0.086 mm 0.18 m 0.315 m/s 0.322 m/s 0.80 8.3 5.6 1.5 Scour depth measurements in the test M7P3 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 𝑡𝑑 (h) 𝑑𝑠𝑚 (m) 0.00 0.0000 2.00 0.0275 28.30 0.0534 102.55 0.0831 0.05 0.0065 2.50 0.0289 31.30 0.0565 122.55 0.0843 0.08 0.0099 3.00 0.0292 31.97 0.0569 167.55 0.0869 0.17 0.0149 4.00 0.0317 35.97 0.0588 172.30 0.0889 0.25 0.0170 5.00 0.0323 47.80 0.0620 176.22 0.0895 0.33 0.0190 6.00 0.0365 50.80 0.0633 191.80 0.0938 0.50 0.0199 7.00 0.0397 55.63 0.0642 201.22 0.0946 0.75 0.0222 8.00 0.0417 71.80 0.0727 219.30 0.0961 1.00 0.0233 13.00 0.0441 77.13 0.0741 1.33 0.0241 23.30 0.0484 80.13 0.0770 1.67 0.0249 25.80 0.0511 95.80 0.0808 0.00 0.04 0.08 0.12 0.16 0.20 0.24 072 144 216 288 360 ds (m) t(h)